## Perfect gas law for methan

## Perfect gas law for methan

(OP)

Given that PV=ZnRT for a vessel. For a given Volume, Temp, and initial pressure, and Mole Weight of methane, the LbMoles of methane can be calculated.

Now, add some more methane to the vessel from a high pressure source. Now, the mole wt in the vessel has changed. Assuming no change in temperature, or volume, AND, I know how many lb moles of Methane are added, how do I calculate the new pressure? Z, being the compressibility factor, is a function of temp and pressure. New pressure is unknown and so is the new Z factor. ??? 1 equation, but 2 unknowns. Is there another equation for Z or P that I can use to solve for the 2 unknowns? I greatly appreciate the help.

PS, this is not a student question, but deals with fueling of a CNG vehicle.

Now, add some more methane to the vessel from a high pressure source. Now, the mole wt in the vessel has changed. Assuming no change in temperature, or volume, AND, I know how many lb moles of Methane are added, how do I calculate the new pressure? Z, being the compressibility factor, is a function of temp and pressure. New pressure is unknown and so is the new Z factor. ??? 1 equation, but 2 unknowns. Is there another equation for Z or P that I can use to solve for the 2 unknowns? I greatly appreciate the help.

PS, this is not a student question, but deals with fueling of a CNG vehicle.

## RE: Perfect gas law for methan

_{1}= P_{1}V/Z_{1}RTFor Z use any valid EOS. The corresponding state theory is easy.

n

_{2}= n_{1}+ Δn"I know how many lb moles of Methane are added" = Δn

P

_{2}= n_{2}Z_{2}RT/VOn the first calculation use Z

_{2}= Z_{1}.With that P

_{2}, calculate a new Z_{2}.Repeat last step until P

_{2}and Z_{2}do not change (i.e. converge).Good luck,

Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

## RE: Perfect gas law for methan

## RE: Perfect gas law for methan

P1V=n1Z1RT 1)

P2V=n2Z2RT 2)

1)/2) =>

P1/P2= n1*Z1/(n2*Z2)

Isolating <=>

P2=P1*n2*Z2/(n1*Z1), k=P1*n2/(n1*Z2) <=>

P2=k*Z2

Since both P2 and Z2 are unknow i dont think that this can be solved itteratively

But unless the added volume is large (and hence the pressure increase high) then i think its pretty safe to assume that the Z is const. Or unless the is a text book task - you could use a table for Z as a function of P/T, this should be fairly easy to get.

If Z assumes constant the problem reduces to:

P2=P1*n2/n1, where n2=n1+added methane

## RE: Perfect gas law for methan

PV=ZnRT -----> P2 = f(Z2) because V, n, and T are constant in this case.

It's the classic iteration of one variable until convergence.

Good luck,

Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

## RE: Perfect gas law for methan

## RE: Perfect gas law for methan

Are you saying more than one EOS is needed (for methane)? I hope not.

"If you use Z2=z1 in the first equation you also get P1=P2, end of iteration."

No, because n

_{1}≠ n_{2}."If you "guess" or assume thing else you would either have something that just bounces around, or perhaps returns to the original value of Z1 as far as i can see

Z1 = f(T, n1, P1). Z2 = f(T, n2, P2). There should only be one value of Z2 (on the gas/vapor side of the phase envelope) for T, n2 and P2 in a well behaved EOS. Any reasonable guess should converge at Z2, not Z1.

Good luck,

Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

## RE: Perfect gas law for methan

Im not talking about a "special" EOS for methane, I'm saying that the original question assumed "perfect gas law" (in brackets because in the perfect gas law Z=1). So you don't have any predictive measure for calculating Z at all (its composition independent)

step 1 (assumed Z1=Z0) =>

P1=P0*n1/n0, and insert into the first equation P=ZnRT gives P1=Z1n1RT=Z0n1RT - and this is true and i can't see where we go from there

What is this f function that you mention? There is no f function in the perfect gas equation for calculating Z. (am i falsely assuming that perfect=ideal gas law?)

I just want to understand your reasoning and where it is that i fail..

## RE: Perfect gas law for methan

For Z, go to: http://excelcalculations.blogspot.com/2011/10/visc...

2 vessels, each with different volumes, and pressures transferring CH4 between them is the problem.

P*V = Z*N*R*T for high pressure methane, which is what I am dealing with. After a short flow time, a small amount (dm) of methane is transferred between 2 vessels. One vessel has slightly less methane, and the other, slightly more methane. The difference in N (lb moles) is the same (obviously) for both vessels. One vessel's pressure decreases, while the other increases. So, I am trying to determine the pressure drop and rise in the 2 vessels, based on the amount (lb moles) of methane transferred. V, R, and T are constant, while P and Z vary. I have not tried the substitution method yet, been so busy with other stuff. I do appreciate all the comments. Thanks so much.

## RE: Perfect gas law for methan

The OP confused us with "perfect gas law" (PV = nRT with no Z) in the title, and speaking repeatedly of Z in PV=ZnRT in the first post. I assumed they meant to use the two parameter correlation PV = ZnRT, which they just said they did. Otherwise, as you said, the solution is unremarkable.

By two parameter correlation, Z = f(T

_{r}, P_{r}). I read this as “Z is equal to a function of T_{r}and P_{r}”. f ≡ function.Initially, the OP knows P1, V, and T. They can calculate Z1 directly from P1 and T. Then they calculate n1.

Then, a known quantity of CH4 is added to get n2 lb-moles of CH4 total. Now, they have to calculate P2.

P2 = Z2n2RT/V

All is known on the right hand side, except Z2. Z2 = f (Tr, Pr2) = f (T/Tc, P2/Pc). Since T and Tc and Pc are known, then in reality Z2 = f (P2). Anyone who has looked at Corresponding Theory’s generalized compressibility chart knows, Z is nonlinear with Tr and Pr. The classical solution to nonlinear algebraic equations is iterative.

First put the equation in this format: f(P2) = P2 - Z2n2RT/V = 0

Then, there are many techniques to solve it, like graphical, spreadsheet, regular falsi, Newton’s Rule, or successive substitution (requires P2 = Z2n2RT/V format).

My previous posts suggested successive substitution, because the generalized compressibility charts are not a single equation, but a chart, which is best handled numerically, which works nicely with successive substitution.

I also suggested to start with Z2(1) = Z1.

Then P2(1) = Z2(1)n2RT/V

Then Z2(2) = f(Tr, Pr2(1)) Generalized Compressibility Chart

Then P2(2) = Z2(2)n2RT/V

Then Z2(3) = f(Tr, Pr2(2)) Generalized Compressibility Chart

Then P2(3) = Z2(3)n2RT/V

Then Z2(4) = f(Tr, Pr2(3)) Generalized Compressibility Chart

Then P2(4) = Z2(4)n2RT/V

Then Z2(5) = f(Tr, Pr2(4)) Generalized Compressibility Chart

Then P2(5) = Z2(5)n2RT/V

Keep iterating until Z2 and P2 do not change significantly.

It works. I've done it many times.

Good luck,

Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

## RE: Perfect gas law for methan

## RE: Perfect gas law for methan

Good luck,

Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.