| Name | TDE.UNIFAC.ActivityCoefficients |
|---|---|
| Name | TDE.UNIFAC.ActivityCoefficients |
| Comment | Activity coefficients model |
| Variable GEX | Excess Gibbs energy |
| Variable T | Temperature |
| Variable x1 | Mole fraction of component 1 |
| Variable x2 | Mole fraction of component 2 |
| Parameter a | Array (0 to nTerms) |
| Constant r1 | Calculated with published group parameters (Ref 29) |
| Constant q1 | Calculated with published group parameters (Ref 29) |
| Constant r2 | Calculated with published group parameters (Ref 29) |
| Constant q2 | Calculated with published group parameters (Ref 29) |
| Constant size1 | Size or array 1 |
| Constant type1 | Array: types of groups in component 1 |
| Constant MainGroup1 | Array: main group types in component 1 |
| Constant number1 | Array: numbers of groups in component 1 |
| Constant size2 | Size or array 2 |
| Constant type2 | Array: types of groups in component 2 |
| Constant MainGroup2 | Array: main group types in component 2 |
| Constant number2 | Array: numbers of groups in component 2 |
| Constant R | Gas constant |
The following expressions define the terms leading to the equation for GEX.
φ1 = x1×r1/(x1×r1 + x2×r2); and
φ2 = x2×r2/(x1×r1 + x2×r2)
θ1 = x1×q1/(x1×r1 + x2×q2); and
θ2 = x2×q2/(x1×r1 + x2×q2)
ln(γ1c) = ln(φ1/x1) + 5×q1×ln(θ1/φ1) + l1 - φ1/x1×(x1×l1 + x2×l2)
ln(γ2c) = ln(φ2/x2) + 5×q2×ln(θ2/φ2) + l2 - φ2/x2×(x1×l1 + x2×l2)
x1,i = n1,i / Σn1,i, where the summation is from i = 1 to N.
θ1,i = x1,i×Qtype(i)/Σx1,i×Qtype(i), where the summation is from i = 1 to N.
x2,i and θ2,i are calculated analogously, as are xM,i and θM,i for the mixture. The mixture is indicated by the subscript M.
Ψij = exp[-UNIFAC Parameter{MainGroup(i),MainGroup(j)}/T]
ln(γ1,k) = Qtype(k)×[1 - Σθ1,i×Ψki /Σθ1,j×Ψji - lnΣθ1,j×Ψki], where the summations are from i = 1 to N, j = 1 to N, and i = 1 to N, respectively.
Similarly, γ2,k and γM,k vectors are calculated for component 2 and the mixture. γM,k is based on the mole fractions of structural groups in the mixture:
xM,i = (x1×n1,i + x2×n2,i) / Σ(x1×n1,i + x2×n2,i), where the summation is from i = 1 to N, N is the dimension of the vector of distinct structural group types in the molecules, and n1 and n2 are vectors representing the number of structural groups of each type.
ln(γ1) = ln(γ1,c) + Σn1,i×{lnγi) - ln(γ1,i)}
ln(γ2) = ln(γ2,c) + Σn2,i×{ln(γi) - ln(γ2,i)}
GEX / (R×T) = x1×ln(γ1) + x2×ln(γ2)