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Efficiency of Carnot and Conventional Capacitive Deionization Cycles Daniel Moreno, and Marta C. Hatzell J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05940 • Publication Date (Web): 07 Sep 2018 Downloaded from http://pubs.acs.org on September 7, 2018

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The Journal of Physical Chemistry

Efficiency of Carnot and Conventional Capacitive Deionization Cycles Daniel Moreno and Marta C. Hatzell∗ 1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Ga E-mail: *[email protected] Phone: +1 404-385-4503

2

Abstract

3

Brackish water treatment characteristically suffers from low efficiency. Overcoming

4

this challenge requires a fundamental understanding regarding the energetics of both

5

the ion removal process and the trajectory of the complete deionization cycle. Evalu-

6

ating the processes and cycles in tandem can elucidate potential sources of inefficiency

7

(entropy production), and may promote new operational schemes leading to higher ef-

8

ficiency low saline separations. Here, using a Gouy-Chapman-Stern model we elucidate

9

the efficiency of two capacitive deionization cycles. In the first cycle, electroadsorption

10

occurs as the cell voltage increases, which resembles processes employed experimen-

11

tally. In the second cycle, a theoretical Carnot-like electroadsorption process occurs

12

while maintaining a constant number of ions (N=constant). We show that the pro-

13

jected thermodynamic efficiency of both cycles exhibited similar efficiency which range

14

from 2-4.5%, while operating with a low saline feed (Cfeed = 20 mM) stream. However,

15

at elevated feed concentrations (100 mM), the Carnot-like electroadsorption process

16

resulted in a significant improvement in thermodynamic efficiency (30%), when com-

17

pared with the conventional electroadsorption process (15%). While the Carnot-like

1

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electroadsorption processes is not technically feasible, it may serve as a benchmark for

19

understanding thermodynamic limits associated with low saline separations achieved

20

through electrosorption.

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21


Introduction

22

The inextricable connection between water and energy promotes investigations that re-

23

duce energy consumption during desalination processes. Moving toward the use of low saline

24

brackish water as a feed solution is one simple approach to achieve low specific energy con-

25

sumption (SEC) desalination. This is because the theoretical minimum energy required for

26

separating brackish waters (≤0.3 kWh/m3 ) is significantly less than that required for seawa-

27

ter separations (3-10 kWh/m3 ). 1,2 Brackish water separation is also increasingly favorable

28

in remote or inland regions which do not have reliable access to seawater. 3

29

A growing interest beyond attaining low SEC is achieving high desalination efficiency.

30

The efficiency by which desalination technologies are evaluated are based on thermodynamic

31

principles or exergy considerations. The thermodynamic energy efficiency (TEE) provides

32

information regarding how far a technology is from the theoretical minimum, whereas exer-

33

getic efficiencies (ExE) provide guidance on how far a technology is away from a practical

34

minimum, based on chemical exergy changes. The TEE has primarily been the guiding tool

35

to measure the efficiency of reverse osmosis (RO), with efficiencies improving from only 5%

36

in the 1970s to over 50% today. 4,5 It should be noted that achieving 100% is not practically

37

possible; therefore little gains in terms of energy efficiency can be made through solely im-

38

proving reverse osmosis for seawater desalination. This is one reason why there is greater

39

interest in mitigating energy consumption in alternative water treatment processes such as

40

pre or post treatment. 6

41

Despite the near ideal performance, RO does not maintain this efficiency when moving

42

toward low saline solutions (brackish water). 7 The SEC for brackish water RO decreases, 8–10

43

but the corresponding decrease in the Gibbs free energy of mixing is greater. This low

44

efficiency is often overlooked, as there is a greater emphasis on SEC. Furthermore, exergetic

45

efficiencies for brackish water RO are less than 10%, 11–13 with the highest reported value

46

of 16%. 14 This is why historically alternative technologies (electrodialysis and capacitive

47

deionzation) are discussed for brackish water treatment. 15–19 Most capacitive deionization 3



48

cycles yield efficiencies in the regime of 1-5% with feed solutions of on the order of 20

49

mM; 16,20–23 however, the aim of these investigations was not on optimizing TEE. In more

50

recent efforts which aimed to improve TEE, maximum values 9% were shown to be possible. 24

51

Here, we aim to analyze the expected thermodynamic and exergetic efficiency of two

