Simulation of Chemical Reactors using the Least-Squares Spectral Element method

Abstract

The least–squares spectral element method is a relatively novel method that can be used to solve any well–posed problem. It has been extensively used in computational fluid dynamics, and in recent years has been applied in the field of chemical engineering. This work focuses on the use of the least–squares spectral element method for the simulation of chemical reactors from a general point of view.

 The document presents an analysis on the common challenges that chemical reactor models pose and give guidelines to overcome them. It also presents details on a series of numerical tools and models developed based on the least–squares formulation. Various numerical experiments and simulations are presented, comparing the results with published data when available. The simulations include a 1D axial dispersion model for a multi-tube fixed bed reactor, Navier–Stokes equations for recirculating flows, and a novel two phase flow model for an isothermic bubble column.

It is shown here that the least–squares spectral element method is capable of solving most models used in simulations of chemical reactors. Unlike other methods where the effort is put on the design of the numerical scheme, most of the efforts when using the least–squares formulations were spent on defining a well-posed set of equations.