Global Sensitivity Analysis To Characterize Operational Limits and

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Sustainability Engineering and Green Chemistry

Global sensitivity analysis to characterize operational limits and prioritize performance goals of capacitive deionization technologies Steven Hand, Xia Shang, Jeremy S. Guest, Kyle Christopher Smith, and Roland D. Cusick Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b06709 • Publication Date (Web): 01 Mar 2019 Downloaded from http://pubs.acs.org on March 4, 2019

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Environmental Science & Technology

Global sensitivity analysis to characterize operational limits and prioritize performance goals of capacitive deionization technologies

Steven Hand1, Xia Shang2, Jeremy S. Guest1, Kyle C. Smith2,3,4,5, and Roland D. Cusick1*

1 2

Department of Civil and Environmental Engineering

Department of Mechanical Science and Engineering 3

4

Department of Materials Science and Engineering

Beckman Institute for Advanced Science and Technology 5

Computational Science and Engineering Program

University of Illinois at Urbana-Champaign, Urbana, IL 61801-2352

*Corresponding author 3217 Newmark Civil Engineering Laboratory 205 North Mathews Avenue Urbana, IL 61801-2352 E-mail: [email protected]; Phone: +1 (217) 244-6727

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ACS Paragon Plus Environment


1

Abstract

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Capacitive deionization (CDI) technologies couple electronic and ionic charge

3

storage, enabling improved thermodynamic efficiency of brackish desalination by

4

recovering energy released during discharge. However, insight into CDI has been

5

limited by discrete experimental observations at low desalination depths (Δc, typically

6

reducing influent salinity by 10 mM or less). In this study, the performance and

7

sensitivity of three common CDI configurations (standard CDI, membrane CDI [MCDI],

8

and flowable electrode CDI [FCDI]) were evaluated across the operational and material

9

design landscape by varying eight common input parameters (electrode thickness,

10

influent concentration, current density, electrode flow rate, specific capacitance, contact

11

resistance, porosity, and fixed charge). All combinations of designs were evaluated for

12

two influent concentrations with a calibrated and validated 1-D porous electrode model.

13

Sensitivity analyses were carried out via Monte Carlo and Morris methods, focusing on

14

six performance metrics. Across all performance metrics, high sensitivity was observed

15

to input parameters which impact cycle length (current, resistance, and capacitance).

16

Simulations demonstrated the importance of maintaining both charge and round-trip

17

efficiencies, which limit the performance of CDI and FCDI, respectively. Accounting for

18

energy recovery, only MCDI was capable of operating at thermodynamic efficiencies

19

similar to reverse osmosis.

20 21 22 23 24 25

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26 27


Graphical Abstract:

CDI Design Space MCDI

28 29 30 31

FCDI

Normalized Value [0-1]

1

0.5

0 SAC

ENAS

2

CE

2RTE

2T

1. Introduction

32

Capacitive deionization (CDI) is an electrochemical desalination technology which

33

has been investigated as an energy efficient alternative to reverse osmosis (RO) and

34

electrodialysis (ED) for low salinity or brackish waters.1–5 In CDI, porous carbon

35

electrodes are polarized during charging, removing and storing ions from solution in

36

electrical double layers (EDLs), depending on the degree of polarization.1,6,7 Unlike RO

37

and ED, a portion of the applied energy during charging can be directly recovered as

38

electrical energy during discharge/brine generation.8,9 In theory, all input energy apart

39

from the thermodynamic minimum energy of separation should be recoverable. In

40

practice, parasitic side reactions, low charge efficiency, and electronic/ionic resistance

41

limit energy recovery.6,9–11

42

In order to achieve efficient desalination, several operational, material, and

43

architectural variations of CDI have been proposed. CDI has been operated in multiple

44

charging modes, most notably constant current (CC) or constant voltage (CV)8,12,13. In

45

order to recover energy, CDI systems must be discharged at non-zero cell voltages, which

46

is typically achieved through CC operation.8 However, CC operation often exhibits lower

47

charge efficiency (the ratio of charge applied to equivalents of salt removed) than CV

3



48

operation.13 The lower charge efficiency of CC operation is due partially to brine/product

49

water half-cycle overlap.6,14,15 This effect has been directly characterized as flow

50

efficiency by Hawks et al.,15 and has been shown to substantially impact CDI performance

51

in shorter charging cycles (higher applied current).

