Implementation of Porous Media Flow Model in Sodium Sulfur Battery Simulations

Sodium sulfur batteries are comprises of liquid electrode materials suspended in porous media. The sodium anode and the sulfur/sodium-polysulfide cathode are separated by a solid electrolyte made of beta-alumina or NASICON material. Due to the presence of porous media, capillary pressure and the resulting capillary action become important. Because of the exponential dependence of capillary pressure on wetting phase saturation, sharp concentration gradients are possible between the inert gas and the sulfur/sodium polysulfide liquid within the cathode. These gradients may result in areas of high electrical potential variation leading to increased reaction rates which in turn can cause overconsumption of sodium in the cathode during discharge, thus preventing sodium from penetrating the entire depth of the cathode. During charge, high reaction rates cause sulfur to accumulate on the electrolyte surface at a rate faster than the sodium-polysulfide can displace it producing an insulating effect. Both of these occurrences can lead to even higher potential variations, which can lead to decreased efficiency and even cause failures due to effects of overheating.

A porous media flow model is implemented into a three-dimensional, time dependent, multiphysics model for sodium sulfur batteries in order to study the aforementioned phenomena. Transport equations for charge, mass and heat transport are discretized using the finite volume method and then solved simultaneously in a time marching fashion. Properties required for solving the transport equations, including fluid density, heat capacity and ionic conductivity, are calculated and updated at each grid location as a function of time based on the volumetric content and phase of each species within each control volume.  Electro-chemical boundary conditions range from prescribed voltage to external circuitry, including resistance, power consuming and power producing loads (for the purpose of charging). Mass transport is coupled with charge transport via Faraday’s law. Darcy’s law is used to model capillary action within the porous media between the wetting phase (liquid) and non-wetting phase (inert gas). The porous media model is coupled with the continuity equation and with a separate diffusion equation which is solved only within the liquid phase. The porous media model has been verified and validated by simplified analytical solutions and numerical results from similar models found in the literature. This validated model is being applied to sodium sulfur batteries currently. A comparison study will be performed to analyze the importance of porous media effects in multiphysics sodium sulfur battery modelling.