On the significance of sulphuric acid dissociation in the modelling of vanadium redox flow batteries

Abstract

A recent asymptotic model for the operation of a vanadium redox flow battery (VRFB) is extended to include the dissociation of sulphuric acid—a bulk chemical reaction that occurs in the battery’s porous flow-through electrodes, but which is often omitted from VRFB models. Using asymptotic methods and time-dependent two-dimensional numerical simulations, we show that the charge–discharge curve for the model with the dissociation reaction is almost identical to that for the model without, even though the concentrations of the ionic species in the recirculating tanks, although not the state of charge, are considerably different in the two models. The ability of the asymptotic model to extract both the qualitative and quantitative behaviour of the considerably more time-consuming numerical simulations correctly indicates that it should be possible to add further physical phenomena to the model without incurring significant computational expense.

Appendix A: Model validation against experimental data from [3]

For the purposes of validating our model, we use experimental data from You et al. [3], who provide the cell potential as a function of state of charge for charging and discharging at 400 and 800 Am$^{-2};$ the comparison is shown in Fig. 10. The agreement is very good for the charging phase, although less so for the discharging phase, where it is in line with the comparison against this experimental data made by Chen et al. [11], albeit it only at 400 Am$^{-2}$. It can be noted that You et al. [3] also presented a model which gave the best agreement of all at both 400 and 800 Am$^{-2}$, although a shift in cell potential of 140 mV was required to achieve it; here, we have not employed any shift. Note also that we have used the same model data as in [3], although with the value for active surface area—A in equations (2.11) and (2.12)—given in [9].

Fig. 10

Cell potential, $E_{\text {cell}}$, as a function of state of charge, SOC, during charge and discharge from experiments [3], the 2D transient model and the 2-term reduced asymptotic model at a current density, $i_{{\mathrm {app}}}$, of: a 400 $\hbox {Am}^{-2}$; b 800 $\hbox {Am}^{-2}$

Lastly, we point out that, even though the model is now being used for a completely different set of parameter values, and in particular for a much higher applied current density, the agreement between the results of the 2D transient model and the reduced asymptotic model remains very good.