A new automated model brings stability to finite‐element simulations of capacitive deionization

Abstract

The massive need for freshwater is driving new desalination technologies such as capacitive deionization (CDI), wherein an applied electric field between porous electrodes removes salt ions from water. In this work, we present substantial advances in numerical approaches to 2D finite‐element models that make it possible to tractably and accurately simulate the local transport, charge‐transfer, and ion‐adsorption processes. This is achieved by introducing a new numerical approach that improves the stability of the method (SmD), which further allows precise and effective modeling that was previously too unstable for use in the state‐of‐the‐art 2D models. The results show that the model now accurately and reliably simulates CDI processes while being effectively applicable to a wider range of structural (device level) and operational conditions (like flow). Crucially, this opens up new opportunities that allow us to provide novel insights into the CDI processes, especially relating to ion‐starved conditions. Finally, novel algorithms support fully automatic implementation with simultaneous fit to multiple data sets and we openly provide all software code to increase accessibility. Thus, we fundamentally believe that the developed model will provide a solid foundation for 2D spatiotemporal simulations of capacitive deionization and aid the future development of CDI technology.

Langmuir-Based Modeling Produces Steady Two-Dimensional Simulations of Capacitive Deionization via Relaxed Adsorption-Flow Coupling

“…Full 2D modeling often uses extensive sets of coupled PDEs to simulate the device performance. , However, the complexities can limit the possible parameter-extraction methods and poor convergence can cause programs to crash. This lack of stability constrains the model’s practical usefulness for feasibly predicting the performance, especially of large-scale and complex CDI structures.…”

“…Because interest in the applications of CDI is growing, 2D-modeling of large-scale interconnected CDI devices is becoming increasingly important. The dominant 2D-modeling approaches today employ computationally complex 2D-PDE systems for predicting ion adsorption in small devices. , Therefore, we have proposed and validated a relaxed adsorption-flow coupling approach. The relaxation allows simulations to reach the state-of-the-art modeling accuracy with enhanced stability that greatly expands its tractability for realistic large-scale modeling.…”

“…This relaxation is achieved in two ways by practically integrating the DL electroadsorption model (eq ) into the COMSOL’s reaction module. First, the DL model locally determines the adsorption using ordinary differential equations (ODE), in contrast to previous models that compute potential and ion-concentration distributions in extensive connected partial differential equations (PDE). , The “relaxed” part of relaxed coupling here means that the model is fully 2D while using less spatial information, enhancing computational stability. Second, we simplifyingly assume that the adsorption–desorption constants are uniform throughout the electrode volume, which limits the system’s degrees of freedom.…”

“… 18 Thus, researchers have developed models that capture some of this spatial information, such as in 1D, 58 − 60 partial 2D, 61 or full 2D. 18 , 62 …”

“…The process is strongly susceptible to changes in operational and structural conditions, such as the voltage, − ion concentration − and composition, − flow rate, , electrode material, − electrode modifications, , device structure, − flow mode, , and presence of ion-selective membranes. ,, Also, the ion-concentration dependency makes the intracellular dynamics important . Thus, researchers have developed models that capture some of this spatial information, such as in 1D, − partial 2D, or full 2D. , …”