Finite Element Analysis of Flow-Electrode Capacitive Deionization
Authors: Pohlman Garrett , Haddad Andrew , Akuzum Bilen , Agar Ertan , Hackl Lukas 
Published: August 2024

As access to freshwater diminishes due to climate change and population growth, drought-stricken regions across the globe continue to turn to groundwater and desalination. A largely untapped water resource in many parts of the world is brackish water - defined as water with total dissolved solids (TDS) in the range of 500 ppm to 10,000 ppm. Flow Capacitive Deionization (FCDI) is an electrochemical ion removal technology that is well-suited for the continuous desalination of brackish waters. Traditional Capacitive Deionization (CDI) consists of two fixed capacitive electrodes which are charged and discharged cyclically to capture ions from the solution being treated, and then regenerated to create a waste brine stream. During FCDI operation however, an applied potential drives ions out of a center water channel, typically through a pair of cation and anion exchange membranes (CEM/AEM), and into two flowing capacitive slurry electrodes (Figure 1). Because the electrodes are mobile, they can be moved into an adjacent cell for regeneration, thus enabling continuous operation of the desalination system without cyclical charge/discharge. The cathode and anode slurries typically consist of activated carbon suspended in a salt solution.
Because the electrodes are flowing in FCDI, models describing this system must translate the Eulerian derivative to describe transient capacitive charge/discharge to a Lagrangian material derivative following the electrode material flowing through space. A flowing capacitive electrode is a significantly more complex system than a stationary porous and capacitive electrode matrix, incorporating the fluid dynamics of the slurries, ion transport within the slurry’s electrolyte medium, etc. Despite nearly a decade of research into FCDI, few researchers have probed the transient and spatially dependent mechanisms of ion transport and electro-adsoprtion within flow electrodes. While the overall electrodialytic contributions to ion capture within FCDI systems have been studied (1,2), the mechanism of competition between the electrodialysis and capacitive ion capture within the flow electrodes remains somewhat elusive. Additional analysis of the ion transport phenomena within these flow electrodes could bring forth insights into optimal design of FCDI devices and/or electrode formulations.
In this study, an existing 2-dimensional mathematical model (3,4) for electrochemical flow capacitors is adapted to FCDI and solved via finite element analysis in COMSOL Multiphysics. Transport equations describing the advection of overpotential along with the flowing electrode are coupled with the Nernst-Planck equations which govern ion transport within the CEM/AEM, center water channel, and slurry electrolyte medium. This study investigates the effect of slurry flow velocity and sodium chloride concentration in the influent water on electrical potential profiles within an FCDI cell, and illustrates the active regions of capacitive electro-adsorption through the depth of the flow channel. Models of electrodialysis and FCDI are compared to understand the fundamental differences in driving forces for ion removal between the two technologies. The model shows agreement with experimental data through prediction of salt adsorption rate trends (mmol NaCl m-2 s-1) vs. influent sodium chloride concentrations. Through this analysis, it is shown that this model may serve as a valuable groundwork for expansion of FCDI modeling capabilities to include three dimensional cell geometries and subsequent optimization of operational parameters and cell dimensions.

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Figure 1