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

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

(OP)

"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!

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!

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

265 x 15458 = 4096370 ft3 x psia

115 x 15458 = 1777670 ft3 x paia

Increase in volume factor

4096370 / 17776701 = 2.304

New gas volume

V2 = 2.304 x 15458 = 35621 ft3

Volume added to reach 250 psig

35651 -15458 = 20163 ft3

90 MMSCFD x 15 / (250+15) = 6.36 MMCFD @ 250 psig

20163/6360000 = 0.00317 days

0.0761 h

4.56 minutes

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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

How is your 300 psi source controlled down to 100 psi?

Does it control on pressure or flow?

If fixed flow it's about

~~35~~minutes. However if flow is impacted by the pressure in this very large vessel then it can change.[Edit] I was working in different units....

Mr 44, you've mixed actual volume and std volume.... Or maybe not

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

I think I remember you thought the same with that last LNG calc I did,, but no, it's not mixed here.

Actual volume / actual flow rate = actual time.

If it takes 30m you've added 90E6 x 15 / 265 x 0.5/24 = 432,629 ft3 @ 265 psia

90,000,000 x 15/265 = 5.1 MMACFD

Or about 3500 Actual ft3/minute

However we can use the average flow rate to get a better time if you are filling from 100 to 250 psig.

90x15/115 = 11.7 MMACFD @ 100 psig

90x15/265 = 6.36 MMACFD @ 250 psig

9 MMACFD

20163/9E6 = 0.0022 Days = 3.2 minutes

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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

My answer is 2'28" with STP (20C and 14.7 PSI)

Mass increase 4570 kg,

Mass flowrate 30.73 kg/s

hypothesis: T=cte, Mass flowrate =cte,

Pierre

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

I got that wrong. I thought 30 mins sounded a bit too high.

But does depend if this is flow controlled or not.

This is pretty basic stuff though....

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Pierre seems to have a lower number.

Yes, FCV Apparently at 90 MMSCFD.

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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

I approached this a bit differently...I approached this from the work equation by integrating for change in pressure. w= ∫ VdP = P1*V1*ln( P2/P1 ). Finding the work to fill the volume from 100PSIG to 250PSIG, then finding the work done by compression , inlet flowrate 90MMSCFD and source pressure 300PSIG. Then dividing the work to fill the volume by the work done by compression to find the time. Flowrate provides the time unit. Is this the correct approach? Maybe more importantly, is my integration correct? It has been a while...

Find work to fill volume:

System Volume = V1 = 15458 ft3 = 12830.26 m3

Final Target Pressure = P2 = 264.7 PSIA = 1825106.5 Pa

Initial Operating Pressure = P1 = 114.7 PSIA = 790856.5 Pa

Work to fill volume = ∫VdP = P1V1 ln( P2/P1 ) = 8485613776.28 J

Find Compression work:

Volume Rate of Flow = V2 = 90 MMSCFD = 29.5 m3/s

Pressure of delivery = P3 = 314.7 PSIA = 2169857 Pa

Compression Work = ∫VdP = P1V2 ln( P3/P1 ) = 23544611.13 J/s

Time to fill volume: Work to fill volume/Compression work = 360.41s = 6.01 min

@1504-44

I tried to take an PV=nRT approach to this with the molar flow rate of the gas but I can't seem to make it work...I kept having the same thought as you...

@ Littleinch

How is your 300 psi source controlled down to 100 psi? DP is pressure drop in the line to the vessel, no control valves.

Does it control on pressure or flow? I would assume, in the real world, flowrate would decrease, and pressure would increase as the flow out has been blocked. In the above approach I have assumed flowrate to be constant.

Thank you all.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

"no control valves" - Aaaaah.

It's a very conservative assumption for sure to just use 90 MMSCFD throughout. I assume there is a fairly long length of pipeline between your vessel and the source point. There will be a significant difference between flow with a DP of 200 psi and one with only 50.

However its still not going to be more than 10 minutes, but only a transient analysis will give you that to any level of accuracy. How accurate do you want it. Would somewhere between 5 to 10 minutes be enough or do you love the false accuracy of a computer analysis which would be 6 minutes, 32.7643 seconds??

Or do it in steps of say 50psi and integrate assuming flow stays the same until the pressure in the vessel increase by 50 psi. Then recalculate your incoming flow and do the same. a little bit conservative, but not as bad as a fixed 90 MMSCFD.

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

I'm only looking for "rule of thumb" accuracy here and am not going to look into any transient analysis. Just need an approximate time required. I'm not sure which one to run with now.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Far easier.

You have your appro times already. Between 5 and 10 minutes.

Actually I forgot as the pressure increaes in the pipeline some of the mass flow will be stored in the pipeline so that's another factor increasing pressurisation time.

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Good Luck,

Latexman

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Note that I supposed that the flow rate was maintained at 90MM for the pressure range 100 to 250psig, as you did not mention any other flow rates.

If there is something different there, tell us now.

Should be the same answer. The mass cancels out.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Maybe not.

A sketch/PFD/P&ID sure would be nice.

Good Luck,

Latexman

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

DP is pressure drop in the line to the vessel, no control valves"

There is a pressure source (well?, offtake? who knows), what must be quite a long pipeline (no data), then this mysterious vessel which is probably kept at 100psi which results in a flow of 90 MMSCFD.

The OP is now trying to work out what happens if the outflow stops. The flow rate will clearly fall as the pressure in the vessel rises assuming the start pressure of 300 psi stays the same.

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

"DP is a pressure drop in the line. No controllers."

Then LI's pipe fill scenario may be important, but only if it involves a lot of pipe volume.

What might affect it more is, without controllers, the pressure build will not be linear and the average flow rate could be a lot lower. Still, ìt may not change the fill time very much. Can't say until, or if we get pipe dimensions and a curve showing how the source pressure rises with flow rate. If there are no flow control valves, something has to do it. Is there a compressor, or what.

I only filled in those info gaps with a system description consistent with the solutions we have arrived at up to this point. It gives the OP an idea of what might need clarification. We should let him do that now.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

a) Upstream flow is set on flow control at an upstream FCV - in this case, flow will increase when the outlet from the vessel is shut - the control valve will open more than it was initially.

b) Upstream flow is set at a fixed manual throttle valve - in this case, flow will decrease when the outlet from the vessel is shut. Flow is initially in choke flow mode, since p2 < 0.5x p1, but will later become subsonic as p2 > 0.5 x p1

Which one do you have ? Or is it some other configuration ? As you can infer, the result will differ considerably depending on configuration

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

To add to the discussion :

https://community.ptc.com/t5/Mathcad/Time-to-fill-...

Pierre

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Pipe pressure is initially 100psig.

It changes to 250 when the vessel is full.

Flow is 90MM.

Problem is that nobody knows the upstream boundary conditions, Q vs P.

We should probably assume the simplest config.

No valves at all, with a 100psig discharge when vessel is open through and 250 when finished.

That the vessel defines the downstream boundary conditions.

Pipe pressure rises according to the volume added to the vessel, initially at 100 psig and Q=90MM,

No valves at all, with a 100psig discharge when vessel is open through,

backing up to 250psig when vessel is closed.

BUT flow would decrease as the vessel pressure rises to 250, which violates the 90MM constant flow.

If that scenario is allowed, it can be solved iteratively, stepping through time.

And takes a bit longer than 4m, but probably not too much.

It also looked like too much work yesterday morning. It was a lot easier to assume a constant 90MM flow as stated.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

@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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Good Luck,

Latexman

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

## RE: Need Expert Advice on Calculating Pressure Buildup in Fixed Volume Vessel

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