52

different capacitive deionization cycles. In the first cycle, electroadsorption and desorption

53

occur as the cell voltage is incrementally increased. This cycle is practically feasible as one

54

can execute the cycle experimentally. The second cycle is purely theoretical, and is based on

55

prior definitions of a Carnot-like chemical cycle for capacitive mixing. 25 In the second cycle,

56

salt removal occurs while maintaining a fixed number of ions (N=constant). By examining

57

both cycles, we aim to discern if the electroadsorption processes within a given desalination

58

cycle (Carnot or conventional) can limit the maximum efficiency. Furthermore, we aim to

59

better describe thermodynamic limitations associated with dilute solution separations.

60

Theory

61

The desalination cycle employed in most capacitive deionization studies includes four

62

consecutive processes. However, just like with thermal energy systems, these cycles can

63

operate using different modes. Thus, achieving ion removal is possible by various different

64

processes. 26–28 Here, we investigate two thermodynamic deionization cycles.

65

In the first cycle, we employ four processes which can be executed in a conventional CDI

66

system. Process one consists of deionization up to a set voltage Vmax . Next in process two,

67

as the feed is switched to a brine the electrodes are continued to be charged at fixed voltage

68

(iso-V - switch). In process three, the electrodes are discharged while the concentration

69

decreases. Then in process four, the electrodes are brought back to the initial conditions

70

(Cfeed replaces Cbrine ) using a constant voltage process (iso-V - switch). Since this cycle

71

operates using conventional processes, we term this the conventional cycle (Figure 1a and

72

b). Evaluating energy consumption will take place through the use of V-σ curves (Figure

4


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73


1e).

74

In the second cycle, we employ processes which are analogous to a Carnot refrigeration

75

cycle. The Carnot cycles for thermal systems represent the ideal (reversible) cycle. It is well

76

known that Carnot cycles cannot be executed in reality, but the theoretical insight provides

77

guidance on how far a real cycle is away from an ideal system. The chemical Carnot cycle

78

was previously described in prior work. 25 Briefly, process one is described by deionization

79

at constant number of ions (iso-N), process two is described by deionization at constant

80

chemical potential (iso-µ), process three is described by resalination at constant number of

81

ions (iso-N), and process four is described by another resalination step at constant chemical

82

potential (iso-µ) (Figure 1c and d). We will refer to this cycle as the Carnot cycle, and

83

energy consumption will be detailed on the µ-N diagram (Figure 1f).

84

For both cycles, we assume a quasi-equilibrium condition, which implies that the cycle

85

operates on an infinitesimally slow flow rate to minimize irreversibilities. This greatly sim-

86

plifies the model since it eliminates the need to specify time dependent parameters, such

87

as current and flow rate. Additionally, considerations regarding cell geometry are not con-

88

sidered, since all quantities here will be evaluated on a per area or per volume basis. The

89

model also does not consider Faradaic losses due to side reactions or resistive losses due to

90

components such as membranes or contacts.

91

In order to describe various iso-property (µ, N, V, C, T, σ) processes for a given capacitive

92

deionization cycle a description for the electric double layer is needed. Here we employed the

93

well documented Gouy-Chapman-Stern (GCS) model to describe the electric double layer

94

dynamics necessary for ion removal. 20 In each of the simulations the maximum voltage Vmax

95

was limited to 1.2 V. In addition, the feed (Cfeed ) remained constant while the deionized

96

concentration (Cmin =Cdeionized ) and water recovery ratio α=Vdeionized /Vfeed were varied. In

97

order to maintain an ion balance during the cycle, the resulting brine concentration Cbrine is

98

determined by:

5



Cbrine =

Cf eed − αCmin 1−α

Page 6 of 24

(1)

99

Since the Carnot analog cycles is constrained to limits of only two concentrations, the high

100

concentration is the brine Cbrine and the low concentration is the diluate Cmin . The chemical

101

potential in the cell at any point is:

µ = RT ln(

C ) Cref

(2)

102

where T is temperature, R is the universal gas constant, and Cref represents a reference

103

concentration, taken to be 1 M. 25 The total number of ions in the cell (per electrode area)

104

N is:

N = Γ + CLe Nav

(3)

105

where Nav is Avogadro’s constant, Le represents the pore length between carbon particles

106

(pore volume/pore area), taken in this study to be 4 nm, and Γ is the excess surface charge.

