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All properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature).

Nusselt numbers Nu₀ from sections 1-1 to 1-3 have to be corrected for temperature-dependent fluid properties according to section 1-4.

1-1 Thermally Developing, Hydrodynamically Developed Laminar Flow (Re<2300)

Constant wall temperature:

Constant wall heat flux:

1-2 Simultaneously Developing Laminar Flow (Re<2300)

Constant wall temperature:

Constant wall heat flux:

which is valid over the range 0.7 < Pr < 7 or if Re Pr D/L < 33 also for Pr > 7.

1-3 Fully Developed Turbulent and Transition Flow (Re>2300)

Constant wall heat flux:

Constant wall temperature:

For fluids with Pr > 0.7 correlation for constant wall heat flux can be used with negligible error.

1-4 Effects of Property Variation with Temperature

Liquids, laminar and turbulent flow:

Subscript w: at wall temperature, without subscript: at mean fluid temperature.

Gases, laminar flow:

Gases, turbulent flow:

Temperatures in Kelvin.

Section 2: Forced Convection Flow Inside Concentric Annular Ducts, Turbulent (Re > 2300)

Dh = Do - Di All properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature).

Heat transfer at the inner wall, outer wall insulated:

Heat transfer at the outer wall, inner wall insulated:

Heat transfer at both walls, same wall temperatures:

Section 3: Forced Convection Flow Inside Non-Circular Ducts, Turbulent (Re > 2300)

Equations for circular tube with hydraulic diameter:

Section 4: Forced Convection Flow Across Single Circular Cylinders and Tube Bundles

D = cylinder diameter, u_m = free-stream velocity, all properties at fluid bulk mean temperature. Correction for temperature dependent fluid properties see section 4-4.

4-1 Smooth Circular Cylinder

Valid over the ranges 10 < Re_l < 10⁷ and 0.6 < Pr < 1000.

4-2 Tube Bundle

Transverse pitch ratio

Longitudinal pitch ratio

Void ratio for b > 1

for b < 1

Nu_0,bundle = f_ANu_l,0 (Gnielinski)

Nu_l,0 according to section 4-1 with instead of Re_l.

Arrangement factor f_A depends on tube bundle arrangement.

In line arrangement:

Eq. (23)

Staggered arrangement:

Eq. (24)

4-3 Finned Tube Bundle

In-line tube bundle arrangement:

Eq. (25)

Staggered tube bundle arrangement:

Eq. (26)

4-4 Effects of Property Variation with Temperature

Liquids:

Eq. (27)

Eq. (28)

Subscript w: at wall temperature, without subscript: at mean fluid temperature.

Gases:

Eq. (29)

Eq. (30)

Temperatures in Kelvin.

Section 5: Forced Convection Flow over a Flat Plate

All properties at mean film temperature .

Laminar boundary layer, constant wall temperature:

(Pohlhausen)

Eq. (31)

valid for Re_L < 2·10⁵, 0.6 < Pr < 10

Turbulent boundary layer along the whole plate, constant wall temperature:

(Petukhov)

Eq. (32)

Boundary layer with laminar-turbulent transition:

(Gnielinski)

Eq. (33)

Section 6: Natural Convection

All properties at .

L = characteristic length (see below)

For ideal gases: (temperature in K)

(Churchill, Thelen)

Eq. (34)

valid for 10^-4 < Gr Pr < 4·10¹⁴, 0.022 < Pr < 7640, and constant wall temperature.

Section 7: Film Condensation

All properties without subscript are for condensate at the mean temperature .

Exception: ?_D = vapor density at saturation temperature T_s

7-1 Laminar Film Condensation

Vertical wall or tube:

(Nusselt)

Eq. (35)

T_w = mean wall temperature

Horizontal cylinder:

(Nusselt)

Eq. (36)

T_w = const.

7-2 Turbulent Film Condensation

For vertical wall:

Re = C A^m

Re_crit = 350

For turbulent film: C = 3.8 x 10^-3 and m = 3/2 (Grigull).

Section 8: Nucleate Pool Boiling

T_w = temperature of heating surface

T_s = saturation temperature

Heat transfer at ambient pressure:

(Stephan and Preuber)

Eq. (37)

' saturated liquid

'' saturated vapor

Bubble departure diameter

Angle ?₀ = ?/4 rad for water = 0.0175 rad for low-boiling liquids = 0.611 rad for other liquids

For water in the range of 0.5 bar < p < 20 bar and 10⁴ W/m² << 10⁶ W/m² the following equation may be applied:

(Fritz)

Eq. (38)

List of Symbols

cp	specific heat capacity at constant pressure
D, d	diamter
g	gravitational acceleration
h	mean heat transfer coefficient
Δh	enthalpy of evaporation
H	height
k	thermal conductivity
L	length
	heat flux
T	temperature
u	flow velocity
α	thermal diffusivity
β	coefficient of thermal expansion
μ	dynamic viscosity
υ	kinematic viscosity
ρ	density
σ	surface tension

Subscripts

Dimensionless Numbers

References

1. Churchill, S.W.: Free convection around immersed bodies. Chapter 2.5.7 of Heat Exchanger Design Handbook, Hemisphere (1983).
2. Fritz, W.: In VDI-Wärmeatlas, Düsseldorf (1963), Hb2.
3. Gnielinski, V.: Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen. Forschung im Ingenieurwesen 41, 8-16 (1975).
4. Gnielinski, V.: Berechnung mittlerer Wärme- und Stoffübergangskoeffizienten an laminar und turbulent überströmten Einzelkörpern mit Hilfe einer einheitlichen Gleichung. Forschung im Ingenieurwesen 41, 145-153 (1975).
5. Grigull, U.: Wärmeübergang bei der Kondensation mit turbulenter Wasserhaut. Forschung im Ingenieurwesen 13, 49-57 (1942).
6. Hausen, H.: Neue Gleichungen für die Wärmeübertragung bei freier und erzwungener Strömung. Allg. Wärmetechnik 9, 75-79 (1959).
7. Nusselt, W.: Die Oberflächenkondensation des Wasserdampfes. VDI Z. 60, 541-546 and 569-575 (1916).
8. Petukhov, B.S.: Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv. Heat Transfer 6, 503-565 (1970).
9. Petukhov, B.S. and L.I. Roizen: High Temperature 2, 65-68 (1964).
10. Pohlhausen, E.: Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung. Z. Angew. Math. Mech. 1, 115-121 (1921).
11. Shah, R.K.: Thermal entry length solutions for the circular tube and parallel plates. Proc. 3^rd Natnl. Heat Mass Transfer Conference, Indian Inst. Technol Bombay, Vol. I, Paper HMT-11-75 (1975).
12. Stephan, K.: Wärmeübergang und Druckabfall bei nicht ausgebildeter Laminarströmung in Rohren und ebenen Spalten. Chem.-Ing.-Tech. 31, 773-778 (1959).
13. Stephan, K.: Chem.-Ing.-Tech. 34, 207-212 (1962).
14. Stephan, K. and P. Preußer: Wärmeübergang und maximale Wärmestromdichte beim Behältersieden binärer und ternärer Flüssigkeitsgemische. Chem.-Ing.-Tech. 51, 37 (1979).
15. VDI-Wärmeatlas, 7^th edition, Düsseldorf 1994.

I need to commission a plant and intend to use low pressure air for leak testing. Can I pressurise lines through a pump? In other words, if a line runs from the bottom of a tank, through a pump, and into another tank, can the whole line from bottom outlet on 1st tank to the inlet on 2nd tank be tested at once? Or, is it necessary to test the line in two sections (before and after the pump)? Can the same be done when testing for leaks using vacuum?

"If you're commissioning a plant, you can use clean, regulated compressed air for leak testing. {parse block="google_articles"}Of course, as you know, this will only show that the joints and other leak-prone areas do not leak at the testing temperature -not at the process temperatures which can be higher. What I have done in the past is applied masking tape around the flanges' gasketed joint with a small pin hole made afterwards. Then I use "soap and bubble" technology with a fine brush, searching for the tell-tale bubbles that reveal an air leak. If the flange joint leaks, the pin hole will form a soap bubble.

Be aware that before you undertake to subject your process or unit to a pneumatic pressure, you should have a thorough and detailed knowledge of the lowest pressure rating in your pressurized system. You must be careful not to surpass the lowest pressure rating. For example, you may be using cast iron casings on your centrifugal pumps and these are normally rated well below the pressure rating of the connected piping. If some of the equipment is rated below the pipe, you can isolate the equipment and test the pipe on its own rating, followed by testing the equipment one-by-one. I have seen what a misguided pneumatic test can cause with a ruptured piece of equipment. That is why I am very, very cautious of pneumatic testing and would use it only if I were in control of all the procedures. I am particularly of any cast iron equipment. Cast iron pieces or components can have foundry defects or flaws and this can be devasting if they fail under a pneumatic test because the net effect is the same as a grenade exploding. That is why I prefer to test plant equipment hydrostatically - with water. The result of a hydrostatic test failure is benign compared with a pneumatic one.

A vacuum test is safer but is difficult to detect leaks. The only practical measure you have is loss of the vacuum as witnessed on a sensitive pressure gauge. This takes time and patience.

Again, while you can pneumatically test an entire unit at one time, take time and trouble to make sure you are in complete control as to the safe, rated pressure on each component in your system before applying air pressure. I would recommend that you use a 2-stage air regulator to set the test pressure. This is much more accurate and is considered safer that a single stage regulator.

Take care and good luck."

I will stress "the correct way" so don't expect short cuts and rules of thumbs. Notice, I use the word "I" a lot. These will be my thoughts, my ideas. I will present facts and in instances, my interpretation of the facts. I might even editorialize. This inaugural column starts a series on Relief Valves.

The Problem

In the May 2000 issue of Chemical Engineering Progress¹ (CEP), there was an article entitled "Ease Relief System Design and Documentation". While I'm not intending to discuss the article in whole, the author stated something that appeared to get one reader's attention. The author wrote,

If you want to reduce the size of a relief device for cost savings, then design it at a higher set pressure; however, the MAWP of the weakest link should not be ignored.

This statement prompted a "Letters to the Editor" in the October 200 issue of CEP² (no, it wasn't me) where a reader wrote,

This is not true; for a certain MAWP, the capacity of the relief device is not a function of its set point, but of MAWP alone. For example, for a MAWP of 100 psig, the relief valve capacity will be same whether it is set at 80 psig or 100 psig. In both cases, the maximum relieving pressure for the ASME non-fire case (or BS 5500 fire case) is 124.7 psia and the discharge capacity will remain identical. The only difference is that if the set point is 80 psig, the allowable overpressure will be 37.5%, while, at the same for a set point of 100 psig, it will be 10%. For the ASME fire case, the values will be 51.25% and 21% respectively. These are defined very clearly in API 520, Tables 2 to 6.

I'm seeing that people do not quite understand what API 520³ and the ASME Boiler and Pressure Vessel Code, Section VIII, Division 1⁴, are really saying. (For those not familiar with API and ASME, ASME, or the American Society of Mechanical Engineers, is the organization that sets the codes in the United States that determine how pressure vessels are to be designed and protected. These codes are law and must be followed. The American Petroleum Institute, or API, sets the standards by which the codes are followed. API publishes the Recommended Practices 520 and 521, among others.)

MAWP and Design Pressure

In paragraph 1.2.3.2, para b, API 520 defines maximum allowable working pressure (MAWP) as:

... the maximum gauge pressure permissible at the top of a completed vessel in its normal operating position at the designated coincident temperature specified for that pressure.

The operative word here is "completed". {parse block="google_articles"}The vessel is completed when a fabricator, according to the code laid down by ASME, has designed it. The vessel's fabricator, not the Process Engineer, determines MAWP. (Some may try to stretch my definition of "completed" to mean that the vessel is also erected in place. Not quite because the certified vessel drawings, which are delivered way before the vessel is, contains this information).

In the same paragraph, API 520 says that the MAWP is normally greater than design pressure. The Process Engineer usually sets the design pressure at the time the vessel specification is being written. The design pressure is the value obtained after adding a margin to the most severe pressure expected during normal operation at a coincident temperature. Depending upon the company the engineer works for, this margin is typically the maximum of 25 psig or 10%. The vessel specification sheet contains the design pressure, along with the design temperature, size, normal operating conditions and material of construction among others. It is this document that will eventually end up in a fabricator's lap and from which the mechanical design is made.

Relief Valve Set Pressure

Unfortunately, project schedules may require that relief valve sizing be carried out way before the fabricator has finished the mechanical design and certified the MAWP. The Process Engineer must use some pressure on which to base the relieving rate calculations. In paragraph 1.2.3.2, para. c, API 520 states that the design pressure may be used in place of the MAWP in all cases where the MAWP has not been established. Guess what pressure the Process Engineer usually sets relief valves at? There are even times when the relief valve must be set even lower than design pressure. For example, a high design pressure may be desirable for mechanical integrity but a PSV set at the design pressure may end up with a coincidental temperature that would require the use of exotic materials of construction or that promotes decomposition and/or run-away reaction.

So, Why the Confusion?

The confusion faced by the reader who wrote the "Letters to the Editor", and probably many others, is due to a number of reasons. First and I think foremost, is the way ASME does not relate the maximum allowable pressure limits to relief valve capacity. ASME, Section VIII, Division 1, refers to MAWP throughout the entire document when talking about relief valve set pressure and allowable overpressure. I believe the reader may have been referring to and interpreting what is stated in paragraph UG-125 of ASME Section VIII, Division 1. It states in part,

All pressure vessels other than unfired steam boilers shall be protected by a pressure relief device that shall prevent the pressure from rising more than 10% or 3 psi, whichever is greater, above the maximum allowable working pressure except as permitted in (1) and (2) below.

Sub-paragraphs (1) and (2) mention cases where the pressure rise may be higher.

However, when ASME talks about certifying the capacity of a relief device, MAWP is never mentioned. ASME Section VIII, Division 1 clearly states in Paragraph UG-131, para c(1) that

Capacity certification tests shall be conducted at a pressure which does not exceed the pressure for which the pressure relief valve is set to operate by more than 10% or 3 psi, whichever is greater, except as provided in para c(2)...

Sub-paragraph para c(2) covers a fire case. {parse block="google_articles"}Again, capacity certification is based only on the set pressure of the relief valve and is unrelated to MAWP, unless of course the set pressure is MAWP.

Another area of confusion might involve the definition of capacity and how the term is used in ASME and API. Relieving rates are determined from "what can go wrong" scenarios and if allowed to go unchecked, would overpressure the vessel. Once the Process Engineer determines the controlling relieving rate from all the scenarios, the required relief valve orifice size is determined using the appropriate equation given in API. Once the required relief valve orifice size is calculated, an actual orifice size equal to or greater than the calculated orifice size is chosen from a selection available from a particular manufacturer. The maximum flow through this actual valve will be the valve's capacity.

Conclusion

The problem and solution can be summarized as follows:

CODE AS WRITTEN
Capacity based on Set Pressure + Allowable Overpressure

Code clearly requires that the relief valve's capacity be based solely on set pressure and not on the vessel's maximum allowable working pressure. Indeed, as shown above, if the relief valve's capacity was based on MAWP, then code might even force the Process Engineer into an unsafe design. A good analogy is highway speed limits. In the United Stated, many highway speed limits are set for 65 miles per hour. This does not mean a driver cannot travel slower and, under certain conditions for safety, it is almost a necessity that one does.

If it is safe to do so and the protected vessel can be allowed to pressurize to a greater extent, the relief valve set pressure can be increased, thereby reducing the relief valve's size and cost. Remember also that there is piping and possibly downstream equipment to "catch" and process the relieving fluid associated with the relief valve which may also benefit by this reduction.

One way of accomplishing a reduction in relief valve size is by increasing the vessel's design pressure. There is an economic trade off here as the vessel's cost can increase above what you may save by reducing the size of the valve. Another approach to consider is increasing the relief valve's set pressure right up to MAWP after receiving the certified vessel drawings. However, depending on project schedule, the cost savings may be offset by the high costs associated with late design changes.

Final Say

I welcome and encourage your feedback. Feel free to E-Mail me at the Internet address below. All correspondences that include a name will be published in this column. Better yet, I encourage discussion of any topic I cover utilizing The Chemical Engineers' Resource Message Board. This will enable the entire Internet community to join and learn.

References

1. Ahmad, S.
2. Letters to the Editor
3. API
4. ASME
"Ease Relief System Design and Documentation," Chem. Eng. Progress, pp 43-50 (May 2000) Chem. Eng. Progress, p 10 (October 2000) (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000) (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)


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Author/Community Member Discussion Regarding This Article

The following discussions were added July 21, 2001.

Discussion One

From Mr. Jeffrey Niemeier:

Philip,

I am responding to your column in Cheresources.com. {parse block="google_articles"}I disagree with your interpretation of the ASME code. The capacity of a relief device that is used to determine adequacy of design is based on the allowable overpressure. If the overpressure is higher the flow will be higher. You can take credit for this. UG-125 makes it clear that the only requirement is that the pressure not exceed 110% of the MAWP (121% for a fire). The stamped capacity is there only for reference. It could not possibly be used to make a judgement on two-phase flow capacity.

Also, contrary to what you have in your article it is many times advantageous to have a set pressure much lower than the MAWP. This is especially true if runaway reaction is a possibility. A low set pressure allows the reactants to start venting much earlier, thereby removing reactant from the vessel before the temperature and reaction rate get too high. Check out the DIERS literature.

I think you should remove your column.

Philip Replies:

Mr. Niemeier,

Thank you for taking the time to read my article "Relief Valve Set Pressures" in the "Process Engineering-As I See It" section of "The Chemical Engineers' Resource Page and for your feedback.

Allow me to respond.

You write,
"I disagree with your interpretation of the ASME code. The capacity of a relief device that is used to determine adequacy of design is based on the allowable overpressure. If the overpressure is higher the flow will be higher. You can take credit for this. UG-125 makes it clear that the only requirement is that the pressure not exceed 110% of the MAWP (121% for a fire). The stamped capacity is there only for reference."

You are falling into the same trap that most people fall into and this is precisely why I wrote the article in the first place. The certified capacity which determines adequacy of design of a relief valve (which is the 'device' I assume you are referring to since the capacity of a stand alone rupture disk is different) is based on the criteria described in ASME Section VIII, Divison 1, Paragraph UG-131, not Paragraph UG-125. Paragraph UG-131 states that, except for some very specific exceptions, the overpressure is to be 10% or 3 psi, whichever is greater and is to be referenced to set pressure. If set pressure happens to be equal to MAWP, fine, but as you point out
later in your letter, this is not always the case. There are no provisions that I can find that allow a vendor to certify a relief valve for
overpressures greater than these. In addition, the certified capacity is the only flow that is guaranteed by the relief valve vendors, nothing more or less. Using greater overpressures than the 10% or 3 psi described above in calculations for required relieving rate does not alter the guaranteed capacity provided by the vendor and which is required by ASME, Paragraph UG-129.

If you require further evidence of these points, feel free to contact Farris Engineering, a well-known relief valve vendor at http://www.cwfc.com/. However, I can save you some time because I didn't write the article without doing some research first.

Now, you think capacity certification (stamped capacity) is just for reference?!? It is this certified capacity, not the calculated maximum relieving rate, which must be used when sizing inlet lines to the relief valve (using the 3% rule, ASME Section VIII, Division 1, Appendix M, Paragraph M-7) and in many cases, the outlet lines as well.

I invite you to re-read the article, specifically the paragraph titled "So, Why the Confusion? and also read ASME Section VIII, Division 1, Paragraph UG-131. The code is like a bowl of spaghetti. You have to weave through all the pertinent paragraphs to get to the end... and the full story.

For your information, the stamped capacity for relief valves in vapor/gas service is usually given in terms of SCFM of air at set pressure plus 10% overpressure and 60 degress F. Valves in steam service are stamped in terms of pounds per hour of steam at set pressure plus 10% overpressure at the saturation temperature. ASME Section VIII, Division 1, Appendix 11 gives you a means for converting to your particular vapor/gas. Valves in liquid service are given in terms of gallons per minute of water at set pressure
plus 10% overpressure and 70 degrees F.

You continued in your letter with the following (still referring to the stamped capacity):

"It could not possibly be used to make a judgement on two-phase flow capacity."

I don't know why you mention two-phase flow since I didn't in my article. However, I agree, relief valve manufacturers at the present time do not have capacity certification capability for two-phase flow.

You then added:

"Also, contrary to what you have in your article it is many times advantageous to have a set pressure much lower than the MAWP."

I invite you to re-read my paragraph titled, "Relief Valve Set Pressure" specifically the sixth line where I write, "There are even times when the relief valve must be set even lower than design pressure."

Are we talking about the same article here? Did you actually read my article?

You finish your letter with:

"I think you should remove your column."

MAWP, design pressure, relief valve set pressure, what is allowed overpressure, calculated relieving rates, certified capacity, etc. appears to be a very confusing and misunderstood concept that most people are having when dealing with safety relief systems; you included. And this is precisely why my column must not only stay but also grow. My only regret at this time is that I obviously did not get the point across to you and for that I apologize. I hope this response clarifies those points you misunderstood. I will be more than happy to answer any other concerns you may have or even further discuss the points you already brought up.

Mr. Jeffrey Niemeier Replies:

I still disagree with you. It is basic physics that you will get more flow if you have a higher driving pressure. There is no reason not to take credit for overpressures above 10% as long as you don't go above the maximum allowable pressure for the valve. See the following memo from Paul Papa, director of engineering for Farris:

As you mentioned, all of our certified capacities are based on testing that is done at 10% overpressure. Nameplates are therefore marked with capacities at 10% overpressure in the appropriate certification fluid (steam, air, or water). From a selection standpoint, valves are typically sized based on 10 % overpressure. As you correctly pointed out, Section VIII of the ASME Code indicates that ASME Code stamped pressure vessels require a relief device that must pass all of the required flow without allowing the pressure to go any higher than 10% above the maximum allowable working pressure (MAWP).

There are many cases where a vessel is being used at a pressure at much less than its MAWP. In those cases, you can size and select the valve at an overpressure greater than 10%. This will allow you to use a smaller valve as
the valves capacity will increase as the pressure increases. Per ASME Code, the pressure must still be kept to the 10% accumulation pressure, that is no more than 10% above the MAWP.

For the most part, this is not a problem for the valve as long as the higher overpressure does not exceed the maximum pressure limit of the valve at the relieving temperature.

Philip Replies:

Jeff,

I'm not saying, nor have I ever said that you can't calculate the required relieving rate for the MAWP + overpressure and then choose a valve based on this. Remember fire cases? They go to 21% overpressure (set pressure basis) don't they and are often the sizing criteria for the valve. However, this still does not alter the guaranteed (stamped capacity) flow rate of the valve which is based strictly on set pressure + 10% (for the most part). And it is this flow that your maximum calculated relieving requirement cannot exceed and which is subsequently used in the hydraulic calculations, per ASME. I don't know how many times I have to say this. And this is what my article was strictly about; the criteria used to obtain the certified (stamped) capacity. Also, I also don't see in the Farris response you sent me where they will guarantee any number other than what they are allowed to stamp even if MAWP is 100 psig and you want to allow the pressure to go to 110 psig. If a valve is set for 50 psig, it will be certified based on 55 psig, clear and simple! Neither Farris nor any other vendor will guarantee that your valve will pass a different flow rate at any other condition. Nor will they tell you to use any other value in subsequent hydraulic or downstream sizing equations.

I would love to see you prove the calculations that give you that extra margin you keep talking about. You think it's simple? Try doing the calculations at a high pressure for something very non-ideal such as ethylene. All of the equations shown in ASME and API fall apart rather severely since they are all based on ideal gas. Try convincing an OSHA inspector that at conditions which exceeded the capacity certification test at the time of equipment failure that your valve was properly sized and should have been big enough. If you can do this via flow equations derived properly for non-ideal gases from the sound use of thermodynamics, great and there is no argument from me. Heck, I'll even write about it!! After all, ASME and API specifically state that the engineer is to use good engineering judgment and if in question, work with the relief valve vendor. As a matter of fact, you can even deviate from the code if you can prove that a given relief valve will not be adversely affected from whatever you are trying to do. As an example, I am currently on a project where the inlet line loss for one particular valve is in the 6% range. Notwithstanding the fact that the 3% rule is "non-mandatory" (but is still considered good engineering practice), we are working with Farris to determine if this would adversely
affect the valve. If it doesn't, we can live with the current piping configuration.

What I wrote was about stamped capacity and how this is what is recognized by Code, nothing more or less. Stamped capacity being the only guaranteed flow rate is fact, not interpretation. When to use stamped capacity has been set down by both Code and interpretation. You can disagree all you want with what I wrote. That is fine and I just love getting into these types of discussions. How else can we learn and grow? But you made some rather inaccurate statements in your first letter about what was stated, or not
stated in the article and that still leads me to feel you didn't totally understand it.

I've been giving this debate some further thought and I hope this will finally put it to rest. You and I seem to be disagreeing on the concept of sizing versus what you do with the valve once it has been sized.

My article on the Web site starts off with a statement made by the author of an article published in the May 2000 issue of CEP. This person made a statement that basically said if you want to decrease the size of a given relief valve, find a way to increase it's set pressure. However, the following Letter to the Editor in the October 2000 issue inspired my article. It stated, "This is not true; for a certain MAWP, the capacity of the relief device is not a function of its set point, but of MAWP alone." Now, had you really read my article, you would have seen these quotes! As I've said before and written in my article, per ASME, capacity for a given valve (which I am defining as certified capacity) is a function of set point only, not MAWP. Therefore, to increase the certified capacity of a given
size valve, one can increase the set pressure. Alternatively, to reduce the size and cost of the purchased valve, one can increase the set pressure of a smaller valve and maintain the same certified capacity.

The whole point should be "safety", not who can buy the smallest relief valve. If you want to stretch what ASME is trying to convey just to buy a smaller relief valve, go ahead; you don't work for me. If you did work for me, I wouldn't allow it. I'll take the conservative approach, it just isn't worth the potential liability. After all Jeff, you'll never know if the valve you bought is the right one unless the system over pressure is caused by the controlling scenario and the valve does or does not work. And guess what? This rarely happens since most controlling scenarios are loaded with conservative assumptions that are never achieved in real life.

One last point if I may. I still can't understand why you would want to set the relief valve at a lower pressure (50 psig) and still allow the system to achieve the much higher pressure (110 psig). This makes no engineering sense to me. You should just specify the set pressure at MAWP and go with the allowable overpressures. Then you won't have any debates. You mention run away reaction? I'm sorry but this is bad engineering practice and if you do this at your site, I would stop the practice. Run away reactions can occur
too fast for relief valves to react. I would use a stand alone rupture disk set at the lower burst pressure (your 50 psig example) for the run away reaction scenario and use the relief valve for other scenarios set at the 100 psig MAWP. This is a much safer design.

Discussion Two

From Mr. Don Gregurich:

Dear Mr. Leckner,

I read your about Relief Valve Set Pressures with interest because the issue came up several years ago and we had quite an internal debate (at a different company). {parse block="google_articles"}I don't remember the details, or resolution, but I was on the opposite side of the argument. Essentially, the situation is that there is a vessel with a design pressure of 150 psig (and let's assume same MAWP) and we want to use a relief valve set at 30 psig (There could be a number of process reasons for doing so.) Then, if this is the only relief on the vessel, does it need to be sized to accommodate the worst credible non-fire overpressure case flow at a relieving pressure of 33 psig or 165 psig? I felt that the answer was 165 psig, if, of course, all of the design was appropriate (valve body can handle the pressure/temperature at the relieving conditions, the inlet and outlet piping are sized correctly for those relieving conditions etc.) It certainly seemed to me that this was consistent with the spirit of the code, after all, the whole point is to limit the pressure in the vessel and this would meet that requirement.

Of course we must also be consistent with the letter of the code, if we are to avoid jail time, but I didn't see anything in the code that contradicted the above interpretation. Although I see your quote regarding rating of valves, don't see where it explicitly states that a valve can not be operated above its "official rated capacity" to perform the required service. I see that the code states that "the valve must have the capacity to relieve the load*" and that "the official rated capacity is that which is stamped*" but I don't see where it says that the valve must be able to relieve the load at the official rated capacity. So if I look at this in the strictest sense (by the letter of the code) I do not see that we can't size it based on the 165 psig. I don't think this is unreasonable: rating a pump at a given pressure/flow point serves to define the pump's capacity - but the pump can operate at different flows and pressures then at the rated point. Likewise for the relief valve. In fact, we could have selected this same valve, used a spring for 150 psig, and it would be functioning the same at the relieving conditions, as if it would with the 30 psig spring.

I confess that I haven't taken the time to reread through the code, but I was convinced back then that my interpretation met the spirit and letter of the code. I'd be interested to hear what you have to say about my position.

Thanks

Don Gregurich

Phlip Replies:

Don,

First, call me Phil and thanks for taking the time to read my column. Second, I do not agree with your position even though on the surface it appears to be sound, and this is why.

First (and this really doesn't answer the question but I just couldn't help but comment) I couldn't figure out why anyone would want to have such a low set pressure and still allow the relieving pressure to go so high. It is not logical and seems to defeat the purpose of having a low set pressure. You might as well have just set the valve for 150 psig and taken the conventional 10% overpressure and eliminate the controversy. But then I thought of a run-away reaction scenario where you may want the valve to pop open early and allow the vessel to slowly relieve its contents but still allow the pressure to build-up. However, this uses the relief valve as a
depressurization valve and I am not in favor of this. There are designs with proper use of control valves to do this.

In your E-Mail, you say "Then, if this is the only relief on the vessel, does it need to be sized to accommodate the worst credible non-fire overpressure case flow at a relieving pressure of 33 psig or 165 psig? I felt that the answer was 165 psig,...".

It is very clear that the valve does not "need" to be sized for 165 psig. It only "needs" to be sized for set pressure +10% overpressure (non-fire, single device case) in order to be consistent with the calculation of the certified (stamped) capacity. However, you are correct in that on the surface (at least as far as I can tell), the code (ASME Section VIII, Division 1, 1998 Edition) does not seem to prohibit one from sizing the valve based on such a high overpressure. ASME appears to only be concerned that the MAWP is not exceeded beyond its requirements. And as you say in your E-Mail, "I don't see where it says that the valve must be able to relieve the load at the official rated capacity."

However, a relief valve vendor will only guarantee the stamped capacity and ASME is very clear how this is to be determined. Therefore, in the event of an accident, how would you have guaranteed to an OSHA inspector that the catastrophic failure of the vessel or attached piping/equipment was not a result of an improperly sized relief valve since you have no guarantee of the flow rate through the valve? I guess you could try to prove that your calculations were reasonably accurate using real properties, accurate vapor
flow equations and the correct thermodynamics. Is all this really worth the potential liability just to buy a somewhat smaller relief valve? Not where this Process Engineer stands! So Don, that's Process Engineering-As I See It!

Mr. Don Gregurich Replies:

Thanks Phil,

I appreciate your insight; I understand what you're saying about the rated capacity of the valve as the only real figure that you can hang your hat on.I honestly can't remember the details of the situation, only that it never did get to the point where we needed to make a final decision on the set point issue. It's those applications that lie outside of the norm that really make us think about what we're doing, which hopefully leads to a better understanding.

I do have another one for you, this one also seem "sensible" to me, but I don't know what the code would think:

If an ASME stamped pressure vessel is being used for an "atmospheric" operation with an open vent to atmosphere that has been properly sized, is a relief valve (or disk) required? "Proper sizing" of the vent line means application of the same analysis and calculations that would be done for sizing of a relief device. The vent line would be sized to accommodate the worst credible upset condition at a relieving pressure that is under 15 psig. The location is in a jurisdiction that requires compliance with the ASME code.

Thanks again,

Don

Philip Replies:

Don,

I am not on any committee so I can't give you an official answer. However, ASME specifically states in Section VIII, Div 1, 1998 Edition, paragraph UG-125(a)"All pressure vessels within the Scope of this Division, irrespective of size or pressure, shall be provided with pressure relief devices in accordance with the requirements of UG-125 through UG-137." The key here is what they consider part of the "Scope". The Indroduction, Paragraph U-1, goes into the definition of "Scope" and it can get rather complex. I would have to read through this very slowly and carefully to see if this exact situation is addressed. I do have some other sources I can
review for interpretations and your question may not be able to be answered without a direct interpretation from the ASME committee. I would agree with you that it doesn't make sense to need a pressure relief device for this situation. I can tell you that in the past, when facing a situation where we do have an ASME coded vessel but cannot come up with any credible scanrio, nothing at all, we put a 3/4" x 1" relief valve on the vessel and call it out for thermal expansion - end of story.

I think I have an answer for the second question you asked me concerning an ASME stamped pressure vessel being used for an "atmospheric" operation with an open vent to atmosphere. Based on ASME Section VIII, Division 1, Introduction, Paragraph U-1 para c(2)(h), vessels having an internal or external operating pressure not exceeding 15 psi (103 kPa) would not fall under the scope even though it has a stamp. As long as any pressure vessel meets all the applicable requirments of the Division, it may carry the Code U Symbol.

The Problem

Accidents not only damage equipment but also cause injury or even death to plant personnel. To reduce the number of incidents of accidents, it is the job of the Process Engineer to analyze the process design, determine the "what can go wrong" scenario and either find a way to "design" out of it or provide protection against catastrophic failure in the event an accident does occur, i.e. install a relieving device such as a relief valve and/or rupture disk.{parse block="google_articles"}

For the purposes of this discussion and those that will follow, a "what can go wrong" scenario is defined as an action that will cause a vessel containing a gas or liquid to overpressure, leading to a catastrophic failure of that vessel if it were not for the presence of a relief valve or rupture disk. To find these potentially deadly incidences, the Process Engineer goes through a type of "self HAZOP" (Hazardous and Operability Study), analyzing the process to determine what these scenarios are. For each credible scenario identified, the Process Engineer performs calculations to determine the amount of vapor or liquid that must be relieved from the vessel in order to prevent the overpressure from occurring (the relieving load).

Fair warning, this discussion and those that will follow in future installments assume the reader is at least somewhat knowledgeable in Process Design. Safety analysis should never be left up to the junior Process Engineer unless closely supervised. So if you Mr., Mrs., Ms. Reader become confused or somewhat lost in some of the terminology used, I sincerely apologize. I welcome your very direct and specific questions about anything I write and would be happy to help you understand what I am saying. This is an extremely important function for Process Engineers.

