Most models of lithium-ion batteries follow the one-dimensional analysis approach. The major drawback of this is that the porosity and liquid-phase salt transport and solid-phase electronic conductivity are not explicitly resolved and the diffusion of lithium into and out of solid is modeled using representative spherical particles assuming perfect symmetry. These modeling assumptions limit the achievable accuracy; refinement of spatial computational grid and time steps cannot overcome the modeling error introduced by the above assumptions.
Researchers at Battery Design LLC and CD-adapco set out on a new approach, one that would avoid the limitations of the standard approach by resolving the structure of the electrode and explicitly modeling the transport of lithium in the electrolyte and solid phases. The following factors motivated the researchers to go down this path.
It is now possible to obtain exact geometry of solid particles in electrodes. While the resolution of scanning devices currently is relatively poor for such microscopic structures, there is no doubt that within a few years an adequate resolution will be possible. This will allow for the building of CAD models of solid and fluid regions of battery cell electrodes.
Commercial software allows creation of quality grids in arbitrarily complex geometries. Grid-generation methods based on tetrahedral elements have been available for a long time. These elements are not best suited for diffusion-dominated problems such as those in battery electrodes, requiring layered (prismatic) meshes along solid-liquid interfaces. However, over the past decade methods of generating polyhedral grids with prismatic layers along interfaces have been developed, allowing for an adequate resolution of complex geometry present in electrodes.
Computing power is steadily growing. Computational grids made of hundreds of millions of control volumes currently are used in some advanced niche applications, such as Formula One, but it will become commonplace in the near future.
The method to allow a detailed modeling of porous electrodes and associated processes is by explicitly separating solid and fluid regions within electrodes and performing a three-dimensional discretization based on the finite volume method. Used for this research were manufactured geometries that have similar porosity, tortuosity, and active-surface-area-to-volume ratio comparable to real electrode material in order to develop the basic models and computational procedure. Real geometries can then be introduced as they become available without the need to modify the solution method. Other research groups are pursuing similar approaches.
The complex model was implemented within the finite volume framework of the computational continuum mechanic software STAR-CCM+. A sample application was undertaken, focused on a small region of a LiMn2O4 chemistry cell. The results were compared with an established 1-D model, and favorable and realistic trends are shown within the 3-D model. Further studies will include the analysis of grid and time step dependence and the determination of minimum size of computational domain needed to obtain reliable solutions with minimum effort.
Having shown the credibility compared to a 1-D model, this 3-D model will be further enhanced to include detailed analysis of effects at the solid electrolyte interphase (SEI) layer to account for possible Li-ion plating due to local conditions. As the understanding of other capacity-fade processes evolves within literature, these can be added to this base modeling framework.
Attention will also now turn to improvements in the generation of representative models and the overall user process to enable industry to repeat and extend the reported work. In parallel to the generation of further idealized models (which will include binder, conducting aid, range of particle sizes and shapes, etc.), this code will also be used on data generated from scanning tomography of actual electrode samples, as soon as they become available with sufficient quality needed to generate computational models of the presented kind. Further effects that can be accounted for in the future include electrolyte flow, expansion and contraction of solid material during charging and discharging, edge effects, etc.
This article is based on SAE technical paper 2012-01-0663 by Robert Spotnitz of Battery Design LLC; and Boris Kaludercic, Samir Muzaferija, Milovan Peric, Gaetan Damblanc, and Steve Hartridge of CD-adapco.