Advancing electrochemical reactors for redox flow batteries through mathematical models and experimental diagnostics

Resumen

The global energy transition requires new power and energy systems integrated in society, earth and economy for the development of broad international frameworks for deep decarbonization. Clean energy technologies -¿ such as renewable energies and energy storage systems (ESS)-¿ have been adopted as the main strategy to power stationary and mobile applications in the future. Among the different energy storage systems, electrochemical ESS is poised to play a pivotal role in the energy transition, offering a wide range of round-trip efficiencies, costs, and energy-to-power ratios. Nowadays, a mix of battery solutions is available for widespread application, however this technology covers only 1.17% of the total global energy storage capacity. Redox flow batteries (RFBs) are prime candidates for stationary energy storage, enabling the widespread integration of renewable, yet intermittent, generation sources. Beyond the ability of offering frequency regulation services at different time scales, their unique capability to decouple energy and power makes them suitable for long discharge and storage times. Currently, several vanadium RFB plants have been installed worldwide. Despite its promising potential, this technology still faces technical and costs challenges that ultimately hamper and limit their economic competitiveness. To facilitate energy market penetration, the overall efficiency and economic competitiveness need further improvement. One strategy is to increase the electrochemical performance while decreasing the pumping power required to flow the electrolytes. Research efforts have focused on improving electrolyte chemistries, developing new materials for the electrodes and membranes, optimizing flow cell architecture and adjusting the operating conditions. However, the current generation of RFBs still lacks of appropriate reactor engineering and operating guidelines to achieve optimal system performance. Pursuant to this necessity, this PhD thesis aims to leverage relevant operational envelopes and advanced flow cell architectures for RFBs, aided by both experimental and numerical diagnostics techniques. In the first part of the thesis, a continuum macroscopic model of an electrochemical unit-cell of an all-vanadium redox flow battery (VRFB) is developed in two dimensions (longitudinal cross section of the flow cell). The model is built up in an isothermal and steady-state basis. All physicochemical phenomena occurring in the cell are included through comprehensive descriptions, integrating state-of-the-art descriptions with new features including local mass transfer coefficients for active species, sulfuric acid dissociation kinetics, and experimental parameters for the electrokinetics and electrolyte properties. The mass transport of species within the cell is locally defined using mass transfer coefficients as a function of the electrolyte local properties and velocity. The dissociation equilibrium of the sulfuric acid influences the species concentration (protons and sulphates) and overpotential impacting on the electrochemistry of the flow cell. For this reason, the sulphates balance, equilibrium rate constant and electroneutrality equation are integrated in the model. The electrokinetic parameters of the vanadium redox reactions in carbon electrodes acting as catalyst are measured. Furthermore, the electrolyte properties are characterized experimentally at different state of charge and total vanadium concentration. The electrochemical and fluid dynamic definitions in the model are coupled through the local velocity field. The model is validated using polarization, electrolyte conductivity, and open circuit measurements at different flow rates and states of charge without fitting parameters other than the electrode specific surface area. Once validated, new insights into the effects of operating conditions on every multiphysics affecting the flow reactor performance can be explored, enlightening potential operational strategies. This analysis enables the understanding of the distribution of local variables such as current density, overpotentials, active species concentration, and mass transport rates at different operating conditions. Controlling state of charge and flow rate can partly mitigate undesirable effects such as crossover, self-discharge and hydrogen and oxygen evolution. As a result, electrolyte imbalance and subsequent capacity decay can be alleviated. High flow rates and low state of charge during operation decrease the generation rate of parasitic hydrogen evolution. Operating under elevated flow rates reduces crossover, self-discharge and local deviations in mass transfer rates. Charging and discharging closely to the open circuit potential do not provide large power density, however, it alleviates undesirable phenomena that unbalance the battery. The sulfuric acid dissociation grade needs to be taken in account since it is demonstrated to be significantly displaced depending on the state of charge, causing big variations in proton and sulphates concentration affecting for example hydrogen evolution. Last, when operating at low flow rates, high variations in the transport of species occurring depending on the cell region. Thus, it is recommended to consider local mass transfer coefficients instead of an averaged value in these cases, and only at high flow rates (>30 mL min-1) this assumption can be valid for flow-through configurations. Subsequently, the model is extended to include non-isothermal effects. The energy balance equation is included in the model and all possible sources of heat are considered. The electrokinetic parameters are extended as local variables and function of temperature, using state-of-the art correlations. Besides, the electrolyte properties were measured at different operating