The Checklist

Since there are many potential causes of failure, it would be nice to have a checklist to make the analysis organized and somewhat standard. After all, those of us in Process Design may be working on a project for a chemical plant today and end up on a project for a pharmaceutical plant tomorrow (it happens, believe me). A pretty good checklist is given by Table 2 in Section 3 of The American Petroleum Institute (API) publication, "Guide for Pressure-Relieving and Depressuring Systems"², better known as API Recommended Practice 521 (or just API 521). For those not familiar with API, this is the organization in the United States that sets the standards by which codes (laws) are followed. API publishes the Recommended Practices 520 and 521, among others. A condensed version of the API checklist is presented in Table 1 below.

In this installment, I want to establish a framework for analyzing a given process. In future installments, I will begin to tackle the scenarios (Overpressure Cause) themselves in some detail. The ultimate goal is for the Process Engineer to identify credible "what can go wrong" scenarios, perform relieving load calculations to prevent catastrophic failure and eventually size the relieving device and system.

The Concept of Double Jeopardy

I can't begin to tell you how many people still don't understand this concept. API allows you to "ignore" failures that fall under the "Double Jeopardy" principle (See API 521, March 1997, 4^th edition, paragraph 2.2). Double Jeopardy basically means two unrelated failures occurring at the exact same time, i.e. simultaneous. This does not mean the failures occurred one minute, one second or even one millisecond apart. It means at exactly the same instant in time! Let's look at some examples.{parse block="google_articles"}

There is a loss of power to a pump causing stoppage of cooling water to a condenser on a distillation column. Because vapor from the distillation column can no longer be condensed, pressure builds up to the point of popping the relief valve, i.e. the system goes into relief. At the same time, the control room operator strokes open a steam flow control valve to the reboiler on that same distillation column causing the generation of an excessive amount of vapor. When calculating the total amount of vapor that must be relieved to prevent damage, should one take into account the excessive vapor produced by the wide-opened steam valve? Or, should we consider only the normal amount of vapor exiting the column; API 521, paragraph 2.3.2 says that the control valve should be considered to be in its normal operating position unless its function is affected by the primary cause of failure, this being loss of power to a pump.

The answer is, this is a Double Jeopardy failure, two unrelated events occurring at the same time. One has nothing to do with the other. Therefore, you only need to calculate the relief load for one scenario at a time. For the loss of power to a pump scenario, the relief load would be based on the amount of vapor generated at the "normal" rate of steam to the reboiler.

Let's look at the situation again. With the pump stopped, cooling water is lost to the condenser causing the distillation column to go into relief. However, this time the control room operator realizes that the relief valve has opened and attempts to stop steam flow to the reboiler. The operator puts the steam control valve in manual and tries to close it but it won't respond because it is stuck. To free it, he strokes it wide-open, shooting steam into the reboiler and causing the generation of an excessive amount of vapor. Now we have two failures occurring at the exact same time but are now related. The power failure stops the pump and thus the cooling water to the column condenser. This causes the column to go into relief, which then causes the operator to react, initiating the second failure.

A very obvious example of a Double Jeopardy failure would be a tube rupture in the reboiler occurring at the same time cooling water flow was lost to the condenser. Two very unrelated failures occurring at exactly the same time.

By the way, stuck opened control valves occurring simultaneously with a second failure does NOT constitute Double Jeopardy. That valve may have been stuck in its operating position for a significant amount of time before the second failure has occurred. The first failure was the mechanical failure of the valve (sticking) and that did not happen at the same time as the second failure. These are unrelated failures but they do not occur simultaneously!

Being Conservative

There are times when a failure may be obvious, cooling water stops to a condenser. Then there are times when it will take some stretching to find any, a pressure vessel operating in a nonflammable, low-pressure system with little fluid throughput. There are three approaches you can take when analyzing your process. You can be CONSERVATIVE. You can be conservative or, as I like to think of myself, you can be CONSERvative. I follow API 520 and 521 to the letter as a minimum. If my company or the client I am working for happens to have more stringent rules, these obviously supercede what is in API documents. For example, API 521, paragraph 3.15.1.1 basically allows you to "ignore" heights above 25 feet when considering how much of a vessel to include in a fire zone calculation. I worked for a company that used 50 feet for its standard.{parse block="google_articles"}

I will perform the necessary relieving load calculations for any scenario that cannot be rationally explained away, even if there is only a remote possibility that the failure will ever occur. The alternative is to perform fault tree analysis, risk assessment, etc. If it can be shown that a given scenario is indeed a 1 million to 1 long shot, then I'll label it as being not credible. Until then, it's only a relatively small amount of time that needs to be spent to perform the necessary calculations to be safe.

In the case of analyzing for Double Jeopardy, this is where I get my most grief; my conservatism tells me to error on the safe side, the client's money tells me to make the scenario go away. If I feel that even a Double Jeopardy failure can lead to a loss of life or major equipment damage, I might go ahead and do the relieving load calculations anyways (this does not usually go over too well with the powers-to-be because this usually results in larger relief systems).

API 521, paragraph 3.4 states that one can take credit for operator response after 10-30 minutes. I stick with the higher end at all times.

When analyzing a system for failures of control valves, I will always assume all my valves will fail as they are intended (fail close will indeed fail close, fail open will indeed fail open) except for the one control valve that will cause an overpressure hazard! This valve I assume to fail in the opposite direction (fails closed if it is intended to fail open).

When analyzing a system for "what can go wrong" scenarios, plant instrumentation sometimes may be used to justify the elimination of some scenarios. For example, if I have a hard wired (opposed to a Distributed Control System-DCS) pressure interlock that will shut steam off to the reboiler when the column pressure rises to some predetermined value, and there are redundant pressure switches, I might consider cooling water failure to the condenser as not being a credible scenario. On the other hand, once a credible scenario has been established, you are never to take into account the use of instrumentation as a means of reducing the relieving load.

Final Say for this Installment

Always analyze the system as a whole. Don't get tunnel vision on one area of the process. Of course you will consider individual "what can go wrong" scenarios but remember the example I used when discussing Double Jeopardy. I considered two actual failures that combined into one. I found these two by considering the system as a whole.{parse block="google_articles"}

"What can go wrong" scenario analysis is a very important but complex process. I do not intend to cover every nuance associated with it (simply because it will be impossible). I also don't expect everyone to agree with my analysis for every API RP521 Item number (Table 1 above). That's the fun and scary part of doing this type of work. Some of it can be highly subjective as to what constitutes a credible scenario. I strongly suggest you get a copy of API 520³ and 521² and the ASME Boiler and Pressure Vessel Code, Section VIII, Division 1⁴ and try to read through them (the operative word here is "try").

I welcome and encourage your feedback. Feel free to E-Mail me at the Internet address below. All correspondences that include a name will be published in this column. Better yet, I encourage discussion of any topic I cover utilizing The Chemical Engineers' Resource Message Board. This will enable the entire Internet community to join and learn. And, don't forget to check back for future installments on this series.

References

1. "Boiler and Pressure Vessel Accidents Soar," Chem. Eng. Progress, p 13 (August 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
4. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)

Before I begin, let me point out that most of what is included in this series of articles can be found in API RP520¹ and API RP521², and ASME Section VIII, Division 1³.  Much of what is found in these documents can also be found in vendor literature.

Why and When to Use Rupture Disks

Why Do We Use a Stand-Alone Rupture Disk?

A rupture disk is just another pressure relieving device. It is used for the same purpose as a relief valve, to protect a vessel or system from overpressure that can cause catastrophic failure and even a death.

When Do We Use a Stand-Alone Rupture Disk?

Some of the more common reasons are listed below. You may think of others.

Figure 1: Basic Components of a Rupture Disk

1.  Capital and Maintenance Savings: Rupture disks cost less than relief valves. They generally require little to no maintenance.

2.  Contents will be lost, but who cares? A rupture disk is a nonreclosing device, which means once it opens, it doesn't close. Whatever is in the system will get out and continue to do so until stopped by some form of intervention. If loss of contents is not an issue, then a rupture disk may be the relief device of choice. 

3.  Benign service: It is preferable that the relieving contents be non-toxic, non-hazardous, etc. However, this is not a requirement when deciding to use, or not use, a stand-alone rupture disk.

4.  Rupture disks are extremely fast acting: Rupture disks should be considered first when there is a potential for runaway reactions. In this application, relief valves will not react fast enough to prevent a catastrophic failure. A relief valve may still be installed on the vessel to protect against other relieving scenarios. Some engineers prefer to use rupture disks for heat exchanger tube rupture scenarios rather than relief valves. They are concerned that relief valves won't respond fast enough to pressure spikes that may be experienced if gas/vapor is the driving force or liquid flashing occurs.

Figure 2: Rupture Disk Mounted on a Vessel

5.  The system contents can plug the relief valve during relief: There are some liquids that may actually freeze when undergoing rapid depressurization. This may cause blockage within a relief valve that would render it useless. Also, if the vessel contains solids, there is a danger of the relief valve plugging during relief.

6.  High viscosity liquids. If the system is filled with highly viscous liquids such as polymers, the rupture disk should seriously be considered as the preferable relieving device. Flow through a relief valve will be very difficult to calculate accurately. Also, very viscous fluid may not relieve fast enough through a relief valve.

Cost Comparison Between Comparable Stand-Alone Rupture Disk and Relief Valve

Rupture disk manufacturers burst at least two disks per lot before shipping them to a customer. {parse block="google_articles"}As a consequence even if you want just one rupture disk you will be buying three. Therefore, the first usable rupture disk is comparatively expensive. Also for new installations, each installed rupture disk must be purchased along with a holder. However, the same holder may be used for replacement purchases as long as you buy the exact same rupture disk from the same manufacturer.

Below is a capital cost comparison between Continental Disc Corp. (www.contdisc.com) 3" Ultrx Hastelloy C rupture disks with holders and Farris Engineering (www.cwfc.com) 2600 series relief valves, based on a budget estimate in year 2001 dollars.

This capital cost comparison will vary considerably with size and material of construction but you get the point. However please note that everything has a value and the loss of contents should be considered in the overall cost difference between a rupture disk and a relief valve.

When Do We Use a Rupture Disk-Relief Valve Combination?

Rupture disks are often used in combination with and installed just upstream and/or just downstream of a relief valve.  You may want to choose the combination option if:

Figure 3: Rupture Disk- Relief Valve Combination

1.  You need to ensure a positive seal of the system (the system contains a toxic substance and you are concerned that the relief valve may leak). Application: rupture disk installed upstream of the relief valve.

2.  The system contains solids that may plug the relief valve over time. Remember, the relief valve is continuously exposed to the system. Application: rupture disk installed upstream of the relief valve.

3.  TO SAVE MONEY!  If the system is a corrosive environment, the rupture disk is specified with the more exotic and corrosion resistant material. It acts as the barrier between the corrosive system and the relief valve. Application: rupture disk installed either upstream and/or downstream of the relief valve.

Below is a capital cost comparison between combination Hastelloy C rupture disks with stainless steel relief valves and three stand-alone Hastelloy C relief valves. Again, this is based on a budget estimate in year 2001 dollars using Continental Disc Corp. rupture disks and holders and Farris Engineering relief valves.

Combination of Hastelloy C Disk and SS Relief Valve

Single Installation Total = $10,200

Total for three installations = $27,140

Three stand-alone Hastelloy C relief valves = $40,200

Summary

A stand-alone rupture disk is used when:

1. You are looking for capital and maintenance savings

2. You can afford to loose the system contents

3. The system contents are relatively benign

4. You need a pressure relief device that is fast acting

5. A relief valve is not suitable due to the nature of the system contents

A rupture disk / relief valve combination is used when:

1. You need to ensure a positive seal of the system
   
2. The system contains solids that may plug the relief valve over time
   
3. TO SAVE MONEY!  If the system is a corrosive environment, the rupture disk is specified with the more exotic and corrosion resistant material

References

1. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)

Before I begin, let me point out that most of what is included in this series of articles can be found in API RP520¹ and API RP521², and ASME Section VIII, Division 1³. Much of what is found in these documents can also be found in vendor literature

Sizing

Sizing the rupture disk is a two-part procedure. First, determine how much flow the rupture disk needs to pass. Then determine how big it needs to be.{parse block="google_articles"}

How much flow does it need to pass?

Answering this question is the same as determining the required relieving rate for the system. There is no difference between determining the relieving rate for a rupture disk and a relief valve. They both require a set pressure (burst pressure for rupture disk), an allowable overpressure, an evaluation and calculation of the required relieving rate for each credible scenario and then choosing the flow rate associated with the worst-case scenario. Determining the controlling relieving rate is a paper in of itself and I will not attempt to get into details here.

How Big?

There are two recognized methods that can be used to answer this question, the Resistance to Flow Method or the Coefficient of Discharge Method.

Resistance to Flow Method

The Resistance to Flow Method analyzes the flow capacity of the relief piping. The analysis takes into account frictional losses of the relief piping and all piping components. Calculations are performed using accepted engineering practices for determining fluid flow through piping systems such as the Bernoulli equation for liquids, the Isothermal or adiabatic flow equations for vapor/gas and DIERS methodology for two-phase flow.

Piping component losses may include nozzle entrances and exits, elbows, tees, reducers, valves and the rupture disk (note that the rupture disk and its holder are considered a unit). Let me emphasize that in this method, the rupture disk is considered to be just another piping component, nothing more, and nothing less. Therefore the rupture disk's contribution to the over all frictional loss in the piping system needs to be determined. This is accomplished by using "Kr", which is analogous to the K value of other piping components. Kr is determined experimentally in flow laboratories by the manufacturer for their line of products and is certified per ASME Section VIII, Division 1³. It is a measure of the flow resistance through the rupture disk and accounts for the holder and the bursting characteristics of the disk.

Below is a list of some models of Continental Disc Corporation rupture disks with their certified Kr values⁴.

For comparison, the following is a list of some models of Fike rupture disks with their certified Kr values⁵.

If at the time of sizing the manufacturer and model of the rupture disk are unknown, there are guidelines to help you choose Kr. API RP521² recommends using a K of 1.5. However, ASME Section VIII, Division 1³ states that a Kr of 2.4 shall be used. Which one? Remember that ASME is Code (meaning LAW for the most part) and API is a recommended practice. In addition, as can be seen in the tables above, even ASME may not be as conservative as you may think. Therefore, it is in the engineer's best interest to determine ahead of time the manufacturer and model of the rupture disk that eventually will be purchased. This can be done without knowing the exact size, as Kr is more manufacturer and model specific than size specific (see above tables). If a number of manufacturers are on the allowable purchase list, then at the very least choose the most likely models you would buy from each manufacturer and use the largest Kr from that list. This will be a significantly better guess than just using guidelines.

Once the piping system is laid out and all the fitting types are known, including the rupture disk, the engineer can proceed with the calculations in the following manner (presented here as a suggestion, there are many ways to do it).

1. Known are the two terminal pressures, these being the relieving pressure (upstream) and the downstream pressure (a knock-out pot, atmosphere, etc.).
   
2. Also known are the fluid properties and required relieving rate (the flow the rupture disk needs to pass).
   

3. Choose a pipe size. This will be the size to use for all components, including the rupture disk.

4. For vapor/gas or two-phase flow, use one of the accepted calculation methods to determine the maximum flow through the system. The maximum flow through the system is commonly known as critical flow or choked flow. For liquids, use the Bernoulli equation to calculate the flow that will balance the system pressure losses.

5. Per ASME Section VIII, Division 1, multiply this flow by 0.9 to take into account inaccuracies in the system parameters. Compare the adjusted calculated flow to the required relieving rate. If it is greater, then the calculation is basically done. However, the next smaller line size should also be checked to make sure the system is optimized; you want the smallest sized system possible. If the adjusted calculated flow is less than the required relieving rate, the pipe is too small, choose a larger size and repeat the calculations.

Why not just choose a large Kr? Isn't that more conservative?

Many times, relief is not to atmosphere but to some downstream collection and treatment system, e.g. knockout drums and flares or thermal oxidizers. These are more often than not specified at a time period in the design that predates the actual purchase of the rupture disk. The flow used to size this equipment will be based on the capacity of your relief system as determined above.

If the rupture disk contributes a significant portion of the frictional losses to the system, a fictitiously large Kr might result in an oversized piping system. Sounds all right on the surface but once the actual rupture disk is chosen, the calculation must be repeated with the "real" Kr and this may be a much lower value than originally used. More fluid will flow through the system than previously determined because there will actually be less resistance to flow. The result is that the downstream processing equipment may have been undersized.

The opposite is also true. An initial guess of a fictitiously small Kr might ultimately result in oversized downstream equipment and the excessive expenditure of a significant amount of money.

Atmospheric discharge must also be similarly analyzed because the flow capacity determined after rupture disk selection may have a major impact on the emissions reported for permitting if they were based on the initial value of Kr.

Coefficient of Discharge Model

The second calculational method is the Coefficient of Discharge Method. The rupture disk is treated as a relief valve with the flow area calculated utilizing relief valve formulas and a fixed coefficient of discharge, ‘Kd', of 0.62. This method does NOT directly take into account piping so there are restrictions in its use. These restrictions are known as the "8 & 5 Rule" which states that in order to use this method to {parse block="google_articles"}size the rupture disk ALL of the following four conditions MUST be met³:

The rupture disk must be installed within 8 pipe diameters of the vessel or other overpressure source.

1. The rupture disk discharge pipe must not exceed 5 pipe diameters.
2. The rupture disk must discharge directly to atmosphere.
3. The inlet and outlet piping is at least the same nominal pipe size as the rupture disk.

A sketch of the "8 & 5" rule starting with a 2" nominal sized pipe is shown at the below.

The flow area calculated with this method is called the Minimum Net Flow Area or MNFA. The MNFA is the rupture disk's minimum cross

Figure 1: Diagram Showing the "8 & 5" Rule

sectional area required to meet the needed flow.

This is not the area (and thus the size) you specify. Just like a pipe with a nominal size and an actual inside diameter, the rupture disk has a nominal size and an actual Net Flow Area or NFA. The rupture disk purchased must have a NFA equal to or greater than the MNFA. The manufacturer publishes the NFA for every rupture disk model and size they sell. The NFA also accounts for bursting characteristics of the disk and the holder.

Below is a list of some Continental Disc Corporation rupture disks with their NFA⁴.

Once the actual NFA of the rupture disk is determined, the calculations must be repeated, basically for the same reasons discussed above for the Resistance to Flow Method.

Why I Don't Like the Coefficient of Discharge Model

• It's too restrictive! During the basic design phase of a project, actual piping configuration is unknown. You may think you are within the "8 & 5" rule at first but may not be when the final details are worked out. Remember, the "5" means 5 pipe diameters. For a 3" line, that is only a nominal 15". For a 6' vertical vessel with a rupture disk discharge being piped to a drain hub on the floor, the 15" maximum length is exceeded without even thinking.
  

• Using the Resistance to Flow Method is valid for all cases. All sizing calculations can be standardized.{parse block="google_articles"}

• The Kr used in the Resistance to Flow Method is obtained by actual flow data for a given model of rupture disk and holder. Its use will provide a much more accurate calculation. The 0.62 coefficient of discharge used in the Coefficient of Discharge Method is very general and independent of rupture disk manufacturer model and type, holder, disk bursting characteristics and flow restrictions of the total relief system.

• Two-phase flow can be a major concern when using this method. The coefficient of discharge was established mainly for true vapors. Its application to liquids is questionable and its application to two-phase flow is totally fictitious. Granted, for the Resistance to Flow Method the Kr is not particularly applicable to two-phase systems either but one can easily compensate for this in the system calculations. Also, the rupture disk is only a part of an entire piping system and its overall contribution to the system frictional losses may not be greatly significant. Therefore, errors in Kr may not be very significant. In the Coefficient of Discharge Method, it is the only device considered. If the coefficient of discharge is grossly in error, the MNFA calculated will also be grossly in error.

• The same argument can be made for highly viscous liquid systems such as polymers.

In Summary

• Obtain the required relieving rate using good sound "what can go wrong" scenario analysis.

• Use the Resistance to Flow Method to calculate the size of the rupture disk (use the Coefficient of Discharge Method if you really must and you fall within the "8 & 5" rule).
  
• For the Resistance to Flow Method, try to choose the manufacturer and model of rupture disk you intend to purchase ahead of time or at least have a list of acceptable manufacturers and a good idea of the model you intend to use from each.
  
• For the Resistance to Flow Method use the ASME Kr value of 2.4 if you have no idea who the manufacturer(s) will be at the time of sizing.

References

1. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)
4. Continental Disc Corporation (www.contdisc.com), Certiflow^TM Catalogue 1-1112
5. Fike (www.fike.com), Technical Bulletin TB8104, December 1999
6. Another good rupture disk manufacturer to investigate would be Oseco (www.oseco.com).
7. A good reference source for calculating flow through the system for liquids and gas/vapors is CRANE Technical Paper 410, "Flow of Fluids Through Valves, Fittings, and Pipe"
8. A great source and one that I feel should be the bible on two-phase flow is: Leung, J.C. "Easily Size Relief Device and Piping for Two-Phase Flow", Chemical Engineering Progress, December, 1996

Before I begin, let me point out that most of what is included in this series of articles can be found in API RP520¹ and API RP521², and ASME Section VIII, Division 1³. Much of what is found in these documents can also be found in vendor literature.

Problem{parse block="google_articles"}

1. What is the maximum allowable specified burst pressure?
2. What should the expected stamped (rated) burst pressure of the rupture disk be?
3. At what pressure(s) can we expect the delivered rupture disk to actually burst at?
4. What is the maximum allowable operating pressure in the vessel?

All these questions must be considered in order to properly set the burst pressure of a rupture disk.

What is the Maximum Allowable Specified Burst Pressure?

Burst Pressure

What do we mean by burst pressure? This is the pressure at which the rupture disk will open or burst. It is analogous to the set pressure of a relief valve and is specified by the process engineer.

Design Pressure

To find the maximum allowable specified burst pressure, the process engineer first needs to define a vessel design pressure. The design pressure is an arbitrary value above the vessel maximum operating pressure. One guideline used by many process design engineers is to increase the maximum operating pressure by 25 psig or 10% whichever is greater. For example, if the maximum operating pressure is 70 psig, then 25 psig should be added to arrive at the design pressure since 10% is only 7 psig. The design pressure would then be set at a nice round 100 psig. Other criteria to determine design pressure may be used but I recommend that the margins never be less than what I described above (the reason will become apparent later).

Maximum Allowable Working Pressure (MAWP)

The next step is to determine the Maximum Allowable Working Pressure (MAWP) of the vessel. A vessel specification stating design pressure, the coincident design temperature and other parameters is sent to the manufacturer. The manufacturer performs a series of calculations utilizing these parameters, amongst others, to determine material thickness for use in vessel fabrication. A standard material thickness (greater than or equal to what was calculated) is chosen. With the actual material thickness known, the true MAWP is calculated. The vessel design documents are then stamped (certified) at this pressure in accordance with code. However, for one reason or another, the MAWP calculation is not always done and the vendor will just stamp the vessel at the specified design pressure.

The Maximum Allowable Specified Burst Pressure

So, what is the maximum allowable specified burst pressure? Theoretically it is the MAWP. However, rupture disks are typically specified during basic engineering, which is performed way before the vessel is mechanically designed. This, combined with the fact that the true MAWP may never really be known (as mentioned above), the maximum allowable specified burst pressure will more typically be the vessel's design pressure.

Note if the rupture disk is to be used in conjunction with another relief device to fulfill the total required relieving capacity, the maximum allowable specified burst pressure could be 5% or even 10% greater than the design pressure (or MAWP). See ASME Section VIII, Division 1 paragraphs UG-125 and UG-134.

Also note that the specified burst pressure can be lower than the maximum allowable. Indeed, this is often the case if the rupture disk is used to protect reactor vessels against over pressure due to run-away reactions.

Stamped Burst Pressure

What should the expected stamped (rated) burst pressure of the rupture disk be?

What do we mean by "stamped or rated" burst pressure? Per code, the rupture disk vendor must provide a tag containing, amongst other things, the rated or what is typically called the stamped burst pressure. This is a guaranteed value so the user knows (within an allowable tolerance; more on this later) the exact bursting pressure of the rupture disk. Also this stamped burst pressure must never exceed the design pressure (or MAWP); except for the special case mentioned above.

So, the rupture disk vendor stamps the disk with the burst pressure specified by the process engineer? Not necessarily!

Manufacturing Range (MR)

Figure 1: Graphical Representation of the Manufacturing Range

A rupture disk is made out of a sheet of material, e.g. stainless steel, high alloys, ceramics, etc. Like all things in this world, this sheet of material is not perfect. To quantify the inaccuracies in sheet material thickness, the vendor uses what is called the Manufacturing Range (MR).

Figure 2A: Specified and Stamped Burst Pressure

The MR is expressed as ±% of the specified burst pressure. It determines the highest pressure above the specified burst pressure or the lowest pressure below the specified burst pressure that the disk can be stamped at. This is shown graphically in Figure 1.

Figure 1 shows the two extremes, a MR of ± 0% and a MR of ± some value%. Note that other combinations may be used such as + 0% and - some value% or - 0% and + some value%.

Let's look at an example. If the specified burst pressure is 100 psig with a MR of ± 0%, the stamped or rated burst pressure will be 100 psig (see Figure 2A). However, if the MR is +5% and - 10%, the disk can be delivered with a stamped burst pressure of 105 psig, 90 psig or anywhere in between (see Figure 2B). That's right, if the MR is anything but ± 0%, the user won't know the stamped burst pressure until the rupture disk is ready for shipment!

Figure 2B: Differences in Specified and Stamped Burst Pressures

Do you see anything wrong with this rupture disk as specified?

Remember, the stamped or rated burst pressure must never exceed the vessel's design pressure or MAWP (assumes a single device, no special cases). Since the specified burst pressure is the design pressure, this particular rupture disk is not acceptable because the delivered rupture disk may have a stamped burst pressure of 105 psig or 5 psig greater than design!

How can we avoid this problem? There are a number of ways.

The process engineer specifies the Manufacturing Range, not the manufacturer. You can ask for any range within the capability of fabrication including ± 0%. Considering the potential problems, why specify anything other than ± 0%? Cost. A MR of +5% and -10% can save as much as 40% off the cost of a similar rupture disk with a MR of ± 0%. Even if you demand +0% (which you should), you can still realize some cost savings if a stamped burst pressure lower than specified is acceptable (not always a good idea as will be discussed later). Note that code only affects the upper stamped limit, not the lower.

Another way to avoid the potential violation of code and still get a cheaper rupture disk is to specify a burst pressure that will be lower than the vessel design pressure. Thus, when the MR is added the stamped burst pressure will not exceed the design pressure. The maximum allowable specified burst pressure could be determined in the following manner:

P_{spec_max} = (DP) - (+MR/100) x (P_{spec_max})

Where DP = Design pressure

So:

P_{spec_max} = (DP) / [1+(+MR)/100]

Since DP = 100 psig and the upper value of MR = +5%,

P_{spec_max} = 100 /[1+(+5/100)] = 100/(1+0.05) = 100/1.05 = 95.2 psig

This rupture disk would be specified with a burst pressure no higher than 95.2 psig while the stamped burst pressure may be as high as 100 psig.

Note that the standard Manufacturing Range for most manufacturers is ± 0% and this is reflected in the base price you will be quoted.

Where Will the Disk Burst?

At what pressure(s) can we expect the delivered rupture disk to burst at?

Trick question? The answer should be the stamped burst pressure. But again the world isn't perfect.

Burst Tolerance

Figure 3A: Burst Tolerance

The Manufacturing Range is applied to the specified burst pressure but there is yet another unknown due to imperfections in the material used to fabricate the rupture disk. This is accounted for in the burst tolerance. Burst tolerance is applied to the stamped burst pressure and is set by code. For stamped burst pressures of 40 psig and lower, the burst tolerance is ± 2 psi. For stamped burst pressures above 40 psig, the burst tolerance is ± 5%.

Let's look at the examples again but apply the burst tolerance. For this discussion, I'm changing the specified burst pressure for the case of a rupture disk with a Manufacturing Range of +5% and -10% to 95.2 psig (see Figure 3B) so the stamped burst pressure can't exceed code.

The important thing to notice is that in both Figures 3A and 3B, the upper limit of the stamped burst pressure is equal to the design pressure but the maximum bursting pressure is 105 psig, or 5 psig over design pressure. Unlike the stamped burst pressure, which by code cannot exceed the design pressure (or MAWP), the maximum expected burst pressure can if it is caused by the burst tolerance.

Figure 3B: Specified, Stamped, and Maximum Burst

Maximum Allowable Operating Pressure

What is the maximum allowable operating pressure in the vessel?

Up to now, the discussions focused on the upper limit of the stamped burst pressure because this is governed by code. But the lower limit is extremely important to consider as well because of the possible affect it has on the maximum allowable operating pressure in the vessel.

Operating Ratio (OR)

The operating ratio is defined as the ratio of the maximum operating pressure to the lowest stamped burst pressure. The OR is used to protect against premature bursting of the rupture disk. If the operating pressure is too close to the lowest stamped burst pressure, or the system pressure cycles (pressure rises and falls during operation) too close to the stamped burst pressure, the material will fatigue and can {parse block="google_articles"}eventually loose its structural integrity. This is a classic reason for premature bursting of a rupture disk.

The manufacturer publishes the Operating Ratio for every rupture disk model they sell. For example, the Continental Disc Corporation's ULTRX rupture disk has an operating ratio of 90%⁴. This means the system pressure can operate to within 90% of the lowest stamped burst pressure without the fear of premature bursting. However, it's always best to operate as far away from the lowest stamped burst pressure as you can to avoid material fatigue.

From Figure 3B above, the lower limit or minimum stamped burst pressure is 85.7 psig:

P_{stamped_min} = (P_spec) - ABS [(-MR/100)] x (P_spec)

Where ‘ABS' stands for Absolute Value.

So:

P_{stamped_min} = (P_spec) x {1- ABS [(-MR/100)]}

Since P_spec = 95.2 psig and the lower value of MR = -10%,

P_{stamped_min} = 95.2 x {1 - ABS [(-10/100)]} = 95.2 x {1-ABS [(-0.1)]} = 95.2 x (1-0.1) = 95.2 x 0.9 = 85.7 psig

Therefore based on an OR of 90%, the maximum allowable operating pressure should not be greater than:

P_op = P_{stamped_min} x OR = 85.7 x 0.9 = 77 psig.

Since our discussions have been based on a maximum operating pressure of 70 psig, this rupture disk is acceptable. But note that this 10% cushion exists only because of the design pressure margin used (25 psig). Had the margin been less, say only 10%, the rupture disk we would want to use would be unacceptable.

How to avoid this problem?

• Set the design pressure appropriately
• Choose a rupture disk with a MR of ± 0%
• Choose a rupture disk with a OR of 90% (they don't really go much higher)

There is one more point to consider. Although I have never seen any mention of checking the maximum allowable operating pressure against the minimum expected burst pressure (arrived at by taking into account the burst tolerance), I think it only makes good engineering sense to do so. After all, if the disk can burst at this lower pressure, one certainly does not want to operate too close to it!

Getting back to our question, what is the maximum allowable operating pressure in the vessel? In this case, it is 77 psig.

Summary

• What is the maximum allowable specified burst pressure?

- Design Pressure or MAWP if the rupture disk is the only relief device

OR

- For special cases, 105% (or even 110%) of design pressure or MAWP if the rupture disk is a secondary device

• What should be the expected stamped (rated) burst pressure of the rupture disk?

- As specified by the process engineer for a Manufacturing Range of ± 0%

OR

- As specified by the process engineer but could be adjusted per the Manufacturing Range if other than ± 0%

• At what pressure(s) can we expect the delivered rupture disk to actually burst at?

- ± 5% of stamped burst pressure for stamped pressures greater than 40 psig

OR

- ± 2 psi for stamped pressures 40 psig and lower

• What is the maximum allowable operating pressure in the vessel?

- Specified by the process engineer based on operating need but must be checked against the Operating Ratio of the rupture disk
- I strongly suggest you also check against the minimum expected burst pressure as well.

• Manufacturing Range is applied to the specified burst pressure
• Burst Tolerance is applied to the stamped burst pressure
• Set the design pressure appropriately
• Choose a rupture disk with a MR of ± 0%
• Choose a rupture disk with a OR of 90%

References

1. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)
4. Continental Disc Corporation, ULTRX ^® Catalogue 3-2210-3

Before I begin, let me point out that most of what is included in this series of articles can be found in API RP520¹ and API RP521², and ASME Section VIII, Division 1³.  Much of what is found in these documents can also be found in vendor literature.

Temperature and Backpressure Considerations

In Part 3, I discussed how to set the burst pressure of the rupture disk. However, the discussion is not complete without considering the affects of temperature and backpressure on the bursting pressure.

Temperature

The rupture disk manufacturer uses both the specified burst pressure and the specified temperature when designing and stamping the disk. (In this instance, I use the term design to mean arriving at the correct burst pressure, not mechanical integrity). However, it is more than likely that the temperature of the rupture disk will not be at the specified temperature when it is called into service. Why is this so?{parse block="google_articles"}

The temperature most commonly specified is that of the relieving fluid coincident with the burst pressure, i.e. relieving conditions. Sounds logical, but remember that the disk is continuously exposed to the process stream for hours, days, weeks or even months before it may ever be needed. Or, the disk may be exposed to ambient conditions. Therefore, expect the disk temperature to be approximately equal to its environment during normal operation of the system. When a process upset occurs, system pressure rises until it reaches relief (burst). The temperature of the relieving fluid also rises per thermodynamics. However, the time interval between normal system operation and relief is usually so small that the rupture disk's temperature hardly has time to come to equilibrium with the higher process fluid temperature. Therefore the disk can actually be colder than it's specified temperature. The affects?

In general, burst pressure varies inversely with temperature. For some rupture disks, the burst pressure can be as much as 15 psi greater than stamped if the actual temperature is 100^oF lower than specified, e.g. a disk specified with a burst pressure of 350 psig at a temperature of 400^oF will actually burst at 365 psig if its temperature is only 300^oF⁴. This doesn't sound like a big difference but if 350 psig were the design pressure (or MAWP) of the vessel, then a burst pressure of 365 psig would be in violation of code (LAW). The opposite is also true. A disk at a temperature hotter than specified when called into service will burst at a pressure lower than stamped. Although this is considered to be the more conservative approach because code can't be violated and there is no risk of catastrophic failure of the vessel, specifying too low of a temperature can lead to the not so desirable action of premature bursting.

