Calculating tank cooling upon venting

[HazGas]

I'm embarrassed to say that I need help explaining this real world observation. It's been too long since I've had my thermo class, and as an operations jack-of-all trades it's easy to forget the finer points.

We have a 13,000 gallon well-insulated tank. It is filled with nitrogen at approximately 525 R. (Slightly cool from isenthalpic expansion across the tank pressurization valve.) The tank is filled from ambient to 65 Psia. It rests for 20 minutes. It is then vented very rapidly to 15 psia through a large 3" ball valve. Upon venting, the temperature drops to somewhere around 450 R, possibly less. These are measured numbers.

I try to calculate this temperature drop as an adiabatic expansion process, but I am not getting the right numbers. Can anyone point me in the right direction? Thanks.

 

[georgeverghese]

You'll need a process simulator to run gas depressurisation routines on vessels.

Simulators you could use are Pro II, Hysys or VMGSim

In the first 2, the inexactness appears in the manual input on isentropic efficiency - as you increase Eisen, the final vessel or gas temp drops lower. Theorectically Eisen should be 1.0.

Though I'm not familiar with the last, I've heard there is no manual input required for Eisen.

The routines include inputs for the vessel metal contents, insulation, the Cv of the discharge valve, initial and final pressures etc. Temperature profiles can be generated for the gas and the metal wall as the vessel pressure drops in time.

There are more sophistacted programs in use in oil and gas engineering projects for much higher starting pressures and gases with significant auto refrigeration effects, which are used to specify materials of construction on high pressure vessels ( Blowdown from AspenTech , DYNSIM from Sismci - Pro II, LNGDYN from Technip).

It wont be possible to get this done with a manual calc

 

[EmmanuelTop]

It appears quite strange that you are getting almost 42 degC temperature drop for reducing the pressure from 450 kPaa to 100 kPaa. Let's try to elaborate more on the initial and final data:

1) Nitrogen tank volume is 13,000 gallons. Initial pressure is 450 kPaa (~65 psia) and initial temperature is 18.5 degC (525 R);
2) After depressurization (which I assume stands for emptying inventory of the tank till the internal pressure equalizes with the downstream pressure = apparently ambient P), the tank pressure is 100 kpaa (~15 psia) and the final temperature inside the tank is -23 degC (450 R).
3) The tank is well insulated, which means that heat gains from the surrounding can be considered zero.

Can you confirm this? And where exactly the temperature is measured, physically?

Dejan IVANOVIC
Process Engineer, MSChE

 

[HazGas]

Emmanueltop, that is exactly correct. It seemed odd to me also that the tank cooled this much upon venting. I was expecting minimal cooling dropping from only 65 psia. Last night I vented a gas sample through a small valve, so that the pressure in the tank was minimally impacted by the discharge. The gas sample came out at ambient temperature, with no cooling observed on this small discharge tube. So I am convinced the phenomenon is cooling as the tank rapidly depressurizes and the gas expands.

The measurement was made by a "skin" thermocouple on the pipe immediately upstream of the discharge ball valve. It would read ambient and then upon discharge go to approximately 470R. Therefore the contents of the tank were actually cooler than this, and my estimate of 450R or less.

I do not have access to a process simulator. All of my calculations must be done by hand - it seems that venting a tank should be relatively simple to calculate but maybe not.

 

[StoneCold]

HaxGas
Can you observe the depressurization? Does the area where the thermocouple sits frost over?
I am just wondering if the numbers you have can be verified by some real world observations.

Thanks
StoneCold

 

[EmmanuelTop]

It appears that rapid expansion pushes the process closer towards isentropic (adiabatic) expansion. I have ran several cases in Aspen with variable orifice (valve) size in order to evaluate effects of depressurization time on the fluid temperature. The two extreme cases were (1) if the tank is depressurized within 30 seconds and (2) if the tank is depressurized within 15 minutes. The difference in the minimum gas temperature inside the vessel is substantial: 16.8 degC for the 15 min case, and -70 degC for the 30 seconds case. Your case is likely somewhere between the two, so I would assume that depressurization of the tanks lasts much longer than 30 seconds.

The only way to decrease enthalpy of a fluid during expansion (for a perfectly insulated system), is to have the fluid performing work. Obviously, in case of vessel depressurization, it is very questionable what this work may represent. One can always argue if displacing the fluid that sits in the discharge line (or in the surrounding atmosphere if tank is vented directly to the surrounding air) can be considered as work, or not. I have read a few studies which evaluate effects of gas withdrawal rate on the final gas temperature, when gas is pulled from storage caverns. The conclusion of the studies (resulting from very complex mathematical models which were built to fit the actual measurements) is that the final gas temperature decreases more with increase of the gas withdrawal rate and with increasing size (volume) of storage. This means that the Nitrogen tank would see even lower temperatures if its size would increase, and/or if the valve Cv increases.

I don't know if you have raised this question purely from curiosity, or you have real concerns with regards to vessel integrity due to low temperature excursions. If the latter is the case, I'd strongly suggest you fit a restriction orifice or a globe valve with "moderate Cv" in the discharge piping, in order to control the depressurization rate and avoid low temperature problems.

Dejan IVANOVIC
Process Engineer, MSChE

 

[HazGas]

The phenomenon is definitely real - I had my hands on the discharge line and it frosted over quite quickly and became so cold I couldn't keep my hands on it. The depressurization takes place in approximately 1.5 minutes.

