Reduced Order Models Derived from Perturbation Solutions and Applied to a Lithium Ion Intercalation Electrode
Mark W. Verbrugge, Daniel R. Baker
Abstract
We derive and implement a new reduced order model (ROM1) based on a perturbation solution. We compare and contrast ROM1, which employs a single-particle model as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation describing diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for diffusion, with a simpler-to-implement but lower-accuracy perturbation solution, ROM0, which was derived by a similar procedure, and whose leading-order solution is that of dynamic equilibrium for the cell (D. R. Baker and M. W. Verbrugge, J. Electrochem. Soc ., 168(2021)050526). ROM0, ROM1, and the full model all utilize the MSMR (multi-site, multi-reaction) formulation, which has been shown to yield accurate representations of the thermodynamics and reaction kinetics of many different electrode materials. We find ROM1 provides an accurate representation of the full model solution for an electric-vehicle cell over reasonable use cases.