Solving hyperbolic conservation laws with active counteraction against numerical errors: Isothermal fixed-bed adsorption

Abstract

First-order partial differential equations are frequently applied for the simulation of adsorption and reaction processes. The numerous numerical methods available are typically applied without any further modifications despite of various well-known errors caused by, for example, numerical dissipation and crude approximations of certain phenomena. In this work, we analyzed a classical mixing cell model that is capable to simulate isothermal liquid chromatographic separation processes with incompressible mobile phases. This model corresponds to a 1D model of a chromatographic column discretized with a first-order finite volume method. It is our aim to counteract actively two errors, namely numerical dispersion (i.e. the second-order spatial derivative in truncation error) and partition inconsistency related to the nonlinear partition quantified by a competitive adsorption isotherm model. The new numerical method introduced in this article maintains characteristics of the first-order base scheme (non-oscillatory and conditionally stable) and offers enhanced accuracy (smaller numerical errors and improved description of shock waves). Furthermore, the method does not require solving the system of differential-algebraic equations that cause large matrix computations, but rather solves nonlinear equations ‘cell-by-cell’. The numerical routines can be easily parallelized to accelerate computation time with multi-core CPUs. To test the method developed, four-zone simulated moving bed adsorption as a challenging example was considered, which causes dynamically changing complex concentration profiles by periodic operation using several columns.