Optimization of Electrochemical Flow Capacitor (EFC) design via finite element modeling
Graphical abstract
Introduction
The Electrochemical Flow Capacitor (EFC) is one of the promising candidates for electrochemical energy storage (EES) for grid-scale applications [1]. EFCs work by charging and discharging carbon particles, which act as electrodes in a liquid electrolyte (the so-called slurry), forming a double layer of charges close to the electrode and electrolyte interface. EFC technology shares the traits of both supercapacitor and flow batteries. The architecture of EFC is similar to flow batteries and supports the scalability of energy storage capacity, while the energy storage mechanism is identical to supercapacitors [1]. Ideally, the energy is stored in the Electric Double Layer (EDL) of charges at the electrode-electrolyte interface and not through inherently slower faradic processes. A recent report proves the coexistence of faradic and non-faradic reactions in electrochemical cells [2]. The EFC is also capable of working in continuous operation; the charged slurry from one cell can be fed to another cell following the reverse process to recover the charge instantly [3].
The schematic of a single EFC cell is shown in Fig. 1. The architecture of a basic cell consists of two flow channels and respective Current Collectors (CCs). An ion-permeable membrane between the flow channels allows the flow of ionic current while preventing electronic current. The applied voltage polarizes the uncharged slurry, introduced from the inlet, and the ions from the electrolyte phase, which are electrostatically attracted to the counterion at the electrode, interface to form an EDL of charges.
The expected performance of EFCs makes them a viable solution for large-scale energy storage [4,5]. However, there is a lack of detailed scientific literature for primary development, even if using slurry in electrodes already for different applications [6], [7], [8], [9], [10]. Carbon black slurry used in an electrochemical reactor at different flow rates demonstrated convincing results for oxidation and degradation of hazardous compounds for wastewater treatment [11]. The intensive electric field (1.2 MV/m) in the microchannel due to external polarization disturbs the translational path of the charged particle across the channel in the two-phase dynamic system [12], [13], [14], [15], [16], [17]. Gravity affected fluidized bed electrodes were expected to increase the electronic conductivity of the slurry. Still, it exhibited lower values than the slurry alone because of the unclear transport mechanism. Spherical-shaped carbon particles were optimal for interface activity in EFC as compared to any other anisometric particles because of low viscosity values in the slurry [18]. The conductivity of the activated carbon in the suspension also influences the interaction of particles at the boundaries of flow channels [19]. Three-dimensional reticulated porous carbon in a slurry enhanced the charge percolation network and power density ten folds [20]. The device performance was affected by active adsorption sites during the static operation mode; while in flowing operation mode, electronic conductivity was much more critical than adsorption sites [21]. The flow rate of the suspension in the flow channels and their geometrical designs are the essential parameters that, through optimization, enhance the cell performance. The CC active surface area in contact with the carbon surface is also vital for EDL formation in supercapacitors. The electrochemical impedance spectroscopy of modified aluminum current collectors showed that increasing the active surface area causes a significant decrease in the internal resistance [22]. This internal resistance also reported as the potential dependent later for stainless steel current collectors forming a passive oxide layer in aqueous electrolyte [23]. The flowable slurry with a carbon concentration of 5 mg/ml assisted with 3 wt% of Carboxymethyl Cellulose (CMC) in aqueous medium achieved the capacity of 0.3 F/L, yielding 7 mWh/Kg of energy density [24]. The redox reactions of quinonic/hydroquinonic compounds in aqueous slurry electrolytes with impregnated carbon beads (9.8 wt%) showed a drastic increase in the energy density in the capacitor. Under static operation, the energy density of the slurry electrolytes was 20 Wh/kg at a power density of 38 W/Kg [25]. The experimental results highlighted the need for a deeper understanding of the charge transport mechanism in slurry electrodes.
EFC models based on the resistance-capacitance circuit analog studied by C. R. Dennison [26] shows that most of the charging phenomenon occurs near the boundaries of the flow channels. At a flow rate of 8 ml/h, the state of charge difference ranged from 71% near the current collector to 21% near the separator, providing the evidence of the material underutilization [26]. The modeling of half cells of EFC attempts also predicted the considerable difference in the resistance offered in the cell due to the static or flowing nature of the suspension [27,28]. The model combined the linear current collectors parallel to the separating membrane to study the charge transfer during contact of particles with the current collector [28]. Despite all the modeling studies in the past about the flowing slurry and charge percolation, no model addressed both flow channels simultaneously. The change of the geometrical design of the flow cell and its effects on the performance of the EFC device cannot be understood on experimental results alone.
In the present work, the macroscopic model of the geometrical design sensitivity of a full EFC with high surface area carbon as an electrode was investigated to evaluate the capacitive charge storage performance, the ionic transport mechanisms, and its limitations. The approach in the following research characterizes the combined simulation and experimental work that exploits the geometrical design sensitivity accomplished by parameter estimation with optimization methods to understand the ionic transport limitations and mechanisms in the device.
Section snippets
Used materials and experimental setup
In the experimental analysis, the prototype consisted of two stainless-steel flow channels supported by Teflon (Fig. 1b) and separated by an ion-conducting cellulose membrane. The thickness of the membrane was 150 µm, with each flow channel 5 mm wide. The charging of the flowable slurry occurred in tubular stainless-steel CCs. The length of each column of the flow channel was 120 mm, and about 100 mm2 of the membrane was in direct contact with the slurry.
The flowable slurry was a suspension of
Validation and parameter estimation
The geometry used for the optimization of the modeling parameters was analogous to the experimental geometry. The ionic conductivity, k obtained by using diffusion coefficients and concentrations in Eq. (6) is 111.2 mS/cm. The presence of the slurry electrode may affect the diffusion coefficient slightly, but the volume loadings of electrode material and electrolyte concentration are low enough to leave the diffusion coefficient unaffected. The specific surface area (smaller than 1000 cm2/cm3)
Conclusion
A mathematical model based on the finite element method has been designed to study the temporal evolution of the capacitive current and geometrical design sensitivity of the EDL flow capacitor. The model was used to investigate the effects of geometrical shape and depth of flow channels on the electronic current density distribution, transport of electrolytic ions in the flow channels, and the double-layer saturation on the carbon surface. The geometry with circularly-shaped flow channels
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work has been supported by Estonian Research Council grant # IUT 20-14, PUT-1149, PUT-1372, Information Technology Foundation Education (Hariduse Infotehnoloogia Sihtasutus, HITSA), Estonian Centre of Excellence in ICT Research (EXCITE), Graduate School of Functional Materials and Technologies (GSFMT) and European Regional Development Fund in University of Tartu, Estonia.
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