The bottom line is that the specified burst temperature must be carefully considered. Specify the lowest temperature at the time the disk is expected to burst. Consider that this might be the normal process operating temperature or even ambient rather than the calculated relieving temperature.

Note that different materials and different types of rupture disks have different sensitivities to temperature. This is an excellent topic of discussion for your rupture disk manufacturer!

Backpressure

A rupture disk is actually a differential pressure device where the specified burst pressure is equal to the difference between the desired upstream pressure (vessel) at the time of rupture disk burst and the downstream pressure (backpressure):{parse block="google_articles"}

P_burst = P_vessel - P_backpressure

Or alternately the desired upstream pressure (vessel) at the time of rupture disk burst is equal to the sum of the specified burst pressure and the downstream pressure (backpressure):

P_vessel = P_burst + P_backpressure

Either way, it is apparent that the vessel pressure at the time the rupture disk bursts (commonly called the relief pressure) is directly dependent on backpressure.

When discussing relief systems, three types of backpressure are considered, these being constant, built-up and superimposed.

Figure 1A: Single Vessel, Single Rupture Disk Protection, Expected Constant Back pressure = 0 psig

Figure 1A shows a system comprised of a single vessel protected by a single rupture disk with a specified burst pressure of 100 psig. The relief pipe discharges a few inches below the liquid surface in a knockout drum, which is held at a constant 0-psig pressure. Therefore, the rupture disk sees a constant (fixed) backpressure of 0 psig. If the vessel were to go into relief, this disk will burst at 100 psig and the vessel relief pressure will be 100 psig (100 + 0 = 100).

Figure 1B: Single Vessel, Single Rupture Disk Protection, Actual Constant Back pressure >  Expected

Figure 1B is the same system however for some reason the pressure in the knockout drum is to be maintained at 5 psig instead of 0 psig. The constant (fixed) backpressure against the rupture disk is now 5 psig. If the vessel were to go into relief, the rupture disk would still burst at 100 psig but the vessel relief pressure would now be 105 psig (100 + 5 = 105) rather than the 100 psig expected. This situation could result in a violation of code³.

Figure 1C: Single Vessel, Single Rupture Disk Protection, Actual Constant Back pressure <  Expected

Figure 1C is again the system however for some reason the pressure in the knockout drum is to be maintained at -5 psig instead of 0 psig. The constant (fixed) backpressure against the rupture disk is now -5 psig. If the vessel were to go into relief, the rupture disk would still burst at 100 psig but the vessel relief pressure would now be only 95 psig (100 + (- 5) = 95) rather than the 100 psig expected. There is no particular safety concern here because the vessel can't over pressure. However, the Operating Ratio is affected, which can result in a very premature bursting of the rupture disk.

For the vessel relief pressure to be specified correctly, the rupture disk vendor must be told the constant back pressure so that the rupture disk can be designed accordingly. And, if you truly want the vessel relief pressure to be at a specific value then the "constant" backpressure given to the vendor must be maintained at all times.

The key point is that during design, be aware of the constant backpressure and ensure that the vessel relief pressure will not violate code or affect normal operation.

Figure 2A: Two Vessel System - Common Discharge Built-up and Superimposed Back Pressures

Now let's look at the system shown in Figure 2A. A second vessel with a single rupture disk also specified to burst at 100 psig is added in close proximity to the first vessel. The relief piping from the two vessels is tied into a common header before discharging into a knockout drum in the same manner as before, the tie-in occurs near the vessels. At the exact moment Vessel No. 2 goes into relief and its rupture disk bursts, Vessel No. 2's relief pressure is 100 psig due to the constant 0-psig backpressure as described above. After the disk bursts, flow is established causing pressure to build up in the piping system (built-up backpressure). The amount of built-up backpressure is dependent on the system pressure drop and possibly even the phenomenon of choked flow.  For the purpose of this discussion, assume total built-up backpressure is 10 psig after rupture disk No. 2 bursts and the pressure in Vessel No. 2 is about 110 psig. Because of the proximity of the two discharge pipes and vessels, the pressure near vessel No. 1 will also be at about 110 psig. This pressure, which is exerted or imposed onto rupture disk No. 1, is called the superimposed backpressure with respect to rupture disk No. 1. If vessel No. 1 were to go into relief shortly afterwards, then for rupture disk No. 1 to burst, the pressure in vessel No. 1 would have to build to about 210 psig (100 + 110)!   This is clearly unacceptable!!

One solution to this potentially catastrophic condition is to separate the two relief lines so that one cannot directly affect the other (see Figure 2B below). Of course the answer may very well be that this is not an application for rupture disks but for relief valves! The key point is, avoid combining multiple rupture disk piping into a common relief header.

Figure 2B: Two Vessel System - Common Discharge Built-up and Superimposed Back Pressures

Note that built-up backpressure is variable and depends on the relieving rate, which is a function of the relieving scenario. Also, built-up backpressure has no affect on the vessel's relief pressure for systems such as those shown in Figure 1 above. Built-up backpressure is the result of fluid flow only and there is no fluid flow before the rupture disk bursts.

Therefore, along with the Manufacturing Range (MR), Operating Ratio (OR) and Burst Tolerance (BT) that were discussed in Part 3, the process design engineer must also strongly consider the backpressure (especially superimposed backpressure) when specifying the rupture disk.

In Summary

• Generally, burst pressure varies inversely with temperature so the specified burst temperature must be carefully considered.
  - Specify the lowest temperature at the time the disk is expected to burst.
  - Different materials and different types of rupture disks have different sensitivities to temperature effects.{parse block="google_articles"}
  
• The rupture disk is a differential pressure device.
  - The specified burst pressure is a value equal to the vessel relief pressure minus the backpressure.
                                                                   Or
  - The vessel relief pressure equals the specified burst pressure plus the backpressure.
  
• There are three types of backpressure to consider, these being constant, built-up and superimposed.
  - Constant backpressure is the pressure in the system that does not vary. It is generally a predictable component of the superimposed backpressure.
  - Built-up backpressure is the pressure created in the system as a result of fluid flow. It is a varying component of the superimposed backpressure.
  - Superimposed backpressure is the total pressure exerted (imposed) on the rupture disk by other sources. It is a variable that directly increases or decreases a vessel's relief pressure. It can also interfere with the expected operating ratio of the disk.
  
• Do not pipe multiple vessel relief systems into a common header; keep the piping separate. However, the individual piping may go to a common disposal system.
  
• Along with the Manufacturing Range (MR), Operating Ratio (OR) and Burst Tolerance (BT), the process design engineer must also consider backpressure when specifying the rupture disk.

References

1. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)
4. Nazario, F. N., "Rupture Discs, A Primer", Chemical Engineering Magazine, June 20, 1988.

For the relief valve/rupture disk combination (Figure 1), rupture disk sizing is totally dependent on relief valve sizing, regardless whether the rupture disk is installed upstream or downstream of the relief valve. Consequently, the discussion at this point must turn to a brief overview of relief valves.

Relief Valve Sizing Overview

Basically, the relief valve is treated as an ideal nozzle, i.e. isentropic (constant entropy) flow. A correction factor, the coefficient of discharge, is incorporated into the sizing equations to take into account the fact that this is not an ideal nozzle. The sizing equations themselves can be found in one or more of the references presented at the end.

To size a relief valve, the process engineer first determines the required relieving flow and fluid properties based on an analysis of "what can go wrong" scenarios. The flow and properties are then inserted into the appropriate sizing equation to arrive at a calculated relief valve area. If this were a stand-alone relief valve, the process engineer would use this calculated relief valve area to choose an actual relief valve from

Figure 1: Relief Valve/Rupture Disk Combination

a vendor catalog. But since this is a discussion of the relief valve/rupture disk combination, adjustments should be made to the calculated relief valve area before the actual relief valve is chosen.

The Rupture Disk Affect

The presence of a rupture disk acts to de-rate the relief valve capacity. This de-rating factor, called the Combination Capacity Factor (CCF), may or may not be implicitly included in the sizing formulas. Nevertheless, it is the responsibility of the process engineer to apply the factor correctly.

The Combination Capacity Factor (CCF) 

The Combination Capacity Factor (CCF) is a calculated value that is derived from data obtained during certified capacity testing of the stand-alone relief valve and the relief valve/rupture disk combination. The manufacturer first determines the capacity of the stand-alone relief valve. The rupture disk is then added, close-coupled, to the inlet of the relief valve and the capacity of the relief valve/rupture disk combination is determined. Finally, the CCF is calculated as the ratio of the relief valve/rupture disk combination capacity to the stand-alone relief valve capacity:

CCF = Flow _{Combination Capacity} / Flow _{Stand-Alone Relief Valve Capacity}

Below is a list of certified Combination Capacity Factors for the Continental Disc Corporation model ULTRX ^® rupture disks with the Crosby JOS/JBS Relief Valve ⁴.

For comparison, the following is a list of certified Combination Capacity Factors for the Fike model MRK rupture disk with the Crosby JOS/JBS Relief Valve⁵.

Note that the CCF is a certified value and is only good for the design of the relief valve and the rupture disk that are used in the test. Since it is in the best interest of the rupture disk manufacturer to certify as many of their rupture disk designs with as many different types of relief valve designs as possible, it is typical for the rupture disk manufacturer to perform this testing and reporting of the CCF. The certified CCF will always be less than or equal to 1.0.

If the manufacturer and/or model of the rupture disk and relief valve are unknown at the time of sizing, or there is no published value for a relief valve/rupture disk combination, ASME³ requires that the CCF is not to exceed 0.9.

Applying the CCF

API Recommended Practices 520¹ shows the CCF as being applied to the denominator of the relief valve sizing equation. For example, a typical sizing equation for gas relief might look something like this:

Eq. (1)

Where:
W = required relieving rate, mass flow
T  = relieving temperature, absolute
Z  = compressibility factor
M = molecular weight
C = gas constant = a function of (C_p / C_v)
C_p = specific heat at constant pressure (consistent units)
C_v = specific heat at constant volume (consistent units)
K_d = coefficient of discharge, dimensionless
K_b = backpressure correction factor, dimensionless
P1 = relief pressure (absolute)

Note that this is the same as dividing the calculated, stand-alone relief valve area by the CCF to arrive at a required relief valve area for the combination unit:

Eq. (2)

And:

The process engineer will use this required relief valve area as the basis for choosing a relief valve from the vendor catalog.

One important thing to note is that the preceding methodology is not a requirement of code (ASME). ASME only requires that the stand-alone relief valve's certified flow capacity be de-rated by the CCF:

There is no mention of using the CCF to arrive at a relief valve area. Indeed, prior to the most recent edition of API RP520¹, the sizing equations themselves did not explicitly include a correction factor for the relief valve/rupture disk combination.

Note also that de-rating the certified flow capacity is only required if the rupture disk is installed upstream of the relief valve, it is not required if installed downstream of the relief valve.

Certified (Rated) Capacity

As stated above, each stand-alone relief valve will have associated with it a certified flow capacity, which is a function of both the relief valve area and the set pressure. This flow is determined by certified capacity testing procedures and is to be considered the guaranteed flow rate that can be achieved through the particular valve. With very few exceptions, this flow is used in determining both the relief valve inlet and outlet (tail pipe) line sizes. The certified flow capacity is officially stamped on the relief valve documentation. For relief valve/rupture disk combinations, the de-rated certified flow will also be stamped on the documentation.

Although the relief valve is chosen based on area, the process engineer must still ensure that the certified flow capacity is greater than or equal to the required relieving flow:

Certified Flow Capacity ³ Required Relieving Flow

If it is not, the chosen relief valve is too small. For the relief valve/rupture disk combination, the required relieving flow would be compared to the de-rated or combination certified flow capacity:

Combination Certified Flow Capacity ³ Required Relieving Flow

Relief Valve Sizing

Inlet Line

The relief valve inlet line is defined as the piping between the inlet to the system (e.g. the inlet to a vessel nozzle) and the relief valve inlet flange. Sizing this inlet line is a trial-and-error procedure. First, the process engineer chooses a line size using guidelines set by code; code requires that the flow area of the line and all associated piping components be at least equal to the relief valve inlet flow area. Then, using {parse block="google_articles"}accepted fluid flow equations (e.g. Darcy for single phase liquid or gas/vapor and DIERS for two phase) and the certified flow capacity of the stand-alone relief valve the non-recoverable frictional losses in the line are determined. The sum of all non-recoverable losses should be less than 3% of the relief valve set pressure, this criteria is commonly referred to as the 3% Rule. In general, if the 3% Rule is exceeded then the chosen line size is too small.

Outlet Line (Tail Pipe) Sizing Overview 

The sizing of the tail pipe is done in a similar manner to that outlined above for the inlet line. The process engineer first chooses a pipe size. Then, using accepted fluid flow equations (e.g. Darcy for liquids, Isothermal or Adiabatic for gas/vapor and DIERS for two-phase) and the same certified flow capacity as used for the inlet line, a built-up (variable) backpressure is calculated. The built-up backpressure is converted to a percentage of the relief valve set pressure and is then compared to some maximum value that is set by the particular relief valve manufacturer. For example, tail pipes on conventional style relief valves would be sized such that the built-up (variable) backpressure does not exceed 10% of the relief valve set pressure. For balanced bellows style relief valves, tail pipes would be sized such that the built-up (variable) backpressure does not exceed 30% to 55% of the relief valve set pressure, depending on manufacturer. If the calculated percentage is less than or equal to these maximums, the line size is acceptable. If the calculated percentage is greater, the line size may or may not be acceptable. This is because the only requirement of code is that the built-up backpressure does not affect the relief valve's ability to relieve the required amount of flow necessary to protect the system. Built-up backpressures greater than the stated maximums require a de-rating of the relief valve based on curves developed by the manufactures. As long as the de-rated valve can still relieve the required relieving flow, the line size chosen is acceptable. If not, then the line is too small.

Now that we've sized the relief valve in the relief valve/rupture disk combination, what about sizing the rupture disk? Actually, we already did!

The Rupure Disk

Sizing

You will recall from Part 2 of this series that sizing the rupture disk is a two-part procedure. First, determine how much flow the rupture disk needs to pass. Then determine how big it needs to be.

Both criteria have been met with the relief valve sizing. How much flow? The rupture disk must be able to pass the certified flow capacity of the relief valve. How big? The rupture disk must be big enough so that its contribution to the frictional losses does not pose a significant impact on the ability of the relief valve to protect the system. For a rupture disk installed in the inlet line, the rupture disk's net flow area must be at least equal to the relief valve inlet flow area; it may be larger. Also, its contribution to the non-recoverable frictional losses should be minimal so as to ensure that the piping system meets the 3% Rule. Indeed, you may even find that the rupture disk must be one-size larger than the inlet to the relief valve in order to satisfy the 3% Rule. For example (Figure 2), a 2" x 3" relief valve (2" being the inlet flange size and 3" being the outlet flange size) may require a 3" rupture disk!

Figure 2: 2" x 3" Relief Valve

Figure 3: Rupture Disk is Larger than Outlet Flange

For a rupture disk installed in the tail pipe, the rupture disk size should be large enough so that it contributes minimally to the built-up backpressure. And again, the rupture disk may very well have to be a size larger than the relief valve outlet flange to accomplish this (Figure 3).

For both the inlet line and tail pipe calculations, the rupture disk's certified K_r is used in the friction loss calculations.

What the Code Says About...

Bursting

The stamped (certified) burst pressure of the rupture disk must be between 90% and 100% of the relief valve set pressure. Also, the bursting of the rupture disk and the opening of the relief valve must be essentially coincident with each other.

Backpressure

When specifying a rupture disk that will be used upstream of a relief valve, it is expected that the superimposed backpressure will be constant and essentially zero (after all, there should be nothing between the rupture disk and the relief valve but some trapped air). However, over time the rupture disk may leak for a variety of reasons. This leakage will cause a build-up of pressure between the rupture disk and the relief valve. As we saw in Part 4, unexpected backpressure on the rupture disk will change the relieving pressure of the vessel or system. To guard against this, code requires the use of a "tell-tale". The "tell-tale" must consist of, as a minimum, a pressure gage and a vent line inserted between the rupture disk and the relief valve. Typically, a valve is put into the vent line for a more controlled design (Figure 4). In installations where the rupture disk holder is close-coupled with the relief valve, this system is inserted into a chamber within the holder. Note that a better tell-tale design would include a pressure transmitter with an alarm as well as the pressure gage.

Figure 4: Valve in Vent Line

For rupture disks installed after the relief valve, the disk's bursting pressure must not be affected by any backpressure affects nor can there be allowed a pressure build-up between the relief valve and rupture disk that may affect the operation of either device. A "tell-tale" should be used to protect against pressure build-up between the devices due to leaks through the relief valve. The only way to protect against backpressure affects is to make sure the superimposed backpressure is well defined and constant (see Part 4 of this series).

Obstructions

A bursting rupture disk must not cause obstruction of the relief valve or the relief piping. Therefore, the non-fragmenting rupture disk is used in this service. This disk will break cleanly, with no material being broken off.

Final Thoughts

• Above I discuss the fact that the rupture disk needs to be able to pass the certified flow capacity of the relief valve! But which flow capacity, the stand-alone relief valve or the relief valve/rupture disk combination? Unfortunately, the way ASME³ reads, there is plenty room for interpretation. For example, paragraph UG-127 (a) (3) (b') (5) basically says the rupture disk must be able to pass the certified capacity of the relief valve/rupture combination. However, for the rupture disk installed in the tail pipe, paragraph UG-127 (a) (3) (c') (4) says the rupture disk must be able to pass, "...the rated capacity of {parse block="google_articles"}the attached pressure relief valve without exceeding the allowable overpressure." Now, for individual cases where the rupture disk is installed only upstream of the relief valve or only downstream of the relief valve, I can buy into this as not being contradictory, i.e. use rated capacity of the relief valve/rupture combination for the inlet line or use the rated capacity of the stand-alone relief valve for the tail pipe. But what about the case where the rupture disk is installed both upstream and downstream of the relief valve?
  
  The flow used to evaluate the inlet line is to be the same flow used to evaluate the tail pipe. And, the 3% Rule clearly wants you to use the certified capacity of the stand-alone relief valve with the rupture disk being treated as just another piping component.
  
  So which do I suggest we Process Design Engineers use? The certified flow capacity of the stand-alone relief valve in all instances; it will be a little more conservative.

• The code requirements discussed above help to emphasize the importance of the material presented in Parts 3 and 4 of this series, i.e. the maximum allowable specified burst pressure, the Manufacturing Range, the Burst Tolerance, the Operating Ratio, and superimposed, built-up and variable backpressures; especially as they relate to the relief valve/rupture disk combination

Summary

• Rupture disks may be installed upstream and/or downstream of a relief valve.

• The rupture disk acts to de-rate the relief valve capacity. This de-rating factor is called the Combination Capacity Factor. Standards call for the use of this factor in determining relief valve area and in de-rating the stand-alone relief valve's certified capacity. Code only requires the use of this factor in de-rating the stand-alone relief valve's certified capacity.

• The size of the rupture disk in this application is totally dependent on relief valve sizing.

• The rupture disk must be able to pass the certified flow of the relief valve.

• The size of a rupture disk installed at the inlet of the relief valve should have minimal affect on the 3% Rule and must have a flow area of at least equal to the inlet flow area of the relief valve.

• The size of a rupture disk installed at the outlet of the relief valve should provide minimal contribution to the built-up backpressure.

• Code governs how a rupture disk is applied to a relief valve installation and the general type of rupture disk to use (non-fragmenting).

• Code addresses rupture disk bursting requirements.

• Code addresses backpressure affects and what must be done to avoid it.

• When specifying a rupture disk, especially in combination service with a relief valve, the maximum allowable specified burst pressure, the Manufacturing Range, the Burst Tolerance and the Operating Ratio all must be considered very carefully.

References

1. API (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)
4. Continental Disc Corporation (www.contdisc.com), ASME Combination Capacity Factors, Catalogue 1-1111
5. Fike (www.fike.com), Technical Bulletin TB8103, July 1999

I will also touch upon the type of rupture disks you can purchase. Before I begin, let me point out that most of what is included in this series of articles can be found in API RP520¹ and API RP521², and ASME Section VIII, Division 1³.  Much of what is found in these documents can also be found in vendor literature.{parse block="google_articles"}

We've answered the two questions required to size a rupture disk, how much flow and how big. Now it's time to specify the rupture disk so that it can be purchased for our process. Although API RP520¹ provides a specification sheet that can be adapted by any company as a standard, there are fifty-three separate items asked for in this specification sheet. Much of what is on this specification sheet is not required by the manufacturer to be able to provide you with the correct disk. Let's look at the basic minimum information you, the Process Design Engineer must provide.

Must Haves

Project Identifier/Company Information/Device identifier/Number of Devices

The vendor will want to know who you are. It is also necessary to "name" the relief device for proper documentation. A unique instrument Tag number should suffice for each device ordered.

Code/Standard Requirements

Various codes and standards dictate how the rupture disk is to be marked and stamped.

Maximum Operating Conditions

Temperature

The maximum operating temperature is used to determine materials compatibility.

Pressure

The maximum operating pressure will be used with the stamped burst pressure to determine the Operating Ratio. The Operating Ratio will help determine the type of disk to purchase.

Rupture Disk Burst Conditions

Temperature

This must be coincident with the bursting pressure and will also be stamped on the disk. You will recall from Part 4 that this parameter is extremely important in making sure the disk will burst at the pressure you need it to burst, not less or greater. Also remember that it is not necessarily the same as the maximum operating temperature of the system.

Pressure

This is the pressure that meets system protection requirements, taking into account the Manufacturing Range. The vendor will stamp this value on the disk. It is also used with the Maximum Operating Pressure to determine the Operating Ratio.

Process Media (Liquid/Gas/2-Phase)

Some rupture disk models are designed according to the media in which they are used. Process media is also used to determine materials compatibility.

Backpressure/Vacuum

The manufacturer uses the backpressure to help determine disk type and how it is to be supported in the system. Vacuum service will either require the use of a special support for disk installation or even dictate the type of disk to use. Note that exposure to vacuum conditions must be considered both upstream and downstream of the disk.

Service Conditions (Status/Cyclic/Pulsating)

This typically refers to the upstream conditions. Cyclic service is considered to be large changes in pressure over a relatively long period of time. Pulsating service is considered to be small changes in pressure but occurring frequently or even rapidly. Both of these can have a major affect on the Operating Ratio. The manufacturer uses the service conditions to help determine disk type and how the disk is to be supported in the system.

Rupture Disk and Holder Material Requirements

Many installations require the rupture disk to be mounted inside a holder. The holder is then bolted onto a vessel nozzle or between pipe flanges. Make very certain the materials of construction of both the disk and its holder is totally compatible with the system media and operating conditions.

Disk Size

This is the nominal size you determined when answering the question, how big?

Flange Connection Details

These tell the manufacturer how big the holder needs to be (connection size), the pressure rating of the system it will be installed in (class) and the type of connection, e.g. raised or flat faced flanges, sanitary connections, etc.

The pressure rating or class can be a most confusing concept. This refers to the flanges in the piping system. More common flange ratings are 150 and 300 pounds (pressure pounds, not weight) but they can go very much higher. A major difference in these classes is the thickness of material, number of boltholes and the bolthole pattern you would get in the flange.

Required Accessories for Rupture Disk

Options can be added to the basic design. For instance to enhance corrosion protection, coatings or linings can be applied.  Some types of rupture disks can withstand upstream vacuum conditions without doing anything special to them others may need special supports.

Required Accessories for Holder

Options can be added to the rupture disk holder as well. For instance to enhance corrosion protection, coatings or linings can be applied. Tell-tales may be specified under this header or can be specified under the heading of "Special Considerations".

Other Special Considerations

You can specify just about anything under this heading including the need for a tell-tale. You may want to give more specific detail of a particular design item. You can ask for burst detection and alarms, etc., etc. and etc. The best reference source would be your manufacturer and/or their catalog.

Again, the above should be considered just the minimum amount of information the manufacturer needs to provide the proper rupture disk. Of course your particular manufacturer, or even your company standards, may require much more.

Should you stop here, perhaps not? Below is some information that I consider to be "should haves".

Should Haves

MAWP (or Design Pressure) of the Vessel or System

A vendor does not necessarily require this information (they were already told what to stamp the disk for). However a good vendor will actually be your second set of eyes and make sure that this, along with the other information given, is consistent with Code requirements.

Manufacturing Range

One would think that this should fall under the "must haves" but not really. When the burst pressure was specified in the "must haves", the manufacturing range had to be taken into account. All the vendor needs to know is what to stamp the rupture disk at and will therefore design the disk with the appropriate manufacturing range to accommodate. However, it never hurts to spell it out so there are no misunderstandings.

In Combination with a PSV

With this information, the rupture disk vendor will be able to recommend the proper type of rupture disk to use for this service. They will also be able to recommend proper installation techniques. And again, the vendor is your second set of eyes and may be able to tell whether your specification data is consistent.

Calculate and Report the Operating Ratio

I could never quite figure out why the vendor cannot just do the simple math but I've seen this as requested information on a number of vendor's specification sheets.

What about all the rest of the information usually included in many specification sheets, e.g. required relieving flow, molecular weight, specific heat ratio, specific gravity, compressibility factor, viscosity, etc.? These are definitely important, but really only to the Process Design Engineer. You need this information to answer the two questions, how much flow and how big? The vendor doesn't need these but we all seem to include them on our specification sheets nevertheless!

The best suggestion I can make is to talk to the vendor first, find out exactly what they need and provide it. But of course, never violate your own company standards.

Types of Rupture Disks

The manufacturer can recommend the type of rupture disk that will best suit your application based on the information supplied. However, it doesn't hurt to have some knowledge {parse block="google_articles"}of the type of rupture disks that can be purchased. There are a multitude of different types and the following only represents the most common types you will most likely come across.

Forward Acting Solid Metal

This rupture disk is domed shape and installed such that the media is on the concave side of the disk (Figure 1). It can be used in systems where the Operating Ratio is at about 70% or less. It has a random bursting pattern which means it can be fragmenting (loose material) and thus cannot be used in combination with relief valves. This type of rupture disk can be used in vacuum or larger backpressure services but will require special supports to prevent reverse flexing. Its number one advantage is that it is cheap.

Figure 1: Forward Acting Solid Metal Rupture Disk

Forward Acting Scored Metal

This rupture disk is similar to its solid metal cousin (Figure 1) except that the disk is scored (Figure 2). Unlike the ill-defined bursting pattern of the solid metal design, this rupture disk has scored lines that will force the disk to burst along a fixed pattern. This design is a little more expensive but increases the useful Operating Ratio to about 85 to 90%. It also eliminates fragmenting, which means it can be used in combination with a relief valve. Also, there are many designs that allow this type of disk to be installed in vacuum environments without requiring special supports; it will still need special supports in high backpressure service to prevent reverse flexing.

Figure 2: Forward Acting Scored Rupture Disk

 Forward Acting Composite

This rupture disk can be flat or domed and is comprised of a top section preceded by a bottom seal (Figure 3). The burst pressure is a function of these two sections. It is not uncommon for the bottom section to be of a totally different material of construction from that of the top section, even non-metallic. The domed disk design will burst due to pressure applied to the concave side whereas the flat disk design may bedesigned to burst in either direction! 

Figure 3: Forward Acting Composite Rupture Disk

Slits and tabs in the top section control burst pressure and the bursting pattern. The flat construction can be used for the protection of low-pressure systems. Operating ratios are typically around 80% for the dome construction and 50% for the flat construction. This disk may require special supports to be used in vacuum or high backpressure conditions. Some designs are non-fragmenting, which means they can be used in relief valve combination.

Reverse Acting

This rupture disk is domed shape and installed such that the media is on the convex side of the disk (Figure 4). It is designed such that pressure pushes against the disk causing it to flex back into a forwarding acting disk and then burst. This rupture disk can be used in systems where the Operating Ratio is at about 90% or less. It can be, and very often is, manufactured to be non-fragmenting and thus is a good choice for use in combination with relief valves. This type of rupture disk can be used in vacuum or larger backpressure services without special supports.

Figure 4: Reverse Acting Scored Rupture Disk

Final Thoughts

Liquids

Liquids are treated the same way as gases/vapors in all aspects of determining those two questions, how much and how big. However, do not forget to take the hydraulic pressure into account. Pressure in the system will not be equal throughout. If the rupture disk is installed on a nozzle or in a pipe at the top of a liquid filled vessel, the pressure at the rupture disk will be less than all points below it. If the rupture disk is installed on a nozzle at the bottom of a liquid filled vessel, the pressure at the rupture disk will be greater than all points above it.{parse block="google_articles"}

What are the implications of this? If the rupture disk is located at the top of the vessel, the vessel pressure will be greater than the bursting pressure so specify the burst pressure to be less than the vessel's MAWP or design pressure. If the rupture disk is at the bottom of the vessel, the vessel pressure will be less than the bursting pressure. However, the rupture disk cannot be specified at a pressure higher than MAWP or design. Therefore, realize that the disk will burst even though the pressure at the top of the vessel will be less than design or MAWP.

Also note that normal variations in level will cause normal variations in the pressure, i.e. the rupture disk will experience pressure cycling or pulsing. Unlike gases/vapors where normal system pressure cycling or pulsing is usually minimal, it may be significant in liquid filled systems.

One More Option to Consider

Ask your manufacturer if they provide a "Fail Safe" design. This design will provide pressure relief at or below the certified burst pressure even if the disk is damaged or installed improperly. It will function in this capacity equally well in gas/vapor or liquid service. The major drawback is that it is only available in forward acting non-composite rupture disks.

Other Non-Close Relief Devices

Figure 5A: Rupture Pin Relief Device End of Pipe with Atmospheric Discharge

Figure 5B: Rupture Pin Relief Device Discharge to Header

There are other options to consider for non-closing relief devices other than rupture disks. Although details are beyond the scope of this article, there is one particular device I wish to bring to your attention and which is gaining in popularity, the Rupture Pin^{6, 7}. Although ASME will not allow what is called a Breaking Pin device to be used as a primary relief device, as of May 1990, it will allow the use of the Rupture Pin device. The two are similar but for the Breaking Pin device to work, the pin must completely break but for the Rupture Pin device to work, the pin only needs to bend or buckle. Another name for this device is the Buckling Pin.  Figures 5A and 5B show two types of rupture pin devices. Device "A" might be used directly on a vessel and will relieve to atmosphere. Device "B" might relieve into a piping header.

The rupture pin device usually consists of a piston or plunger on a seat, kept in position by a slender, usually cylindrical pin. At set point, axial forces caused by system pressure acting on the piston or plunger area causes the pin to buckle. The unrestrained pin length, the pin diameter and the modulus of elasticity of the pin material determine the buckling point of the pin.

There is virtually no device size limitation. They have been manufactured as small as 1/8" and as large as 48". There are virtually no pressure or vacuum limits either. They can be designed for a set pressure as low as 2" of water to as high as 35,000 psi and vacuums to as low as 1 psi. Unlike rupture disks, which are solely differential devices, the rupture pin can be designed to sense system pressure only, or differential pressure.

You are now ready to sit through one of those manufacturer's presentations and hopefully understand what he is talking about!

Summary

• API RP520 provides a specification sheet that can be adapted by any company as a standard
• Not all of the information asked for in the API specification sheet is actually required by the manufacturer in order to design the correct rupture disk. This information can be broken down into "must haves", "should haves" and "what is needed to size the disk".
• The manufacturer will always be provided with the "must haves".
• The manufacturer should also be given the "should haves" as this is a way to utilize them as a second pair of eyes and for a consistency check of the sizing.
• There are many different types of rupture disks on the market. Before selecting the correct rupture disk for your particular application, always discuss this with the manufacturer.
• Liquid service has its own set of potential problems for rupture disk design. It is highly recommended that you discuss liquid service with your manufacturer.
• There are other "non-closing" relief devices that can be considered for use. Some can only be used as secondary relief devices. However the one that can be used as a primary relief device and is gaining in popularity is the Rupture Pin.

References

1. API  (www.api.org) Recommended Practice 520, "Sizing, Selection, and Installation of Pressure-Relieving Device in Refineries, Part 1-Sizing and Selection", 7^th Edition (January 2000)
2. API (www.api.org) Recommended Practice 521, "Guide for Pressure-Relieving and Depressuring Systems", 4^th Edition (March 1997)
3. ASME (www.asme.org) "Boiler and Pressure Vessel Code, Section VIII, Division 1" (1998)
4. Continental Disc Corporation (www.contdisc.com), ASME Combination Capacity Factors, Catalogue 1-1111
5. Fike (www.fike.com), Technical Bulletin TB8103, July 1999
6. www.burstpressuresystems.com
7. www.rupturepin.com

Despite all the care in operation and maintenance, engineers often face the statement "the pump has failed i.e. it can no longer be kept in service". Inability to deliver the desired flow and head is just one of the most common conditions for taking a pump out of service. {parse block="google_articles"}There are other many conditions in which a pump, despite suffering no loss in flow or head, is considered to have failed and has to be pulled out of service as soon as possible. These include seal related problems (leakages, loss of flushing, cooling, quenching systems, etc), pump and motor bearings related problems (loss of lubrication, cooling, contamination of oil, abnormal noise, etc), leakages from pump casing, very high noise and vibration levels, or driver (motor or turbine) related problems.

The list of pump failure conditions mentioned above is neither exhaustive nor are the conditions mutually exclusive. Often the root causes of failure are the same but the symptoms are different. A little care when first symptoms of a problem appear can save the pumps from permanent failures. Thus the most important task in such situations is to find out whether the pump has failed mechanically or if there is some process deficiency, or both. Many times when the pumps are sent to the workshop, the maintenance people do not find anything wrong on disassembling it. Thus the decision to pull a pump out of service for maintenance / repair should be made after a detailed analysis of the symptoms and root causes of the pump failure. Also, in case of any mechanical failure or physical damage of pump internals, the operating engineer should be able to relate the failure to the process unit's operating problems.

