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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.

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
  

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)

Setting Equation 8 equal to Equation 9 and solving for T2 yields:

Eq. (10)

Equation 10 provides another useful tool for analyzing insulation and its impact on a process. Equation 10 has been incorporated into the "Insulated Pipe Temperature Prediction Spreadsheet" available in the Download Section.

One example may be the importance of designing insulation thickness to prevent condensation on cold lines. Usually, when we hear the word "insulation" we instantly think of hot lines. However, there are times when insulation is used to prevent heat from entering a line. In this situation, the dew point temperature of the ambient air must be considered. Table 6 and Table 7 show dewpoint temperatures as a function of relative humidity and dry bulb temperatures.

Table 6: Dew Point Temperatures of Air (Fahrenheit)		Table 7: Dew Point Temperatures of Air (Celsius)

It is crucial that sufficient insulation is added so that the outer temperature of the insulation remains above the dewpoint temperature. At the dewpoint temperature, moisture in the air will condense onto the insulation and essentially ruin it.

Special Case

For the case of a bare pipe running outside, the chart below can be used to adjust the external heat transfer coefficient from 50 W/m2 K (8.8 Btu/h ft2 °F) to account for temperature difference and wind velocity:

Figure 6: Bare Pipe External Heat Transfer Coefficient Adjustment

{parse block="google_articles"}In the figure above, a typical reactor feed preheater (interchanger) is shown. The heat exchanger resides on the first level of the structure while the reactor is on the second level. During construction, stream 2 was not insulated because it runs from the exchanger directly to the ceiling away from workers so it posed no safety risk. The reaction is endothermic, so heat is supplied by a Dowtherm jacket surrounding the vessel. The equivalent length of the pipe containing stream 2 is 100 meters. A recent rise is fuel oil costs (which is used to heat the Dowtherm) has prompted the company to search for ways to conserve energy. With the data provided below, you recognize an opportunity for energy savings. Any increase in the reactor feed temperature will reduce the reactor duty and save money. What is the current reactor entrance temperature compared with the entrance temperature after applying the economic insulation thickness to the pipe?

Data:
Calcium silicate insulation
Temperature of stream 2 exiting the heat exchanger is 400 ^°C (752 ^°F)
Ambient temperature is 23.8 ^°C (75 ^°F)
Mass flow = 350,000 kg/h (771,470 lbs/h)
R_{inside pipe} = R1 = 101.6 mm (4.0 in)
R_{outside pipe} = R2 = 108.0 mm (4.25 in)
Thermal conductivity of pipe = k_pipe = 30 W/m K (56.2 Btu/h ft ^°F)
Ambient air heat transfer coefficient = ho = 50 W/m² K (8.8 Btu/h ft^{2 °}F)
Fluid heat capacity = Cp_fluid = 2.57 kJ/kg K (2.0 Btu/lb ^°F)
Fluid thermal conductivity = k_fluid = 0.60 W/m K (1.12 Btu/h ft ^°F)
Fluid viscosity = u_fluid = 5.2 cP
Energy costs = $4.74/million kJ ($5.00/million Btu)
Equivalent length of pipe = 100 meters (328 feet)

Calculations:

Temperature difference with insulation is nearly 5 ⁰C. While this doesn't sound too dramatic, consider the energy savings over one year with the insulation:

Q = mass flow x Cpfluid x temperature difference
Q = (350,000 kg/h)(2.57 kJ/kg K)(5.0K) = 4497500 kJ/h
4497500 kJ/h x 8760 hours/year = 39,398 million kJ/year
39,398 million kJ/year x $4.74/million kJ = $186,746 per year

By insulating the pipe, energy costs have decreased by nearly $187,000 per year

Summary

There are many factors to consider when thinking about insulation. Insulation save money for certain, but it can also be effective as a safety and process control device. Insulation can be used to regulate process temperatures, protect workers from serious injury, and save thousands of dollars in energy costs. One should never overlook it's usefulness. It's also bad practice to consider only one of the important factors discussed in this article. The key is to consider all factors that will be affected by installing insulation on a pipe or any other piece of equipment.

The various types of jackets used in process industry are :{parse block="google_articles"}

1. Spirally baffled jackets/ conventional jackets
2. Dimple jackets
3. Partial-pipe coil /limpet jacket
4. Panel type/ plate type coil jackets

Commonly used heat transfer medias include water, steam (various pressures), hot oil (such as Therminol™), and Dowtherm™ vapor.

Matching Jacket Types to Heat Transfer Media

Water: Depending on the process temperature, stress corrosion cracking can sometimes be a concern due to the chlorides usually found in water. In some cases, dimple jackets may requires the use of high-nickel alloys which are very expensive. The half-pipe coil can use 1/4'' thick carbon steel for the jacketing but their economy versus conventional jackets must to be considered. With services involving large volumes of water (used to maintain a high temperature difference) the conventional jacket usually offers the best solution.

Steam: Both dimple and half coil jackets are well suited use with high pressure steam. The dimple jackets are generally limited to 300 psig design pressure while half-coil jackets can be used up to a design pressure of 750 psig. For half-pipe coil jacket, the higher heat flux rate may require multiple sections of jackets to avoid having condensate covering too much of the heat transfer area. For low pressure steam services convention jackets are a much more economical choice.

Hot Oils and Heat Transfer Fluids: Although pressures are usually low when using oils or heat transfer fluids, the temperatures are usually high. The result is low allowable stress values for the inner-vessel material. Therefore both half-pipe jackets and dimple jackets can provide good solutions. Conventional jackets require a greater shell thickness along with expansion joints to eliminate stresses induced by the difference in thermal expansion when the jacket is not manufacturered from the same material as that of shell.

Dowtherm™ Vapors:The ability to vary the distance between the outer and innver vessel walls makes conventional jackets ideally suited to handle Dowtherm™ vapors. Also since Dowtherm vapor has a low enthalpy (1/10 that of steam) a large jacket space is needed for given heat flux. The jacket must be designed in accordance with ASME Code specifications. The maximum allowable space is limited by section UA-104 Paragraph c and s.

Conventional Jackets

Figure 1: Conventional Jacket

"Conventional jackets" can be divided into two (2) main categories: baffled and non-baffled. Baffled jackets often utilize what is known as a spirally wound baffle. The baffle consist of a metal strip wound around the inner vessel wall from the jacket utility inlet to the utility outlet. The baffle directs the flow in a spiral path with a fluid velocity of 1-4 ft/s. The fabrication methods does allow for small internal leakage or bypass around the baffle. Generally, bypass flows can exceed 1/3 to 1/2 of the total circulating flow.{parse block="google_articles"}

Conventional baffled jackets are usually applied with small vessels using high temperatures where the internal pressure in more than twice the jacket pressure.

Spirally baffled jackets are limited to a pressure of 100 psig because vessel wall thickness becomes large and the heat transfer is greatly reduced. In the case of an alloy reactor, a very costly vessel can result. For high temperature applications, the thermal expansion differential must be considered when choosing materials for the vessel and jacket. Design and construction details are given in Division 1 of the ASME Code, Section VIII, Appendix IX, "Jacketed Vessel".

Heat Transfer Coefficients: Conventional Jackets without Baffles

Figure 2: Schematic of Conventional Jacket

Where:
h_j = Local heat transfer coefficient on the jacket side
D_e = Equivalent hydraulic diameter
N_Re = Reynolds Number
N_Pr = Prandtl Number
L = Length of jacket passage
D_jo = Outer diameter of jacket
D_ji = Inner diameter of jacket
N_Gr = Graetz number

N_Re = DVρ/μ
Where D is the equivalent diameter, V is the fluid velocity, ρ is the fluid density, μ and is the fluid viscosity.

The Prandtl Number is defined as:

N_Pr = C_p μ / k
Where Cp is the specific heat, μ is the viscosity, and k is the thermal conducitivity of the fluid.

The Graetz Number is defined as:

N_Gr = (m C_p) / (k L)
Where m is the mass flow rate, C_p is the specific heat, k is the thermal conducitivity, and L is the jacket passage length.

The equivalent diameter is defined as follows:

D_e = D_jo-D_ji for laminar flow
D_e = ((D_jo)2 - (D_ji)2)/D_ji for turbulent flow

Conventional Jackets with Baffles

For conventional jackets with baffles, the following can be used to calculate the heat transfer coefficient:

Figure 3: Schematic of Conventional Jacket with Baffle

Two new variables are introduced. Dc is defined as the centerline diameter of the jacket passage. It is calculated as D_ji + ((D_jo-D_ji)/2). The viscosity at the jacket wall is now defined as µ_w. When calculating the heat transfer cofficients, an effective mass flow rate should be taken as 0.60 x feed mass flow rate to account for the substantial bypassing that will be expected. D_e is defined at 4 x jacket spacing. The flow cross sectional area is defined as the baffle pitch x jacket spacing.

Eq. (4) Eq. (5) Eq. (6)

Half Pipe Coil Jackets

Figure 4: Half Pipe Coil Jacket

Half pipe coils provide high velocity and turbulence. The velocity can be closely controlled to achieve a good film coefficient. The good heat transfer rates, combined with the structural rigidity of the design, make half-pipe coils a good choice for a wide range of applications. A good design velocity for liquid utilities is 2.5 to 5 ft/s. {parse block="google_articles"}The maximumspacing between coils should be limited to 3/4". Half-pipe coils are ideally suited for high temperature applications where the utility fluid is a liquid.

There are no limitations of the number of inlet and outlet nozzles, so the jacket can be divided in multipass zones for maximum flexibility. The rigidity of the half-pipe coil design can also minimize the thickness of the inner vessel wall which can be especially attractive when utilizing alloys.

Half-pipe coil jackets are not covered in Section VIII, Division I of the ASME code. Generally, they are limited to 600 psig design pressure and a design temperature up to 720 °F. A carbon steel half-pipe jacket can be applied to a stainless steel vessel up to 300 °F. Over 300 °F, the jacket should be stainless steel as well.

Heat Transfer Coefficients: Half-Pipe Coil Jackets

Half-pipe coil jackets are generally manufactured with either 180° or 120° central angles (D_ci):

Figure 5: Depiction of Center Angles

Figure 6: Half-Pipe Coil to Tank Details

For a 180° central angle:

Equivalent Heat Transfer Diameter, De = Π / (4 D_ci)

Cross Section Area of Flow, Ax = Π / (8 (D_ci²))

For a 120° central angle:

Equivalent Heat Transfer Diameter, De = 0.708 D_ci

Cross Section Area of Flow, Ax = 0.154 (D_ci²)

Using the same nomenclature as previous, the heat transfer coefficients are calculated as follows:

Do not confuse D_ci with D_c. D_c is defined as D_ji + ((D_jo-D_ji)/2).

Hydraulic Radius: Half-Pipe Coil Jackets

Figure 7: Hydraulic Radius Dimensions

Referring to Figure7:

Eq. (9)

Dimple Jackets or Plate Coils

The design of dimple jackets permits construction from light gauge metals without sacrificing the strength required to withstand the specified pressure. This results in considerable cost saving as compared to convention jackets. Design calculation begin with an assumed flow velocity between 2 and 5 ft/s. As a rule of thumb the jacket pressure will be governing when internal pressure of vessel is less than 1.67 times the jacket pressure. {parse block="google_articles"}At such conditions, dimple jackets are typically more economical than other choices. However in small vessels (less than 10 gallons) it is not practical to apply dimple jackets.