107

Γ is determined as a function of both the electrode surface charge σ and additional crossover

108

charge σ * : √ Γ = σ 2 + σ ∗2 − σ ∗

σ∗ =

1 2πλB λD

(4)

(5)

109

where the Debye and Bjerrum lengths for the electrolyte, λB and λD determine the crossover

110

charge. 20 Crossover charge is defined as the charge at which attractive forces from counter

111

ions and repulsive forces from co-ions are balanced. 29 When crossover charge exceeds surface

112

charge, the increase in counter ions exceeds the decrease in concentration of co-ions, resulting

113

in a net increase in number of ions adsorbed. 30 If surface charge is smaller, then Γ is directly 6


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114


proportional to σ. The diffuse layer voltage difference ∆VD is given by: s

∆VD = 2VT sinh−1 σ

πkB 2Cf eed Nav

(6)

115

where kB is Boltzmanns constant. The thermal voltage VT is defined as VT = RT/F, where F

116

is Faraday’s constant. For the Stern layer voltage ∆Vst , Gauss law is used for a 1:1 electrolyte

117

(as in the case with NaCl):

∆Vst = σe/Cst

(7)

118

where Cst is the Stern capacity and e is the elementary charge. Previous studies using GCS

119

models have assumed a constant Stern capacity around 0.2 F/m2 . 31,32 Assuming a symmetric

120

cell configuration, the diffuse and Stern layer potentials can be summed and then doubled

121

to provide the total voltage ∆Vcell through the cell:

∆Vcell = 2VT (∆Vst + ∆VD )

(8)

123

For CDI cycles, thermodynamic energy efficiency (TEE) is the ratio of the Gibbs energy H of mixing ∆Gmix to the input cycle work Wcycle , 33,34 measured by V dσ. To equate units

124

with the Gibbs energy of mixing, σ is represented as a volumetric-based charge after dividing

125

by 2x the pore length Le . For any generic separations process, the Gibbs energy of mixing

126

is defined as: 35

122

∆Gmix = nRT

hC

0

α

ln

C − αC C C − αC i 0 min min 0 min − ln C0 (1 − α) α Cmin (1 − α)

ηT EE =

∆Gmix Wcycle

(9)

(10)

127

where n is the van ’ t Hoff Factor, which for 1 : 1 electrolytes assumes a value of 2. Thus,

128

taking relevant limits, mixing energy should maximize when Cmin is lowest and when α is 7



129

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highest.

130

In the case of Carnot analog cycle, the GCS theory imposes constraints on the allowable

131

values for α and Cmin (Figure S1). These limitations occur in the recharging stage, in order

132

to maintain the constant number of ions condition. The limit varies with the chosen feed

133

concentration, water recovery ratio, and maximum allowable voltage. As a result, recovery

134

ratios above the allowable range are not computed. Detail on how this limit was found is

135

included in Supporting Information.

136

Chemical exergy of a feed can be calculated using electrolytic solution models (which use

137

feed concentration references) or Szargut models (which use lithosphere as the reference). In

138

an ideal mixture, molar chemical exergy can be calculated as a function of concentration of

139

water as well as the salt solution:

eCh sol =

X

xi eCh i + RT

i

X

xi lnxi

(11)

i

140

where xi is the mole fraction of the species considered, and eCh is standard molar chemical

141

exergy of this species. Here, the Szargut model for exergy calculation reduces to only consider

142

the activities and molar concentrations of H2 O and NaCl: s Bch = nH2 O eH2 O + nN aCl eN aCl + RT (nH2 O ln(aH2 O ) + nN aCl ln(mN aCl γN aCl ))

(12)

143

where n represents the molar concentration of each species, mNaCl is the molality of NaCl

144

solution (in mol/kg of solvent) and activity coefficients are given as aH2 O for H2 O and γ NaCl

145

for NaCl. 36 Changes in chemical exergy will be accounted for during both the charging

146

and discharging stages. Exergy will be evaluated using the Szargut model, 37 while activity

147

coefficients will be evaluated using the Pitzer model. 38 This is discussed in further detail in

148

Supporting Information (also see Figure S2 for comparative plots of chemical exergy changes

149

at varying concentrations).

