Using an Artificial Neural Network for Reduced Order Modeling

Artificial neural networks can be used to build a reduced order model of a piece of equipment, such as a methanol synthesis reactor. The model can then be harnessed for real-time optimization of the application.

In recent years, real-time optimization (RTO) applications have been implemented in various petrochemical and chemical applications. For instance, the modeling of an industrial-scale depropanizer column for RTO was carried out using equation-oriented and sequential modular approaches by Mendoza et al. (1). Optimization (either real-time or offline) tends to be computationally expensive, especially if the models are large and complex. This is mainly due to the fact that the models are typically represented by governing ordinary or partial differential equations (ODEs and PDEs), which describe the physics of the equipment or processes. These models must be solved iteratively to find the optimized solutions. This presents a challenge in using rigorous models for optimization, especially for RTO applications.

One way to reduce the computational time is to represent first-principle models with simplified models, usually referred to as reduced order models (ROMs). ROMs significantly reduce computational time, while preserving the accuracies obtained from the physics-based models.

Artificial neural networks (ANNs) are one of the most popular methods for constructing ROMs. ANNs are able to capture the nonlinearities typically encountered in chemical processes. For example, Zhang et al. (2) combined ANN models with first-principle models in the RTO of two chemical processes that involved a continuous stirred-tank reactor (CSTR) and a distillation column. Many commercial process simulators such as Aspen Plus and Aspen HYSYS now also incorporate ANNs as part of the simulation workflow. The reduced order modeling approach has also been studied in other fields such as nuclear engineering (see an example in Ref. 3).

This article describes the development of a kinetic model to optimize the production of methanol. A case study demonstrates how multivariate regression using an ANN can be used to accurately represent the kinetic model. All of the work in this study was conducted in MATLAB, a general-purpose computing platform by Mathworks.