4. Estimation of saline retention in electrodes

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

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.

completely formed for concentrations around 0.1 M.

Figure 8. RS for different configurations.

44 Desalination and Water Treatment

Figure 9. RP for different configurations.

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

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

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 the distance between electrodes is reduced.

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 ionic retention.

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 electrodes.

Figure 11. Estimated relative retention for cell configurations of two electrodes at different separations (d) and for different initial concentrations (c0).

obtained in the previous test, an estimation of milligrams of salt retained per gram of activated carbon was also calculated.

magnitudes and a trade-off between them will be necessary. Figure 13 also shows the time required by the electrodes to reach saturation, after which the salt retention capability drops.

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 47

As already mentioned, one of the most interesting aspects of CDI is the possibility of reusing the energy stored in capacitive cells or modules once the deionization phase has finished. The regenerative use of energy in CDI technology consists of using the energy stored in the CDI cell once it is saturated (the deionization process is finished and the cleaning process begins) and transferring it to other modules that begin their deionization phase. This strategy can be applied to several cells that exchange the energy involved in the process, thus defining a cycle

In order to be able to transfer the energy stored in the CDI cell to another one, it is necessary to

Figure 14. Desalination diagram with an up-down converter for energy transfer from CDI cell-1 to CDI cell-2.

5. Up/down DC/DC converter for energy recovery

Figure 13. Estimated salt retention at different charging current (iC).

include a DC/DC power converter in the system (Figure 14).

to produce clean water.

The data plotted in Figure 12 are susceptible of a logarithmic adjustment in the whole range and a linear adjustment for low concentrations. Both present a good correlation (R<sup>2</sup> > 0.94).

One important parameter to be analyzed during the diffusion of ions in the charging/ discharging process is the amplitude of the current used.

By reducing the amplitude of the current used during the charging process of the CDI cell, ions have a longer time to move into the carbon porosities, thus increasing the salt retention. This phenomenon seems to reach a limit at which the amount of salt retained remains the same even if the current is doubled (from iC = 1 to 2 A). From this, it can be concluded that the amplitude of the charge/discharge current and the amount of salt retained are two opposed

Figure 12. Estimated relative retention for cell configurations of two electrodes and different initial concentrations (c0).

Figure 13. Estimated salt retention at different charging current (iC).

obtained in the previous test, an estimation of milligrams of salt retained per gram of activated

Figure 11. Estimated relative retention for cell configurations of two electrodes at different separations (d) and for

The data plotted in Figure 12 are susceptible of a logarithmic adjustment in the whole range and a linear adjustment for low concentrations. Both present a good correlation (R<sup>2</sup> > 0.94).

One important parameter to be analyzed during the diffusion of ions in the charging/

By reducing the amplitude of the current used during the charging process of the CDI cell, ions have a longer time to move into the carbon porosities, thus increasing the salt retention. This phenomenon seems to reach a limit at which the amount of salt retained remains the same even if the current is doubled (from iC = 1 to 2 A). From this, it can be concluded that the amplitude of the charge/discharge current and the amount of salt retained are two opposed

Figure 12. Estimated relative retention for cell configurations of two electrodes and different initial concentrations (c0).

carbon was also calculated.

different initial concentrations (c0).

46 Desalination and Water Treatment

discharging process is the amplitude of the current used.

magnitudes and a trade-off between them will be necessary. Figure 13 also shows the time required by the electrodes to reach saturation, after which the salt retention capability drops.

#### 5. Up/down DC/DC converter for energy recovery

As already mentioned, one of the most interesting aspects of CDI is the possibility of reusing the energy stored in capacitive cells or modules once the deionization phase has finished. The regenerative use of energy in CDI technology consists of using the energy stored in the CDI cell once it is saturated (the deionization process is finished and the cleaning process begins) and transferring it to other modules that begin their deionization phase. This strategy can be applied to several cells that exchange the energy involved in the process, thus defining a cycle to produce clean water.

