Parameter estimation in dynamic multiphase liquid–liquid equilibrium systems

Modeling dynamic systems with a variable number of liquid phases is a challenging task, especially in scenarios where the model is designed for optimization tasks such as parameter estimation. Although there exist methods to model the appearance and disappearance of liquid phases in dynamic systems, they usually require integer variables. In this work, the smoothed continuous approach (SCA) is developed for use with a large number of solvers, since it relies only on continuous variables. To demonstrate the applicability of the new method, the SCA is then applied to model the batch esterification of acetic acid with 1-propanol to water and propyl acetate, and to estimate the reaction parameters. Since the mixture may separate into two liquid phases during the course of the reaction, the parameters are estimated with information on the liquid compositions of both separated liquid phases, which improves the accuracy of the parameter estimates and opens new possibilities for optimal experimental design. • New method exists to model dynamic systems with a variable number of liquid phases. • Standard DAE solvers can solve the resulting differential–algebraic equation system. • The resulting dynamic model can be used for gradient-based parameter estimation.