Theoretical Investigation of Thermal Effects in an Adiabatic Chromatographic Column Using a Lumped Kinetic Model Incorporating Heat Transfer Resistances

Abstract

A nonequilibrium nonisothermal lumped kinetic model (LKM) is analytically and numerically investigated to evaluate the effects of inherent temperature fluctuations in an adiabatic chromatographic column. The model comprises convection–diffusion partial differential equations quantifying mass and energy balances in the mobile phase coupled with differential and algebraic equations for mass and energy in the stationary phase. Besides two mass transfer coefficients, two heat transfer coefficients are involved in the model equations. The properties of the considered model are investigated for linear concentration and temperature dependencies of the equilibrium loadings. The Laplace transformation and Eigen decomposition techniques are utilized to solve the set of equations. These solutions are helpful for understanding, analyzing, and interpreting the propagation speeds and shapes of both concentration and thermal fronts migrating in chromatographic columns. The moment generating property of the Laplace domain solutions is employed to obtain explicit analytical temporal moments of the concentration and energy profiles which provide instructive tools to analyze the properties of the model considered and to estimate unknown model parameters from measured transients. For illustration, several case studies are carried out by assuming realistic model parameters. The applicability range of the analytical solutions derived is assessed by comparing selected specific results with numerical results of a nonequilibrium and nonisothermal model by considering nonlinear adsorption isotherms.