2 replies to this topic

[Impey]

Members...

This is my first post so please be gentle. However I have a question regarding the zing of a psv tailpipe, which discharges to atmosphere. The exercise I am performing is for my own knowledge and I am hoping you can help me fill in the missing pieces and apologies for the long post.

After reading through API 520 part I & II along with API 521 & numerous other sources I am trying to understand the method behind how I should correctly size the discharge piping of the PSV. For this exercise I have to calculate everything manually as I have no access to software, here is my understanding and if I am wrong you can perhaps point me in the right direction?

Set the Scene:-

• PSV required, in the event of emergency, to vent gas (not 2-phase) from a high-pressure flow line
• PSV type 3J4 (3” 600# inlet, 4" 150# outlet) - Rated Capacity = 21.35kg/s with orifice of 8.30cm^2
• Mass flow rate = 21.73 kg/s (78228kg/hr)
• MW = 19.1kg/kmol
• Cp/Cv = 1.3
• Viscosity Cp = 0.013
• PSV Inlet temp = 20C (293K) - Assuming outlet to be same (???)
• Pipe Roughness = 0.5μm
• PSV set pressure = 125barg (12500KPa)
• Z - Compressibility factor = 0.93 - using an average factor
• Vent outlet to atmosphere

Here is my approach:-

First determine the velocity of the gas flowing through the PSV in the event of relief, using:-

C = 91.2 * (k*T/MW)^0.5

From this I determine the velocity © to be 407m/s - from what I gather this speed can be considered sonic flow (maximum speed of the gas through a fixed conduit size???)
(Question is this value now considered as the Mach 1 value?)

To calculate the Backpressure I used the Isothermal Flow Method. Firstly using the equation stated in API 521 (pg 107 eqn 27) – I determined the Mach Number at the exit of the tailpipe – using the known pressure (atmospheric 101Kpa) and Diameter of the PSV outlet = 0.102m

From this I get Ma2 = 9 according to API standards and my company standards an acceptable Mach Value = 0.8 – Therefore obviously this is not an acceptable outlet size; I think you can also check this by doing a Pcritical calculation??

However in combination with an acceptable Mach Outlet the total backpressure on the PSV must also be within the allowable limit (For the basis of this exercise it was determined to be 10% of set pressure) - So now I calculated the total backpressure in the system

Therefore using the isothermal flow equation as specified by API 521 (pg 106 eqn 25) I then calculated the backpressure by working through in a stepwise manner starting at outlet to the PSV. For this scenario I considered the exit for the tailpipe to the outlet of the PSV to be one whole section

1 – Outlet of tailpipe = 5m long and also including equivalent length for fitting (90 Deg Elbow calculated to be approx = 1.3m) which then connects to the outlet of the PSV

So I calculated the moody friction factor = 0.025 then using the isothermal flow chart (fig 14 from the API 521) I then estimated an inlet pressure (P1) – Incorporating also the error found in the standard (should be P2/P1 on the y-axis)

I find P1 = 201Kpa or approximately 2.0barg – Which is within the 10% tolerance level.

Ok so now I have determined that the outlet size needs to be increased to prevent choked flow – I have two options;

1 - Use a trial and error approach in combination with different size diameter piping (I.E 6”, 8”, 12” etc) However if I am correct you can also use the vent stack sizing equation (as stated in API 521 pg 137 eqn 65) -using v= (0.8Mach, which in this case is 0.8 *407m/s = 325m/s)
After I plug in the numbers I find the equation suggests that the diameter of the PSV tailpipe = 0.32m which is approximately DN 300 (NPS 12”)

Now I know that the Mach level will be acceptable, however the back pressure must again be calculated to see that its within the allowable limit (10% of set pressure)

Which means this time I must calculated the Backpressure through 12”piping and also 2 x expanders, one 4x8” expander and one 8x12” expander. However this is where I become confused of what to do. As it states in the API standard that the Isothermal flow equation does not take into account enlargements or contractions in the piping and no variation in the Mach
Number. Therefore how do I calculate the backpressure through this new system to ensure it is within the 10%limit??

Furthermore is my analysis thus far correct? Or are there things which I have forgotten or incorrect. This is my first adventure with PSV’s so apologies for any silly mistakes. I’ve been going round in circles and I would appreciate some help. If you require more info let me know

Also unfortunately I do not have access to the Crane TP401 paper, which I hear is helpful

Cheers Alex

[Impey]

Can anyone provide insight?

Thanks

Alex

[avsp]

Hi

I am bit "lost" in your lengthy query above ....however, from whatever I understood from what you have written above, I guess you are quite brave in doing a calculation manually, which usually I would either use a computerised approach or use a graphical approach ......


With whatever knowledge I have of Flare system designs, I reckon that the hydraulics for a relief discharge pipe work could be simplified if you are able to define the system outlet pressure (....say, the pressure of the Flare KO Drum, which of course would have been defined from the pressure at the Flare Stack tip and working back the system). Then, it is a matter of working back through the system to verify the acceptable back pressure at each relief device for the corresponding flow and hence arrive at an appropriate sizes of the Relief device tailpipes and the headers.

However, a good relief system design must not ignore the importance of checking on the hydraulics of your relief device inlet piping. A proper design of the relief devices inlet lines would ensure that excessive pressure drops in the inlet lines do not damage relief valves due to chattering (..I am sure you may be aware about the recommendation of maintaining pressure drop in the inlet lines equal to or below 3 % of the releif device set pressure as set out in API 520 as well as in ASME Sec. VIII, Div. 1 Nonmandatory Appendix M)

The following below should be of help to you....
i) Section 7 of API 521 (5th Ed.)
ii) Philip Leckner's article on relief device sizing (...sorry cant remember the exact title, but it can be found in this website itself...I thought the article was good....so I guess you should read it...)
iii) This article gives a worked out example of a Flare system design....I attach a copy of that article herewith....

Hope the above helps....

cheers,

Attached Files

•  PRdesign.pdf   373.67KB   532 downloads