Analysis of temperature variations in fixed-bed columns using non-isothermal and non-equilibrium transport model

Abstract

A non-isothermal and non-equilibrium two-component lumped kinetic model of fixed-bed column liquid chromatography is formulated with the linearized isotherm and solved analytically to study the influence of temperature variations on the process. The model equations constitute a system of convection-diffusion PDE for mass and energy balances in the bulk phase coupled with differential equations for mass and energy balances in the stationary phase. The analytical solutions are derived for Dirichlet boundary conditions by implementing the Laplace transformation, Tschirnhaus-Vieta approach, the linear decomposition technique and an elementary solution technique of ODE. An efficient and accurate numerical Laplace inversion technique is applied to bring back the solution in the actual time domain. In order to validate the derived analytical solutions for concentration and temperature fronts, the high resolution upwind finite volume scheme is applied to approximate the model equations numerically. Various case studies are carried out assuming realistic model parameters. The results obtained will be beneficial for interpreting mass and energy profiles in non-equilibrium and non-isothermal liquid chromatographic columns and provide deeper insight into the sensitivity of the separation process without performing costly and time-consuming laboratory experiments.