Comparison of approximate solution methods for the solid phase diffusion equation in a porous electrode model

Abstract

Approximation methods are often used in porous electrode models to eliminate the need to solve the local solid phase diffusion equation. These methods include Duhamel's superposition method, a diffusion length method and a polynomial approximation method which have long been used in the literature. The pseudo steady state (PSS) method is a method that has been used recently to develop a solution to the diffusion equation in a spherical particle with time dependent boundary conditions, but the PSS method has not been used in a porous electrode model. These methods are compared to each other in a dimensionless analysis study, and they are used in a porous electrode model to predict the discharge curves for a LiCoO 2 electrode. Simulation results presented here indicate that the PSS method or the high order polynomial method should be used in a porous electrode model to obtain accuracy and save computation time.