Modified orthogonal collocation for accurate flux-based material balance calculations in slab, cylindrical, and spherical geometries

Abstract

This study addresses a challenge in the application of the weighted Orthogonal Collocation method for solving flux-based material balances in diffusion and reaction systems where Fick’s law is not applicable. The conventional approach encounters difficulties due to the non-zero gradient boundary condition of flux at $x=$ 0, which leads to increased errors and inaccuracies in the solution. To resolve this problem, a modification to the Orthogonal Collocation method is proposed, adjusted specifically to handle the complexities of flux-based material balances. The modified method adapts the traditional collocation approach, ensuring it can accommodate the boundary condition peculiarities inherent in these systems. Testing and comparison demonstrated that the modified method achieves accuracies comparable to the original Orthogonal Collocation method when applied to concentration-based material balances, whereas incorrect use of the original scheme leads to errors that are orders of magnitude greater.