Modeling Remineralization of Desalinated Water by Micronized

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Modeling Remineralization of Desalinated Water by Micronized Calcite Dissolution David Hasson, Larissa Fine, Abraham Sagiv, Raphael Semiat, and Hilla Shemer Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03069 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 23, 2017

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Environmental Science & Technology

1

Modeling Remineralization of Desalinated Water

2

by Micronized Calcite Dissolution

3

David Hasson*, Larissa Fine, Abraham Sagiv, Raphael Semiat, Hilla Shemer

4

Rabin Desalination Laboratory, Technion-Israel Institute of Technology, Haifa 32000, Israel

5 6

*Corresponding author. Tel.:+972 4 8292936; e-mail: [email protected] (D.H).

7 8

ABSTRACT: A widely used process for remineralization of desalinated water consists of

9

dissolution of calcite particles by flow of acidified desalinated water through a bed packed

10

with millimeter-size calcite particles. An alternative process consists of calcite dissolution by

11

slurry flow of micron-size calcite particles with acidified desalinated water. The objective of

12

this investigation is to provide theoretical models enabling design of remineralization by

13

calcite slurry dissolution with carbonic and sulfuric acids. Extensive experimental results are

14

presented displaying the effects of acid concentration, slurry feed concentration and

15

dissolution contact time. The experimental data are shown to be in agreement within less than

16

10% with theoretical predictions based on the simplifying assumption that the slurry consists

17

of uniform particles represented by the surface mean diameter of the powder. Agreement

18

between theory and experiment is improved by 1 to 8% by taking into account the powder

19

size distribution. Apart from the practical value of this work in providing a hitherto lacking

20

design tool for a promising novel technology, the paper has the merit of being among the

21

very few, publications, providing experimental confirmation to the theory describing reaction

22

kinetics in a segregated flow system.

1 ACS Paragon Plus Environment

Volume (%)


15

Remineralized water

10

[Acid]out [Ca]out [S0]out dP0 out

5

·

0 0

Desalinated water [Acid]0 [Ca]0=0 [S0]in dP0 in

· 2

4

6

Inlet Outlet

23

Page 2 of 23

8

10

12

14

Size (µ µm)

24 25

1. INTRODUCTION

26

The final step in the production of desalinated water is a process of remineralization.

27

Minerals essential for human health and for suppressing the corrosive properties of pure

28

water are added to the permeate. Typically, the water is remineralized to provide a calcium

29

content in the range of 60 to 120 mg/L as CaCO3 and alkalinity in the range of 50 to 150

30

mg/L as CaCO3.1-3

31

A widely used remineralization process consists of dissolution of calcite particles by

32

desalinated water, rendered acidic through dosage of carbon dioxide or sulfuric acid at a pH

33

below 4.5. The overall reactions involved are:

34

CaCO3 + CO 2 + H 2 O → Ca 2 + + 2HCO3−

(1)

35

2CaCO3 + H 2SO 4 → 2Ca 2+ + 2HCO3− + SO 24−

(2)

36

The process is undertaken by flow of acidified desalinated water through a bed of millimeter-

37

size calcite particles. Typical Empty Bed Contact Times (EBCT) are in the range of 20 to 35

38

min and typical superficial flow velocities through the bed are in the range of 5 to 15 m h-1.

39

A major parameter governing the kinetics of solid particles dissolution is the contact

40

area exposed by the particles. Since contact area per unit volume is inversely proportional to

41

particle size, micron-size particles expose a contact area three orders of magnitude larger than


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42

that of millimeter size particles.4 Dissolution of micron size particles is therefore expected to

43

have the adavantage of reacting at very high rates.

44

Recently, a novel remineralization process based on dissolution of a miconized calcite

45

slurry by carbon dioxide has been publicized.5-9 However no information is available on the

46

kinetics of dissolution which is essential for optimizing the process by quantitative evaluation

47

of the effect of feed conditions on the final slurry composition. The objective of this research

48

was to develop theoretical models describing the kinetics of slurry dissolution of micronized

49

calcite particles and to confront model predictions with experimental data. This research

50

analyzes dissolution of micronized calcite particles with carbonic and sulfuric acids and

51

compares the capabilities of the two acid systems.

52 53

2. MODELING CALCITE POWDER DISSOLUTION

54

2.1 Equilibrium Solubility of Calcite in Carbonic Acid Solution. The maximum calcium

55

concentration obtained from a given feed acidity is governed by the calcite solubility product

56

and the first and second equilibrium dissociation constants of carbonic acid. For the usual

57

case of calcium bicarbonate free inlet water ([Ca2+]0=[HCO3]0=0) the equilibrium calcium ion

58

solubility [Ca2+]e for a carbonic feed acidity [CO2]0 is:3

59 60

[ CO2 ]o =

3 4K 2 ⋅ Ca 2+  + Ca 2+  e e K1Ksp

(3)

The residual carbonate species are given by: 3

KK  HCO 3−  Ca  =  = 1 sp [CO 2 ]e  e 4K 2  2 e 2+ 3

61

(4)

62

2.2 Equilibrium Solubility of Calcite in Sulfuric Acid Solution. As before, the equilibrium

63

calcium solubility obtained from a given sulfuric acid feed concentration [ST] is governed by



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64

calcite solubility product and the first and second equilibrium dissociation constants of

65

carbonic acid.

