Design Fundamentals of High Power Density, Pulsed Discharge, Lead‐Acid Batteries: II . Modeling

Two time‐dependent, one‐dimensional mathematical models of lead‐acid cells have been solved to help understand the pulsed discharge behavior (0.002 second discharge) of thin cells. One model considered only the outer (cross‐sectional) surface area of the electrodes; the other assumed that only the surface area internal to the porous electrodes contributed significantly. The porous electrode model was a macroscopic model which ignored the concentration gradients within the microscopic electrode pores. It was found that the model which considered the outer surface area more accurately predicted experimentally observed behavior during the initial 0.0001s of discharge. When the porous electrode model was altered to include acid concentration variations within the electrode pores, it also predicted the behavior of experimental cells during this initial 0.0001s of discharge. The effects of delayed precipitation were also included in the porous electrode model. When this was done, the model successfully predicted the shape of discharge curves from experimental cells for longer time periods. The modeling results supported experimental evidence that the steep decline in current densities from actual cells during the first 0.0001s of discharge is due to concentration polarization, and that passivation can severely limit the performance of thin lead acid cells after several hundred microseconds. Finally, when the product of the electrode specific internal surface area (cm−1) and the electrode length (cm) is close to or less than 1, the outer surface area should be considered in modeling electrode behavior.