# Using Peng-Robison equation to deterimine fluid lost due to leak

1. Feb 19, 2010

### EvilKermit

1. The problem statement, all variables and given/known data

A container having a volume of 40 L contains one of the following fluids att the given initial conditions. After a leak, the temperature and pressure are remeasured. For each option, determine the kilograms of fluid lost due to the leak, using Peng_robinson equation.

methane T(initial) = 300 K, P(initial) = 100 bar T(final) = 300 K, P(final) = 50 bars

2. Relevant equations

The Peng robinson equation of state is written as:

Z = $$\frac{1}{1-bp}$$ - $$\frac{a}{bRT}\frac{bp}{1+2bp - b^{2}*p^{2}}$$

3. The attempt at a solution

I know how to solve for a and b. If you find it necessary for me to show you this, i can. But I don't see the purpose. However p, which stands for molar density (n/V), I do not understand. Considering the whole point is to find the amount of moles lost, I can't see how this can be solved unless I know the moles in the tank.

2. Feb 19, 2010

### poso

I do not understand how you can solve anything if in
the initial statement the initial ratio of liquid to gas is not defined.

3. Feb 20, 2010

### EvilKermit

You can just ignore this, there's actually another way for the equation to be rearranged so that you don't need to know the value of molar density.

4. Feb 21, 2010

### poso

I can see a practical reason why my earlier question on the level of fluid in the container was irrelevant. The critical temperature for methane is 190 K and the critical pressure is 45 bar. It would seem that the storing conditions you mentioned at 50 and 100 bar and 300 K define the enclosed methane to be in one uniform supercritical fluid state. A fluid level measurement could thus not be done I think.

Anyway, about the PR equation. I have thought a little bit about applying it to your question of the leak. On the left hand side of the equation Z, the compressibility factor is placed. It is defined as: Z = (pressure*molar volume)/(gasconstant*temperature) Molar volume V is equal to 1/p in the equation you have shown. a and b are gas constants for methane. Since you know gas temerature and pressure you can now solve the initial and final state eqations for the differing values of p. Combining it with the known volume gives you the number of moles for both states, with the leak the difference between the two amounts.

What do you think? I at least found it wonderfull to read and think about a state equation for methane!