In order to be able to transfer the energy stored in the CDI cell to another one, it is necessary to include a DC/DC power converter in the system (Figure 14).

Figure 14. Desalination diagram with an up-down converter for energy transfer from CDI cell-1 to CDI cell-2.

uc<sup>2</sup>ð Þ<sup>i</sup> ¼ uc<sup>2</sup>ð Þ <sup>i</sup>�<sup>1</sup> þ

1 toni þ toff <sup>i</sup>

�

iRMSC<sup>1</sup><sup>i</sup> ¼

1 toni þ toff <sup>i</sup>

Pcond ¼

Pswitch ¼

P i i 2 RMSC1<sup>i</sup> þ i

1

<sup>2</sup> � ð Þ tr <sup>þ</sup> tf <sup>P</sup>

The parameter R represents the total series resistance along the conduction path.

ECRpi <sup>¼</sup> <sup>1</sup> RP � uc<sup>2</sup>

voltages of capacitors C1 and C2 can be recalculated as follows:

<sup>Δ</sup>EC1<sup>i</sup> <sup>¼</sup> <sup>1</sup>

<sup>Δ</sup>EC2<sup>i</sup> <sup>¼</sup> <sup>1</sup>

iRMSC<sup>2</sup><sup>i</sup> ¼

switching losses can be estimated:

period "i" due to self-discharge:

The RMS currents through the cells in each switching period can also be determined by:

� ðtoni

<sup>ð</sup> toniþtoff <sup>i</sup>

toni

0

Based on the RMS current values calculated with the equations above, conduction and

2 RMSC2i � � � toni <sup>þ</sup> toff <sup>i</sup>

i

Voltage losses due to cell self-discharge are also taken into account in the model by incorporating the following expression that represents the energy lost in a cell during the switching

Once the energy dissipated in each cycle (ECcond: energy loosed during conduction stage, ECswitch: energy loosed during switching stage, ECp: energy loosed in RP) is known, the real

<sup>2</sup> � <sup>C</sup><sup>1</sup> � uc<sup>2</sup>

<sup>2</sup> � <sup>C</sup><sup>2</sup> � uc<sup>2</sup>

From the previous expressions, the real voltage across each capacitor can be derived:

Ttotal

Ttotal

<sup>i</sup> tONi þ tOFFi

<sup>1</sup>ð Þ <sup>i</sup>þ<sup>1</sup> � <sup>1</sup>

<sup>2</sup>ð Þ <sup>i</sup>þ<sup>1</sup> � <sup>1</sup>

<sup>2</sup> � <sup>C</sup><sup>1</sup> � uc<sup>2</sup>

<sup>2</sup> � <sup>C</sup><sup>2</sup> � uc<sup>2</sup>

ΔErealC1<sup>i</sup> ¼ ΔEC1<sup>i</sup> � EC1condi � EC1switchi � ECRpi (14)

ΔErealC2<sup>i</sup> ¼ ΔEC2<sup>i</sup> � EC2condi � EC2switchi � ECRpi (15)

ILmax þ ILmin

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Imin � Imax toff <sup>i</sup>

Imax � Imin toni

� <sup>t</sup> <sup>þ</sup> <sup>I</sup>min � �<sup>2</sup>

vuuut (7)

� ð Þþ <sup>t</sup> � toni <sup>I</sup>max � �<sup>2</sup>

� � � <sup>R</sup>

Imin � uc1<sup>i</sup> þ uc<sup>2</sup>ð Þ <sup>i</sup>þ<sup>1</sup> � �<sup>þ</sup>

Imax � uc<sup>1</sup>ð Þ <sup>i</sup>þ<sup>1</sup> þ uc2<sup>i</sup> � � !

vuuuut (8)

<sup>2</sup> � <sup>C</sup> � toff ið Þ �<sup>1</sup> (6)

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

� dt

� � (11)

<sup>1</sup><sup>i</sup> (12)

<sup>2</sup><sup>i</sup> (13)

� dt

(9)

49

(10)

Figure 15. Voltage and current waveforms in the DC/DC converter.

