Activity coefficient models

nrtl(X, T, alpha, g, g1)

The non-random two-liquid (NRTL) activity coefficient model is a a local composition model, widely used to describe vapor-liquid, liquid-liquid and vapor-liquid-liquid equilibria. This function returns array of natural logarithm of the activity coefficients.

\[g^e = \sum_{i=1}^c x_i \frac{\sum_{j=1}^c \tau_{ji}G_{ji}x_j}{\sum_{l=1}^c G_{li}x_l}\]

\[\tau = g/T + g_1\]

Parameters:

• X (array) – Molar fractions
• T (float) – Absolute temperature [K]
• g (array) – Matrix of energy interactions [K]
• g1 (array) – Matrix of energy interactions [1/K]
• alpha (array) – Matrix of aleatory factors

wilson(X, T, A, vl)

Wilson activity coefficient model is a local composition model recommended for vapor-liquid equilibria calculation. It can’t predict liquid liquid equilibrium. Function returns array of natural logarithm of activity coefficients.

\[g^e = \sum_{i=1}^c x_i \ln ( \sum_{j=1}^c x_j \Lambda_{ij})\]

Parameters:

• X (array) – Molar fractions
• T (float) – Absolute temperature [K]
• A (array like) – Matrix of energy interactions [K]
• vl (function) – Returns liquid volume of species [\(\mathrm{cm^3/mol}\)] given temperature [K] as argument.

rk(x, T, C, C1, combinatory)

Redlich-Kister activity coefficient model for multicomponent mixtures. This method uses a polynomial fit of Gibbs excess energy. It is not recommended to use more than 5 terms of the polynomial expansion. Function returns array of natural logarithm of activity coefficients.

\[g^e_{ij} = x_ix_j \sum_{k=0}^m C_k (x_i - x_j)^k\]

\[G = C + C_1/T\]

Parameters:

• X (array) – Molar fractions
• T (float) – Absolute temperature [K]
• C (array) – Polynomial coefficient values adim
• C1 (array) – Polynomial coefficient values [K]

unifac(x, T, qi, ri, ri34, Vk, Qk, tethai, a0, a1, a2)

Dortmund Modified-UNIFAC activity coefficient model for multicomponent mixtures is a group contribution method, which uses group definitions and parameter values from Dortmund public database. Function returns array of natural logarithm of activity coefficients.

\[\ln \gamma_i = \ln \gamma_i^{comb} + \ln \gamma_i^{res}\]

Energy interaction equation is

\[a_{mn} = a_0 + a_1 T + a_2 T^2\]

Parameters:

• X (array) – Molar fractions
• T (float) – Absolute temperature [K]
• qi (array) – Component surface array
• ri (array) – Component volumes array
• ri34 (array) – Component volume array, exponent 3/4
• Vk (array) – Group volumes
• Qk (array) – Group surface array
• tethai (array) – Surface fractions
• a0 (array) – Energy interactions polynomial coefficients
• a1 (array) – Energy interactions polynomial coefficients
• a2 (array) – Energy interactions polynomial coefficients