Variance-Based Sensitivity of Localized Sulphation to Microporous Separator Properties Using a Distributed Parameter Model of a Valve-Regulated Lead-Acid Battery

Abstract

Modern applications such as electric and hybrid-electric vehicles require high-rate partial state-of-charge (HRPSoC) duty from battery systems. A major cause of premature capacity loss in lead-acid batteries under HRPSoC duty is irreversible passivation by progressive sulphation of the negative electrode. Notable advances have been made in the form of desulphating charge algorithms as well as carbon additives to the negative electrode that seem to restrict PbSO4 crystal growth. However, a method that substantially curbs irreversible sulphation has yet to be developed. During a high-rate discharge, the PbSO4 crystals that nucleate and grow on the porous electrodes are small and needle-like, implying a high crystal geometry factor. The available surface area for dissolution during a subsequent charge is significantly larger than if preceded by a low-rate discharge. Apart from the size, shape and distribution of the PbSO4 crystals, their dissolution also depends on the local electrolyte concentration. A high-rate discharge results in a particularly non-uniform concentration profile and, consequently, areas with low crystal solubility. Our focus is on a new valve-regulated lead-acid (VRLA) battery with immobilized electrolyte undergoing a high-rate discharge. We investigate the microporous separator’s design for healthier end-of-discharge (EOD) conditions. More specifically, we consider EOD conditions that would be favorable to the dissolution of PbSO4 crystals in a subsequent charge. We use a comprehensive electrochemical model that accounts for full mass transport over three regions: the positive electrode, the separator and the negative electrode. Partial differential equations describing the local PbSO4 crystals are also included. The model is verified in COMSOL Multiphysics®and used to simulate a high-rate discharge at 728 A until 12 Ah (50% DOD) followed by a short rest period, all at 25 °C. A variance-based sensitivity analysis (VBSA) is performed to determine the sensitivity of several output variables to changes in selected input parameters. The input space, consisting of the separator’s porosity, thickness and tortuosity, is explored in a Monte Carlo experiment using Quasi-random sampling. The output variables of interest are the local PbSO4 volume fraction and solubility, and the crystal geometry factor. First-order sensitivity explains the effect of a single parameter whereas the total sensitivity takes parameter interactions into account. Figure 1 shows the local PbSO4 volume fraction and solubility during a high-rate discharge. As the battery discharges, the electrolyte concentration decreases and the PbSO4 solubility increases. This solubility is much lower at the negative electrode and more crystals form at the separator interfaces than in other electrode regions. A greater volume fraction of PbSO4 has formed at the positive electrode but considering the local solubility, these crystals should dissolve during the following charge. Table 1 summarizes the sensitivity at the EOD for both separator interfaces calculated using 500 model evaluations. The separator tortuosity seems to have a negligible effect on the PbSO4 crystals at the interfaces during a high-rate discharge. Figure 2 shows the output variables at the EOD against the most influential parameter for each interface. For faster dissolution of the PbSO4 crystals at the negative electrode, we would like the highest crystal geometry factor and solubility but the smallest fraction of PbSO4 crystals. Figure 2 indicates the selection of a separator with thickness between 0.05 and 0.1 cm and porosity between 0.7 and 0.75. Figure 3 illustrates how the electrolyte concentration becomes more uniform in the negative electrode during a rest period after discharge, but the concentration in the positive electrode becomes more non-uniform. Equation (1) is used to calculate the concentration non-uniformity. Figure 3 also indicates that homogenization of the concentration in the negative electrode occurs faster when the separator thickness is roughly between 0.08 and 0.1 cm. At separator thicknesses greater than 0.125 cm, it seems that diffusion takes longer within the negative electrode. The VBSA results suggest that the separator thickness has the greatest effect on the PbSO4 crystals at the negative electrode simply because it influences the concentration profile so severely. We conclude from the VBSA results that optimal values for the separator thickness and porosity, to enable healthier EOD conditions, do exist. It is possible to design a microporous separator that improves the dissolution, during recharge, of the PbSO4 film on the negative electrode that initially formed during a high-rate discharge. Irreversible sulphation of the negative electrode in a lead-acid battery under HRPSoC duty might be curbed by simple yet calculated changes to the separator sandwiched between two porous electrodes. The quantitative approach we have followed can be used to quickly evaluate thousands of different separator designs and determine a suitable starting point for experimental work. Figure 1