Electrochemical Desalination via Capacitive Deionization: COMSOL Simulation with Ag/rGO Conductive Concrete Electrodes

To complement the experimental investigation of electrochemical water desalination using conductive concrete electrodes, a comprehensive numerical model was developed using COMSOL Multiphysics 6.3. This simulation replicates the ion removal mechanisms in a membrane-free CDI system by modeling the electroadsorption of sodium (Na⁺) and chloride (Cl⁻) ions onto oppositely charged porous electrodes under direct current (DC) voltage.

The model integrates Electrostatics, Transport of Diluted Species, and Secondary Current Distribution physics to capture the electrochemical interactions within a stagnant water domain. A two-dimensional domain was selected, leveraging the CDI cell’s horizontal symmetry and the unidirectional electric field across the electrode gap [13].

2.1 Model geometry and physics interfaces

The simulation adopts a two-dimensional cross-section of the experimental CDI configuration, consisting of two square porous electrodes (50 mm × 50 mm) separated by a stagnant saline gap of 10 cm. The complete unit spans 30 cm (length) × 20 cm (width) × 5 cm (height). Figure 1 illustrates Na⁺ migration toward the cathode and Cl⁻ toward the anode under the influence of the applied voltage.

Figure 1. Schematic representation of the membrane-free capacitive deionization (CDI) cell with conductive concrete electrodes and stagnant saline water

The following physics were coupled:

• Secondary Current Distribution for simulating electronic and ionic conduction.

• Transport of Diluted Species for modeling Na⁺ and Cl⁻ transport.

Modified Donnan Adsorption module for ion storage in micropores, based on the thermodynamically consistent framework of Nordstrand et al. [13].

Material properties were defined as follows:

• Electrodes: Porous conductive concrete doped with Ag/rGO, electrical conductivity = 0.1 S/m.

• Electrolyte: Stationary NaCl solution (5–20 mM), with ion diffusivities of 1.33 × 10⁻⁹ m²/s (Na⁺) and 2.03 × 10⁻⁹ m²/s (Cl⁻).

• Temperature: Baseline of 20℃, with additional simulations at elevated temperatures.

• Voltage: DC voltages ranging from 5 to 25 V applied across electrode boundaries.

2.2 Finite element mesh

To resolve gradients in EDL regions, a 50-layer boundary mesh was applied to each electrode interface (thickness: 5 mm, stretch factor: 1.2). The bulk saline domain was meshed with coarser triangular elements to optimize simulation speed.

A mesh convergence study verified independence from element count. As shown in Figure 2, the final outlet NaCl concentration stabilized (< 211 parts per million (ppm)) once the domain mesh exceeded 5826 elements, validating mesh adequacy.

Figure 2. Finite element mesh structure used in COMSOL, showing boundary-layer refinement near electrodes and coarser meshing in the bulk saline region

To verify mesh adequacy, a grid-convergence study was performed by comparing the final outlet NaCl concentration at progressively finer mesh densities. Figure 3 shows the relationship between the total element count and the final concentration obtained at 5 V applied voltage, a 10 cm electrode gap, and 20℃ ambient temperatures. The solution stabilises below 211 ppm when the mesh exceeds 5826 domain elements (with a 50-layer boundary refinement), indicating mesh independence. Consequently, this mesh configuration was adopted for all subsequent simulations. Figure 4 confirms that with the refined mesh, concentration decay remained stable and free of oscillations, ensuring reliable simulation of electroadsorption dynamics.

Figure 3. Variation of the NaCl concentration parts per million (ppm) with the mesh numbers at 5 voltages applied, 10 cm gap between electrodes, and 20℃

Figure 4. Mesh-independence verification showing stable NaCl reduction over time

2.3 Modelling assumptions

The following assumptions were adopted to simplify the numerical model while capturing the essential physics of CDI using conductive concrete electrodes:

• Binary, dilute NaCl electrolyte; effective diffusivity De for both ions [15].

• Quasi-electroneutrality is enforced in macropores (i.e., no space charge), while space-charge effects are resolved inside micropores via the modified Donnan (mD) model.

•  Water is treated as incompressible and stationary (u = 0), reflecting a no-flow (batch-mode) CDI operation.

•  A constant volumetric capacitance C_m and constant attraction potential μ_att are assumed throughout the micropore domain.

•  No ion-exchange membrane is included between the electrodes, similar to the experimental cell design.

