Compressibility of Nitrogen Gas and Liquid Water

[tb012]

I need to pressurize a volume of 4823 cubic inches to 9500 psi using a set volume of water and nitrogen gas on top. What I don't understand is how to relate the compressibility of the gas to the volume of water and nitrogen needed. The temperature will be around 80 degrees F. I need to develop a relationship to determine the volume of Nitrogen needed, using the compressibility of Nitrogen, pressure of the chamber, and the water volume. Is that enough known information to develop the equation?

 

[georgeverghese]

Compressibility factor z is roughly 1.61 for N2 at this high pressure from T-S diagram of N2 in Perry Chapter 3
Find n

n=P.V/z.R.T

n= kgmoles of N2 gas
V= actual volume of gas space in m3
P=pressure = 656e2 kpa abs
R=8.314kJ/kgmole/degK
T= 300degK

Actual mass of N2 required, kg = n x 28
Standard volume of N2 required, Sm3 = n x 23.645

Henry's Law solubility of N2 in water is most likely small and is ignored here.

 

[georgeverghese]

Accounting for N2 solubility in water at 655 barg, Google tells me H = 6e-5 / MPa, where solubility of N2, the Henry's Law constant, is expressed as mole fraction of N2 / kgmole of water. Simplifying, this works out to 6.2kg of N2 dissolved / m3 of water. Add the corresponding mass dissolved in your volume of water to the mass of N2 in the gas space. Note : Standard volume for gas in Sm3 references 1atm, 15.6degC

 

[pierreick]

George,
My calculation using PR EOS is 1.42 for Z at 26.66C and 656 bars Abs.
Regarding dissolved N2/m3 of aqueous solution, I got 11. 1 to 11.8 kg/m3
Attached Henry's coefficients with references.
Pierre

 

[LittleInch]

You're not going to end up with many cubic inches of gas....

note that the equations above are all at the same temperature. Unless you pressurises really slowly, the gas will heat up - a lot.

I'm not really following the question though. Is the 4382 cubic inches the fixed volume and your injecting loads of Nitrogen or are you pressurising that starting at 1bara? and filling with water?

It's all a bit vague.

A drawing or sketch would help hugely to figure out what exactly you're doing, the start point and the end point.

And why also helps as that is one mother of a pressure.

 

[georgeverghese]

This is where I got the solubility curve for N2 from

SOLUBILITY

www.thermopedia.com

I havent been able to get a cross reference check ( so far) to this graph elsewhere at these high pressures. H shows a pressure dependence at high pressures.

And the z value was calculated from the value of the product PV shown in fig 2-13 on page 2-258 (T-S diagram for N2) in the 7th edn of Perry. The compressibility tables for N2 in Perry ( Table 2-179) stops at 500atm, 300degK, z=1.36

 

[pierreick]

Thanks George.

 

[georgeverghese]

Linear extrapolation from 500bar to 655bar from that table 2-179 in Perry gives z=1.54