Predictive Soave-Redlich-Kwong (PSRK)
Generic cubic equation of state
<math> P = { { R * T } \over { V - b } } - { { a(T) } \over { ( V + \epsilon * b ) * ( V + \sigma * b ) } } </math>
Parameters for Soave-Redlich-Kwong equation are:
<math> \epsilon = 0</math> and <math> \sigma = 1</math>
Thus:
<math> P = { { R * T } \over { V - b } } - { { a(T) } \over { V * ( V + b ) } } </math>
PSRK mixing rule for calculating a(T) and b
Cohesion pressure (attractive parameter):
<math> a(T) = b*R*T * ( \sum x_i * { {a_{ii}(T)} \over {b_i*R*T} } + { { { {g_0^E} \over {R*T} } + \sum x_i * ln( b / b_i ) } \over { ln( u / (u + 1) )} } )</math>; <math> u = 1.1 </math>
with <math> a_{ii}(T) = \Psi * { { \alpha_i (T_{r,i}) * R^2 * T_{C,i}^2 } \over { P_{C,i} } } </math>; <math> \Psi = 0.42748 </math>
Excluded volume or "co-volume" (repulsive parameter):
<math> b = \sum x_i*b_i </math>
with <math> b_i = \Omega * { { R*T_{C,i} } \over { P_{C,i} } } </math>; <math> \Omega = 0.08664 </math>
Mathias-Copeman equation
Fitting experimental data with Mathias-Copeman parameters <math> c_{1,i} </math>, <math> c_{2,i} </math> and <math> c_{3,i} </math>:
<math> \alpha_i (T_{r,i}) =[ 1 + c_{1,i}*(1 - \sqrt{T_{r,i}}) + c_{2,i}*(1 - \sqrt{T_{r,i}})^2 + + c_{3,i}*(1 - \sqrt{T_{r,i}})^3 ]^2 </math>
General form if no experimental data available:
<math> c_{1,i} = 0.48 + 1.574 \omega_i - 0.176 \omega_i^2 </math>
<math> c_{2,i} = 0 </math>
<math> c_{3,i} = 0 </math>
Gibbs-Excess energy
<math> g^E = g_{c}^E + g_{r}^E</math>
<math> g_{c}^E = R*T * \sum x_i ln( {{\omega_i} \over {x_i}} ) </math>
<math> g_{r}^E = R*T * \sum x_i * {{z} \over {2}} * q_i * ln( { {\theta_{ii}} \over {\theta_i} } ) </math>
<math> -> g_{0}^E = R*T_0 * \sum x_i * ( ln( {{\omega_i} \over {x_i}} ) + {{z} \over {2}} + q_i * ln( { {\theta_{ii}} \over {\theta_i} } ) ) </math>
modified UNIFAC
<math> r_i = \sum_k \nu_k^{(i)} * R_k </math>
<math> q_i = \sum_k \nu_k^{(i)} * Q_k </math>
Modified volume fraction [Kikic et al.; 1980]:
<math> \omega_i = {{x_i * r_i^{2/3}} \over {\sum_j x_j * r_j^{2/3}}} </math>
Group mole fraction:
<math> X_k = {{\sum_i \nu_k^{(i)} * x_i} \over {\sum_i \sum_l \nu_l^{(i)} * x_i}} </math>
<math> \theta_j = { {X_j * Q_j} \over {\sum_k X_k * Q_k} } </math>
<math> \theta_{ji} = { {\theta_j * \tau_{ji}} \over {\sum_m \theta_m * \tau_{mi}} } </math>; <math> \tau_{mi} = \Psi_{nm} </math>
Group interaction parameter:
<math> \Psi_{nm} = exp(- { {a_{nm} + b_{nm}*T + c_{nm}*T^2} \over {T} }) </math>
a, b and c are the binary interaction parameters
<math> a_{nm} \ne a_{mn} </math>; <math> b_{nm} \ne b_{mn} </math>; <math> c_{nm} \ne c_{mn} </math>
Procedure for calculating vapor-liquid equilibria (VLE)
Equilibrium condition:
<math> x_i * \phi_i^L = y_i * \phi_i^V </math>
Fugacity coefficient for the liquid phase:
Fugacity coefficient for the vapor phase:
K-factor:
<math> K_i = { {y_i} \over {x_i} } = { {\phi_i^L} \over {\phi_i^V} } </math>
Sum of mole fractions:
<math> S = \sum y_i = \sum K_i * x_i </math>
Flow diagram for calculating isothermal VLE using PSRK: