Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel 4

[_METCON]

"Hello community,

I'm currently facing a challenging situation and would greatly appreciate some expert advice. Here's the scenario:

I have a fixed volume vessel with a total volume of 15458 ft³. The volumetric flow rate through this volume is 90 MMSCFD. The initial temperature of the gas is 80°F, with a Compressibility Factor of approximately 0.91 and a Molecular Weight of 22.9. The source pressure is 300 PSIG, and the normal operating pressure is 100 PSIG.

My concern is understanding the time it would take for the pressure to reach 250 PSIG if the exit of the vessel were to be suddenly shut. Assume no heat transfer and no additional information on piping dimensions.

I'm reaching out to this knowledgeable community for assistance in calculating this pressure buildup time. Any insights, formulas, or guidance on how to approach this problem would be immensely helpful.

Your expertise is highly valued, and I'm eager to hear your thoughts on this matter. Thank you in advance for your time and assistance!"

Feel free to make any adjustments or let me know if you have specific preferences!

 

[_METCON]

Thank you everyone.

@Pierreick, That mathcad solution is intriguing.

@Mr George: Option B.

@Mr. 44, LI, & LM, Some additional detail...

You could assume this is a long pipe fed by a valve controlling 300PSIG on the inlet of that pipe. The pipe feeds a vessel, no inlet control valve.

The vessel is maintained at 100 PSIG by a back pressure control valve. Flowrate is measured as 90MMSCFD.

Walk me through how one would use the Volumetric flowrate or mass flowrate to solve if you would. I got caught up in that, then switched to compression work. I usually try to keep the K.I.S.S. approach but went off in the weeds...

Best

 

[1503-44]

Volumetric is as per my calculation above.
P1 V1 = P2 V2

If temperature changes its this, use absolute temperatures and pressures.
P1 V1 /T1= P2 V2/T2

If you want to use mass, just multiply those volumes by the density of the das at the corresponding pressure and temperature.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[LittleInch]

The problem is georges option B doesn't equate to "a valve controlling 300PSIG on the inlet of that pipe". If it controls then it isn't in a fixed manual position.

For the volumetric flow first calculate how long it would take for the pressure to rise to say 150 psi. That is T1.
Then you need to work out what your new flowrate is with an inlet pressure of 300 psi (assuming the inlet is "controlled" at 300 psi)

For volume I would just convert everything to standard volume and use perfect gas law.
So 250 psig of gas in a volume of 15,500 actual cf is 265/14.5 x 15,500 = 283,000acf
Starting at 100 psi is 115/14.5 *15,500= 122,000. scf
If it was a fixed 90 mmscfd you would get 283000-122000 = 161000 scf. 90mmscfd/24/3600 = 1040 scf/sec. so 154 seconds or 2.6 minutes
Happy for someone to prove me wrong....

For the volumetric flow first calculate how long it would take for the pressure to rise to say 150 psi. That is T1.
Then you need to work out what your new flowrate is with an inlet pressure of 300 psi (assuming the inlet is "controlled" at 300 psi) and an exit pressure now of 150 psi, not 100 as before.
Repeat for the new flow rate up to a pressure of 200 psi - = T2, then re cacualt flow base don a diff pressure of 300 in to 200 out.
repeat for 250 psi = T3

total up time.

Still conservative as the flow will drop between each step and there may be some element of line pack in the long pipe as pressure rises, but in this case conservative is probably a good thing. you could do it in smaller steps, but doesn't add much to the accuracy.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[1503-44]

If you have 300 upstream and some initial vessel pressure, then you must calculate the flow rate of the filling pipe, or somehow otherwise know it is 90Mm. If you know its 90Mm then you can calculate vessel inlet pressure using the flow rate.

Slightly easier, at least for me, to calculate the volume added to the vessel first during a flow rate time step of your choice. I say that, because you know the initial flow rate and have to calculate volume change from that before you can calculate the vessel pressure.

Take the initial flow rate through the pipe. Then calculate the new vessel pressure. Then calculate new flow rate in the pipe from the new upstream and vessel pressures. The shorter the time step, the more accurate the results.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[Latexman]

I’ll just attach my calc.

Good Luck,
Latexman

 

[georgeverghese]

@LittleInch, Think he means there is another control mechanism upstream of this manual fixed valve that maintain press upstream of this manual valve at 300psig. Essentially, press upstream of this fixed throttle valve stays at 300psig throughout this incident.

So what is the ID and length of this feed pipe - this complicates things a bit. Compute a K value for this length, add it to the eqvt length for the fixed choke, and then transform the total to an overall Cv for the subsequent calcs.

 

[pierreick]

Hi LI,
Your calculation is similar to mine except that you are mixing units, Actual and Standard.
To me the best way is to use mass.
Pierre

 

[Latexman]

Hi Pierre,

If I had used constant mass flow rate like you, we’d have essentially the same answer. (10,077 lb)/(4146 lb/min) = 2.43 min = 2’26” vs your 2’28”. Same, same.

Good Luck,
Latexman

 

[LittleInch]

Pierre, yes mass is probably more accurate, I was only trying to get an easy and approx time, but we all end up within 5% of each other.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[1503-44]

Mass cancels out. It cannot be more accurate.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[_METCON]

Thank you all.

Glad to see the many different ways to skin this cat.

If I ever do a dynamic model of this or get to witness it in real life I'll be sure to update...

-M