conditions and state of the charge, and are included in the model as empirical correlations. The battery electrochemical performance and open circuit potential predicted by the model are validated experimentally using a climatic chamber to set different system temperatures through polarization and cell equilibrium potential measurements. After validation, thermal effects within the electrochemical flow cell are explored, with special emphasis on the impact of operating conditions on cell overheating. The different heat contributions to the total cell heating are deconvoluted and analyzed in every domain (negative and positive half-cell and membrane) and at different cell voltages. The most important contributions to cell heating are the Joule heating associated with the activation losses in the negative half-cell and the ohmic losses in the membrane. The entropic heat of the electrochemical reactions has a comparable contribution, with the negative half-cell having a remarkable dominant role. On the contrary, the heat generated from the displacement of the sulfuric acid equilibrium and self-discharge reactions take more modest values in both half-cells, with the latest being even neglectable in comparison with the rest of heat sources. In parallel, the electrochemical performance of the battery is evaluated at different system temperatures. While higher operating temperature enhances mass transport in the flow cells, the higher activation overpotentials negatively impact on the battery performance. As a consequence, increasing temperature enhances system performance up to an optimum found in 35¿C. The operation of the battery during charge, at low flow rates, and extreme cell voltages, is seen to exacerbate cell heating. Thus, we leverage high flow rates (e.g., 30 mL min-1) and operating cell voltages close to open circuit potential as an optimal pathway to operate the battery. When increasing the cell size, the cell overheating is found to rise proportionally, reaching increments of 0.63 K m-1. In addition, a new strategy to improve battery performance is proposed, consisting of operating the electrolytes with asymmetric temperatures. The highest performance is achieved when pumping the negative electrolyte at the lowest temperature (e.g., 5 ¿C) and the positive electrolyte at the highest temperature (e.g., 45¿C). Thus, the electrokinetics of both electrolytes are enhanced simultaneously, and the battery reaches higher current and power densities. This operating approach will need of external heat sources or sinks. A possible application to consider this strategy without additional energy expenditure could be the hybridization of flow batteries with heat storage systems based on geothermal heat exchangers. Overall, this VRFB model is a versatile and reliable tool that provides practical guidance for selecting optimal operating conditions in redox flow batteries implementing vanadium chemistry. A future extension to a dynamic model version can open more accurate pathway to predict charge-discharge cycles and battery imbalance over time. In the second part of the thesis, the impact of the flow reactor design on the performance of RFBs is investigated through fluidic and electrochemical techniques. Flow cell design studies are conducted to broaden the knowledge in this area and propose alternative concepts. A first systematic study is performed to compare several performance metrics of the flow reactor with six distinct flow field geometries based on conventional designs in combination with two electrodes with different microstructures. The elected flow fields for this study are a flow-through, serpentine and four different interdigitated (ID) flow fields consisting of a traditional ID design, ID with wide ribs, dense ID (large number of channels) and light ID (low number of channels). The two porous electrodes selected for the study are a carbon paper electrode and a carbon cloth electrode. The interaction between the flow field geometry and electrode microstructure is demonstrated to have a coupled influence on system performance. The electrode-flow field interaction strongly depends simultaneously on the dimensions and position of the channels that distribute the electrolyte and the type of microstructure of the porous electrode. The most critical factors to be considered during the engineering of the flow field are the type of induced flow -¿ in-plane, through-plane or flow-by-¿ and the dimensions of the flow channels -¿ channel and rib width, channel density, electrolyte exchange perimeter, and hierarchical and fractal structure. In parallel, the particular microstructure of each porous electrode material is determined by the pore size distribution, pore morphology, fibre alignment, and anisotropic ratio, which leads to materials holding unimodal and bimodal pore size distributions (PSD). The fluid dynamic analyses (i.e., pressure drop) and electrochemical characterization (i.e., polarization and impedance) provide a deep understanding of the physicochemical effects behind the coupled effects of the electrode and flow field. The results reveal the role of electrolyte exchange perimeter on the homogeneous reactant distribution and the importance of wide ribs for higher reaction volume accessibility. When balancing the electrochemical performance with the consequent pressure loss, promising performance trade-offs are found. Interdigitated flow fields are found to be more suitable for paper electrode microstructures with unimodal pore size distributions, whereas flow fields inducing mostly in-plane flows, such as flow-through, are the best combination for cloth electrode microstructures with bimodal pore size distribution. Moreover, interdigitated flow fields with wide ribs are found to be a potential combination for both paper and cloth electrodes, due to the higher reaction surface area accessibility and larger induced in-plane flow. Based on the