One possible option for the converter topology is a buck-boost that operates at the variable frequency with hysteresis control where the maximum (iLmax) and minimum (iLmin) inductor current is fixed (Figure 15).

Limiting the inductor current (iLmin, iLmax) conditions the efficiency of the system, since these values are related to conduction and switching losses. The converter operation is based on transferring part of the energy stored at the input cell-1 to the inductor L during the period when transistor M1 is closed and M2 is open (tON). This period finishes when the inductor current reaches the maximum value defined by the converter control (iLmax). After this, transistor M2 is closed (M1 is opened) during time tOFF and the energy stored in the inductor is discharged on the output cell-2. This stage typically finishes when the inductor current becomes equal to zero (iLmin = 0).

Therefore, iLmax can be used as the control parameter of the up/down converter during the energy transfer between the input CDI cell, which is completely charged, and the output CDI cell, which is initially completely discharged. By increasing the value of iLmax, the time involved in the transfer will be reduced.

To optimize the efficiency of the CDI system, it is necessary to define the value of iLmax during the energy recovery process. High values of this parameter will increase conduction losses, whereas low values of iLmax will increase the transfer time and the self-discharge through the parallel resistance RP. On the other hand, the estimation of iLmax depends on the salt concentration (M) and the geometry of the CDI cells, which define the parameters RP, RS and C of the electrical model.

The DC/DC converter can be mathematically modeled assuming linear evolutions of the inductor current in each switching period (i) during the charge and discharge [13]. Therefore, when transistor M1 is conducting (M2 off), the discharge of the input cell is ideally described by:

$$\mathfrak{uuc}\_{1(i)} = \mathfrak{ucc}\_{1(i-1)} - \frac{I\_{L\max} + I\_{L\min}}{\mathfrak{2} \cdot \mathbb{C}} \cdot t\_{\mathfrak{ou}(i-1)} \tag{5}$$

Similarly, the output cell increases its voltage when M2 is on (M1 off). The equation defining such a process in each switching cycle is:

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 49

$$\mathfrak{u}\mathfrak{c}\_{2(i)} = \mathfrak{u}\mathfrak{c}\_{2(i-1)} + \frac{I\_{\text{Lmax}} + I\_{\text{Lmin}}}{\mathbf{2} \cdot \mathbb{C}} \cdot t\_{\text{off}(i-1)} \tag{6}$$

The RMS currents through the cells in each switching period can also be determined by:

$$i\_{\rm RMS1\_i} = \sqrt{\frac{1}{t n\_i + t \theta f\_i} \cdot \int\_0^{t n\_i} \left(\frac{I\_{\rm max} - I\_{\rm min}}{t n\_i} \cdot t + I\_{\rm min}\right)^2 \cdot dt} \tag{7}$$

$$\dot{q}\_{\text{RMSC2}\_i} = \sqrt{\frac{1}{tron\_i + tgf\_i} \cdot \int\_{tou\_i}^{tou\_i + tgf\_i} \left(\frac{I\_{\text{min}} - I\_{\text{max}}}{tgf\_i} \cdot (t - ton\_i) + I\_{\text{max}}\right)^2} \cdot dt} \tag{8}$$

Based on the RMS current values calculated with the equations above, conduction and switching losses can be estimated:

$$P\_{cond} = \frac{\sum\_{i} \left( i\_{\text{RMS1i}}^2 + i\_{\text{RMS2i}}^2 \right) \cdot \left( ton\_i + tof\_i \right) \cdot R}{T\_{total}} \tag{9}$$

$$P\_{switch} = \frac{\frac{1}{2} \cdot (tr + tf) \sum\_{i} \left( \frac{I\_{\min} \cdot \left( \mu c\_{1i} + \mu c\_{2(i+1)} \right) +}{I\_{\max} \cdot \left( \mu c\_{1(i+1)} + \mu c\_{2i} \right)} \right)}{T\_{total}} \tag{10}$$

The parameter R represents the total series resistance along the conduction path.

