Aspects to Consider When Modeling Batteries or Fuel Cells

Batteries and fuel cells are electrochemical energy extraction devices that work by using a conducting domain to separate two regions, where the two halves of an overall favorable chemical reaction proceed. By preventing the mixing of reactants and instead forcing the reaction to proceed by mediation of electrical current between the separated reactants, energy can be extracted as a voltage.

In a battery, there is a finite supply of reactant and the system is closed. In a fuel cell, by contrast, there is a continuous feed of reactant to the system. A battery can be simpler since it involves a single closed system, but a fuel cell may have other advantages such as decreasing overall weight since it separates the site of energy storage from that of energy extraction.

A battery does not have a steady state condition since its feedstock of reactants progressively depletes until it is consumed. Once consumed, the battery is discharged and it will no longer provide a voltage as its source of electrochemical energy has run out. In a rechargeable battery, the process is reversible and the application of a voltage can return the battery to saturation with feedstock under charging.


	The electrochemistry in a battery model usually does not have a steady state, and so it is not appropriate to use a Stationary study with a battery interface.

Fuel cells do have steady states, although transient effects may also be important in fuel cell research. In a fuel cell, it is typically important to identify what features of the system may be rate-limiting for the steady-state current: the transport of reactants to the electrodes, the electrode kinetics themselves and the transport of current through the electrolyte may all cause bottlenecks.

The maximum achievable voltage in a battery or fuel cell is the difference between the half-cell potentials. The discharge mode is the direction in which the overall reaction is thermodynamically downhill (negative ΔG).


	There can be variation in the literature between whether the charge or discharge mode is assumed when an electrode in a battery is referred to as the “anode” or “cathode”. Each electrode can operate in both roles, depending on whether the battery is charging or discharging.

Typically a battery model can be set up using to describe charge transport since the long charge and discharge times ensure that conductivities remain relatively uniform through the cell. If coupling to species transport is required, can be added with an condition.

Predefined Battery Interfaces

Certain common battery types have predefined physics interfaces. Common for all these interfaces is that by the use of concentrated electrolyte theory for the charge and mass transport in the electrolyte, a more accurate electrolyte transport model is achieved, compared to the Nernst-Planck equations described earlier in this chapter.

is used for solving problems in batteries where the anode (in discharge mode) is lithium metal intercalated into a material such as graphite, and the cathode (in discharge mode) is lithium ions intercalated into a transition metal oxide. The electrical current through the electrolyte is carried by lithium ions, typically in an organic solution. Because both the anode and cathode materials are typically porous to maximize the active surface area, the domain node is standard do define each electrode.

The interface can be used for a range of general battery types involving porous electrodes and current transfer through an ionic conductor. An example is the nickel-metal hydride battery — an early type of rechargeable battery in which the discharge anode is a metal hydride, the discharge cathode is a hydrated nickel oxide, and the current is transferred by high concentration potassium hydroxide in aqueous solution.

The interface is designed for batteries in which the discharge process is the conproportionation of Pb(0) and Pb(IV) through a sulfuric acid medium.

Fuel Cell Modeling

Fuel cell modeling is complex since it is a closely coupled multiphysics problem involving charge, mass and momentum conservation. These physics are normally set up by coupling for the charge transfer, for gas phase mass transport, and for momentum transport (fluid flow) in the porous gas diffusion layers and the free flow gas channels. The latter is a combination of for free flow and for porous flow.

In a fuel cell, any one of electrochemical reactivity, mass transport of reactants to either electrode, and electrical resistance can cause a “bottleneck”, limiting the current drawn for a given voltage. An accurate study of the polarization curve of a fuel cell must therefore incorporate all of the physical effects to identify the voltages at which the fuel cell behavior varies from transport-limited to being limited by the kinetics of the electrolysis reaction.


	When setting up a fuel cell study, it is a good idea to include physics interfaces one at a time. In particular, make sure that Fluid Flow physics interfaces are correctly set up before proceeding to incorporate species transport. See also Solving Electrochemical Models below.

•

The Transport of Concentrated Species Interface

•

The Free and Porous Media Flow Interface

•

The Primary and Secondary Current Distribution Interfaces