Multi-objective reactor design under uncertainty: A decomposition approach based on cubature rules

Abstract

Model-based strategies for chemical reactor design proved to be a reliable tool for the systematic design of resource and energy efficient chemical reactors. The adequacy and accuracy of the underlying model equations (e.g. reaction kinetics and kinetics for heat and mass transport) are crucial for the success of such design approaches. However, the models used in chemical engineering are typically based on experimental data and predictive expressions for the fundamental phenomena and thus the respective model parameters are inevitably subject to uncertainty. Therefore, consideration of parametric uncertainty in the design strategy is necessary to obtain reliable chemical reactor designs. Moreover, the design of chemical reactors involves almost always multiple conflicting objectives which poses an additional challenge.In the present work, we propose an efficient reactor design strategy to tackle the combined challenges of parametric uncertainty and multiple conflicting objectives. The approach combines a scalarization method with a cubature rule to efficiently determine robust compromise solutions. The cubature rule is used to approximate the first two statistical moments of the objectives and of all critical inequality constraints. The approximation of the statistical moments is performed separate from the optimization problem. This leads to an iterative approach with improved computational performance. The proposed approach is illustrated and compared to an existing approach from literature by studying three different reactor design case studies, namely the optimization of a batch, semi-batch and multi-tubular fixed-bed reactor.The results of the newly proposed reactor design approach and the existing method from literature are in very good agreement for all considered case studies. The advantage of the new approach is a significantly lower computational effort compared to the existing method. This is especially visible for the more complex case studies with a higher number of uncertain parameters. The advantage of the approach proposed in the present work is thus particularly relevant and important for the application to complex reactor design tasks such as, e.g., the design of polymerization reactors or multi-phase reactors.