The Vanadium Redox Flow Battery: an Asymptotic Perspective

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

“…As in [16], we consider a model geometry consisting of positive and negative porous flow-through electrodes and a proton exchange membrane, as shown in Fig. 2.…”

“…In addition, we assume that: the geometry is two-dimensional; the cell is isothermal; the membrane is fully humidified; H + ions can cross over the membrane, but all other ions cannot; the dilute-solution approximation is valid; the porosities of each electrode are constant and identical. The rationale behind these assumptions is given at length in [16], and therefore not repeated here.…”

“…In general, the models in question consist of a system of partial differential equations that describe the transient mass, momentum and charge transport that occur in the processes mentioned above [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], and invariably require numerical solution. However, recent work by Vynnycky and Assunc ¸ão [16] demonstrated that a standard and often-used VRFB model could be reduced asymptotically to give a much simpler set of equations which had a quasi-analytical solution; moreover, the reduced model was found to require around 250 times less computational time than the original one. Having said that, the model considered only the global mechanism described by reactions (1.1) and (1.2), which makes sense in light of the uncertainty in the kinetics and a lack of characterization of material parameters.…”

“…Having said that, the model considered only the global mechanism described by reactions (1.1) and (1.2), which makes sense in light of the uncertainty in the kinetics and a lack of characterization of material parameters. Nevertheless, other phenomena are also believed to be at play: oxygen and hydrogen evolution via the gas-evolving side-reactions [4,5,17] 2H 2 O + 2e − ⇋ H 2 + 2OH (hydrogen evolution) , 2H 2 O ⇋ O 2 + 4e − + 4H + (oxygen evolution) ; thermal effects [2,[10][11][12][13]; acid dissociation [9,18,19]; vanadium crossover [9], whereby V 2+ and V 3+ ions are transported from the negative electrode across the membrane Thus, it would be of interest to see if any or all of these, amongst others, can be incorporated into the asymptotic framework of [16], especially in view of the computational advantage of doing so. In this light, we focus in this paper on the dissociation of sulphuric acid (H 2 SO 4 ), as this is the mechanism that is included in the VRFB starting model available in the commercially available finite element software Comsol Multiphysics [20].…”

“…In Sect. 2, we formulate a transient twodimensional (2D) model for VRFB operation, extending the description in [16] to include the dissociation of sulphuric acid; in Sect. 3, the governing equations are nondimensionalized.…”