The design of dimple jackets is governed by the National Board of Boiler and Pressure Vessel Inspectors and can be stamped in accordance with ASME Unfired Pressure Vessel Code. Dimple jackets are limited to a pressure of 300 psi by Section VIII, Div.I of the ASME Code. The design temperature is limited to 700 °F. At high temperatures, it is mandatory that jacket be fabricated from a metal having same thermal coefficient of expansion as that used in inner vessel.

Figure 8: Vessel with Dimple Jacket Installed		Figure 9: Dimple Jacket Details

Heat Transfer Coefficients: Dimple Jackets

All other variables are as previously defined. Garvin (CEP Magazine, April 2001) reports an average error of 9.8% with manufacturers data for the above correlation and a maximum error of 30% over 116 data points. This results in average deviations in the heat transfer coefficient of 15-20% most of which was at velocities below 2 ft/s. Good agreement with manufacturers data was found between 3 and 6 ft/s. A recommended excess area of 15% should be used in this velocity range.

The correlation above is for integrally welded jackets (ie. jackets welded directly to the vessel). If a dimple jacket is clamped onto an existing vessel and adhered with heat transfer mastic, the overall heat transfer coefficient of the system will be very low. Mastic is used to try to minimize air pocket resistances between the vessel wall and the jacket. Historically, this arrangement results in poor heat transfer. A recommended overall heat transfer coefficient of 10-15 Btu/h ft² °F should be used for such systems regardless of the utility used.

Pressure Drop: Dimple Jackets

The pressure loss in a dimple jacket can be estimated from the following for water or water-like fluids:

Pressure Loss in Jacket = (Total Lenght of Flow, ft) x ((0.40 x Velocity, ft/s) - 0.35)

Pressure Loss Across Entire Jacket (including inlets and outlets) = Pressure Loss in Jacket + (0.10)(Pressure Loss in Jacket)

The above estimates should be used for velocities ranging from 1.5 to 6 ft/s.

This method is based on a graph found on page 217 of the Encyclopedia of Pharmaceutical Technology by James Swarbrick.

For detailed design, it is advisable to rely on manufacturer's data for pressure drop calculations.

Heat Transfer Coefficients Inside Agitated Vessels

In order to complete the overall heat transfer coefficient calculation, an estimate must also be made inside the process vessel. The following estimate should yield reasonable results:

Eq. (11)

Where:

A_d = agitator diameter
N = agitator speed, rev/s
All other variables as previously defined
a is defined by the table below:

Calculating the Overall Heat Transfer Coefficient

When calculating the overall heat transfer coefficient for a system, the vessel wall resistance and any jacket fouling must be taken into account:

Eq. (12)

Notice that the thermal conducitivity of the vessel wall and the wall thickness are included in the calculation. A typical jacket fouling factor is around 0.001 h ft² °F/Btu. When calculating the overall heat transfer coefficient, use a "common sense" analysis of the final value. The tables below will give some guidance to reasonable final values:

Table 2: Estimated Overall Heat Transfer Coefficients for Jacketed Tank Systems (Imperial Units)		Table 3: Estimated Overall Heat Transfer Coefficients for Jacketed Tank Systems (Metric Units)

References

1. Heat Transfer Design Methods by 'John J. McKetta'
2. Hand Book of chemical Engineering Calculation 3rd Edition by 'Micclas P. Chopey'.
3. Applied Process Design for Chemical and Petrochemical Plants by 'Ludwig' Volume 3.
4. Estimate Heat Transfer and Friction in Dimple Jackets, 'John Garvin', CEP Magazine, April 2001, p. 73
5. Heat Transfer in Agitated Jacketed Vessels, 'Robert Dream', Chemical Engineering, January 1999, p. 90
6. Encyclopedia of Pharmaceutical Technology, 'James Swarbrick', p. 217
7. Tranter Plate Coil Product Manual

A few of the frequently asked questions are:

1. Are the existing processes as energy efficient as they should be?
2. How can new projects be evaluated with respect to their energy requirements?{parse block="google_articles"}
3. What changes can be made to increase the energy efficiency without incurring any cost?
4. What investments can be made to improve energy efficiency?
5. What is the most appropriate utility mix for the process?
6. How to put energy efficiency and other targets like reducing emissions, increasing plant capacities, improve product qualities etc, into a one coherent strategic plan for the overall site?

All of these questions and more can be answered with a full understanding of Pinch Technology and an awareness of the available tools. for applying it in a practical way. This article aims to provide the basic knowledge of the concepts in pinch technology and how they have been be applied across a wide range of process industries.

What is Pinch Technology

Meaning of the Term "Pinch Technology"

The term "Pinch Technology" was introduced by Linnhoff and Vredeveld to represent a new set of thermodynamically based methods that guarantee minimum energy levels in design of heat exchanger networks. Over the last two decades it has emerged as an unconventional development in process design and energy conservation. The term ‘Pinch Analysis’ is often used to represent the application of the tools and algorithms of Pinch Technology for studying industrial processes. Developments of rigorous software programs like PinchExpressTM, SuperTargetTM, Aspen PinchTM have proved to be very useful in pinch analysis of complex industrial processes with speed and efficiency.

Basis of Pinch Analysis

Pinch technology presents a simple methodology for systematically analysing chemical processes and the surrounding utility systems with the help of the First and Second Laws of Thermodynamics. The First Law of Thermodynamics provides the energy equation for calculating the enthalpy changes (dH) in the streams passing through a heat exchanger. The Second Law determines the direction of heat flow. That is, heat energy may only flow in the direction of hot to cold. This prohibits ‘temperature crossovers’ of the hot and cold stream profiles through the exchanger unit. In a heat exchanger unit neither a hot stream can be cooled below cold stream supply temperature nor a cold stream can be heated to a temperature more than the supply temperature of hot stream. In practice the hot stream can only be cooled to a temperature defined by the ‘temperature approach’ of the heat exchanger. The temperature approach is the minimum allowable temperature difference (DTmin) in the stream temperature profiles, for the heat exchanger unit. The temperature level at which DTmin is observed in the process is referred to as "pinch point" or "pinch condition". The pinch defines the minimum driving force allowed in the exchanger unit.

Objectives of the Pinch Analysis

Pinch Analysis is used to identify energy cost and heat exchanger network (HEN) capital cost targets for a process and recognizing the pinch point. The procedure first predicts, ahead of design, the minimum requirements of external energy, network area, and the number of units for a given process at the pinch point. Next a heat exchanger network design that satisfies these targets is synthesized. Finally the network is optimized by comparing energy cost and the capital cost of the network so that the total annual cost is minimized. Thus, the prime objective of pinch analysis is to achieve financial savings by better process heat integration (maximizing process-to-process heat recovery and reducing the external utility loads). The concept of process heat integration is illustrated in the example discussed below.

A Simple Example of Process Integration by Pinch Analysis

Consider the following simple process [Figure 1a] where feed stream to a reactor is heated before inlet to a reactor and the product stream is to be cooled. The heating and cooling are done by use of steam (Heat Exchanger -1) and cooling water (Heat Exchanger-2), respectively. The Temperature (T) vs. Enthalpy (H) plot for the feed and product streams depicts the hot (Steam) and cold (CW) utility loads when there is no vertical overlap of the hot and cold stream profiles.

Figure 1a: A Simple Flow Scheme with T-H profile	Figure 1b: Improved Flow Scheme with T-H profile

An alternative, improved scheme is shown in Figure 1b where the addition of a new ‘Heat Exchanger–3’ recovers product heat (X) to preheat the feed. The steam and cooling water requirements also get reduced by the same amount (X). The amount of heat recovered (X) depends on the ‘minimum approach temperature’ allowed for the new exchanger. The minimum temperature approach between the two curves on the vertical axis is DTmin and the point where this occurs is defined as the "pinch". From the T-H plot, the X amount corresponds to a DTmin value of 20 oC. Increasing the DTmin value leads to higher utility requirements and lower area requirements.

Development of the Pinch Technology Approach

When the process involves single hot and cold streams (as in above example) it is easy to design an optimum heat recovery exchanger network intuitively by heuristic methods. In any industrial set-up the number of streams is so large that the traditional design approach has been found to be limiting in the design of a good network. With the development of pinch technology in the late 1980’s, not only optimal network design was made possible, but also considerable process improvements could be discovered. Both the traditional and pinch approaches are depicted in Figure 2.

Figure 2: Graphic Representation of Traditional and Pinch Design Approaches

First, the core of the process is designed with fixed flow rates and temperatures yielding the heat and mass balance for the process. Then the design of a heat recovery system is completed. Next, the remaining duties are satisfied by the use of the utility system. Each of these exercises is performed independently of the others.

Process integration using pinch technology offers a novel approach to generate targets for minimum energy consumption before heat recovery network design. Heat recovery and utility system constraints are then considered in the design of the core process. Interactions between the heat recovery and utility systems are also considered. The pinch design can reveal opportunities to modify the core process to improve heat integration. The pinch approach is unique because it treats all processes with multiple streams as a single, integrated system. This method helps to optimize the heat transfer equipment during the design of the equipment.{parse block="google_articles"}

Pinch originated in the petrochemical sector and is now being applied to solve a wide range of problems in mainstream chemical engineering. Wherever heating and cooling of process materials takes places there is a potential opportunity. Thus initial applications of the technology were found in projects relating to energy saving in industries as diverse as iron and steel, food and drink, textiles, paper and cardboard, cement, base chemicals, oil, and petrochemicals.

Early emphasis on energy conservation led to the misconception that conservation is the main area of application for pinch technology. The technology, when applied with imagination, can affect reactor design, separator design, and the overall process optimization in any plant. It has been applied to processing problems that go far beyond energy conservation. It has been employed to solve problems as diverse as improving effluent quality, reducing emissions, increasing product yield, debottlenecking, increasing throughput, and improving the flexibility and safety of the processes.

Since its commercial introduction, pinch technology has achieved an outstanding record of success in the design and retrofit of chemical manufacturing facilities. Documented results reported in the literature show that energy costs have been reduced by 15-40%, capacity debottlenecking achieved by 5-15% for retrofits, and capital cost reduction of 5-10% for new designs.

Basic Concepts of Pinch Analysis

Most industrial processes involve transfer of heat either from one process stream to another process stream (interchanging) or from a utility stream to a process stream. In the present energy crisis scenario all over the world, the target in any industrial process design is to maximize the process-to-process heat recovery and to minimize the utility (energy) requirements. To meet the goal of maximum energy recovery or minimum energy requirement (MER) an appropriate heat exchanger network (HEN) is required. The design of such a network is not an easy task considering the fact that most processes involve a large number of process and utility streams. As explained in the previous section, the traditional design approach has resulted in networks with high capital and utility costs. With the advent of pinch analysis concepts, the network design has become very systematic and methodical.{parse block="google_articles"}

A summary of the key concepts, their significance, and the nomenclature used in pinch analysis is given below:

• Combined (Hot and Cold ) Composite Curves: Used to predict targets for:
  • Minimum energy (both hot and cold utility) required,
  • Minimum network area required, and
  • Minimum number of exchanger units required.
• DTmin and Pinch Point: The DTmin value determines how closely the hot and cold composite curves can be ‘pinched’ (or squeezed) without violating the Second Law of Thermodynamics (none of the heat exchangers can have a temperature crossover).
• Grand Composite Curve: Used to select appropriate levels of utilities (maximize cheaper utilities) to meet over all energy requirements.
• Energy and Capital Cost Targeting: Used to calculate total annual cost of utilities and capital cost of heat exchanger network.
• Total Cost Targeting: Used to determine the optimum level of heat recovery or the optimum DTmin value, by balancing energy and capital costs. Using this method, it is possible to obtain an accurate estimate (within 10 - 15%) of overall heat recovery system costs without having to design the system. The essence of the pinch approach is the speed of economic evaluation.
• Plus/Minus and Appropriate Placement Principles: The "Plus/Minus" Principle provides guidance regarding how a process can be modified in order to reduce associated utility needs and costs. The Appropriate Placement Principles provide insights for proper integration of key equipments like distillation columns, evaporators, furnaces, heat engines, heat pumps, etc. in order to reduce the utility requirements of the combined system.
• Total Site Analysis: This concept enables the analysis of the energy usage for an entire plant site that consists of several processes served by a central utility system.