Emmanueltop, thank you for running the models. I had actually looked at it as a constant entropy process and got a temperature that I thought was too cold. But you e clarified that time and size dictate how ideal the isentropic model is. This is a lesson I will not soon forget. So thanks again.

The tank in question is actually a cryogenic dewar, so low temperature is not a problem. We were warming it up for maintenance. It was taking a long time. I preferred a flow-through purge to warm it, but the standard process around here is to purge by pressurizing and then venting. After many purge/vent cycles from the top of the tank, someone decided to vent from the bottom of the tank, thinking that this would help warm it up. Since the bottom valve is a ball valve meant to flow liquid, the discharge was rapid and the cooling extreme. This led everyone to believe the tank was still cold inside, since we did not believe that ambient temperature gas dropping 50 psi could lead to such cold temperatures.

This is a good operations lesson to be sure. I burned a ridiculous amount of nitrogen for no reason.

 

[HazGas]

One other parameter of note. The tank has a vent line approximately 600 yards long and 6" pipe, so quite significant. If, as you say, the fluid in the tank expanding is doing work on the fluid in this vent line, might that also drive it closer to an isentropic process?

 

[georgeverghese]

Gas flow through a pipe itself is an isenthalpic process ( isentropic work expended in friction is converted back to heat).

The isentropic work is by the gas expanding out from the vessel against the superimposed backpressure from the exit point.

In the more sophisticated simulators, the temp profile on the vessel wall is different from the temp profile seen on the exit nozzle. And if you have a long exit line, the temp profile here also changes with time and distance.

 

[EmmanuelTop]

HazGas,

I believe the key issue is rapid expansion. Whether Nitrogen goes directly to atmosphere or into a long-distance line, I doubt it would affect the final result significantly - as long as the expansion inside the tank occurs at the same rate, dV/dt. The "PV work" term is very debatable in both cases, but the observed and documented fact is that the fluid undergoes a substantial decrease of internal energy when expanded rapidly.

If you look at the p-H chart for Nitrogen (attached), you can observe that isotherms are almost 90 degrees vertical (red lines) for pressures 100-450 kPaa and temperatures from -20 to +50 degC, i.e. they follow iso-enthalpy lines. Therefore a typical, low-rate depressurization process, would cause insignificant decrease of temperature (green line). If expanded adiabatically, temperatures go very low (black line). Apparently, the faster is the depressurization, the closer is the approach between the actual expansion process and the isentropic expansion process.

I am sorry I cannot provide you with a scientific explanation of these phenomena and give you a set of simple equations that will be applicable for each case. Obviously, integration of the p(V)dV equation during depressurization process would have to consider decreasing mass inside the system as a function of time. I have participated in so many discussions on this topic during last 10 years, and not even on a single occasion I could say that all the participants reached a common conclusion. Thank you for bringing some real-life, field experience to this subject.

Dejan IVANOVIC
Process Engineer, MSChE

 

[EmmanuelTop]

This is an example study done for LPG and the interesting part is the conclusion that rapid expansion leads to almost isentropic process which, for boiling liquids, results in catastrophic explosion (you can Google the term "BLEVE" for more information, there is very illustrative video at

https://www.youtube.com/watch?v=UM0jtD_OWLU

The LPG/BLEVE phenomenon is quite different from expanding low pressure gaseous Nitrogen, but the thermodynamics behind the two processes have very much in common.

Dejan IVANOVIC
Process Engineer, MSChE

 

[OldDoc]

HazGas,
if you imagine a single molecule (no interactions with other molecules) expanding from initial to final conditions the path is isentropic,
a problem, simulating a real behaviour, is that each molecule interact with each other and the final result is difficult to estimate,
simulators allow to define parameters as isentropic efficiency which keeps in account for that (i.e. heat transfer between different volumes of fluid etc.) but in practice one doesn't know which values to adopt for new projects (altough you may be able to regress these values for existing projects).
Also simulators generally solve predefined models which do not keep in account for real heat transfer mechanisms in external piping, main scope being to estimate the lowest temperature for the vessel,
if you add a long vent line the temperature at the end could be significantly different from that inside the vessel as you noted.
For these (and other) reasons I suspect that results from these calc's may be less accurate than one would hope.
As others here I utilize a software (a depressuring unit in Prode Properties) for these calc's and results are not too different from those provided by EmmanuelTop,
not sure how useful these numbers can be for you.

 

[HazGas]

Again, I'd like to thank everyone for their insight. I feel a lot better about myself after wracking my brain for hours trying to figure out what equation to use, and then trying to derive one, and finally just following lines on charts trying to find anything that made sense (this is when I did the isenthalpic process but decided it was too cold.). So at least I learned that my lack of ability doesn't make me the worlds worst engineer at thermodynamics.

Interesting you mention BLEVEs. Been there, done that, and ran like hell because of it. It was nitrogen also, liquid at 300 psig so nearly critical, when the tank came unzipped. The tank was not a coded vessel, it was an experimental vessel for spaceflight. It wasn't supposed to fail catastrophically so our clear distances were inadequate (there were lots of contributing factors) but when the head blew off of it about 30 feet away from me on the other side of sheet metal, yeah... I learned about BLEVEs. They are unpleasant.

 

[HazGas]

Excuse me, I meant to say isentropic in the last message, not isenthalpic.