Faster lead-acid battery simulations from porous-electrode theory: Part I. Physical model

An isothermal porous-electrode model of a discharging lead-acid battery is
presented, which includes an extension of concentrated-solution theory that
accounts for excluded-volume effects, local pressure variation, and a detailed
microscopic water balance. The approach accounts for three typically neglected
physical phenomena: convection, pressure diffusion, and variation of liquid
volume with state of charge. Rescaling of the governing equations uncovers a
set of fundamental dimensionless parameters that control the battery's
response. Total volume change during discharge and nonuniform pressure prove to
be higher-order effects in cells where variations occur in just one spatial
dimension. A numerical solution is developed and exploited to predict transient
cell voltages and internal concentration profiles in response to a range of
C-rates. The dependence of discharge capacity on C-rate deviates substantially
from Peukert's simple power law: charge capacity is concentration-limited at
low C-rates, and voltage-limited at high C-rates. The model is fit to
experimental data, showing good agreement.