Gas Compression as Vessel Level Rises 1

[ChemEngSquirrel]

i have a nitrogen blanketed water storage vessel. If the vessel is initially 25% full of water and then filled to 50% full, how can i calculate the final temperature and pressure of the compressed nitrogen gas?

This query is based on an upset scenario where the vessel is filled but no gas vented from the vessel.

Thanks.

 

[zdas04]

Mostly you don't. If the process is "fast" (i.e., elapsed time less than a couple of seconds), then you can use the ideal gas law to calculate a new pressure and the adiabatic heat of compression to calculate the gas temperature. The problem is the water is such an enormous heat sink that you will be dumping heat from the gas from the first micro-second. That rate of heat transfer is indeterminate.

If the process takes more than a few seconds, then you can calculate the heat of compression, convert that to energy using the specific heat of the gas, transfer that heat in its entirety to the water and calculate a new water temp. Water temp will most likely go up by a small fraction of a degree.

In my GasBuster, I use inflow of water to compress gas about 5 compression ratios, and the CFD models that I had run do not show a measurable temperature increase because of the heat transfer into the water. In the field we cannot detect any temperature change during the process (and it is really fast).

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[LittleInch]

That sounds good to me. Just remember that pressure is in absolute terms and temp is in Kelvin. Hence for a gas blanketing system where pressure is typically very low, sat 2 psig, 16.5 psia, assuming as zdas 04 says that temp is virtually identical and even if it does go up won't go up much in terms of absolute temp, reduction on volume of 50/75 then equates to 24.75 psia, 10 psig (I think).

You will get a more accurate calculation using z factor and proper software, but I doubt it will be more than 1-2 psi difference asuming these values are correct.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[rotw]

Assuming no heat transfer to the water, I agree with LittleInch calculation of pressure ratio also assuming the compressibility is not changing (actually it will be it is quite negligible).

I used to calculate the temperature this formula:

T2 = T1 x (P2/P1)^((k-1)/k)
T1, T2 are the initial, final temperature respectively (deg K)
k = Cp/Cv assumed constant = 1.4
P2/P1 = 1.5

So for example if the initial temperature is 15 deg C, the resulting is 50 deg C assuming a fast compression process and prior to any tangible heat exchange yet with the water.

Any comments or correction as the formula I have used is the one I use for dynamic compressors just setting the polytropic efficiency to 100% assuming it should be equal to adiabatic reversible process (am I right) ?

 

[zdas04]

The first sentence invalidates the rest. Heat transfer to the water is quite significant and very quick. In my GasBuster we are sometimes doing 5 compression ratios in under 2 seconds with water squashing gas. Temperature change of the gas is not measurable (gas temperature looks identical to initial water temperature within the accuracy of my Fluke instrument (2 decimal places). I've done the math and an infinitesimal increase in evaporation eats the heat of compression to keep it isothermal. The equation above only works for insignificant heat transfer to the environment. Using water to compress gas does not satisfy that boundary condition.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[rotw]

Zdas,

Do you think the dynamic is identical if you consider a lower pressure ratio (say 1.5 to 2) that will keep the temperature sufficiently below water evaporation point ? So you would have heat exchange only between Liquid water and Nitrogen.

I have no experience with such Gasbuster and the question is just out of curiosity.

 

[zdas04]

Water will evaporate at room temperature. One degree above room temperature it will evaporate slightly faster. Every unit mass that evaporates sucks an appreciable amount of heat from the environment. What happens in my invention (the GasBuster, you can see an animation at the "Samples" page of my web site, right column at the bottom) is that if you assume adiabatic compression and compress the mass of natural gas (that is in the head space when the vent valve closes) 5 compression ratios, you get a temperature change of 233ºF. With the mass of gas in the head space, this equates to adding 95 BTU to the space. The latent heat of vaporization of water is 972 BTU/lb so to remain isothermal you only have to vaporize about 0.1 lb of water--45 mL out from a 350 L volume (0.012% of the total volume). This is a pretty rough approximation since the heat of compression number is significantly overstated (you can't use the adiabatic compression equation in a system with a significant heat sink), but with lower heat of compression the amount of water vaporized to maintain isothermal conditions is even less than almost none.

I have found the equation you showed to be a reasonable approximation to reality at 1.1 compression ratios and less (it even matches reality reasonably well in expansion). The boundary conditions of the equation are all centered around loosing or gaining heat to/from the environment and the reversibility of the reactions. Not the magnitude of any term. It doesn't work at all with an irreversible process like phase change or with a heat sink the magnitude of a vessel full of liquid.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[rotw]

I read your article on the the GasBuster.
It will take me time to understand but I continue reading.
It is a fascinating invention really.

 

[zdas04]

Thank you. It came from living so dang far outside the box.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"