The current study investigates a nonequilibrium and nonlinear
two-dimensional
lumped kinetic transport model of nonisothermal reactive liquid chromatography,
considering the Bi-Langmuir adsorption isotherm, heterogeneous reaction
rates, radial and axial concentration variations, and the adsorption
and reaction enthalpies. The mathematical models of packed bed chromatographic
processes are expressed by a highly nonlinear system of coupled partial
differential algebraic equations connecting the phenomena of convection,
diffusion, and reaction, for mass and energy balance, the differential
algebraic equations for mass balance in the solid phase, and the algebraical
expressions for the adsorption isotherms and for the reaction rates.
The nonlinearity of the reaction term and the adsorption isotherm
preclude the derivation of an analytical solution for the model equations.
For this reason, a semidiscrete, high-resolution, finite-volume technique
is extended and employed in this study to obtain the numerical solution.
Several consistency checks are performed to evaluate the model predictions
and analyze the precision of the proposed numerical scheme. A number
of heterogeneously catalyzed stoichiometric reactions are numerically
simulated to examine reactor performance under the influence of temperature
and Bi-Langmuir adsorption dynamics, the level of coupling between
mass and energy fronts, and to study the effects of various critical
parameters. The numerical results obtained are beneficial for optimal
predictive control and process optimization during production and
the development of methods for systematic design and fault detection
of nonisothermal liquid chromatographic reactors, and hence constitute
the first step to provide deeper insight into the overall evaluation
of integrated reaction and separation processes.