52

Similar to operational variations, modifications to cell architecture and design have

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been proposed to improve CDI performance, such as membrane capacitive deionization

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(MCDI),2,9,13,16,17 flowable electrode capacitive deionization (FCDI),16,18–22 and modified

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carbons with fixed charge.23,24 In MCDI architectures ion exchange membranes (IEMs)

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are added which separate the electrodes from the flow channel to be desalinated. By

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trapping co-ions behind IEMs during charging/discharging, MCDI systems improve

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charge efficiency and reduce the macropore depletion seen in traditional CDI.17,25 As

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opposed to incorporating IEMs, immobilizing fixed charge on the surface of treated

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carbons has been shown to reduce co-ion repulsion and promote additional counter-ion

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adsorption in the micropores.23,26 Lastly, in order to achieve greater desalination depth,

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flowable carbon slurries have been substituted for stationary electrodes in FCDI (typically

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in combination with IEMs to provide a barrier between the flowable electrodes and

64

treatment stream).

65

While MCDI and FCDI have been advantageous over CDI under certain

66

conditions, there has been little investigation of their comparative performance across the

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CDI design space. By utilizing flowable electrodes, FCDI is capable of decoupling

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electrode geometry and carbon loading, but flowable electrodes are typically limited by

69

higher overall resistance than stationary electrodes.27–29 The expectedly poor energetic

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performance of FCDI has received little evaluation as few studies have reported the

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energetic performance of FCDI.21,22 Conversely, many studies have found that MCDI

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outperforms CDI in both in desalination and energy consumption, but few studies have

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evaluated the thermodynamic efficiency of MCDI for comparison with other desalination

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technologies.4,9,17,30 Notably, Hemmatifar et al.4 have shown thermodynamic efficiency

75

(ηT) calculated for previous studies to be limited by low desalination depth typically seen

76

in CDI experiments (typically less than Δc = 10 mM).

77

In this study, the performance and sensitivity of three common CDI configurations

78

(standard CDI, MCDI, and FCDI) were evaluated with a calibrated and validated 1-D

79

porous electrode model across operational and material design landscape. Simulations

80

were operated at a fixed effluent concentration necessary for practical treatment of

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brackish water (total dissolved solids concentration of 500 mg L-1). The performance of

82

CDI, MCDI, and FCDI were investigated using thermodynamic efficiency and five other

83

common performance metrics while varying eight common operational and material

84

parameters. Operational tradeoffs were explored to identify conditions for optimal

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desalination with capacitive materials (Fig. 1). Lastly, we examine the impacts of

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increasing water recovery on thermodynamic efficiency.

87

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INPUTS Operational

Architecture

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OUTPUTS Material SAC

Electrode Thickness

Specific Capacitance

Influent Concentration

Contact Resistance

IEMs

CDI

Ω

ENAS ηCE

MCDI Porosity Current Density

NH3+ NH3+

FCDI

88

ASAR

Electrode Flow Rate

COO-

ηRTE

COO-

Fixed Charge

ηT

89 90 91

Figure 1: Conceptual flow diagram for system configurations and design variables investigated. Input ranges and distributions were determined from reported values in literature.

92 93

2. Materials and Methods

94

2.1 CDI, MCDI, and FCDI Models

95

In all architectures, ion removal was simulated with a 1-D porous electrode model

96

in a single cell composed of a flow channel and two symmetrically sized carbon electrodes

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(0.41 g of carbon fixed in CDI/MCDI and flowing in FCDI) as described in Shang et al.6 In

98

order to constrain the effluent concentration across all runs, the cell was operated at

99

constant current under concentration threshold pulsed flow, in which individual aliquots

100

of water are desalinated until the target effluent concentration is reached and another

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aliquot is flown into the cell for desalination. Diffusion and migration transport processes

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within dilute NaCl solution were assumed to occur with equal diffusion coefficients for

103

cations and anions using the model described in our previous work6 that also utilizes the

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amphoteric Donnan model23 for ion electrosorption. We refer the reader to our previous

105

study for equations and boundary conditions governing the salt concentration and

106

potential distributions within porous electrodes and flow channels.6 All simulations were

107

initialized with uniform concentration across the cell, and zero electronic charge density

108

in the electrodes. Leakage current associated with parasitic reactions was incorporated

109

into CDI simulations but not in FCDI/MCDI where leakage current which is typically far

110

lower due to the presence of IEMs.31 Faradaic reaction parameters were not varied in

111

simulations and were previously fitted for CDI (see Shang et al.6 for additional details

112

regarding parameter fit). All simulated CDI cells were allowed to reach a limit cycle (ten

113

cycles were sufficient to reach steady-state in all architectures) and operated with the

114

same total carbon loading regardless of geometry or electrode thickness.

