Simple numerical scheme for solving the impregnation equations in a porous pellet

TL;DR

This work tackles the impregnation problem in a porous pellet by formulating a moving-boundary convection–diffusion–reaction model for solute and adsorbed species on a sphere. It introduces a numerical scheme that discretizes the equations on a front-aligned, consistent space–time grid, solving a nonlinear system via iterative updates of $\theta$ and $u$ at each time step. The approach is demonstrated through a numerical example using a simplified hydrodynamics scenario, with validation based on mass balance $M_1(\tau)=M_2(\tau)$ and MATLAB implementation, showing accuracy and computational efficiency on standard hardware. The method provides a practical and robust tool for simulating impregnation processes in catalyst preparation, where front motion and domain evolution are key features.

Abstract

This paper proposes a numerical scheme for solving a system of convection-reaction-diffusion equations describing the process of preparing a catalyst on a porous support by the impregnation method. In the case of a considered porous spherical pellet, the equations are defined on an interval, one end of which, associated with the front of the impregnating liquid, moves according to a given law. The law of front motion is used to create a consistent space-time grid for discretizing the system. Examples of numerical solutions of the impregnation problem are given, demonstrating the effectiveness of the proposed scheme.

Figures (3)

• Figure 1: Solution of system (1), (2) for $K^+=10$.
• Figure 2: Solution of system (1), (2) for $K^+=100$.
• Figure 3: $M_1$ -- thick black line, $M_2$ -- thin yellow line.