Any operating engineer, who typically has a chemical engineering background and who desires to protect his pumps from frequent failures must develop not only a good understanding of the process but also thorough knowledge of the mechanics of the pump. Effective troubleshooting requires an ability to observe changes in performance over time, and in the event of a failure, the capacity to thoroughly investigate the cause of the failure and take measures to prevent the problem from re-occurring.

The fact of the matter is that there are three types of problems mostly encountered with centrifugal pumps:

• design errors
• poor operation
• poor maintenance practices

The present article is being presented in three parts, covering all aspects of operation, maintenance, and troubleshooting of centrifugal pumps. The article has been written keeping in mind the level and interests of students and the beginners in operation. Any comments or queries are most welcome.

Working Mechanism of a Centrifugal Pump

A centrifugal pump is one of the simplest pieces of equipment in any process plant. Its purpose is to convert energy of a prime mover (a electric motor or turbine) first into velocity or kinetic energy and then into pressure energy of a fluid that is being pumped.

The energy changes occur by virtue of two main parts of the pump, the impeller and the volute or diffuser. The impeller is the rotating part that converts driver energy into the kinetic energy. The volute or diffuser is the stationary part that converts the kinetic energy into pressure energy.

Generation of Centrifugal Force

Figure 1: Liquid Flow Path Inside a Centrifugal Pump

The process liquid enters the suction nozzle and then into eye (center) of a revolving device known as an impeller. When the impeller rotates, it spins the liquid{parse block="google_articles"} sitting in the cavities between the vanes outward and provides centrifugal acceleration. As liquid leaves the eye of the impeller a low-pressure area is created causing more liquid to flow toward the inlet. Because the impeller blades are curved, the fluid is pushed in a tangential and radial direction by the centrifugal force. This force acting inside the pump is the same one that keeps water inside a bucket that is rotating at the end of a string. Figure A.01 below depicts a side cross-section of a centrifugal pump indicating the movement of the liquid.

Conversion of Kinetic Energy to Pressure Energy

The key idea is that the energy created by the centrifugal force is kinetic energy. The amount of energy given to the liquid is proportional to the velocity at the edge or vane tip of the impeller. The faster the impeller revolves or the bigger the impeller is, then the higher will be the velocity of the liquid at the vane tip and the greater the energy imparted to the liquid.

This kinetic energy of a liquid coming out of an impeller is harnessed by creating a resistance to the flow. The first resistance is created by the pump volute (casing) that catches the liquid and slows it down. In the discharge nozzle, the liquid further decelerates and its velocity is converted to pressure according to Bernoulli's principle.

Therefore, the head (pressure in terms of height of liquid) developed is approximately equal to the velocity energy at the periphery of the impeller expressed by the following well-known formula:

A handy formula for peripheral velocity is:

This head can also be calculated from the readings on the pressure gauges attached to the suction and discharge lines.

One fact that must always be remembered: A pump does not create pressure, it only provides flow.
Pressure is a just an indication of the amount of resistance to flow.

Pump curves relate flow rate and pressure (head) developed by the pump at different impeller sizes and rotational speeds. The centrifugal pump operation should conform to the pump curves supplied by the manufacturer. In order to read and understand the pump curves, it is very important to develop a clear understanding of the terms used in the curves. This topic will be covered later.

General Components of Centrifugal Pumps

A centrifugal pump has two main components:

A rotating component comprised of an impeller and a shaft

A stationary component comprised of a casing, casing cover, and bearings.

The general components, both stationary and rotary, are depicted in Figure 2. The main components are discussed in brief below. Figure3 shows these parts on a photograph of a pump in the field.

Figure 2: General Components of Centrifugal Pump	Figure 3: General Components of Centrifugal Pump

Stationary Components

Casings

Figure 4: Cut-Away of a Pump Showing Volute Casing

Casings are generally of two types: volute and circular. The impellers are fitted inside the casings.

Volute Casings

Volute casings build a higher head; circular casings are used for low head and high capacity. A volute is a curved funnel increasing in area to the discharge port as shown in Figure 4. As the area of the cross-section increases, the volute reduces the speed of the liquid and increases the pressure of the liquid. One of the main purposes of a volute casing is to help balance the hydraulic pressure on the shaft of the pump. However, this occurs best at the manufacturer's recommended capacity. Running volute-style pumps at a lower capacity than the manufacturer recommends can put lateral stress on the shaft of the pump, increasing wear-and-tear on the seals and bearings, and on the shaft itself. Double-volute casings are used when the radial thrusts become significant at reduced capacities.

Circular Casings

Circular casing have stationary diffusion vanes surrounding the impeller periphery that convert velocity energy to pressure energy. Conventionally, the diffusers are applied to multi-stage pumps.

Figure 5: Solid Casing

The casings can be designed either as solid casings or split casings. Solid casing implies a design in which the entire casing including the discharge nozzle is all contained in one casting or fabricated piece. A split casing implies two or more parts are fastened together. When the casing parts are divided by horizontal plane, the casing is described as horizontally split or axially split casing. When the split is in a vertical plane perpendicular to the rotation axis, the casing is described as vertically split or radially split casing. Casing Wear rings act as the seal between the casing and the impeller.

Suction and Discharge Nozzles

The suction and discharge nozzles are part of the casings itself. They commonly have the following configurationstwo of which are shown in Figure 6:

Figure 6: Suction and Discharge Nozzle Locations

End Suction/Top Discharge

The suction nozzle is located at the end of, and concentric to, the shaft while the discharge nozzle is located at the top of the case perpendicular to the shaft. This pump is always of an overhung type and typically has lower NPSHr because the liquid feeds directly into the impeller eye

Top Suction/Top Discharge

The suction and discharge nozzles are located at the top of the case perpendicular to the shaft. This pump can either be an overhung type or between-bearing type but is always a radially split case pump.

Side Suction/Side Discharge

The suction and discharge nozzles are located at the sides of the case perpendicular to the shaft. This pump can have either an axially or radially split case type.

Seal Chamber and Stuffing Box

Figure 7: Parts of a Simple Seal Chamber

Seal chamber and Stuffing box both refer to a chamber, either integral with or separate from the pump case housing that forms the region between the shaft and casing where sealing media are installed. When the sealing is achieved by means of a mechanical seal, the chamber is commonly referred to as a Seal Chamber. When the sealing is achieved by means of packing, the chamber is referred to as a Stuffing Box. Both the seal chamber and the stuffing box have the primary function of protecting the pump against leakage at the point where the shaft passes out through the pump pressure casing. When the pressure at the bottom of the chamber is below atmospheric, it prevents air leakage into the pump. When the pressure is above atmospheric, the chambers prevent liquid leakage out of the pump. The seal chambers and stuffing boxes are also provided with cooling or heating arrangement for proper temperature control. Figure7depicts an externally mounted seal chamber and its parts.

Glands

The gland is a very important part of the seal chamber or the stuffing box. It gives the packings or the mechanical seal the desired fit on the shaft sleeve. It can be easily adjusted in axial direction. The gland comprises of the seal flush, quench, cooling, drain, and vent connection ports as per the standard codes like API 68

Throat Bushing

The bottom or inside end of the chamber is provided with a stationary device called throat bushing that forms a restrictive close clearance around the sleeve (or shaft) between the seal and the impeller.

Throttle Bushing{parse block="google_articles"}

The throttle bushing refers to a device that forms a restrictive close clearance around the sleeve (or shaft) at the outboard end of a mechanical seal gland.

Internal Circulating Device

The internal circulating device refers to device located in the seal chamber to circulate seal chamber fluid through a cooler or barrier/buffer fluid reservoir. Usually it is referred to as a pumping ring.

Mechanical Seal

Mechanical seals will be discussed further in part two of this article series.

Bearing Housing

The bearing housing encloses the bearings mounted on the shaft. The bearings keep the shaft or rotor in correct alignment with the stationary parts under the action of radial and transverse loads. The bearing house also includes an oil reservoir for lubrication, constant level oiler, jacket for cooling by circulating cooling water.

Rotating Components

Impeller

The impeller is the main rotating part that provides the centrifugal acceleration to the fluid. They are often classified in many ways:

1. Based on major direction of flow in reference to the axis of rotation:
   Radial flow
   Axial flow
   Mixed flow
   
2. Based on suction type:
   Single-suction: Liquid inlet on one side.
   Double-suction: Liquid inlet to the impeller symmetrically from both sides.

3. Based on mechanical construction (Figure 8)
   Closed: Shrouds or sidewall enclosing the vanes.
   Open: No shrouds or wall to enclose the vanes.
   Semi-open or vortex type.

   Figure 8: Impeller Types

Closed impellers require wear rings and these wear rings present another maintenance problem. Open and semi-open impellers are less likely to clog, but need manual adjustment to the volute or back-plate to get the proper impeller setting and prevent internal re-circulation. Vortex pump impellers are great for solids and "stringy" materials but they are up to 50% less efficient than conventional designs. The number of impellers determines the number of stages of the pump. A single stage pump has one impeller only and is best for low head service. A two-stage pump has two impellers in series for medium head service. A multi-stage pump has three or more impellers in series for high head service.

Wear ring provides an easily and economically renewable leakage joint between the impeller and the casing. clearance becomes too large the pump efficiency will be lowered causing heat and vibration problems. Most manufacturers require that you disassemble the pump to check the wear ring clearance and replace the rings when this clearance doubles.

Shaft

The basic purpose of a centrifugal pump shaft is to transmit the torques encountered when starting and during operation while supporting the impeller and other rotating parts. It must do this job with a deflection less than the minimum clearance between the rotating and stationary parts.

Figure 9: Shaft Sleeve

Shaft Sleeves

Pump shafts are usually protected from erosion, corrosion, and wear at the seal chambers, leakage joints, internal bearings, and in the waterways by renewable sleeves. Unless otherwise specified, a shaft sleeve of wear, corrosion, and erosion-resistant material shall be provided to protect the shaft. The sleeve shall be sealed at one end. The shaft sleeve assembly shall extend beyond the outer face of the seal gland plate. (Leakage between the shaft and the sleeve should not be confused with leakage through the mechanical seal).

Coupling

Couplings can compensate for axial growth of the shaft and transmit torque to the impeller. Shaft couplings can be broadly classified into two groups: rigid and flexible. Rigid couplings are used in applications where there is absolutely no possibility or room for any misalignment. Flexible shaft couplings are more prone to selection, installation and maintenance errors. Flexible shaft couplings can be divided into two basic groups: elastomeric and non-elastomeric

1. Elastomeric couplings use either rubber or polymer elements to achieve flexibility. These elements can either be in shear or in compression. Tire and rubber sleeve designs are elastomer in shear couplings; jaw and pin and bushing designs are elastomer in compression couplings.
2. Non-elastomeric couplings use metallic elements to obtain flexibility. These can be one of two types: lubricated or non-lubricated. Lubricated designs accommodate misalignment by the sliding action of their components, hence the need for lubrication. The non-lubricated designs accommodate misalignment through flexing. Gear, grid and chain couplings are examples of non-elastomeric, lubricated couplings. Disc and diaphragm couplings are non-elastomeric and non-lubricated.

Auxilliary Components

Auxiliary components generally include the following piping systems for the following services:

1. Seal flushing , cooling , quenching systems
2. Seal drains and vents
3. Bearing lubrication , cooling systems
4. Seal chamber or stuffing box cooling, heating systems
5. Pump pedestal cooling systems

Auxiliary piping systems include tubing, piping, isolating valves, control valves, relief valves, temperature gauges and thermocouples, pressure gauges, sight flow indicators, orifices, seal flush coolers, dual seal barrier/buffer fluid reservoirs, and all related vents and drains.

All auxiliary components shall comply with the requirements as per standard codes like API 610 (refinery services), API 682 (shaft sealing systems) etc.

Definition of Important Terms

The key performance parameters of centrifugal pumps are capacity, head, BHP (Brake horse power), BEP (Best efficiency point) and specific speed. The pump curves provide the operating window within which these parameters can be varied for satisfactory pump operation. The following parameters or terms are discussed in detail in this section.

Capacity

Head

• Significance of using Head instead of Pressure
• Pressure to Head Conversion formula
• Static Suction Head, h_S
• Static Discharge Head, h_d {parse block="google_articles"}
• Friction Head, hf
• Vapor pressure Head, hvp
• Pressure Head, hp
• Velocity Head, hv
• Total Suction Head H_S
• Total Discharge Head H_d
• Total Differential Head H_T

NPSH

• Net Positive Suction Head Required NPSHr
• Net Positive Suction Head Available NPSHa

Power (Brake Horse Power, B.H.P) and Efficiency (Best Efficiency Point, B.E.P)

Specific Speed (Ns)

Affinity Laws

Capacity

Capacity means the flow rate with which liquid is moved or pushed by the pump to the desired point in the process. It is commonly measured in either gallons per minute (gpm) or cubic meters per hour (m³/hr). The capacity usually changes with the changes in operation of the process. For example, a boiler feed pump is an application that needs a constant pressure with varying capacities to meet a changing steam demand.

The capacity depends on a number of factors like:

• Process liquid characteristics i.e. density, viscosity
• Size of the pump and its inlet and outlet sections
• Impeller size
• Impeller rotational speed RPM
• Size and shape of cavities between the vanes
• Pump suction and discharge temperature and pressure conditions

For a pump with a particular impeller running at a certain speed in a liquid, the only items on the list above that can change the amount flowing through the pump are the pressures at the pump inlet and outlet. The effect on the flow through a pump by changing the outlet pressures is graphed on a pump curve.

As liquids are essentially incompressible, the capacity is directly related with the velocity of flow in the suction pipe. This relationship is as follows:

Head

Significance of Using the Term "Head" Instead of the Term "Pressure"

The pressure at any point in a liquid can be thought of as being caused by a vertical column of the liquid due to its weight. The height of this column is called the static head and is expressed in terms of feet of liquid.

The same head term is used to measure the kinetic energy created by the pump. In other words, head is a measurement of the height of a liquid column that the pump could create from the kinetic energy imparted to the liquid. Imagine a pipe shooting a jet of water straight up into the air, the height the water goes up would be the head.

The head is not equivalent to pressure. Head is a term that has units of a length or feet and pressure has units of force per unit area or pound per square inch. The main reason for using head instead of pressure to measure a centrifugal pump's energy is that the pressure from a pump will change if the specific gravity (weight) of the liquid changes, but the head will not change. Since any given centrifugal pump can move a lot of different fluids, with different specific gravities, it is simpler to discuss the pump's head and forget about the pressure.

So a centrifugal pump's performance on any Newtonian fluid, whether it's heavy (sulfuric acid) or light (gasoline) is described by using the term 'head'. The pump performance curves are mostly described in terms of head.

Pressure to Head Conversion Formula

The static head corresponding to any specific pressure is dependent upon the weight of the liquid according to the following formula:

Eq. (4)

Newtonian liquids have specific gravities typically ranging from 0.5 (light, like light hydrocarbons) to 1.8 (heavy, like concentrated sulfuric acid). Water is a benchmark, having a specific gravity of 1.0.

This formula helps in converting pump gauge pressures to head for reading the pump curves.

The various head terms are discussed below.

Note: The Subscripts 's' refers to suction conditions and 'd' refers to discharge conditions.

• Static Suction Head, h_S
• Static Discharge Head, h_d
• Friction Head, h_f
• Vapor pressure Head, h_vp
• Pressure Head, h_p
• Velocity Head, h_v
• Total Suction Head H_S
• Total Discharge Head H_d
• Total Differential Head H_T
• Net Positive Suction Head Required NPSHr
• Net Positive Suction Head Available NPSHa

Static Suction Head (h_s)

Head resulting from elevation of the liquid relative to the pump center line. If the liquid level is above pump centerline, h_S is positive. If the liquid level is below pump centerline, h_S is negative. Negative h_S condition is commonly denoted as a "suction lift" condition.

Static Discharge Head, (h_d)

It is the vertical distance in feet between the pump centerline and the point of free discharge or the surface of the liquid in the discharge tank.

Friction Head (h_f)

The head required to overcome the resistance to flow in the pipe and fittings. It is dependent upon the size, condition and type of pipe, number and type of pipefittings, flow rate, and nature of the liquid.

Vapor Pressure Head (h_vp)

Vapor pressure is the pressure at which a liquid and its vapor co-exist in equilibrium at a given temperature. The vapor pressure of liquid can be obtained from vapor pressure tables. When the vapor pressure is converted to head, it is referred to as vapor pressure head, h_vp. The value of h_vp of a liquid increases with the rising temperature and in effect, opposes the pressure on the liquid surface, the positive force that tends to cause liquid flow into the pump suction i.e. it reduces the suction pressure head.

Pressure Head (h_p)

Pressure Head must be considered when a pumping system either begins or terminates in a tank which is under some pressure other than atmospheric. The pressure in such a tank must first be converted to feet of liquid. Denoted as h_p, pressure head refers to absolute pressure on the surface of the liquid reservoir supplying the pump suction, converted to feet of head. If the system is open, h_p equals atmospheric pressure head.

Velocity Head (h_v)

Refers to the energy of a liquid as a result of its motion at some velocity 'v'. It is the equivalent head in feet through which the water would have to fall to acquire the same velocity, or in other words, the head necessary to accelerate the water. The velocity head is usually insignificant and can be ignored in most high head systems. However, it can be a large factor and must be considered in low head systems.

Total Suction Head (H_s)

The suction reservoir pressure head (hp_S) plus the static suction head (h_S) plus the velocity head at the pump suction flange (h_VS) minus the friction head in the suction line (hf_S).

The total suction head is the reading of the gauge on the suction flange, converted to feet of liquid.

Total Discharge Head (H_d)

The discharge reservoir pressure head (hp_d) plus static discharge head (h_d) plus the velocity head at the pump discharge flange (hv_d) plus the total friction head in the discharge line (hf_d).

The total discharge head is the reading of a gauge at the discharge flange, converted to feet of liquid.

Total Differential Head (H_T)

It is the total discharge head minus the total suction head or

NPSH

When discussing centrifugal pumps, the two most important head terms are NPSHr and NPSHa.

Net Positive Suction Head Required, NPSHr

NPSH is one of the most widely used and least understood terms associated with pumps. Understanding the significance of NPSH is very much essential during installation as well as operation of the pumps.

Pumps Can Only Pump Liquids, Not Vapor{parse block="google_articles"}

The satisfactory operation of a pump requires that vaporization of the liquid being pumped does not occur at any condition of operation. This is so desired because when a liquid vaporizes its volume increases very much. For example, 1 ft³ of water at room temperature becomes 1700 ft³ of vapor at the same temperature. This makes it clear that if we are to pump a fluid effectively, it must be kept always in the liquid form.

Rise in temperature and fall in pressure induces vaporization

The vaporization begins when the vapor pressure of the liquid at the operating temperature equals the external system pressure, which, in an open system is always equal to atmospheric pressure. Any decrease in external pressure or rise in operating temperature can induce vaporization and the pump stops pumping. Thus, the pump always needs to have a sufficient amount of suction head present to prevent this vaporization at the lowest pressure point in the pump.

NPSH as a measure to prevent liquid vaporization

The manufacturer usually tests the pump with water at different capacities, created by throttling the suction side. When the first signs of vaporization induced cavitation occur, the suction pressure is noted (the term cavitation is discussed in detail later). This pressure is converted into the head. This head number is published on the pump curve and is referred as the "net positive suction head required (NPSHr) or sometimes in short as the NPSH. Thus the Net Positive Suction Head (NPSH) is the total head at the suction flange of the pump less the vapor pressure converted to fluid column height of the liquid.

NPSHr is a function of pump design

NPSH required is a function of the pump design and is determined based on actual pump test by the vendor. As the liquid passes from the pump suction to the eye of the impeller, the velocity increases and the pressure decreases. There are also pressure losses due to shock and turbulence as the liquid strikes the impeller. The centrifugal force of the impeller vanes further increases the velocity and decreases the pressure of the liquid. The NPSH required is the positive head in feet absolute required at the pump suction to overcome these pressure drops in the pump and maintain the majority of the liquid above its vapor pressure.

The NPSH is always positive since it is expressed in terms of absolute fluid column height. The term "Net" refers to the actual pressure head at the pump suction flange and not the static suction head.

NPSHr increases as capacity increases

The NPSH required varies with speed and capacity within any particular pump. The NPSH required increase as the capacity is increasing because the velocity of the liquid is increasing, and as anytime the velocity of a liquid goes up, the pressure or head comes down. Pump manufacturer's curves normally provide this information. The NPSH is independent of the fluid density as are all head terms.

Net Positive Suction Head Available, NPSHa

NPSHa is a function of system design

Net Positive Suction Head Available is a function of the system in which the pump operates. It is the excess pressure of the liquid in feet absolute over its vapor pressure as it arrives at the pump suction, to be sure that the pump selected does not cavitate. It is calculated based on system or process conditions.

NPSHa calculation

The formula for calculating the NPSHa is stated below:

NPSHa in a Nutshell

In a nutshell, NPSH available is defined as:

In an existing system, the NPSHa can also be approximated by a gauge on the pump suction using the formula:

Significance of NPSHr and NPSHa

The NPSH available must always be greater than the NPSH required for the pump to operate properly. It is normal practice to have at least 2 to 3 feet of extra NPSH available at the suction flange to avoid any problems at the duty point.

Power and Efficiency

Brake Horse Power (BHP)

The work performed by a pump is a function of the total head and the weight of the liquid pumped in a given time period. Pump input or brake horsepower (BHP) is the actual horsepower delivered to the pump shaft. Pump output or hydraulic or water horsepower (WHP) is the liquid horsepower delivered by the pump. These two terms are defined by the following formulas.

The constant 3960 is obtained by dividing the number or foot-pounds for one horsepower (33,000) by the weight of one gallon of water (8.33 pounds). BHP can also be read from the pump curves at any flow rate. Pump curves are based on a specific gravity of 1.0. Other liquids' specific gravity must be considered. The brake horsepower or input to a pump is greater than the hydraulic horsepower or output due to the mechanical and hydraulic losses incurred in the pump. Therefore the pump efficiency is the ratio of these two values.

Eq. (14)

Best Efficiency Point (BEP)

The H, NPSHr, efficiency, and BHP all vary with flow rate, Q. Best Efficiency Point (BEP) is the capacity at maximum impeller diameter at which the efficiency is highest. All points to the right or left of BEP have a lower efficiency.

BEP as a measure of optimum energy conversion

When sizing and selecting centrifugal pumps for a given application the pump efficiency at design should be taken into consideration. The efficiency of centrifugal pumps is stated as a percentage and represents a unit of measure describing the change of centrifugal force (expressed as the velocity of the fluid) into pressure energy. The B.E.P. (best efficiency point) is the area on the curve where the change of velocity energy into pressure energy at a given gallon per minute is optimum; in essence, the point where the pump is most efficient.

BEP as a measure of mechanically stable operation

The impeller is subject to non-symmetrical forces when operating to the right or left of the BEP. These forces manifest themselves in many mechanically unstable conditions like vibration, excessive hydraulic thrust, temperature rise, and erosion and separation cavitation. Thus the operation of a centrifugal pump should not be outside the furthest left or right efficiency curves published by the manufacturer. Performance in these areas induces premature bearing and mechanical seal failures due to shaft deflection, and an increase in temperature of the process fluid in the pump casing causing seizure of close tolerance parts and cavitation.

BEP as an important parameter in calculations

BEP is an important parameter in that many parametric calculations such as specific speed, suction specific speed, hydrodynamic size, viscosity correction, head rise to shut-off, etc. are based on capacity at BEP. Many users prefer that pumps operate within 80% to 110% of BEP for optimum performance.

Specific Speed

Specific speed (N_s) is a non-dimensional design index that identifies the geometric similarity of pumps. It is used to classify pump impellers as to their type and proportions. Pumps of the same Ns but of different size are considered to be geometrically similar, one pump being a size-factor of the other.

Specific Speed Calculation

The following formula is used to determine specific speed:

The understanding of this definition is of design engineering significance only, however, and specific speed should be thought of only as an index used to predict certain pump characteristics.

As per the above formula, it is defined as the speed in revolutions per minute at which a geometrically similar impeller would operate if it were of such a size as to deliver one gallon per minute flow against one-foot head.

Specific Speed as a Measure of the Shape or Class of the Impellers

The specific speed determines the general shape or class of the impellers. As the specific speed increases, the ratio of the impeller outlet diameter, D2, to the inlet or eye diameter, D1, decreases. This ratio becomes 1.0 for a true axial flow impeller. Radial flow impellers develop head principally through centrifugal force. Radial impellers are generally low flow high head designs. Pumps of higher specific speeds develop head partly by centrifugal force and partly by axial force. A higher specific speed indicates a pump design with head generation more by axial forces and less by centrifugal forces. An axial flow or propeller pump with a specific speed of 10,000 or greater generates its head exclusively through axial forces. Axial flow impellers are high flow low head designs.

Specific speed identifies the approximate acceptable ratio of the impeller eye diameter (D1) to the impeller maximum diameter (D2) in designing a good impeller.

Ns: 500 to 5000;D1/D2 > 1.5 -radial flow pump
Ns: 5000 to 10000;D1/D2 < 1.5 -mixed flow pump
Ns: 10000 to 15000; D1/D2 = 1 - axial flow pump

Specific speed is also used in designing a new pump by size-factoring a smaller pump of the same specific speed. The performance and construction of the smaller pump are used to predict the performance and model the construction of the new pump.

Suction Specific Speed (Nss)

Suction specific speed (Nss) is a dimensionless number or index that defines the suction characteristics of a pump. It is calculated from the same formula as Ns by substituting H by NPSHr.

In multi-stage pump the NPSHr is based on the first stage impeller NPSHR. Nss is commonly used as a basis for estimating the safe operating range of capacity for a pump. The higher the Nss is, the narrower is its safe operating range from its BEP. The numbers range between 3,000 and 20,000. Most users prefer that their pumps have Nss in the range of 8000 to 11000 for optimum and trouble-free operation.

The Affinity Laws

The Affinity Laws are mathematical expressions that define changes in pump capacity, head, and BHP when a change is made to pump speed, impeller diameter, or both. According to the Affinity Laws:

Capacity (Q) changes in direct proportion to impeller diameter D ratio, or to speed N ratio:

Head (H) changes in direct proportion to the square of impeller diameter D ratio, or the square of speed N ratio:

BHP changes in direct proportion to the cube of impeller diameter ratio, or the cube of speed ratio:

Where the subscript: 1 refers to initial condition, 2 refer to new condition.

If changes are made to both impeller diameter and pump speed the equations can be combined to:

These equations are used to hand-calculate the impeller trim diameter from a given pump performance curve at a bigger diameter.

The Affinity Laws are valid only under conditions of constant efficiency

Understanding Centrifugal Pump Performance Curves

The capacity and pressure needs of any system can be defined with the help of a graph called a system curve. Similarly the capacity vs. pressure variation graph for a particular pump defines its characteristic pump performance curve.

The pump suppliers try to match the system curve supplied by the user with a pump curve that satisfies these needs as closely as possible. A pumping system operates where the pump curve and the system resistance curve intersect. The intersection of the two curves defines the operating point of both pump and process. However, it is impossible for one operating point to meet all desired operating conditions. For example, when the discharge valve is throttled, the system resistance curve shift left and so does the operating point.

Figure 10: Typical System and Pump Performance Curves

Developing a System Curve

The system resistance or system head curve is the change in flow with respect to head of the system. It must be developed by the user based upon the conditions of service. These include physical layout, {parse block="google_articles"}process conditions, and fluid characteristics. It represents the relationship between flow and hydraulic losses in a system in a graphic form and, since friction losses vary as a square of the flow rate, the system curve is parabolic in shape. Hydraulic losses in piping systems are composed of pipe friction losses, valves, elbows and other fittings, entrance and exit losses, and losses from changes in pipe size by enlargement or reduction in diameter.

Developing a Pump Performance Curve

A pump's performance is shown in its characteristics performance curve where its capacity i.e. flow rate is plotted against its developed head. The pump performance curve also shows its efficiency (BEP), required input power (in BHP), NPSHr, speed (in RPM), and other information such as pump size and type, impeller size, etc. This curve is plotted for a constant speed (rpm) and a given impeller diameter (or series of diameters). It is generated by tests performed by the pump manufacturer. Pump curves are based on a specific gravity of 1.0. Other specific gravities must be considered by the user.

Normal Operation Range

A typical performance curve (Figure 10) is a plot of Total Head vs. Flow rate for a specific impeller diameter. The plot starts at zero flow. The head at this point corresponds to the shut-off head point of the pump. The curve then decreases to a point where the flow is maximum and the head minimum. This point is sometimes called the run-out point. The pump curve is relatively flat and the head decreases gradually as the flow increases. This pattern is common for radial flow pumps. Beyond the run-out point, the pump cannot operate. The pump's range of operation is from the shut-off head point to the run-out point. Trying to run a pump off the right end of the curve will result in pump cavitation and eventually destroy the pump.

By plotting the system head curve and pump curve together, you can determine:

1.Where the pump will operate on its curve?
2.What changes will occur if the system head curve or the pump performance curve changes?

Requirements for Consistent Operation

References

In Part I of this article, two basic requirements for trouble free operation and longer service life of centrifugal pumps are mentioned in brief:

• Prevent cavitation
  Cavitation of the pump should not occur throughout its operating capacity range.
• Minimize low flow operation{parse block="google_articles"}
  Continuous operation of centrifugal pumps at low flows i.e. reduced capacities, leads to a number of unfavorable conditions. These include reduced motor efficiency, excessive radial thrusts, excessive temperature rise in the pumping fluid, internal re-circulation, etc. A certain minimum continuous flow (MCF) should be maintained during the pump operation.

The condition of cavitation is essentially an indication of an abnormality in the pump suction system, whereas the condition of low flow indicates an abnormality in the entire pumping system or process. The two conditions are also inter-linked such that a low flow situation can also induce cavitation.

Cavitation is a common occurrence but is the least understood of all pumping problems. Cavitation means different things to different people. Some say when a pump makes a rattling or knocking sound along with vibrations, it is cavitating. Some call it slippage as the pump discharge pressure slips and flow becomes erratic. When cavitating, the pump not only fails to serve its basic purpose of pumping the liquid but also may experience internal damage, leakage from the seal and casing, bearing failure, etc.

In summary, cavitation is an abnormal condition that can result in loss of production, equipment damage and worst of all, injury to personnel.

The plant engineer's job is to quickly detect the signs of cavitation, correctly identify the type and cause of the cavitation and eliminate it. A good understanding of the concept is the key to troubleshooting any cavitation related pumping problem.

The Meaning of Cavitation

The term ‘cavitation' comes from the Latin word cavus, which means a hollow space or a cavity. Webster's Dictionary defines the word ‘cavitation' as the rapid formation and collapse of cavities in a flowing liquid in regions of very low pressure.

In any discussion on centrifugal pumps various terms like vapor pockets, gas pockets, holes, bubbles, etc. are used in place of the term cavities. These are one and the same thing and need not be confused. The term bubble shall be used hereafter in the discussion.

Generally, the bubbles that form inside the liquid are of two types: Vapor bubbles or Gas bubbles.

1. Vapor bubbles are formed due to the vaporisation of a process liquid that is being pumped. The cavitation condition induced by formation and collapse of vapor bubbles is commonly referred to as Vaporous Cavitation.
2. Gas bubbles are formed due to the presence of dissolved gases in the liquid that is being pumped (generally air but may be any gas in the system). The cavitation condition induced by the formation and collapse of gas bubbles is commonly referred to as Gaseous Cavitation.

Both types of bubbles are formed at a point inside the pump where the local static pressure is less than the vapor pressure of the liquid (vaporous cavitation) or saturation pressure of the gas (gaseous cavitation).

Vaporous cavitation is the most common form of cavitation found in process plants. Generally it occurs due to insufficiency of the available NPSH or internal recirculation phenomenon. It generally manifests itself in the form of reduced pump performance, excessive noise and vibrations and wear of pump parts. The extent of the cavitation damage can range from a relatively minor amount of pitting after years of service to catastrophic failure in a relatively short period of time.

Gaseous cavitation occurs when any gas (most commonly air) enters a centrifugal pump along with liquid. A centrifugal pump can handle air in the range of ½ % by volume. If the amount of air is increased to 6%, the pump starts cavitating. The cavitation condition
is also referred to as Air binding. It seldom causes damage to the impeller or casing. The main effect of gaseous cavitation is loss of capacity.

The different types of cavitation, their specific symptoms and specific corrective actions shall be explored in the next part of the article. However, in order to clearly identify the type of cavitation, let us first understand the mechanism of cavitation, i.e. how cavitation occurs. Unless otherwise specified, the term cavitation shall refer to vaporous cavitation.

Important Definitions

To enable a clear understanding of mechanism of cavitation, definitions of following important terms are explored:

• Static pressure
• Dynamic pressure{parse block="google_articles"}
• Total pressure
• Static pressure head
• Velocity head
• Vapor pressure

Static Pressure (P_s)

The static pressure in a fluid stream is the normal force per unit area on a solid boundary moving with the fluid. It describes the difference between the pressure inside and outside a system, disregarding any motion in the system. For instance, when referring to an air duct, static pressure is the difference between the pressure inside the duct and outside the duct, disregarding any airflow inside the duct. In energy terms, the static pressure is a measure of the potential energy of the fluid.

Dynamic Pressure (P_d)

A moving fluid stream exerts a pressure higher than the static pressure due to the kinetic energy (½ mv²) of the fluid. This additional pressure is defined as the dynamic pressure. The dynamic pressure can be measured by converting the kinetic energy of the fluid stream into the potential energy. In other words, it is pressure that would exist in a fluid stream that has been decelerated from its velocity ‘v' to ‘zero' velocity.

Total Pressure (P_t)

The sum of static pressure and dynamic pressure is defined as the total pressure. It is a measure of total energy of the moving fluid stream. i.e. both potential and kinetic energy.

Relationship Between P_s, P_d, and P_t

In an incompressible flow, the relation between static, dynamic and total pressures can be found out using a simple device called Pitot tube (named after Henri Pitot in 1732) shown in Figure 1.

The Pitot tube has two tubes:

Figure 1: Sketch of a Pilot Tube

1. Static tube (b'): The opening of the static tube is parallel to the direction of flow. It measures the static pressure, since there is no velocity component perpendicular to its opening.
2. Impact tube (a): The opening of the impact tube is perpendicular to the flow direction. The point at the entrance of the impact tube is called as the stagnation point .At this point the kinetic energy of the fluid is converted to the potential energy. Thus, the impact tube measures the total pressure (also referred to as stagnation pressure) i.e. both static pressure and dynamic pressure (also referred to as impact pressure).

