Elsevier

Journal of Power Sources

Volume 216, 15 October 2012, Pages 489-501
Journal of Power Sources

Thermal modelling of battery configuration and self-discharge reactions in vanadium redox flow battery

https://doi.org/10.1016/j.jpowsour.2012.06.052Get rights and content

Abstract

During the operation of vanadium redox flow battery, the vanadium ions diffuse across the membrane as a result of concentration gradients between the two half-cells in the stack, leading to self-discharge reactions in both half-cells that will release heat to the electrolyte and subsequently increase the electrolyte temperature. In order to avoid possible thermal precipitation in the electrolyte solution and prevent possible overheating of the cell components, the electrolyte temperature needs to be known. In this study, the effect of the self-discharge reactions was incorporated into a thermal model based on energy and mass balances, developed for the purpose of electrolyte temperature control. Simulations results have shown that the proposed model can be used to investigate the thermal effect of the self-discharge reactions on both continuous charge–discharge cycling and during standby periods, and can help optimize battery designs and fabrication for different applications.

Highlights

► Precipitation of vanadium ions occurs at low or high electrolyte temperature. ► Vanadium ion diffusion leads to self-discharge and capacity loss. ► Self-discharge reactions release heat into the supporting electrolyte. ► Mathematical modelling can help with predicting the variation in electrolyte temperature and the loss of capacity. ► Temperature and rebalancing control systems can be developed based on the model to optimize the battery operation.

Introduction

The all-vanadium redox flow battery (VFB) is a typical electrochemical energy storage system which was initially invented by Skyllas-Kazacos and co-workers at University of New South Wales (UNSW) dating back to the 1980s [1], [2]. Studies on the VFB began at UNSW and subsequently proceeded in Japan, UK, China and elsewhere covering a wide range of topics. With a number of successful field trials and applications around the world, the development of VFBs has to date reached commercial fruition and been regarded as one of the most suitable large-scale energy storage solutions. The VFB stores energy chemically in external reservoirs, while the redox reactions take place at inert electrode in the cell stack. The capacity and the power rating can therefore be independently designed by selection of stack size for the required power rating and electrolyte volume for kWh capacity. Other than its flexibility for scale-up, most of the competitive features of the VFB are associated with the use of the same element in both half-cells, thus effectively eliminating the cross contamination over extended charge–discharge operation. Several other major advantages include high energy efficiency, long life cycle and low capital cost.

Despite the elimination of cross contamination in the vanadium redox flow battery however, the diffusion of different ions across the membrane inevitably takes place due to the concentration gradients between the two half-cell electrolytes during charge–discharge cycling. While the crossover of hydrogen ions carries the current and helps facilitate the electron transfer reactions, the diffusion of the different vanadium ions will give rise to self-discharge which subsequently leads to capacity loss. Such a loss of capacity in the VFB can be restored by simply remixing the electrolytes periodically. In addition to the capacity loss however, the self-discharge processes also release heat which can accumulate in the cell stack and increase the electrolyte temperature. Although flow batteries have an advantage over conventional batteries of having a built-in heat exchanger that can extract heat from the cell stack during electrolyte circulation, severe heat accumulation in the cell stack could occur during standby periods when the pumps are switched off, or during slow charge–discharge cycles when there is an inadequate electrolyte flow rate. As a result, thermal precipitation of VO2+ in the positive electrolyte could occur if the electrolyte temperature exceeds a certain limit that depends on the vanadium electrolyte concentrations [3]. Any thermal precipitation of VO2+ in the positive electrolyte would not only further contribute to capacity loss, but potential blockage of the electrolyte channels could restrict flow into the cells, leading to premature voltage cut-off during operation.