66

The equilibrium sulfate species are related by the second dissociation constant of sulfuric

67

acid:

[H +]e ⋅ [SO4 2− ]e = 10−2 mol L−1 at 25o C − [HSO4 ]e

68

K 2S =

69

ST = [H SO 4 − ]e + [SO 4 2− ]e

(5)

(6)

70

Eq 5 shows that at the pH conditions prevailing in this study (pHe > 3.3), [HSO4-]e

71

concentration is negligible ([HSO4-]/[SO4] < 0.05) and ST ~ [SO42-]e.

72

The equilibrium calcite solubility is obtained fromthe mass and electricconservation relation:

73 74 75

76

[Ca2+ ]e ⋅ ( 2 − α1 − 2 ⋅α2 ) + [H+ ]e = 2 ⋅ ST +

Kw [H+ ]e

(7)

Kw is dissociation constant of water, and α1 and α2 are the carbonate species fractions: [HCO 3 ]e  [H + ]e K  α1 = = + 1 + +2  [C T ] [H ]e   K1 α2 =

[CO 23 − ]e [C T ]

−1

 [H + ]e 2 [H + ]e  = +1+  K2   K1 ⋅ K 2

(8) −1

(9)

77

[CT] is the total carbonate species released which equals the calcium released.The residual

78

acidity [H+]e is found by eliminating ([Ca2+]e from eq 7 using the calcite solubility product

79

expression:

80

Ksp α2

⋅ ( 2 − α1 − 2 ⋅ α2 ) + [H+ ]e = 2 ⋅ [ST ] +

Kw [H + ]e

(10)

81

2.3 Kinetics of Calcite Dissolution Under Fixed Bed Conditions. Dissolution is usually a

82

mass transfer controlled process.3,10 The mass transfer model developed by Yamauchi et al.11

83

describing calcite dissolution by desalinated water acidified with carbonic acid in a fixed bed

84

is supported by extensive experimental data. The system considered is a column of length L 4 ACS Paragon Plus Environment

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85

packed at a porosity fraction ε with calcite particles of average size dp and shape factor φ (φ

86

=1 for a sphere, φ< 1 for irregular shape). Desalinated water at an initial acid concentration

87

[CO2]0 flows down the column in the plug mode at a flowrate of Q and a superficial flow

88

velocity u based on the empty column.

89 90

The rate of calcium ion release per unit particles surface R is given by:

R=

Q ⋅ d[Ca] = k s ⋅ ([CO2 ] − [CO2 ]e ) ds

(11)

91

where s is the total area of the particles, ks is the dissolution mass transfer coefficient, [CO2]

92

is the local concentration of the carbonic acid and [CO2]e is the equilibrium concentration of

93

the carbonic acid. The particles area and flowrate expressions show that:

94

ds dL 6 6 = .(1 − ε). = dt.(1 − ε). Q u dp dp

(12)

95

where t is the contact time based on the empty column given by t=EBTC=L·u-1. Eqs 11 and

96

12 show that the rate of CO2 depletion along the column resulting from calcite dissolution is

97

given by:

98 99 100

−

d ([CO 2 ]) d ([Ca]) 6k s (1 − ε) = = ⋅ ⋅ ([CO 2 ] − [CO 2 ]e ) dt dt φ dp

(13)

The exit solution composition is given by integration of Eq 13:

ln

[Ca]e − [Ca]L [CO2 ]L − [CO2 ]e 6k (1 − ε) L = ln =− s ⋅ ⋅ [Ca]e − [Ca]o [CO2 ]0 − [CO2 ]e φ dp u

(14)

101

2.4 Slurry Mixed Flow Acid Dissolution of Micronized Calcite Particles. The final

102

dissolution equations derived below for carbonic acid dissolution apply also to sulfuric acid

103

dissolution the only modification being in the different values of the calcium equilibrium

104

solubility. Slurry flow dissolution of powder particles differs from the fixed bed dissolution

105

presented above in several respects. (i) Both dP0, the initial particle size and S0, the initial

106

mass concentration per unit solution volume of the particles in the slurry are reduced at



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107

increasing contact time t. Eq 14 adjusted for this difference results in the following kinetic

108

expression:  6 ⋅ S  d[CO2 ] d[Ca 2+ ]  6 ⋅ S  2+ 2+ = =  ⋅ k s ⋅ [CO2 ] − [CO2 ]e =   ⋅ ks ⋅ {[Ca ]e − [Ca ]} dt dt d d ⋅ρ ⋅ρ  p   p 

109

−

110

(15)

111

where dp and S are instantaneous values at contact time t and ρ is the calcite density.