•  Porous conductive concrete electrodes are modeled as microporous media that adsorb ions following the Donnan equilibrium governed by μ_att.

2.4 Governing equations

2.4.1 Electronic and ionic conduction

• In the electrolyte:

$\nabla \cdot\left(\sigma_l \nabla \varnothing_l\right)=0, \sigma_l=\frac{F^2}{R T} \sum_i z_i^2 D_i c_i$              (1)

where, $\sigma_l$ is updated with the instantaneous ion concentration [3]. $\phi_l$ is the electrolyte potential; $\sigma_l$ is the ionic conductivity, dynamically updated based on local concentration; $D_i$ is the diffusion coefficient (m²/s for ion (Na, Cl); $z_i$ is the charge number of species $i$; $c_i$ is the concentration of species i; F is the faraday constant; $R$ is the universal gas constant; $T$ is the temperature.

• In the concrete matrix (electrode):

$\nabla \cdot\left(\sigma_s \nabla \varnothing_s\right)=0$                 (2)

where, ϕ_s is the solid-phase potential and σ_s is the electronic conductivity of the concrete matrix.

2.4.2 Ion Transport—Transport of Diluted Species (interface)

For each species i (Na⁺, Cl⁻)

$\frac{\partial\left(\varepsilon_p c_i\right)}{\partial t}+\nabla \cdot\left(-D_{\text {eff }, i} \nabla c_i\right)=R_i$              (3)

where, $c_i$ is the ion concentration $\left(\mathrm{mol} / \mathrm{m}^3\right) ; \varepsilon_p$ is the porosity with $D_{e f f, i}=\varepsilon_p^{3 / 2} D_i$ (Bruggeman correction); $R_i$ is the reaction/source term from adsorption.

• Alternative Nernst-Planck:

$\frac{\partial c_i}{\partial t}+\nabla \cdot N_i=R_i$                (4)

$N_i=-D_i \nabla c_i-z_i u_i F c_i \nabla \mathrm{F}$               (5)

where, $u_i$ is the ion mobility; $V$ is electric potential.

2.4.3 Modified-Donnan adsorption

Adsorption within micropores is modeled by the modified Donnan approach.

• Micropore concentration:

$c_{m, i=c_M, i} e^{-z \Delta \emptyset D+\mu_{a t t}}$               (6)

• Micropore charge:

$q_m=-2 c e^{\mu a t t} \sinh \left[\Delta \phi^{-} D\right]$                   (7)

where, $\Delta \emptyset^{-} D=\Delta \emptyset D / V_T$ and $V_T=R T / F[15] ; \Delta \phi D$ is the Donnan potential drop; VT $=$ FRT refers to the thermal voltage; $\mu_{a++}$ is the non-electrostatic attractive potential.

• Micropore potential-charge relation:

$\Delta \emptyset_m=-\frac{2 F}{C_m} q_m$               (8)

where, C_m is the capacitance of the micropore layer; q_m is the stored charge.

2.4.4 Charge balance and Randles analogy

The local current density is modeled using a capacitive Randles circuit analogy:

$i_{t o t}=C_{d l} \frac{\partial}{\partial t}\left(\varnothing_s-\varnothing_t\right)+\frac{\varnothing_s-\varnothing_t}{R_L}$               (9)

Eq. (9) satisfies the classic Randles circuit used for zero-dimensional validation. C_dl is the double-layer capacitance (F/m²); R_L is the leakage resistance; ϕ_sand ϕ_tpresent the solid and electrolyte potentials, respectively.

This equation is used to validate the time-domain charging behavior against a zero-dimensional capacitor model.

2.4.5 Stern layer capacitance model

The volumetric capacitance within micropores is defined as:

$C=C_{r e f}+\alpha\left(z_{\mathrm{Na}^{+} \mathrm{CNa}^{+}, \text {micro }}+z_{\mathrm{Cl}^{-} \mathrm{cCl}^{-}, \text {micro}}\right)^2$                 (10)

where, C is the total volumetric capacitance (F/m³); C_ref is the reference (intrinsic) capacitance; α is the capacitance sensitivity coefficient; and micro is the micropore ion concentrations.

2.4.6 Micropore attractive potential

To account for non-electrostatic interactions:

$\mu_{a t t}=\frac{E}{\left(c_{s u m}+10^{-9}\right) K_b T N_A}$                  (11)

where, E is the attractive energy constant; c_sum is the total micropore ion concentration; K_bis the Boltzmann constant; T is the temperature, and N_A is Avogadro’s number.

