PNNL

Abstract

Cross-over is the transport of active species through the membrane between the positive and negative side of a battery. Such a process causes self-discharge and electrolyte imbalance that results in capacity and energy decay of redox flow batteries (RFBs) over long cycles. Accurate modeling of the cross-over and performance decay is thus important for improving RFB’s long-term performance and reducing maintenance costs. However, challenges exist because a) solving the coupled flow, reaction, and transport in both electrodes and membrane across multiple scales over long cycles is very time-consuming, b) mechanisms that control the cross-over at the membrane electrode interface are not clear, and c) key parameters that control the cross-over are not widely available. To address these issues, we present a hybrid analytical and numerical model that combines a two-dimensional analytical solution to the active species in a vanadium RFB, a one-dimensional analytical model for the cross-over mechanisms, and a zero-dimensional numerical model for the concentrations of active species at cell outlet. By comparing the model with an experiment over 41 cycles (ca. 144 hours), the model reported an average voltage difference of 0.0089 V, an average time difference of 14 seconds per cycle (of 3.5 hours), a maximum relative difference for capacity and energy of 1.34% and 1.63% respectively. The model-predicted average concentrations for V$^{2+}$, V$^{3+}$, and VO$_2^+$ in the membrane are also of the same order (65% to 77%) of values compared to those reported in the literature. With the validated model, the effects on migration and convection on cell voltage, electrolyte imbalance, and net fluxes are further studied. The model reproduced similar behaviors in electrolyte imbalance as those observed in experiments and numerical models, and revealed the combined effects of cross-over, self-discharge, stoichiometry of side reactions, and Coulombic efficiency on electrolyte imbalance. In addition, the model demonstrates excellent computational efficiency which can simulate the 41 cycles (around 37,000 data points) within 3 to 4 seconds using a single-core processor. The demonstrated efficiency and accuracy for predicting cross-over and its impacts on cell voltage, capacity & energy decay, membrane concentrations, and electrolyte imbalance makes it a reliable and effective tool for holistic evaluation and optimization of the long-term performance of redox flow batteries.