The two tubes are connected to the legs of a manometer or equivalent device for measuring pressure.

The relation between p_s, p_d and p_t can be derived by applying a simple energy balance.

As mentioned earlier, in the case of a fluid or gas the potential energy is represented by the static pressure and the kinetic energy by dynamic pressure. The kinetic energy is a function of the motion of the fluid, and of course it's mass. It is generally more convenient to use the density of the fluid (ρ) as the mass representation.

The corresponding pressure balance equation is^:

Eq. (3)

In place of the pressure terms as used above, it is more appropriate to speak of the energy during pumping as the energy per unit weight of the liquid pumped and the units of energy expressed this way are foot-pounds per pound (Newton-meters per Newton) or just feet (meters) i.e. the units of head. Thus the energy of the liquid at a given point in flow stream can be expressed in terms of head of liquid in feet.

The pressure term can be converted to head term by division with the factor ‘ρ g'. For unit inter-conversions the factor ‘ρ g/g_c'. should be used in place of ‘ρg'.

Static Pressure Head

The head corresponding to the static pressure is called as the static pressure head.

Eq. (4)

Velocity Head

The head corresponding to dynamic pressure is called the velocity head.

Eq. (5)

From the reading h_mof the manometer velocity of flow can be calculated and thus velocity head can be calculated. The pressure difference, dP (P_t - P_s) indicated by the manometer is the dynamic pressure.

	Eq. (6)
	Eq. (7)

Vapor Pressure (P_v)

Vapor pressure is the pressure required to keep a liquid in a liquid state. If the pressure applied to the surface of the liquid is not enough to keep the molecules pretty close together, the molecules will be free to separate and roam around as a gas or vapor. The vapor pressure is dependent upon the temperature of the liquid. Higher the temperature, higher will be the vapor pressure.

Mechanism of Cavitation

The phenomenon of cavitation is a stepwise process as shown in Figure 2.

Figure 2: Steps in Cavitation

The bubbles form inside the liquid when it vaporises i.e. phase change from liquid to vapor. But how does vaporization of the liquid occur during a pumping operation?

Vaporization of any liquid inside a closed container can occur if either pressure on the liquid surface decreases such that it becomes equal to or less than the liquid vapor pressure at the operating temperature, or the temperature of the liquid rises, raising the vapor pressure such that it becomes equal to or greater than the operating pressure at the liquid surface. For example, if water at room temperature (about 77 °F) is kept in a closed container and the system pressure is reduced to its vapor pressure (about 0.52 psia), the water quickly changes to a vapor. Also, if the operating pressure is to remain constant at about 0.52 psia and the temperature is allowed to rise above 77 ^°F, then the water quickly changes to a vapor.

Just like in a closed container, vaporization of the liquid can occur in centrifugal pumps when the local static pressure reduces below that of the vapor pressure of the liquid at the pumping temperature.

Step One: Formation of Bubbles

To understand vaporization, two important points to remember are:

1. We consider only the static pressure and not the total pressure when determining if the system pressure is less than or greater than the liquid vapor pressure. The total pressure is the sum of the static pressure and dynamic pressure (due to velocity). {parse block="google_articles"}
2. The terms pressure and head have different meanings and they should not be confused. As a convention in this article, the term "pressure" shall be used to understand the concept of cavitation whereas the term "head" shall be used in equations.

Thus, the key concept is - vapor bubbles form due to vaporization of the liquid being pumped when the local static pressure at any point inside the pump becomes equal to or less than the vapor pressure of the liquid at the pumping temperature.

The reduction in local static pressure at any point inside the pump can occur under two conditions:

1. The actual pressure drop in the external suction system is greater than that considered during design. As a result, the pressure available at pump suction is not sufficiently high enough to overcome the design pressure drop inside the pump.
2. The actual pressure drop inside the pump is greater than that considered during the pump design.

Pressure Reduction in the External Suction of the Pump

Figure 3: External Suction System

A simple sketch of a pump external suction system in shown in Figure 3. The nomenclature used for this figure is as follows:

ρ - Liquid density in lb_m / ft³

G - Acceleration due to gravity in ft / s²

Psn - p refers to local static pressure (absolute). Subscript s refers to suction and subscript n refers to the point of measurement. The pressure at any point can be converted to the head term by division with the factor - ρ g

p_s1 - Static pressure (absolute) of the suction vessel in psia

hp_s1 - Static pressure head i.e. absolute static pressure on the liquid surface in the suction vessel, converted to feet of head (p_s1/ ρ g/g_c). If the system is open, hp_s1 equals the atmospheric pressure head.

v_s1 - Liquid velocity on the surface in the suction vessel in ft/s

hv_s1 - Velocity head i.e. the energy of a liquid as a result of its motion at some velocity ‘v_s1'. (v²_s1 / 2g). It is the equivalent head in feet through which the liquid would have to fall to acquire the same velocity, or the head necessary to accelerate the liquid to velocity v_s1. In a large suction vessel, the velocity head is practically zero and is typically ignored in calculations.

h_s - Static suction head. . . . i.e. head resulting from elevation of the liquid relative to the pump centerline. If the liquid level is above pump centerline, h_S is positive. If the liquid level is below pump centerline, h_S is negative. A negative h_S condition is commonly referred to as "suction lift".

hf_s - Friction head i.e. the head required to overcome the resistance to flow in the pipe, valves and fittings between points A and B, inclusive of the entrance losses at the point of connection of suction piping to the suction vessel (point A in Figure 1). The friction head is dependent upon the size, condition and type of pipe, number and type of fittings, valves, flow rate and the nature of the liquid. The friction head varies as the square of the average velocity of the flowing fluid.

p_s2 - Absolute static pressure at the suction flange in psia

hp_s2 - Static pressure head at the suction flange i.e. absolute pressure of the liquid at the suction flange, converted to feet of head - p_s2 / ρ g/g_c

v_s2 - Velocity of the moving liquid at the suction flange in ft/s. The pump suction piping is sized such that the velocity at the suction remains low.

hv_s2 - Velocity head at suction flange i.e. the energy of a liquid as a result of its motion at average velocity ‘v_s2' equal to v²_s2 / 2g.

p_v - Absolute vapor pressure of the liquid at operating temperature in psia.

hp_v - Vapor Pressure head i.e. absolute vapor pressure converted to feet of head (p_v / ρ g/g_c).

H_s - Total Suction Head available at the suction flange in ft.

Note: As pressure is measured in absolute, total head is also in absolute.

The pump takes suction from a vessel having a certain liquid level. The vessel can be pressurised (as shown in the Figure 3) or can be at atmospheric pressure or under vacuum.

Calculation of the Total Suction Head, H_s

The external suction system of the pump provides a certain amount of head at the suction flange. This is referred to as Total Suction Head (TSH), H_s.

TSH can be calculated by application of the energy balance. The incompressible liquid can have energy in the form of velocity, pressure or elevation. Energy in various forms is either added to or subtracted from the liquid as it passes through the suction piping. The head term in feet (or meters) is used as an expression of the energy of the liquid at any given point in the flow stream.

As shown in Figure 3, the total suction head, H_s, available at the suction flange is given by the equation,

For an existing system, Hs can also be calculated from the pressure gauge reading at pump suction flange,

Equations8 and9 above include the velocity head terms hv_s1 and hv_s2, respectively.

Velocity Head

There is a lot of confusion as to whether the velocity head terms should be added or subtracted in the head calculations. To avoid any confusion remember the following:

Just like a static tube of Pitot, a pressure gauge can measure only the static pressure at the point of connection. It does not measure the dynamic pressure as the opening of the gauge impulse pipe is parallel to the direction of flow and there is no velocity component perpendicular to its opening.

Figure 4: Measuing Static Pressure

In Figure 4 below, flow through a pipe of varying cross section area is shown. As the cross section at point B reduces, the velocity of flow increases. The rise in kinetic energy happens at the expense of potential energy. Assuming that there are no friction losses, the total energy (sum of potential energy and kinetic energy) of fluid at point A, B and C remains constant. The pressure gauges at point A, B and C measure only the potential energy i.e. the static pressures at respective points. The drop in static pressure from 10 psi (point A) to 5 psi (point B') occurs owing to rise the dynamic pressure by 5 psi i.e. increase in velocity at point B. However the gauge at point B records only the static pressure. The velocity decreases from point B to C and the static pressure is recovered again to 10 psi.

At a particular point of flow, the total pressure is the sum of the static pressure and the dynamic pressure. Thus, theoretically, the velocity head terms must always be added and not subtracted, in calculating Total Suction Head (TSH), H_s. However, practically speaking, the value of these terms is not significant in comparison to the other terms in the equation.

• hv_s1: In industrial scale suction vessels, the value of hv_s1 is practically zero and it can be safely ignored.
• hv_s2: It is good piping design practice to reduce the friction losses and prevent unnecessary flow turbulence by sizing the suction pipes for fluid velocities in the three to five feet per second range only. The velocity head corresponding to a velocity of 5 ft/s at the suction flange is only about 0.4 ft. Thus, for all practical purposes, in high head systems the velocity head at the suction flange is not significant and can be safely ignored. Only in low head systems does the factor need to be considered.

Therefore, neglecting the velocity head terms, Equations8 and9 simplify to:

Two important inferences can be drawn from the above equations:

• The pressure reduction in the external suction system is primarily due to frictional loss in the suction piping (Equation 10).
• For all practical purposes, the total head at the suction flange is the static pressure head at the suction flange (Equation 11).

Therefore the pump's external suction system should be designed such that the static pressure available at the suction flange is always positive and higher than the vapor pressure of the liquid at the pumping temperature.

For no vaporization at pump suction flange,

As the liquid enters the pump, there is a further reduction in the static pressure. If the value of p_s2 is not sufficiently higher than p_v, at some point inside the pump the static pressure can reduce to the value of p_v. In pumping terminology, the head difference term corresponding to Equation 5 (hp_s2 - hp_v) is called the Net Positive Suction Head or NPSH. The NPSH term shall be explored in detail in the next part of the article. For now, the readers should focus only on how the static pressure within the pump may be reduced to a value lower than that of the liquid vapor pressure.

Pressure Reduction in the Internal Suction System of the Pump

The pressure of the fluid at the suction flange is further reduced inside the internal suction system of the pump.

Figure 5: Internal Pump Locations	Figure 6: Internal Pump Nomenclature

The internal suction system is comprised of the pump's suction nozzle and impeller. Figures 5 and 6 depict the internal parts in detail. A closer look at the graphic is a must in understanding the mechanism of pressure drop inside the pump.

In Figure 7, it can be seen that the passage from the suction flange (point 2) to the impeller suction zone (point 3) and to the impeller eye (point 4) acts like a venturi i.e. there is gradual reduction in the cross-section area.

Figure 7: Pump Internal Suction System

In the impeller, the point of minimum radius (r_eye) with reference to pump centerline is referred to as the "eye" of the impeller (Figure 8).

According to Bernoulli's principle, when a constant amount of liquid moves through a path of decreasing cross-section area (as in a venturi), the velocity increases and the static pressure decreases. In other words, total system energy i.e. sum of the potential and kinetic energy, remains constant in a flowing system (neglecting friction). The gain in velocity occurs at the expense of pressure. At the point of minimum cross-section, the velocity is at a maximum and the static pressure is at a minimum.

The pressure at the suction flange, p_s2 (Point 2) decreases as the liquid flows from the suction flange, through the suction nozzle and into the impeller eye. This decrease in pressure occurs not only due to the venturi effect but also due to the friction in the inlet passage. However, the pressure drop due to friction between the suction nozzle and the impeller eye is comparatively small for most pumps. However the pressure reduction due to the venturi effect is very significant as the velocity at the impeller increases to 15 to 20 ft/s. There is a further drop in pressure due to shock and turbulence as the liquid strikes and loads the edges of impeller vanes. The net effect of all the pressure drops is the creation of a very low-pressure area around the impeller eye and at the beginning of the trailing edge of the impeller vanes.

Figure 8: Impeller Eye	Figure 9: Pressure Profile in a Pump

The pressure reduction profile within the pump is depicted in Figure 9.

As shown in Figure 9, the impeller eye is the point where the static pressure is at a minimum, p_4. During pump operation, if the local static pressure of the liquid at the lowest pressure becomes equal to or less than the vapor pressure (p_v) of the liquid at the operating temperature, vaporization of the liquid (the formation of bubbles) begins i.e. when p₄ <= p_v.

It is at the beginning of the trailing edge of the vanes near the impeller eye where the pressure actually falls to below the liquid vapor pressure. The region of bubble formation is shown in Figure 10.

Figure 10: Impeller Cavitation Regions

In summary, vaporization of the liquid (bubble formation) occurs due to the reduction of the static pressure to a value below that of the liquid vapor pressure. The reduction of static pressure in the external suction system occurs mainly due to friction in suction piping. The reduction of static pressure in the internal suction system occurs mainly due to the rise in the velocity at the impeller eye.

Step Two: Growth of Bubbles

Unless there is no change in the operating conditions, new bubbles continue to form and old bubbles grow in size. The bubbles then get carried in the liquid as it flows from the impeller eye to the impeller exit tip along the vane trailing edge. Due to impeller rotating action, the bubbles attain very high velocity and eventually reach the regions of high pressure within the impeller where they start collapsing. The life cycle of a bubble has been estimated to be in the order of 0.003 seconds.

Step Three: Collapse of Bubbles

Figure 11: Collapse of Vapor Bubbles

As the vapor bubbles move along the impeller vanes, the pressure around the bubbles begins to increase until a point is reached where the pressure on the outside of the bubble is greater than the pressure inside the bubble. The bubble collapses. The process is not an explosion but rather an implosion (inward bursting). Hundreds of bubbles collapse at approximately the same point on each impeller vane. Bubbles collapse non-symmetrically such that the surrounding liquid rushes to fill the void forming a liquid microjet. The micro jet subsequently ruptures the bubble with such force that a hammering action occurs.Bubble collapse pressures greater than 1 GPa (145x10⁶ psi) have been reported. The highly localized hammering effect can pit the pump impeller. The pitting effect is illustrated schematically in Figure 11.

After the bubble collapses, a shock wave emanates outward from the point of collapse. This shock wave is what we actually hear and what we call "cavitation". The implosion of bubbles and emanation of shock waves (red color) is shown in a small video clip shown below.

In nutshell, the mechanism of cavitation is all about formation, growth and collapse of bubbles inside the liquid being pumped. But how can the knowledge of mechanism of cavitation can really help in troubleshooting a cavitation problem. The concept of mechanism can help in identifying the type of bubbles and the cause of their formation and collapse. The troubleshooting method shall be explored in detail in the next part of the article.

Next let us explore the general symptoms of cavitation and its affects on pump performance.

Perceptible indications of the cavitation during pump operation are more or less loud noises, vibrations and an unsteadily working pump. Fluctuations in flow and discharge pressure take place with a sudden and drastic reduction in head rise and pump capacity. Depending upon the size and quantum of the bubbles formed and the severity of their collapse, the pump faces problems ranging from a partial loss in{parse block="google_articles"} capacity and head to total failure in pumping along with irreparable damages to the internal parts. It requires a lot of experience and thorough investigation of effects of cavitation on pump parts to clearly identify the type and root causes of cavitation.

A detailed description of the general symptoms is given as follows.

Reduction in Capacity of the Pump

The formation of bubbles causes a volume increase decreasing the space available for the liquid and thus diminish pumping capacity. For example, when water changes state from liquid to gas its volume increases by approximately 1,700 times. If the bubbles get big enough at the eye of the impeller, the pump "chokes" i.e. loses all suction resulting in a total reduction in flow. The unequal and uneven formation and collapse of bubbles causes fluctuations in the flow and the pumping of liquid occurs in spurts. This symptom is common to all types of cavitations.

Decrease in the Head Developed

Bubbles unlike liquid are compressible. The head developed diminishes drastically because energy has to be expended to increase the velocity of the liquid used to fill up the cavities, as the bubbles collapse. As mentioned earlier, The Hydraulic Standards Institute defines cavitation as condition of 3 % drop in head developed across the pump. Like reduction in capacity, this symptom is also common to all types of cavitations.

Figure 12: Pump Performance Curves

Thus, the hydraulic effect of a cavitating pump is that the pump performance drops off of its expected performance curve, referred to as break away, producing a lower than expected head and flow. The Figure 12 depicts the typical performance curves. The solid line curves represent a condition of adequate NPSHa whereas the dotted lines depict the condition of inadequate NPSHa i.e. the condition of cavitation.

Abnormal Sound and Vibration

It is movement of bubbles with very high velocities from low-pressure area to a high-pressure area and subsequent collapse that creates shockwaves producing abnormal sounds and vibrations. It has been estimated that during collapse of bubbles the pressures of the order of 10⁴ atm develops.

The sound of cavitation can be described as similar to small hard particles or gravel rapidly striking or bouncing off the interior parts of a pump or valve. Various terms like rattling, knocking, crackling are used to describe the abnormal sounds. The sound of pumps operating while cavitating can range from a low-pitched steady knocking sound (like on a door) to a high-pitched and random crackling (similar to a metallic impact). People can easily mistake cavitation for a bad bearing in a pump motor. To distinguish between the noise due to a bad bearing or cavitation, operate the pump with no flow. The disappearance of noise will be an indication of cavitation.

Similarly, vibration is due to the uneven loading of the impeller as the mixture of vapor and liquid passes through it, and to the local shock wave that occurs as each bubble collapses. Very few vibration reference manuals agree on the primary vibration characteristic associated with pump cavitation. Formation and collapsing of bubbles will alternate periodically with the frequency resulting out of the product of speed and number of blades. Some suggest that the vibrations associated with cavitation produce a broadband peak at high frequencies above 2,000 Hertz. Some suggest that cavitation follows the vane pass frequency (number of vanes times the running speed frequency) and yet another indicate that it affects peak vibration amplitude at one times running speed. All of these indications are correct in that pump cavitation can produce various vibration frequencies depending on the cavitation type, pump design, installation and use. The excessive vibration caused by cavitation often subsequently causes a failure of the pump's seal and/or bearings. This is the most likely failure mode of a cavitating pump,

Damage to Pump Parts

Cavitation Erosion or Pitting

Figure 13: Photographic Evidence of Cavitation

During cavitation, the collapse of the bubbles occurs at sonic speed ejecting destructive micro jets of extremely high velocity (up to 1000 m/s) liquid strong enough to cause extreme erosion of the pump parts, particularly impellers. The bubble is trying to collapse from all sides, but if the bubble is lying against a piece of metal such as the impeller or volute it cannot collapse from that side. So the fluid comes in from the opposite side at this high velocity and bangs against the metal creating the impression that the metal was hit with a "ball pin hammer". The resulting long-term material damage begins to become visible by so called

Pits (see Figure 11), which are plastic deformations of very small dimensions (order of magnitude of micrometers). The damage caused due to action of bubble collapse is commonly referred as Cavitation erosion or pitting. The Figure 13 depicts the cavitation pitting effect on impeller and diffuser surface.

Cavitation erosion from bubble collapse occurs primarily by fatigue fracture due to repeated bubble implosions on the cavitating surface, if the implosions have sufficient impact force. The erosion or pitting effect is quite similar to sand blasting. High head pumps are more likely to suffer from cavitation erosion, making cavitation a "high-energy" pump phenomenon.

The most sensitive areas where cavitation erosion has been observed arethe low-pressure sides of the impeller vanes near the inlet edge. The cavitation erosion damages at the impeller are more or less spread out. The pitting has also been observed on impeller vanes, diffuser vanes, and impeller tips etc. In some instances, cavitation has been severe enough to wear holes in the impeller and damage the vanes to such a degree that the impeller becomes completely ineffective. A damaged impeller is shown in Figure 14.

Figure 14: Cavitation Damage on Impellers

The damaged impeller shows that the shock waves occurred near the outside edge of the impeller, where damage is evident. This part of the impeller is where the pressure builds to its highest point. This pressure implodes the gas bubbles, changing the water's state from gas into liquid. When cavitation is less severe, the damage can occur further down towards the eye of the impeller. A careful investigation and diagnosis of point of the impeller erosion on impeller, volute, diffuser etc. can help predict the type and cause of cavitation.

The extent of cavitation erosion or pitting depends on a number of factors like presence of foreign materials in the liquid, liquid temperature, age of equipment and velocity of the collapsing bubble.

Mechanical Deformation

Apart from erosion of pump parts, in bigger pumps, longer duration of cavitation condition can result in unbalancing (due to un-equal distribution in bubble formation and collapse) of radial and axial thrusts on the impeller. This unbalancing often leads to following mechanical problems:

• bending and deflection of shafts,
• bearing damage and rubs from radial vibration,
• thrust bearing damage from axial movement,
• breaking of impeller check-nuts,
• seal faces damage etc.

These mechanical deformations can completely wreck the pump and require replacement of parts. The cost of such replacements can be huge.

Cavitation Corrosion

Frequently cavitation is combined with corrosion. The implosion of bubbles destroys existing protective layers making the metal surface permanently activated for the chemical attack. Thus, in this way even in case of slight cavitation it may lead to considerable damage to the materials. The rate of erosion may be accentuated if the liquid itself has corrosive tendencies such as water with large amounts of dissolved oxygen to acids.

Cavitation- The Pump Heart Attack

Thus fundamentally, cavitation refers to an abnormal condition inside the pump that arises during pump operation due to formation and subsequent collapse of vapor filled cavities or bubbles inside the liquid being pumped. The condition of cavitation can obstruct the pump, impair performance and flow capacity, and damage the impeller and other sensitive components. In short, Cavitation can be termed as "the heart attack of the pump".

References

1. " New Monitoring Systems Warns of Cavitation and Low Flow Instabilities", Pumps and Systems Magazine, April 1996, Robert A. Atkins, Chung E.Lee, Henry F.Taylor
2. "Understanding Pump Cavitation", Chemical Processing, Feb 1997, W.E. Nelson
3. "Centrifugal pumps operation at off-design conditions", Chemical Processing April, May, June 1987, Igor J. Karassik {parse block="google_articles"}
4. "Understanding NPSH for Pumps", Technical Publishing Co. 1975, Travis F. Glover
5. "Centrifugal Pumps for General Refinery Services", Refining Department, API Standard 610, 6th Edition, January 1981
6. "Controlling Centrifugal Pumps", Hydrocarbon Processing, July 1995, Walter Driedger
7. "Don't Run Centrifugal Pumps Off The Right Side of the Curve", Mike Sondalini
8. "Pump Handbook", Third Edition, Igor j. Karassik, Joseph P.Messina, Paul cooper Charles C.Heald
9. "Centrifugal Pumps and System Hydraulics", Chemical Engineering, October 4, 1982, pp. 84-106. , Karassik, I.J.,
10. Unit Operations of Chemical Engineering (5th Edition), McGraw-Hill, 1993, pp. 188-204. , McCabe, W.L., J.C. Smith, and P. Harriott,
11. "CAVISMONITOR: Cavitation Monitoring In Hydraulic Machines With Aid Of A Computer Aided Visualization Method", Bernd Bachert, Henrik Lohrberg, Bernd Stoffel Laboratory for Turbomachinery and Fluid Power Darmstadt University of Technology Magdalenenstrasse 4, 64289 Darmstadt, Germany
12. "The Hydraulic Pump Inlet Condition: Impact on Hydraulic Pump Cavitation Potential", G.E. Totten and R.J. Bishop, Jr.Union Carbide Corporation Tarrytown, NY
13. "Study of Cavitation Collapse Pressure and Erosion, Part I: A Method for Measurement of Collapse Pressure", Wear, 1989, Vol. 133, p.219-232, T. Okada, Y. Iwai and K. Awazu,
14. "Key Centrifugal Pump Parameters and How They Impact Your Applications" Part 1 Pumps and Systems: They Go Together, Doug Kriebel, PE, Kriebel Engineered Equipment
15. "How to compute Net Positive Suction Head for centrifugal pumps". J. J. Paugh, P.E.Vice President, Engineering, Warren Pumps Inc.
16. "New Monitoring System Warns of Cavitation and Low-Flow Instabilities", APRIL 1996 PUMPS AND SYSTEMS MAGAZINE, Robert A. Atkins, Chung E. lee and Henry F. Taylor
17. "Detecting Cavitation in Centrifugal Pumps", Experimental Results of the Pump Laboratory, Jeremy Jensen Project Engineer, Bentley Rotor Dynamics Research Corporation

Uniform Attack

Figure 1: Uniform Corrosion Attack

Galvanic Corrosion

Figure 2: Galvanic Corrosion

Crevice Corrosion

Figure 3: Crevice Corrosion

Pitting

Figure 4: Pitting Corrosion

Intergranular Corrosion

Figure 5: Intergranular Corrosion

Selective Leaching

Figure 6: Example of Selective Leaching

Erosion-Corrosion

Figure 7: Example of Erosion-Corrosion

Stress Corrosion

Figure 8: Stress Corrosion Cracking

References

• Callister, William D., Materials Science and Engineering, 3rd Ed., Wiley, New York, 1985
  
• InterCorr.com website
  
• NASA website
  

Crystals are grown in many shapes, which are dependent upon downstream processing or final product requirements.  {parse block="google_articles"}Crystal shapes can include cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic, and trigonal.  In order for crystallization to take place a solution must be "supersaturated".   Supersaturation refers to a state in which the liquid (solvent) contains more dissolved solids (solute) than can ordinarily be accomodated at that temperature.

Understanding the Basics of Crystallization

As with any separation method, equilibrium plays an important role.  Below is a general solubility curve for a solid that forms hydrate (a compound that has one or more water molecules attached) as it cools.

In Figure 1, X may be any solid that can form hydrates such as Na₂S₂O₃.  The number of hydrate molecules shown in Figure 1 is strictly arbitrary and will vary for each substance.

Figure 1: Example of a Solubility Curve

 So how do you grow crystals?  Let's consider an example that is fairly easy to envision.  Take a pot of boiling water and add table salt while stirring to make a water-salt solution.  Continue adding salt until no more salt will dissolve in the solution (this is a saturated solution).  Now add one final teaspoon of salt.  The salt that will not dissolve will help the first step in crystallization begin.  This first step is called "nucleation" or primary nucleation.  The salt resting at the bottom of the pot will provide a site for nucleation to occur.

On an industrial scale, a large supersaturation driving force is necessary to initiate primary nucleation.  The initiation of primary nucleation via this driving force is not fully understood which makes it difficult to model (experiments are the best guide).  Usually, the instantaneous formation of many nuclei can be observed "crashing out" of the solution.  You can think of the supersaturation driving force as being created by a combination of high solute concentration and rapid cooling.  In the salt example, cooling will be gradual so we need to provide a "seed" for the crystals to grow on.   In continuous crystallization, once primary nucleation has begun, the crystal size distribution begins to take shape.  Think about our salty water, as you look at Figure 2 describing the progression of crystallization.

 The second chief mechanism in crystallization is called secondary nucleation.  In this phase of crystallization, crystal growth is initiated with contact.  The contact can be between the solution and other crystals, a mixer blade, a pipe, a vessel wall, etc.  This phase of crystallization occurs at lower supersaturation (than primary nucleation) where crystal growth is optimal.   

Figure 2: Progression of Crystallization

Again, no complete theory is available to model secondary nucleation and it's behavior can only be anticipated by experimentation.  Mathematic relationships do exist to correlate experimental data.  However, correlating experimental data to model crystallization is time consuming and often considered extreme for batch operations, but can easily be justified for continuous processes where larger capital expenditures are necessary.  For batch operations, only preliminary data measurements are truly necessary.

We've discussed how crystallization occurs once supersaturation is reached, but how do we reach supersaturation?  We have already covered one such method in our salt crystallization example.  Since the solubility of salt in water decreases with decreasing temperature, as the solution cools, its saturation increases until it reaches supersaturation and crystallization begins (Figure 3).  Cooling is one of the four most common methods of achieving supersaturation.  It should be noted that cooling will only help reach supersaturation in systems where solubility and temperature are directly related.  Although this is nearly always the case, there are exceptions.  In Figure 3, you'll note that Ce₂(SO₄)₃ actually becomes less soluble in water at higher temperatures. 

Figure 3: Solubilities of Several Solids

The four most common methods of reaching supersaturation in industrial processes are:

1. Cooling (with some exceptions)
2. Solvent Evaporation
3. Drowning
4. Chemical Reaction

In an industrial setting, the solute-solvent mixture is commonly referred to as the "mother liquor".

Drowning describes the addition of a nonsolvent to the solution which decreases the solubility of the solid.  A chemical reaction can be used to alter the dissolved solid to decrease its solubility in the solvent, thus working toward supersaturation.  Each method of achieving supersaturation has its own benefits.  For cooling and evaporative crystallization, supersaturation can be generated near a heat transfer surface and usually at moderate rates.  Drowning or reactive crystallization allows for localized, rapid crystallization where the mixing mechanism can exert significant influence on the product characteristics.

Equipment Used in Crystallization

Tank Crystallizers

This is probably the oldest and most basic method of crystallization.  In fact, the "pot of salt water" is a good example of tank crystallization.  Hot, saturated solutions are allowed to cool in open tanks.  {parse block="google_articles"}After crystallization, the mother liquor is drained and the crystals are collected.  Controlling nucleation and the size of the crystals is difficult.   The crystallization is essentially just "allowed to happen".  Heat transfer coils and agitation can be used.  Labor costs are high, thus this type of crystallization is typically used only in the fine chemical or pharmaceutical industries where the product value and preservation can justify the high operating costs.

Scraped-Surface Crystallizers

An example may be the Swenson-Walker crystallizer consisting of a trough about 2 feet wide with a semi-circular bottom.  The outside is jacketed with cooling coils and an agitator blade gently passes close to the trough wall removing crystals that grow on the vessel wall.

Forced Circulating Liquid Evaporator-Crystallizer

Just as the name implies, these crystallizers combine crystallization and evaporation, thus the driving forces toward supersaturation.  The circulating liquid is forced through the tubeside of a steam heater.  The heated liquid flows into the vapor space of the crystallization vessel.  Here, flash evaporation occurs, reducing the amount of solvent in the solution (increasing solute concentration), thus driving the mother liquor towards supersaturation.  The supersaturated liquor flows down through a tube, then up through a fluidized area of crystals and liquor where crystallization takes place via secondary nucleation.  Larger product crystals are withdrawn while the liquor is recycled, mixed with the feed, and reheated.

Figure  4: Forced Circulating Liquid Evaporator-Crystallizer

Circulating Magma Vacuum Crystallizer

In this type of crystallizer, the crystal/solution mixture (magma) is circulated out of the vessel body.  The magma is heated gently and mixed back into the vessel.  A vacuum in the vapor space causes boiling at the surface of the liquid.  The evaporation causes crystallization and the crystals are drawn off near the bottom of the vessel body.

Figure 5: Circulating Magma Vacuum Crystallizer

References

1. Price, Chris J., "Take Some Solid Steps to Improve Crystallization", Chemical Engineering Progress, September 1997, p. 34.
2. Geankoplis, Christie J., Transport Processes and Unit Operations, 3rd Ed., Prentice Hall, New Jersey, 1993, ISBN: 0-13-930439-8
3. Brown, Theodore L., Chemistry: The Central Science, 5th Ed., Prentice Hall, New Jersey, 1991, ISBN: 0-13-126202-5
4. Swenson Process Equipment web site at http://www.swensontechnology.com/

Types of Cooling Towers

Figure 1: Closed Loop Cooling Tower System

Mechanical Draft Towers

Figure 2: Mechanical Draft Counterflow Tower

Figure 3: Mechanical Draft Crossflow Tower

Cooling Tower Theory

Figure 4: Water Drop with Interfacial Film

Eq. (1)

Eq. (2)

Eq. (3)

The tower characteristic value can be calculated by solving Equation 1 with the Chebyshev numberical method:

Eq. (4)

Figure 5: Graphical Representation of the Tower Characteristic

Figure 6: Adjusted Hot Water Temperature

• Increase in the length of line CD, and a CD line shift to the right
  
• Increases in hot and cold water temperatures
  
• Increases in range and approach areas
  

Preliminary Cooling Tower Design

• A change in wet bulb temperature (due to atmospheric conditions) will not change the tower characteristic (KaV/L)
  
• A change in the cooling range will not change KaV/L
  
• Only a change in the L/G ratio will change KaV/L
  

Figure 7: A Typical Set of Tower Characteristic Curves

• Plant engineer defines the cooling water flowrate, and the inlet and outlet water temperatures for the tower.
  
• Manufacturer designs the tower to be able to meet this criteria on a "worst case scenario" (ie. during the hottest months). The tower characteristic curves and the estimate is given to the plant engineer.
  
• Plant engineer reviews bids and makes a selection
  

Other Design Considerations

• Cooling range
  
• Approach to wet bulb temperature
  
• Mass flowrate of water
  
• Web bulb temperature
  
• Air velocity through tower or individual tower cell
  
• Tower height
  

Operation Considerations

Water Makeup

Cold Weather Operation

References

• The Standard Handbook of Plant Engineering, 2nd Edition, Rosaler, Robert C., McGraw-Hill, New York, 1995
  
• Perry's Chemical Engineers' Handbook, 6th Edition, Green, Don W. et al, McGraw-Hill, New York, 1984
  

Asking the Right Questions

Is there a phase change involved?

How many zones are there in my system?

Figure 1: Zones Analysis

What are the flowrates and operating pressures involved in my system?

What are the physical properties of the streams involved?

What are the allowable pressure drops and velocities in the exchanger?

What is the heat duty of the system?

What is the estimated area of the exchanger?

What geometric configuration is right for my exchanger?

Now that I have a geometry in mind, what is the actual overall heat transfer coefficient?

What is the actual area of the exchanger using the 'actual' heat transfer coefficient?

Enter the Calculation Loop

• ZONED ANALYSIS
  
• ACCURACY OF INITIAL OVERALL HEAT TRANSFER COEFFICIENT
  

As you can see it is a rigorous and costly process that must be followed to get a new drug to your medicine cabinet.  It is estimated on average a company may spend $300 to $400 million dollars to get just one drug to your medicine cabinet.  It is not hard to see why some new medicines on the market are so expensive.  Let's take a look at the steps involved in developing a new drug.{parse block="google_articles"}

Preclinical Testing

This is the initial phase of the testing that begins in the laboratory.  A pharmaceutical company will conduct studies in the lab and on animals to show the biological activity of the compound against a targeted disease. The compound is then evaluated for safety.  These tests take about 3 1/2 to 4 years to complete.   The chemical engineer would be heavily involved in this phase of  drug development.

