Cubic plus association equation of state

The cubic plus association equation of state, discussed in Chapter 4, is a combination of the Soave-Redlich-Kwong equation with first-order perturbation theory for associating fluids that is essentially the same as in the SAFT equation, and is given by Michelsen and Hendricks. The cubic plus association equation of state has been reviewed in refs 188, 189 and 190. Because of the association term, similar to that used for SAFT, the equation is no longer cubic. The cubic plus association equation of state is as follows  

The radial distribution function g for the reference fluid has been approximated 

The term in eq 5.192 is the association strength between site A on molecule i and site B on molecule j given by  

The cubic association equation requires mixing rules for the a and b of the SRK and those typically used are eq 5.13 and eq 5.15 with combining rules given by eqs 5.31 and 5.32 with jSab= 1- Combining rules for the association terms are only required for the cross-association energy and volume Suresh and Beckman used 

For the Elliott-Suresh-Donohue equation/ which will not be discussed further here, the combining rules for of eq 5.192 were proposed by Suresh and Elliott as 

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Kontogeorgis, G. M., M. L. Michelsen, G. K. Folas, S. Derawi, N. von Solms, and E. H. Stenby. 2006a. Ten years with the applications of cubic-plus-association EOS to pure organic compounds and self-associating system (cubic-plus-association) equation of state. Part 1. Pure compounds and self-associating systems. Industrial and Engineering Chemistry Research. 45, 4855. 

In the thermodynamic model presented here, the Cubic-Plus-Association equation of state combined is used to model the fluid phases. The hydrate phase is modelled by the solid solution theory of van der Waals and Platteeuw. Good agreement between the model predictions and experimental data is observed, demonstrating the reliability and robustness of the developed model. The CPA EoS is shown to be a very successful model for multi-phase multi-component mixtures containing hydrocarbons, glycols and water. 

For mixtures of hydrocarbons and alcohols, often involved in hydrate inhibition, the cubic plus association equation of state has been used to estimate the (vapour + liquid) and (liquid-b Uquid) equilibria. In both cases no combining rules are needed for the association parameters and for (alcohol + hydrocarbon). 

Ma J, Li J, Fan D, Peng C, Liu H, Hu Y (2011) Modeling pVT properties and vapor-liquid equilibrium of ionic liquids using cubic-plus-association equation of state. Chin J Chem Eng 19 1009-1016... 

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