Original UNIFAC

The Original UNIFAC model consists of the following equations:

<math> ln \gamma_i = ln \gamma_i^C + ln \gamma_i^R</math>

<math> ln \gamma_i^C = 1 - V_i + ln V_i - 5 q_i(1 - \frac{V_i}{F_i} + ln \frac{V_i}{F_i}) </math>

Volume/mole fraction ratio for component i (j: component index) in the mixture:

<math> V_i = \frac{r_i}{\sum_j r_j x_j} </math>

Surface area/mole fraction ratio for component i (j: component index) in the mixture:

<math> F_i = \frac{q_i}{\sum_j q_j x_j} </math>

Molecular volume parameter for component i (k: subgroup index):

<math> r_i = \sum_k \nu_k^{(i)} R_k </math>

Molecular surface area parameter for component i (k: subgroup index):

<math> q_i = \sum_k \nu_k^{(i)} Q_k </math>

<math> ln \gamma_i^R = \sum_i \nu_k^{(i)} (ln \Gamma_k - ln \Gamma^{(i)}_k ) = \sum_i \nu_k^{(i)} \frac{ln \Gamma_k}{ln \Gamma^{(i)}_k} </math>

For <math> ln \Gamma_k </math> group mole fractions (<math>X_k</math>) and surface area fractions (<math> \Theta_m </math>) are calculated with the composition (<math>x_j</math>) of the mixture.

For <math> ln \Gamma^{(i)}_k </math> group mole fractions (<math>X_k^{(i)}</math>) and surface area fractions (<math> \Theta_m </math>) are calculated with <math>x^{(i)} = 1</math> for the pure component i.

<math> ln \Gamma_k = Q_k [ 1 - ln (\sum_m \Theta_m \Psi_{mk}) - \sum_m \frac{\Theta_m \Psi_{km}}{\sum_n \Theta_n \Psi_{nm}}] </math>

<math> \Theta_m = \frac{Q_m X_m}{\sum_n Q_n X_n} </math>

<math> X_m = \frac{\sum_j \nu_m^{(j)} x_j}{\sum_j \sum_n \nu_n^{(j)} x_j} </math>

<math> \Psi_{nm} = exp(- { {a_{nm} } \over {T} }) </math>

See also

• Group Contribution Methods

• Modified UNIFAC (Dortmund)

• Predictive Soave-Redlich-Kwong (PSRK)