Extending the Van Laar Model to Multicomponent Systems

• Published in: The open thermodynamics journal 2010-01, Vol.4 (1), p.129-140
• Main Author: Peng, Ding-Yu
• Format: Article
• Language: English
• Subjects: Cubic equations; Energy of formation; Gibbs free energy; Hydrocarbons; Interaction parameters; Liquids; Mathematical analysis; Mathematical models
• ISSN: 1874-396X; 1874-396X
• DOI: 10.2174/1874396X01004010129

The original van Laar equation for representing the excess Gibbs free energies of liquid mixtures contains certain deficiencies that have prevented the equation from being applied to multicomponent systems. We have analyzed the temperature dependency of the energy parameter in modern cubic equations of state and modified the original van Laar equation with a view to extending the equation to multicomponent systems. It is found that the consideration of the temperature dependency of the energy parameter has lead to a modified van Laar equation involving additional terms. These extra terms serve to provide some physical significance that can be attached to the van Laar equation to allow it to unambiguously represent the behavior of the excess Gibbs free energy and activity coefficients of nonideal solutions. The final form of the modified van Laar equation for multicomponent mixtures involves two size parameters and an interaction parameter for each of the constituent binary pairs; the latter parameter replaces a term consisting of a combination of the two energy parameters and two size parameters for the components in a binary mixture. For mixtures involving only hydrocarbons the size parameters can be readily calculated from the critical properties by means of any of the cubic equations of state of the van der Waals type.