With further research, new topics like ‘Regional Energy Analysis’, ‘Network Pinch’, ‘Top Level Analysis’, ‘Optimisation of Combined Heat & Power’, ‘Water Pinch’, and ‘Hydrogen Pinch’ are being developed. These basic terms and concepts have become the foundation of what we now call Pinch Technology.

Steps of the Pinch Analysis

In any Pinch Analysis problem, whether a new project or a retrofit situation, a well-defined stepwise procedure is followed (Figure 3). It should be noted that these steps are not necessarily performed on a once-through basis, independent of one another. Additional activities such as re-simulation and data modification occur as the analysis proceeds and some iteration between the various steps is always required.

Figure 3: Steps in Pinch Analysis

Step 1: Identification of the Hot, Cold and Utility Streams in the Process

• ‘Hot Streams’ are those that must be cooled or are available to be cooled. e.g. product cooling before storage
• ‘Cold Streams’ are those that must be heated e.g. feed preheat before a reactor.
• ‘Utility Streams’ are used to heat or cool process streams, when heat exchange between process streams is not practical or economic. A number of different hot utilities (steam, hot water, flue gas, etc.) and cold utilities (cooling water, air, refrigerant, etc.) are used in industry.

The identification of streams needs to be done with care as sometimes, despite undergoing changes in temperature, the stream is not available for heat exchange. For example, when a gas stream is compressed the stream temperature rises because of the conversion of mechanical energy into heat and not by any fluid to fluid heat exchange. Hence such a stream may not be available to take part in any heat exchange. In the context of pinch analysis, this stream may or may not be considered to be a process stream.

Step 2: Thermal Data Extraction for Process & Utility Streams

For each hot, cold and utility stream identified, the following thermal data is extracted from the process material and heat balance flow sheet:

• Supply temperature (TS °C) : the temperature at which the stream is available.
• Target temperature (TT °C) : the temperature the stream must be taken to.
• Heat capacity flow rate (CP kW/ °C) : the product of flow rate (m) in kg/sec and specific heat (Cp kJ/kg °C).
  CP = m x Cp
• Enthalpy Change (dH) associated with a stream passing through the exchanger is given by the First Law of Thermodynamics:
  First Law energy equation: d H = Q ± W
  In a heat exchanger, no mechanical work is being performed:
  W = 0 (zero)
  The above equation simplifies to: d H = Q, where Q represents the heat supply or demand associated with the stream. It is given by the relationship: Q= CP x (TS - TT).
  Enthalpy Change, dH = CP x (TS - TT)
  ** Here the specific heat values have been assumed to be temperature independent within the operating range.

The stream data and their potential effect on the conclusions of a pinch analysis should be considered during all steps of the analysis. Any erroneous or incorrect data can lead to false conclusions. In order to avoid mistakes, the data extraction is based on certain qualified principles.

Step 3: Selection of the Initial DTmin Value

The design of any heat transfer equipment must always adhere to the Second Law of Thermodynamics that prohibits any temperature crossover between the hot and the cold stream i.e. a minimum heat transfer driving force must always be allowed for a feasible heat transfer design. Thus the temperature of the hot and cold streams at any point in the exchanger must always have a minimum temperature difference (DTmin). This DTmin value represents the bottleneck in the heat recovery.

In mathematical terms, at any point in the exchanger:

The value of DTmin is determined by the overall heat transfer coefficients (U) and the geometry of the heat exchanger. In a network design, the type of heat exchanger to be used at the pinch will determine the practical Dtmin for the network. For example, an initial selection for the Dtmin value for shell and tubes may be 3-5 0C (at best) while compact exchangers such as plate and frame often allow for an initial selection of 2-3 0C. The heat transfer equation, which relates Q, U, A and LMTD (Log Mean Temperature Difference) is depicted in Figure 4.

Figure 4: The Heat Transfer Equation

For a given value of heat transfer load (Q), if smaller values of DTmin are chosen, the area requirements rise. If a higher value of DTmin is selected the heat recovery in the exchanger decreases and demand for external utilities increases. Thus, the selection of DTmin value has implications for both capital and energy costs. This concept will become clearer with the help of composite curves and total cost targeting discussed later.

Just as for a single heat exchanger, the choice of DTmin (or approach temperature) is vital in the design of a heat exchanger networks. To begin the process an initial DTmin value is chosen and pinch analysis is carried out. Typical DTmin values based on experience are available in literature for reference. A few values based on Linnoff March’s application experience are tabulated below for shell and tube heat exchangers.

Step 4: Construction of the Composite Curves and Grand Composite Curve

• COMPOSITE CURVES: Temperature - Enthalpy (T - H) plots known as ‘Composite curves’ have been used for many years to set energy targets ahead of design. Composite curves consist of temperature (T) – enthalpy (H) profiles of heat availability in the process (the hot composite curve) and heat demands in the process (the cold composite curve) together in a graphical representation.

In general any stream with a constant heat capacity (CP) value is represented on a T - H diagram by a straight line running from stream supply temperature to stream target temperature. When there are a number of hot and cold streams, the construction of hot and cold composite curves simply involves the addition of the enthalpy changes of the streams in the respective temperature intervals. An example of hot composite curve construction is shown in Figure 5a and b. A complete hot or cold composite curve consists of a series of connected straight lines, each change in slope represents a change in overall hot stream heat capacity flow rate (CP).{parse block="google_articles"}

For heat exchange to occur from the hot stream to the cold stream, the hot stream cooling curve must lie above the cold stream-heating curve. Because of the ‘kinked’ nature of the composite curves (Figure 6), they approach each other most closely at one point defined as the minimum approach temperature (DTmin). DTmin can be measured directly from the T-H profiles as being the minimum vertical difference between the hot and cold curves. This point of minimum temperature difference represents a bottleneck in heat recovery and is commonly referred to as the "Pinch". Increasing the DTmin value results in shifting the of the curves horizontally apart resulting in lower process to process heat exchange and higher utility requirements. At a particular DTmin value, the overlap shows the maximum possible scope for heat recovery within the process.  The hot end and cold end overshoots indicate minimum hot utility requirement (QHmin) and minimum cold utility requirement (QCmin), of the process for the chosen DTmin.

Figure 5: Temperature-Enthalpy Relations Used to Construct Composite Curves		Figure 6: Combined Composite Curves

Thus, the energy requirement for a process is supplied via process to process heat exchange and/or exchange with several utility levels (steam levels, refrigeration levels, hot oil circuit, furnace flue gas, etc.).

Graphical constructions are not the most convenient means of determining energy needs. A numerical approach called the "Problem Table Algorithm" (PTA) was developed by Linnhoff & Flower (1978) as a means of determining the utility needs of a process and the location of the process pinch. The PTA lends itself to hand calculations of the energy targets. 

To summarize, the composite curves provide overall energy targets but do not clearly indicate how much energy must be supplied by different utility levels. The utility mix is determined by the Grand Composite Curve.

• GRAND COMPOSITE CURVE (GCC): In selecting utilities to be used, determining utility temperatures, and deciding on utility requirements, the composite curves and PTA are not particularily useful. The introduction of a new tool, the Grand Composite Curve (GCC), was introduced in 1982 by Itoh, Shiroko and Umeda. The GCC (Figure 7) shows the variation of heat supply and demand within the process. Using this diagram  the designer can  find which utilities are to be used. The designer aims to maximize the use of the cheaper utility levels and minimize the use of the expensive utility levels. Low-pressure steam and cooling water are preferred instead of high-pressure steam and refrigeration, respectively.

The information required for the construction of the GCC comes directly from the Problem Table Algorithm developed by Linnhoff & Flower (1978). The method involves shifting (along the temperature [Y] axis) of the hot composite curve down by ½ DTmin and that of cold composite curve up by ½ DTmin. The vertical axis on the shifted composite curves shows process  interval temperature. In other words, the curves are shifted by subtracting part of the allowable temperature approach from the hot stream temperatures and adding the remaining part of the allowable temperature approach to the cold stream temperatures. The result is a scale based upon process temperature having an allowance for temperature approach (DTmin). The Grand Composite Curve is then constructed from the enthalpy (horizontal) differences between the shifted composite curves at different temperatures. On the GCC, the horizontal distance separating the curve from the vertical axis at the top of the temperature scale shows the overall hot utility consumption of the process.

Figure 7: Grand Composite Curve

Figure 7 shows that it is not necessary to supply the hot utility at the top temperature level. The GCC indicates that we can supply the hot utility over two temperature levels TH1 (HP steam) and TH2 (LP steam).  Recall that, when placing utilities in the GCC, intervals, and not actual utility temperatures, should be used. The total minimum hot utility requirement remains the same: QHmin = H1 (HP steam) + H2 (LP steam). Similarly, QCmin = C1 (Refrigerant) +C2 (CW). The points TH2 and TC2 where the H2 and C2 levels touch the grand composite curve are called the "Utility Pinches." The shaded green pockets represent the process-to-process heat exchange.

In summary, the grand composite curve is one of the most basic tools used in pinch analysis for the selection of the appropriate utility levels and for targeting of a given set of multiple utility levels. The targeting involves setting appropriate loads for the various utility levels by maximizing the least expensive utility loads and minimizing the loads on the most expensive utilities.

Step 5: Estimation of Minimum Energy Cost Targets

Once the DTmin is chosen, minimum hot and cold utility requirements can be evaluated from the composite curves. The GCC provides information regarding the utility levels selected to meet QHmin and QCmin requirements.

If the unit cost of each utility is known, the total energy cost can be calculated using the energy equation given below.

Eq. (1)

where Q_U = Duty of utility, kW, C_U = Unit cost of utility U, $/kW per year, and U = Total number of utilities used.

Step 6: Estimation of Heat Exchanger Network ( HEN ) Capital Cost Targets

The capital cost of a heat exchanger network is dependent upon three factors:

1. the number of exchangers,
2. the overall network area,
3. the distribution of area between the exchangers

Pinch analysis enables targets for the overall heat transfer area and minimum number of units of a heat exchanger network (HEN) to be predicted prior to detailed design. It is assumed that the area is evenly distributed between the units. The area distribution cannot be predicted ahead of design.

