Electrochemical transport simulation of 3D lithium-ion battery electrode microstructures

Lithium-ion batteries are commonly modeled using a volume-averaged formulation (porous electrode theory) in order to simulate battery behavior on a large scale. These methods utilize effective material properties and assume a simplified spherical geometry of the electrode particles. In contrast, a particle-scale (non-porous electrode) simulation applied to resolved electrode geometries predicts localized phenomena. Complete simulations of batteries require a coupling of the two scales to resolve the relevant physics. A central focus of this thesis is to develop a fully-coupled finite volume methodology for the simulation of the electrochemical equations in a lithium-ion battery cell at both the particle scale and using volume-averaged formulations. Due to highly complex electrode geometries at the particle scale, the formulation employs an unstructured computational mesh and is implemented within the MEMOSA software framework of Purdue’s PRISM (Prediction of Reliability, Integrity and Survivability of Microsystems) center. Stable and efficient algorithms are developed for full coupling of the nonlinear species transport equations, electrostatics, and Butler-Volmer kinetics. The model is applied to synthetic electrode particle beds for comparison with porous electrode theory simulations and to evaluate numerical performance capabilities. The model is also applied to a half-cell mesh created from a real cathode particle bed reconstruction to demonstrate the feasibility of such simulations. The second focus of the thesis is to investigate 3D battery electrode architectures that offer potential energy density and power density improvements over traditional particle bed battery geometries. A singular feature of these geometries is their interpenetrating nature, which significantly reduces diffusion distance. Advancement of micro-scale additive manufacturing techniques has made it possible to fabricate these electrode microarchitectures. A fully-coupled finite volume methodology for the transport equations coupled to the relevant electrochemistry is implemented in the PETSc (Portable, Extensible Toolkit for Scientific Computation) software framework which allows for a straightforward scalable simulation on orthogonal hexahedral meshes. Such scalability becomes important when performing simulations on fully resolved microstructures with many parameter sweeps across multiple variables. Using the computational model, a variety of 3D battery electrode geometries are simulated and compared across various battery discharge rates and length scales in order to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density and power density of the 3D battery microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle bed electrode designs are observed, and electrode microarchitectures derived from minimal surfaces are shown to be superior under a minimum feature size constraint. An average Thiele modulus formulation is presented to predict the performance trends of 3D microbattery electrode geometries. As a natural extension of the 3D battery particle-scale modeling, the third and final focus of the thesis is the development and evaluation of a volume-averaged porous electrode theory formulation for these unique 3D interpenetrating geometries. It is necessary to average all three material domains (anode, cathode, and electrolyte) together, in contrast to traditional two material volume-averaging formulations for particle bed geometries. This model is discretized and implemented in the PETSc software framework in a manner similar to the particle-scale implementation and enables battery-level simulations of interpenetrating 3D battery electrode architectures. Electrode concentration gradients are modeled using a characteristic diffusion length, and results for plate and cylinder electrode geometries are compared to particle-scale simulation results. Additionally, effective diffusion lengths that minimize error with respect to particle-scale results for gyroid and Schwarz P electrode microstructures are determined, since a theoretical single diffusion length is not easily calculated. Using these models, the porous electrode formulation for these 3D interpenetrating geometries is shown to match the results of particle-scale models very well.