One possible option for the converter topology is a buck-boost that operates at the variable frequency with hysteresis control where the maximum (iLmax) and minimum (iLmin) inductor

Limiting the inductor current (iLmin, iLmax) conditions the efficiency of the system, since these values are related to conduction and switching losses. The converter operation is based on transferring part of the energy stored at the input cell-1 to the inductor L during the period when transistor M1 is closed and M2 is open (tON). This period finishes when the inductor current reaches the maximum value defined by the converter control (iLmax). After this, transistor M2 is closed (M1 is opened) during time tOFF and the energy stored in the inductor is discharged on the output cell-2. This stage typically finishes when the inductor current

Therefore, iLmax can be used as the control parameter of the up/down converter during the energy transfer between the input CDI cell, which is completely charged, and the output CDI cell, which is initially completely discharged. By increasing the value of iLmax, the time

To optimize the efficiency of the CDI system, it is necessary to define the value of iLmax during the energy recovery process. High values of this parameter will increase conduction losses, whereas low values of iLmax will increase the transfer time and the self-discharge through the parallel resistance RP. On the other hand, the estimation of iLmax depends on the salt concentration (M) and the geometry of the CDI cells, which define the parameters RP, RS and C of the electrical model.

The DC/DC converter can be mathematically modeled assuming linear evolutions of the inductor current in each switching period (i) during the charge and discharge [13]. Therefore, when transistor M1 is conducting (M2 off), the discharge of the input cell is ideally described by:

Similarly, the output cell increases its voltage when M2 is on (M1 off). The equation defining

<sup>2</sup> � <sup>C</sup> � ton ið Þ �<sup>1</sup> (5)

uc<sup>1</sup>ð Þ<sup>i</sup> <sup>¼</sup> uc<sup>1</sup>ð Þ <sup>i</sup>�<sup>1</sup> � ILmax <sup>þ</sup> ILmin

current is fixed (Figure 15).

48 Desalination and Water Treatment

Figure 15. Voltage and current waveforms in the DC/DC converter.

becomes equal to zero (iLmin = 0).

involved in the transfer will be reduced.

such a process in each switching cycle is:

Voltage losses due to cell self-discharge are also taken into account in the model by incorporating the following expression that represents the energy lost in a cell during the switching period "i" due to self-discharge:

$$E c\_{\mathcal{R}p^i} = \frac{1}{\mathcal{R}\_P} \cdot \mu c\_i^2 \left( t\_{\mathcal{ON}\_i} + t\_{\text{OFF}\_i} \right) \tag{11}$$

Once the energy dissipated in each cycle (ECcond: energy loosed during conduction stage, ECswitch: energy loosed during switching stage, ECp: energy loosed in RP) is known, the real voltages of capacitors C1 and C2 can be recalculated as follows:

$$
\Delta E\_{C1i} = \frac{1}{2} \cdot \mathbf{C1} \cdot \boldsymbol{\omega} c\_{1(i+1)}^2 - \frac{1}{2} \cdot \mathbf{C1} \cdot \boldsymbol{\omega} c\_{1i}^2 \tag{12}
$$

$$
\Delta E\_{\rm C2i} = \frac{1}{2} \cdot \mathbf{C2} \cdot \mu c\_{2(i+1)}^2 - \frac{1}{2} \cdot \mathbf{C2} \cdot \mu c\_{2i}^2 \tag{13}
$$

$$
\Delta\text{Freal}\_{\text{C1i}} = \Delta E\_{\text{C1i}} - E\_{\text{C1cond}\_i} - E\_{\text{C1swidth}\_i} - E\_{\text{Cg}\_{\overline{\text{\gamma}}}} \tag{14}
$$

$$
\Delta\text{Freal}\_{\text{C2i}} = \Delta\text{E}\_{\text{C2i}} - \text{E}\_{\text{C2cond}\_i} - \text{E}\_{\text{C2switch}\_i} - \text{E}\_{\text{C}\_{\text{N}\_i}} \tag{15}
$$