• AREA TARGETING: The calculation of surface area for a single counter-current heat exchanger requires the knowledge of the temperatures of streams in and out (dTLM i.e. Log Mean Temperature Difference or LMTD), overall heat transfer coefficient (U-value), and total heat transferred (Q). The area is given by the relation:

Eq. (2)

Figure 8: HEN AREA min Estimation from Composite Curves

The composite curves can be divided into a set of adjoining enthalpy intervals such that within each interval, the hot and cold composite curves do not change slope. Here the heat exchange is assumed to be "vertical" (pure counter-current heat exchange). The hot streams in any enthalpy interval, at any point, exchanges heat with the cold streams at the temperature vertically below it. The total area of the HEN (Amin) is given by the formula in Figure 8, where i denotes the ith enthalpy and interval j denotes the jth stream and dT_LM denotes LMTD in the ith interval.

The actual HEN total area required is generally within 10% of the area target as calculated above. With inclusion of temperature correction factors area targeting can be extended to non counter-current heat exchange as well

• NUMBER OF UNITS TARGETING: For the minimum number of heat exchanger units (N_min) required for MER (minimum energy requirement or maximum energy recovery), the HEN can be evaluated prior to HEN design by using a simplified form of Euler’s graph theorem. In designing for the minimum energy requirement (MER), no heat transfer is allowed across the pinch and so a realistic target for the minimum number of units (N_minMER) is the sum of the targets evaluated both above and below the pinch separately.

Eq. (3)

Where N_h = Number of hot streams, N_c=Number of cold streams, N_u = Number of utility streams, AP / BP : Above / Below Pinch

• HEN TOTAL CAPITAL COST TARGETING: The targets for the minimum surface area (Amin) and the number of units (Nmin) can be combined together with the heat exchanger cost law to determine the targets for HEN capital cost (CHEN). The capital cost is annualized using an annualization factor that takes into account interest payments on borrowed capital. The equation used for calculating the total capital cost and exchanger cost law is given below.

Eq. (4)

where a, b, and c are constants in the heat exchanger cost law, Exchanger cost ($) = a + b(Area)^c

For the Exchanger Cost Equation shown above, typical values for a carbon steel shell and tube exchnager would be a = 16,000, b = 3,200, and c = 0.7. The installed cost can be considered to be 3.5 times the purchased cost given by the Exchanger Cost Equation.

Step 7: Estimation of the Optimum DTmin Value by Energy-Capital Trade Off

Figure 9: Energy-Capital Cost Trade Off (Optimum DTmin)

To arrive at an optimum DTmin value, the total annual cost (the sum of total annual energy and capital cost) is plotted at varying DTmin values (Figure 7). Three key observations can be made from Figure 9:

1. An increase in DTmin values result in higher energy costs and lower capital costs.
2. A decrease in DTmin values result in lower energy costs and higher capital costs.
3. An optimum DTmin exists where the total annual cost of energy and capital costs is minimized.{parse block="google_articles"}

Thus, by systematically varying the temperature approach we can determine the optimum heat recovery level or the DT_minOPTIMUM for the process.

Step 8: Estimation of Practical Targets for HEN Design

The heat exchanger network designed on the basis of the estimated optimum DTmin value is not always the most appropriate design. A very small DTmin value, perhaps 8 0C, can lead to a very complicated network design with a large total area due to low driving forces. The designer, in practice, selects a higher value (15 °C) and calculates the marginal increases in utility duties and area requirements. If the marginal cost increase is small, the higher value of DTmin is selected as the practical pinch point for the HEN design.

Recognizing the significance of the pinch temperature allows energy targets to be realized by design of appropriate heat recovery network.

So what is the signficance of the pinch temperature?

The pinch divides the process into two separate systems each of which is in enthalpy balance with the utility. The pinch point is unique for each process. Above the pinch, only the hot utility is required. Below the pinch, only the cold utility is required. Hence, for an optimum design, no heat should be transferred across the pinch. This is known as the key concept in Pinch Technology.

To summarize, Pinch Technology gives three rules that form the basis for practical network design:

• No external heating below the Pinch.
• No external cooling above the Pinch.
• No heat transfer across the Pinch.

Violation of any of the above rules results in higher energy requirements than the minimum requirements theoretically possible.

The Plus/Minus Principle

The overall energy needs of a process can be further reduced by introducing process changes (changes in the process heat and material balance). There are several parameters that could be changed such as reactor conversions, distillation column operating pressures and reflux ratios, feed vaporization pressures, or pump-around flow rates. The number of possible process changes is nearly infinite. By applying the pinch rules as discussed above, it is possible to identify changes in the appropriate process parameter that will have a favorable impact on energy consumption. This is called the "Plus/Minus Principle."

Applying the pinch rules to study of composite curves provide us the following guidelines:

• Increase (+) in hot stream duty above the pinch.
• Decrease (-) in cold stream duty above the pinch.

This will result in a reduced hot utility target, and any

• Decrease (-) in hot stream duty below the pinch.
• Increase (+) in cold stream duty below the pinch

will result in a reduced cold utility target.

These simple guidelines provide a definite reference for the adjustment of single heat duties such as vaporization of a recycle, pump-around condensing duty, and others. Often it is possible to change temperatures rather than the heat duties. The target should be to

• Shift hot streams from below the pinch to above and
• Shift cold streams from above the pinch to below.

The process changes that can help achieve such stream shifts essentially involve changes in following operating parameters:

• reactor pressure/temperatures
• distillation column temperatures, reflux ratios, feed conditions, pump around conditions, intermediate condensers
• evaporator pressures
• storage vessel temperatures

For example, if the pressure for a feed vaporizer is lowered, vaporization duty can shift from above to below the pinch. The leads to reduction in both hot and cold utilities.

Appropriate Placement Principles

Apart from the changes in process parameters, proper integration of key equipment in process with respect to the pinch point should also be considered. The pinch concept of "Appropriate Placement" (integration of operations in such a way that there is reduction in the utility requirement of the combined system) is used for this purpose. Appropriate placement principles have been developed for distillation columns, evaporators, heat engines, furnaces, and heat pumps. For example, a single-effect evaporator having equal vaporization and condensation loads, should be placed such that both loads balance each other and the evaporator can be operated without any utility costs. This means that appropriate placement of the evaporator is on either side of the pinch and not across the pinch.

In addition to the above pinch rules and principles, a large number of factors must also be considered during the design of heat recovery networks. The most important are operating cost, capital cost, safety, operability, future requirements, and plant operating integrity. Operating costs are dependent on hot and cold utility requirements as well as pumping and compressor costs. The capital cost of a network is dependent on a number of factors including the number of heat exchangers, heat transfer areas, materials of construction, piping, and the cost of supporting foundations and structures.

With a little practice, the above principles enable the designer to quickly pan through 40-50 possible modifications and choose 3 or 4 that will lead to the best overall cost effects.

The essence of the pinch approach is to explore the options of modifying the core process design, heat exchangers, and utility systems with the ultimate goal of reducing the energy and/or capital cost.

Step 9: Design of the Heat Exchanger Network

The design of a new HEN is best executed using the "Pinch Design Method (PDM)". The systematic application of the PDM allows the design of a good network that achieves the energy targets within practical limits. The method incorporates two fundamentally important features: (1) it recognizes that the pinch region is the most constrained part of the problem (consequently it starts the design at the pinch and develops by moving away) and (2) it allows the designer to choose between match options.

Figure 10: Typical Grid Diagram

In effect, the design of network examines which "hot" streams can be matched to "cold" streams via heat recovery. This can be achieved by employing "tick off" heuristics to identify the heat loads on the pinch exchanger. Every match brings one stream to it target temperature. As the pinch divides the heat exchange system into two thermally independent regions, HENs for both above and below pinch regions are designed separately. When the heat recovery is maximized the remaining thermal needs must be supplied by hot utility.

The graphical method of representing flow streams and heat recovery matches is called a ‘grid diagram’ (Figure 10).

All the cold (blue lines) and hot (red line) streams are represented by horizontal lines. The entrance and exit temperatures are shown at either end. The vertical line in the middle represents the pinch temperature. The circles represent heat exchangers. Unconnected circles represent exchangers using utility heating and cooling.

The design of a network is based on certain guidelines like the "CP Inequality Rule", "Stream Splitting", "Driving Force Plot" and "Remaining Problem Analysis". The stepwise procedure can be understood better with the help of an example problem.

Having made all the possible matches, the two designs above and below the pinch are then brought together and usually refined to further minimize the capital cost. After the network has been designed according to the pinch rules, it can be further subjected to energy optimization. Optimizing the network involves both topological and parametric changes of the initial design in order to minimize the total cost.

Benefits and Applications for Pinch Technology

One of the main advantages of Pinch Technology over conventional design methods is the ability to set energy and capital cost targets for an individual process or for an entire production site ahead of design. Therefore, in advance of identifying any projects, we know the scope for energy savings and investment requirements.

General Process Improvements

In addition to energy conservation studies, Pinch Technology enables process engineers to achieve the following general process improvements:

Update or Modify Process Flow Diagrams (PFDs){parse block="google_articles"}

Pinch quantifies the savings available by changing the process itself. It shows where process changes reduce the overall energy target, not just local energy consumption.

Conduct Process Simulation Studies

Pinch replaces the old energy studies with information that can be easily updated using simulation. Such simulation studies can help avoid unnecessary capital costs by identifying energy savings with a smaller investment before the projects are implemented.

Set Practical Targets

By taking into account practical constraints (difficult fluids, layout, safety, etc.), theoretical targets are modified so that they can be realistically achieved. Comparing practical with theoretical targets quantifies opportunities "lost" by constraints - a vital insight for long-term development.

Debottlenecking

Pinch Analysis, when specifically applied to debottlenecking studies, can lead to the following benefits compared to a conventional revamp:

• Reduction in capital costs
• Decrease in specific energy demand giving a more competitive production facility

For example, debottlenecking of distillation columns by Column Targeting can be used to identify less expensive alternatives to column retraying or installation of a new column.

Determine Opportunities for Combined Heat and Power (CHP) Generation

A well-designed CHP system significantly reduces power costs. Pinch shows the best type of CHP system that matches the inherent thermodynamic opportunities on the site. Unnecessary investments and operating costs can be avoided by sizing plants to supply energy that takes heat recovery into consideration. Heat recovery should be optimized by Pinch Analysis before specifying CHP systems.

Decide what to do with low-grade waste heat: Pinch shows, which waste heat streams, can be recovered and lends insight into the most effective means of recovery.

Industrial Applications

The application of Pinch Technology has resulted in significant improvements in the energy and capital efficiency of industrial facilities worldwide. It has been successfully applied in many different industries from petroleum and base chemicals to food and paper. Both continuous and batch processes have been successfully analyzed on an individual unit and site-wide basis. Pinch technology has been extensively used to capitalize on the mistakes of the past. It identifies the existence of built-in spare heat transfer areas and presents the designer with opportunities for cheap retrofits. In case of the design of new plants, Pinch Analysis has played a very important role and minimized capital costs.

A Case Study

When Pennzoil was adding a residual catalytic cracking (RCC) unit, the gas plant associated with the RCC and an alkylation unit at its Atlas Refining facility in Shreveport, energy efficiency was one of their major considerations in engineering the refinery expansion. Electric Power Research Institute (EPRI) and Pennzoil's energy provider, SWEPCO, used pinch technology to carry out an optimization study of the new units and the utility systems that serve them rather than simply incorporating standard process packages provided by licensors. The pinch study identified opportunities for saving up to 23.7% of the process heating through improved heat integration. Net savings for Pennzoil were estimated at $13.7 million over 10 years.

