Parameter Estimation Using Binary Critical Point Data

4 PARAMETER ESTIMATION USING BINARY CRITICAL POINT DATA 

Prior work on the use of critical point data to estimate binary interaction parameters employed the minimization of a summation of squared differences between experimental and calculated critical temperature and/or pressure (Equation 14.39). During that minimization the EoS uses the current parameter estimates in order to compute the critical pressure and/or the critical temperature. However, the initial estimates are often away from the optimum and as a consequence, such iterative computations are difficult to converge and the overall computational requirements are significant. 

It is assumed that there are available NCP experimental binary critical point data. These data include values of the pressure, Pc, the temperature, Tc, and the mole fraction, xc, of one of the components at each of the critical points for the binary mixture. The vector k of interaction parameters is determined by fitting the EoS to the critical data. In explicit formulations the interaction parameters are obtained by the minimization of the following least squares objective function  

14 VLE data and calculated phase diagram for the methane-n-hexane system [reprinted from Industrial Engineering Chemistry Research with permission from the American Chemical Society], 

The values of qi and q2 are usually taken equal to one. Hissong and Kay (1970) assigned a value of four for the ratio of q2 overqi. 

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Parameter Estimation Using Binary Critical Point Data... 

Englezos, P., G. Bygrave, and N. Kalogerakis, "Interaction Parameter Estimation in Cubic Equations of State Using Binary Phase Equilibrium Critical Point Data", Ind. Eng Chem. Res.31(5), 1613-1618 (1998). 

Kikic et al. (41) employed only the values of P and T at the UCEP to evaluate these two constants ky and /y). The location of the UCEP was estimated from the experimental data by locating the intersection of the S-L-V line and (L = V) critical locus curve. For a type IP-Ttrace (with no temperature minimum with increasing pressure, e.g., a naphthalene-ethylene system), the solubility isotherm at Tucep provides an inflection point at P = PucEP (13). By setting the first and second derivatives to zero at this point, one can obtain the two equations needed for the two binary interaction parameters, kij and ly, respectively. When this approach was used for the inter-... 

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