How to calculate number of moles and gas formation volume factor?

[glocki35]

Homework Statement

I am trying to calculate the gas formation volume factor for a reservior, however I am stuck when trying to find the value n - number of moles for a gas to plug into the equation to find Bg, this is what I know;

Bg (gas FVF)= volume of gas at reservoir conditions / volume of gas at standard conditions, I know I have to apply the real gas law here i.e PV=znrt = V=znrt/p, I have the following knowns;

z=0.81
n=??
R=10.73 psia ft3 / lb mol Deg R
T=580 deg R
P=2195 psia

Zsc=0.99
n=??
R= as above
Tsc= 520 deg R
Psc = 14.7 psia

Volume %
methane 83.4
Ethane 9.8
Propane 4.5
isobutane 1.4
n-butane

I am completely stuck when trying to find n, as I do not know the gas volume (only in %)or the gas weight, I know n=total gas weight / molecular weight, I have tried to work this out by calculating the gas density but I can not progress further than this, I am completely stuck!

Is there any guidance you can offer me on this?

Homework Equations

The Attempt at a Solution

 

[Akinbola]

To calculate Number of moles for a gas mixture, is like finding the proportional behaviour of each gas constituent in the mixture. You have a %proportion of each constituent in the mixture, you will use this to get a proportional molecular weight for the mixture
i.e. ƩYi*Mwi=Mw Yi is the proportional percentages for each member gas in the mixture, while, Mwi is there corresponding Molecular weights which you know.
From the real gas eqn:
V=nZRT/P
also recall that density, ρ=m/V
therefore, ρ=mP/nZRT
note that m/n = Mw and in this case it will be Mw for the mixture which you have gotten from ƩYi*Mwi=Mw.
therefore, ρ=Mw*P/ZRT
With the above calculation, you can use it to get the density,ρ, at reservoir condition and the density,ρ, at standard conditions.
formation value factor Bg = ρr/ρsc.
Best of luck

 

[Chestermiller]

Assume you have 1 mole of gas. You have the value of z under reservoir conditions, so you can calculate the volume under reservoir conditions. You know the value of z under standard conditions (520?, 14.7 psi), so you can calculate the volume under standard conditions.