Abstract
A multicomponent nonisothermal lumped kinetic model (LKM) of fixed-bed liquid chromatographic reactor is introduced and numerically approximated. The model incorporates nonlinear Bi-Langmuir and Toth adsorption isotherms, reaction kinetics, axial and temporal variations of concentrations, and enthalpies of reaction and adsorption. The resulting model equations constitute a nonlinear coupled system of convection-diffusion-reaction partial differential equations (CDR-PDEs) for mass and energy balances in both the mobile and stationary phases, augmented by differential mass balances in the stationary phase and algebraic expressions for reaction rates and adsorption isotherms. Due to the nonlinearity of adsorption isotherms and reaction kinetics, which is impeding the derivation of closed-form solutions, a local-projection discontinuous Galerkin finite element (DG-FE) method is applied for space discretization. The emerging semidiscrete system of ordinary differential equations in time is solved numerically by employing a total variation bounded (TVB) Runge-Kutta method. To analyze the process performance, parametric studies are conducted using numerical simulations. A series of rigorous consistency tests are elucidating the interplay between thermal and concentration gradients, showcasing the impact of temperature on reactor performance, and highlighting the aspects of reactant conversion into products. Subsequently, a thorough comparison is performed among the considered adsorption isotherms to scrutinize the numerical findings and to augment the originality of research. The results obtained verify the validity of model equations and precision of the numerical technique used. Moreover, the outcomes of this study can be utilized to understand mass and energy distributions in nonequilibrium and nonisothermal liquid chromatographic reactors and to provide profound insights into the complexities of this separation-conversion process.