Modeling of Porous Catalytic Pellets with Various Morphologies Suspended in Batch Reactor and CSTR from Analytical Solutions of Reaction-Diffusion Equations

Abstract

Analytical solutions of transient concentration of a reactant in a batch or a continuous stirred-tank reactor (CSTR) containing catalytic pellets were derived by solving systems of reaction-diffusion equations. The material balance equations for bulk phase and catalytic particles were solved by applying the Laplace transform, assuming spherical, cylindrical, and slab-type shapes of catalytic particles. The residue and convolution theorems were applied for inversion of the Laplace transform results to obtain analytical solutions for bulk concentration and the concentration profile inside the catalytic particles. In CSTRs, input of reactant as step or impulse inputs methods were considered, while, initially, empty pellets were assumed in batch reactors. In addition to the intraparticle diffusion coefficient, film resistance near the particle surface could be represented as a Biot number during modeling. In a batch reactor, both the Thiele modulus and catalyst loading influenced the reactant concentration, whereas, in a CSTR, retention time influenced the reactant concentration. For numerical computations, eigenvalues as imaginary numbers were obtained graphically to predict transient behaviors of the catalytic batch and CSTRs. To estimate the effect of the inert core thickness, core-shell particles with an inert core were assumed to be present in the reactor.

Keywords

• Catalytic Pellets
• Catalytic Reactors
• Reaction-diffusion Equation
• Coupled Differential Equations
• Laplace Transform