Predicting operational capacity of redox flow battery using a generalized empirical correlation derived from dimensional analysis

The design and scale-up of a redox flow battery (RFB) can be aided by the presence of rational methods capable of predicting its operational capacity. Developing a generalized empirical correlation between dimensionless numbers composed of relevant geometrical and physical variables is one of the approaches to predict the operational capacity of a RFB being operated under specific conditions. Keeping the discharge time (t_d) as a dependent variable, this study utilized the fundamental principles of dimensional analysis to derive a series of novel and relevant dimensionless numbers namely, Theoretical Capacity Utilization (TCU) and Number of Volume Units (NVU). These dimensionless numbers along with Wagner Number (Wa), and Reciprocal of Damkӧhler number (RDa) were used to establish an empirical correlation between them. The derived correlation was experimentally validated for a vanadium redox flow battery (VRFB) by carrying-out a set of carefully designed experiments followed by application of predictive methods such as multiple linear regression. The validated correlation comfortably predicts the t_d of a VRFB within an error range of ±7% and was shown to be statistically adequate. Moreover, the correlation was also used to predict t_d for a few of extracted data of the published literature. The correlation developed herein accurately predicted t_d to within ±10% for the data set whose parameters fell within the ranges of the dimensionless numbers for which the correlation has been developed.