Electrochemical and equivalent-circuit modeling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be useful to support battery management, on-line diagnostics, and cell design. We analyze a thermodynamically consistent, isothermal porous-electrode model of a discharging lead-acid battery. Asymptotic analysis of this full model produces three reduced-order models, which relate the electrical behavior to microscopic material properties, but simulate discharge at speeds approaching an equivalent circuit. A lumped-parameter model, which neglects spatial property variations, proves accurate for C-rates below 0.1C, while a spatially resolved higher-order solution retains accuracy up to 5C. The problem of parameter estimation is addressed by fitting experimental data with the reduced-order models. (C) 2019 The Electrochemical Society.