Need help with soave-redlich-kwong equation.

[reed2100]

I'm in a reservoir fluids class and currently we're going over some equations of state. In a homework assignment he asks us the following :

"You are provided that there is a hydrocarbon mixture of methane (28 mol %), ethane (24 mol %), propane (14 mol %), n-butane (20 mol %), i-butane (3 mol %), n-pentane (6 mol %), n-hexane (3 mol %) and n-heptane (2 mol %). You are asked to calculate the molar volume of this mixture at P=500 psia and T = 68, 90, 120, 150 and 180 oF; and at P=1500 psia and T = 180, 200, 220 and 250 oF. Use the generalized correlation chart and the Redlich Kwong Soave Equation of State to solve this."

Now, I've looked at the equation over and over, and I know the mixing rules to get the proper constants. However, I can't seem to rearrange the redlich kwong equation into a form that gives me molar volume as a function of temperature and pressure. I know I can also say "V=ZRT/P", but that would require me to find a z factor for this mixture, correct? And I would have to find some chart, probably this generalized correlation chart the problem mentions? Or is that not the right way to go about this? I chose to do these problems in matlab, so I thought maybe I could just use vectors of Pressure and volume for each temperature given to me to make the calculations, and look at the resulting plots for each isotherm to find the molar volume at the pressure I was given for said isotherm.

Do you think I'm overthinking this? Am I missing something, can I put the equation into a form of V=f(T,P)? I'm not seeing how, but if I could that would make this much easier. However, I feel like that's not the right way because he mentioned the charts, which makes me think of z factors for mixtures? I'm not sure how I should approach this. Any and all help is appreciated.

 

[Chestermiller]

Let's suppose that you have developed the RKS parameters for the combination of species, and now you have to use the RKS equation to determine what you want to determine. The general form of the RKS equation is f(V,P,T)=0. So now, you have P and T, and you need to solve for V. So you have a non-linear algebraic equation to solve for V. You can use Newton's method to solve, but you need a good initial guess. What do you think a good initial guess would be?

Chet