Future Outlook

The development of Pinch Technology started in the late 1970s and still continues. Besides applications in energy conservation, new developments in Pinch Analysis are being made in the areas of water use minimization, waste minimization, hydrogen management, plastics manufacturing, and others. A few of key areas of research are mentioned decribed below.

Regional Energy Analysis

By examining the net energy demands of different companies combined, the potential for sharing heat between companies can be identified. These analyses can lend insight into the amount and temperature of waste heat in an industrial area that is available for export. Depending on the temperature of this waste heat, it can be used for district heating or power generation.

Total Site Analysis

Typically, refinery and petrochemical processes operate as parts of large sites or factories. These sites have several processes serviced by a centralized utility system. There is both consumption and recovery of process steam via the steam mains. The site imports or exports power to balance the on-site power generation. The process stream heating and cooling demands, and co-generation potential, dictate the site-wide fuel demand via the utility system.{parse block="google_articles"}

In such large sites, usually the individual production processes and the central services are controlled by different departments which operate independently. The site infrastructure usually suffers from inadequate integration. To improve integration, a simultaneous approach to consider individual process issues alongside sitewide utility planning is necessary. Similar to a single process, a Total Site Analysis using Pinch Technology can be used to calculate energy targets for the entire site. For example, how much low pressure, medium pressure, and high pressure steam should the site be using? How much steam can be raised and how much power it can generate? This also helps to identify key process changes that will lower the overall site utility consumption.

Network Pinch

When optimizing energy consumption in an existing industrial process, a number of practical constraints must be recognized. Traditional Pinch Technology focuses on new network designs. Network Pinch addresses the additional constraints in problems associated with existing facilities. This analysis identifies the heat exchanger forming the bottleneck to increasing heat recovery. Then provides a systematic approach to remove this bottleneck. This step-by-step method provides an approach for implementing energy savings in a series of consecutive projects.

Top Level Analysis

Gathering the required data in industrial areas is not an easy task. With a Top Level Analysis, only efficiencies and constraints of the utility system are used to determine which utility is worth saving. Data can be gathered from those processes or units that use these utilities. A pinch analysis can then be performed on this equipment.

Optimization of Combined Heat and Power

Typically, multiple steam turbines are used in complex steam systems. CHP optimization gives a way to determine the load distribution in a network of turbines with a given total load.

Water Pinch

In view of rising fresh water costs and more stringent discharge regulations, Pinch Analysis is helping companies to systematically minimize freshwater and wastewater volumes. Water Pinch is a systematic technique for analyzing water networks and reducing water costs for processes. It uses advanced algorithms to identify and optimize the best water reuse, regeneration, and effluent treatment opportunities. It has also helped to reduce losses of both feedstock and valuable products in effluent streams.

Hydrogen Pinch

The Pinch Technology approach applied to hydrogen management is called Hydrogen Pinch. Hydrogen Pinch enables a designer to set targets for the minimum hydrogen plant production and/or imports without the need for any process design. Methods have also been developed for the design of hydrogen distribution networks in order to achieve the targets. Hydrogen Pinch also lends insight into the effective use of hydrogen purification units.

Conclusions

With all of the tools that pinch analysis provides, one of the most important challenges before process engineers is to properly integrate pinch tools into the conceptual process design phase. Decisions made in this phase of planning affect the entire life cycle of a process facility. Using pinch technology tools and understanding the process does not ensure the desired results. These tools must be applied at the right point in the process design phase. Just as it would be incorrect to conduct a Pinch Analysis after completion of the process design phase, wherein critical process parameters have been fixed, it is just as incorrect to conduct a Pinch Analysis without direct interaction with the process specialists and downstream engineering disciplines. It is Pinch Technology's role to identify "what might be". However, input from other engineering disciplines ultimately determines "what can be".{parse block="google_articles"}

References

1. General Process Improvements Through Pinch Technology, B. Linnhoff and G.T.Polley, Univ of Manchaster, U.K and V.Sahdev, Linnhoff March Ltd., U.K., Chemical Engineering Progress, June 1988
2. Pinch Technology Has Come of Age, B. Linnhoff, Univ of Manchaster, U.K, Don R.Vredeveld, Union Carbide Corp., Chemical Engineering Progress, July 1984
3. Don't let the Pinch Pinch You, Polley G.T. & Heggs P.J., Chemical Engineering Progress, December, 1999
4. Practical Process Integration - An Introduction to Pinch Technology, By Su Ahmad, Ph.D, Stephen G. Hall, Ph.D, Steve W. Morgan, and Stuart J. Parker, Ph.D, Aspen Technology, Inc.
5. B. Linnhoff and J. R. Flower, AIChEJ. 24, (4), pp 633-642, July, (1978).

A Quick Look at the Basics

Plate heat exchangers consist of pressed, corrugated metal plates fitted between a thick, carbon steel frame. Each plate flow channel is sealed with a gasket, a weld, or an alternating combination of the two. It is not uncommon for plate and frame heat exchangers to have overall heat transfer coefficient that are 3-4 times those found in shell and tube heat exchangers.

Eq. (1)

Specifying a Plate and Frame Heat Exchanger

Figure 1: Parts Structure for a Plate Heat Exchanger

Engineers often fail to realize the differences between heat transfer technologies when preparing a specification. This specification is then sent to vendors of different types of heat exchangers. Consider the following example:

A process stream requires C276 material to guard against corrosion. The stream needs to be cooled with cooling water before being sent to storage. The metallurgy makes the process stream an immediate candidate for the tubeside of a shell and tube heat exchanger. The cooling water is available at 80 °F and must be returned at a temperature no higher than 115 °F. The process engineer realizes that with the water flow being placed on the shellside, larger flowrates will enhance the heat transfer coefficient. The basis for the heat exchanger quotation was specified as follows:

According to the engineer's calculations, these basic parameters should provide a good shell and tube design with a minimum amount of C276 material (an expensive alloy). The completed specification sheet is forwarded to many manufacturers, including those that could easily quote plate and frame or another compact technology. A typical plate and frame unit designed to meet this specification would have about 650 ft² of area compared to about 420 ft² for a shell and tube exchanger. A plate and frame unit designed to the above specification is limited by the allowable pressure drop on the cooling water. If the cooling water flow is reduced to 655 GPM and the outlet water temperature allowed to rise to 115 °F, the plate and frame heat exchanger would contain about 185 ft² of area. The unit is smaller, less expensive, and uses less water. The load being transferred to the cooling tower is the same.

The theory that applied to the shell and tube heat exchanger (increasing water flow will minimize heat transfer area), works in exactly the opposite direction for compact technologies. The larger water flow actually drives the cost of the unit upward. Rather than supplying a rigid specification to all heat exchanger manufacturers, the engineer should have explained his goal in regards to the process stream. Then he could have stated the following:

The process stream is to be cooled with cooling water. Up to 2000 GPM of water is available at 80 °F. The maximum return temperature is 115 °F.

This simple statement could result in vastly different configurations when compared with the designs that would result from the original specification.

Design Charts for Plate and Frame Heat Exchangers

Often, in compact heat transfer technology, engineers find themselves at the mercy of the manufacturers of the equipment. For example, limited literature correlations are available to help in the preliminary design of plate and frame heat exchangers. We will introduce a series of charts that can be used for performing preliminary sizing of plate and frame exchangers. After introducing the charts, we will follow with examples to help clarify the use of the charts. The following should be noted regarding the use of the charts:

1. These charts are valid for single pass units with 0.50 mm thick plates. The accuracy of the charts will not be compromised for most materials of construction.
2. Wetted material thermal conductivity is taken as 8.67 Btu/h ft °F (value for SS)
3. Heat transfer correlations are valid for single phase, liquid-liquid designs
4. The following physical properties were used for the basis:
   

   Table 2: Physical Property Data Used for Chart Construction

   	Hydrocarbon- Based Fluids	Water- Based Fluids
   Thermal Conductivity (Btu/h ft2 °F)	0.06	0.33
   Density (lb/ft3)	55	62
   Heat Capacity (Btu/lb °F)	0.85	0.85

5. Degree of accuracy should be within ± 15% of the service value for the overall heat transfer coefficient, assuming a nominal 10% excess heat transfer area.
6. For fluids with viscosities between 100 and 500 cP, used the 100 cP line of the graphs. For fluids in excess of 500 cP, consult with manufacturers.

Figure 2: Heat Transfer Data for 0.25 < NTU < 2.0 for Plate and Frame Heat Exchangers, Water Based Properties		Figure 3: Heat Transfer Data for 2.0 < NTU < 4.0 for Plate and Frame Heat Exchangers, Water Based Properties		Figure 4: Heat Transfer Data for 4.0 < NTU < 5.0 for Plate and Frame Heat Exchangers, Water Based Properties
Figure 5: Heat Transfer Data for 0.25 < NTU < 2.0 for Plate and Frame Heat Exchangers, Hydrocarbon Based Properties		Figure 6: Heat Transfer Data for 2.0 < NTU < 4.0 for Plate and Frame Heat Exchangers, Hydrocarbon Based Properties		Figure 7: Heat Transfer Data for 4.0 < NTU < 5.0 for Plate and Frame Heat Exchangers, Hydrocarbon Based Properties

Example Problem

Consider the following example:

150,000 lb/h of water is being cooled from 200 °F to 175 °F by 75,000 lb/h of SAE 30 oil. The oil enters the exchanger at 60 °F and leaves at 168 °F. The average viscosity of the water passing through the unit is 0.33 cP and the average viscosity of the oil in the unit is 215 cP. The maximum allowable pressure drop through the plate heat exchanger is 15 psig on the hot and cold sides.

Step 1: Calculate the LMTD

Eq. (2)

Step 2: Calculate NTU_HOT and NTU_COLD

Eq. (3)

Step 3: Read h_Hot from 0.25 < NTU < 2.0 chart for hydrocarbons

Although is there not a viscosity line for 215 cP, the line representing "100 cP" can be or viscosities up to about 400-500 cP. The heat exchanger will be pressure drop limited and the heat transfer coefficient will not change appreciably over this viscosity range for plate and frame exchangers. Reading from the chart, a pressure drop of 15 psig corresponds to h_Hot @ 50 Btu/h ft² °F.

Step 4: Read h_Cold from 0.25 < NTU < 2.0 chart for water based liquids

Again, you will note that the exact viscosity line needed for pure water (0.33 cP) in this case is not available. However, the "1.0 cP" line on the chart will provide a very good estimate of the heat transfer coefficient that pure water will exhibit. Reading from the chart, a pressure drop of 15 psig corresponds to h_Cold @ 3000 Btu/h ft² °F.

Step 5: Calculate the Overall Heat Transfer Coefficient (OHTC)

Assume a stainless steel plate with a thickness of 0.50 mm is being used. 316 stainless steel has a thermal conductivity of 8.67 Btu/h ft °F.

Eq. (4)

Another Example

150,000 lb/h of water is being cooled from 200 °°F by 150,000 lb/h of NaCl brine. The brine enters the exchanger at 50 °F and leaves at 171 °F. The average viscosity of the water passing through the unit is 0.46 cP and the average viscosity of the brine in the unit is 1.10 cP. The maximum allowable pressure drop through the plate heat exchanger is 10 psig on the hot (water) side and 20 psig on the cold (brine) side.

