An improved Green's function method for isothermal effectiveness factor determination in one- and two-dimensional catalyst geometries

Abstract

Traditional approach to effectiveness factor calculations uses finite difference methods to discretize two-point boundary value differential equations. The finite difference method (FDM) approximates derivatives using only nearby concentration values; however, an approach that takes into account the influence of concentrations away from a point is highly intuitive and requires careful consideration. In this paper we extend the integral formulation for the case when external limitations are present. We also propose a new approach based on the use of two-dimensional Green's function for effectiveness factor calculations in two-dimensional geometries, and provide a generic procedure for concentration profile calculation in one- and two-dimensional geometries. The proposed approach retains the representation rigor of analytical approach and reduces the computational complexities associated with FDM. It has been shown that the presence of external transport limitation shall modify the Green's function obtained considering only internal transport limitations. The problem of very high sensitivity of the boundary contribution term in the Green's Function Solution for two-dimensional cylindrical particle is addressed by variable transformation. It has been shown in this paper that Green's Function method provides superior performance for larger step size when compared with the FDM approach, thus providing computationally efficient approach.