112

The following mass balance relating the decrease in powder concentration and in particle

113

size with the increase in solution calcium ion concentration [Ca2+] mM enables elimination of

114

S and dp from Eq 16:

115

 (d3p )   S (So − S) ⋅ 1000 [Ca ] − [Ca ]o = = 10 ⋅ So ⋅ 1 −  = 10 ⋅ So 1 − 3  Mw  So   (d p0 ) 

116

where S is in units of g cm-3 and Mw= 100 g mol-1 is the molecular weight of calcite.

117 118

119

2+

2+

(16)

(ii) The mass transfer coefficient of the particles moving in slurry flow is given by the Froessling correlation:12

Sh =

ks ⋅ dp Dv

1/3

1/2

 d p ⋅ u p ⋅ρ   µ ρ  = 2 + 0.6 ⋅    ⋅ µ    Dv 

(17)

120

where Dv is the diffusivity of Ca(HCO3)2 ions (≈0.85×10-5 cm2 s-1)13, up is the relative

121

velocity of the solution past the particles, ρ is the solution density and µ is the eq 17

122

simplifies to Sh=2.

123

Combining eqs 15, 16 and 17, the final differential form of the calcite dissolution equation is: 1

124

d  Ca 2 +  dt

  Ca 2 +  −  Ca 2 +   3   o 2+ 2+ = A ⋅  Ca  −  Ca  ⋅ 1 −   e 10 ⋅ So  

{

}

125

12 ⋅ S ⋅ D  A= 2 o v  d Po ⋅ ρ p 

126

where ρp is the calcite density.

(18)

(19)


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127

(iii) Dissolution of the particles occurs in fully mixed flow instead of the plug flow

128

mode in the fixed bed system. It is important to note that although dissolution of the particles

129

occurs in a fully mixed system, the dissolution reaction occurs under "segregated mixed flow

130

conditions". The particle aggregates behave as a "macro fluid" and particle bundles react in

131

the batch mode at different time periods according to the residence distribution of a fully

132

mixed flow system.12

133

(iv) Two solution paths need to be considered: dissolution of a concentrated slurry

134

containing an excess of the calcite powder quantity required to fully neutralize the solution

135

feed acidity and dissolution of a dilute slurry containing an initial powder concentation below

136

the quantity required to fully neutralize the solution feed acidity. In both cases the reaction

137

kinetics are governed by dissolution of macro-aggregates rather than micro-aggregates.

138

2.5 Segregated dissolution of a concentrated slurry. In this case the molar calcium content

139

in the initial powder concentration (10S0 mM where S0 is in g cm-3) is larger than the

140

equilibrium calcium solubility [Ca2+]e of the feed acidity.

141

conditions each slurry element behaves as a "macro fluid" residing at a different time period

142

in the reactor. Assuming an ideal CSTR system the residence time distribution of the various

143

slurry elements is given by:12

144

E(t) =

For segregated mixed flow

exp( − t / τ) τ

(20)

145

where E(t)·dt represents the fraction of the slurry residing in the reaction vessel in the time

146

interval between t and t+dt. The average residence time is given by τ=V·Qwhere V is the

147

reaction volume and Q is the flow rate. The exit concentration for segregated flow is: ∞

148

Cout = Cbatch ( t ) ⋅ E ⋅ dt

∫

(21)

0

149

In the present case the corresponding Ca2+batch(t) value for a slurry element residing for a

150

reaction time t is given by: 7 ACS Paragon Plus Environment


Ca 2+ ( t )

t=

151

∫

d  Ca 2 +    Ca  −  Ca     0 A ⋅  Ca 2 +  −  Ca 2 +  ⋅ 1 −   e S0  

0

{

2+

}

2+

1 3

Page 8 of 23

= f1 (Ca 2 + )

(22)

152

The exit calcium concentration [Ca2+]out is obtained by integrating the calcium contributions

153

of the slurry elements reacting at different time elements, t, extending from zero to infinity: ∞

∞

exp(−t / τ) ⋅ Ca2+ (t) ⋅ dt τ 0

2+ 2+ Ca out = ∫ E(t) ⋅ Ca (t) ⋅ dt = ∫

154

0

155 156 157

where Ca2+(t) is given by solution of eq 18. Denoting d[Ca2+]/dt by f2(Ca2+) the variable t can be eliminated from eq 23 to provide the following final equation:

exp(−t / τ) ⋅ Ca2+  dt ⋅ d Ca2+  1 [Ca ]e  exp(−f1 (Ca2+ ) / τ) ⋅ Ca2+   2+ Ca  = ∫ ⋅ = ∫   ⋅ d Ca  2+ 2+ out τ τ 0  f2 (Ca ) d Ca  0   2+

