A method is presented for predicting shunt currents in stacks of undivided and divided bipolar plate cells. The method is an efficient way of solving the coupled sets of algebraic equations that arise from using circuit analog models to represent the current paths in stacks of undivided or divided bipolar plate cells. These algebraic equations can be ei- ther linear or nonlinear depending upon the current-potential relationships used in the model (i.e., nonlinear circuit ele- ments can be included). The method is used to show the importance of including nonsymmetrical resistances and nonlinear circuit elements in the models. Also, the method is used to predict the shunt currents for a nine celt stack of pilot plant scale bipolar plate, membrane chlor-alkali cells. It is shown that these predictions agree qualitatively with measured values. Finally, the method is used to predict the shunt currents for stacks of 60 and 120 of these cells.
A mathematical model is presented for a zinc/bromine flow cell. The model includes a thin porous layer on the bromine electrode and a porous separator. The independent parameters of the porous layer are defined and their effect on cell performance during charge and discharge is investigated. The dependence of the round-trip energy efficiency on the thickness of the porous layer and mode of discharge is presented. The predictions of the model show that a maximum round-trip energy efficiency of 70% should be possible under the design conditions considered.
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
A previously presented parallel plate electrochemical reactor model with multiple electrode reactions is extended so it satisfies a material balance closure test for consistency, which is achieved by reformulating the previously presented methods used to calculate the average concentration and average current density. This model is simplified and referred to as a one step model by assuming that the current density along each electrode is fixed. The one step model provides a qualitative evaluation of cell performance and adds insight into understanding of the previous model, while requiring only 1/40th the computational time. The models are compared using a hypothetical case of the electrowinning of copper from a chloride solution. For the case of small aspect ratios (S/L), the models show that a set of the independent parameters for the system are cell potential (E//c//e//l//l), electrode area per reactor volume (1/S), and residence time (L/v//a//v//g).
A mathematical model is presented for a system comprised of a parallel plate electrochemical reactor (ER) and a continuous, stirred-tank reactor (CSTR) under both total and partial recycle. The model is used to predict the time dependent behaviour of the electrowinning of copper from an aqueous, hydrochloric acid solution. The model includes many important aspects of an ER/CSTR system which have been neglected previously. These aspects are the kinetics of electrode reactions, the electroneutrality condition, three mass transfer processes for ionic species in the electrolyte (diffusion, ionic migration, and convection) and the electrode gap in the ER, and the inclusion of a true CSTR in the recycle stream.
A mathematical model of a parallel plate electro-chemical cell with multiple electrode reactions, a separator, and a homogeneous bulk reaction is presented. The model is based on the Zn/Br//2 redox couple and can be used as an aid for the design of an efficient rechargeable storage battery. It is shown that four independent variables exist for the system at a fixed temperature - the effective separator thickness, the residence time, the channel width, and the cell potential. Performance criteria of interest for the Zn/Br//2 battery are defined. Predictions of performance improves as the effective thickness of the separator is increased, despite the associated greater cell resistance. It is also shown that a change in the residence time over the range considered has little effect on cell performance.
