public subroutine Ge_combinatorial(self, n, T, Ge, dGe_dn, dGe_dn2)

UNIFAC combinatorial term

Calculate the UNIFAC combinatorial term of Gibbs excess energy

Description

Calculate the UNIFAC combinatorial term of reduced Gibbs excess energy. The subroutine uses the Flory-Huggins and Staverman-Guggenheim combinatory terms as follows:

Flory-Huggins

$$G^{E,FH} = RT \left(\sum_i^{NC} n_i \, \text{ln} \, r_i - n \, \text{ln} \, \sum_j^{NC} n_j r_j + n \, \text{ln} \, n \right)$$

$$\frac{dG^{E,FH}}{dn_i} = RT \left(\text{ln} \, r_i - \text{ln} \, \sum_j^{NC} n_j r_j + \text{ln} \, n + 1 - \frac{n r_i}{\displaystyle \sum_j^{NC} n_j r_j} \right)$$

$$\frac{d^2G^{E,FH}}{dn_i dn_j} = RT \left(- \frac{r_i + r_j}{\displaystyle \sum_l^{NC} n_l r_l} + \frac{1}{n} + \frac{n r_i r_j}{\displaystyle \left(\sum_l^{NC} n_l r_l \right)^2} \right)$$

Staverman-Guggenheim

$$\frac{G^{E,SG}}{RT} = \frac{z}{2} \sum_i^{NC} n_i q_i \left(\text{ln} \frac{q_i}{r_i} - \text{ln} \, \sum_j^{NC} n_j q_j + \text{ln} \, \sum_j^{NC} n_j r_j \right)$$

$$\frac{1}{RT}\frac{dG^{E,SG}}{dn_i} = \frac{z}{2} q_i \left( - \text{ln} \, \left( \frac{r_i \sum_j^{NC} n_j q_j}{\displaystyle q_i \sum_j^{NC} n_j r_j} \right) - 1 + \frac{\displaystyle r_i \sum_j^{NC} n_j q_j}{\displaystyle q_i \sum_j^{NC} n_j r_j} \right)$$

$$\frac{1}{RT}\frac{d^2G^{E,SG}}{dn_i dn_j} = \frac{z}{2} \left(- \frac{q_i q_j}{\displaystyle \sum_l^{NC} n_lq_l} + \frac{q_i r_j + q_j r_i}{\displaystyle \sum_l^{NC} n_l r_l} - \frac{\displaystyle r_i r_j \sum_l^{NC} n_l q_l} {\left(\displaystyle \sum_l^{NC} n_l r_l \right)^2} \right)$$

Fredenslund et al. (UNIFAC)

$$\frac{G^{E,\text{UNIFAC}}}{RT} = \frac{G^{E,FH}}{RT} + \frac{G^{E,SG}}{RT}$$

References

1. SINTEF - Thermopack

Arguments