2.4.7 Empirical charge efficiency relation

The charge efficiency Λ varies with voltage:

$\Lambda=1-\frac{V_0}{V_{\text {ext}}}$              (12)

Eq. (12) is adapted from the dynamic Langmuir isotherm to approximate voltage-dependent ion adsorption behaviour.

2.5 Number of iterations and convergence criterion

A time-dependent solver using the Backward Differentiation Equation (BDF) was configured with:

Figure 5. Error versus iteration number in the nonlinear solver showing exponential convergence within 4 iterations during the time-dependent simulation of the capacitive deionization model

The simulation parameters were set as follows: a relative tolerance of 1 × 10⁻⁴, absolute tolerances of 1 × 10⁻⁶ V for potential and 1 × 10⁻⁵ mol/m³ for concentration, and an initial time step of 0.1 s (with a maximum step from 10 to100 s, and a minimum step of 1 × 10⁻⁵ s). As shown in Figure 5, simulations typically converged within four iterations, confirming numerical stability.

This section presents the numerical simulation results of electrochemical desalination using a CDI cell with conductive concrete electrodes. Simulations were performed in COMSOL Multiphysics 6.3, evaluating the effects of key operational parameters including applied voltage, electrode spacing, water temperature, and initial NaCl concentration.

The results provide insight into the spatial and temporal behavior of Na⁺ and Cl⁻ ions in a stagnant saline environment. Ion accumulation near the respective electrodes and electric field development across the cell were clearly observed.

Figure 10. Simulated surface concentration of Na⁺ ions, showing migration toward the cathode

Figure 11. Simulated surface concentration of Cl⁻ ions, showing directional migration toward the anode

Figures 10 and 11 illustrate the surface concentrations of Na⁺ and Cl⁻ ions under an applied DC voltage. Na⁺ ions migrate toward the cathode (left), while Cl⁻ ions move toward the anode (right). The superimposed streamlines confirm directional ion migration and electroadsorption driven by the electric field. Edge effects and curvature near electrode corners further validate the model’s accuracy in capturing transport dynamics.

This section presents the numerical simulation results of the electrochemical desalination process using a CDI cell equipped with conductive concrete electrodes. The simulations were conducted using COMSOL Multiphysics 6.3, focusing on the various operational parameters such as the applied voltage, inter-electrode spacing, water temperature, and ionic concentration.

These results offer insight into the spatiotemporal transport of Na⁺ and Cl⁻ ions within the stagnant saline water domain, their accumulation near the respective electrodes, and the development of electric fields and attractive electrostatic potentials inside the CDI cell [29, 30].

4.1 Study the capacitive deionization cell at different voltages applied

Figure 12 displays the time-dependent NaCl concentration at various applied voltages (5–25 V). A higher applied voltage correlates with faster and deeper ion removal. Starting from 420 ppm, the concentration dropped to 228 ppm at 5 V, 189 ppm at 10 V, 127 ppm at 15 V, 96 ppm at 20 V, and 91 ppm at 25 V after 3600 seconds. These findings affirm that a stronger electric field accelerates ion migration and enhances electrosorption efficiency, consistent with the EDL theory [31-35].

Figure 12. Variation of NaCl concentration over time at different applied voltages (5–25 V)

Figure 13. Effect of applied voltage on residual NaCl concentration after the CDI process

Figure 13 shows the linear relationship between applied voltage and final NaCl concentration. The regression model (R² = 0.9315) confirms that each 1 V increase results in approximately 7.34 ppm reduction in salinity, validating the voltage-dependence of CDI efficiency.

4.2 Specific energy consumption

The SEC was calculated based on the experimental data for NaCl removal at different applied voltages (5–25 V) using a 2 L batch CDI cell. The SEC was calculated from the time-integrated electrical energy normalized by the treated water volume according to Eq. (13) as shown in Table 2.

Table 2. Estimated specific energy consumption values compared with literature ranges

In this study, the treated volume was 2 L. The current was estimated from the salt adsorption using Faraday’s law, assuming a charge efficiency of 0.85 and monovalent NaCl ions.

