Discontinuous-Galerkin finite-element method for approximating a model of non-equilibrium liquid chromatography considering Bi-Langmuir isotherm

Abstract

In this paper, a discontinuous-Galerkin finite-element method (DG-FEM) is applied for the numerical solution of multi-component, non-equilibrium, lump kinetic model of liquid chromatography under nonlinear conditions. The model is analyzed for standard Bi-Langmuir type adsorption isotherms using Danckwert boundary conditions. Packed bed processes of liquid chromatography are modeled as convection-diffusion partial differential equations (PDE). In these models, the diffusion term is strongly dominated by the convection term. Therefore simulation of packed bed chromatographic processes requires specialized numerical techniques. In this study, the (DG-FEM) is utilized for the space discretization and the resulting semi-discrete system of ordinary differential equations is solved numerically by using a total variation bounded (TVB) Runge–Kutta method. This technique resolves sharp discontinuities and achieves a high order accuracy. To inspect the impact of different parameters, the results of the proposed method are authenticated against the high-resolution finite-volume scheme (HR-FVS). These numerical results include a single-solute flow, two-component mixture flow, and three-component mixture flow. The developed numerical results could be helpful in optimal predictive control, systematic monitoring and efficient operation of chromatographic processes.

Graphical Abstract

Keywords:

• Discontinuous-Galerkin method
• Bi-Langmuir isotherm
• non-equilibrium transport
• lump kinetic model
• numerical simulations