Original UNIFAC

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The Original UNIFAC model consists of the following equations[1]:

 ln \gamma_i = ln \gamma_i^C + ln \gamma_i^R

 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})

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

 V_i = \frac{r_i}{\sum_j r_j x_j}

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

 F_i = \frac{q_i}{\sum_j q_j x_j}

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

 r_i = \sum_k \nu_k^{(i)} R_k

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

 q_i = \sum_k \nu_k^{(i)} Q_k

 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}

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

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

 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}}]

 \Theta_m = \frac{Q_m X_m}{\sum_n Q_n X_n}

 X_m = \frac{\sum_j \nu_m^{(j)} x_j}{\sum_j \sum_n \nu_n^{(j)} x_j}

 \Psi_{nm} = exp(- { {a_{nm} } \over {T} })

References

  1. Gmehling, Kolbe, Kleiber, Rarey; Chemical Thermodynamics for Process Simulation; February 2012; Wiley ISBN 9783527312771

See also