3. CDI module characterization

The interface between an electrically charged electrode and an electrolytic solution is a problem widely studied as part of the so-called surface phenomena. In this interface, a region of ionic accumulation is formed, commonly called electric double-layer, in which the ionic species present in the electrolytic medium are spatially distributed in a characteristic manner responding to the electronic charge present in the electrode. In this type of interfaces, it is known that the accumulated charge density depends on the voltage level of the electrode, the concentration of the solution and its chemical composition.

The double-layer name comes from the first theoretical model formulated to explain the accumulation of charge in these interfaces. In 1883, Helmholtz assumes that the electric charges in the electrode form a layer that induces another layer in the solution, of ionic character and polarity opposite to that of the electrode. In the Helmholtz model, the layer present in the solution is formed by ions intimately in contact with the outer surface of the electrode (the surface in contact with the solution) and it is assumed that there are no further interactions within the solution due to the influence of the electrode beyond this layer adjacent to the surface.

Assuming a flat electrode, the Helmholtz model is equivalent to the classical model of a flatparallel capacitor (Figure 3) where A is the effective electrode surface, XH is the distance between ions and ε<sup>r</sup> is the permittivity.

Figure 3. Classical double-layer model of a flat-parallel capacitor.

(or counter-ions) can move freely through the membrane, while the movement of ions with a

During the purification phase, the electrodes invert the polarity to facilitate the desorption of the adsorbed ions in the previous desalination phase. The re-adsorption of ions is avoided

In both cases, CDI or MCDI, another important parameter, is the effective electrode surface. This parameter is related to the equivalent capacitance that represents the deionization cell

The interface between an electrically charged electrode and an electrolytic solution is a problem widely studied as part of the so-called surface phenomena. In this interface, a region of ionic accumulation is formed, commonly called electric double-layer, in which the ionic species present in the electrolytic medium are spatially distributed in a characteristic manner responding to the electronic charge present in the electrode. In this type of interfaces, it is known that the accumulated charge density depends on the voltage level of the electrode, the

The double-layer name comes from the first theoretical model formulated to explain the accumulation of charge in these interfaces. In 1883, Helmholtz assumes that the electric charges in the electrode form a layer that induces another layer in the solution, of ionic character and polarity opposite to that of the electrode. In the Helmholtz model, the layer present in the solution is formed by ions intimately in contact with the outer surface of the electrode (the surface in contact with the solution) and it is assumed that there are no further interactions within the solution due to the influence of the electrode beyond this layer adjacent

Assuming a flat electrode, the Helmholtz model is equivalent to the classical model of a flatparallel capacitor (Figure 3) where A is the effective electrode surface, XH is the distance

charge of the same sign is blocked.

40 Desalination and Water Treatment

thanks to the barrier posed by the membranes.

Figure 2. Schematic of a membrane capacitive deionization cell.

3. CDI module characterization

between ions and ε<sup>r</sup> is the permittivity.

to the surface.

and, therefore, to the quantity of salt that can be adsorbed.

concentration of the solution and its chemical composition.

$$\mathbb{C}\_{H} = A \cdot \frac{\mathbb{E}\_{r} \cdot \varepsilon\_{0}}{\chi\_{H}} \tag{1}$$

The desalination cell is built by piling several electrodes to increase the capability of water processing. In Figure 4, several electrodes are piled controlling the distance between them, "d," and the number of electrodes placed in series, "n."

Although there are more complex models of the ion distribution around the electrodes [10–12], the whole desalination cell can be modeled with the traditional circuit used to characterize a capacitor C. In this model two additional resistances are included, a series resistance RS to model conduction losses, and a parallel resistance RP that represents the self-discharge of the module.

The proposed electric model of the CDI cell (Figure 5) will allow the desalinization system to be simulated together with the power topology used for the energy recovery. The electrical parameters defined, RS, RP and C, depending on the geometrical characteristics of the CDI cell and on the salt molar concentration (M). In order to obtain their values, a current source is applied to the cell that generates a linear evolution in the voltage across the terminals.

The CDI cell is initially completely discharged. At t = 0, a constant current, IDC, is applied to initiate the charging process (Figure 6). Therefore, since the equivalent capacitor C is initially discharged, the value of the voltage VC(t = 0+) measured will determine the value of RS expressed in Ω.

$$R\_S = \frac{\Delta V\_1}{I\_{D\mathbb{C}}} \tag{2}$$

The capacitance of the CDI module, C, can be obtained from the linear charging process, during which the parallel resistance, RP, can be neglected:

Figure 4. (a) Schematic of a planar desalination module and (b) prototype.