Investigational New Drug Application (IND)

After the above preclinical testing is completed the company then files an IND with the FDA to begin testing the drug in people.  The IND will become effective if the FDA does not disprove it within 30 days. The IND will show results of previous experiments, how, where and by whom the new studies will be conducted.   The IND also looks at the chemical structure of the compound, how it works in the body, and any toxic effects found in the animal studies. The IND will also look at how the compound is manufactured.   The IND must be reviewed and approved by the Institutional Review Board where the study will be conducted, and progress reports on clinical trials must be submitted at least annually to the FDA.

Clinical Trials, Phase I, II, & III

After the IND has not been disapproved within 30 days, then the next phase of testing begins, which is the clinical trials.

Phase I  

This phase of the testing takes about a year and involves about 20 to 80 normal, healthy volunteers. The tests study a drug's safety profile, including the safe dosage range. The studies also determine how a drug is absorbed, distributed, metabolized and excreted, and the duration of its action. 

Phase II 

In this phase, controlled studies of approximately 100 to 300 volunteer patients (people with the disease) assess the drug's effectiveness.  This phase normally takes about 2 years.

Phase III 

This phase involves 1,000 to 3,000 patients in clinics and hospitals. Physicians monitor patients closely to determine the efficacy and identify adverse reactions. This phase lasts about three years. 

New Drug Application (NDA)

After all of the clinical trials mentioned above are completed, then the company analyzes the data and files an NDA with the FDA if the data successfully demonstrates safety and effectiveness. The NDA is usually about 100,000 pages or more and contains all of the scientific information that the company has gathered. By law, the FDA is allowed six months to review an NDA.  In most cases the time from first submission of an NDA and final FDA approval usually exceeds six months. The average NDA review time for new molecular entities approved in 1992 was 29.9 months.{parse block="google_articles"}

Approval

Once the FDA approves the NDA, the new medicine becomes available for physicians to prescribe.  The company must continue to submit periodic reports to the FDA, including any cases of adverse reactions and appropriate quality control records.  The FDA requires some medicines to have additional studies (Phase IV) to evaluate the long-term effects of the drugs.

After reading the above steps in the development of a new drug, it is not hard to see why drugs cost so much when they finally do get to our medicine cabinets.  Many people in the pharmaceutical industry   are looking for ways to expedite the development of drugs and to decrease some of the money put into this development.  One resource that is being utilized in the development of new drugs is bioinformatics.  The Bioinformatics industry is still in its infancy stages, but it has started to change the way drug development has emerged since 1998.  Bioinformatics helps to take some of the fragmentation out of the development of new drugs.  Most drug development has been more or less by trial and error.  Bioinformatics uses information technology to be able to develop large databases and algorithms which help in the development of new drugs.

An example of this is the European Bioinformatics Industry (EBI).  The EBI serves researchers in molecular biology, genetics, medicine and agriculture from academia.  The EBI also serves the agricultural, biotechnology, chemical and pharmaceutical industries.  The EBI is able to serve these researchers and industries by building, maintaining and making available databases and information services that relate to molecular biology.  The EBI also carries out research in bioinformatics and computational molecular biology.  More information about EBI can be obtained from going to their website which is as follows: http://www.ebi.ac.uk/Information/index.html  

For those of you who are interested in learning more about the pharmaceutical pipeline (an industry term used for the research and development process of creating new drugs), Searle's Research and Development Department has a web site for you.  This web site actually takes you step by step in the development of a new drug.  The web site is as follows: http://www.searlehealthnet.com/pipeline.html   On this web site you can select from a few diseases such as cancer, cardiovascular related diseases, or arthritis as your primary target to be able to develop a new drug for. 

If the virtual formulation of a new drug is not enough, then all of you are invited to visit the following site from John Hopkins University, in which you can actually be the participant in a research study.  Most of these studies involve the development or refinement of drugs but some don't involve any drugs at all.   There is also a monetary incentive involved with some studies.  The web site is as follows:  http://www.jhbmc.jhu.edu/studies/index.html   Due to geographic limitations, it may be difficult to be able to attend the clinic visits that are required.  To be able to find out research studies in your local area, check with the nearest teaching/university based hospital and I am sure they would be more than happy to get you involved in a research study.

In summation, it is easy to see the vital role that chemical engineers play in the development of new drugs.  It takes the knowledge and skill of many disciplines to formulate a new drug.  When all of these discipline work together, it helps to expedite the formation of new drugs to help alleviate the effects of diseases for people around the world. 

Through the simplicity of its construction (Figure 1), the steam-jet ejector provides many years of troublefree operation. {parse block="google_articles"}When a problem does occur, many plant personnel do not have the experience to effectively troubleshoot an ejector system, and precious production time is lost.

For example, a loss of vacuum in a multistage ejector system might have many plant personnel disassembling the first-stage ejector booster, on the assumption that one must check a unit from inlet to outlet. In fact (as will be shown later in this article), this is the last place to look. Fortunately, downtime can be kept to a minimum when a logical sequence of steps -- a checklist -- is followed to locate the source of trouble.

 Ejector Basics

Figure 1: Typical Ejector Arrangement

Ejectors can be classified as single-stage or multistage. Multistage ejectors may be further divided into condensing or noncondensing types. The single-stage ejector, the simplest and most common type, is generally recommended for pressures ranging from atmospheric pressure (30 in. Hg absolute) to 3 in. Hg abs. Discharge is typically at or near atmospheric pressure. The boxed section of Figure 1 shows a single-stage system. The effects of injected steam on process vapors is shown in figure 4. Multistage noncondensing ejectors (MNEs) are used to produce suction pressures lower than 3 or 4 in. Hg abs. Steam consumption in an MNE is relatively high. Each successive stage is required to handle the load plus the motive steam from the previous stage. MNEs are frequently used when low first cost is more important than long-range economy. They are also used for intermittent service or when condensing water is not available. MNEs are usually two-stage, although six-stage units have been used successfully.

Multistage condensing ejectors (MCEs) are available in two through six stages. Intercondensers (surface or direct-contact) between stages condense steam from the preceding stage, reducing the load to be compressed in the succeeding stage. A multistage system is shown in Figure 1.

Four-, five- and six-stage ejectors are used to achieve suction pressures as low as 5 µm Hg abs. Under such vacuum conditions, pressure between the preliminary stages is too low to permit condensation of ejector steam, and only the final two stages are fitted with condensers. MCEs remove condensable vapor ahead of a given ejector stage. They also permit use of a smaller ejector, and a reduction in the amount of steam required. Condenser nomenclature is determined by the corresponding operating conditions and functions.

Precondensers are used when the absolute pressure of the process is sufficiently high to allow condensation at the temperature of the available water supply. Noncondensables are removed from the precondenser by one or more ejector stages. Condensers or inter-condensers liquefy process vapor and motive steam from one or more preceding booster ejectors. Aftercondensers condense steam discharging from the last-stage ejector, generally at atmospheric pressures.

There are two basic types of condensers -- direct-contact and surface-contact. In direct-contact (countercurrent, barometric design) condensers, cooling water is mixed directly with the vapor to be condensed, then discharged to atmosphere through a barometric leg or tailpipe of sufficient length to overcome the atmospheric pressure. A means of cleaning up or otherwise disposing the water that has become contaminated by process material is often required. The surface-contact condenser permits main-condenser cooling water to be used as cooling water through inter- and aftercondensers, for energy and process-water conservation.

Where to Start

When a vacuum problem arises there are several preliminary checks that should be made on an ejector system before components are disassembled. First, is the system design data readily available? Most ejector systems are custom-designed to operate at a specified vacuum, given process loads, minimum available steam pressure, maximum steam temperature, maximum discharge pressure and maximum water temperature. It is impossible to evaluate the complete system unless the manufacturer's design parameters are known.

{parse block="google_articles"}A data sheet can be obtained from the manufacturer of the ejector system and should list the design vacuum, capacity, interstage ejector vacuums, motive steam pressure and temperature, condenser water-inlet and -outlet temperatures, and discharge pressure. Critical dimensions such as the diameters of the ejector nozzle orifice and the diffuser bore should also be know.

Once the design data are located, there is an ordered series of steps to take in isolating ejector problems. One should check:

• Gauges
• Steam
• Water
• Process loads
• Field report and process logs

Pay Attention to Instruments

When troubleshooting the ejector system, accurate pressure and temperature measurements are needed to quickly locate the source of the problem. Therefore, a check of the system's instrumentation is a necessity. All vacuum, pressure, and temperature gages should be calibrated or replaced. A malfunctioning vacuum gage may be found to be the entire vacuum "problem."

If the vacuum gage is several feet or more from the ejector system, check the line running from the system to the gage for air leakage. It would take a very small amount of air leakage in an instrument vacuum line to throw off the measurement. If leakage is suspected, connect the test gage directly to the ejector and compare vacuum measurements. If there is a valve in the vacuum line, close it and observe the vacuum line, close it and observe the vacuum gage. If it slowly loses vacuum, air leakage is occurring.

Figure 2. Steam-jet Ejectors Often Provide a Compact Means of Delivering Vacuum.

Typically, an absolute mercury manometer is used for measuring the vacuum in the Y and Z stages (Figure 2). It can be flooded with water and still give a relatively accurate reading.

Replacement mercury U-tubes are also inexpensive, and are available from various suppliers. Mercury-free units are also available, and are typically used for the higher-vacuum ejectors such as W or X stages. There are also many manufacturers of electronic vacuum gages that offer very accurate and portable instruments. The gages are well worth the investment and should be kept in stock only to be used when troubleshooting ejector systems.

Steam-pressure gages should be located on the steam chest of the ejectors or as close to the unit as possible. It is important to know the actual operating steam pressure since an ejector of critical-flow design (suction pressure less than half discharge pressure) will not operate properly when even a few psi below its design motive pressure. Compound steam pressure gages are recommended since they will not be damaged when exposed to vacuum.

Steam

Motive steam plays probably the most important role in the operation of a steam jet ejector. Since internal dimensions are fixed, the ejector is designed for only one steam condition. When the steam condition changes there will be a change in the operation and efficiency of the ejector.

{parse block="google_articles"}In a critical-flow ejector a decrease in steam pressure of just a few psi will result in a broken or unstable vacuum. An increase in steam pressure above design will not have a noticeable effect in the operation of an ejector unless the increase is significant (>25%).

Besides wasting steam, excess motive pressure tends to choke the venturi with steam, thereby decreasing the suction capacity of the ejector. Note too that the performance of ejectors designed for saturated steam will be adversely affected if operated with super-heated steam.

The specific volume of steam increases with increasing temperature, which may require an increase in pressure to maintain required steam flow. Otherwise, as in the case of low steam pressure, the manufacturer must be consulted for a redesign of the ejectors.

Excess moisture in steam is one of the most common problems found in ejectors. Wet steam causes poor performance and, depending on the degree of wetness, can permanently damage an ejector in a very short period of time. A steam quality of less than 2% moisture is tolerable with most moderate vacuum systems. However, ejectors designed for a vacuum of 5 mm Hg abs or less should have steam that is completely dry or with a few degrees of superheat.

A telltale sign of wet steam is a fluttering needle on a steam pressure gage during operation. But the only sure way to determine quality of steam is to test it with a throttling calorimeter. This is a constant-enthalpy device that measures steam pressure and temperature. When used in combination with a Mollier chart, a reading of steam quality is obtained.

If steam is found to be wet, a steam separator should be installed in the steam line as close to the ejector as possible. Keeping all steam piping, and the steam separator, completely insulated will also help prevent the formation of wet steam.

Water

Multiple-stage ejector systems will normally include condensers between some or all stages. Condenser designs are based on maximum water temperature and available flow. When inlet water temperature increases above design maximum, loads to the following stage increase, resulting in a poorer vacuum at that stage. If the affected stage is the last (Z) stage, then the vacuums of all the preceding stages could also be affected.

Figure 3: Ejector Profiles (expand for more info)

In direct-contact condensers, high or low water flowrates can cause problems in the vacuum system. High water flow could flood the condenser, increasing pressure drop, and therefore, the back pressure on the stage discharging into it. Low water flow may not be distributed properly, allowing condensable load to bypass into the following ejector and resulting in a poor vacuum.

Process Loads

A change in process load will have a direct effect on the ejector system. Ejectors operate over a unique capacity curve, and any increase in load will result in a higher absolute pressure. An increase in noncondensables will travel through the system, affecting the following ejector stages. Discharge pressures of each stage will increase to the point of a breakdown in operation. As in the case of a changed steam condition, a change in process load will require redesign by the manufacturer, if design vacuum is to be maintained.

Check the Logs

Manufacturers' field service reports or process logs may offer clues to present operational problems. the symptoms of a vacuum problem may be similar to a past problem outlined, with solutions, in a service report. Process logs may also indicate problems with steam pressure or changes in process conditions that will have a direct effect on the vacuum system.

Now Look at the Process

If the preliminary checklist is completed with no obvious problems found, the next step is to determine whether the problem lies in the ejector system or the process. The steps remaining to be considered are: no-load vacuum test (single- or multistage) and an internal inspection.

The best way to determine if the vacuum problem lies in the ejector system or the process is to isolate and test the ejector separate from the process. The standard method of testing an ejector is to attach a blank, or blind flange, on the suction flange of the ejector and measure the vacuum at no-load conditions. A stable no-load vacuum is more difficult for an ejector to reach than a point under load conditions, simply because there is a greater suction-to-discharge pressure differential.

Figure 4: A Piccolo Gauge is Used to Check Vacuum Quality

If the no-load vacuum measures the same as the manufacturer's test, then it is reasonably safe to assume that the ejector is working at its design load point. The problem may lie upstream from the suction of the ejector- possibly an increase in air leakage or process load. It should be noted that unless specified, an ejector may not have a stable vacuum at no-load even though it works at its design load.

To test an ejector at its design load point involves metering the design load into the suction of the ejector. Use a calibrated orifice or a series of orifices (such as can be found on an instrument known as a piccolo -- Figure 5), and then compare the measured vacuum to the design vacuum. A curve can be plotted and compared with the manufacturer's. This procedure should be considered only after all other tests are exhausted. (The manufacturer should be consulted for the proper field testing procedure if a test under design load conditions is desired.)

If the ejector does not obtain the manufacturer's tested no-load vacuum, the ejector should then be disassembled and internally inspected. No-load testing is easily accomplished on a single-stage ejector system, but a multistage ejector system must be evaluated by checking the last stage first.

Multistage, No Load Vacuum

Typically, a multistage ejector system is started up backwards from the last (Z) stage to the first. The Y stage cannot operate properly until the Z stage is working, the X stage will not work unless the Y and Z are operating, and so on.

{parse block="google_articles"}Troubleshooting a multistage ejector system should also proceed in this back-to-front order. Check the vacuum of each stage during process load conditions, and compare it to its design value. When the measured vacuum of a stage is worse than its design, the cause of the problem at that stage must be found and corrected before proceeding any further.

The next step is to performance-test the stage in question by checking its no-load vacuum. For example, if the stage being checked is the Y stage of a three-stage ejector system, a blank should be installed on the Y suction flange. Since the Y stage is designed to discharge to a vacuum created by the Z stage, the Z stage, and intercondenser if present, must operate simultaneously during this test.

With the Y stage steam valved off, first check and record the Z stage no-load vacuum to be sure it is meeting the manufacturer's tested value. Then, with the vacuum gage still connected to the Z stage, turn the Y stage steam on. If the Z stage vacuum steadily falls off, the intercondenser is most likely the cause of trouble and should be inspected.

As mentioned in the preliminary checklist, a condenser temperature rise much greater or less than design may be an indication of a water-flow problem. A water-flow problem can result in a higher condenser temperature and an overloading of the following stage with uncondensed vapor. In this case, as the Z stage falls off, the Y stage vacuum would follow.

Examples of direct-contact condenser problems include: a blocked tailpipe, air leakage into tailpipe, damaged water distributor, or a plugged water nozzle. Surface condenser problems include: a blocked drain, air leakage into tailpipe, or split or fouled tubes.

If the Z stage vacuum is within specifications, move the vacuum gage to the Y stage. If the Y stage vacuum measures exactly the same as that of the Z stage, a blocked Y stage nozzle may be the cause. However, at this point, if the Y stage vacuum does not measure reasonably close to the manufacturer's tested no-load value, the stage should be disassembled for internal inspection.

Finding the Y and Z stage vacuums within specifications, remove the blind flange from the Y stage suction and repeat the procedure at the X stage. It is important to remember that each stage must meet its design vacuum before continuing the testing.

At times it may be impractical to make and install a blind flange on the suction connection of an ejector due to the size of the unit. In most cases, however, these larger stages will be the W or X. If the no-load testing has ruled out the Y and Z stages and the condensers ass possible causes of the vacuum problem, and internal inspection of these larger stages may be the more practical step to follow.

Internal Inspection

There are several things to look for when performing internal inspection of an ejector. Usually any kind of corrosion or erosion that is obvious to the eye and touch will affect the performance of an ejector. An indication of wet steam will show as lines ("wiredrawing") etched up and down the inside of the steam nozzle. The point along the diameter where the steam contacts the venturi is another location that may be gouged due to wet steam.

Steam leaking around the nozzle puts an artificial load on that stage, resulting in poor vacuum. Leakage of this sort should be noticeable as a discoloration where the nozzle seats on the steam chest, or as erosion of the nozzle threads. A process that causes corrosion or buildup of material on the internals of an ejector will also effect the performance of that unit.

Critical dimensions such as the nozzle orifice or venturi bore diameter, obtained from the manufacturer, will enable a measurement of dimensions to determine extent of wear. Part numbers of the various ejector components should be checked to ensure they are in the right unit. Many ejector parts, and complete stages, are physically interchangeable and care must be taken not to mix them.

Keep Spares on Hand

At a minimum, keep at least the following components in stock:

• One steam nozzle for every single nozzle ejector stage
• One diffuser for every stage, at least in sizes through 6 in. -- higher, if continuity of service is critical

If continuity of service is important to a process, keep a spare steam nozzle in stock for every size ejector in the system. Spare diffusers are also worthwhile to keep in stock, especially for smaller systems. While it is theoretically possible for the plant engineer to recondition these parts, the practice is not recommended because critical dimensions may be altered.

Since most nozzles are relatively inexpensive they should be considered sacrificial; if wear is evident they may be discarded and easily replaced. A complete Z stage should be kept in stock for important systems in critical operations.

If these simple tips fail, don't despair. Check the nameplate and call the manufacturer. A condition may be new to you, but chances are the manufacturer has seen it, and corrected it, many times before. Since troubleshooting an ejector system is quite straightforward, suppliers can usually work with you over the phone to get the problem corrected. Experienced service people estimate that at least 50% or more of the troubles referred to them can be solved over the phone.

Of all vacuum-producing devices, the steam-jet ejector is the most forgiving. Occasional inspection, replacement of parts, and adherence to design conditions will keep it operating reliable for many years. Knowledge of these simple procedures for avoiding trouble, and locating it if it does occur, will save time and product in you plant.

These properties are entered into a computer program or spreadsheet along with some pipe physical data (pipe schedule and roughness factor) {parse block="google_articles"}and out pops a series of line sizes with associated Reynolds Number, velocity, friction factor and pressure drop per linear dimension. The pipe size is then selected based on a compromise between the velocity and the pressure drop. With the line now sized and the pressure drop per linear dimension determined, the pressure loss from the inlet to the outlet of the pipe can be calculated.

Calculating Pressure Drop

The most commonly used equation for determining pressure drop in a straight pipe is the Darcy Weisbach equation. One common form of the equation which gives pressure drop in terms of feet of head is given below:

Eq. (1)

The term is commonly referred to as the Velocity Head.

Another common form of the Darcy Weisbach equation that is most often used by engineers because it gives pressure drop in units of pounds per square inch (psi) is:

Eq. (2)

To obtain pressure drop in units of psi/100 ft, the value of 100 replaces L in Equation 2.

The total pressure drop in the pipe is typically calculated using these five steps.

1. Determine the total length of all horizontal and vertical straight pipe runs.
2. Determine the number of valves and fittings in the pipe. For example, there may be two gate valves, a 90^o elbow and a flow thru tee.
3. Determine the means of incorporating the valves and fittings into the Darcy equation. To accomplish this, most engineers use a table of equivalent lengths. This table lists the valve and fitting and an associated length of straight pipe of the same diameter, which will incur the same pressure loss as that valve or fitting. For example, if a 2" 90^o elbow were to produce a pressure drop of 1 psi, the equivalent length would be a length of 2" straight pipe that would also give a pressure drop of 1 psi. The engineer then multiplies the quantity of each type of valve and fitting by its respective equivalent length and adds them together.
4. The total equivalent length is usually added to the total straight pipe length obtained in step one to give a total pipe equivalent length.
5. This total pipe equivalent length is then substituted for L in Equation 2 to obtain the pressure drop in the pipe.

See any problems with this method?

Relationship Between K, Friction Factor, and Equivalent Length

The following discussion is based on concepts found in reference 1, the CRANE Technical Paper No. 410. It is the author's opinion that this manual is the closest thing the industry has to a standard on performing various piping calculations. If the reader currently does not own this manual, it is highly recommended that it be obtained.

As in straight pipe, velocity increases through valves and fittings at the expense of head loss. This can be expressed by another form of the Darcy equation similar to Equation 1:

Eq. (3)

When comparing Equations 1 and 3, it becomes apparent that:

Eq. (4)

K is called the resistance coefficient and is defined as the number of velocity heads lost due to the valve or fitting. It is a measure of the following pressure losses in a valve or fitting:{parse block="google_articles"}

• Pipe friction in the inlet and outlet straight portions of the valve or fitting
• Changes in direction of flow path
• Obstructions in the flow path
• Sudden or gradual changes in the cross-section and shape of the flow path

Pipe friction in the inlet and outlet straight portions of the valve or fitting is very small when compared to the other three. Since friction factor and Reynolds Number are mainly related to pipe friction, K can be considered to be independent of both friction factor and Reynolds Number. Therefore, K is treated as a constant for any given valve or fitting under all flow conditions, including laminar flow. Indeed, experiments showed¹ that for a given valve or fitting type, the tendency is for K to vary only with valve or fitting size. Note that this is also true for the friction factor in straight clean commercial steel pipe as long as flow conditions are in the fully developed turbulent zone. It was also found that the ratio L/D tends towards a constant for all sizes of a given valve or fitting type at the same flow conditions. The ratio L/D is defined as the equivalent length of the valve or fitting in pipe diameters and L is the equivalent length itself.

In Equation 4, f therefore varies only with valve and fitting size and is independent of Reynolds Number. This only occurs if the fluid flow is in the zone of complete turbulence (see the Moody Chart in reference 1 or in any textbook on fluid flow). Consequently, f in Equation 4 is not the same f as in the Darcy equation for straight pipe, which is a function of Reynolds Number. For valves and fittings, f is the friction factor in the zone of complete turbulence and is designated f_t, and the equivalent length of the valve or fitting is designated L_eq. Equation 4 should now read (with D being the diameter of the valve or fitting):

Eq. (5)

The equivalent length, L_eq, is related to f_t, not f, the friction factor of the flowing fluid in the pipe. Going back to step four in our five step procedure for calculating the total pressure drop in the pipe, adding the equivalent length to the straight pipe length for use in Equation 1 is fundamentally wrong.

Calculating Pressure Drop, The Correct Way

So how should we use equivalent lengths to get the pressure drop contribution of the valve or fitting? A form of Equation 1 can be used if we substitute f_t for f and L_eq for L (with d being the diameter of the valve or fitting):

Eq. (6)

The pressure drop for the valves and fittings is then added to the pressure drop for the straight pipe to give the total pipe pressure drop.

Another approach would be to use the K values of the individual valves and fittings. The quantity of each type of valve and fitting is multiplied by its respective K value and added together to obtain a total K. This total K is then substituted into the following equation:

Eq. (7)

Notice that use of equivalent length and friction factor in the pressure drop equation is eliminated, although both are still required to calculate the values of K¹. As a matter of fact, there is nothing stopping the engineer from converting the straight pipe length into a K value and adding this to the K values for the valves and fittings before using Equation 7. This is accomplished by using Equation 4, where D is the pipe diameter and f is the pipeline friction factor.

How significant is the error caused by mismatching friction factors? The answer is, it depends. Below is a real world example showing the difference between the Equivalent Length method (as applied by most engineers) and the K value method to calculate pressure drop.

An Example

The fluid being pumped is 94% Sulfuric Acid through a 3", Schedule 40, Carbon Steel pipe:

Notes:

1. K values and L_eq/D are obtained from Reference 1.
2. K values and L_eq are given in terms of the larger sized pipe.
3. L_eq is calculated using Equation 5 above.
4. The reducer is really an expansion; the pump discharge nozzle is 1" (Schedule 80) but the connecting pipe is 3". In piping terms, there are no expanders, just reducers. It is standard to specify the reducer with the larger size shown first. The K value for the expansion is calculated as a gradual enlargement with a 30^o angle.
5. There is no L/D associated with an expansion or contraction. The equivalent length must be back calculated from the K value using Equation 5 above.

The line pressure drop is greater by about 4.5 psi (about 62%) using the typical equivalent length method (adding straight pipe length to the equivalent length of the fittings and valves and using the pipe line fiction factor in Equation 1).

One can argue that if the fluid is water or a hydrocarbon, the pipeline friction factor would be closer to the friction factor at full turbulence and the error would not be so great, if at all significant; and they would be correct. However hydraulic calculations, like all calculations, should be done in a correct and consistent manner. If the engineer gets into the habit of performing hydraulic calculations using fundamentally incorrect equations, he takes the risk of falling into the trap when confronted by a pumping situation as shown above.

Another point to consider is how the engineer treats a reducer when using the typical equivalent length method. As we saw above, the equivalent length of the reducer had to be back-calculated using equation 5. To do this, we had to use f_t and K.

Why not use these for the rest of the fittings and apply the calculation correctly in the first place?

Final Thoughts on K Values

The 1976 edition of the Crane Technical Paper No. 410 first discussed and used the two-friction factor method for calculating the total pressure drop in a piping system (f for straight pipe and f_t for valves and fittings). Since then, Hooper² suggested a 2-K method for calculating the pressure loss contribution for valves and fittings. His argument was that the equivalent length in pipe diameters (L/D) and K was indeed a function of Reynolds Number (at flow rates less than that obtained at fully developed turbulent flow) and the exact geometries of smaller valves and fittings. K for a given valve or fitting is a {parse block="google_articles"}combination of two Ks, one being the K found in CRANE Technical Paper No. 410, designated K_Y, and the other being defined as the K of the valve or fitting at a Reynolds Number equal to 1, designated K₁. The two are related by the following equation:

K = K₁ / N_RE + K_? (1 + 1/D)

The term (1+1/D) takes into account scaling between different sizes within a given valve or fitting group. Values for K₁ can be found in the reference article² and pressure drop is then calculated using Equation 7. For flow in the fully turbulent zone and larger size valves and fittings, K becomes consistent with that given in CRANE.

Darby³ expanded on the 2-K method. He suggests adding a third K term to the mix. Darby states that the 2-K method does not accurately represent the effect of scaling the sizes of valves and fittings. The reader is encouraged to get a copy of this article.

The use of the 2-K method has been around since 1981 and does not appear to have "caught" on as of yet. Some newer commercial computer programs allow for the use of the 2-K method, but most engineers inclined to use the K method instead of the Equivalent Length method still use the procedures given in CRANE. The latest 3-K method comes from data reported in the recent CCPS Guidlines⁴ and appears to be destined to become the new standard; we shall see.

Conclusion

Consistency, accuracy and correctness should be what the Process Design Engineer strives for. We all add our "fat" or safety factors to theoretical calculations to account for real-world situations. It would be comforting to know that the "fat" was added to a basis using sound and fundamentally correct methods for calculations.

Questions and Answers

Question #1

Could you please give me in layman terms a better definition for K values. I know that K is defined as "the number of velocity heads lost"...But what exactly does that mean???

Mr. Leckner's reply to this question:

Question #2

It appears that the K values in CRANE TP-410 were established using a liquid (water) flow loop. Is this K value also valid for compressible media systems? (Can a K value be used for both compressible and incompressible service?)

Mr. Leckner's reply to this question:

Question #3

When answering my first question, you stated:  'Velocity of any fluid increases through pipes, valves and fittings at the expense of pressure.'  When you say this, you are talking about compressible (gas) flow right?  For example, in a pipe of constant area, the velocity of a gas would increase as the fluid traveled down the pipe (due to the decreasing pressure).   However, the velocity of a liquid would remain constant as it traveled down the same pipe (even with the decreasing pressure).  Is this a correct statement?

Mr. Leckner's reply to this question:

Question #4

I'm reading the Crane Technical Paper #410 and I have the following
questions/comments:

Page 2-8 of TP 410 states that:
"Velocity in a pipe is obtained at the expense of static head".  This makes sense and Equation 2-1 shows this relationship where the static head is converted to velocity head.  However, there is no diameter associated with this.  So is it correct to say based on equation 2-1 that if you had a barrel of water with a short length of pipe attached to the bottom that discharged to atmosphere, and in this barrel you had 5 feet of water (5' of static head), the resulting water velocity would be 17.94 ft/sec (regardless
of the pipe diameter).

Maybe the real question is how do you use equation 2-1.  Do you have to know the velocity and then you can calculate the headloss?  And why does equation 2-1 and equation 2-3 seem to show headloss equaling two different things?

Also, why does it say that a diameter is always associtated with the K value, when as I mentioned above there is no diameter associated with equation 2-1?

Maybe I'm trying to read into all of this too deeply, but I still do not feel that I fully grasp what page 2-8 is trying to reveal.

Mr. Leckner's reply to this question:

Nomenclature

References

1. Crane Co., "Flow of Fluids through Valves, Fittings and Pipe", Crane Technical Paper No. 410, New York, 1991.
2. Hooper, W. B., The Two-K Method Predicts Head Losses in Pipe Fittings, Chem. Eng., p. 97-100, August 24, 1981.
3. Darby, R., Correlate Pressure Drops through Fittings, Chem. Eng., p. 101-104, July, 1999.
4. AIChE Center for Chemical Process Safety, "Guidelines for Pressure Relief and Effluent Handling systems", pp. 265-268, New York, 1998.

When I think of such rules, two authors come to my mind, Walas and Branan. Dr. Walas' book, Chemical Process Equipment: Selection and Design has been widely used in the process industry and in chemical engineering education for years. Mr. Branan has either helped write or edit numerous books concerning this topic. Perhaps his most popular is Rules of Thumb for Chemical Engineers. Here, I'll share some of these rules with you along with some of my own. Now, be aware that these rules are for estimation and are not necessary meant to replace rigorous calculations when such calculations should be performed. But at many stages of analysis and design, these rules can save you hours and hours.

Download these rules of thumb in MS Excel format.

Physical Properties

** Viscosities of organic liquids vary widely with temperature

Liquid densities vary with temperature to this approximation:

Eq. (1)

Gas densities can be calculated by:

Eq. (2)

The boiling point of water can be approximated as a function of pressure by:

Eq. (3)

Materials of Construction

Compressors and Vacuum Equipment

A. The following chart is used to determine what type of compressor is to be used:

Figure 1: Range Chart for Various Types of Compressors

B. Fans should be used to raise pressure about 3% (12 in water), blowers to raise to less than 2.75 barg (40 psig), and compressors to higher pressures.

C. The theoretical reversible adiabatic power is estimated by:

where:
T₁ is the inlet temperature
R is the gas constant
z₁ is the compressibility
m is the molar flow rate
a = (k-1)/k
k = Cp/Cv

D. The outlet for the adiabatic reversible flow, T₂ = T₁ (P₂ / P₁)a

E. Exit temperatures should not exceed 204 °C (400 °F).

F. For diatomic gases (Cp/Cv = 1.4) this corresponds to a compression ratio of about 4

G. Compression ratios should be about the same in each stage for a multistage unit, the ratio = (Pn / P1) 1/n, with n stages.

H. Efficiencies for reciprocating compressors are as follows:
65% at compression ratios of 1.5
75% at compression ratios of 2.0
80-85% at compression ratios between 3 and 6

I. Efficiencies of large centrifugal compressors handling 2.8 to 47 m3/s (6000-100,000 acfm) at suction is about 76-78%

J. Reciprocating piston vacuum pumps are generally capable of vacuum to 1 torr absolute, rotary piston types can achieve vacuums of 0.001 torr.

K. Single stage jet ejectors are capable of vacuums to 100 torr absolute, two stage to 10 torr, three stage to 1 torr, and five stage to 0.05 torr.

L. A three stage ejector requires about 100 lb steam/lb air to maintain a pressure of 1 torr.

M. Air leakage into vacuum equipment can be approximated as follows:
Leakage = k V(2/3)
where:
k =0.20 for P >90 torr, 0.08 for 3 < P < 20 torr, and 0.025 for P < 1 torr
V = equipment volume in cubic feet
Leakage = air leakage into equipment in lb/h

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Cooling Towers

A. With industrial cooling towers, cooling to 90% of the ambient air saturation level is possible.

B. Relative tower size is dependent on the water temperature approach to the wet bulb temperature:

C. Water circulation rates are generally 2-4 GPM/ft² (81-162 L/min m²) and air velocities are usually 5-7 ft/s (1.5-2.0 m/s){parse block="google_articles"}

D. Countercurrent induced draft towers are the most common. These towers are capable of cooling to within 2 °F (1.1 °C) of the wet bulb temperature. A 5-10 °F (2.8-5.5 °C) approach is more common.

E. Evaporation losses are about 1% by mass of the circulation rate for every 10 °F (5.5 °C) of cooling. Drift losses are around 0.25% of the circulation rate. A blowdown of about 3% of the circulation rate is needed to prevent salt and chemical treatment buildup.

Conveyors

A. Pneumatic conveyors are best suited for high capacity applications over distances of up to about 400 ft. Pneumatic conveying is also appropriate for multiple sources and destinations. Vacuum or low pressure (6-12 psig or 0.4 to 0.8 bar) is used for generate air velocities from 35 to 120 ft/s (10.7-36.6 m/s). Air requirements are usually in the range of 1 to 7 cubic feet of air per cubic foot of solids (0.03 to 0.5 cubic meters of air per cubic meter of solids).

