Effect of Concentration and Temperature on Mass Transfer in Metal

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EFFECT OF CONCENTRATION AND TEMPERATURE ON MASS-TRANSFER IN METAL ION-EXCHANGE Lourdes Bilbao, Monika Ortueta, and Federico Mijangos Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00398 • Publication Date (Web): 13 Jun 2016 Downloaded from http://pubs.acs.org on June 14, 2016

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Industrial & Engineering Chemistry Research

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EFFECT OF CONCENTRATION AND TEMPERATURE ON MASS-TRANSFER IN

2

METAL ION-EXCHANGE

3 4

L. Bilbao, M. Ortueta and F. Mijangos

5

Chemical Engineering Department, University of the Basque Country UPV/EHU, P.O.

6

Box 644, 48080 Bilbao, Bizkaia, email: [email protected]

7 8

Abstract

9

The effect of metal concentration and temperature on mass transfer has been

10

investigated for an ion exchange system. The kinetics of copper load on an

11

iminodiacetic-type commercial resin (Lewatit TP208) has been analyzed using the

12

heterogeneous shrinking core model (SCM) to estimate the mass transfer coefficient and

13

the effective diffusion coefficient at different experimental conditions. In spite of the

14

fact that the hydrodynamic conditions remain unchanged throughout the experiments,

15

the Sherwood number determined experimentally shows a large dependence on the

16

concentration of the diffusing cation, with external mass transfer being the controlling

17

step for low concentrations. The Sherwood number increases with metal load because

18

the effective diffusion coefficient, Def, decreases substantially with higher metal

19

concentrations in the resin phase. This effect is explained in terms of the parallel

20

diffusion model. The temperature affects both the diffusion process and the chemical

21

equilibrium, with metal uptake in the resin phase being faster and higher at higher

22

temperatures. The thermodynamic parameters correspond to an endothermic

23

(∆Hº=+4.14 kcal/mol) and entropic (∆S´=+24.1 kcal/mol K) process in nature. The

24

Arrhenius equation provides a good fit of the effective diffusion coefficients calculated

25

from copper load curves at different temperatures. The associated activation energy

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values are within the range of the characteristics for physical processes such as

27

diffusion, but the calculated values depend on solution pH and copper concentration.

28 29

Introduction

30

Ion exchange is defined as a chemical operation based on electric charge in

31

which ions from the bulk solution displace ions with the same charge from a solid

32

phase1,2,3. From a kinetic point of view, ion exchange is a diffusional process rather than

33

a chemical reaction: a phenomenon of mass transfer due to a concentration gradient

34

between the phases4. Most ion exchange models do not involve direct interaction

35

between the ions and the functional groups and consequently the chemical control of the

36

overall rate is usually not considered. In the models listed by Zagorodni5, ion exchange

37

is interpreted as a distribution process involving the whole material. Chelating ion

38

exchange systems are characterized by the existence of specific chemical interactions of

39

sorbed ions with functional groups, with exchange networks and/or with other species in

40

solution. These interactions may make the ion exchange system highly selective, which

41

enables highly effective processes to be designed. The ion exchange mechanism may

42

include an association between functional groups and counterions promoting the high

43

affinity of the material towards the ion or group of ions.

44

Macroscopic models do not consider the behavior of individual ions as discrete

45

particles and the ion exchange is represented as a purely mechanical process. However,

46

microscopic models consider direct interactions between ions, molecules, fragments and

47

functional groups of the matrix6,7,8.

48

The metal loading during an operational cycle is determined primarily by the

49

mass transfer process across the external bulk solution and a subsequent diffusion

50

through the porous structure of the exchanger. Usually industrial processes are designed

51

using simplified mathematical models that describe mass transfer in the solid phase by 2 ACS Paragon Plus Environment

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intraparticular diffusion or by film diffusion equations9. The design and optimization of

53

such processes requires sufficient knowledge of fundamentals and the development of

54

adequate kinetic models to determine the influence of operating parameters, such as

55

temperature and concentration. This need for a deeper understanding of the kinetics of

56

heavy metal uptake on a chelating resin has led us to undertake this study, which has

57

been implemented using a commercial chelating resin with a macroporous matrix with

58

an iminodiacetate group.

59 60

Methodology of the Experiments

61

The experiments were performed by changing metal concentration and pH in

62

bulk solution. A method was developed using a thermostatized stirred batch vessel

63

provided with an autoburete to control solution pH which guarantees that it remains

64

constant throughout the process. Data analysis was applied to (copper, monometallic)

65

and two metal loading systems (copper and cobalt, bimetallic). As temperature affects

66

diffusion processes, reaction rate and the chemical equilibrium of the ion exchange, this

67

study also investigates a wide range of temperatures to clarify what mechanisms

68

determine the rate of the overall process and, therefore, to analyze its influence on ion

69

exchange kinetics.

