To obtain a semi-theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi-chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi-chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters.

The UNIQUAC equation gives good representation of both vapor-liquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well-defined simplifying assumptions are introduced into the generalized quasi-chemical treatment, the UNIQUAC equation reduces to any one of several well-known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations.

The effects of molecular size and shape are introduced through structural parameters obtained from pure-component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.

Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems

A group-contribution method is presented for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method combines the solution-of-functional-groups concept with a model for activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). The resulting UNIFAC model (UNIQUAC Functional-group Activity Coefficients) contains two adjustable parameters per pair of functional groups.

By using group-interaction parameters obtained from data reduction, activity coefficients in a large number of binary and multicomponent mixtures may be predicted, often with good accuracy. This is demonstrated for mixtures containing water, hydrocarbons, alcohols, chlorides, nitriles, ketones, amines, and other organic fluids in the temperature range 275° to 400°K.

Group‐contribution estimation of activity coefficients in nonideal liquid mixtures

A modified SAFT equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain reference fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixtures of small spherical molecules such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassociating molecules were identified for 78 substances by correlating vapor pressures and liquid volumes. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor−liquid equilibria of mixtures, the equation of state shows substantial predictive capabilities and good precision for correlating mixtures. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng−Robinson model is also given for vapor−liquid equilibria of binary systems, confirming the good performance of the suggested equation of state. ...

Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules

A heat transfer textbook

Carbon capture and storage (CCS) is broadly recognised as having the potential to play a key role in meeting climate change targets, delivering low carbon heat and power, decarbonising industry and, more recently, its ability to facilitate the net removal of CO2 from the atmosphere. However, despite this broad consensus and its technical maturity, CCS has not yet been deployed on a scale commensurate with the ambitions articulated a decade ago. Thus, in this paper we review the current state-of-the-art of CO2 capture, transport, utilisation and storage from a multi-scale perspective, moving from the global to molecular scales. In light of the COP21 commitments to limit warming to less than 2 °C, we extend the remit of this study to include the key negative emissions technologies (NETs) of bioenergy with CCS (BECCS), and direct air capture (DAC). Cognisant of the non-technical barriers to deploying CCS, we reflect on recent experience from the UK's CCS commercialisation programme and consider the commercial and political barriers to the large-scale deployment of CCS. In all areas, we focus on identifying and clearly articulating the key research challenges that could usefully be addressed in the coming decade.

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Carbon capture and storage (CCS): the way forward

A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two-liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α12 which makes it applicable to a large variety of mixtures. By proper selection of α12, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor-liquid and ternary liquid-liquid equilibria based on binary data alone.

Local compositions in thermodynamic excess functions for liquid mixtures

1. The Phase Equilibrium Problem. 2. Classical Thermodynamics of Phase Equilibria. 3. Thermodynamic Properties from Volumetric Data. 4. Intermolecular Forces, Corresponding States and Osmotic Systems. 5. Fugacities in Gas Mixtures. 6. Fugacities in Liquid Mixtures: Excess Functions. 7. Fugacities in Liquid Mixtures: Models and Theories of Solutions. 8. Polymers: Solutions, Blends, Membranes, and Gels. 9. Electrolyte Solutions. 10. Solubilities of Gases in Liquids. 11. Solubilities of Solids in Liquids. 12. High-Pressure Phase Equilibria. Appendix A. Uniformity of Intensive Potentials as a Criterion of Phase Equilibrium. Appendix B. A Brief Introduction to Statistical Thermodynamics. Appendix C. Virial Coefficients for Quantum Gases. Appendix D. The Gibbs-Duhem Equation. Appendix E. Liquid-Liquid Equilibria in Binary and Multicomponent Systems. Appendix F. Estimation of Activity Coefficients. Appendix G. A General Theorem for Mixtures with Associating or Solvating Molecules. Appendix H. Brief Introduction to Perturbation Theory of Dense Fluids. Appendix I. The Ion-Interaction Model of Pitzer for Multielectrolyte Solutions. Appendix J. Conversion Factors and Constants. Index.

Molecular Thermodynamics of Fluid-Phase Equilibria

Generalized van der Waals theory is used to establish a partition function that considers the effect of density on rotational and vibrational motions in addition to translational degrees of freedom. A three-parameter equation of state is derived from this partition function. The equation of state is applicable to small, spherical (argon-like) molecules and also to large, structurally complex molecules, including polymers. Parameters are presented for three polymers and twenty-two common fluids including light hydrocarbons, heavy hydrocarbons, nitrogen, carbon dioxide, hydrogen, carbon monoxide, hydrogen sulfide, sulfur dioxide, and water. The equation of state gives good liquid densities, and vapor pressures, and fair second virial coefficients.

John M. Prausnitz

Papers

Local compositions in thermodynamic excess functions for liquid mixtures

Molecular Thermodynamics of Fluid-Phase Equilibria

Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems

Perturbed hard-chain theory: An equation of state for fluids containing small or large molecules

Computerized Design of Multicomponent Distillation Columns Using the UNIFAC Group Contribution Method for Calculation of Activity Coefficients