Mathematical modelling of flow and adsorption in a gas chromatograph

TL;DR

This paper presents a simplified and efficient mathematical model for gas chromatography that accurately predicts compound concentration profiles by decoupling equations and fitting only two parameters per analyte, verified against experimental data.

Contribution

It introduces a novel approach that simplifies the modeling process by decoupling multi-component equations and reducing parameter fitting, improving computational efficiency.

Findings

Laplace transform provides accurate solutions compared to full numerical methods.

Decoupling equations reduces computational complexity significantly.

Model validated with experimental BTEX chromatography data.

Abstract

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.