public subroutine UNIFAC_temperature_dependence(self, systems_groups, T, psi, dpsi_dt, dpsi_dt2)

UNIFAC temperature dependence

Implementation of the $\psi(T)$ function of the UNIFAC model.

$$\psi_{ij}(T) = \exp(-\frac{A_{ij}}{T})$$

$$\frac{d \psi_{ij}(T)}{dT} = \frac{A_{ij}}{T^2} \exp(-\frac{A_{ij}}{T})$$

$$\frac{d^2 \psi_{ij}(T)}{dT^2} = \frac{Aij (Aij - 2T)}{T^4} \exp(-\frac{A_{ij}}{T})$$

References

1. Dortmund Data Bank Software & Separation Technology
2. Fredenslund, A., Jones, R. L., & Prausnitz, J. M. (1975). Group‐contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal, 21(6), 1086–1099. https://doi.org/10.1002/aic.690210607
3. Skjold-Jorgensen, S., Kolbe, B., Gmehling, J., & Rasmussen, P. (1979). Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Industrial & Engineering Chemistry Process Design and Development, 18(4), 714–722. https://doi.org/10.1021/i260072a024
4. Gmehling, J., Rasmussen, P., & Fredenslund, A. (1982). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 2. Industrial & Engineering Chemistry Process Design and Development, 21(1), 118–127. https://doi.org/10.1021/i200016a021
5. Macedo, E. A., Weidlich, U., Gmehling, J., & Rasmussen, P. (1983). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 3. Industrial & Engineering Chemistry Process Design and Development, 22(4), 676–678. https://doi.org/10.1021/i200023a023
6. Tiegs, D., Rasmussen, P., Gmehling, J., & Fredenslund, A. (1987). Vapor-liquid equilibria by UNIFAC group contribution. 4. Revision and extension. Industrial & Engineering Chemistry Research, 26(1), 159–161. https://doi.org/10.1021/ie00061a030
7. Hansen, H. K., Rasmussen, P., Fredenslund, A., Schiller, M., & Gmehling, J. (1991). Vapor-liquid equilibria by UNIFAC group contribution. 5. Revision and extension. Industrial & Engineering Chemistry Research, 30 (10), 2352–2355. https://doi.org/10.1021/ie00058a017
8. Wittig, R., Lohmann, J., & Gmehling, J. (2003). Vapor−Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. Industrial & Engineering Chemistry Research, 42(1), 183–188. https://doi.org/10.1021/ie020506l
9. SINTEF - Thermopack

Type Bound

UNIFACPsi

Arguments

Type	Intent	Optional	Attributes		Name
class(UNIFACPsi)				::	self	$\psi$ function
class(Groups)				::	systems_groups	Groups in the system
real(kind=pr),	intent(in)			::	T	Temperature [K]
real(kind=pr),	intent(out),	optional		::	psi(:,:)	$\psi$
real(kind=pr),	intent(out),	optional		::	dpsi_dt(:,:)	$\frac{d \psi}{dT}$
real(kind=pr),	intent(out),	optional		::	dpsi_dt2(:,:)	$\frac{d^2 \psi}{dT^2}$

Variables

Type	Visibility	Attributes		Name		Initial
real(kind=pr),	public		::	Eij(size(self%Aij,1),size(self%Aij,2))
integer,	public		::	ngroups