As before, the LMTD is calculated to be 38.5 °F. NTU_Hot and NTU_Cold are calculated as 2.59 and 3.14 respectively. Reading hHot and hCold from the chart for 2.0 < NTU < 4.0 (water based), gives about 2000 Btu/h ft² °F and 2500 Btu/h ft² °F respectively. Although the material of choice may be Titanium or Palladium stabilized Titanium, we will use the properties for stainless steel for our preliminary sizing. Calculating the OHTC as before yields 918 Btu/h ft² °F.

Implications for Size Reduction

We have seen that alternative technologies have significant size advantage over shell-and-tube heat exchangers. Now let's consider the implications of this. The first advantage is smaller plot plan for the process plant. The spacing between process equipment can be reduced. So, if the plant is to be housed in a building, the size of the building can be reduced. In any event, the amount of structural steel used to support the plant can be reduced and given the weight saving, the load on that structure is also reduced. The weight advantage extends to the design of the foundations used to support the plant.

Since, the spacing between individual equipment items is reduced, expenditure on piping is reduced. Once more we stress the savings associated with size and weight reduction can only be achieved if these advantages are recognized at the earliest stages of the plant design.{parse block="google_articles"}

As we will briefly show, the use of alternative exchanger technologies can result in significant reduction in plant complexity. This not only enforces the savings associated with reduced size and weight (reduced plot space, structural cost savings, piping cost reduction etc.) but also has safety implications. The simpler the plant structure the easier it is for the process operator to understand the plant. The simpler the plant structure, the safer, easier and more straight forward the plant maintenance (the fewer the pipe branches that must be blanked etc.).

The alternative technologies result in reduced complexity by reducing the number of heat exchangers. This is achieved through:

• improved 'thermal contacting'
• multi-streaming.

Mechanical constraints play a significant role in the design of shell-and-tube heat exchangers. For instance, it is common to find that some users place restrictions on the length of the tubes used in such a unit. Such a restriction can have important implications for the design. In the case of exchangers requiring large surface areas the restriction drives the design towards large tube counts. If such tube counts then lead to low tube side velocity, the designer is tempted to increase the number of tube side passes in order to maintain a reasonable tube-side heat transfer coefficient.

Thermal expansion considerations can also lead the designer to opt for multiple tube passes for the cost of a floating head is generally lower than the cost of installing an expansion bellows in the exchanger shell.

The use of multiple tube passes has four detrimental effects. First, it leads to a reduction in the number of tubes that can be accommodated in a given size of shell (so it leads to increased shell diameter and cost). Second, for bundles having more than four tube passes, the pass partition lanes introduced into the bundle give rise to an increase in the quantity of shell-side fluid bypassing the tube bundle and a reduction in tube-side heat transfer coefficient. Thirdly, it gives rise to wasted tube side pressure drop in the return headers. Finally, and most significantly, the use of multiple tube passes results in the thermal contacting of the streams not being pure counter-flow. This has two effects. The first is that the Effective Mean Temperature Driving Force is reduced. The second, and more serious effect, is that a 'temperature cross' can occur.

If a 'temperature cross' occurs, the designer must split the duty between a number of individual heat exchangers arranged in series. Figures 8 and 9 below illustrate the difference between temperatures that are said to be 'crossing' and those that are not.

Many of the alternative heat exchanger technologies allow the application of pure counter-flow across all size and flow ranges. The results are better use of available temperature driving force and the use of single heat exchangers.

Figure 8: No Temerature Cross		Figure 9: Deep Temperature Cross

Let's now consider multi-streaming. The traditional shell-and-tube heat exchanger only handles one hot and one cold stream. Some heat exchanger technologies (most notably plate-fin and printed circuit exchangers) can handle many streams. It is not uncommon to find plate-fin heat exchangers transferring heat between ten individual process. Such units can be considered to contain a whole heat exchanger network within the body of a single exchanger. Distribution and recombination of process flows is undertaken inside the exchanger. The result is a major saving in piping cost.

Engineers often over-look the opportunities of using a plate and frame unit as a multi-stream unit. (Again, this will be a regular oversight if exchanger selection is not made until after the flow sheet has been developed).

A good example of multi-streaming is the use of a plate heat exchanger serving as a process interchanger on one side and a trim cooler on the other. This arrangement is particularly useful for product streams that are exiting a process and must be cooled for storage. Another popular function of multi-streaming is in lowering material costs. Often times, once streams are cooled to a certain temperature, they pose much less of a corrosion risk. Half of the exchanger can contain a higher alloy, while the other side can utilize stainless steel or a lower alloy.

In Figure 10 we show how a plate and frame unit has been applied to a problem involving three process streams. The heat transfer properties used for styrene are given in Table 3. Just one unit is used and this unit has 1,335 sq.ft. of effective surface area.

In Figure 11 we show the equivalent shell-and-tube solution. In order to avoid temperature crosses we need six individual exchangers: the cooler having two shells in series (each having 1,440 sq.ft of effective surface); the heat recovery unit having four shells in series (each having 2,116 sq.ft. of surface).

So, our plate-and-frame design involves the use of 1,335 sq.ft. of surface in a single unit. The equivalent shell-and-tube design has 11,344 sq.ft. of surface distributed across four separate exchangers.

Figure 10: A Multi-Stream Plate Exchanger Serving as an Interchanger and a Trim Cooler		Figure 11: Equivalent Shell and Tube Design

Heat Transfer Resources

Although most engineers who are asked to specify a heat exchanger may have the appropriate background in heat transfer knowledge, there are cases when the engineer could benefit from a refresher on the basics of heat transfer and the equipment types involved. Here are some resources that will help you review the basics of industrial heat transfer:

Industrial Heat Transfer Basics:
http://www.cheresources.com/heat_transfer_basics.shtml

Design Considerations for Shell and Tube Exchangers
http://www.cheresources.com/designexzz.shtml

Overall Heat Transfer Coefficients in Heat Exchangers
http://www.cheresources.com/uexchangers.shtml

Correlations for Convective Heat Transfer
http://www.cheresources.com/convection.shtml

Shell and Tube Heat Exchanger Design Manual
http://www.wlv.com/products/databook/databook.pdf

Recognizing and Evaluating the Duty Requirements

The first step in specifying any heat exchanger is to properly evaluate and identify the necessary heat transfer duty requirements. In other words, "what do you need the exchanger to do once it's installed?"�

A useful tool in evaluating heat transfer duty requirements is the T-Q diagram. This visual tool can help the specifying engineer easily determine what is possible in a given heat exchanger. Let's begin with a simple example.

Due to a process change, one of the plant's main products is exiting the process unit 30 °F higher than before. Sending the product to the storage tank at this elevated temperature may cause safety concerns. As the plant engineer, you've been tasked with specifying a product cooler for this new requirement. The total product stream flow rate is 500,000 lb/h

Previously, the product stream was sent to storage at approximately 130 °F. Now, it's exiting the processing unit at 160 °F. The new product cooler must be able to cool the product stream back down to 130 °F for safe operation. The product stream has physical properties that are very close to those of phenol. For the initial heat balance examination, we'll check the heat capacity of phenol at the midpoint of the cooling duty which is 145 °F to get an average heat capacity through the exchanger. At 145 °F, the heat capacity of phenol is reported as 0.529 Btu/lb °F. Using the following equations:

Eq. (1)

Eq. (2)

Where:

Q = heat transferred in thermal unit per time (Btu/h or kW)
M = mass flow rate
T = temperature
Cp = heat capacity or specific heat of fluid
Subscript "H"� = hot fluid
Subscript "C"� = cold fluid

Solving Equation 1, we find that the heat transfer duty is:

Q_H = (500,000 lb/h) x (0.529 Btu/lb °F) x (160 - 130 °F) = 7,935,000 Btu/h

Now, we make the following assumption:

1. The heat capacity of the cooling tower water is 1.0 Btu/lb °F
2. Cooling tower water is available at 88 °F during the warmest summer month
3. Q_H = Q_C (perfect heat transfer, a typical assumption)
4. The tower water can undergo a 20 °F temperature rise in the exchanger

Then, we solve Equation 2 for m_C.

m_C = (7,935,000 Btu/h) / (1.0 Btu/lb °F x 20 °F) = 396,750 lb/h

This is converted to gallon per minute as follows:

(396,740 lb/h) / (8.27 lb/gal) / (60 min/h) = 800 GPM (nearly a factor of 500, actually 496)

Now, we can construct our T-Q diagram for our system:

Figure 1: T-Q Diagram for the First Example

Now, we have the basis for what our heat exchanger needs to perform and we've begun to identify the utility requirements for the duty. At this time, we need to note of couple of items. Firstly, as defined, our heat exchanger may require as much as 800 GPM of cooling tower water to perform the cooling task. An investigation should be made to determine if 800 GPM of cooling tower water is actually available. If not, the duty must be re-examined. In this situation, the engineer finds that he has up to 1000 GPM of water available, so this will not be a concern.

Secondly, we note that our duty does not contain any thermodynamic violations and it does not contain a temperature cross. There are two cases are illustrated below in Figure 2:

Figure 2: T-Q Diagram Showing a Violation		Figure 3: T-Q Diagram Showing a Temperature Cross

Notice the T-Q diagram that shows a thermodynamic violation. The cold side is being heated to a temperature that is above the inlet temperature of the hot side. Suppose that in our example, the engineer found that there were only 100 GPM of water available. His analysis would have shown the water would have exited the exchanger far above the 160 °F hot side inlet temperature. In short, this is not enough water to accomplish the duty. At that point, he would have to investigate other utility options.

In the second image above, the T-Q diagram shows what is know as a temperature cross. The cold side outlet temperature is higher than the hot side outlet temperature. It's important to note whether or not your duty contains a temperature cross as it will have a significant impact on the type and number of heat exchangers that may be required to perform the duty.

As the engineer is examining a new heat transfer duty, the concept of NTU or Number of Transfer Units should be used to help guide the specification. A good rule of thumb is that a single shell and tube heat exchanger should be designed with a minimum temperature approach of 10 °F. The "temperature approach"� is defined as the temperature difference between the hot side outlet temperature and the cold side outlet temperature. In our example above, the approach temperature is 130 °F-108°F = 22 °F. This duty can easily be accomplished in a single shell and tube heat exchanger.

Now, consider the following duty shown in "Duty 2"� above. This unit has a deep "temperature cross"�. This is where the concept of NTU can be helpful. For Duty 2 above (Figure 3), we calculate the NTU for the hot side and the cold side as follows:

Eq. (3)

Eq. (4)

Eq. (5)

LMTD = 39.15 °F
NTU_HOT = 150 / 39.15 = 3.83
NTU_COLD = 170 / 39.15 = 4.34

Figure 4: Shell and Tube Heat Exchanger Flow Pattern

The NTU can be translated into the approximate number of shell and tube heat exchangers in series that will be required to perform a given duty. The engineer must realize that if it is necessary to perform Duty 2 just as it is shown, it will be an expensive proposition in terms of purchased equipment costs, installation costs, and maintenance costs over the life of the shell and tube heat exchangers.

Shell and tube heat exchanger do a relatively poor job of "temperature crossing"� due to their lack of purely countercurrent flow as shown in Figure 4.

