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 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 first-order 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 reaction rate limited and internal diffusion limited.

Axial Dispersion Plug Flow Model for Methanol Dehydration Reactor

One-dimensional heterogeneous dispersed plug flow (DPF) model is employed to model an adiabatic fixed-bed reactor for the catalytic dehydration of methanol to dimethyl ether (DME). The mass and heat transfer equations are numerically solved for the reactor. The concentration of the reactant and products and also the temperature varies along the reactor, therefore the effectiveness factor would also change in the reactor. We used the effectiveness factor that was simulated according to the diffusion and reaction in the catalyst pellet as a pore network model. The predicted distribution for the effectiveness factor was utilized for the reactor simulation. The simulation results were compared to the experimental data and a satisfactory agreement was confirmed.

Application of Pseudohomogeneous and Heterogeneous Models in Assessing the Behavior of a Fluidized-Bed Catalytic Reactor

Comparative analysis of the steady-state and transient properties of a bubbling fluidized-bed catalytic reactor obtained according to different mathematical models of the emulsion zone was performed to verify the commonly used assumption regarding the pseudohomogeneous nature of this zone. Four different mathematical models of the fluidized-bed reactor dynamics were formulated, based on different thermal and diffusional conditions at the gas-solid interface and within the catalyst pellet, namely the model based on the assumption of pseudohomogeneous character for the emulsion zone, and a group of two-scale models accounting for the heterogeneous character of this zone. It was demonstrated that, while the pseudohomogeneous model of the emulsion zone predicts almost identical behavior of the reactor at steady-state as the proposed heterogeneous models, it may fail in the prediction of the reactor start-up behavior, especially when dealing with highly exothermic processes run at relatively high fluidization velocity.