Effects of Deep Cycling on Lead Positive Plates

Classical models are not successful in describing discharge characteristics of a lead-acid battery when the current density is varied over a wide range. A model is developed in this work to overcome this lacuna by introducing into the standard models two mechanisms that have not been used earlier. Lead sulfate particles nucleate and grow on active materials of electrodes during discharge, resulting in coverage of active area. Increasing rate of discharge builds supersaturation of lead sulfate rapidly, and causes increased extents of nucleation and coverage. Electrodes behave almost like an insulator due to deposition of lead sulfate when active materials are converted to a critical extent, and this can stop discharge process. Influence of this mechanism is also rate dependent. The new model developed is tested against data on polarization behavior, and capacity drawn as a function of current. The model successfully predicts both polarization curves and Peukert behavior. The model is used to predict charge that can be drawn at a current after partial discharge at a different current. Model suggests that altering nucleation behavior can be useful in enhancing capacity available for discharge.Batteries are used at different discharge rates depending on the application and need. Often, the discharge rate may not even be constant during use. Models based on the physico-chemical processes occurring are the most reliable tools to describe performance, and for designing to meet criteria. Equations are derived from such models by combining with appropriate balance laws the rates of (a) charge transfer reactions, (b) diffusion and migration of ions, and (c) conduction of electrons. Tiedemann and Newman 1 state that fundamental knowledge of the rate of charge transfer reactions in a lead-acid battery is incomplete, and its description still remains empirical. In view of this, the following generic form of Butler-Volmer equation is widely used 1-4 for quantifying the rate of charge transfer reactions in a leadacid battery:Thus, physico-chemical models mainly need three parameters for each electrode. These are (i) the exchange current density, i re f o , (ii) the surface area of active material per unit volume of the electrode in a fully charged battery, a o , and (iii) a coverage factor, F, which is the fractional decrease in the area of active materials during discharge. The first is a property of active materials, and their surface structure. The second is determined by the shape and size of particles of the active materials. F can be expected to be a function of, U , the fraction of the theoretical capacity of a fully charged electrode, Q theo , utilized. Q theo should depend only upon the dimensions of the electrodes and the volume fraction of electrodes' active material. Clearly, a o , i o and Q theo are expected to be independent of the rate of discharge. A model that accounts for all the physical and chemical processes should predict performance of the battery at all the discharge rates when these physically realistic...

Section: Resultssupporting

confidence: 91%

Section: Model Equationsmentioning

confidence: 99%

Modeling of Effect of Nucleation Rate and Electrodes’ Resistance on Discharge Characteristics of Lead-Acid Batteries

Gandhi

2015

“…For a given value of AGv (i.e., degree of supersaturation), we can see that the surface energy contribution (first term on the right side of Eq. [14]) is dominant at small r and for large r the volume contribution to the free energy of the cluster is dominant. There exists a maximum value of AG 2 The equation nb= 0 is a consequence of the boundary condition that the solution is saturated in lead ions at this point--since the solution is not oversaturated nucleation and precipitation of PbSO4 cannot occur.…”

Section: Otmentioning

confidence: 96%

“…The model presented here can predict the number of PbSO4 particles nucleated as a function of discharge rate, which can ultimately determine the electrode capacity (1,14). The number density is a function of initial acid concentration and temperature, as well as discharge current density (1); however, the scope of this work will be limited to the effect of discharge rate.…”

mentioning

confidence: 99%

Nucleation of Lead Sulfate in Porous Lead‐Dioxide Electrodes

Bernardi

1990

A one‐dimensional mathematical model of a porous lead‐dioxide electrode is described and used to investigate lead‐sulfate nucleation and growth during discharge. Derivation of a nucleation rate expression that is based on classical, heterogeneous nucleation theory is outlined. An electrochemical kinetic expression is derived based on a reaction mechanism involving elementary steps, and concentrated ternary electrolyte theory is used in formulating material‐transport equations. Nucleation and electrochemical kinetic parameters are estimated by comparison of model results with experimental results available in the literature. The interplay of nucleation and growth kinetics of lead sulfate is responsible for the initial minimum in the voltage‐time curve that is commonly observed during constant‐current discharge. The model simulates the voltage minimum, which is referred to as the coup de fouet, and calculates the degree of lead‐ion supersaturation, the number density of lead‐sulfate particles, and the free energy of formation as well as the size of critical nuclei. The model also predicts a disappearance of the voltage minimum with the addition of seed particles for lead‐sulfate nucleation, which is experimentally observed. The satisfactory agreement between model and experimental results confirms that the voltage dip is caused by a temporary oversaturation of lead ions during discharge and supports the proposed theoretical approach.

“…9͒ and, consequently, a SOC Ͼ 10% could be achieved before the voltage lid is reached. 16 Also, a partial charge to a lower SOC could be significantly shorter than the 2 h theoretical value for a full charge. …”

Section: Discussionmentioning

confidence: 92%

Study of Charge Kinetics in Valve-Regulated Lead-Acid Cells

Bernardi

Ying

Watson

2004

Model predictions of half-cell voltages, current, and gassing behavior are compared to experimental results of valve-regulated lead-acid ͑VRLA͒ cells to elucidate the charge mechanisms. Good comparisons of experimental Pb half-cell voltages with model predictions confirm the importance of liquid-phase Pb 2ϩ transport early during charge. In the latter stages of Pb-electrode charge, limitations in the PbSO 4 dissolution rate are more important than those of Pb 2ϩ transport and control charge behavior. Model predictions with an analogous mechanism for the PbO 2 electrode ͑i.e., involving dissolution and Pb 2ϩ transport͒ were not consistent with the charge polarization behavior, since comparisons of experimental half-cell voltages with model results were poor. Satisfactory comparisons with a model that incorporates a solid-state PbO 2 charge mechanism confirmed the insignificance of dissolution and transport in PbO 2 charging. The good agreement between model and experimental current behavior during the constant-voltage portion of charge support our conclusions regarding the electrode charging mechanisms. Conditions under which to expect charging difficulties as well as improved charge regimes are also discussed. The model also predicted the characteristic double-peak gas-flow behavior seen when charging VRLA cells with constant current to a specific voltage lid. The first peak is due to the onset of significant amounts of O 2 generation even though the internal residual gas is dominantly H 2 . The second peak is due to the onset of H 2 evolution.