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New vapor-liquid equilibrium (VLE) data are continuously being measured and new parameter values, e.g., for the nonrandom two-liquid (NRTL) model are estimated and published. The parameter α, the nonrandomness parameter of NRTL, is often not estimated but is heuristically fixed to a constant value based on the involved components. This can be seen as a manual application of a (subset selection) regularization method. In this work, the practical parameter identifiability of the NRTL model for describing the VLE is analyzed. It is shown that fixing α is not always a good decision and sometimes leads to worse prediction properties of the final parameter estimates. Popular regularization techniques are compared and Generalized Orthogonalization is proposed as an alternative to this heuristic. In addition, the sequential Optimal Experimental Design and Parameter Estimation (sOED-PE) method is applied to study the influence of the regularization methods on the performance of the sOED-PE loop.
Models are commonly utilized in chemical engineering to simulate real-world processes and phenomena. Given their role in guiding decision-making, accurately quantifying the uncertainty of these models is essential. Typically, these models are calibrated using experimental data that contain measurement errors, leading to uncertainty in the fitted model parameters. Current methods for estimating the prediction uncertainty of nonlinear regression models are often either computationally intensive or biased. In this study, we use sparse cubature formulas to estimate the prediction uncertainty of nonlinear regression models. Our findings indicate that this method provides a favorable balance between accuracy and computational efficiency, making it suitable for application in chemical engineering. We validate the performance of our proposed method through various regression case studies, including both theoretical toy models and practical models from chemical engineering.
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.
