Mathematical Modeling of Electrochemical Flow Capacitors

Abstract

Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. Electrochemical flow capacitors are a recently introduced technology that has gained considerable interest for grid-scale energy applications.1,2 These devices work by charging and discharging the double layers that exist at the interfaces between immersed electronically conducting particles and the electrolyte solution in a flowable slurry electrode. After having their surfaces charged, these particles are then subsequently stored in external tanks where they are available to be pumped back through the cell during discharge. External storage of the charged slurry allows for decoupling of power and energy -tanks can be independently scaled to be as large as desired for a particular application.A schematic of an EFC is shown in Figure 1. The design consists of two half cells and their respective positive and negative current collectors. A membrane between the two half-cells prevents electronic charge transfer between the respective negative and positive halves but permits the exchange of ionic current. During charging, slurry is continuously pumped from separate tanks of uncharged particles through the positive and negative half cells. As the separate slurry streams flow through the cells, the double layer capacitances that exist at the interfaces between the particles and the solution are charged. The now-charged slurry particles are then directed into storage tanks where the charge can be maintained for later use during discharge.In general, EFCs have so far been limited to low current density operations (<10 mA/cm 2 ); design improvements must therefore be sought. This paper reports on a mathematical model with the goal of achieving design improvements. So far, mathematical models for electrochemical flow capacitors have been...

Characterizing Slurry Electrodes Using Electrochemical Impedance Spectroscopy

“…When using ferrous salts, solutions were made under a continuous nitrogen blanket and experiments were performed with the electrolyte under a continuous nitrogen purge to mitigate the air oxidation of ferrous to ferric iron. 37,38 All tests were conducted at room temperature (20)(21)(22)(23)(24)(25) • C). It was observed that when the volume fraction of the solid particles was above some critical concentration, there was no longer enough liquid in the slurry to fully wet all of the particles.…”

“…At low frequency, the current response tends toward the steady-state, DC charging value that can be predicted using available models. 24,25 Thus, even in the situation with a separator present, the Nyquist plot still returns to the real axis at low frequency (instead of having its imaginary component diverge to negative infinity as in the stationary case). The evolution of the Nyquist plot at intermediate frequencies is difficult to ascertain though as the advection-diffusion of surface charge combined with sinusoidal perturbations requires time-dependent, two-dimensional numerical simulations of the governing slurry electrode equations.…”

“…23 However, this advective capacitive current (also called "hydraulic current" 23 ) has multi-dimensional characteristics (e.g. boundary layers of overpotential that grow as the slurry flow proceeds downstream along the electrode 24,25 ) that make analysis with 1-D equivalent circuit models problematic. Thus, impedance analysis of these situations is difficult.…”

Current Density Scaling in Electrochemical Flow Capacitors

“…In our earlier work, 6 the capacitive Prandtl number of a typical candidate EFC slurry was shown to generally be a very large number; this suggests that the overpotential boundary layers grow much more slowly than the hydraulic boundary layers with respect to distance along the electrode. The challenges of achieving satisfactory current densities in an EFC is therefore similar to the challenges encountered in heat transfer into high Prandtl number fluids -possible remedies of which include designs that break up the overpotential boundary layers or induce turbulence.…”

Review Article: Flow battery systems with solid electroactive materials

“…Research efforts have pursued new materials, flow cell designs, surface modification, and mathematical modeling. 42,44,92,[99][100][101][102] More detailed discussion on the current status and research perspectives for supercapacitors and EFCs can be found in these recent reviews. 29,40,45,46,103,104 Capacitive water deionization is another application where solid suspensions have been coupled into a system with electrodes and electrical potential driving forces.…”