RESUMO
Core-shell particles enable the separation of intricate mixtures in a highly efficient and rapid manner. The porous shell particles increased the separation efficiency with expedited flow rates due to an abatement in the pore volume accessible for longitudinal diffusion and a decrease in diffusion path length. This study focuses on the numerical approximation of a nonlinear isothermal general rate model applied to stationary bed columns that are replete with inert core adsorbents featuring double adsorption sites. The transport of solute in heterogeneous porous media can be modeled by a nonlinear convection acquiescent partial differential equation system together with a specific nonlinear algebraic relation: the bi-Langmuir adsorption isotherm. Therefore, it is important to develop accurate and reliable numerical techniques that can perform accurate numerical simulations of these models. We extended and implemented a second-order, semidiscrete, high-resolution finite volume method to simulate the governing equations of the model. Single solute flow and multi component mixture flows are assessed through a series of numerical experiments to theoretically illustrate the repercussions of intraparticle diffusion, film mass resistance, axial dispersion, and the size of the inert core radius upon simulated elution curves. Standard performance criteria are assessed to determine the optimal core radius fraction range for optimizing the separation performance.
RESUMO
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.
