Two-dimensional mathematical model of a lead-acid cell

A two-dimensional mathematical model of the lead-acid cell that details nonuniformities along cell height as well as thickness is presented. The model is an extension of earlier, one-dimensional models that simulate variation across the cell thickness alone. The model results show significant variations of current density and other variables in cell height, even at relatively low rates of discharge. The local electrochemical reaction rates are lowest at the bottom center of the electrodes and highest at the top. As discharge proceeds, the distributions in reaction rates and current density become more uniform from the top to the bottom of the cell. Also, significant variations in sulfuric acid concentration throughout the cell develop during discharge. The most concentrated acid is located at the bottom center of the negative electrode, and the most dilute acid is located at the top center of the positive electrode. Predictions of cell voltage are nearly that on one-dimensional model results for the conditions studied; however, variations across cell thickness by one-dimensional models should be considered as an average of the behavior along cell height for all practical operating conditions.