The results show that SEC obtained SEC values (0.59–4.45 kWh/m³) that fall within or near the reported ranges for CDI (0.5–3 kWh/m³) [26, 27]. These comparisons confirm that Ag/rGO-enhanced conductive concrete electrodes can achieve competitive energy performance.

4.3 Study the effect of electrode spacing

Electric field behavior varies with electrode spacing. At 5 cm spacing, the field is intense and confined, enabling rapid and efficient ion transport, but with reduced coverage near sidewalls. Wider spacing (10–12.5 cm) leads to weaker, more dispersed fields, decreasing overall efficiency.

Figure 14. Effect of electrode spacing on NaCl concentration reduction over time at constant applied voltage

Figure 14 presents the influence of different electrode spacings, specifically 5, 7.5, 10, and 12.5 cm, on the reduction of NaCl concentration over a (3600 s) period under 15 V voltage conditions. Moderate spacing (7.5 cm) achieved a balance between field intensity and domain coverage. The results indicate that shortening the electrode spacing significantly improves the electrosorption performance and electric field intensity, which leads to improved desalination efficiency [36].

This behavior is consistent with previous findings that show how field line concentration improves charge transport and electroadsorption efficiency at narrower electrode gaps [29-30]. This reduces the electrostatic driving force, especially in the middle region, and may lead to slower ion transport and diminished desalination performance [35]. However, this narrow spacing also increases the gap between the electrodes and the sidewalls of the cell, reducing the field’s reach to the outer regions. As a result, while ion removal in the central path improves, peripheral areas may retain higher salt concentrations [37].

These findings demonstrate that reduced spacing enhances the electric field strength and electrosorption performance, but extremely narrow gaps may limit lateral coverage. Optimal performance is achieved between 5 and 7.5 cm spacing.

Overall, the analysis confirms that minimizing electrode spacing strengthens the electric field and accelerates ion transport, resulting in more efficient removal of salt from the solution.

4.4 Effect of initial NaCl concentration on capacitive deionization performance

To evaluate the impact of feedwater salinity on CDI performance, a range of initial NaCl concentrations was simulated using COMSOL Multiphysics under fixed operating conditions: 15 V applied voltage, 25℃ temperature, and 7.5 cm electrode spacing. The selected concentrations represent realistic scenarios ranging from brackish water (250–500 ppm) to highly saline conditions (8,000 ppm), such as those reported in Basra, Iraq, due to saltwater intrusion. At low salinity (250 and 500 ppm), the CDI cell performs efficiently, achieving final concentrations below 100 ppm after 1 hour, consistent with earlier observations that efficient charge transfer and minimized electrode saturation occur at low ionic concentrations [38].

Simulation results reveal that NaCl concentration decreases over time in all cases, confirming active electroadsorption. However, the efficiency of ion removal is strongly influenced by the initial salinity:

• Low salinity (250–500 ppm): Rapid and efficient desalination is observed, with final concentrations dropping below 100 ppm after 1 hour. This agrees with Shocron and Suss [16], who reported enhanced charge transfer and minimized electrode saturation at low ionic strengths.

• Moderate salinity (1,000–2,000 ppm): Ion removal continues but at a slower rate. As Uralcan et al. [17] noted, higher ionic strength leads to condensed ionic adlayers and less uniform charge distribution within the electric double layer, reducing adsorption efficiency.

• High salinity (8,000 ppm): The CDI cell exhibits the slowest performance, with residual concentrations exceeding 3,000 ppm. This is consistent with Rommerskirchen et al. [18], who found that compressed electric double layers at high salinity hinder electrostatic attraction and ion transport.

Figure 15 presents the aggregated system behavior under these varying salinity levels. These findings underscore that the initial NaCl concentration is a critical factor governing CDI efficiency. Lower salinity enhances electroadsorption and charge efficiency, while higher salinity introduces limitations in electric field-driven separation and double-layer capacity.

Figure 15. ppm after 1 hour at various initial concentrations

Figure 16. ppm as a function of time showing progressive electroadsorption efficiency over 3 hours of capacitive deionization operation at 15 V applied voltage, 7.5 cm spacing between electrodes, and at 25℃

4.5 Effect of extended operation time on NaCl concentration reduction

Simulation results indicate a clear time-dependent improvement in CDI performance: as operating time increases from 1 to 3 hours, the NaCl concentration in the treated water steadily decreases Figure 16. This reflects progressive electroadsorption driven by continued ion transport toward the electrodes. At 1 hour, the concentration decreases from 8,000 ppm to 1,664 ppm. By 3 hours, it drops significantly to 72 ppm, well below the WHO-recommended limit for drinking water (< 500 ppm). This prolonged exposure enhances electric double layer formation and charge transfer efficiency, particularly critical for high-salinity scenarios such as those found in Basra, Iraq, where salinity often exceeds 8,000–10,000 ppm.

