Material Balance Modification in One‐Dimensional Modeling of Porous Electrodes

Abstract

The material balance used previously in one-dimensional mathematical models of porous electrodes is invalid when there is a nonzero volume change associated with the reaction. It is shown here how the material balance should be modified either to account for a loss in volume, or to account for an inflow of electrolyte from the header into the active pores. A one-dimensional mathematical model is used to illustrate the effect of this correction on the prediction of the delivered capacity and the electrolyte concentration in a lithium/thionyl chloride primary battery.

Computational Fluid Dynamics Modeling of a Lithium/Thionyl Chloride Battery with Electrolyte Flow

“…1. The system is identical to the one studied most recently by Jain et al 5,6 Basically, the cell consists of a lithium foil anode and LiCl film, a separator (glass matting), and a porous carbon cathode support with the electrolyte being lithium tetrachloraluminate (LiAlCl 4 ) salt dissolved in the thionyl chloride (SOCl 2 ). The passive lithium chloride (LiCl) film forms on the lithium foil due to lithium corrosion, namely 4Li ϩ 2SOCl 2 r 4LiCl(s) ϩ SO 2 ϩ S [1] S0013-4651(99)06-102-9 CCC: $7.00 © The Electrochemical Society, Inc.…”

“…Applying the general species conservation equation in Table I of Wang et al 9 to the species of interest in the Li/SOCl 2 system, one obtains [4] for Li ϩ , and [5] for SOCl 2 . Here, ٌ ϭ ∂/∂x i ϩ ∂/∂y j is for the two-dimensional Cartesian coordinate system, c is the concentration of a species in the electrolyte, and j is the volumetric reaction current resulting in production or consumption of the species.…”

“…It is also interesting to note that the modified one-dimensional model of Jain et al, 5,6 which assumes that the electrolyte flows down from the head space into the cathode, produced nearly identical discharge curves. This fact prompts us to show that the present twodimensional model is reduced identically to the model of Jain et al 5,6 under one-dimensional assumptions. Appendix B describes this derivation in detail and concludes that the two key equations in Jain and Weidner's one-dimensional model 5 are indeed recovered.…”

“…Other modeling efforts employed concentrated solution theory and porous electrode theory in the various regions of the cell (e.g., separator, porous cathode) to develop one-dimensional models of the battery. [3][4][5][6] These models examined utilization issues at low to moderate currents, but they differ in how the excess electrolyte was treated.In the lithium/thionyl chloride cell, the solvent is also the reactant, and the volume it occupies is more than that of the reaction products. Therefore, more electrolyte is placed in the cell than can occupy the initial void volume of the separator and porous cathode.…”

Modeling Volume Change in Dual Insertion Electrodes

“…18,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] In many of these models, the dimensions of the porous electrode are often assumed constant and any volume changes in the active material result in only porosity changes. 21,22 Gomadam and Weidner 18 developed a model to allow both porosity and dimensional changes to occur. However, they assume an a priori split between these two.…”