Diffusion and Surface Reaction in Porous Cubical Catalyst: A Mathematical Approach

Background: Catalysts are the most vital part of any chemical industry. Catalyst is a substance that affects the rate of reaction, but the catalyst itself does not take part in the reaction. Catalysts offer different pathways of reaction by diffusing the reactant inside it to provide a large surface area within a small volume, thus, lowering the activation energy of molecules for reaction. Most of the catalytic reactions take place in a liquid- solid or gas-solid interface where catalysts are mostly porous in nature. Spherical and cubic-shaped catalyst particles are commonly used in different industries. Methods: In the first phase of the present study, the physics behind the diffusion inside the catalyst pellet has been discussed. In the second part, governing differential equations have been established at a steady-state condition. For solving the differential equation, the equation is made dimensionless. Physical boundary conditions were used to solve the diffusion equation. The assumption of writing the differential equation of the reaction is elementary. Then, the Thiele modulus is derived in terms of the reaction and geometrical parameter (Length). Results and Conclusion: In the third part, the differential equation is solved for firstorder reaction with some constant values of the Thiele modulus, and three-dimensional plots are obtained using numerical analysis. After that, the obtained Thiele modulus and effectiveness factor plot are compared to draw the conclusion of rate limiting reaction and internal diffusion.