150

Exergy efficiency (here referred to as ExE) is determined as the ratio of the chemical

8


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151

exergy change during charging and discharging, to the input electrical exergy Bel , which we

152

take to be the equivalent of the input work (Wcycle ):

ηExE = ∆Bch /∆Bel = ∆Bch /Wcycle

153

Results and Discussion

154

Impact of capacitive desalination cycle

(13)

155

Differences in the energetics of a complete capacitive deionization cycle is indicated by

156

a change in the area of a V-σ or µ-N diagram. The larger the area represents a cycle with

157

greater energy consumption (Figure 1e and f). Experimentalists are able to easily evaluate V-

158

σ diagrams through extrapolating experimental voltage and current (charge) data, whereas

159

in practice µ-N diagrams cannot be measured as easily since the total number of ions in the

160

cell cannot be precisely determined. However, from the differential form of the Helmholtz

161

free energy (dF=µ dN+Vdσ), one can easily see that for a complete thermodynamic cycle

162

where a system returns to the initial state (no net change in energy dF=0), the two integrals

163

are equal in magnitude and opposite in sign (µ dN=-Vdσ). Therefore, both profiles are

164

effective for evaluating total energy consumed during a capacitive deionization cycle (Figure

165

S3).

166

By fixing the initial and final conditions (Cfeed =20 mM, Vmax =1.2 V, and Cmin =1 mM),

167

of a desalination cycle, the measured energy consumption can be normalized per the same

168

number of ions removed, independent of the cycle trajectory (thermodynamic cycle). Here,

169

the fixed conditions equate to a desalination test with 75% salt removal and 50% water

170

recovery (conditions commonly employed by experimentalists). For these conditions, the

171

energy or area of both the V-σ (Figure 2a) and µ-N (Figure 2b) graphs was slightly greater

172

for the Carnot analog than for the conventional operation. For this scenario, the energy

173

consumed was 0.96 kWh/m3 (93 kT/ion) for the Carnot cycle, whereas only 0.48 kWh/m3 9



174

(47 kT/ion) was consumed through the conventional operation.

175

The larger energy consumed during the complete cycle can be attributed to either an

176

increased energy consumption during charging, or to a reduction in energy recovery during

177

discharging. For the individual deionization process (not the entire cycle) the energy is

178

indicated by the area under the 1-2-3 curve and 1’ -2’ -3’ on Figure 2. This energy for ion

179

removal is 8.7 kWh/m3 for the conventional operation and 7.9 kWh/m3 for the Carnot analog.

180

Thus, the Carnot analog did consume less energy during the deionization process than when

181

the cycle had operated conventionally, indicating that adsorption is indeed more ideal, albeit

182

small. Thus the reduction in cycle energy consumption is due to the conventional operation

183

recovering a larger portion of that energy. The corresponding thermodynamic efficiency

184

for the conventional operation and Carnot analog was TEE=3.6% and TEE=1.8%. The

185

thermodynamic efficiency appears low, but this is in line with other reported values. 16,21–23 As

186

the cycles studied here operate without transient or geometric considerations, we are limited

187

in the full range of explorable design parameters. Employing these additional capabilities

188

while tending to optimal operating conditions can allow for an increase in efficiencies. 24

189

Impact of feed water concentration

190

To evaluate the effect of the various boundary conditions, the TEE was measured for both

191

the Carnot analog and the conventional operation as the water recovery (α) and percent of

192

salt removed (∆C/Cfeed ) was varied (Figure 3). In all tests, the starting concentration C0

193

remained fixed at either 20 mM or 100 mM, maximum cell voltage Vmax was constrained

194

to 1.2 V, and minimum cell voltage Vmin was 0.1 V. With the 20 mM feed, increasing the

195

percent of salt removed, and water recovery resulted in a greater TEE irregardless of cycle

196

(Figure 3a and b). The TEE again was on average two times greater for the conventional

197

operation than for the Carnot cycle, but never exceeded 4%. While the percent of salt

198

removal had a significant effect on the apparent maximum thermodynamic efficiency, the

199

water recovery did not. Increasing the water recovery (α) from 25% to 75% only increased 10


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200

the TEE by 0.5% for the conventional operation, and 2% for the Carnot cycle. The increase

201

observed at higher salt removal is due to a greater Gibbs energy of mixing needed for the

202

cycle, which grows faster than the required cycle work.

203

When the feed increased from 20 mM to 100 mM, the TEE increased by nearly four times.