These findings align with previous studies: Shocron and Suss [16] demonstrated that extended charging enhances ion uptake, while Rommerskirchen et al. [18] emphasized the role of prolonged operation in overcoming diffusion limitations and electrode saturation.

The data follow a linear trend described by the regression equation:

$y=-0.6774 x+5897.8$

where, y is ppm and x is time (s). The negative slope confirms the downward trend, though the moderate R² value (0.733) suggests diminishing returns beyond 1 hour due to electrode saturation and equilibrium effects.

4.6 Production rate in large-scale capacitive deionization tanks

4.6.1 The simulation results for the 1000-liter CDI tank

A static 1,000-liter CDI tank was simulated to evaluate the effect of applied voltage (15–50 V) on NaCl removal over a 24-hour batch cycle. The system began with an initial salinity of 8,000 ppm. Results in Table 3 show that:

• Low voltages (15–25 V): Desalination is slow, with outlet concentrations remaining above 2,000 ppm after 10 hours and only reaching potable levels (< 500 ppm) after 20 hours.

• High voltages (30–50 V): Salt removal is substantially faster. At 50 V, the concentration drops below 500 ppm in under 10 hours and reaches < 100 ppm by the end of the cycle.

The optimal operating window is 35–45 V, balancing effective desalination, energy efficiency, and system longevity. Within this range, salinity drops to < 500 ppm in approximately 10–12 hours. Accounting for tank drainage, electrode regeneration, and refilling (2–3 hours), the system supports two full batch cycles per day, enabling production of about 2000 liters/day of potable water.

Table 3. Time-dependent ppm in the 1000-liter capacitive deionization tank at various voltages (15–50 V) over 24 hours

4.6.2 The simulation results for the 10000-liter capacitive deionization tank

The 10000-liter CDI tank was simulated to assess desalination performance under voltages ranging from 15 to 80 V. According to Table 4.

• Lower voltages (15–30 V): Desalination remains inefficient, with outlet salinity exceeding 3000 ppm even after 12 hours of operation.

• Higher voltages (60–80 V): Salt removal improves significantly. At 80 V, the concentration decreases to < 500 ppm within 12–14 hours and reaches < 100 ppm by the end of the cycle.

The optimal voltage range of 60–80 V ensures rapid desalination with manageable energy use and electrode stress. With additional time (2–3 hours) for flushing and refilling, each batch cycle lasts 14–17 hours, enabling up to 1.5 cycles/day and about 15000 liters/day of treated water under continuous operation.

Table 4. Time-dependent ppm in the 10000-liter capacitive deionization tank at various voltages (15–80 V) over 24 hours

4.7 Numerical and experimental results validation

To check the accuracy of the simulation model, a laboratory experiment was carried out using a 2-liter CDI cell with the same dimensions as the one used in the simulation. The NaCl concentration was measured over time under applied voltages of 5 V, 10 V, 15 V, 20 V, and 25 V. As illustrated in Figure 17, both the experimental and simulation results show a steady decrease in NaCl concentration over time. Higher voltages resulted in more efficient ion removal, confirming that stronger electric fields enhance the electroadsorption capacity. At 5 V, the simulation slightly overpredicts the removal rate compared to the experimental results, likely because the model assumes ideal conditions and does not account for factors like salt buildup on the electrodes. At voltages of 15 V and above, the simulation results closely match the experimental data, indicating that the model successfully captures the main processes, including EDL formation, ion migration, and adsorption behavior under higher electric fields.

Figure 17. Comparison of experimental and numerical NaCl concentration vs. time at different applied voltages

Table 5. The validation of numerical and experimental salt removal efficiency at different applied voltages

Table 5 illustrates the comparison between experimental and numerical salt removal efficiencies at various applied voltages ranging from 5 V to 25 V. The salt removal efficiency was computed using the equation:

$Salt\ removal\ efficiency (\%)=\frac{\text {Initial concentration}- \text {Final concentration}}{\text {Initial concentration}} \times 100 \%$