∞

158

(23)

2+

159

(24)

160

2.6 Segregated Dissolution of a Dilute Slurry. In a dilute slurry the initial powder

161

concentation is below the quantity required to fully neutralize the solution feed acidity. In this

162

case the maximum solution concentration that can be obtained is the molar calcium content of

163

the initial slurry concentration

164

Consider a feed of initial concentration S0 and initial particle size dP0 reacting with an

165

acid concentration providing a calcium solubility [Ca2+]e. Integration of eq 18 determines the

166

time necessary for complete dissolution of the particles under batch flow conditions: 10S0

167

t batch =

∫ 0

d[Ca 2 + ] 1/3

  [Ca 2+ ] − [Ca 2 + ]0   A ⋅ {[Ca 2+ ]e − [Ca 2 + ]} ⋅ 1 −   S0    

(25)

168

All slurry elements residing at t > tbatch will be fully dissolved. Slurry elements residing at t
tbatch is given by: ∞

177

[Ca 2II+ ]( τ) = 10S0 ⋅

∫

t batch

178 179

exp( − t / τ)  t  ⋅ dt = 10S0 ⋅ exp  − batch  τ τ  

(28)

The exit calcium concentration of a dilute slurry is thus: 2+ [Ca out ] = [ Ca 2I + ] + [Ca 2II+ ]

(29)

180 181

3. MATERIALS AND METHODS

182

3.1 Experimental System. The experimental system shown in Figure 1 was designed to

183

enable calcite powder dissolution by acidified desalinated water under continuous mixed flow

184

conditions. A convenient way for efficient mixing of a slurry is by a recycle flow scheme.

185

The four main elements of the system were: A 10 L CaCO3 slurry preparation vessel

186

connected to a dosing pump supplying a concentrated slurry feed at a flow rate in the range of

187

200-400 mL min-1; A 120 L desalinated water vessel supplying fresh water feed in the range

188

of 1-11 L min-1; A 50 m long pipe, 1.25'' diameter, providing a 40 L dissolution reaction

189

volume, fully mixed by a high recycle flow rate of the order of 60-70 L min-1; An acid supply

190

system enabling dosage of CO2 gas or H2SO4. The CO2 gas was fed from a CO2 cylinder at a

191

flow rate in the range of 0.02-0.40 L min-1 (0.05-8.4 mM). The required flow rate of the CO2 9 ACS Paragon Plus Environment


Page 10 of 23

192

gas was controlled by adjusting the gas outlet pressure and the rotameter reading. The H2SO4

193

solution was fed from a 25 L holding vessel at a flow rate of 15-100 mL min-1.

194

The experimental system was initially operated at relatively high retention times of the

195

order of 20-40 min. As results indicated that at such retention times dissolution was at near

196

equilibrium conditions, the experimental system was modified to include a higher flow rate

197

distilled water pump which enabled operation at low retention times of the order of 3-10 min. Remineralized water

CaCO3 Dosing pump Slurry Flow meter

Pressure relief valve

FI

L= 50 m; d=2.5 cm pipe

Flow meter

CO2 PI

Pressure Indicator

FI

Flow meter

FI

Circulation pump 60-70 L min -1 Check valve

Feed Desalinated Water Bypass H2SO4

198 199

Dosing pump

Figure 1. Schematic diagram of the experimental system.

200 201

3.2 Calcite Powder Characterization. The calcite powder used was a product of Solvay

202

Chemicals International Belgium, denoted as Socal. The density measured with a

203

pycnometer was 2.5 g cm-3. The particle size distribution was measured by Mastersizer 2000

204

(Malvern, UK). Typical size distribution curves are displayed in Section 4.4. The surface

205

mean diameters (D3,2) of samples used in the different runs was in the range of 2 to 3 µm.

206

3.3 Experimental Procedure. A run started with recirculating the acidified feed solution

207

containing the metered dose of calcite slurry. The course of dissolution was followed by

208

periodic analyses of the product water (calcium and alkalinity contents of non-filtered and 10 ACS Paragon Plus Environment

Page 11 of 23


209

filtered outlet stream, pH, turbidity, and temperature). To ensure that the system was at steady

210

state each experiment was continued for an additional period of 4 retention times after

211

measurements indicated steady state. Full steady state conditions were reached in about 7

212

retention times.

213 214

4. RESULTS AND DISCUSSION

215

The first period of experiments involved runs conducted at relatively long retention times,

216

resulting in very high conversions nearing equilibrium conditions. Theoretically predicted

217

conversions from the kinetic model were found to be almost identical to values calculated

218

from the equilibrium conversion expressions. The good agreement between predicted and

219

experimental conversions provided convincing evidence on the accuracy of the equilibrium

220

model but was not sufficient to confirm the kinetic model.