204

With the Carnot cycle, the constant number of ions criteria could not be maintained at high

205

percent salt removal or higher concentrations. To overcome this model limitation, additional

206

boundary conditions with respect to the minimum concentration and water recovery were

207

placed on each simulation, taking into account the input voltage (discussed in greater detail

208

in Supporting Information; see Figure S1 and S4). It should also be noted that most CDI

209

systems do not operate with 100 mM salt solutions, as the limited available surface area

210

would likely result in salt removal of only 1% to 50% depending on the size of the system.

211

However, the aim in investigating these conditions was to evaluate the thermodynamics of the

212

separations process, as there is a greater amount of thermodynamic separations data available

213

at higher concentrations. Furthermore, with the development of CDI with unlimited surface

214

area (e.g. flow electrodes), capacitive deionization technologies are beginning to evaluate

215

higher saline solutions. 39,40

216

With 100 mM feed solutions, the TEE increases substantially from only 5% at 20 mM

217

to 20% at 100 mM (Figure 3c and d). In addition to the increase in efficiency, the Carnot

218

analog achieves higher TEE at corresponding salt removal rates and water recovery. This is

219

because for this concentration range, the Carnot cycle operates at nearly optimal conditions.

220

The higher conditions allow for the minimum cell charge to approach zero during discharge

221

(with the constant number of ions criteria), which substantially reduces the total cycle work

222

consumed. At higher concentration ranges (≥ 100 mM), the theoretical efficiency even begins

223

to approach 100% (Figure 4a). The conventional operating cycle, on the other hand, achieves

224

maximum efficiencies around 5-10% (Figure 4b).

225

The effect of feed water concentration (Figure S5), shows that there is a sharp increase

226

in the TEE for the Carnot analog if high water recovery is possible, with TEE approaching

11



227

30%. Unlike the Carnot analog (Figure S5a), the conventional operation does not show a

228

dependence on water recovery (Figure S5b). The stronger dependence for the Carnot analog

229

is an indicator that the cycle is approaching its near-ideal limiting cases at higher concentra-

230

tion. Thus, moving to even higher salinity feed streams would increase the theoretical limit

231

to above 50% which is in line with observed TEE found in most state of the art membrane

232

based technologies. At higher concentration, it also becomes apparent that the Carnot ana-

233

log and conventional electrosorption process differ. With the same concentration limits, the

234

Carnot analog exceeds the traditional cycle’s efficiency of ≈15% by over 2x.

235

For the cycle limits established, the effect on charge over the various concentrations was

236

also examined. Charge for the surface, crossover, and total excess charge are nearly the same

237

magnitude in all cases (Figure S6). As a result, efficiencies are not affected by charge, but

238

rather by deviations within these values during cycling which change the work required to

239

operate (See Figure 1b).

240

Exergetic efficiency of capacitive deionization cycles

241

Similar to TEE, exergetic efficiency (ExE) for the conventional cycle exceeded those of

242

the Carnot analog using the baseline conditions (Cfeed =20 mM, Cmin =1 mM, Vcell =1.2 V,

243

α=50%). ExE also generally increased with salt removal at high and low water recoveries,

244

for both the conventional cycle and the Carnot analog (Figure S7). For this nominal test

245

case, the maximum value for ExE observed was 12%, at a nearly 80% salt removal for the

246

conventional cycle (Figure S7b). This is comparable to the maximum values observed in

247

prior studies on MCDI. 14,36 As this study was computational and assumed to run infinitely

248

slow, additional exergy losses that did not need to be considered for this study (i.e. pumps)

249

would need to be accounted for in experiments, and would lower exergetic performance.

250

However in both cycles, the ExE (Figure 4c and d) efficiency increased with an increase

251

in water recovery and generally with increased salt removed. Furthermore, theoretical ExE

252

values approached 100% for the Carnot cycle and 30% for the conventional operation mode. 12


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253


Conclusions

254

Various system properties and processes contribute to the observed thermodynamic and

255

exergetic efficiency of a capacitive deionization cycle. Here, we evaluate two deionization

256

cycles. One mimics an executable approach whereby ion removal occurs during charging

257

with constant voltage switching, the other is a Carnot analog cycle where ion removal occurs

258

while maintaining a constant number of ions. Under low saline conditions the energetics