The shell side of the exchanger is almost always baffled so that a reasonable heat transfer coefficient can be obtained. The tube side flow in this image shows a single tube pass. While this is possible, it's not very common. The tube side velocity is the key to the tube side heat transfer coefficient and the ability to mitigate fouling. For these reasons, multiple tube passes are typically used in shell and tube exchangers. The result of these flow patterns is a lack of countercurrent flow. In fact, the LMTD or Log Mean Temperature Difference in shell and tube heat exchangers has be corrected for these flow patterns. Typically, the calculated LMTD has to be multiplied by a factor of 0.70 to 0.90 to account for the flow patterns.

If Duty 2 is required, the engineer may want to consider a heat exchanger type with truly countercurrent flow such as a pipe-in-pipe (commonly called a hairpin exchanger) or a plate heat exchanger. These devices, with their truly countercurrent flow patterns, can perform duties with temperature crosses in a single unit rather than requiring multiple units in series.

Regardless of the heat exchanger type chosen, the engineer must be aware of this scenario during the initial specification stage for the heat exchanger.

At this point, the engineer has established the basic parameters for the heat exchanger and now other factors need to be investigated prior to the specification process.

Exploring Other Considerations in Heat Exchanger Specification

Prior to completing the heat exchanger specification data sheet, the engineer should answer questions such as:

• Are there any phase changes expected to occur in the heat exchanger?

• Are there any dissolved gases in either stream?{parse block="google_articles"}

• Are there any dissolved or suspended solids in either stream?

• What are the operating pressures of the streams?

• How much pressure loss is available in the exchanger (for existing pumps)?

• What are the fouling tendencies of the fluids involved?

• Are either of the fluids non-newtonian?

• Are either of the fluids corrosive? What material of constructions are required?

• What types of elastomers and/or compression gaskets are compatible with the fluids?

• Are either of the fluids considered lethal to plant personnel?

• Is mechanical cleaning expected to be necessary for one or both fluids?

• Is there a cleaning solution that may be effective for the exchanger?

• How much room is required for maintenance of the new exchanger?

Having answers to these questions can help ensure that your heat exchanger specification, and ultimately the heat exchanger that you purchase, is right for your heat transfer duty.

Phase Change

Even in liquid-liquid heat transfer duties, it's important to recognize the potential for phase changes inside the heat exchanger. For example, if a process stream is available to 350 °F to plant water from 100 °F to 300 °F, it's very important to note that both the inlet and outlet pressure of the plant water stream. If the water stream is not under enough pressure, it may undergo partial vaporization. In this case, the vapor pressure of water at 300 °F is about 52 psig. So, for a heat exchanger with a nominal pressure loss of 10 psig, the process water should enter the exchanger at a minimum pressure of around 70 psig.

Dissolved Gases

While not always common, there are several instances where a mostly liquid process stream may pickup dissolved gases. It's important to recognize that dissolved gases can have a profound negative impact on liquid heat transfer as the dissolved gases serve as a significant resistance to heat transfer. If you suspect that dissolved gases may be present, the best bet is to run the process stream through a separation vessel to allow for vapor disengagement prior to transferring heat to or from the stream. Trying to design for a stream with dissolved gases is very difficult and often times uneconomical. A classic example of this can often be found in the interchangers in amine units used to treat natural gases. Through the absorption column, the amine solutions can pick up significant quantities of carbon dioxide that should be removed prior to transferring heat with the amine solution.

Dissolved and Suspended Solids

Dissolved solids can be very common in the chemical processing industry. In fact, a general rule of thumb for cooling tower water is that it should not be heated to temperatures in excess of 120 °F. The reason behind this guideline is that at temperatures above 120 °F, some of the common water treatment chemicals used in the water can quickly plate out onto heat transfer surfaces. Usually, these are carbonate salts which follow an inverse solubility curve. This means that as temperature increases, the salts actually become less soluble in water rather than more soluble as is usually the case. Inverse soluble salts can be found in other processing stream as well and are not confined only to cooling tower water.

Suspended solids can pose obvious problems for heat exchangers. Aside from the common problem of pluggage, suspended solids can also cause erosion of the heat transfer surfaces if the velocity in the heat exchanger is too high. If suspended solids are present, it's advisable to obtain a particle size distribution and chemical analysis to determine the relative hardness of the particles. For example, hard particles that range in size from a few microns to up to 0.20 mm would have to be addressed differently than a slurry of relatively soft particles such as a powdered solid. Usually, a plant will have a well documented history of what type of exchangers work well with a solid-laden stream and often times, plants will establish velocity limitations for pipelines and other processing equipment.

Operating Pressure

Examine the operating pressures of each stream that are to enter the heat exchanger. Many companies have policies dictating that the design pressure of a process vessel must be a certain factor above the highest operating pressure. For example, if the highest operating pressure for a heat exchanger is to 100 psi, then a reasonable design pressure may be 150 psi or 200 psi. Remember, that the higher the design pressure, the more expensive the exchanger will become as the wall becomes thicker.

Figure 5: Operating Pressure vs. Time Chart

Additionally, give some thought to what will happen if a leak occurs within the heat exchanger. The higher pressure fluid will leak to the lower pressure fluid. For example, consider a process stream at 50 psi and cooling tower water at 75 psi. If a leak occurs, the cooling tower water will leak into the process stream. The engineer must evaluate the consequences of such leakage and determine which fluid should be at the higher pressure.

As with any piece of chemical process equipment, it can be subject to mechanical fatigue. Consider a heat exchanger where the two streams have operating pressures that are very close to one another. Without extreme pressure stability (which is often difficult to maintain), a run chart of the pressure versus time may look like the chart in Figure 5.

Notice how the stream can be allowed to actually cross pressures in the heat exchanger if the two streams are close in operating pressures. This scenario, if extreme enough, can cause flexing of thinner material surfaces inside of heat exchangers and lead to premature failures.

Available Pressure Loss

If preparing to install a heat exchanger in an existing process system, the engineer should examine any pumps in the system to determine how much pressure loss is available. Generally speaking, most heat exchangers should need between 5 and 15 psi of pressure loss to operate effectively. For known fouling fluids, a higher pressure loss (corresponding to a higher velocity) will help keep the exchanger clean for a longer period of time. Also remember that pressure loss is proportional to the fluid viscosity. Specifying a pressure loss of 5 psi for a process fluid with a viscosity of 300 cP may result in a very large heat exchanger.

If your pumping system cannot handle the necessary additional pressure loss to obtain a good heat exchanger design, then an impeller change out, a new pump, or an additional pump in series may be justified. When utilizing a shell and tube exchanger, you can expect the pressure loss on the tube side to be higher than the shell side in most cases.

Fouling Tendencies of the Fluid

The engineer should also be aware of the fouling tendencies of the fluids involved. Through personal experience, interviews with other plant personnel, or investigation into other heat exchangers, the engineer can usually determine how quickly a particular fluid may foul an exchanger. Many plants will have a library of shell and tube fouling factors for various process duties.

Probably one of the most common errors made in specifying a new heat exchanger is overdesign. Anticipating fouling is smart, overdesigning too far however will ensure that fouling will occur. Choose your fouling coefficient carefully. Remember, that specifying too large a fouling factor will often result in more tube or parallel channels. This will lower the velocity in the exchanger and actually promote the fouling. This is a balancing act that is well worth a little time and effort.

When considering a fouling factor, it's very important to note the type of equipment that may be used in the service. Another common mistake during heat exchanger specification is to apply fouling factor information from one type of equipment to a completely different type of equipment.

Remember that shell and tube fouling factors have been compiled over decades through experience and temperature measurement. Also, realize that typical overall heat transfer coefficients for shell and tube may range from 150 to 400 Btu/h ft² °F while compact heat transfer technologies can easily obtain overall heat transfer coefficients ranging from 600 to 1000 Btu/h ft² °F. If we examine the equation:

Eq. (6)

for a shell and tube exchanger and for a compact heat exchanger, we'll see how the difference can impact designs. If the engineer were to specify a fouling factor of 0.001 h ft² °F/Btu independent of the type of heat exchanger used, the result would look like this:

So, the U-value for the shell and tube went from 136 to 120 Btu/h ft² °F through the fouling coefficient. The U-value for the compact exchanger went from 445 to 308 Btu/h ft² °F through the fouling coefficient. Therefore, the shell and tube overdesign is about 12% while the compact exchanger overdesign is over 40%.

The specifying engineer must realize where the fouling factor information is derived from and apply it properly in the future. While shell and tube exchangers have long used fouling factors, compact heat exchangers generally utilize a "heat transfer margin"� that is typically 10-25% over the clean heat transfer coefficient. This change in language was designed to avoid confusion as shown above and to bring the overdesign between the two technologies onto even ground to avoid problems. Also realize that overdesigning in compact heat exchangers is even more detrimental to performance than in a shell and tube heat exchanger.

Non-Newtonian Fluids

While most fluids in the chemical processing industry are Newtonian in their flow behavior, some are not. In short, a Newtonian fluid is one whose viscosity in NOT dependent on the forces acting upon it (shear stress in heat exchangers), only on the fluid's temperature. Some fluid, know as being non-Newtonian, have flow characteristics such that they can actually become more or less viscous depending on the forces acting on the fluid. Confirming that a fluid is Newtonian during the design stage can save the engineer from procuring a heat exchanger that is vastly over or under sized later.

Corrosion Potential and Materials of Construction

Specifying materials on construction for the heat exchanger is an extremely important part of the overall process. Again, most plants have some history regarding what metals are appropriate for their process fluids. Typically, if one fluid requires a higher metallurgy than another, then that fluid is placed on the tube side of a shell and tube exchanger to minimize costs as cladding a shell can become quite expensive.

It's important to consider temperature and pH when deciding on a material of construction for your exchanger. If you're not sure what metal you need, consult with a corrosion expert as this is one aspect of heat exchanger design that no one can afford to get wrong.

If your duty does require an expensive alloy, then a compact heat exchanger may cost significantly less considering their higher overall heat transfer coefficients. Another point to remember is that just because a fluid is compatible with a stainless steel tube for example, it may not be compatible with a stainless steel plate that has been pre-stressed (during the pressing process). Pre-stressing of metals can make them susceptible to pitting corrosion such as chloride attack. Consult with manufacturers of compact equipment. While they will seldom take the legal responsibility for choosing a material of construction, then can point you in the right direction and save you from making a costly mistake.

Elastomer and Compreesion Gasket Compatibility

Depending on the type of heat transfer technology that is being considered for the application, a check of gasket compatibility may be required. Elastomer gaskets are most commonly offered in materials such as EPDM, Nitrile, PTFE, and FKMG (a generic form of Viton-G from Dupont). Elastomer gaskets can seldom be rated for temperatures in excess of 320 °F. Generally speaking, the engineer should seek a recommendation from the heat exchanger manufacturer as they usually have extensive databases that show the best gasket choice for a given application.

For compression gaskets, such as those used on the heads of shell and tube exchangers, there are a couple of rules of thumb to keep in mind. In addition to the need for the gasket to be compatible with the process or service fluid, the engineer may need to decide between a metallic or non-metallic compression gasket. Consider this guideline:

Lethal Service Requirements

The ASME pressure vessel code stipulates very specific pressure vessel requirements for heat transfer service that are qualified as "lethal"�. If the service requires an ASME "L"� stamp, be sure to specify this to the heat exchanger manufacturer.

