Concentrated Solution Model of Transport in All Vanadium Redox Flow Battery Membrane Separator

Renewable energy sources such as wind, solar and tidal energy typically suffer from intermittency. One possible solution to overcome this issue is to use energy storage. Among different technologies, redox flow batteries (RFB) are considered as a suitable candidate. There are currently several types of RFBs under development, each employing different redox couples. One of the most promising types is the all-vanadium redox flow batteries (VRFB) as originally conceived by Skyllas-Kazacos and coworkers [1]. In contrast to conventional batteries such as lead-acid storage cells, for the VRFBs, the energy is stored externally in two reservoirs containing different redox couples for anolyte (V(II)/V(III)) versus catholyte (V(IV)/V(V)) where the reactants flowing across the electrodes enter from these reservoirs to the electrochemical cell with a porous carbon based electrode, and the electrolytes in the two compartments are separated by an ion-selective membrane.

In order to optimize and improve the VRFB performance; mathematical modeling can be utilized. A good review of these modeling studies  has been reported by A. Z. Weber et al. [2]. In general, the models developed are based on approaches adopted from polymer electrolyte fuel cell modeling and have common assumptions. In all of these models the dilute solution approximation has been utilized for species transport in the electrolyte. Therefore, the motivation for this work is to develop a performance model for VRFBs based on a comprehensive description of mass, charge energy and momentum transport and conservation with concentrated solution theory.

Concentrated solution theory has its basis in irreversible thermodynamics and Maxwell-Stefan diffusion [3]. Solute-solute interactions are included and the theory accounts for transport by diffusion, migration and electrosmotic drag without the need for viscous- or pressure-driven terms. For ion-exchange membranes, since the distinction between solute and solvent is unclear, it is necessary to apply the concentrated solution theory for modeling studies [4]. The equations for material balance, current flow, and electroneutrality remain valid for concentrated solutions, but the flux equation requires modification [5].

A comprehensive review of mathematical modeling of electrokinetics in a concentrated solution has been provided by Bazant et al. [6]. 

Also, detailed model validation is important to ensure veracity of the model assumptions and formulation. Besides charge/discharge cycle validation, we will discuss two additional techniques which provide through-plane and in-plane resolution for detailed model validation. In the first technique, an in-situ local potential measurement using micro potential probes were prepared with Pt materials and the local redox potential measurement was conducted by inserting these probes among multiple layers of carbon paper electrode. This technique was applied by Q. Liu et al. for the positive side of VRFBs [7]. In the second technique, an in-situ methodology will be introduced where the in-plane current distribution using a printed circuit board has been obtained in an operating VRFB.  Together these approaches provide much greater detail for model validation than just charge-discharge curves typically used.

References 

[1] M. Skyllas-Kazacos, M.H. Chakrabarti, S.A. Hajimolana, F.S. Mjalli, M. Salleem, Electrochem. Soc., 158 (8) (2011) R55–R79.

[2] A.Z. Weber, M.M. Mench, J.P. Meyers, P.N. Ross, J.T.Gostick, Q. H. Liu, Journal of Applied Electrochemistry, 41 (2011) 1137–1164.

[3] X. Li, H. Zhang, Z. May, H. Zhang, I.Vankelecom, Energy Environ. Sci., 4 (4) (2011) 1147–1160.

[4] T. F. Fuller, Solid-polymer-electrolyte fuel cells, Lawrence Berkeley Lab., USA, 1992.

[5] J. Newman, K. E. Thomas-Alyea, Electrochemical systems, 3rd Edition. Hoboken, NJ, John Wiley & Sons, Inc., 2004.

[6] M. Z. Bazant, M. S. Kilic, B. D. Storey, A. Ajdari, Advances in Colloid and Interface Science., 152 (2009) 48–88.

[7] Q. Liu, A. Turhan, T. A. Zawodzinski, M. M. Mench, Chem. Commun., 2013, 49, 6292.