Asymptotic reduction of a lithium-ion pouch cell model

A three-dimensional model of a single-layer lithium-ion pouch cell is presented which couples conventional porous electrode theory describing cell electrochemical behavior with an energy balance describing cell thermal behavior. Asymptotic analysis of the model is carried out by exploiting the small aspect ratio typical of pouch cell designs. The analysis reveals the scaling that results in a distinguished limit and highlights the role played by the electrical conductivities of the current collectors. The resulting model comprises a collection of one-dimensional models for the through-cell electrochemical behavior which are coupled via two-dimensional problems for the Ohmic and thermal behavior in the planar current collectors. A further limit is identified which reduces the problem to a single volume-averaged through-cell model, greatly reducing the computational complexity. Numerical simulations are presented which illustrate and validate the asymptotic results.