The COMSOL® Product Suite

Understand, Design, and Optimize Battery Systems

Software for Modeling Electrode Kinetics, Ion Transport, Charge Conservation, Mass Transport, Fluid Flow, and Heat Transfer in 1D, 2D, and 3D

Modeling batteries requires different levels of detail depending of the purpose of the simulations. The Battery Design Module is an add-on to the COMSOL Multiphysics® software that encompasses descriptions over a large range of scales, from the detailed structures in the battery's porous electrode to the battery pack scale including thermal management systems.

The descriptions involve physics phenomena such as transport of charged and neutral species, charge balances, chemical and electrochemical reactions, Joule heating and thermal effects due to electrochemical reactions, heat transfer, fluid flow, as well as other physical phenomena important for the understanding of a battery system. For well-known and verified systems, lumped models are available and may be physics-based or based on equivalent circuits.

Note that the name of this product changed from the Batteries & Fuel Cells Module to the Battery Design Module with the release of version 5.6, while retaining all functionality. For users that model fuel cells and electrolyzers, a new Fuel Cells & Electrolyzers Module is available.

What You Can Model with the Battery Design Module

Lithium-Ion Battery Systems

The lithium-ion battery is the most popular battery for portable applications due to its high power and energy density. The Battery Design Module features state-of-the-art models for lithium-Ion batteries. The so-called Newman model is predefined in the module with the latest findings in scientific literature. For example, different mechanisms for aging have been built-in, such as growth of the SEI, metal plating, short-circuiting, and electrolyte degradation. These high-fidelity models are available for 1D, 2D, and full 3D modeling, with an additional pseudo-dimension for modeling the intercalation of lithium in the electrode particles.

In addition to modeling the electrochemical reactions, when combining with heat transfer, a full energy balance is added. You are also able to account for the structural stresses and strains caused by the expansion and contraction from lithium intercalation, when combined with the Structural Mechanics Module.

For the latest trend in battery modeling, the module also includes functionality for heterogenous models, where the detailed structure of the porous electrodes and the pore electrolyte can be modeled for a representative unit cell of a battery. Such models may be used for a deeper understanding of the impact of the microstructure of a battery.

Lead–Acid Battery System

The Battery Design Module contains one of the most advanced battery models for simulating lead–acid batteries. The software includes the dependent variables for the ionic potential in the electrolyte (both separator and pore electrolyte), the electric potential in the solid electrodes (and current collectors/feeders), the composition of the electrolyte, and the porosity of the electrodes. The module also contains a thermodynamic and kinetic parameters database for the lead–acid battery.

A typical use is to study the effect of design parameters on the performance of the battery, such as thickness and geometry of the electrodes and separators, the geometry of the current collectors and feeders, the porosity of the electrodes, the geometry and composition of the separator, to mention a few.

The studies that can be run include full transient studies, including the effect of double-layer capacitance, as well as impedance spectroscopy studies in the frequency domain.

Generic Battery Systems

The workhorse of the Battery Design Module is the detailed model of the battery unit cells with positive electrode, negative electrode, and separator. In the electrodes, the pore electrolyte is in contact with the electrolyte in the separator.

The porous structure in the electrodes is homogenized, meaning that the pore electrolyte and the solid electrode material are present everywhere in space, and a volume fraction determines the respective properties of the phases. The transport equations and the electrochemical and chemical reactions are treated with so-called porous electrode theory as devised by Newman in the book Electrochemical Systems.

With the generic description of porous electrodes, you can define any number of competing reactions in an electrode and also couple this to an electrolyte of an arbitrary composition. For example, a tutorial model of the vanadium battery is included in the module's Application Library.

The pore electrolyte and the electrolyte in the separator can be described, for any composition, with the theory for concentrated electrolytes, dilute electrolytes (Nernst–Planck equations), and supporting electrolytes.

A specific version for batteries with binary electrolytes is available as predefined functionality. You can use this to model NiMH and NiCd batteries, and allows intercalating materials in the solid phase, such as hydrogen, for example.

Multiphysics UI showing the Porous Electrode settings and a lithium-ion battery pouch cell model with utilization visualized in the Cividis color table. Current distribution and electrode utilization in a large lithium-ion battery pouch cell. The model is a full 3D Newman model with a fourth dimension in every point in the electrodes representing the radius of the electrode particles.
A lead-acid battery model with volume plots for the electrode current density magnitude, in a white to dark purple color gradient, and electrolyte potential, in dark blue to white color gradient. Current density and potential distribution in a grid electrode in a lead–acid battery.
The COMSOL Multiphysics UI showing the Tertiary Current Distribution, Nernst-Planck settings and a surface plot of the concentration in a vanadium flow battery. This 2D tutorial of a vanadium flow battery demonstrates how to couple a tertiary current distribution model for an ion-exchange membrane to tertiary current distribution models for two different free electrolyte compartments of a flow battery. The model accounts for 7 different ions in total.

