Simplified Mathematical Model for Effects of Freezing on the Low-Temperature Performance of the Lead-Acid Battery

Abstract

Discharge periods of lead-acid batteries are significantly reduced at subzero centigrade temperatures. The reduction is more than what can be expected due to decreased rates of various processes caused by a lowering of temperature and occurs despite the fact that active materials are available for discharge. It is proposed that the major cause for this is the freezing of the electrolyte. The concentration of acid decreases during battery discharge with a consequent increase in the freezing temperature. A battery freezes when the discharge temperature falls below the freezing temperature. A mathematical model is developed for conditions where charge-transfer reaction is the rate-limiting step, and Tafel kinetics are applicable. It is argued that freezing begins from the midplanes of electrodes and proceeds toward the reservoir in-between. Ionic conduction stops when one of the electrodes freezes fully and the time taken to reach that point, namely the discharge period, is calculated. The predictions of the model compare well to observations made at low current density ͑C/5͒ and at −20 and −40°C. At higher current densities, however, diffusional resistances become important and a more complicated moving boundary problem needs to be solved to predict the discharge periods. The lead-acid battery was invented as early as 1859 by Raymond Gaston Planté. Today, it happens to be the most widely used storage battery for a range of applications, from powering bicycle headlights to electric vehicles. It offers several advantages: the highest cell voltage among aqueous electrolyte batteries, ability to operate over a wide range of temperatures, an acceptable energy efficiency of over 80%, an acceptable level of charge retention, and nearly 100% recyclability of spent batteries. Predicting the performance of leadacid batteries is therefore of importance, and several models have been developed for this purpose. They take into account the finite rate of the charge-transfer reactions, and ohmic as well as diffusional resistances. To cite a few, Gu et al. 1 7 These models can predict the discharge period of a battery once a cutoff voltage is specified. However, these models have focused on predicting the performance of the battery at normally encountered ambient temperatures. References ͑see, for example, Chapter 23 in Ref. 8 and the book by Bode 9 ͒ do point to severely curtailed discharge periods when the battery is operated at temperatures well below the freezing point of water ͑i.e., 0°C͒. The same is demonstrated by data on discharge at constant current density obtained in our laboratories and shown in Table I: The discharge period is reduced from 5 h at 25°C to 2.75 h at −40°C. As evident from the longer discharge period at 25°C, the discharge period at low temperatures is reduced even though the battery still has a considerable amount of unreacted active materials. The objective of the present paper is to present a simplified model to explain the drastic reduction in discharge periods at low temperatures. A major reason f...

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