221

Simulation calculations were then carried out in order to determine conditions enabling

222

confrontation of the kinetic model with experimental data under conditions relatively distant

223

from equilibrium conversion. As shown below, results of the second period of experiments

224

provide convincing evidence on the validity of the kinetic model. Table 1 summarizes the

225

experimental conditions of all performed tests. Results of the effects of various parameters

226

are displayed in Figures 2 to 6. In each Figure, symbols represent average values of

227

experimental measurements taken at steady state conditions. Predicted values of the calcium

228

in the re-mineralized water, were calculated using Eq. 22 and 24.

229

4.1 Near Equilibrium Experiments. The following parameters were investigated in calcite

230

dissolution tests carried out at relatively high retention times with the two different acids-

231

CO2 and H2SO4: inlet acid concentration, inlet slurry concentration and retention time. The

232

results of these experiments enabled also comparison of the characteristics of calcite

233

dissolution by the two acids.



Page 12 of 23

234

4.1.1 Effect of the Acid Feed Concentration. The effect of the CO2 concentration in the range

235

of 2.2 to 8.4 mM and of the H2SO4 concentration in the range of 0.9 to 3.2 mM was

236

investigated under the conditions of relatively high initial slurry concentration of 4.66 mM

237

and relatively long retention time of 21 min. As expected, higher initial acid dosage resulted

238

in higher [Ca2+] exit concentration. Figure 2 shows that the experimental points are in very

239

good agreement with values predicted by the kinetic model plotted as a continuous curve.

240

The average difference between predicted and experimental results of the eight CO2 runs was

241

5.2 % and that of the four H2SO4 runs was 6.1 %.

242

For both the CO2 and H2SO4 runs, shown in Figure 2, the dashed curve calculated

243

from the theoretical equilibrium equation and the continuous curve calculated from the

244

kinetic model are seen to provide practically identical values so that, as noted before, these

245

experiments do not provide conclusive proof on the validity of the kinetic model. The

246

accuracy in the analytical determination of calcium is of the order of 0.05 mM so that for a

247

[Ca2+]e value of 3 mM the accuracy is of the order of 1.5%. Hence, it is not possible to

248

distinguish between theoretical kinetic values and equilibrium values that differ by over

249

98.5%. As shown below, the same phenomenon of negligible difference between kinetic and

250

equilibrium calcium values was displayed in the results obtained by varying slurry

251

concentration and retention time.

252 253

Table 1. Experimental conditions in the various tests Acid Fig. #

CO2

H2SO4

2

3

4

6

2

3

4

6

Parameter

Inlet

Inlet

Retention

Model

Inlet

Initet

Retention

Model

studied

acid

slurry

time

verification

acid

slurry

time

verification

8.4

5.3/3.4

0.22

2.6

2.6

0.05

21

3, 7, 20

5, 7, 11, 16

[Acid]0 (mM) τ (min)

2.28.4 21

21

13, 21, 40/ 10, 20, 38

3, 5, 7, 10

0.93.2 21


Page 13 of 23


S0 (mM) [Ca2+]e (mM)

0.8-

4.6

4.6

0.22

3.7

3.0/2.3

0.22

3.2

7.1

6.4

6.5

1.73.7

4.6

1.0-6.0

4.6/1.0

0.17

3.7

3.7

0.17

6.9

0.6

2.7

1.64.3

Difference Exp. vs. model

5.2

6.1

(%)

254 5 [Ca2+]out (mM)

4 3 2 1

CO2

H2SO4

0 0

255

1

2

3 4 5 6 Inlet acid (mM)

7

8

9

256

Figure 2. Effect of acid feed concentration on the exit calcium concenentration. Solid line-

257

model prediction, dashed line equilibrium concentrations.

258 259

4.1.2 Effect of the Slurry Concentration. The effect of the initial slurry concentration in the

260

range of 0.5 to 6.5 mM was investigated at a retention time of 22 min with an inlet acid

261

concentration of 8.4 mM in the CO2 tests and an inlet concentration of 2.6 mM in the H2SO4

262

tests. These acid concentrations provide an identical equilibrium solubility of [Ca2+]e=3.7

263

mM.

264

For both acids the experimental data plotted in Figure 3 are seen to coincide with values

265

predicted by the kinetic model (continuous curve) and values calculated from the calcium

266

solubility expression (dashed curve). The average difference between values predicted by the

267

kinetic model and the experimental results of the CO2 runs was 3.2 % and that of the H2SO4

268

runs was 6.9 %.



269

A striking feature of Figure 3 is the presence of two identical distinct regimes in runs

270

performed with the two different acids: (i) an initial regime covering the range of 0 < S0 < 3.7

271

mM in which there is a linear relation between the outlet calcium and the slurry concentration

272

with a slope of unity; (ii) a final regime of runs performed at S0 > 3.7 mM in which the outlet

273

calcium concentration has a constant asymptotic value of 3.7 mM. The above result can be

274

readily understood by recalling that under the high retention time of this run outlet conditions

275

were essentially equilibrium conditions. Consequently, at S0 < [Ca2+]e, [Ca2+]out = S0 and at

276

S0 > [Ca2+]e, [Ca2+]out = [Ca2+]e.