knowledge acquired on the most convenient flow fields for carbon paper electrodes, the engineering of advanced lung-inspired geometries is developed by 3D printing methods for electrodes holding isotropic and unimodal PSD microstructures. Three distinct flow fields are studied in this work: an interdigitated used as a baseline, a lung-inspired design with two levels of branches and another lung-inspired design with three levels of branches. The flow fields are manufactured by stereolithography 3D printing and are covered with conductive coatings after (a first layer of silver paint is added followed by a final coat with platinum sputter coating). Similar electrochemical and hydraulic characterization is followed as in the previous study. Additionally, limiting current experiments are performed to obtain the mass transfer coefficients for each flow field combination. Moreover, numerical simulations of one half-cell are included here to understand better the underlying local physicochemical phenomena. The results reveal that using Lung-inspired flow fields, the electrolyte distribution in the electrode is more homogeneous leading to higher mass transfer coefficients, which is a consequence of the high electrolyte exchange perimeter and the specific geometry of this natural patterns. In the 3D numerical simulations, a more uniform concentration and current profiles are observed throughout the entire porous electrode. Furthermore, the streamlines reveal an enhanced electrolyte mix with more homogeneous velocity profiles, which support the improved mass transport rates observed in the experimental results. Lung 2L flow field with two level of branches achieves higher electrochemical performance than Lung 3L with three level of branches. This is a result of the wider ribs of Lung 2L and low channel contact area, which enables larger accessibility to the electrode reaction volume. This is supported by the simulations results where greater reactant consumption is observed from the concentration distribution results in the 3D electrode domain. When balancing the electrochemical performance with the pumping power required to sustain a certain electrolyte flow, lung-inspired flow fields with two level of branches is found to be the optimum selection. Lung 2L provides high current density at low pressure drop, demonstrating a performance trade-off more favourable than traditional interdigitated flow fields. The simultaneous beneficial effects of high electrolyte exchange perimeter, wider ribs, and low channel contact area that lung-inspired flow field provides, offer a promising pathway for next-generation flow field designs in redox flow batteries. Last, the optimal electrode thickness is studied for flow cell configurations with two prevailing flow fields and electrodes. A conventional interdigitated and flow-through flow field are selected together with a carbon paper and carbon cloth electrodes. The methodology followed to increase electrode thickness consists of stacking electrode layers. Similar experimental diagnostics are used to characterize the hydraulic and electrochemical performance. In this case, the understanding of the different performance metrics is aided by pore network modelling simulations in the 3D porous microstructure of the electrode. The experimental results show that stacking electrode layers alleviates pressure drop in flow-through configurations, whereas, in interdigitated flow fields it has a detrimental impact due to the increasing flow rate required to sustain a constant electrolyte velocity. Polarization measurements reveal that increasing electrode thickness enhances electrochemical performance driven by the beneficial impact of decreasing charge and mass transfer overpotentials. This results from the larger reaction electrode surface area and better distribution of species. However, when stacking electrode layers the ohmic overpotential becomes higher due to larger ionic and contact resistance. As a consequence, the competing effects of increased ohmic resistance and decreased charge and mass transfer overpotentials as more electrode layers are stacked, lead to an optimum of two layers of electrode for all cases in terms of electrochemical performance. However, depending on the electrode-flow field combination, the electrochemical performance gain quantified by the current density is improved in different magnitude. Although stacking electrodes increases the available reaction volume, pore network model simulations reveal that with thicker electrodes the electrolyte distribution and current density profiles are less uniform, which impact negatively on the electrochemical performance. The distinct interactions between electrode and flow field geometry are demonstrated to influence the optimal electrode thickness. When balancing the achievable current density and the involved pressure losses, using an electrode with two layers is posed as a facile pathway to increase the overall efficiency in flow cells with both paper and cloth electrodes and flow-through flow fields. In contrast, in cells with interdigitated flow fields, the low performance gain does not compensate for the higher pumping power required to sustain the increased pressure drop when adding electrode layers. Stacking commercial electrodes is proposed as a facile pathway to reach the optimal electrode thickness in RFBs, thereby improving the overall system efficiency. The development of a single-cell all-vanadium RFB model serves as a versatile tool for optimizing RFBs operation. The successful experimental validation of this model offers a reliable and facile pathway to predict cell performance under different geometries, materials and operating conditions. In parallel, the understanding and engineering of flow cell architecture concepts open new research lines and concepts for advancing the design of electrochemical flow reactors for future electrochemical technologies.