Figure 5. Electric charge/discharge circuit used for the parasitic determination (RS, RP, C).

$$\mathcal{C} = \frac{I\_{\rm DC}}{t g \alpha} \tag{3}$$

With the proposed method, the values of RS, RP, and C can be obtained as a function of geometrical parameters: distance between electrodes "d," number of electrodes "n," the surface of electrodes "S" and NaCl molar concentration (M). To determine the tendencies of these

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 43

From Figure 7, it can be concluded that capacity C is almost independent of the distance

This fact demonstrates that the capacity is mainly due to the formation of the electric double layer. The addition of several electrodes is equivalent to adding capacitors in series; therefore, the total capacity is reduced although the voltage across the cell can be increased, increasing

Figure 7. Capacity as a function of M (concentration of NaCl) for different configurations depending on n (number of

values in an actual CDI cell, the prototype shown in Figure 4 was built and tested.

Figure 6. Electric charge/discharge test used for the parasitic determination.

between electrodes.

plates-electrode) and d (distance between electrodes).

Finally, to determine the parallel resistance, RP, the current source is turned off, and an exponential evolution of the voltage across the CDI cell (VC) can be approximated by the expression:

$$V\_{\mathbb{C}}(t) = V\_{\mathbb{C}\text{max}} \cdot e^{-t/\mathbb{R}\_{\mathbb{P}} \cdot \mathbb{C}} \tag{4}$$

where VCmax is the maximum voltage across the CDI module once current IDC turns to 0 A. Several tests were performed, and the absolute error obtained in the adjustment of the RP calculation was lower than 1%.

Figure 6. Electric charge/discharge test used for the parasitic determination.

<sup>C</sup> <sup>¼</sup> IDC

Figure 5. Electric charge/discharge circuit used for the parasitic determination (RS, RP, C).

Figure 4. (a) Schematic of a planar desalination module and (b) prototype.

42 Desalination and Water Treatment

Finally, to determine the parallel resistance, RP, the current source is turned off, and an exponential evolution of the voltage across the CDI cell (VC) can be approximated by the expression: VCðÞ¼ t VCmax � e

where VCmax is the maximum voltage across the CDI module once current IDC turns to 0 A. Several tests were performed, and the absolute error obtained in the adjustment of the RP

calculation was lower than 1%.

tg<sup>α</sup> (3)

�t=RP�<sup>C</sup> (4)

With the proposed method, the values of RS, RP, and C can be obtained as a function of geometrical parameters: distance between electrodes "d," number of electrodes "n," the surface of electrodes "S" and NaCl molar concentration (M). To determine the tendencies of these values in an actual CDI cell, the prototype shown in Figure 4 was built and tested.

From Figure 7, it can be concluded that capacity C is almost independent of the distance between electrodes.

This fact demonstrates that the capacity is mainly due to the formation of the electric double layer. The addition of several electrodes is equivalent to adding capacitors in series; therefore, the total capacity is reduced although the voltage across the cell can be increased, increasing

Figure 7. Capacity as a function of M (concentration of NaCl) for different configurations depending on n (number of plates-electrode) and d (distance between electrodes).

With reference to the parallel resistance, RP, (Figure 9) the data measured show that it increases at low concentrations and presents a linear trend with a small or very small slope

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 45

Tests have been carried out using the CDI cell shown in Figure 4 to estimate the amount of salt that can be captured by the electrodes of this type of cells when they are completely filled with salt water. The molar salt concentration (M) is one of the parameters used to characterize the cell. The first tests (performed at zero water flow) consist of series of charge/discharge cycles of the

It can be pointed out that, as shown in Figure 10, the electrodes present very high retention values taking into account that the initial concentration is 0.6 M. There is a variation through-

In the second set of tests (Figure 11), two-electrode cells were used considering different initial concentrations, c0, and changing the distance between electrodes (d) to identify the influence of this parameter on the salt retention. The results obtained show that salt retention increases as

This effect can be justified if we take into account that the series resistance presented in the cell increases with the distance "d," especially at concentrations below 0.3 M, which presumably results in a decrease in the effective voltage in the electric double-layer and, as a result, a lower

Controlling the thickness of the nanoporous carbon layer deposited on the electrode surface, the quantity in grams of activated carbon per electrode can be determined. With the results

Figure 10. Results obtained by application of several charge-discharge cycles to cell configurations of more than two

CDI cell using a solution with the maximum concentration considered (0.6 M).

out the series, tending to stabilize as the number of cycles increase.

the distance between electrodes is reduced.

4. Estimation of saline retention in electrodes

starting at 0.3 M.

ionic retention.

electrodes.

Figure 8. RS for different configurations.

the total energy stored. For high concentrations (>0.1 to 0.6 M), the change in C is linear with a very little slope (≤1Farad per 0.1 M). This is so because the double electric layer is almost completely formed for concentrations around 0.1 M.

Regarding RS, the series resistance (Figure 8), it can be seen that it increases a lot for low concentration values, M, and presents a linear trend with small or very small slope from 0.3 M on.

Figure 9. RP for different configurations.

With reference to the parallel resistance, RP, (Figure 9) the data measured show that it increases at low concentrations and presents a linear trend with a small or very small slope starting at 0.3 M.
