1D Isothermal Nickel–Metal Hydride Battery

This example simulates the discharge of a nickel–metal hydride (Ni–MH) battery using the Battery with Binary Electrolyte interface. The geometry is in one dimension and the model is isothermal. The model serves as an introduction to Ni–MH modeling, and can be further extended to include various side reactions. The model is based on a study by Paxton and Newman (Ref. 1), with updated equilibrium potentials from a more recent study by Albertus and others (Ref. 2).

Figure 1: Cross section of a NiMH battery showing the main electrochemical processes that occur during discharge.

The model includes the following processes:

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Electronic current conduction in the electrodes

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Ionic charge transport in the electrodes and electrolyte/separator

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Material transport in the electrolyte

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Material transport within the spherical particles that form the electrodes

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Butler-Volmer electrode kinetics using experimentally measured discharge curves for the equilibrium potential.

Model Definition

This example models the battery cross section in 1D, which implies that edge effects in the length and height of the battery are neglected. The example uses the following domains:

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Negative porous electrode (metal hydride): 350 μm

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Separator (electrolyte): 250 μm

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Positive porous electrode (nickel oxide): 843 μm

The electric potential in the electron conducting phase,

, is calculated using a charge balance based on Ohm’s law, where the charge transfer reactions result in source or sink term. For the porous electrodes effective conductivities, σseff, are used that take porosity and tortuosity into account as given by the following expression:

where γ is the Bruggeman coefficient, which is set to 1.5 in this model, corresponding to a packed bed of spherical particles. Also, the diffusion coefficient for the electrolyte salt is corrected for the tortuosity and the porosity in this way.

The ionic charge balances and material balances are modeled according to the equations for a binary 1:1 electrolyte, with both the anion (OH-) and the solvent (H2O) participating in the electrode reactions (Ref. 1).

Fickian diffusion describes the transport in the spherical particles. The diffusion equation is expressed in spherical coordinates for the material balance of intercalated hydrogen atoms in the particles.

Butler-Volmer electrode kinetics describes the local charge transfer current density in the electrodes. The Butler-Volmer expressions are introduced as source or sink terms in the charge balances and material balances.

Boundary Conditions

For the electronic current balance, a potential of 0 V is set on the negative electrode’s current collector/feeder boundary. At the positive electrode current collector/feeder, the current density is specified to a constant discharge current density. The inner boundaries facing the separator are insulating for electric currents.

For the ionic charge balance in the electrolyte, the current collector/feeder boundaries are insulating. Insulating conditions also apply to the material balances.

At the particle surface in the local particle model, the material flux is determined by the local electrochemical reaction rate.

Material Properties

The material properties are those of a typical NiMH. The electrolyte is KOH, diluted in water to a 30% (wt) solution. The active electrode materials are a metal hydride (LaNi5Hx) for the negative electrode and a nickel oxide (NiOHOHy) for the positive electrode.

The equilibrium potential of the negative and positive electrodes are composition dependent through experimentally measured data. This data is tabulated in interpolating functions in the model and the properties vary significantly during charge and discharge due to the changes in composition.

The model uses constant values for the electrolyte conductivity, the electrolyte diffusivity, and the activity variation with concentration in the electrolyte. The activity coefficients are assumed to be constant in the electrode reactions. For more accurate simulations you can use concentration-dependent expressions for these properties (Ref. 1).

Figure 2 displays the equilibrium potentials for the negative and positive electrodes as functions of the measured state of charge (SOC).

Figure 2: The equilibrium voltage of the electrode materials.

The initial concentration values within the electrode particles are set to correspond to a fully charged battery.

For complete details on the material properties and constants, see Ref. 1.

Results and Discussion

Discharge Curves

The battery is initially at a fully charged state, discharge at two different current densities are simulated and displayed here. This model defines end-of-discharge as the time when the cell voltage drops below 0.99 V. The nominal discharge current density, corresponding to case 1C below (a current density corresponding to a theoretical full discharge in one hour), is 430 A/m2.

Figure 3: Discharge curves for various discharge rates.

Figure 3 shows that the maximum discharge capacity of 430 Ah/m2 is obtained for the a current density of 43 A/m2 (0.1 C). It can also be seen that the discharge capacity decreases slightly when applying a 1 C discharge current. At 1 C, the battery delivers approximately 90% of the theoretical capacity before it reaches a cell voltage of 1 V.

At the beginning of the discharge the voltage is higher than what is normally seen in a NiMH battery. The reason for this is the absence of side reactions in the model (Ref. 2). (The high voltage on the positive electrode results in a self discharge process in which oxygen is evolved on the positive electrode and transported over to the negative electrode where it is reduced).

The discharge curves are similar to those presented in Ref. 1, with slight deviation due different sources of experimental data for the equilibrium potentials.

Analysis of voltage losses

It is possible to visualize the contributions of the different losses to the total overpotential. You can compare the contribution from the activation overpotential and the electrolyte potential by plotting the electrolyte potential with a bias of 0.91 V as shown in Figure 4. In this way the two plots are within similar range of potential.

Figure 4: Voltage losses in the battery during discharge.

The overpotential at the positive electrode is the largest contributor to the potential losses during a 1C discharge. The figure does not include the electronic potential profile in the solid phase, but the simulations show that contributions from the ohmic losses in the electronic conductors are negligible.

To further investigate the reason for the steep voltage decrease, you can plot the concentration profile in the electrolyte. Figure 5 depicts the profile at several stages during the discharge of the cell.

Figure 5: Electrolyte-phase concentration profiles at various times.

The concentration gradients are quite low and the cell experiences only minor concentration polarization due to electrolyte transport limitations.

Figure 6 shows that the local current density distribution varies during discharge, Initially it is evenly distributed, but toward the end of the discharge more of the current is produced closer to the current collectors, the effect is more pronounced for the negative electrode.

Figure 6: Local current-density distribution within the battery at various stages during the discharge.

The current density is related to the concentration in the solid phase at the surface of the particles. Figure 7 depicts the distribution of the concentration in the solid-phase particles. At the end of discharge most of the concentration of intercalating material is depleted close to the separator at the negative electrode, this explains the lower current densities in this region of the battery, as was shown in Figure 6.