Cleaning Considerations

Some process fluids can leave fouling deposits that can be especially difficult to remove. Sometimes, these deposits can be removed by chemical cleaning. Chemical cleaning of heat exchangers, in general, is popular in industries that utilize sanitary protocols (food, pharmaceutical, etc.) and chemical cleaning is widely accepted in the chemical process industry in Europe. Chemical cleaning requires additional equipment, cleaning chemical, and a method of disposing of the chemical cleaning agent. Chemical cleaning can be a good choice in the following instances:

1. The fouling deposit can be easily dissolved and removed by a readily available cleaning agent.
2. The heat exchanger fouls quickly and must be cleaned fairly often (4 or more times a year)
3. The heat exchanger to be cleaned has a relatively small hold up volume so that chemical cleaning equipment and the volume of cleaning agents can be minimized.

For heat transfer duties where chemical cleaning does not seem like the best choice, the engineer must be sure that the fouling fluid is placed on a side of the heat exchanger that is readily accessible for mechanical cleaning. Mechanical cleaning usually consists of a high pressure water spray of the affect area, although additional scraping can sometimes be necessary. Floating head shell and tube heat exchangers, gasketed plate exchangers, spiral heat exchangers, and some welded plate heat exchangers allow good access for mechanical cleaning.

A final consideration for mechanical cleaning is the space required around the heat exchanger. When choosing an installation location, be sure that the necessary maintenance space is available for proper and safe maintenance of the new equipment.

Shell and Tube Exchangers: Where Should I Put the Fluids?

In shell and tube heat exchangers, the specifying engineer has to decide whether each fluid should be placed on the shell side or the tube side. In general, fluids that exhibit these characteristic are preferred for the tube side:

1. High pressure fluids{parse block="google_articles"}
2. Corrosive fluids
3. Fouling fluids
4. Viscous fluids
5. Slurries or fluids with significant solid loading

Placing the high pressure fluid in the tubes will minimize the cost associated with the exchanger because the cost of thicker tube walls is generally less expensive than a thick shell. Corrosive fluids that require a higher alloy are also best placed in the tubes so that the shell does not have to be cladded with or fabricated from an expensive material. It is a "must"� to place the most fouling fluid inside the tubes. The shell sides of shell and tube heat exchangers are notoriously difficult to clean. Viscous fluids are certainly good candidates for tube side flow as well. The heat transfer coefficient in an exchanger with a viscous fluid will almost certainly be limited by the viscous fluid. The heat transfer coefficient of a viscous fluid will be higher on the tube side than the shell side.

There may be situations where the engineer would prefer both fluids be on the tube side. In such cases, the engineer will have to consider each fluid carefully. In some cases, a shell and tube heat exchanger may not be the best choice and another heat transfer technology may have to be considered.

TEMA Designations for Liquid-Liquid Shell and Tube Exchangers

Shell and tube heat exchangers are available in a wide range of configurations as defined by the Tubular Exchanger Manufacturers Association (TEMA, www.tema.org). In essence, a shell and tube exchanger is a pressure vessel with many tubes inside of it. One process fluids flows through the tubes of the exchanger while the other flows outside of the tubes within the shell. The tube side and shell side fluids are separated by a tube sheet.{parse block="google_articles"}

Each shell and tube exchanger is designated by a three (3) letter code. The letters refer to the specific type of stationary head at the front, the shell type, and rear head type. Fixed tube sheet style exchangers with TEMA designations of BEM, AEM, or NEN are fairly common for liquid-liquid heat transfer duties. While fixed head arrangements have the advantage of being inexpensive and avoiding gaskets or packing to contain the shell side fluid, they do not allow for mechanical cleaning of the shell side.

For liquid-liquid heat transfer duties where the ability to mechanically clean the shell side as well as the tube side is a requirement, a floating head design should be chosen. With a floating head design, the tube bundle can be pulled out of the shell to allow access to the shell side. Some of the most commonly used floating head designs for liquid-liquid duties include AES and BES. Another advantage of the floating head design is the ability to accommodate larger temperature differentials between the hot side and cold side fluids.

Figure 6: TEMA Designations for Shell and Tube Heat Exchangers

Figure 7: Photo of a U-tube Bundle

All of the designations discussed so far (BEM, AEM, NEN, AES, and BES) allow for multiple tube passes which are usually required for liquid-liquid duties so that the tube side velocities can be manipulated during the design stage of the exchanger.

The final type of shell and tube exchanger commonly used for liquid-liquid duties is commonly referred to as the "U-tube"� type. Common TEMA designations are BEU and AEU. In this arrangement the tubes are bent into a series of concentrically tighter U-shapes with the end of the tubes being attached to the tube sheet.

The U-tube bundle can be removed to access the shell side for mechanical cleaning. The U-tube design is preferred for services with temperature or pressure cycling, intermittent service, and when there is a large temperature differential between the shell side and tube side fluids.

Since the "U"� bend of the tubes cannot be accessed for mechanical cleaning, the tube side fluid should be clean or a suitable chemical cleaning agent should be identified.

Methods of Estimating Physical Properties

When specifying a liquid-liquid heat exchanger, the specifying engineer must be able to provide physical properties that are as accurate as possible. For liquid-liquid duties, the following data should be provided for each fluid: density, thermal conductivity, specific heat (sometimes called heat capacity), and viscosity. Ideally, these properties should be provided for each fluid at both the inlet and outlet temperature of the exchanger.{parse block="google_articles"}

If data is limited, there are some estimating rules that be of assistance. The physical properties that will impact the design of the exchangers the most are the viscosity and the specific heat. Recall that the specific heat of a fluid is required in order to accurately specify the exchanger. Now, we'll examine estimation methods for each of the physical properties. While actual plant data or experimentally determined data is preferred, these methods can be used when no other data is available. For our estimation methods, we'll assume that typical process fluids are made up of mixtures of components and that the data for each component is available. This is almost always the case.

Specific Heat

For fluid mixtures where there is no known heat of mixing, a weighted average can be used:

Eq. (8)

Where:

C_pmix = Heat capacity of the mixture in consistent units
W₁ = Weight fraction of component one
C_pL1 = Heat capacity of component one in consistent units
W₂ = Weight fraction of component two
C_pL2 = Heat capacity of component two in consistent units

If using the above method, look up the heat capacity of the components at the average temperature through the heat exchanger. It's not uncommon to provide heat exchanger designers with a single heat capacity point for each fluid. Be aware that the heat capacity of most liquids will increase with temperature.

Viscosity

While it's not critical to supply a physical property point at the inlet and outlet temperature for other properties, it's very beneficial to do for the viscosity of the fluids. Using only a single viscosity point will affect both the heat transfer and pressure drop calculation of any heat exchanger.

For non-polar mixtures, the following has shown to provide viscosity estimates to within +/- 5 -10%:

Eq. (9)

Where:

µ_mix = Viscosity of mixture in centipoise
W₁ = Weight fraction of component one
µ₁ = Viscosity of component one in centipoise
W₂ = Weight fraction of component two
µ₂ = Viscosity of component two in centipoises

Figure 8: Viscosity Correlation Chart

For polar fluids, electrolyte solutions, and non-newtonian fluids, it is highly advisable to either find reliable data or have an outside lab perform testing. There is an estimation method available for polar mixtures called the "Method of Grunberg and Nissan"�. This method is detailed in Properties of Liquids and Gases, Edition 4 by Reid et al. (ISBN 0070517991, see page 474).

If viscosity data is available at one temperature, the following correlation chart (Figure 8) that has been used for years to estimate the viscosity at a second temperature. This chart is used by finding the single available viscosity point on the Y-axis and move left to meet the curve. Then, on the X-axis, adjust the temperature difference up or down by the temperature change required. Next, move up to hit the curve again and read the resulting viscosity from the Y-axis.

Thermal Conductivity

The thermal conductivities of mixtures can be estimated via the same weighted average method shown in Equation 9 for specific heat calculations. The calculation is the same, just replace the component specific heats with the component thermal conductivities. In cases where there is a complete absence of data, keep the following ranges in mind:

Water based mixtures, thermal conductivity range is about 0.28 to 0.35 Btu/ h ft °F

Hydrocarbon based mixtures, thermal conductivity range is about 0.055 to 0.080 Btu/ h ft °F

Density

The density of mixtures represents another case where a weighted average method is usually adequate as an estimate for heat exchanger design.

Avoiding Specifications That Are Too Specific

One final pitfall that the specifying engineer should avoid is making the heat exchanger specification too rigid. The engineers that design the heat exchangers are the experts, give them as much freedom as possible and allow them to present you with the best option(s) that will work well for your application.

As an example, consider the following:

A process stream requires Alloy C-276 material to guard against corrosion. The stream needs to be cooled with cooling water before being sent to storage. The metallurgy makes the process stream an immediate candidate for the tube side of a shell and tube heat exchanger. The cooling water is available at 80 ⁰F and must be returned at a temperature no higher than 115 ⁰F. The process engineer realizes that with the water flow being placed on the shell side, larger flow rates will enhance the heat transfer coefficient. The basis for the heat exchanger quotation was specified as follows:

According to the engineer's calculations, these basic parameters should provide a good shell and tube design with a minimum amount of Alloy C-276 material (an expensive alloy). The completed specification sheet is forwarded to many manufacturers, including those that could easily quote plate and frame or another compact technology. A typical plate and frame unit designed to meet this specification would have about 650 ft² of area compared to about 420 ft² for a shell and tube exchanger. A plate and frame unit designed to the above specification is limited by the allowable pressure drop on the cooling water. If the cooling water flow is reduced to 655 GPM and the outlet water temperature rose to 115 ^°F, the plate and frame heat exchanger would contain about 185 ft² of area. The unit is smaller, less expensive, and uses less water. The load being transferred to the cooling tower is the same.

The theory that applied to the shell and tube heat exchanger (increasing water flow will minimize heat transfer area), works in exactly the opposite direction for compact technologies. The larger water flow actually drives the cost of the unit upward. Rather than supplying a rigid specification to all heat exchanger manufacturers, the engineer should have explained his goal in regards to the process stream. Then he could have stated the following:

This simple statement could result in vastly different configurations when compared with the designs that would result from the original specification.

Completing the TEMA Specification Sheet

The TEMA specification sheet shown below has been color coded to help explain which information should be provided by the specifying engineer and which information should be provided by the designer/manufacturer. Green cells are to be completed by the specifying engineer, yellow cells by the designer/manufacturer, and gray cells could be completed by either party.{parse block="google_articles"}

The information on the first page of the specification is essentially a description of the problem as has been covered herein. On the second page, the specifying engineer is asked to indicate the design pressure and temperature. The test pressure is generally accepted as 1.3 times the design pressure as specified by the latest version of the ASME Pressure Vessel code. Some times, however, the specifying engineer may request a higher design pressure (perhaps 1.5 times design pressure). The engineer is also expected to specify materials or choices of materials for the heads, shell, tube sheets, tubes, and the compression gaskets (if applicable).

The specifying engineer can also indicate any required corrosion allowances required as well as any special mechanical or non-destructive testing that may be required for an exchanger to be installed in a particular duty.

If the installation of the exchanger would be simplified by a particular nozzle arrangement or maximum overall length, this type of information can be provided in the sketch box or in the remarks section. Use the remarks section to convey any other pertinent information to the designer.

Figure 9: TEMA Specification Sheet, Page 1		Figure 10: TEMA Specifiation Sheet, Page 2

Conclusions