B. Drag-type conveyors (Redler) are completed enclosed and suited to short distances. Sizes range from 3 to 19 inches square (75 to 480 mm). Travel velocities can be from 30 to 250 ft/min (10 to 75 meters/min). The power requirements for these conveyors is higher than other types.

C. Bucket elevators are generally used for the vertical transport of sticky or abrasive materials. With a bucket measuring 20 in x 20 in (500 mm x 500 mm), capacities of 1000 cubic feet/hr (28 cubic meters/hr) can be reached at speeds of 100 ft/min (30 m/min). Speeds up to 300 ft/min (90 m/min) are possible.

D. Belt conveyors can be used for high capacity and long distance transports. Inclines up to 30° are possible. A 24 in (635 mm) belt can transport 3000 ft³./h (85 m³/h) at speeds of 100 ft/min (30.5 m/min). Speeds can be as high as 600 ft/min (183 m/min). Power consumption is relatively low.

E. Screw conveyors can be used for sticky or abrasive solids for transports up to 150 ft (46 m). Inclines can be up to about 20°. A 12 in (305 mm) diameter screw conveyor can transport 1000-3000 ft³./h (28-85 m³/h) at around 40-60 rpm.

Crystallization

A. During most crystallizations, C/C_sat (concentration/saturated concentration) is kept near 1.02 to 1.05

B. Crystal growth rates and crystal sizes are controlled by limiting the degree of supersaturation.

C. During crystallization by cooling, the temperature of the solution is kept 1-2 °F (0.5-1.2 °C) below the saturation point at the given concentration.

D. A generally acceptable crystal growth rate is 0.10 - 0.80 mm/h

Drivers and Power Recovery

A. Efficiencies: 85-95% for motors, 40-75% for steam turbines, 28-38% for gas engines and turbines.

B. Electric motors are nearly always used for under 100 HP (75 kW). They are available up to 20,000 HP (14,915 kW).

C. Induction motors are most popular. Synchronous motors have speeds as low as 150 rpm at ratings above 50 HP (37.3 kW) only. Synchronous motors are good for low speed reciprocating compressors.

D. Steam turbines are seldom used below 100 HP (75 kW). Their speeds can be controlled and they make good spares for motors in case of a power failure.

E. Gas expanders may be justified for recovering several hundred horsepower. At lower recoveries, pressure let down will most likely be through a throttling valve.

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Drum Type Vessels

A. Liquid drums are usually horizontal. Gas/Liquid separators are usually vertical.

B. Optimum Length/Diameter ratio is usually 3, range is 2.5 to 5.

C. Holdup time is 5 minutes for half full reflux drums and gas/liquid separators. Design for a 5-10 minute holdup for drums feeding another column.{parse block="google_articles"}

D. For drums feeding a furnace, a holdup of 30 minutes is a good estimate.

E. Knockout drum in front of compressors should be designed for a holdup of 10 times the liquid volume passing per minute.

F. Liquid/Liquid separators should be designed for settling velocities of 2-3 inches/min

G. Gas velocities in gas/liquid separators:

Eq. (5)

where:
k is 0.35 with horizontal mesh de-entrainers and 0.167 with vertical mesh deentrainers
k is 0.1 without mesh de-entrainers
velocity is in ft/s
?_L is liquid density (lb/ft³)
?_V is vapor density (lb/ft³)

H. A six inch mesh pad thickness is very popular for such vessels.

I. For positive pressure separations, disengagement spaces of 6-18 inches before the mesh pad and 12 inches after the pad are generally suitable.

Drying of Solids

A. Spray dryer have drying times of a few seconds. Rotary dryers have drying times ranging from a few minutes to up to an hour.

B. Continuous tray and belt dryers have drying times of 10-200 minutes for granular materials or 3-15 mm pellets.

C. Drum dryers used for highly viscous fluids use contact times of 3-12 seconds and produce flakes 1-3 mm thick. Diameters are generally 1.5-5 ft (0.5 - 1.5 m). Rotation speeds are 2-10 rpm and the maximum evaporation capacity is around 3000 lb/h (1363 kg/h).

D. Rotary cylindrical dryers operate with air velocities of 5-10 ft/s (1.5-3 m/s), up to 35 ft/s (10.5 m/s). Residence times range from 5-90 min. For initial design purposes, an 85% free cross sectional area is used. Countercurrent design should yield an exit gas temperature that is 18-35 °F (10-20 °C) above the solids temperature. Parallel flow should yield an exiting solids temperature of 212 °F (100 °C). Rotation speeds of 4-5 rpm are common. The product of rpm and diameter (in feet) should be 15-25.

E. Pneumatic conveying dryers are appropriate for particles 1-3 mm in diameter and in some cases up to 10 mm. Air velocities are usually 33-100 ft/s (10-30 m/s). Single pass residence time is typically near one minute. Size range from 0.6-1.0 ft (0.2-0.3 m) in diameter by 3.3-125 ft (1-38 m) in length.

F. Fluidized bed dryers work well with particles up to 4.0 mm in diameter. Designing for a gas velocity that is 1.7-2 times the minimum fluidization velocity is good practice. Normally, drying times of 1-2 minutes are sufficient in continuous operation.

Electric Motors and Turbines

A. Efficiencies range from 85-95% for electric motors, 42-78% for steam turbines 28-38% for gas engines and turbines.

B. For services under 75 kW (100 hp), electric motors are almost always used. They can be used for services up to about 15000 kW (20000 hp).

C. Turbines can be justified in services where they will yield several hundred horsepowers. Otherwise, throttle valves are used to release pressure.

D. A quick estimate of the energy available to a turbine is given by:

Eq. (6)

where:

?H = actual available energy, Btu/lb
C_p = heat capacity at constant pressure, Btu/lb °F
T₁ = inlet temperature, °R
P₁ = inlet pressure, psia
P₂ = outlet pressure, psia
x = C_p/C_v

Evaporation

A. Most popular types are long tube vertical with natural or forced circulation. Tubes range from 3/4"" to 2.5"" (19-63 mm) in diameter and 12-30 ft (3.6-9.1 m) in length.

B. Forced circulation tube velocities are generally in the 15-20 ft/s (4.5-6 m/s) range.

C. Boiling Point Elevation (BPE) as a result of having dissolved solids must be accounted for in the differences between the solution temperature and the temperature of the saturated vapor.

D. BPE's greater than 7 °F (3.9 °C) usually result in 4-6 effects in series (feed-forward) as an economical solution. With smaller BPE's, more effects in series are typically more economical, depending on the cost of steam.

E. Reverse feed results in the more concentrated solution being heated with the hottest steam to minimize surface area. However, the solution must be pumped from one stage to the next.

F. Interstage steam pressures can be increased with ejectors (20-30% efficient) or mechanical compressors (70-75% efficient).

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Filtration

A. Initially, processes are classified according to their cake buildup in a laboratory vacuum leaf filter : 0.10 - 10.0 cm/s (rapid), 0.10-10.0 cm/min (medium), 0.10-10.0 cm/h (slow).

B. Continuous filtration methods should not be used if 0.35 sm of cake cannot be formed in less than 5 minutes.

C. Belts, top feed drums, and pusher-type centrifuges are best for rapid filtering.

D. Vacuum drums and disk or peeler-type centrifuges are best for medium filtering.{parse block="google_articles"}

E. Pressure filters or sedimenting centrifuges are best for slow filtering.

F. Cartridges, precoat drums, and sand filters can be used for clarification duties with negligible buildup.

G. Finely ground mineral ores can utilize rotary drum rates of 1500 lb/day ft² (7335 kg/day m²) at 20 rev/h and 18-25 in Hg (457-635 mm Hg) vacuum.

H. Course solids and crystals can be filtered at rates of 6000 lb/day ft² (29,340 kg/day m²) at 20 rev/h and 2-6 in Hg (51-152 mm Hg) vacuum.

Heat Exchangers

A. For the heat exchanger equation, Q = UAF (LMTD), use F = 0.9 when charts for the LMTD correction factor are not available.

B. Most commonly used tubes are 3/4 in. (1.9 cm) in outer diameter on a 1 in triangular spacing at 16 ft (4.9 m) long.

C. A 1 ft (30 cm) shell will contains about 100 ft2 (9.3 m2)
A 2 ft (60 cm) shell will contain about 400 ft2 (37.2 m2)
A 3 ft (90 cm) shell will contain about 1100 ft2 (102 m2)

D. Typical velocities in the tubes should be 3-10 ft/s (1-3 m/s) for liquids and 30-100 ft/s (9-30 m/s) for gases.

E. Flows that are corrosive, fouling, scaling, or under high pressure are usually placed in the tubes.

F. Viscous and condensing fluids are typically placed on the shell side.

G. Pressure drops are about 1.5 psi (0.1 bar) for vaporization and 3-10 psi (0.2-0.68 bar) for other services.

H. The minimum approach temperature for shell and tube exchangers is about 20 °F (10 °C) for fluids and 10 °F (5 °C) for refrigerants.

I. Cooling tower water is typically available at a maximum temperature of 90 °F (30 °C) and should be returned to the tower no higher than 115 °F (45 °C)

J. Shell and Tube heat transfer coefficient for estimation purposes can be found in many reference books or an online list can be found at one of the two following addresses:
http://www.cheresources.com/uexchangers.shtml

K. Double pipe heat exchangers may be a good choice for areas from 100 to 200 ft2 (9.3-18.6 m2)

L. Spiral heat exchangers are often used to slurry interchangers and other services containing solids

M. Plate heat exchanger with gaskets can be used up to 320 °F (160 °C) and are often used for interchanging duties due to their high efficiencies and ability to "cross" temperatures. More about compact heat exchangers can be found at: http://www.virginiaheattransfer.com/

Mixing and Agitation

A. Mild agitation results from superficial fluid velocities of 0.10-0.20 ft/s (0.03-0.06 m/s). Intense agitation results from velocities of 0.70-1.0 ft/s (0.21-0.30 m/s).

B. For baffled tanks, agitation intensity is measured by power input and impeller tip speeds:

C. Various geometries of an agitated tank relative to diameter (D) of the vessel include:
Liquid Level = D
Turbine Impeller Diameter = D/3
Impeller Level Above Bottom = D/3
Impeller Blade Width = D/15
Four Vertical Baffle Width = D/10

D. For settling velocities around 0.03 ft/s, solids suspension can be accomplished with turbine or propeller impellers. For settling velocities above 0.15 ft/s, intense propeller agitation is needed.

E. Power to mix a fluid of gas and liquid can be 25-50% less than the power to mix the liquid alone.

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Pressure and Storage Vessels

Pressure Vessels

A. Design Temperatures between -30 and 345 °C (-22 to 653 °F) is typically about 25 °C (77 °F) above maximum operating temperature, margins increase above this range.

B. Design pressure is 10% or 0.69 to 1.7 bar (10 to 25 psi) above the maximum operating pressure, {parse block="google_articles"}whichever is greater. The maximum operating pressure is taken as 1.7 bar (25 psi) above the normal operation pressure.

C. For vacuum operations, design pressures are 1 barg (15 psig) to full vacuum.

D. Minimum thicknesses for maintaining tank structure are:
6.4 mm (0.25 in) for 1.07 m (42 in) diameter and under
8.1 mm (0.32 in) for 1.07-1.52 m (42-60 in) diameter
9.7 mm (0.38 in) for diameters over 1.52 m (60 in)

E. Allowable working stresses are taken as 1/4 of the ultimate strength of the material.

F. Maximum allowable working stresses:

G. Thickness based on pressure and radius is given by:

Eq. (7)

where pressure is in psig, radius in inches, stress in psi, corrosion allowance in inches.
**Weld Efficiency can usually be taken as 0.85 for initial design work

H. Guidelines for corrosion allowances are as follows: 0.35 in (9 mm) for known corrosive fluids, 0.15 in (4 mm) for non-corrosive fluids, and 0.06 in (1.5 mm) for steam drums and air receivers.

Storage Vessels

I. For less than 3.8 m3 (1000 gallons) use vertical tanks on legs

J. Between 3.8 m3 and 38 m3 (1000 to 10,000 gallons) use horizontal tanks on concrete supports.

K. Beyond 38 m3 (10,000 gallons) use vertical tanks on concrete pads.

L. Liquids with low vapor pressures, use tanks with floating roofs.

M. Raw material feed tanks are often specified for 30 days feed supplies.

N. Storage tank capacity should be at 1.5 times the capacity of mobile supply vessels. For example, 28.4 m3 (7500 gallon) tanker truck, 130 m3 (34,500 gallon) rail cars.

Piping

A. Liquid lines should be sized for a velocity of (5+D/3) ft/s and a pressure drop of 2.0 psi/100 ft of pipe at pump discharges. At the pump suction, size for (1.3+D/6) ft/s and a pressure drop of 0.4 psi/100 ft of pipe. **D is pipe diameter in inches.

B. Steam or gas lines can be sized for 20D ft/s and pressure drops of 0.5 psi/100 ft of pipe.

C. Limits on superheated, dry steam or line should be 61 m/s (200 ft/s) and a pressure drop of 0.1 bar/100 m or 0.5 psi/100 ft of pipe.

D. For turbulent flow in commercial steel pipes, use the following:

Eq. (8)

where:
ΔP = fricitional pressure drop (psi) / 100 equivalent feet of pipe
M = mass flow, lb/hr
μ = viscosity, cP
ρ = density, lb/ft³
D = pipe inside diameter, in.
** for smooth heat exchanger steel tubes, replace 20,000 with 23,000

E. For two phase flow, an estimate often used is Lockhart and Martinelli:
First, the pressure drops are calculated as if each phase exist alone in the pipe, then

Eq. (9)

now, the total pressure drop can be calculated by one of the following:

Eq. (10)

where:
Y_L = 4.6X^-1.78 + 12.5X^-0.68 + 0.65
Y_G = X² Y_L

F. Control valves require at least 0.69 bar (10 psi) pressure drop for sufficient control.

G. Flange ratings include 10, 20, 40, 103, and 175 bar (150, 300, 600, 1500, and 2500 psig).

H. Globe valves are most commonly used for gases and when tight shutoff is required. Gate valves are common for most other services.

I. Screwed fitting are generally used for line sizes 2 inches and smaller. Larger connections should utilize flanges or welding to eliminate leakage.

J. Pipe Schedule Number = 1000P/S (approximate) where P is the internal pressure rating in psig and S is the allowable working stress of the material is psi. Schedule 40 is the most common.

Pumps

A. Power estimates for pumping liquids:

**Efficiency expressed as a fraction in these relations

B. NPSH is defined as:

Common range is 1.2 to 6.1 m (4-20 ft) of liquid.

C. An equation developed for efficiency based on the GPSA Engineering Data Book is:

where Efficiency is in fraction form, F is developed head in feet, G is flow in GPM
Ranges of applicability are F=50-300 ft and G=100-1000 GPM
Error documented at 3.5%

D. Centrifugal pumps: Single stage for 0.057-18.9 m3/min (15-5000 GPM), 152 m (500 ft) maximum head;
For flow of 0.076-41.6 m3/min (20-11,000 GPM) use multistage, 1675 m (5500 ft) maximum head;
Efficiencies of 45% at 0.378 m3/min (100 GPM), 70% at 1.89 m3/min (500 GPM), 80% at 37.8 m3/min (10,000 GPM).

E. Axial pumps can be used for flows of 0.076-378 m3/min (20-100,000 GPM). Expect heads up to 12 m (40 ft) and efficiencies of about 65-85%.

F. Rotary pumps can be used for flows of 0.00378-18.9 m3/min (1-5000 GPM). Expect heads up to 15,200 m (50,000 ft) and efficiencies of about 50-80%.

G. Reciporating pumps can be used for 0.0378-37.8 m3/min (10-100,000 GPM). Expect heads up to 300,000 m (1,000,000 ft). Efficiencies: 70% at 7.46 kW (10 hp), 85% at 37.3 kW (50 hp), and 90% at 373 kW (500 hp).

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Tray Towers

A. For ideal mixtures, relative volatility can be taken as the ratio of pure component vapor pressures.

B. Tower operating pressure is most often determined by the cooling medium in condenser or the maximum allowable reboiler temperature to avoid degradation of the process fluid.

C. For sequencing columns: {parse block="google_articles"}

1. Perform the easiest separation first (least trays and lowest reflux.
2. If relative volatility nor feed composition vary widely, take products off one at time as the overhead.
3. If the relative volatility of components do vary significantly, remove products in order of decreasing volatility.
4. If the concentrations of the feed vary significantly but the relative volatility do not, remove products in order of decreasing concentration.

D. The most economic reflux ratio usually is between 1.2Rmin and 1.5Rmin.

E. The most economic number of trays is usually about twice the minimum number of trays. The minimum number of trays is determined with the Fenske-Underwood Equation.

F. Typically, 10% more trays than are calculated are specified for a tower.

G. Tray spacings should be from 18 to 24 inches, with accessibility in mind.

H. Peak tray efficiencies usually occur at linear vapor velocities of 2 ft/s (0.6 m/s) at moderate pressures, or 6 ft/s (1.8 m/s) under vacuum conditions.

I. A typical pressure drop per tray is 0.1 psi (0.007 bar).

J. Tray efficiencies for aqueous solutions are usually in the range of 60-90% while gas absorption and stripping typically have efficiencies closer to 10-20%.

K. The three most common types of trays are valve, sieve, and bubble cap. Bubble cap trays are typically used when low-turn down is expected or a lower pressure drop than the valve or sieve trays can provide is necessary.

L. Seive tray holes are 0.25 to 0.50 in. diameter with the total hole area being about 10% of the total active tray area.

M. Valve trays typically have 1.5 in. diameter holes each with a lifting cap. 12-14 caps/square foot of tray is a good benchmark. Valve trays usually cost less than seive trays.

N. The most common weir heights are 2 and 3 in and the weir length is typically 75% of the tray diameter.

O. Reflux pumps should be at least 25% overdesigned.

P. The optimum Kremser absorption factor is usually in the range of 1.25 to 2.00.

Q. Reflux drums are almost always horizontally mounted and designed for a 5 min holdup at half of the drum's capacity.

R. For towers that are at least 3 ft (0.9 m) is diameter, 4 ft (1.2 m) should be added to the top for vapor release and 6 ft (1.8 m) should be added to the bottom to account for the liquid level and reboiler return.

S. Limit tower heights to 175 ft (53 m) due to wind load and foundation considerations.

T. The Length/Diameter ratio of a tower should be no more than 30 and preferrably below 20.

U. A rough estimate of reboiler duty as a function of tower diameter is given by:
Q = 0.5 D² for pressure distillation
Q = 0.3 D² for atmospheric distillation
Q = 0.15 D² for vacuum distillation
where Q is in Million Btu/hr and D is tower diameter in feet.

Packed Towers

A. Packed towers almost always have lower pressure drop than comparable tray towers.

B. Packing is often retrofitted into existing tray towers to increase capacity or separation.

C. For gas flowrates of 500 ft³/min (14.2 m³/min) use 1 in (2.5 cm) packing, for gas flows of 2000 ft³/min (56.6 m³/min) or more, use 2 in (5 cm) packing.

D. Ratio of tower diameter to packing diameter should usually be at least 15.

E. Due to the possibility of deformation, plastic packing should be limited to an unsupported depth of 10-15 ft (3-4 m) while metallatic packing can withstand 20-25 ft (6-7.6 m).

F. Liquid distributor should be placed every 5-10 tower diameters (along the length) for pall rings and every 20 ft (6.5 m) for other types of random packings.

G. For redistribution, there should be 8-12 streams per sq. foot of tower area for tower larger than three feet in diameter. They should be even more numerous in smaller towers.

H. Packed columns should operate near 70% flooding.

I. Height Equivalent to Theoretical Stage (HETS) for vapor-liquid contacting is 1.3-1.8 ft (0.4-0.56 m) for 1 in pall rings and 2.5-3.0 ft (0.76-0.90 m) for 2 in pall rings

J. Design pressure drops should be as follows:

Reactors

A. The rate of reaction must be established in the laboratory and the residence time or space velocity will eventually have to be determined in a pilot plant.

B. Catalyst particle sizes: 0.10 mm for fluidized beds, 1 mm in slurry beds, and 2-5 mm in fixed beds.

C. For homogeneous stirred tank reactions, the agitor power input should be about 0.5-1.5 hp/1000 gal (0.1-0.3 kW/m3), however, if heat is to be transferred, the agitation should be about three times these amounts.

D. Ideal CSTR behavior is usually reached when the mean residence time is 5-10 times the length needed to achieve homogeneity. Homogeneity is typically reached with 500-2000 revolutions of a properly designed stirrer.

E. Relatively slow reactions between liquids or slurries are usually conducted most economically in a battery of 3-5 CSTR's in series.

F. Tubular flow reactors are typically used for high productions rates and when the residence times are short. Tubular reactors are also a good choice when significant heat transfer to or from the reactor is necessary.

G. For conversion under 95% of equilibrium, the reaction performance of a 5 stages CSTR approaches that of a plug flow reactor.

H. Typically the chemical reaction rate will double for a 18 °F (10 °C) increase in temperature.

I. The reaction rate in a heterogeneous reaction is often controlled more by the rate of heat or mass transfer than by chemical kinetics.

J. Sometimes, catalysts usefulness is in improving selectivity rather than increasing the rate of the reaction.

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The following need to be carefully evaluated when optimizing the design and operation of the extraction processes.{parse block="google_articles"}

• Solvent selection
• Operating Conditions
• Mode of Operation
• Extractor Type
• Design Criteria

Solvent Selection

Solvents differ in their extraction capabilities depending on their own and the solute's chemical structure. Robbins (1) presents a table showing Organic-Group interactions from which one can identify the desired functional group(s) in the solvent for any given solute.

Once the functional group is identified, possible solvents can be screened in the laboratory. The distribution coefficient and selectivity are the most important parameters that govern solvent selection. The distribution coefficient (m) or partition coefficient for a component (A) is defined as the ratio of concentration of a A in extract phase to that in raffinate phase. Selectivity can be defined as the ability of the solvent to pick up the desired component in the feed as compared to other components. The desired properties of solvents are a high distribution coefficient, good selectivity towards solute and little or no miscibility with feed solution. Also, the solvent should be easily recoverable for recycle. Designing an extractor is usually a fine balance between capital and operating costs. Usually, good solvents also exhibit some miscibility with feed solution (see Table 1). Consequently, while extracting larger quantities of solute, the solvent could also extract significant amount of feed solution.

Other factors affecting solvent selection are boiling point, density, interfacial tension, viscosity, corrosiveness, flammability, toxicity, stability, compatibility with product, availability and cost.

For an existing process, replacing the solvent is usually a last resort because this this would call for going back to laboratory screening of the solvent and process optimization. However, changes in environmental regulations and economic considerations often induce the need to improve the processes in terms of solute recovery. Also the availability of specialized and proprietary solvents that score over conventional solvents in terms of performance and economics for several extraction processes can provide additional incentives for a solvent change.

Selection of Extraction Conditions

Depending on the nature of the extraction process, the temperature, pH and residence time could have an effect on the yield and selectivity. Operating pressure has a negligible affect on extraction performance and therefore most extractions take place at atmospheric pressure unless governed by vapor pressure considerations.

Temperature can also be used as a variable to alter selectivity. Elevated temperatures are sometimes used in order to keep viscosity low and thereby minimizing mass-transfer resistance. Other parameters to be considered are selectivity, mutual solubility, precipitation of solids and vapor pressure.

The pH becomes significant in metal and bio-extractions. In bio-extractions (e.g., Penicillin) and some agrochemicals (e.g. Orthene), pH is maintained to improve distribution coefficient and minimize degradation of product. In metal extractions, kinetic considerations govern the pH. In dissociation-based extraction of organic molecules, pH can play a significant role (e.g., cresols separation). Sometimes, the solvent itself may participate in undesirable reactions under certain pH conditions (e.g., ethyl acetate may undergo hydrolysis in presence of mineral acids to acetic acid and ethanol).

Residence time is an important parameter in reactive extraction processes (e.g., metals separations, formaldehyde extraction from aqueous streams) and in processes involving short-life components (e.g., antibiotics & vitamins)

Selection of Mode of Operation

Extractors can be operated in crosscurrent or counter-current mode. The following section compares these configurations.

Cross-Current Operation

Crosscurrent mode is mostly used in batch operation. Batch extractors have traditionally been used in low capacity multi-product plants such as are typical in the pharmaceutical and agrochemical industries. For washing and neutralization operations that require very few stages, crosscurrent operation is particularly practical and economical and offers a great deal of flexibility. The extraction equipment is usually an agitated tank that may also be used for the reaction steps. In these tanks, solvent is first added to the feed, the contents are mixed, settled and then separated. Single stage extraction is used when the extraction is fairly simple and can be achieved without a high amount of solvent. If more than one stage is required, multiple solvent-washes are given.{parse block="google_articles"}

Though operation in crosscurrent mode offers more flexibility, it is not very desirable due to the high solvent requirements and low extraction yields. The following illustration gives a quick method to calculate solvent requirements for crosscurrent mode of extraction.

A single-stage extractor can be represented as:

where

F = Feed quantity / rate, massR = Raffinate quantity / rate, massS = Solvent quantity / rate, massE = Extract quantity / rate, mass

X_f, X_r, Y_s, and Y_e are the weight fractions of solute in the feed, raffinate, solvent and extract, respectively.

Partition coefficient 'm' is defined as the ratio of Y_e to X_r at equilibrium conditions

The flows and concentrations are represented in solute-free basis as such a representation leads to simplification of equations. For example, for a 100 kg/hr feed containing 10% weight acetic acid, F = 100-10 = 90 kg/hr, X_r = 0.1/(1-0.1) = 0.111

The component mass balance can be represented as:F X_f + S Y_s = R X_r + E Y_e

Assuming (i) immiscibility of feed and solvent and (ii) the initial solvent is free of solute, i.e., F = R, S = E and Y_s = 0 and using the equilibrium relation of Y_e = m X_r, this equation simplifies to

S = F/m (X_f /X_r-1)

or

reduction ratio, X_f /X_r = 1+ m S/F

For multi-stage crosscurrent operation:

Assuming that the partition coefficient (m) is constant over the concentration range and the solvent quantity in each of the 'n' stages is the same, i.e., S₁ = S₂ =.....=S _n = S/n,

Solvent Requirement is

S = n * F/m [(X_f /X_r)^1/n - 1]

reduction ratio X_f /X_r = (1+mS/nF)ⁿ

It can be proved mathematically that the total solvent quantity would be minimum if the solvent were distributed equally between washes.

Diminishing Returns

The following chart shows solvent requirements for a typical reduction ratio (X _f /X_r) of 10 using crosscurrent extraction.

Figure 1: Reduction Ratio for Crosscurrent Extraction

With one stage, 18,000 kg of solvent is required for 1,000 kg of feed (m = 1 and X_f / X_r = 10). With two stages, solvent requirement reduces to 8,650 kg, and with three stages, it reduces further to 6,930 kg. However, as can be seen from the chart, using more than three stages has minimal effect on solvent usage. This fact combined with practical limitations of solvent handling and increased batch time confines the number of solvent washes to three.

Counter-Current Operation

As described above, the crosscurrent operation is mostly used in low capacity multi-product batch plants. For larger volume operation and more efficient use of solvent, countercurrent mixer-settlers or columns are employed. Countercurrent operation conserves the mass transfer driving force and hence gives optimal performance.

Equations for countercurrent extraction get more complicated with increasing number of stages. It can be shown that for a 'n' stage operation, the raffinate concentration would be

X_r = X_f * (mS/F - 1)/ ( [mS/F] ⁿ⁺¹ -1)

The solvent requirement for any raffinate concentration X_r could be determined by iteration from the above equation.

For mS/F = 1, the equation takes the form of X_r = X_f / (n + 1)

The dimensionless term mS/F, included in all the above equations, is called the extraction factor (E), and is an important parameter in the design of extraction processes. For a given number of stages, the higher the E factor, the higher is the reduction ratio and easier is the extraction. Systems with E of less than 1.3 are not likely to be commercially feasible.

Comparing Counter versus Cross Flow Operation

The following graph compares the reduction ratios (X_f / X_r) of the crosscurrent and countercurrent modes of operation.

Figure 2: Comparing Counter and Cross Flow Extraction

The graph shows that for a given extraction factor (E), and number of stager (n), the countercurrent mode of operation outperforms the crosscurrent mode. This is demonstrated in a case study presented at the end of this paper. Koch-Glitsch has demonstrated these benefits on their pilot and commercial scale extraction columns for several systems.

The equations given above can be used to compare solvent requirements for various modes of operation and can serve as a starting point for identifying scope for optimizing solvent quantity. However, these equations should be used with caution as the assumptions of immiscibility, constancy of partition coefficient over desired range and solute-free fresh solvent are not valid in all practical applications.

As the solvent quantity is reduced, the solute concentration in the extract increases. This usually affects the physical properties and the selectivity. Therefore optimization exercise should be backed up by laboratory extraction data.

Selecting the Type of Extractor

Commercially important extractors can be classified into the following broad categories.

Mixer-Settlers

Centrifugal devices

Column contactors (static) - Examples include spray columns, sieve plate columns, and random or structurally packed columns.

Column contactors (agitated) - Agitated columns can be further split into rotary or reciprocating type. Examples of rotary agitated columns include rotary disc contactor, Scheibel column, Kuhni column. Examples of reciprocating agitated columns include the Karr column and the pulsed column.

Mixer-Settlers

As the name indicates, are usually a series of static or agitated mixers interspersed with settling stages. These are mostly used in the metal industry where intense mixing and high residence time is required by the reactive extraction processes.

In batch mode of operation, these mixer-settlers could be simple batch vessels where feed and solvent are mixed and settled. This operation is repeated with fresh solvent washes as described earlier.

Centrifugal Contactors

Centrifugal contactors are high-speed rotary machines that offer advantages of very low residence time. The number of stages in a centrifugal device is usually limited to one, but currently devices with multiple numbers of stages are common. These extractors are mainly used in pharmaceutical industry.

Counter-current Column Contactors

Counter-current column contactors are most popular in the chemical industry. These could be static or agitated. Several types of extractors are available (see Table 2) and each has its own advantages.

Factors Affecting the Selection of Contactors

Important factors to consider when selecting extractor types are the stage requirements, fluid properties and operational considerations. The following table outlines the capabilities and characteristics of different extractor-types:

The Karr reciprocating plate extractor can effectively handle low interfacial tension systems. Other factors governing extractor selection are presence of solids, safety and maintenance requirements.

Design Criteria

The basic function of extraction equipment is to mix two phases, form and maintain droplets of dispersed phase and subsequently separate the phases. The following section outlines some of the factors that need to be considered while designing and optimizing extraction equipment.

1. Mixing - The amount of mixing required is determined by physical properties such as viscosity, interfacial tension and density differences between the two phases. It is important to provide just the right amount of mixing. Less mixing causes the formation of large droplets and decreases interfacial area (interfacial area varies with the square of the droplet diameter). This reduces mass transfer and decreases stage efficiency. Higher agitation (more mixing) minimizes mass transfer resistance during reactions and extraction but contributes to the formation of small and difficult-to-settle droplets or emulsions. In agitated batch extractors, the agitator design is often optimized for reaction and heat transfer, not extraction, as these are generally multi-purpose vessels.The agitator imparts maximum energy at the tip where the velocity is highest and minimum energy at the center. This creates non-uniform droplet sizes, with the smallest being formed at the agitator tip. Reaching extraction equilibrium is controlled by the largest droplet size and the smallest droplet controls settling time. Therefore, over-agitation sometimes takes its toll by causing difficulties in phase separation. Usually a redesign in terms of configuration or change in agitation speed helps in optimizing batch time.Static extraction columns rely completely on the packing/internals and fluid flow velocities past the internals to create turbulence and droplets. Therefore these are restricted by minimum flow requirement of at least one of the phases. Agitated columns have more operating flexibility as the specific energy input can be varied in most designs. Axial mixing (along column length) in column contactors reduces stage efficiency. Baffles or similar arrangements are used to minimize axial mixing in static as well as agitated columns. It is also important to avoid temperature gradients in columns to prevent thermal currents contributing to axial mixing.
2. Settling - The settling characteristics depend on the fluid properties (density difference, interfacial tension, and continuous phase viscosity) and the amount of mixing. Settling in agitated batch vessels is carried out by stopping the agitator. In continuous columns, a settling section is provided either as a part of the extractor or as a separate piece of equipment downstream of the extractor. Emulsions are usually formed due to over agitation and in such cases, settling needs to be carried out over an extended period. Emulsions can also form due to the inherent nature of the chemical compounds involved or due to contaminants that substantially lower the interfacial tension. Sometimes coagulants are added to prevent or minimize emulsification. Passing the emulsion layer through a coalescer can break some of these emulsions. In continuous extractors, the creation of emulsions is less severe as good droplet size distribution can be attained at lower agitation speeds in a lesser diameter column. Also, columns such as the Karr reciprocating plate extractor impart uniform energy throughout the radius as a result of the reciprocating motion and this creates a much narrower droplet distribution.A similar phenomenon to emulsions is the formation of a 'rag layer'. This is a layer containing loose solid substances that float at the interface. These solid substances are generally foreign impurities that exist in the feed streams or those that precipitate from the system during extraction. In continuous extraction the liquid interface containing the rag layer can be continuously withdrawn, filtered and sent back to extractor. Selection of continuous and dispersed phases can have an effect on formation of emulsion and rag layer. Reversing continuous and dispersed phases sometimes drastically reduces or eliminates emulsion formation. Changing extraction temperature could also help in reducing emulsion and rag layer.
3. Selection of Continuous and Dispersed Phase - In column extractors, the phase with the lower viscosity (lower flow resistance) is generally chosen as the continuous phase. Also note that the phase with the higher flow rate can be dispersed to create more interfacial area and turbulence. This is accomplished by selecting an appropriate material of construction with the desired wetting characteristics. In general, aqueous phases wet metal surfaces and organic phases wet non-metallic surfaces. Change in flows and physical properties along the length of extractor should also be considered. Choosing a continuous phase is generally not available in batch processes, as the larger liquid phase usually becomes the continuous phase.

