Reaction of an irregular particle with a gas: Monte Carlo method for the solution of the pellet-grain model

Abstract

In some instances, actual Monte Carlo simulation of attendant physical phenomena has been carried out in lieu of numerically solving the deterministic model equations. The solution of the partial differential equation which accounts for diffusion and chemical reaction by the Monte Carlo method is not a trivial task. A suitable probabilistic problem equivalent to the finite difference analog of the partial differential equation, usually the random walk of a fictitious particle over the computational nodes, must be formulated. The application of such a technique for gas-solid reactions is especially interesting since the solid particles are irregular in shape. In most applications, the assumption that the particles are of a regular shape, i.e. spherical, cylindrical, or flat slab, is made to simplify the solution of model equations. Nunez and Espiell show experimentally how reaction rates are related to the assumption of shape. In the present work, the solution of the pellet-grain model for an arbitrary irregular particle is shown. First, the Monte Carlo solution is compared with known solutions for regular geometry. Then, solutions for irregular two-dimensional pellets and three-dimensional prismatic pellets are shown. This computationally elegant technique is also applicable in problems involving heat, momentum, or mass transfer in an irregular domain.