A Finite Difference Method Using High-Order Schemes to Simulate an Equilibrium-Dispersive Model of Non-Linear Chromatography

Abstract

High-performance liquid chromatography (HPLC) is a dynamic separation process with a lot of parameters having different roles. The equilibrium-dispersive model is relevant for simulating HPLC because it is relatively simple and suitable for high-efficiency processes. The partial differential equation was simulated in many different methods such as semi-analytical methods, finite element methods, and finite difference methods. Many studies using finite difference methods have used the first-order and second-order schemes, but higher-order schemes have not been reported yet. This work is about solving the equation of the equilibrium-dispersive model, using a finite difference method with high-order schemes. The fourth-order central difference scheme was used for estimating diffusion and the fifth-order upwind schemes were used for simulating advection. The model was evaluated by assessing the area recovery of the peak, testing the non-retained substance behavior, and comparing the calculation results with the experimental data. The solutions of the equation will indicate the effects of the operation parameters on the system suitability ones and can be used to predict the behavior of an HPLC system and calculate the system suitability parameters of a novel method set.

Keywords

• non-linear chromatography
• equilibrium-dispersive model
• numerical solution
• finite difference methods
• high-order schemes
• HPLC