Conclusions

As we have seen in the previous sections, there are a number of factors affecting extraction performance. Laboratory and pilot plant testing using actual feed and solvent help immeasurably in optimization. The study could often be an iterative cycle involving laboratory testing followed by process simulation and design. In most industrial extractors, there is usually a good scope for optimizing solvent usage and energy consumption.

References

1. Robbins, Chem. Eng. Prog., 76(10), 58-61 (1980).
2. Cusack, R.W., & Glatz, D., et al, "A Fresh Look at Liquid-Liquid Extraction", Chemical Engineering, February, March & April 1991.

	Eq. (1)
	Eq. (2)

Figure 1: Correct Example of a T-Q Diagram	Figure 2: Incorrect Example of a T-Q Diagram

Eq. (3)

Examining the "Heat Exchanger Equation"

Figure 3: T-Q Diagram for the Example Problem

Figure 4: Graphical Representation of the Log Mean Temperature Difference

So, for a heat exchanger as described above, we calculate the LMTD as follows:

Figure 5: Exchange Heat Exchanger Duty

Eq. (4)

There can be special cases where the LMTD equation shown above is not applicable. Consider the case below:

Figure 6: Special Case for Calculating LMTD

If you tried apply the LMTD equation to this special case, you'd find that the result would be zero. In this case the LMTD is the same as the temperature difference on each "end" of the heat exchanger, or 100 °F.

A Brief Word on Flow Direction

The Temperature Correction Factor, f

The Overall Heat Transfer Coefficient

Eq. (5)

Eq. (6)

Brief Overview of Heat Exchanger Types

• Liquid to Liquid heat transfer
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• Liquid to Gas heat transfer


• Gas to Gas heat transfer

• Condensing a vapor with a liquid or gas service fluid


• Vaporizing a liquid with a liquid, gas, or condensing fluid

• Shell and Tube Heat Exchangers


• Compact and Extended Surface Heat Exchangers

Compact Heat Exchanger Technologies

Figure 7: Components of a Plate Heat Exchanger

Figure 8: Heat Transfer Duty with No Temperature Cross

Figure 9: Heat Transfer Duty with a Temperature Cross

Figure 10: Finned Tubes

Figure 11: Fin-Fan Heat Exchanger

Shell and Tube Heat Exchanger Technologies

Figure 12: Example of a Shell and Tube Heat Exchanger

Figure 13: TEMA Datasheet

{parse block="google_articles"}Resin is fed to the machine through the hopper.   Colorants are usually fed to the machine directly after the hopper.  The resins enter the injection barrel by gravity though the feed throat.  Upon entrance into the barrel, the resin is heated to the appropriate melting temperature.

The resin is injected into the mold by a reciprocating screw or a ram injector.  The reciprocating screw apparatus is shown above.  The reciprocating screw offers the advantage of being able to inject a smaller percentage of the total shot (amount of melted resin in the barrel).  The ram injector must typically inject at least 20% of the total shot while a screw injector can inject as little as 5% of the total shot.  Essentially, the screw injector is better suited for producing smaller parts.

Figure 1: Diagram of Injection Molding Machine		Figure 2: Photo of Injection Molding Machine		Figure 3: Diagram of Heated Screw Conveyor

The mold is the part of the machine that receives the plastic and shapes it appropriately.  The mold is cooled constantly to a temperature that allows the resin to solidify and be cool to the touch.  The mold plates are held together by hydraulic or mechanical force.  The clamping force is defined as the injection pressure multiplied by the total cavity projected area.  Typically molds are overdesigned depending on the resin to be used.  Each resin has a calculated shrinkage value associated with in.

Some Typical Complications

Burned or Scorched Parts:  Melt temperature may be too high.  Polymer may be becoming trapped and degrading in the injection nozzle.   Cycle time may be too long allowing the resin to overheat.

Warpage of Parts:  Uneven surface temperature of the molds.  Non-uniform wall thickness of mold design.

Surface Imperfections:  Melt temperature may be too high causing resin decomposition and gas evolution (bubbles).  Excessive moisture in the resin.  Low pressure causing incomplete filling of mold.

Incomplete Cavity Filling:  Injection stroke may be too small for mold (ie. not enough resin is being injected).  Injection speed may be too slow causing freezing before mold is filled.

Diagrams courtesy of Plastics: Materials and Processing, Prentice Hall by A. Brent Strong

Torispherical heads are made up of two parts.  The rounded end has a spherical shape.  It has a radius that is described with the numerical value “f” which is the ratio of the dish radius to the vessel shell diameter. {parse block="google_articles"}So, if the diameter of the vessel, D, is 48 inches and the value of “f” is 1.0 then the radius of the dish is 48 inches.  Unless f=0.5, there would be an abrupt angle between the shell and head unless a transition piece is installed. This is the second part of the torispherical head, a transition piece shaped like a donut or torus.  It is called the “knuckle” and there is a knuckle radius that again is related to the vessel diameter with the factor, k. Valid values for f are anything greater than 0.5; k must be greater or equal to 0 and less than or equal to 0.5.

Torispherical heads are also called “F&D” or “flanged and dished”.  The standard F&D head has f = 1.0 and kD = 3 times the metal thickness of the head.  ASME F&D heads require a dish radius no greater than the diameter (f <= 1.0) and knuckle radius no less than 6% of the diameter (k >= 0.06) or three times the metal thickness, whichever is greater.

Figure 1: Torispherical Head Geometry

When calculating the volume of fluid in a torispherical head, the head is divided into three parts.  The first is the lower portion occupied by the knuckle (liquid height 0 to h1 as seen in the diagram).  The second part is the portion covered by the spherical dish section, which also includes the knuckle at the perimeter.  The third portion is that which is entirely within the knuckle but above the spherical section.

Each of the three parts are calculated separately and they each require solving an integral.  I’ll use the integral for the first part for an example in this article.

Eq. (1)

where

            k = knuckle radius

            D = vessel diameter

            h = fill height of the vessel

            n = R – kD + (k²D² – x²)^0.5, where R = vessel radius (= D/2)

            w = R – h

It looks complicated, but solving in Excel is straightforward if it is done sequentially as described below.

Integrals that are too complex to express implicitly are solved using “numerical methods”.  A number of numerical methods have been used for integrals with Simpson’s Rule being one of the best.  I chose to use Simpson’s Rule for this problem.  (Other methods include the trapezoidal rule, Riemann sums, Romberg integration, Gaussian quadratures and the Monte Carlo method).  There are many webpages that give the derivation of Simpson’s Rule and explain it in detail; I won’t repeat that work here.

Simpson’s rule requires that the integral be broken into intervals.  Since the integral is evaluating the area under a curve, from x=0 to x= (2kDh-h²)^.5, the method first calculates the maximum value for x, divides that by the number of intervals, and then evaluates the function for each value of x.  In other words, if the maximum value of x was 10 and there were 10 intervals, then the function would be evaluated with x = 0, 1, 2, 3, 4, etc.   Notice that the term called “n” above includes x in its formula.

An even number of intervals is required.  The more the better.   I found through trial and error that a good number to use for this particular problem is 1000 intervals.

Implementation could be done in a tabular form on an Excel worksheet.  However, it is much more elegant to solve Simpson’s Rule in a Visual Basic for Applications function subroutine.   Listing 1 gives the function.  This is located in a VBA Module within TankVolume.  Each place the calculation is required, the function is called using a cell formula of the form:

= Toris_V1(k, D, h)

where the variables k, D, and h are as defined above.  Since recalculation takes time, which can be noticable, I put the function call in a conditional statement so it is only used when the tank is horizontal with torispherical heads.  Assume the variable “head_type” refers to the type of head and a value of head_type=4 refers to torispherical, the conditional function call becomes:

= if(head_type=4,Toris_V1(k, D, h), 0)

In this case, the function is called only if the heads are torispherical.  Otherwise, a value of “0” is returned.  This is perfectly fine since the result of this cell in the spreadsheet is only used for torispherical heads.

The idea of heat pipes was first suggested by R.S.Gaugler in 1942. However, it was not until 1962, when G.M.Grover invented it, that its remarkable properties were appreciated and serious development began.{parse block="google_articles"}

It consists of a sealed aluminum or copper container whose inner surfaces have a capillary wicking material. A heat pipe is similar to a thermosyphon. It differs from a thermosyphon by virtue of its ability to transport heat against gravity by an evaporation-condensation cycle with the help of porous capillaries that form the wick. The wick provides the capillary driving force to return the condensate to the evaporator. The quality and type of wick usually determines the performance of the heat pipe, for this is the heart of the product. Different types of wicks are used depending on the application for which the heat pipe is being used.

Design Considerations

The three basic components of a heat pipe are:

1. the container
2. the working fluid
3. the wick or capillary structure

Container

The function of the container is to isolate the working fluid from the outside environment. It has to therefore be leak-proof, maintain the pressure differential across its walls, and enable transfer of heat to take place from and into the working fluid.

Selection of the container material depends on many factors. These are as follows:

• Compatibility (both with working fluid and external environment)
• Strength to weight ratio
• Thermal conductivity
• Ease of fabrication, including welding, machineability and ductility
• Porosity
• Wettability

Most of the above are self-explanatory. A high strength to weight ratio is more important in spacecraft applications. The material should be non-porous to prevent the diffusion of vapor. A high thermal conductivity ensures minimum temperature drop between the heat source and the wick.

Working Fluid

A first consideration in the identification of a suitable working fluid is the operating vapour temperature range. Within the approximate temperature band, several possible working fluids may exist, and a variety of characteristics must be examined in order to determine the most acceptable of these fluids for the application considered. The prime requirements are:

• compatibility with wick and wall materials
• good thermal stability
• wettability of wick and wall materials
• vapor pressure not too high or low over the operating temperature range
• high latent heat
• high thermal conductivity
• low liquid and vapor viscosities
• high surface tension
• acceptable freezing or pour point

The selection of the working fluid must also be based on thermodynamic considerations which are concerned with the various limitations to heat flow occurring within the heat pipe like, viscous, sonic, capillary, entrainment and nucleate boiling levels.

In heat pipe design, a high value of surface tension is desirable in order to enable the heat pipe to operate against gravity and to generate a high capillary driving force. In addition to high surface tension, it is necessary for the working fluid to wet the wick and the container material i.e. contact angle should be zero or very small. The vapor pressure over the operating temperature range must be sufficiently great to avoid high vapor velocities, which tend to setup large temperature gradient and cause flow instabilities.

A high latent heat of vaporization is desirable in order to transfer large amounts of heat with minimum fluid flow, and hence to maintain low pressure drops within the heat pipe. The thermal conductivity of the working fluid should preferably be high in order to minimize the radial temperature gradient and to reduce the possibility of nucleate boiling at the wick or wall surface. The resistance to fluid flow will be minimized by choosing fluids with low values of vapor and liquid viscosities. Tabulated below are a few mediums with their useful ranges of temperature.

Wick or Capillary Structure

It is a porous structure made of materials like steel, alumunium, nickel or copper in various ranges of pore sizes. They are fabricated using metal foams, and more particularly felts, the latter being more frequently used. By varying the pressure on the felt during assembly, various pore sizes can be produced. By incorporating removable metal mandrels, an arterial structure can also be molded in the felt.

Fibrous materials, like ceramics, have also been used widely. They generally have smaller pores. The main disadvantage of ceramic fibres is that, they have little stiffness and usually require a continuos support by a metal mesh. Thus while the fibre itself may be chemically compatible with the working fluids, the supporting materials may cause problems. More recently, interest has turned to carbon fibres as a wick material. Carbon fibre filaments have many fine longitudinal grooves on their surface, have high capillary pressures and are chemically stable. A number of heat pipes that have been successfully constructed using carbon fibre wicks seem to show a greater heat transport capability.

The prime purpose of the wick is to generate capillary pressure to transport the working fluid from the condenser to the evaporator. It must also be able to distribute the liquid around the evaporator section to any area where heat is likely to be received by the heat pipe. Often these two functions require wicks of different forms. The selection of the wick for a heat pipe depends on many factors, several of which are closely linked to the properties of the working fluid.

The maximum capillary head generated by a wick increases with decrease in pore size. The wick permeability increases with increasing pore size. Another feature of the wick, which must be optimized, is its thickness. The heat transport capability of the heat pipe is raised by increasing the wick thickness. The overall thermal resistance at the evaporator also depends on the conductivity of the working fluid in the wick. Other necessary properties of the wick are compatibility with the working fluid and wettability.

The most common types of wicks that are used are as follows:

Sintered Powder

This process will provide high power handling, low temperature gradients and high capillary forces for anti-gravity applications. The photograph shows a complex sintered wick with several vapor channels and small arteries to increase the liquid flow rate. Very tight bends in the heat pipe can be achieved with this type of structure.

Grooved Tube

The small capillary driving force generated by the axial grooves is adequate for low power heat pipes when operated horizontally, or with gravity assistance. The tube can be readily bent. When used in conjunction with screen mesh the performance can be considerably enhanced.

Screen Mesh

This type of wick is used in the majority of the products and provides readily variable characteristics in terms of power transport and orientation sensitivity, according to the number of layers and mesh counts used.

Working Principle and Applications

Inside the container is a liquid under its own pressure, that enters the pores of the capillary material, wetting all internal surfaces. Applying heat at any point along the surface of the heat pipe causes the liquid at that point to boil and enter a vapor state. When that happens, the liquid picks up the latent heat of vaporization. The gas, which then has a higher pressure, moves inside the sealed container to a colder location where it condenses. Thus, the gas gives up the latent heat of vaporization and moves heat from the input to the output end of the heat pipe.

Figure 1: Heat Flowing Through a Heat Pipe

Heat pipes have an effective thermal conductivity many thousands of times that of copper. The heat transfer or transport capacity of a heat pipe is specified by its " Axial Power Rating (APC)". It is the energy moving axially along the pipe. The larger the heat pipe diameter, greater is the APR. Similarly, longer the heat pipe lesser is the APR. Heat pipes can be built in almost any size and shape.{parse block="google_articles"}

Heat pipe has been, and is currently being, studied for a variety of applications, covering almost the entire spectrum of temperatures encountered in heat transfer processes. Heat pipes are used in a wide range of products like air-conditioners, refrigerators, heat exchangers, transistors, capacitors, etc. Heat pipes are also used in laptops to reduce the working temperature for better efficiency. Their application in the field of cryogenics is very significant, especially in the development of space technology. We shall now discuss a brief account of the various applications of heat pipe technology.

Space Technology

The use of heat pipes has been mainly limited to this field of science until recently, due to cost effectiveness and complex wick construction of heat pipes. There are several applications of heat pipes in this field like

• Spacecraft temperature equalization
• Component cooling, temperature control and radiator design in satellites.
• Other applications include moderator cooling, removal of heat from the reactor at emitter temperature and elimination of troublesome thermal gradients along the emitter and collector in spacecrafts.

Dehumidification and Air Conditioning

In an air conditioning system, the colder the air as it passes over the cooling coil (evaporator), the more the moisture is condensed out. The heat pipe is designed to have one section in the warm incoming stream and the other in the cold outgoing stream. By transferring heat from the warm return air to the cold supply air, the heat pipes create the double effect of pre-cooling the air before it goes to the evaporator and then re-heating it immediately.

Activated by temperature difference and therefore consuming no energy, the heat pipe, due to its pre-cooling effect, allows the evaporator coil to operate at a lower temperature, increasing the moisture removal capability of the air conditioning system by 50-100%. With lower relative humidity, indoor comfort can be achieved at higher thermostat settings, which results in net energy savings. Generally, for each 1° F rise in thermostat setting, there is a 7% savings in electricity cost. In addition, the pre-cooling effect of the heat pipe allows the use of a smaller compressor.

Laptop Cooling

Heat pipe technology originally used for space applications has been applied it to laptop computer cooling. It is an ideal, cost effective solution. Its light weight (generally less than 40 grams), small, compact profile, and its passive operation, allow it to meet the demanding requirements of laptops.

For an 8 watt CPU with an environmental temperature no greater than 40°C it provides a 6.25°C/watt thermal resistance, allowing the processor to run at full speed under any environmental condition by keeping the case temperature at 90°C or less.

Figure 2: Heat Sink Inside a Laptop

One end of the heat pipe is attached to the processor with a thin, clip-on mounting plate. The other is attached to the heat sink, in this case, a specially designed keyboard RF shield. This approach uses existing parts to minimize weight and complexity. The heat pipe could also be attached to other physical components suitable as a heat sink to dissipate heat. (See photo of inside of laptop computer).

Because there are no moving parts, there is no maintenance and nothing to break. Some are concerned about the possibility of the fluid leaking from the heat pipe into the electronics. The amount of fluid in a heat pipe of this diameter is less than 1cc. In a properly designed heat pipe, the water is totally contained within the capillary wick structure and is at less than 1 atmosphere of pressure. If the integrity of the heat pipe vessel were ever compromised, air would leak into the heat pipe instead of the water leaking out. Then the fluid would slowly vaporize as it reaches its atmospheric boiling point. A heat pipe’s MTTF is estimated to be over 100,000 hours of use.

Laptop Thermal Control

Heat pipes have proven to be the excepted means of providing thermal control in notebook and Mobil PCs systems. Heat pipes can move and dissipate CPU generate heat selectively throughout the system without affecting temperature sensitive components. Low wattage heat pipes (under 20 watts) have standardized input plates to the heat pipe. The connection to the heat exchanger via the heat pipe can have any number of configurations to accommodate component placement, multiple power ranges and fan options.{parse block="google_articles"}

The heat pipe solutions for thermal control at this level is a component and overall systems requirement. Not only do the heat pipes take on a different configuration with multiple heat pipes and cooling fins, but also airflow becomes the critical design factor. Heat pipes designed to move 75 watts are usually flat with fin stacks from three to six inches, in many cases with fins mounted on each side of the CPU input pad. Input pads are standard using stand-offs, transition sockets, and bolster plates on the bottom of the PC board. The spring clips used on the fan/heat sink combination won’t work here. Airflow management is important in the overall efficiency of the heat pipe and should be calculated along with the intended heat pipe design.

Figure 3: Heat Pipe on a 500 MHz System

Thermal solutions are normally designed with multiple heat pipes, dedicated airflow and maximum input area. Fins stacks typically extend over both sides of the CPU. Input attachment to the CPU is with stand-offs, transition sockets or bolster plates.

The 500MHz operating system shown in Figure 3 uses two thermal products, heat pipes to transfer the CPU heat (100 to 300 watts) and a second internal or external cooling source. Input power is generated from multiple CPUs and components with single or multiple heat pipes. Cooling temperatures on the output range from -0° C to - 40° C. This system requires thermal isolation because of dewpoint considerations.

Flexible Solutions

Heat pipes are manufactured in a multitude of sizes and shapes. Unusual application geometry can be easily accommodated by the heat pipe’s versatility to be shaped as a heat transport device. If some range of motion is required, heat pipes can even be made of flexible material.

Two of the most common are:

Constant Temperature: The heat pipe maintains a constant temperature or temperature range.

Diode: The heat pipe will allow heat transfer in only one direction.

Figure 4: Flexible Style Heat Pipes

Mega Flats

Flat heat pipes are typically used for cooling printed circuit boards or for heat leveling to produce an isothermal plane. Mega flats are several flat heat pipes sandwiched together.

Figure 5: Flat Style Heat Pipe Materials

Some of the flat heat pipes manufactured are:

XY Mega Flats: Surface maintained within .01° F isothermal with concentrated load centers. 6" X 6" Mega Flat: Dissipated 850 watts from a printed circuit board.

Weight Reduction Mega Flats:

Standard - aluminum construction.

Lightweight - ½ the weight of aluminum.

Very light weight - 1/3 the weight of aluminum.

SEM C and SEM E Mega Flats in stock. Low and light weight coefficient of thermal expansion (CTE) Mega Flats - any CTE from 2 to 10. Alloy H: 70% more conductive than, or 40% less weight than copper clad invar.

Cost Effectiveness of Heat Pipes

The cost of heat pipes designed for laptop use is very competitive compared to other alternatives. Cost is partially offset and justified by improved system reliability and the increased life of cooler running electronics. Heat pipes, in quantity, cost a few dollars each while an entire cooling system will cost between $5 - $10 in production quantities, depending on the final design. Standard design products are available to reduce cost even further. Heat pipe manufacture has been a difficult area to compete in. Simple in concept, but difficult to apply commercially, the heat pipe is a very elusive technology & holds the key to the future of heat transfer and its allied applications.

Introduction to IAPWS-IF97

That's why a good deal of work has been spent on the investigation and measurement of water properties over the years. Thermodynamic, transport and other properties of water are known better than of any other substance. Accurate data are especially needed for the design of equipment in steam power plants (boilers, turbines, condensers). In this field it's also important that all parties involved, e.g., companies bidding for equipment in a new steam power plant, base their calculations on the same property data values because small differences may produce appreciable differences.

A standard for the thermodynamic properties of water over a wide range of temperature and pressure was developed in the 1960's, the 1967 IFC Formulation for Industrial Use (IFC-67). Since 1967 IFC-67 has been used for "official" calculations such as performance guarantee calculations of power cycles. The equations underlying IFC-97 are published for example in [1].

In 1997, IFC-67 has been replaced by a new formulation, the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam or IAPWS-IF97 for short. IAPWS-IF97 was developed in an international research project coordinated by the International Association for the Properties of Water and Steam (IAPWS). The formulation is described in a paper by W. Wagner et al., "The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam," ASME J. Eng. Gas Turbines and Power, Vol. 122 (2000), pp. 150-182 and several steam table books, among others ASME Steam Tables and Properties of Water and Steam by W. Wagner, Springer 1998.

Download the PDF article supplements in the File Repository.

IAPWS-IF97 uses some property constants of water for evaluating the equations for the thermodynamic properties. The reference values of these constants are as follows.

The value of the specific gas constant

R = 0.461 526 kJ/(kg K)

results from the recommended value of the molar gas constant

R_m = 8.314 51 kJ/(kmol K)

and the molecular weight of ordinary water

M = 18.015 257 kg/kmol

Values of the critical temperature, critical pressure and critical density are taken as

T_c = 647.096 K p_c = 220.64 bar ?_c = 322 kg/m³

The triple-point temperature as defined in the International Temperature Scale of 1990 (ITS-90) is

T_t = 273.16 K = 0.01 °C

and the corresponding pressure at the triple point

p_t = 611.657 Pa

Finally, the temperature at the normal boiling point (at a pressure of 1.013 25 bar) is

T_b = 373.1243 K = 99.9743 °C

Equations of IAPWS-IF97

The IAPWS-IF97 divides the thermodynamic surface into five regions (see Figure 1):

• region 1 for the liquid state from low to high pressures,
• region 2 for the vapor and ideal gas state,
• region 3 for the thermodynamic state around the critical point,
• region 4 for the saturation curve (vapor-liquid equilibrium),
• region 5 for high temperatures above 1073.15 K (800 °C) and pressures up to 10 MPa (100 bar).

Figure 1: Calculation Regions for Water and Steam

For regions 1, 2, 3 and 5 the authors of IAPWS-IF97 have developed fundamental equations of very high accuracy. Regions 1, 2 and 5 are covered by fundamental equations for the Gibbs free energy g(T,p), region 3 by a fundamental equation for the Helmholtz free energy f(T,v). All thermodynamic properties can then be calculated from these fundamental equations by using the appropriate thermodynamic relations. For region 4 a saturation-pressure equation has been developed.

In chemical engineering applications mainly regions 1, 2, 4, and to some extent also region 3 are of interest. The range of validity of these regions, the equations for calculating the thermodynamic properties, and references are summarized in Attachment 1. The equations of the high-temperature region 5 should be looked up in the references.

For regions 1 and 2 the thermodynamic properties are given as a function of temperature and pressure, for region 3 as a function of temperature and density. For other independent variables an iterative calculation is usually required. So-called backward equations are provided in IAPWS-IF97 which allow direct calculation of properties as a function of some other sets of variables (see references).

Accuracy of the equations and consistency along the region boundaries are more than sufficient for engineering applications. Details can be found in the references.

IAPWS Transport Properties

The International Association for the Properties of Water and Steam (IAPWS) has not only developed an international standard for the thermodynamic properties of water and steam but also equations for transport properties and other properties [2-6]. We have summarized the equations for calculating the transport properties dynamic viscosity and thermal conductivity as well as the surface tension of the interface between the liquid and the vapor phase of water in Attachment 2 . IAPWS also gives equations for the static dielectric constant and the refractive index of water which are of less interest in chemical engineering applications. If required these equations can be found in the references [2, 3].

The equations for dynamic viscosity and thermal conductivity are given as a function of temperature and density. The use of density as an independent variable makes it possible to calculate properties of the liquid and vapor phase using one single equation. In most cases, however, temperature and pressure are the independent variables and the density must be determined first from the IAPWS-IF97 equations.

Viscosity can be calculated for temperatures from 0 °C to 900 °C and for pressures up to at least 3000 bar depending on the temperature. The equation for thermal conductivity can be applied for temperatures from 0 °C to 800 °C and pressures up to at least 1000 bar. Surface tension can be calculated over the whole range where a liquid-vapor interface exists, i.e. from the triple point to the critical point of water. Accuracy of the equations is more than sufficient for engineering applications. Details can be found in the references [4-6].

MS™ Excel Add-In

Functions are available for calculating the following properties in the single-phase state for temperatures between 273.15 K and 1073.15 K and pressures between 0 and 1000 bar:

• density
• specific internal energy
• specific enthalpy
• specific entropy
• specific isobaric heat capacity
• specific isochoric heat capacity
• dynamic viscosity
• thermal conductivity

Additionally there are functions for calculating the boiling point temperature as a function of pressure and the vapor pressure as a function of temperature as well as above named properties for the saturated liquid and vapor state both as a function of temperature and pressure between the triple point and the critical point.

The functions are provided as an Add-In file for MS Excel. After downloading and decompressing the archive file the Add-In file "water97_v13.xla" may be loaded in Excel by going to Tools...Add-ins or by simply double clicking on "water97_v13.xla" in Explorer. The water property functions are then available just like built-in functions. In the function wizard list they can be found under User Defined.

The list of available functions with syntax, arguments, units, and examples can be found in the accompanying readme file.

You may use this add-in file for free. However, I retain all rights to it and it may not be sold or distributed as part of another package that is sold without my express permission. All files are provided "as is" without warranty of any kind.

While I can't provide full technical support I will do my best to answer questions or to help via e-mail (see end of article for email link) if you have any problems. Suggestions from users are also welcome.

• Download Add-In (iapwsif97_v13.zip, 51 kB)

References

1. Properties of Water and Steam in SI-Units, 2nd Revised and Updated Printing, Springer 1979.
2. William T. Parry et al., ASME International Steam Tables for Industrial Use, American Society of Mechanical Engineers 2000.
3. W. Wagner, A. Kruse, Properties of Water and Steam, Springer-Verlag, Berlin 1998.
4. IAPWS Release on the Viscosity of Ordinary Water Substance, IAPWS Secretariat 1997.
5. IAPWS Release on the Thermal Conductivity of Ordinary Water Substance, IAPWS Secretariat 1998.
6. IAPWS Release: "Surface Tension of Ordinary Water Substance", IAPWS Secretariat 1994.

IAPWS Releases are available from the Executive Secretary of IAPWS.

Download the PDF article supplements in the File Repository.

While placing insulation onto a pipe is fairly easy, resolving issues such as what type of insulation to use and how much is not so easy. Insulation is available in nearly any material imaginable. The most important characteristics of any insulation material include a low thermal conductivity, low tendency toward absorbing water, and of course the material should be inexpensive. In the chemical industry, {parse block="google_articles"}the most common insulators are various types of calcium silicate or fiberglass. Calcium silicate is generally more appropriate for temperatures above 225 ^°C (437 ^°F), while fiberglass is generally used at temperatures below 225 ^°C.

Figure 1: Thermal Conductivity of Calcium Silicate Insulation		Figure 2: Thermal Conductivity of Fiberglass Insulation

A Brief Look at Theory

The most basic model for insulation on a pipe is shown below. R1 and R2 show the inside and outside radius of the pipe respectively. R3 shows the radius of the insulation. Typically when dealing with insulations, engineers must be concerned with linear heat loss or heat loss per unit length.

Generally, the heat transfer coefficient of ambient air is 40 W/m² K. This coefficient can of course increase with wind velocity if the pipe is outside. A good estimate for an outdoor air coefficient in warm climates with wind speeds under 15 mph is around 50 W/m² K.

Eq. (1)

The total heat loss per unit length is calculated by:

Eq. (2)

Figure 3: Heat Loss vs. Insulation Thickness

Since heat loss through insulation is a conductive heat transfer, there are instances when adding insulation actually increases heat loss. The thickness at which insulation begins to decrease heat loss is described as the critical thickness. Since the critical thickness is almost always a few millimeters, it is seldom (if ever) an issue for piping. Critical thickness is a concern however in insulating wires. Figure 3 shows the heat loss vs. insulation thickness for a typical insulation. It's easy to see why wire insulation is kept to a minimum as adding insulation would increase the heat transfer.

Thinking About Insulation from All Sides

Three major factors play an important role in determining insulation type and thickness. Here, we'll focus on resolving the thickness issue since many manufacturing facilities have a "standard" type of insulation that they use. The three key factors to examine are:

1. Economics
2. Safety
3. Process Conditions

Each situation must be studied to determine how to meet each one of these criteria. First, we'll examine each aspect individually, then we'll see how to consider all three for an example.

Economics

Table 1: Economic Indoor Insulation Thickness (American Units)

Table 2: Economic Indoor Insulation Thickness (Metric Units)

Table 3: Economic Outdoor Insulation Thickness (American Units)

Table 4: Economic Outdoor Insulation Thickness (Metric Units)

Example of Economic Thickness Calculation

Using the tables above, assuming a 6.0 in pipe at 500 ^°F in an indoor setting with an energy cost of $5.00/million Btu, what is the economic thickness?
Answer: Finding the corresponding block to 6.0 in pipe and $5.00/million Btu energy costs, we see temperatures of 250 ^°F, 600 ^°F, 650 ^°F, and 850 ^°F. Since our temperature does not meet 600 ^°F, we use the thickness before it. In this case, 250 ^°F or 1 1/2 inches of insulation. At 600 ^°F, we would increase to 2.0 inches of insulation.
Economic thickness charts from other sources will work in much the same way as this example.

Safety

{parse block="google_articles"}Pipes that are readily accessible by workers are subject to safety constraints. The recommended safe "touch" temperature range is from 130 ^°F to 150 ^°F (54.4 ^°C to 65.5 ^°C). Insulation calculations should aim to keep the outside temperature of the insulation around 140 ^°F (60 ^°C). An additional tool employed to help meet this goal is aluminum covering wrapped around the outside of the insulation. Aluminum's thermal conductivity of 209 W/m K does not offer much resistance to heat transfer, but it does act as another resistance while also holding the insulation in place. Typical thickness of aluminum used for this purpose ranges from 0.2 mm to 0.4 mm. The addition of aluminum adds another resistance term to Equation 1 when calculating the total heat loss:

Eq. (3)

However, when considering safety, engineers need a quick way to calculate the surface temperature that will come into contact with the workers. This can be done with equations or the use of charts. We start by looking at another diagram:

At steady state, the heat transfer rate will be the same for each layer:

Eq. (4)

Rearranging Equation 4 by solving the three expressions for the temperature difference yields:

Eq. (5)

Each term in the denominator of Equation 5 is referred to as the "resistance" of each layer. We will define this as Rs and rewrite the equation as:

Eq. (6)

Figure 4: Equivalent Thickness Chart for Calcium Silicate Insulation

Since the heat loss is constant for each layer, use Equation 4 to calculate Q from the bare pipe, then solve Equation 6 for T4 (surface temperature). Use the economic thickness of your insulation as a basis for your calculation, after all, if the most affordable layer of insulation is safe, that's the one you'd want to use. If the economic thickness results in too high a surface temperature, repeat the calculation by increasing the insulation thickness by 1/2 inch each time until a safe touch temperature is reached.

As you can see, using heat balance equations is certainly a valid means of estimating surface temperatures, but it may not always be the fastest. Charts are available that utilize a characteristic called "equivalent thickness" to simplify the heat balance equations. This correlation also uses the surface resistance of the outer covering of the pipe. Figure 4 shows the equivalent thickness chart for calcium silicate insulation. Table 5 shows surface resistances for three popular covering materials for insulation.

Table 5: Values for Surface Resistances
h ft² °F/Btu (m² °C/W)

With the help of Figure 4 and Table 5 (or similar data for another material you may be dealing with), the relation:

Eq. (7)

can be used to easily determine how much insulation will be needed to achieve a specific surface temperature. Let's look at an example to illustrate the various uses of this equation.

Example of Outer Surface Temperature Determination

Your supervisor asks you to install insulation on a new pipe in the plant. Recently, two workers suffered severe burns while incidentally touching the new piping so safety is of primary concern. He instructs you to be sure that this incident does not repeat itself. The pipe contains a heat transfer fluid at 850 ^°F (454 ^°C). The ambient temperature is usually near 85 ^°F (29.4 ^°C). After checking the supplies that you have available, you notice that you have calcium silicate insulation and aluminum available for covering. You would like to insulate the 16 inch pipe for a surface temperature of 130 ^°F.

Tsurface - Tambient = 130 ^°F - 85 ^°F = 45 ^°F, from Table 5 we estimate a Rs value for aluminum at 0.865 h ft^{2 °}F/Btu.
Taverage = (850 ^°F + 85 ^°F)/2 = 467.5 ^°F (242 ^°C), from Figure 1 we estimate a thermal conductivity of 0.0365 Btu/h ft ^°F (0.06317 W/m ^°C) for calcium silicate insulation.

From Figure 4 above, an equivalent thickness of 6 in corresponds to an actual thickness of nearly 5.0 in of insulation.

Process Conditions

The temperature of a fluid inside an insulated pipe is an important process variable that must be considered in many situations. Consider the length of pipe connecting two pieces of process equipment shown below:

In order to predict T2 for a given insulation thickness, we first make the following assumptions:

1. Constant fluid heat capacity over the fluid temperature range
2. Constant ambient temperature
3. Constant thermal conductivity for fluid, pipe, and insulation
4. Constant overall heat transfer coefficient
5. Turbulent flow inside pipe
6. 15 mph wind for outdoor calculations

where

Eq. (8)

and another heat balance equation yields:

Eq. (9)