A Review of Mathematical Modeling of the Zinc / Bromine Flow Cell and Battery

Mathematical models which have been developed to study various aspects of the zinc/bromine cell and stack of cells are reviewed. Development of these macroscopic models begins with a material balance, a transport equation which includes a migration term for charged species in an electric field, and an electrode kinetic expression. Various types of models are discussed: partial differential equation models that can be used to predict current and potential distributions, an algebraic model that includes shunt currents and associated energy losses and can be used to determine the optimum resistivity of an electrolyte, and ordinary differential equation models that can be used to predict the energy efficiency of the cell as a function of the state of charge. These models have allowed researchers to better understand the physical phenomena occurring within parallel plate electrochemical flow reactors and have been instrumental in the improvement of the zinc/bromine cell design. Suggestions are made for future modeling work. The zinc/bromine (Zn/Br2) flow battery has received much interest as a rechargeable power source because of its good energy density, high cell voltage, high degree of reversibility, and abundant low cost reactants (1-4). Problems with the Zn/Br2 battery include high cost electrodes , material corrosion, the formation of dendrites during zinc deposition on charge, high self-discharge rates, unsatisfactory energy efficiency, and relatively low cycle life (400-600 cycles) (2, 4, 5). Experimental and mod-eling efforts have been conducted to alleviate these problems. Several companies, including Energy Research Corporation (ERC), Gould, and Exxon have developed this battery by building and testing various designs (1). The Exxon design (3, 6-8), which uses a corrosion resistant carbon-plastic composite material for the electrodes, a separator, and a second liquid phase to complex the bro-mine in the electrolyte to prevent it from participating in the self-discharge reaction, effectively deals with most of the problems mentioned earlier. The main concerns at present are to improve battery efficiency and increase cycle life (1, 2) without sacrificing the attractive low cost of the battery. The experimental approach for obtaining the design variables and operating conditions that yield acceptably high efficiencies and cycle lives can be time consuming and costly. Modeling the system can reduce the experimentation required by pointing out to the ex-perimenter the independent design parameters and how they can be changed to better the cell performance. * Electrochemical Society Student Member ** Electrochemical Society Active Member. Several mathematical models of the Zn/Br2 cell and a mathematical model of a stack of cells have been presented (4, 9-14). These models have provided researchers with a means to study the various aspects of the Zn/Br2 cell and gain a greater understanding of the physical phenomena affecting the performance of this battery. The models by Lee and Selman (9), Evans and White (14), and Van Zee et al. (12) provide predictions for many aspects of the Zn/Br2 cell and battery of interest to designers. These predictions include the current density distributions along the electrode surfaces, the overall battery efficiency, and round trip cell efficiencies. The models reviewed here are all steady-state models and macro-scopic in nature. Microscopic models which focus on dendrite initiation and growth during electrodeposition have also been presented (15-17) with one model by Lee (11) which combines a macroscopic model (9) of the Zn/Br2 flow reactor with a microscopic model describing dendrite growth. These microscopic models, which have contributed much to the understanding of dendrite growths and to the steps which can be taken to reduce their adverse effects, are kept separate from the macro-scopic models addressed here and have already been discussed elsewhere (11). Models of the Zn/Br2 cell and a stack of cells are based on the recirculation system shown in Fig. 1 and on the parallel plate geometry of an individual cell shown in Fig. 2. Aqueous electrolyte solutions containing reactive species (see Table I for a typical feed composition) are stored in external tanks and circulated through each cell in the stack. Each cell contains two electrodes at which