277

4.1.3 Effect of Retention Time. The effect of the retention time was investigated with CO2 at

278

three levels in the range of 10 to 40 min at a feed slurry concentration of S0 = 4.6 mM and

279

two inlet CO2 concentrations of 3.4 and 5.3 mM providing [Ca2+]e concentrations of 2.3 and

280

3.0 mM respectively. The effect of the retention time was investigated with H2SO4 at three

281

levels in the range of 3 to 21 min at two feed slurry concentrations of S0 = 1.0 and 4.0 mM

282

and H2SO4 feed concentration of 2.6 mM providing a [Ca2+]e concentration of 3.7 mM. The

283

theoretical kinetic predictions indicate that under these conditions all exit calcium t results are

284

at virtual equilibrium conditions with both acids.

285


Page 14 of 23

Page 15 of 23


[Ca2+]out (mM)

4

CO2

3 2 1 0

[Ca2+]out (mM)

4

0

1

2

3

4

5

6

7

8

H2SO4

3 Experiment Model Equilibrium

2 1 0 0

1

286 287

2

3

4 5 S0 (mM)

6

7

8

Figure 3. Effect of the slurry feed concentration on the exit calcium concentration.

288 The experimental data plotted in Figure 4 are seen to coincide with both values

290

predicted by the kinetic model (continuous curve) and values calculated from the calcium

291

solubility expression (dashed curve). The average difference between values predicted by the

292

kinetic model and the experimental results were 7.1 and 0.6% for CO2 and H2SO4 runs

293

respectively.

[Ca2+]out (mM)

289

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

CO2=3.4 mM H2SO4=1.0 mM

0

294

5

CO2=5.3 mM H2SO4=4.6 mM

10 15 20 25 30 35 40 Retention time (min)



295

Figure 4. Effect of retention time on the exit calcium concentration. Solid line- model

296

prediction, dashed line equilibrium concentrations.

297 298

4.2 Verification of the Kinetic Model. In all tests described in Section 4.1 measurements of

299

solution calcium concentrations were close to equilibrium values so that predicted values

300

based on the kinetic model were close to values predicted by equilibrium conditions. In

301

principle, measurements of calcium conversions at very short retention times could provide

302

data remote from equilibrium conditions. However, measurements of reliable accuracy at

303

such short retention times are very difficult to realize experimentally. Simulation calculations

304

showed that conversions relatively distant from equilibrium values can be achieved at test

305

conditions providing a relatively low dissolution driving force ([Ca2+]e - [Ca2+]). Such

306

conditions are realized at feed conditions in which the equilibrium solubility [Ca2+]e is low

307

and the

308

concentration is small.

difference between the inlet slurry concentration and the calcium equilibrium

309

Two series of tests were carried out to confirm the dissolution model at conversions

310

distanced from near equilibrium conditions. The CO2 series was carried out at an inlet slurry

311

concentration of 0.220 mM and an equilibrium solubility of 0.218 mM. The H2SO4 series at

312

an inlet slurry concentration of 0.170 mM and an equilibrium solubility of 0.165 mM. Figure

313

5 shows good agreement between experimental results and model prediction with both acids.

314

The average difference between values predicted by the kinetic model and the experimental

315

results were 6.4 and 2.7% of the CO2 and H2SO4 runs respectively.


Page 16 of 23

Page 17 of 23


[Ca2+]out (mM)

0.25 0.20 0.15 0.10 CO2

0.05

H2SO4

0.00 0

316

2

4 6 8 10 12 14 16 Retention time (min)

317

Figure 5. Comparison between experimental results (symbols) and model predictions (solid

318

curves) at calcium conversions distanced from equilibrium solubility.

319 320

4.3 Comparison between Calcite Dissolution by CO2 and by H2SO4. Figure 2 displays the

321

calcite dissolution results in which the dissolution by the two acids were carried out at the

322

same inlet slurry concentration of 4.7 mM and the same retention time of 21 min. As

323

expected, a lower concentration of H2SO4 relative to CO2 is required for achieving the same

324

calcium outlet concentration. .

325

Figure 6 displays exit pH values in dissolutions tests carried out at varying slurry inlet

326

concentrations and a constant [Ca2+]e solubility of 3.7 mM. This solubility was obtained with

327

8.4 mM CO2 and 2.7 mM H2SO4 at retention time of 21 min in all tests. When S0 < [Ca2+]e

328

the final pH is governed by the acid concentration S0 that in the H2SO4 tests very low pH

329

values in the range of 2.7-4.7 are obtained in the S0 range of 1.0-2.5 mM. Much higher values

330

in the range of 5.6-6.2 are found in the weak CO2 acid tests in the S0 range of 1.0-2.5 mM. At

331

the high slurry concentrations of 4.6 and 6.0 mM final pH values are seen to be high and

332

quite similar for both acids, around pH 6.5.



