A Green's Function Method based approach for effectiveness factor evaluation in two-dimensional spherical catalyst geometries with non-linear kinetics and partial wetting

The solution of the two-dimensional spherical diffusion equation inside the catalyst particle is proposed using Green's Function Method (GFM). A Green's Function was derived using Eigenfunction expansion in the polar direction and considering jump discontinuity in the radial direction. The advantage of using multi-precision arithmetic in the evaluation of Green's Function has been demonstrated. A precomputed value of Green's Function at a selected precision level was used to calculate the concentration profile inside the fully and partially wetted spherical catalyst particle geometry. The non-linear kinetic rate expression-based formulation for concentration profile calculation gives rise to non-linear equations. These non-linear equations were solved in PETSc (Balay et al., 2017) using various combinations of linear pre-conditioners and Krylov methods. A comparison with the Finite Difference Method (FDM) formulation is presented, and the advantage of the proposed GFM-based formulation for convergence and reduction in computation time is demonstrated.