From the previous expressions, the real voltage across each capacitor can be derived:

$$uc\_{1(i+1)\_{val}} = \sqrt{\frac{2 \cdot \left(\Delta E real\_{\text{C1}i} + \frac{1}{2} \cdot \mathbf{C1} \cdot \mu c\_{1i\_{val}}^2\right)}{\mathbf{C1}}} \tag{16}$$

$$uc\_{2(i+1)\_{ml}} = \sqrt{\frac{2 \cdot \left(\Delta \text{Freal}\_{\text{C2}i} + \frac{1}{2} \cdot \text{C2} \cdot \text{uc}\_{2i\_{ml}}^2\right)}{\text{C2}}} \tag{17}$$

The model described allows users to obtain a large amount of information related to the behavior of the converter: currents, voltages, transfer times, performance. But it can also provide insight into the influence that the desalination cells will have on these parameters. In order for this to be possible, the previous expressions must include the influence of the distance between electrodes "d," the number of electrodes "n," the molarity "M," and the S surface.

$$E\_{Rsm(i)}(d,n,M,S) = R\_S(d,n,M,S) \cdot \left(\mathbf{i}\_{RMSC1\_{(i)}}\right)^2 \cdot t\_{on} \tag{18}$$

$$E\_{\mathcal{R}s\mathcal{G}'(i)}(d,n,M,\mathcal{S}) = \mathcal{R}\_{\mathcal{S}}(d,n,M,\mathcal{S}) \cdot \left(\mathbf{i}\_{\text{RMSC2}\_{(i)}}\right)^2 \cdot \mathbf{t}\_{\text{off}} \tag{19}$$

$$E\_{R\varsigma(i)}(d,n,M,S) = E\_{R\varsigma on(i)}(d,n,M,S) + E\_{R\varsigma off(i)}(d,n,M,S) \tag{20}$$

$$E\_{R\_{\mathcal{P}(i)}}(d, n, M) = \int\_0^{T\_{(i)}} \frac{\left[\mu\_{\mathcal{C}(i)}(t)\right]^2}{Rp(d, n, M)} \cdot dt \tag{21}$$

By controlling the switching times of the semiconductors it is possible to control that the maximum current through the inductor follows the profile defined by the optimum current for each specific cell. Figure 18 shows the efficiency obtained in several cases when the optimal current is used and the maximum voltage is 1.5 V. It is important to point out the necessity of reducing the series resistance because it limits the maximum efficiency that can be obtained.

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 51

Figure 16. Optimum current iLmax estimation flow chart per switching period.

$$E\_{\Gamma(i)}(d, n, M, S) = E\_{\mathbb{R}\_{\bar{S}(i)}}(d, n, M, S) + E\_{\mathbb{R}\_{\bar{V}(i)}}(d, n, M, S) + P\_{\text{coml}(i)}(d, n, M, S) \cdot T + P\_{\text{switch}(i)}(d, n, M, S) \cdot T \tag{22}$$

From the equation system described above, it is possible to determine the overall efficiency of the DC/DC converter together with the desalination cells [14].

Once the equations to calculate losses have been established, it is possible to determine the optimum iLmax current in each switching period by implementing an iterative process according to the flow chart of Figure 16. The procedure consists in increasing the value of iLmax in each switching period until the maximum efficiency is obtained for that switching period. After that, a new switching period is considered and a new iteration with iLmax is carried out in order to derive the optimum iLmax value for the new switching period. The process is repeated until the input CDI cell is completely discharged.