Apart from the thermal precipitation of VO2+, studies also have shown that V2+ could be precipitated in the negative electrolyte at lower electrolyte temperatures, depending on the vanadium concentration used. The electrolyte temperature therefore, plays a crucial role in the performance of the VFB. Varying electrolyte temperature can influence the rate of ion diffusion associated with the membrane property which, in turn, impacts on the amount of heat released by the self-discharge reactions. In practice, the electrolyte temperature can be significantly affected by the surrounding temperature, battery materials and design. It is therefore, vital to manage the electrolyte temperature within the optimal range by designing the batteries and choosing the electrolyte composition to suit the climatic conditions for the specific installation. This is currently achieved by diluting the vanadium electrolyte concentration and limiting the operational state-of-charge range of the battery to prevent any one of the vanadium oxidation states from exceeding their respective solubility limit over the expected temperature range in the specific location. These actions often result in an unnecessary reduction in energy density of the system however, leading to greater footprint or building space. By implementing a sophisticated temperature control system, however, these problems can be avoided.

Mathematical modelling of the all-vanadium redox flow battery can assist in analysing the battery performance under different operating and climatic conditions for the purpose of optimal battery design and control system development. Electrochemical modelling of the cells was initially carried out by Walsh et al., followed by a number of extended models on different aspects [4], [5], [6] such as concentration and temperature gradients within the cell. While these models are useful for predicting cell voltage profiles, they are not suitable for studying the dynamic control or operation of VFBs. These models also neglected the effect of ion diffusion and hydrogen evolution on capacity loss during extended cycling. Skyllas-Kazacos and co-workers recently presented a dynamic model capable of revealing the capacity loss caused by ion diffusion [7] and gassing side reactions by incorporating Fick's law into the material balance equations [8]. Such a model may help the implementation of periodic electrolyte rebalancing. A thermal model of the VFB was also proposed to investigate the variations in electrolyte temperature during extended charging–discharging cycling, as affected by the heat generated inside the stack and exchanged with the surroundings [9]. This model provides flexibility for different VFB designs and environmental conditions and its potential to be employed in the development of a model-based controller for the VFB systems makes it viable to eliminate the precipitation by controlling the electrolyte temperature during operation. The heat released by the self-discharge processes due to the diffusion of vanadium ions across the membrane was not considered in development of the above thermal model however, nor was the impact of electrolyte temperature on the rate of ion diffusion taken into account in the previous study on capacity loss.

In this paper, the thermal model is further developed by coupling the energy balance of the self-discharge reactions with the mass balances that reveal the crossover of vanadium ions through the membrane. Thus, the interaction of vanadium ion diffusion and self-discharge heat is correlated. This coupled model is able to not only predict more precisely the electrolyte temperature, but indicate the level of capacity loss as well. Furthermore, such a model will be useful for both electrolyte temperature control and capacity restoration management that can help optimize the battery performance and enhance the efficiency.

Section snippets

Mathematical model development

In this section, the self-discharge reactions caused by ion diffusion are firstly discussed in detail, followed by the assumptions made in effort to assist in developing the dynamic model. Mass and energy balances are then applied to model the concentrations of vanadium ions in each of the four oxidation states and the electrolyte temperature in both the stack and tanks. The interaction of the electrolyte temperature and the rate of diffusion is linked by means of introducing a serious of

Parameters

The specification of the VFB and the parameters employed in the simulations are listed in Table 2. The VFB system consisting of 19 identical cells in the stack has a nominal rating of 2.5 kW/15 kWh. The electrolyte solutions of each half-cell have a volume of 250 L calculated on the basis of an average cell voltage of 1.4 V and a concentration of 2 M vanadium in 4.4 M total sulphate, being separated by a Nafion membrane 115 [14]. It is assumed that the temperature dependence of the diffusion

Conclusion

A thermal model coupled with mass balance equations is proposed to investigate the thermal effect of self-discharge on electrolyte temperature. The energy balance has incorporated the heat generated by the self-discharge reactions whose rate of reaction is coupled with the diffusion term in mass balance equations. The diffusion coefficients in mass balance equations are also considered to be a function of the stack temperature from the energy balance. In this way, the heat of self-discharge

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