Association equation of state

In principle, it is possible to correlate an adsorption isotherm and a two-dimensional equation of state by working from either direction that is, we may start with an experimental isotherm and develop the associated equation of state (as in going from Equation (8) to Equation (10)), or we may proceed from the equation of state to the isotherm (as illustrated in Example 9.2). 

Interestingly, the activity of C. thermocellum in SCF ethane, SCF CO2, liquid propane, and gaseous propane does not follow the log P trends seen with liquid solvents. Thus, log P may be of limited value when applied to the correlation of metabolic activity in compressed solvents. The traditional definition of log P (25 °C and 0.1 MPa) was extended to our incubation conditions (60 °C and 7 MPa) using the group contribution associating equation of state (GCA-EOS) (48,49) to calculate the mole fraction of the dissolved compressed fluids in octanol and water. Log P logio(x,- /x,- )] correlated well with the total metabolic activity (ratio of total products formed in the treatment to the total products formed in the control) in liquid hydrocarbon solvents (Fig. 2) (37). 

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. 

Pereda, S., Awan, J.A., Mohammadi, A.H. et al. 2009. Solubility of hydrocarbons in water Experimental measurements and modeling using a group contribution with association equation of state (GCA-EoS). Fluid Phase Equilib. 275 52-59. 

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. 

Association equation of state (AEOS). To first introduce the concept of chemical compressibility factor and the association constant K, assume there are tiq moles of a substance in which ail the molecules are in the form of monomers, i.e., singly dispersed molecules. Then, if the fluid behaves as an ideal gas, PV = n HT, where Vq is the volume at pressure P. Let us now assume that some of the molecules will associate so that the true number of moles is then, the ideal gas PVTrela-... 

Solution of the association equation of state (AEOS). The incorporation of the association in the PR-EOS results in the following equation ... 

Plus Association equation of state. With permission from the Institut Frangais du Petr ole. 

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 ... 

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). 

The phase equilibria of the hydroformylation of hex-l-ene in supercritical CO2 was studied experimentally by Jiang et al for different degrees of conversion, involving mixtures of CO, H2, CO2, hex-l-ene and heptanal. Marteel et al conducted the reaction at r= 373 K and p = 18.6 MPa and had to use a CO2 + reactant mass ratio equal to 3 to operate within the homogenous phase. Pereda et modelled the measurements reported by Jiang et al with Group Contribution Association equation of state" " and showed the use of... 

Group Contribution with Association Equation of State (GCA-EoS)... 

There are three terms in the expression of the residual Helmholtz function in the Group Contribution Association equation of state, each one representing the contributions of different intermolecular forces (i), repulsive or free volume A (ii), attractive or dispersive and (iii), specific association forces The residual Helmholtz function in the Group Contribution Association equation of state is given by ... 

Neither the Group Contribution Association equation of state nor Soave-Redlich-Kwong equations of state with MHV2 mixing rules are recommended methods to prediet mixture densities. The Peng-Robinson equation of state with classical mixing rules is the more preeise model among the van der Waals family of equation of state to predict molar volumes of mixtures particularly when the volume eorrection has been used as proposed by Peneloux et... 

In this Chapter the group contribution equations of states are proposed because of their predictive capacity for components for which thermodynamic data is either limited or non-existent. MHV2 and Group Contribution Association equation of state are both suitable models to describe highly non-ideal mixtures. The use of MHV2 is more attractive due to its mathematical simplicity and wider parameter table however, Group Contribution Association equation of state is more appropriate for mixtures that have association elfects and or big size-asymmetry. In this chapter several applications of both models to reactive mixtures have been given. 

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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