Page 18 of 23

Product water pH

7 6 5 4

H2SO4 CO2

3 2 0

333 334

1

2

3 4 S0 (mM)

5

6

7

Figure 6: Exit solution pH as a function of inlet calcite slurry concentration.

335 336

In conclusion, remineralization by sulfuric acid has the clear advantage of requiring less

337

acid to provide the same calcium concentration by lower dissolution retention times.

338

Calculations show that sulfuric acid can advantageously supply common regulatory calcium

339

concentrations while maintaining maximum sulfate concentration below 250 mg L-1.

340

4.4. Effect of the Particle Size Distribution on the Dissolution Kinetics. In Sections 4.1

341

and 4.2 calcium conversions predicted by the calcite dissolution model were confronted with

342

experimental results under the simplifying assumption that the calcite powder is composed of

343

uniform particles represented by the surface mean diameter of the size distribution.

344

Comparison of numerous experimental results with model predictions showed in the majority

345

of tests agreement was within less than 10%. This measure of agreement is quite satisfactory

346

for specifying the design parameters required for a desired hardened solution composition.

347

However, residual solution turbidity, which is another important design parameter, cannot be

348

analyzed by the uniform particles dissolution model since the dissolution extent is strongly

349

affected by the particle size.

350

Figure 7 shows typical particle size distributions before and after acid dissolution. It is

351

seen that the decrease in small particles is more pronounced than that of the larger particles. It

352

is possible to get closer agreement between theory and experiment and also predict the size 18 ACS Paragon Plus Environment

Page 19 of 23


distribution of the final calcite slurry by applying the model on differential size elements of

354

the feed slurry. The computational technique for taking into account the size distribution of

355

the slurry is illustrated by a simple numerical example shown in Table 2.

Volume (%)

353

12

Inlet-CO2

10

Inlet-H2SO4

8

Outlet-CO2

6

Outlet-H2SO4

4 2 0 0

3

356 357

6

9 12 15 Size (µm)

18

21

Figure 7. Typical particle size distributions before and after acid dissolution.

358 359

The Table shows a powder containing particles in the size range of 0 to 7µm subjected

360

to slurry dissolution at the conditions specified in the Table heading. The slurry dissolution is

361

analyzed in three size groups each of which has a different value of the size parameter A (eq

362

19). The exit concentration [Ca2+]out of each size group is calculated from eq 24. The

363

contribution of each element to the final solution concentration is according to the precent

364

volume of each element. Finally the mass balance of eq 16 provides the final size value of the

365

particles in the three size groups.

366

The uniform particle size analysis is based on the surface mean diameter of the powder

367

which in the above example has the value of 1.52 µm. The size parameter has the value of

368

A=7.4 (min-1). Solution of eq 16 shows that the exit concentration based on the mean size

369

simplification gives the value of 0.432 mM which deviates by 14% from the more accurate

370

size distribution analysis.

371



Page 20 of 23

372

Table 2. Illustration of the computational technique for kinetic analysis based on the

373

size distribution of the slurry particles (S0 = 0.7 mM, [Ca2+]e = 0.5 mM, τ = min-1) Size group

Average size

Volume

[Ca2+]out

∆[Ca2+]solution

Final Average size

-1

A

(µm)

(µm)

(%)

(min )

(mM)

(mM)

(µm)

0-2

1.0

50

17.14

0.468

0.468 × 0.5

0.69

2-3

2.5

30

2.74

0.353

0.353 × 0.3

1.98

3.- 7

5.0

20

0.68

0.194

0.194 × 0.2

4.49

Sum

0.379

374 375

To assess the error in the simplified kinetic analysis, dissolution tests carried out with

376

CO2 and H2SO4 with calcite powder feeds shown in Figure 7 were analyzed both according to

377

the uniform size model based on the surface mean diameter and on the size distribution

378

model. The results displayed in Figure 8 show improved accuracy in theoretical prediction for

379

both acids, with a more pronounced effect in the case of carbonic acid. These results are

380

expected, since dissolution by sulfuric acid provides near equilibrium conversions and size

381

effects are insignificant (Figure 7). 2.5

[Ca2+]out

2.0 1.5 H2SO4 CO2 D[3,2] Size distribution

1.0 0.5 0

382

1

2 3 Inlet acid (mM)

4

5

383

Figure 8. Comparison between experimental results (symbols) and model predictions

384

assuming uniform particles (solid curve) and size distribution (dashed curve)

385 386

4.5. Empirical Evaluation of Exit Solution Turbidity. A significant aspect of the slurry

387

dissolution process is the need to ensure economic calarification of the residual turbidity.