115

In order to model MCDI cells, the CDI model was modified to include ideally

116

permselective IEMs (i.e., only allowing transport of counter-ions) as has been previously

117

reported.32–34 Following Refs. 33 and 34 we enforce this condition using the following

118

Neumann boundary condition on the salt concentration field derived from the dilute

119

solution Nernst-Planck fluxes from cations and anions33,34: ())

120

−𝐷$%&' ∇𝑐( = 𝚤 𝑡/,1 − 𝑡(,1

𝐹.

(1)

())

121

Here 𝐷$%&' is the effective diffusion coefficient of salt (which is the harmonic mean of cation

122

and anion effective diffusivities35 and is also adjusted from bulk values to account for

123

porosity and tortuosity6), 𝑐( is salt concentration in the electrolyte, 𝐹 is Faraday’s constant,

124

𝚤 is the ionic current density in the electrolyte, 𝑡/,1 is the cation transference number in

125

the IEM of interest, and 𝑡(,1 is the cation transference number in the electrolyte. For the

126

present ideally permselective IEMs 𝑡/,1 = 1 and 𝑡/,1 = 0 for cation- and anion-selective

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IEMs, respectively. For the present simulations we assume symmetric anion and cation

128

diffusivity such that 𝑡(,1 = 1/2. Across each membrane we account for membrane

129

potential due to Donnan exclusion and diffusion effects following Refs. 33, 34 and 67: ;

130

ϕ:( − ϕ( = 1 − 2𝑡/,1 :/;

:/;

𝑅𝑇 ; 𝑙𝑛 𝑐(: 𝑐( , 𝐹

2

131

Here ϕ(

132

electrolyte on side 𝑖 or side 𝑗 of a certain IEM, 𝑇 is temperature, and 𝑅 is the universal

133

gas constant.

and 𝑐(

are the electric potential and salt concentration, respectively, in the

134

Calibration and validation of simulated CDI system has been previously reported.6

135

Briefly, individual model parameters were determined experimentally or were derived

136

from the literature. Four parameters (Stern-layer capacitance, fixed charge on the positive

137

electrode, exchange current density for oxygen reduction, and effective surface area for

138

faradaic reactions) were used to calibrate fit. The addition of IEMs in simulated MCDI

139

system operation was experimentally validated with cell parameters taken from previous

140

CDI calibration and electrochemical impedance spectroscopy (EIS) characterization of

141

resistances (Fig. S1 and Table S1; for additional details on experimental validation of

142

MCDI, see Supporting Information Section 2). Flowable electrodes in FCDI were modeled

143

as pulsed-flow in which an aliquot of slurry was flowed into the electrode channels at set

144

frequency/residence time. The pulse was collected in a reservoir that was completely

145

mixed before another aliquot returned to the electrode channel, analogous to isolated

146

closed-cycle (ICC) operation of FCDI previously described (Fig. S2).21

147 148

2.2 Performance metrics

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149

Several metrics have been proposed to evaluate CDI performance including salt

150

adsorption capacity (SAC), average salt adsorption rate (ASAR), charge efficiency (λ or

151

ηCE), and round-trip efficiency/energy recovery (ηRTE).1,9,36,37 Because separation

152

conditions vary significantly between RO and CDI, most notably desalination depth (Δc,

153

the difference between influent and effluent concentration), it is critical to develop metrics

154

which allow for direct comparison between desalination technologies. Two of the more

155

relevant metrics for more direct comparison of desalination technologies are energy-

156

normalized adsorbed salt (ENAS)10,14 and thermodynamic efficiency (ηT)4,9, both of which

157

quantify salt removal per unit of input energy. However, while thermodynamic efficiency

158

provides a measure of how efficiently a separations process performs at given conditions

159

it does capture productivity or throughput. As recently proposed,38 volumetric energy

160

consumption (Ew) provides a means of evaluation energy consumption with respect to

161

water production.

162

Salt adsorption capacity (SAC) was calculated as the mass of NaCl (as mg-NaCl)

163

removed during charging normalized to the total carbon loading in the system (as g-

164

carbon).1 Similarly, average salt adsorption rate (ASAR) was measured as the mass of

165

NaCl removed during charging normalized to the total carbon loading in the system and

166

divided by the total length of the cycle (charging + discharging time length).1,36 Energy

167

normalized adsorbed salt was calculated as the salt removed during charging (as µmol-

168

NaCl) normalized to the energy input during charging (as J).10 Charge efficiency (ηCE)

169

was calculated as the ratio of moles of NaCl removed during charging to the equivalents

170

of charge passed during charging.1 Round-trip efficiency (ηRTE) was calculated as the ratio

171

of energy released during discharge to energy input during charging.9 Lastly,

9



172

thermodynamic efficiency (ηT) was calculated as the thermodynamic minimum or Gibbs

173

free energy of separation divided by the input energy during desalination. All energetic

174

values were calculated without considering energy recovery during discharge unless

175

otherwise stated.4,9 When evaluating water recovery, the brine concentration ratio was

176

defined as the ratio of brine to effluent concentration. (Detailed equations for all evaluation

177

metrics can be found in Supporting Information Section 3).