259

associated with voltage regulated electroadsorption were slightly more favorable, and resulted

260

in predicted thermodynamic efficiencies that approach 2-5%. However, when feed solutions

261

were increased to 100 mM the energetics of constant N electroadsorption was favored over

262

the conventional approach, and the maximum thermodynamic efficiencies approached 37%

263

(Figure 5). In all simulations, thermodynamic efficiencies improved as Cfeed , and ∆C (Cfeed -

264

Cmin ) increased. A survey of experimental capacitive deionization system performance will

265

reveal that actual desalination performance data is far below these values (≤ 1 %) for CDI

266

and (≤ 3%) for membrane CDI. However, this is due to the low effective surface area available

267

in lab scale systems, which limit the operation to low Cfeed , ∆C, and only 50% water recovery.

268

As experimentalists begin to further explore the CDI operational space, increased TEE may

269

be observed. Interestingly, this is similar to trends observed with thermal heat engines,

270

whereby increasing the T0 and maximizing ∆T results in higher thermodynamic efficiencies,

271

due to an increase in the theoretical Carnot limit. When evaluating the CDI TEE to a

272

Carnot analog, at low feed concentrations, the actual cycle perform similarly to that of a

273

Carnot analog. This indicates that while efficiencies are low, limitations may exist which

274

prevent substantial improvements. However, efficiency improvements are increased if the

275

feed stream concentration increases.

13



276

Acknowledgement

277

This material is based upon work supported by the National Science Foundation under

278

Grant No. (1821843) for MCH. This work is also supported by the ARCS graduate fellowship

279

to Daniel Moreno.

280

Supporting Information Available

281

The Supporting Information includes additional detail on constraints on the Carnot ana-

282

log cycle and calculation of exergy values. We also show additional modeling result detailing

283

the effect of water recovery, surface charge, and feed concentrations.

284

285

286

287

288

289

290

291

292

293

294

295

This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Spiegler, K. S.; El-Sayed, Y. M. The energetics of desalination processes. Desalination 2001, 134, 109–128. (2) Oren, Y. Capacitive deionization (CDI) for desalination and water treatmentpast, present and future (a review). Desalination 2008, 228, 10–29. (3) Karagiannis, I. C.; Soldatos, P. G. Water desalination cost literature: review and assessment. Desalination 2008, 223, 448–456. (4) Kremen, S. S. Reverse osmosis makes high quality water now. Environ. Sci. Technol. 1975, 9, 314–318. (5) McGovern, R. K.; Lienhard, J. H. On the potential of forward osmosis to energetically outperform reverse osmosis desalination. J. Membr. Sci. 2014, 469, 245–250.

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18


Page 18 of 24

Conventional (b)

Win

++++++++++++++++++

Cfeed

_

+ _

+ _

_

_ +

_

_ _

Cdeionize

+ + + + + + + - - -- -- -- -- -- -- -- -- -- -- -- -- - -

I

+ _

_

+ _

N

+ _

+

_

__ _

_

_

Carnot-analog (d) _

_ +

_

_ _

+ + + + + + + - - - - - - - - - - - - - - - -

Process 1’-2’

Cdeionize

µ

Constant V

Cdeionize

+ + + + + -- -- -- -- -- -- -- -- -- -- -- -- -- --

V

++++++++++++++++++

Cfeed

_

__ ++

Process

Win

(c)

Conventional

++++++++++++++++++

Cfeed

Process

(e)

Win

Win

++++++++++++++++++

Cfeed

_

+ _

__ ++

_

+

__ _

_

_

Cdeionize

+ + + + + -- -- -- -- -- -- -- -- -- -- -- -- -- --

1

Process 2’-3’

(f) 2 3

Carnot-analog

2’

4

Charge

4’

1’

Chemical Potential

(a)

Voltage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Constant N

Page 19 of 24

Constant µ

3’

Number of Ions

Figure 1: (a) Ion removal in the IV cycle occurs through a constant current (iso-I) process followed by a (b) constant voltage (iso-V) process. (c) Ion removal in the Nµ (Carnot-like) cycle occurs through a constant number of ions (iso-N) process followed by (d) a constant chemical potential (iso-µ) process. (e) The trajectory of the cycles is evaluated on a voltage versus charge (σ), or (f) chemical potential (µ) versus number of ions (N) diagram.

