Study of reaction–diffusion problem: modeling, exact analytical solution, and experimental verification

Nonlinear diffusion–reaction problem was investigated experimentally for the reference reaction (hydrogenation of propylene under isothermal conditions; a slab of catalyst pellet i.e., disks of large diameter/width ratio were applied). The diffusion–reaction model in the catalyst pellet with external mass-transfer resistances was solved analytically. Dependently on parameters values, two separate solutions were found: dead zone inside the pellet does not exist or it appears. In the first case, a common model is acceptable (regular model i.e., boundary value problem), in the second one, a model includes additional condition (dead zone model i.e., free boundary problem). Analysis of the solution presented indicated that either regular or “dead zone” model correctly describes the process for specific parameter values (with the only exception—multiple steady-state region—where the correct interpretation requires the combined application of the both). This result shows that the full description of the real process includes solutions of two different BVPs. Experimental research confirmed results anticipated by theory. It allowed to draw conclusions that go beyond this particular example i.e., the regular model, commonly applied in heterogeneous catalysis, does not adequately recognize dead zone problem. If “dead zone” appears, free boundary problem has to be consider, otherwise, process simulations will be incorrect. The conclusions drawn are valid also for biofilms.

Dead zone for hydrogenation of propylene reaction carried out on commercial catalyst pellets

Heterogeneous catalytic processes have for years been of crucial importance in the chemical industry, while biocatalitic processes have become more and more important. For both types of the processes the existence of zones without reactants were reported. Despite the fact that the dead zone can appear in real processes relatively often, the most important problem in practice is the real size of a dead zone inside a catalyst pellet or the real depth of penetration reagents in a biofilm and this is still unsolved. The knowledge of the parameters and some information about the process can allow improvement in yield, and selectivity, reduce consumption of catalyst by reducing the bed size etc. Presented in this work is a simple method of predicting the size of the inactive core of a uniformly activated catalyst pellet. The method is based on a simple mathematical model of catalyst pellet with inactive pellet centre and experimental investigations.