178 179

2.3 Design landscape

180

Eight material (specific capacitance, contact resistance, porosity, and carbon fixed

181

charge) and operational variables (electrode thickness, influent concentration, current

182

density, and flowable electrode flow rate for FCDI) were investigated to measure output

183

sensitivity for all architectures (Fig. 1 and Table S2). In order to simulate energy recovery

184

during operation, all simulations were conducted at constant current. The cell voltage limit

185

for each simulation was fixed at 1.2 V. All other cell parameters (including total electrode

186

mass, carbon conductivity, IEM resistance, diffusion coefficients, etc.) were kept constant

187

during simulations (Table S1). In order to evaluate performance under practical

188

desalination depths necessary for treating brackish water to potable standards, the

189

effluent concentration was constrained to 8.5 mM. All architectures were tested at two

190

influent concentrations (50 and 25 mM) and two electrode thicknesses (300 and 150 µm)

191

for a total of four conditions (50 mM/300µm 25mM/300µm, 50mM/150µm, and

192

25mM/150µm).

193 194

2.4 Sensitivity analyses

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The eight material and operational inputs were evaluated via Monte Carlo

196

simulation with Latin hypercube sampling (LHS) from uniformly distributed probability

197

functions determined from the literature (Table S2). At least 1,000 simulations were run

198

for each of the four influent concentration/electrode thickness conditions and three

199

architectures (totaling 12,000 individual trials). The correlation between input parameters

200

and performance metrics were evaluated using Spearman’s rank correlation coefficients.

201

Additional sensitivity analysis was conducted via the Morris method39 with 4,000

202

simulations for each of the four conditions across all architectures, totaling 16,000

203

simulations across all architectures/conditions. The mean of absolute elementary effects,

204

µ*, and standard deviation, σ, were calculated per Campolongo et al.’s revised method.40

205 206

3. Results and Discussion

207

The raw data outputs of CDI, MCDI, and FCDI from model simulations (totaling

208

12,000 individual trials) were evaluated for common desalination and energetic

209

performance metrics, which were individually normalized to a linear scale between 0

210

(minimum value achieved across all trials) and 1 (maximum value achieved across all

211

trials). While relative performance was typically clustered together according to cell

212

architecture (CDI, MCDI, and FCDI), notable variance was observed in individual metrics

213

for each architecture. In the absence of IEMs, changes in material and operational inputs

214

produced high charge efficiency variance in CDI (Fig. 2). The most uniform distribution of

215

performance for all architectures was seen in round-trip and thermodynamic efficiency

216

because these metrics are significantly affected by operational inputs (current and

217

resistance) as opposed to architectural differences. Broadly, these trends are due to a

218

combination of the performance tradeoffs associated with cell geometry and confounding

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effects between individual operational and material inputs. Specific tradeoffs in

220

performance can be clearly observed in the inverted simulated run distribution between

221

ASAR (which is governed by current density) and ENAS/SAC (which is dependent on

222

multiple operational and material inputs). These results highlight that architecture will

223

constrain performance in terms of salt removal and energy efficiency within specific limits,

224

while operational and material parameters principally serve to change the performance

225

of individual systems within their respective performance spaces. Specifically, CDI

226

desalination efficiency is limited by low charge efficiency and FCDI is limited by low round

227

trip efficiency, regardless of changes in operation.

228

Normalized Value [0-1]

229

230 231 232 233 234 235 236 237 238 239

1 MCDI

0.5

FCDI CDI

0 SAC

ASAR

ENAS

2CE

2RTE

2T

Figure 2: Raw data outputs of CDI, MCDI, and FCDI model simulations (totaling 12,000 individual trials) treated to produce common desalination and energetic performance metrics. Each line represents the performance output for a single randomized trial. Performance metrics were individually normalized to the minimum and maximum value for the total set of CDI (grey), MCDI (blue), and FCDI (red) trials. For example, the trials with normalized SAC values of 0.5 correspond SAC halfway between the minimum and maximum observed SAC. Quantiles of each performance metric are collated by architecture, electrode thickness, and influent concentrations in Figure 3 and summarized in Table S3.

240 241 242

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243 244 245

3.1 Impact of design and operation on salt adsorption capacity

246

influent concentrations and electrode thicknesses (Fig. 3). The difference in MCDI and

247

CDI or FCDI SAC was found to be significant via two-sample t-test at probability value

Global Sensitivity Analysis To Characterize Operational Limits and

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