388

The exit solution turbidity is caused by the residual powder. The concentration [R] mM of the 20 ACS Paragon Plus Environment

Page 21 of 23


389

residual powder is the difference between the inlet slurry concentration [S0] mM and the

390

calcium concentration in the exit solution:

391

[R] = [So ] − [Ca 2 + ]out

(30)

392

Analysis of the turbidity measurements of the runs listed in Table 1, disclosed a simple linear

393

relationship between exit solution turbidity [NTU]out and residual calcium (Figure 9):

394

[NTU]out = 389 ⋅ [R]

(31)

395

This useful empirical correlation enables rapid estimate of the expected exit solution

396

turbidity. These results revealed that the micronized calcite dissolution process would require

397

a removal of the residual turbidity. This can be achieved by threaded microfiber filtration14 or

398

ultrafiltration.15

Turbidity (NTU)

600 500 400 300 200 100 0 0.0

399

0.3 0.6 0.9 1.2 Residual calcium (mM)

1.5

400

Figure 9. Empirical correlation of the residual turbidity with the residual calcium

401

concentration.

402 403

ACKNOWLEDGMENTS This work was partially supported by the Israeli Water Authority

404

and by Mekorot Israel Water Company. The assistance of Michael Greiserman and Enas Saad

405

in performing some tests is gratefuly acknowledged.

406 407

REFERENCES

408

(1) Duranceau, S. J.; Wilder, R. J.; Douglas, S. S. Guidance and recommendations for

409

posttreatment of desalinated water. J. Am. Water Works Assoc. 2012, 104, 510-520. 21 ACS Paragon Plus Environment


410 411 412 413 414

(2) Duranceau, S. J.; Wilder, R. J.; Douglas, S. S. A survey of desalinated permeate posttreatment practices. Desalin. Water Treat. 2012, 37, 185-199. (3) Shemer, H.; Hasson, D.; Semiat, R. State-of-the-art review on post-treatment technologies. Desalination 2015, 356, 285-293. (4) Gude, J. C. J.; Schoonenberg K. F.; van de Ven, W. J. C ;de Moel, P. J.; Verberk, J. Q. J.

415

C.; van Dijk, J. C. Micronized CaCO3: a feasible alternative to limestone filtration for

416

conditioning and (re)mineralization of drinking water? J. Water Supply Res. T. 2011, 60,

417

469-477.

418

(5) Subramani, A.; Poffet, M.; Durand, S.; Oppenheimer, J.; Dedovic-Hammond, S.;

419

Jacangelo, J. G. Reverse osmosis permeate stabilization using micronized calcium

420

carbonate: A potential alternative to lime. Proc. AWWA/AMTA 2012 Membrane

421

Technology Conference.

422

(6) Poffet, M.; Skovby, M.; Nelson, N. C.; Kallenberg, J. New remineralization process using

423

micronized calcite as a sustainable alternative to the lime dosing system. Proc. IDA

424

Desalination and Water Reuse Congress 2013, Tianjin, China, REF: IDAWC/TIAN13-

425

052.

426

(7) Poffet, M.; Kallenberg, J.; Bradley, T. New remineralization process using micronized

427

calcite as a sustainable alternative to the lime dosing system. Proc. AWWA/AMTA 2014

428

Membrane Technology Conference.

429

(8) Nelson, N. C.; Poffet, M.; Kallenberg, J. The retrofit of existing lime dosing system with

430

micronized calcium carbonate. Proc. IDA Desalination and Water Reuse Congress 2015,

431

San Diego, CA, REF: IDAWC15-Nelson 51640.

432

(9) Nelson, N. C.; Poffet, M.; Kallenberg, J. Remineralization processes with micronized

433

calcium carbonate providing superior water quality. Proc. 2016 EDS Conference

434

Desalination for the Environment, Rome, Italy.


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(10)

Harriott, P.; Hamilton, R. M. Solid-liquid mass transfer in turbulent pipe flow. Chem.

Eng. Science 1965, 20, 1073-1078. (11)

Yamauchi, Y; Tanaka, K.; Hattori, K.; Kondo, M.; Ukawa, N. Remineralization of

desalinated water by limestone dissolution. Desalination 1987, 60, 365-383. (12)

Levenspiel, O. Chemical Reaction Engineering, John Wiley & Sons, 3rd Edition,

1999, Chapter 16. (13)

Robinson R. A., Stokes R. H., Electrolyte Solutions, Dover Publications 2nd Edition,

2012. (14)

Shemer, H; Sagiv, A; Holenberg, M;. Zach Maor, A. (In press). Filtration

444

characteristics

445

doi.org/10.1016/j.desal.2017.07.009

446 447

(15)

of

threaded

microfiber

water

filters.

Desalination

2017

Omya Development AG, Micronized CaCO3 slurry injection system for the

remineralization of desalinated and fresh water. Patent WO 2012020056 A1 (2012).

448


Modeling Remineralization of Desalinated Water by Micronized

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