Calculations of equilibrium constants, compressibility factors and densities using the Soave-Redlich-Kwong equation of state
Authors' Data: Zakia Nasri and Housam Binous
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

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Acknowledgement :
This problem was presented in Example 4-10 page 175 by Henley and Seader in Equilibrium-Stage Separation Operations in Chemical Engineering, Wiley, 1981.

Equilibrium data at 175°F and 100 psia for Methane, Ethane and Propane mixture from Henley and Seader.

x[1] = 0.4190; y[1] = 0.9852; x[2] = 0.3783; y[2] = 0.01449; 
    x[3] = 0.2027; y[3] = 0.000312;

Critical Pressure and Temperature and Acentric Factor for Methane, Ethane and Propane.

Pc[1] = 673.1; Tc[1] = 343.9; ω[1] = 0;

Pc[2] = 709.8; Tc[2] = 550.0; ω[2] = 0.1064;

Pc[3] = 617.4; Tc[3] = 665.9; ω[3] = 0.1538;

Equilibrium constants using the ϕ-ϕ methode and the Soave-Redlich-Kwong Equation of State. Values of the Equilibrium constants, obtained in the present work, are the same as those given by Henley and Seader.

Ap[i_] := 0.42747 a[i] Pre[i]/Tre[i]^2

Bp[i_] := 0.08664 Pre[i]/Tre[i]

Tre[i_] := T/Tc[i]

Pre[i_] := P/Pc[i]

(Subscript[ϕ, v])[i_] := 
      Exp[((Subscript[Z, v]) - 1) Bp[i]/(Subscript[B, v]) - Log[(Subscript[Z, v]) - (Subscript[B, v])] - 
          (Subscript[A, v])/(Subscript[B, v]) (2 Ap[i]^0.5/(Subscript[A, v])^0.5 - 
                Bp[i]/(Subscript[B, v])) Log[((Subscript[Z, v]) + (Subscript[B, v]))/(Subscript[Z, v])]]

(Subscript[ϕ, l])[i_] := 
      Exp[((Subscript[Z, l]) - 1) Bp[i]/(Subscript[B, l]) - Log[(Subscript[Z, l]) - (Subscript[B, l])] - 
          (Subscript[A, l])/(Subscript[B, l]) (2 Ap[i]^0.5/(Subscript[A, l])^0.5 - 
                Bp[i]/(Subscript[B, l])) Log[((Subscript[Z, l]) + (Subscript[B, l]))/(Subscript[Z, l])]]

a[i_] := (1 + m[i] (1 - Tre[i]^0.5))^2

m[i_] := 0.480 + 1.574 ω[i] - 0.176 ω[i]^2

(Subscript[A, v]) = (∑_(i = 1)^3)(∑_(j = 1)^3) y[i] y[j] Ab[i, 
                j];

Ab[i_, j_] = (Ap[i] Ap[j])^0.5;

(Subscript[B, v]) = (∑_(i = 1)^3) y[i] Bp[i];

(Subscript[A, l]) = (∑_(i = 1)^3)(∑_(j = 1)^3) x[i] x[j] Ab[i, 
                j];

(Subscript[B, l]) = (∑_(i = 1)^3) x[i] Bp[i];

solv = Solve[
                Z^3 - Z^2 + Z ((Subscript[A, v]) - (Subscript[B, v]) - (Subscript[B, v])^2) - 
                    (Subscript[A, v]) (Subscript[B, v]) == 0, Z] /. 
              T -> (-175 + 459.67) /. P -> 100 // Chop // 
        Sort

soll = Solve[
                Z^3 - Z^2 + Z ((Subscript[A, l]) - (Subscript[B, l]) - (Subscript[B, l])^2) - 
                    (Subscript[A, l]) (Subscript[B, l]) == 0, Z] /. 
              T -> (-175 + 459.67) /. P -> 100 // Chop // 
        Sort

K[i_] = (Subscript[ϕ, l])[i]/(Subscript[ϕ, v])[i];

Table[K[i] /. (Subscript[Z, l]) -> soll[[1, 1, 2]] /. 
              (Subscript[Z, v]) -> solv[[3, 1, 2]] /. 
            T -> (-175 + 459.67) /. P -> 100 // Chop, {i, 
        1, 3}]

Values of the compressibility factors are the same as those found by Henley and Seader

solv[[3, 1, 2]]

soll[[1, 1, 2]]

Molecular Weight of the mixtures

MW[1] = 16.043; MW[2] = 30.070; MW[3] = 44.097;

(Subscript[M, v]) = (∑_(i = 1)^3) y[i] MW[i]

(Subscript[M, l]) = (∑_(i = 1)^3) x[i] MW[i]

Values of the Molar volumes and densities are the same as those found by Henley and Seader

(Subscript[v, l]) = (Subscript[Z, l]) R T/P /. (Subscript[Z, l]) -> soll[[1, 1, 2]] /. 
              T -> (-175 + 459.67) /. P -> 100 /. 
          R -> 10.73 // Chop

(Subscript[v, v]) =  (Subscript[Z, v]) R T/P /. (Subscript[Z, v]) -> solv[[3, 1, 2]] /. 
              T -> (-175 + 459.67) /. P -> 100 /. 
          R -> 10.73 // Chop

(Subscript[ρ, l]) = (Subscript[M, l])/(Subscript[v, l])

(Subscript[ρ, v]) = (Subscript[M, v])/(Subscript[v, v])