Reliable nonlinear parameter estimation in VLE modeling

The reliable solution of nonlinear parameter estimation problems is an important computational problem in the modeling of vapor–liquid equilibrium (VLE). Conventional solution methods may not be reliable since they do not guarantee convergence to the global optimum sought in the parameter estimation problem. We demonstrate here a technique that is based on interval analysis, which can solve the nonlinear parameter estimation problem with complete reliability, and provides a mathematical and computational guarantee that the global optimum is found. As an example, we consider the estimation of parameters in the Wilson equation, using VLE data sets from a variety of binary systems. Results indicate that several sets of parameter values published in the DECHEMA VLE Data Collection correspond to local optima only, with new globally optimal parameter values found by using the interval approach. When applied to VLE modeling, the globally optimal parameters can provide significant improvements in predictive capability. For example, in one case, when the previously published locally optimal parameters are used, the Wilson equation does not predict experimentally observed homogeneous azeotropes, but, when the globally optimal parameters are used, the azeotropes are predicted.