The process mentioned was applied to several cell configurations consisting of four electrodes of 250�250�5mm placed at different distances from one another, in which the salt concentration was also a parameter under control [14]. As an example, Figure 17 shows the optimal current when the cell parameters associated with this configuration are: C = 0.1F, Rs = 25mΩ, and Rp = 40 Ω. Taking these parameters into account, the calculation of the optimum current as indicated above gives rise to the evolution shown in Figure 17.

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 51

Figure 16. Optimum current iLmax estimation flow chart per switching period.

uc<sup>1</sup>ð Þ <sup>i</sup>þ<sup>1</sup> real ¼

uc<sup>2</sup>ð Þ <sup>i</sup>þ<sup>1</sup> real ¼

surface.

50 Desalination and Water Treatment

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C2

� �

� �

<sup>2</sup> � <sup>C</sup><sup>1</sup> � uc<sup>2</sup>

<sup>2</sup> � <sup>C</sup><sup>2</sup> � uc<sup>2</sup>

� �<sup>2</sup>

� �<sup>2</sup>

RPð Þ <sup>d</sup>; <sup>n</sup>; <sup>M</sup> � dt (21)

ERSð Þ<sup>i</sup> ð Þ¼ d; n; M; S ERSon ið Þð Þþ d; n; M; S ERSoff ið Þð Þ d; n; M; S (20)

uC ið Þð Þ<sup>t</sup> � �<sup>2</sup>

� ton (18)

� toff (19)

(22)

1ireal

2ireal

vuut (17)

vuut (16)

<sup>2</sup> � <sup>Δ</sup>ErealC1<sup>i</sup> <sup>þ</sup> <sup>1</sup>

<sup>2</sup> � <sup>Δ</sup>ErealC2<sup>i</sup> <sup>þ</sup> <sup>1</sup>

The model described allows users to obtain a large amount of information related to the behavior of the converter: currents, voltages, transfer times, performance. But it can also provide insight into the influence that the desalination cells will have on these parameters. In order for this to be possible, the previous expressions must include the influence of the distance between electrodes "d," the number of electrodes "n," the molarity "M," and the S

ERSon ið Þð Þ¼ d; n; M; S RSð Þ� d; n; M; S iRMSC<sup>1</sup>ð Þ<sup>i</sup>

ERSoff ið Þð Þ¼ d; n; M; S RSð Þ� d; n; M; S iRMSC<sup>2</sup>ð Þ<sup>i</sup>

ð Tð Þ<sup>i</sup>

0

ET ið Þð Þ¼ d; n; M; S ERS ið Þ ð Þþ d; n; M; S ERP ið Þ ð Þþ d; n; M; S Pcond ið Þð Þ� d; n; M; S T þ Pswitch ið Þð Þ� d; n; M; S T

From the equation system described above, it is possible to determine the overall efficiency of

Once the equations to calculate losses have been established, it is possible to determine the optimum iLmax current in each switching period by implementing an iterative process according to the flow chart of Figure 16. The procedure consists in increasing the value of iLmax in each switching period until the maximum efficiency is obtained for that switching period. After that, a new switching period is considered and a new iteration with iLmax is carried out in order to derive the optimum iLmax value for the new switching period. The

The process mentioned was applied to several cell configurations consisting of four electrodes of 250�250�5mm placed at different distances from one another, in which the salt concentration was also a parameter under control [14]. As an example, Figure 17 shows the optimal current when the cell parameters associated with this configuration are: C = 0.1F, Rs = 25mΩ, and Rp = 40 Ω. Taking these parameters into account, the calculation of the optimum current as

ERP ið Þ ð Þ¼ d; n; M

the DC/DC converter together with the desalination cells [14].

process is repeated until the input CDI cell is completely discharged.

indicated above gives rise to the evolution shown in Figure 17.