Features and Functionality in the Battery Design Module

Porous Electrodes with an Arbitrary Number of Electrochemical Reactions

Battery systems and chemistries are often burdened by unwanted side-reactions at the electrodes, and you can investigate their impact on charge and discharge cycles, as well as for self-discharge. There is a database for predefined reactions, but you can add arbitrary by-reactions to an electrode.

Typical by-reactions that you are able to model include hydrogen evolution, oxygen evolution, the growth of a solid electrolyte interface, metal plating, metal corrosion, and graphite oxidation.

Intercalating Species and Transport in Bimodal Pore Structures

The particles in porous battery electrodes can either be solid (Li-ion electrode) or porous (lead–acid, NiCd).

In the case of solid particles, the porosity in the electrode is found between the packed particles. However, transport and reactions may occur in the solid particles for small atoms such as hydrogen and lithium atoms. These intercalating species are modeled with a separate diffusion-reaction equation defined along the radius of the solid particles. The flux of the intercalating species is coupled at the surface of the particles with the species that are transported in the pore electrolyte between the particles. The intercalation species and reactions are predefined for Li-ion batteries, however, you can use the same functionality to model intercalation of hydrogen in, for example, NiMH batteries.

In the case of porous particles, a bimodal pore structure is obtained: a macroporous structure between the packed particles and a microporous structure inside the particles. The reaction-diffusion equations in the porous particles are defined in a similar fashion as for the intercalation of species in solid particles. This is exemplified in the NiCd tutorial model included in the module's Application Library.

Fully Transient and Impedance Spectroscopy Studies

Battery systems are often closed systems that are difficult to study during operation. Transient methods such as potential step, current interrupt, and impedance spectroscopy can be used to characterize a battery during operation.

The principle of transient studies is that they are able to separate processes in different time scales. For example, kinetics and diffusion are usually processes with different time constants. They would therefore give impedance effects at different frequencies and time scales.

By performing transient studies, we can run parameter estimation at different time scales and frequencies to separate ohmic, kinetics, transport, and other losses that may be responsible for battery aging. Using transient techniques, modeling, and parameter estimation, we can make very accurate estimations of the state of health of a battery system.

Simplified and Lumped Battery Systems

The thermal analysis of battery packs can be time-consuming if we use full 3D models for the electrochemistry. An alternative is to use validated lumped (simplified) models for each battery in a pack. Once validated, the lumped models may give an excellent accuracy within a particular (maybe limited) range of operation.

The Battery Design Module contains lumped models that are physics-based and solve the electrochemical equations in 1D plus a pseudo-dimension (particle dimension); 0D plus a pseudo-dimension; and pure 0D models, such as equivalent circuit models, for example.

The multicomponent model may contain the full range of fidelity, from the detailed 3D models to the lumped 0D models. These models are incorporated as separate components in a multicomponent model file. It is therefore easy to alternate between lumped models and use detailed models when the lumped models need to be updated and validated for a new range of operation.

Built-In Thermodynamic and Material Properties for Battery Systems

One of the more time-consuming and error prone steps in the modeling of battery systems is to gather input data and to use it consistently. For example, it is important that the positive and negative electrodes are defined in the same reference systems. The equilibrium electrode (half-cell) potentials have to be measured or calibrated to the same reference electrodes, electrolytes, and temperatures before they are incorporated in the same battery system model.

The battery material database included in the module contains entries for a number of common electrodes and electrolytes, substantially reducing the amount of work needed for creating new battery models.

The COMSOL Multiphysics UI showing the Porous Electrode Reaction settings and a 1D plot of electrolyte concentration for a lead-acid battery. The positive electrode in a lead–acid battery may suffer from the oxygen evolution by-reaction, which is added in the user interface. The plot shows the electrolyte salt concentration (both pore electrolytes and separator) as a function of time during discharge at 20C.
The COMSOL Multiphysics UI showing the Porous Electrode Reaction settings and a 1D plot of the electric potential in a nickel-cadmium battery. Model of a NiCd battery with detailed electrochemistry and transport of hydrogen ions in the porous microstructure.
The COMSOL Multiphysics UI showing the Particle Intercalation settings and a 1D Nyquist plot of simulated and experimental impedance vs. reference for a lithium-ion battery Parameter estimation of AC impedance spectroscopy with a full physics-based (Newman) model for the lithium-ion battery. The Battery Design Module includes impedance spectroscopy as a predefined study.
The COMSOL Multiphysics UI showing the Voltage Losses settings and a battery pack model in the Graphics window with the temperature visualized using the heat camera color table. Simplified physics-based electrochemical model for a lithium-ion battery combined with a 3D heat transfer analysis. Each battery unit cell in the back gets a simplified temperature-dependent electrochemistry model.
The COMSOL Multiphysics UI showing the Porous Electrode Reaction settings, a battery pack model in the Graphics window, and a list of materials that can be added to the right. The functions for the electrode potential as a function of state of charge (SOC) for different electrodes, and the conductivities for electrolytes as well for electronic conductors can all be obtained from the built-in database for a number of chemistries.

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