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An existing approach for optimization-based process synthesis with abstracted phenomena-based building blocks (PBB) is extended by implementing it into a novel MINLP framework with structural screening. Consistency across the multilayer MINLP framework is guaranteed by creating a MathML/XML data model and subsequently exporting the code to the different program parts. The novel framework focuses both on fidelity by implementing thermodynamically sound models and on generality by employing a state-space superstructure that spans a large search space. In order to retain tractability, we insert a structural screening layer which prescreens based on binary decision variables of the superstructure by graph- and rule-based analyses, penalizing non-physical instances without solution of the underlying MINLP. The MINLP framework is successfully applied on two challenging synthesis tasks to determine the separation of the feed streams of benzene and toluene, as well as of n-pentane, n-hexane, and n-heptane utilizing superstructures with two, respectively four PBB.
Recipe‐Free Synthesis of Optimal Operation Trajectories for Batch Processes Based on Process Models
(2025)
AbstractBatch processes are usually operated following recipes, which are based on experience and expert knowledge. This ensures feasible and safe operation, because process constraints are indirectly included in the recipe. However, the recipe structure itself constrains the solution space and might exclude other more efficient trajectories. Therefore, the hidden constraints are explicitly formulated, and the arising optimization problem is solved without using prior knowledge in the form of recipes. Case studies are performed on rigorous models of a batch reactor and a batch distillation column. It is demonstrated that the optimization problem formulated as a smoothed dynamic nonlinear programming problem outperforms a mixed‐integer formulation. Finally, a multi‐objective case is investigated that strongly outperforms a recipe‐based benchmark.
Isopropyl myristate (IMA) is a fatty ester widely used in cosmetic applications, and it is mainly produced by esterification of myristic acid (MA) and isopropanol (IPA), with water (W) as byproduct. Due to chemical equilibrium limitations, various process intensification approaches have been proposed to improve its production; however, they still involve significant uncertainties as they are based on theoretically predicted phase equilibria due to a lack of experimental-based models. Then, the presented study aimed to experimentally characterize the phase equilibrium behavior of mixtures containing IPA, W, IMA, and MA. Vapor-Liquid Equilibrium (VLE) experiments were conducted under isothermal conditions for the binary systems IMA+IPA and MA+IPA within the range of 55–80 °C. Also, Liquid-Liquid Equilibrium (LLE) data for the ternary systems IPA+W+IMA, IPA+W+MA, and W+IMA+MA were measured at temperatures ranging from 60 to 80 °C. Additionally, Solid-Liquid Equilibrium (SLE) data for mixtures of IMA+MA were obtained at temperature in-between 8 and 50 °C, and pure thermal properties of IMA and MA were characterized via Differential Scanning Calorimetry (DSC) and Thermogravimetric analysis (TGA). Using the collected VLE, LLE and SLE experimental data, binary interaction parameters for NRTL model were fitted through optimization. Conflicting requirements in VLE and LLE data were addressed through Pareto front analysis, yielding two new parameters sets: one for predominant VLE description and the other for more accurate LLE representation. These sets of parameters would be suitable for the conceptual design and simulation of sequential and/or simultaneous reaction-separation processes to produce IMA via esterification.
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.