By controlling the switching times of the semiconductors it is possible to control that the maximum current through the inductor follows the profile defined by the optimum current for each specific cell. Figure 18 shows the efficiency obtained in several cases when the optimal current is used and the maximum voltage is 1.5 V. It is important to point out the necessity of reducing the series resistance because it limits the maximum efficiency that can be obtained.

and the mathematical characterization of the DC/DC converter, it is possible to identify energy losses in the cell either by self-discharge or due to the current handled during the energy

Energy Recovery in Capacitive Deionization Technology http://dx.doi.org/10.5772/intechopen.75537 53

As a result, a clear identification of the power losses in all the system components is obtained. This makes it possible to identify the optimum current to minimize losses and optimize

The feedback parameter used by the converter control strategy described is the maximum current through the inductor, iLmax. This parameter is calculated at each switching period so as to obtain the optimum value that maximizes the efficiency of the energy transfer between

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[3] Fraidenraich N, Vilela OC, Lima GA, Gordon JM. Reverse osmosis desalination: Model-

[4] Oren Y. Capacitive deionization (CDI) for desalination and water treatment-past, present

[5] Gao Y, Li HB, Cheng ZJ, Zhang MC, Zhang YP, Zhang ZJ, Cheng YW, Pan LK, Sun Z. Electrosorption of cupric ions from solutions by carbon nanotubes and nanofibres film electrodes grown on graphite substrates. In: Proceedings of the IEEE Nanoelectronics

[6] Hwang S, Hyun S. Capacitance control of carbon aerogel electrodes. Journal of Non-

[7] Xu P, Drewes JE, Heil D, Wang G. Treatment of brackish produced water using carbon aerogel-based capacitive deionization technology. Water Research. 2008;42:2605-2617

recovery processes, together with the power losses in the converter.

CDI cells.

Author details

References

Francisco J. Álvarez-González

University of Oviedo, Gijón, Spain

\*Address all correspondence to: amartinp@uniovi.es

Water Research and Education. 2009;132:3-10

and future (a review). Desalination. 2008;228:10-29

Crystalline Solids. 2004;347:238-245

process efficiency for any salt concentration once the cell geometry is defined.

Alberto M. Pernía\*, Miguel J. Prieto, Juan A. Martín-Ramos, Pedro J. Villegas and

Report 3. UNESCO Publishing; Mar 2009. http://publishing.unesco.org/

ing and experiment. Applied Physics Letters. 2009;94:124102-124103

Conference INEC 2008; Shanghai, China; 24–27 March 2008. pp. 242-247

Figure 17. Optimum current iLmax estimated.

Figure 18. System efficiency operating at optimum current (red) and average optimum current during the energy transference (green).

The green plot determines the average of the optimal current during the whole energy transference process (right-hand scale).

The efficiency improvement depends on the CDI cell geometry and the salt concentration (M) because these magnitudes condition the values of the parameters that define the electrical model of the cell. Actual measurements confirmed that, by applying this control strategy, the efficiency was improved by 10% in most of the cases as compared to that obtained when using a constant current value during the charge/discharge process.

#### 6. Conclusions

The method presented allows the electrical characterization of the CDI cell in terms of salt concentration in the water and cell geometry. A model proposed is based only on three parameters RP, RS, C, which simplifies mathematical calculations. Using this electrical model and the mathematical characterization of the DC/DC converter, it is possible to identify energy losses in the cell either by self-discharge or due to the current handled during the energy recovery processes, together with the power losses in the converter.

As a result, a clear identification of the power losses in all the system components is obtained. This makes it possible to identify the optimum current to minimize losses and optimize process efficiency for any salt concentration once the cell geometry is defined.

The feedback parameter used by the converter control strategy described is the maximum current through the inductor, iLmax. This parameter is calculated at each switching period so as to obtain the optimum value that maximizes the efficiency of the energy transfer between CDI cells.
