An Alternative to the Doyle-Fuller-Newman Model for Lithium-Ion Batteries: The Two-Equation Model

The Doyle-Fuller-Newman (DFN) model is considered the industrial and academic standard for physics-based modelling of Lithium-ion batteries at the cell scale, and it has prevailed now for 50 years. One can find it referred to under various other names - the Newman model, porous electrode theory, P2D, etc. - and various extensions or simplifications of the original model have come about since its inception [1]. From the perspective of the volume-averaging community, the DFN is a hybrid model: all transport equations are solved on the macroscale, except the mass balance within the active material (AM), which is solved on the microscale. This is one of the key strengths of the DFN, as it captures the slow transport of lithium within the AM, allowing an accurate estimate of the AM surface concentration for use in the Butler-Volmer Equation. However, adopting a hybrid approach comes with drawbacks. Firstly, one is strongly compelled to make simplifying assumptions on the morphology of the microscale domain, as if the real microstructure is kept the resulting model will be highly complex - in the DFN, this manifests as the assumption of isolated and spherical particles. Secondly, by solving the AM mass balance on the microscale, an extra dimension is added to the problem (compared to a fully macroscale model), increasing computational demand. Two-equation models, in which the AM mass balance is also homogenised, are rarely encountered in lithium-ion battery modelling, due to the challenges in approximating AM surface concentration; only two instances can be found [2, 3]. In this work, we present a two-equation model which approximates the surface concentration, and thus the reaction rate, using a mapping variable that is solved for on the electrode microstructure. We compare our model to both the DFN and the microscale model for various electrodes, evaluating it on the basis of cell-voltage prediction, and also computational time. [1] F. Brosa Planella. A continuum of physics-based lithium-ion battery models reviewed. PRGE, 4,10 2022. [2] X. Yang and D. Tartakovsky. Dual-continuum models of electrochemical transport in porous electrodes. J. Electrochem. Soc., 172:20507, 2 2025. [3] H. Arunachalam and S. Onori. Full homogenized macroscale model and pseudo-2-dimensional model for lithium-ion battery dynamics: Comparative analysis, experimental verification and sensitivity analysis. J. Electrochem. Soc., 166, 2019.