19



(a)1.4

Carnot cycle Conventional Cycle

Voltage (V)

1.2

3’ 2 3

1.0

4’

0.8 0.6 0.4 0.2

2’ 1’ 14

0.0 0.0

0.1 0.2 0.3 0.4 0.5 Surface Charge (#/nm2)

(b)-2.5 Chemical Potential

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

-3.0 -3.5 -4.0 1 -4.5 -5.0 -5.5 -6.0 -6.5 -7.0 -7.5 0.0

4 1’

0.6

4’ 3

2’ 0.1

3’

2

0.2 0.3 0.4 0.5 Number of ions (#/nm2)

0.6

Figure 2: (a and b) N-µ and I-V capacitive deionization desalination cycles represented by a V-σ, and µ-N diagrams. Numbers represent each process within the desalination cycle. For both cycles the Cfeed used is 20 mM, with a Cmin of 1 mM and α = 0.5.

20


Page 21 of 24

(b )

(a ) 5

5

α= 0 .2 5 α= 0 .5 α= 0 .7 5 4

4 3

T E E (% )

T E E (% )

3 2

2

1

1 0

0 .0

0 .2

0 .4 ∆C / C

(c )

0 .6

0 .8

0

1 .0

fe e d

(d )

2 0

0 .0

0 .2

0 .4

0 .6

∆C / C

2 0

0 .8

1 .0

0 .8

1 .0

fe e d

1 5 T E E (% )

1 5 T E E (% )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 0

1 0

5 5

0

0 .0

0 .2

0 .4 ∆C / C

0 .6

0 .8

0

1 .0

0 .0

0 .2

0 .4 ∆C / C

fe e d

0 .6 fe e d

Figure 3: Evaluation of thermodynamic energy efficiency with Cfeed = 20 mM feed (a) Carnot analog, and (b) conventional mode. Efficiency measured with Cfeed = 100 mM feed (c) Carnot analog and (d) conventional mode cycle.

21



(b )

1 .0

0 .8

0 .8

0 .6

( b ) 0 .6 fe e d

1 .0

∆C / C

∆C / C

fe e d

(a )

0 .4

1 .0

0 .4

0 .8 0 .2 fe e d

0 .2

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

0 .4 0 .0

1 .0

α

(c )

0 .6 0 .0

∆C / C

0 .0

(d )

0 .2

0 .4

0 .6

0 .8

α

1 .0

0 .2 0 .8

0 .8

fe e d

0 .6

∆C / C

fe e d

0 .0

∆C / C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 24

0 .4 0 .2

0 .6

0 .0

0 .2

0 .4

0 .6

0 .8

T E E /E x E 1 6 4 2 1 1 7 4 3 1 .0 2 1 0 0 0 0 0 0 1 .0

(% ) 0 0 5 2 7 8 2 .5 .9 .2 .1 .3 .8 7 .5 6 .3 7 .2 4 .1 5 .1 0

α

0 .4 0 .2

0 .0

0 .0 0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

0 .0

0 .2

α

0 .4

0 .6

0 .8

1 .0

α

Figure 4: Contour plots of thermodynamic energy efficiency (TEE) and exergetic efficiency (ExE) as a function of water recovery ratio α and salt removal ratio ∆C/Cfeed . In all cases shown here Cfeed = 20 mM. (a) TEE, Carnot analog cycle, (b) TEE, conventional mode cycle, (c) ExE, Carnot analog cycle, (d) ExE, conventional mode cycle.

22


Page 23 of 24

50 Carnot Analog Conventional Operation

40

TEE (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30 20 10 0

0

20

40

60

80

100

Cfeed (mM)

Figure 5: Evaluation of thermodynamic energy efficiency (TEE) at varying initial feed concentrations for a diluate value of Cd = 5 mM and water recovery α = 0.5.

23



Graphical TOC Entry Efficiency of Desalination Cycles

High Salt

++++++++++++++++++

_ _ _ __ _ __ _ + ++ + + + + + -- -- -- -- -- -- -- -- -- -- -- -- -- --

Low Salt

Voltage

384

Carnot-analog 1’ 4’

Conventional 3 2 Chemical Potential

383

+ _

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 24

Win

2’

1 4 Charge

24

3’

Number of Ions


Efficiency of Carnot and Conventional Capacitive ... - ACS Publications

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