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

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 LiCoO2 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.