A Systematic Approach for Regression of Binary VLE Data

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993) 

A set of N VLE experimental data points have been made available. These data are the measurements of the state variables (T, P, x, y) at each of the N performed experiments. Prior to the estimation, one should plot the data and look for potential outliers as discussed in Chapter 8. In addition, a suitable EoS with the corresponding mixing rules should be selected. 

The first task of the estimation procedure is to quickly and efficiently screen all possible sets of interaction parameters that could be used. For example if the Trebble-Bishnoi EoS were to be employed which can utilize up to four binary interaction parameters, the number of possible combinations that should be examined is 15. The implicit LS estimation procedure provides the most efficient means to determine the best set of interaction parameters. The best set is the one that results in the smallest value of the LS objective function after convergence of the minimization algorithm has been achieved. One should not readily accept a set that 

Once the best set of interaction parameters has been found, these parameters should be used with the EoS to perform the VLE calculations. The computed values should be plotted together with the data. A comparison of the data with the EoS based calculated phase behavior reveals whether correct or incorrect phase behavior (erroneous liquid phase splitting) is obtained. 

If the correct phase behavior i.e. absence of erroneous liquid phase splits is predicted by the EoS then the overall fit should be examined and it should be judged whether it is excellent . If the fit is simply acceptable rather than excellent , then the previously computed LS parameter estimates should suffice. This was found to be the case for the n-pentane-acetone and the methane-acetone systems presented later in this chapter. 

---