70 71

Materials

72

Lewatit TP-208 commercial resin was used for the experimental study. This is a

73

weak acidic macroporous cation exchange sorbent with immobilized chelating

74

iminodiacetic acids (IDA resin) for the selective adsorption of heavy metal ions from

75

weak acidic solutions. The resin is supplied in bead form and is pre-conditioned to

76

assure that the functional group is in the Na-form, that is, the resin must be chemically

77

conditioned to ensure loaded ionic form and elastic behavior. To that end, the resin is 3 ACS Paragon Plus Environment


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washed with sulphuric acid and sodium hydroxide solution three times, alternately10,11.

79

Additional information about this resin can be found elsewhere12. After this treatment,

80

the average bead density is 610 g of dry resin per liter of wet particle, it is calculated

81

using a volume of 100 mL of resin settled in distilled water and measured in a graduated

82

vessel. After that, the wet resin weight and the humidity are measured to calculate this

83

parameter. Finally, a commercial sample was sieved and beads that range 750-820 µm

84

in diameter were chosen for these experiments. The diameter is measured by optical

85

microscopy13.

86

The metal solutions were prepared by dissolving copper sulfate penta-hydrate

87

(CuSO4-5H2O) from Panreac, analytical grade (99.5%), sulfate hepta-hydrated cobalt

88

(CoSO4-7H2O) from Panreac analytical grade (99%) and ionic strength as sodium

89

nitrate (NaNO3) analytical grade (99%), all prepared in ultrapure water to ensure the

90

absence of undesirable ions that could interfere with the results.

91 92

Apparatus

93

A stirred jacked batch reactor with pH (Crison micropH 2002 with Orion Glass

94

combined electrode) and temperature control was used for the experiments. A Perkin-

95

Elmer 1100B flame AAS was used to measure the metal concentrations.

96 97

Experimental section

98

A given mass of resin TP-208 in Na-form is added to a solution with a known metal

99

concentration (0.5 L). The time is zeroed when the resin is put into the reactor tank. At

100

different times several liquid samples are taken out for further analysis. The shaking rate

101

is adjusted to 500 rpm, high enough to keep the beads in suspension. During the

102

experiments, the influence on kinetics of different parameters are tested such as the

103

initial concentration of metal in the solution (50, 100, 500 and 1000 mg/L), the 4 ACS Paragon Plus Environment

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temperature (274, 298, 313 and 333 K) and the solution pH (3 and 4). To that end the

105

setup for the experiment is completed with a thermostatic bath and an automatic burette.

106

The resin is initially loaded with sodium (R-COO-Na+) consequently during the ion

107

exchange reaction the carboxylic groups start to hydrolyze and pH tends to increase. To

108

keep it constant, 0.1M HCL is added through the reaction with an automatic burette.

109

Results and Discussion

110 111

Parallel Diffusion Model for Heterogeneous Systems

112

The heterogeneous structure of this commercial resin is revealed by SEM14, 15 as being

113

an ensemble of microspheres (gel phase) with the internal solution filling the space

114

(pores) among them. Consequently, a parallel diffusion model is proposed here

115

(Equation 1) for data analysis which takes into account both pore diffusion and gel

116

diffusion.

117

 ∂ 2 C 2 ∂C  ∂C ∂q  ε p ∂t + (1 − ε p )ρ p ∂t  = ε p D p  ∂r 2 + r ∂r   

118

where the main terms can be grouped as follows:

119

 ∂ 2C 2 ∂C ∂n = ε p Def  2 + ∂t r ∂r  ∂r

120

Considering that

121

 ε p + (1 − ε p )ρ p ⋅ Γ  Dg    ⋅D Def =   D  p εp  p  

/3/

122

n = ε p C + (1 − ε p )ρ p q

/4/

123

 ∂q  Γ=   ∂C 

/5/

  ∂ 2 q 2 ∂q   + (1 − ε p )ρ p Dg  2 +  r ∂r    ∂r

  

/1/

/2/

124

Using the pseudosteady state approach, Equation 2 can easily be integrated to

125

yield an analytical solution that is called the Shrinking Core Model (SCM, Equation 6). 5 ACS Paragon Plus Environment


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126

This approach means that the reaction takes place from the surface of the particle

127

forming a reacted layer behind the reaction front that moves toward the center of the

128

bead – the unreacted core - at a rate considerably lower than that of diffusion, i.e.

129

moving in a pseudosteady state16. The results of experiments can be analyzed by

130

considering this general equation for the overall rate:

131

∫  C C

t



0

0

 dt = τ f ( X )  ∑i i i 

/6/

132

where the values of fi(X) and τi are defined according to the following expressions to

133

consider the contribution of the controlling mechanisms:

134

External diffusion control:

135

τ1 =

136

Internal diffusion control:

137

τ2 =

138

Chemical reaction control:

139

τ3 =

q * χ Ro 3 k L Co

q * χ Ro2 6 Def Co

q * χ Ro k Co

f1 ( X ) = X

/7/

f 2 ( X ) = 1 − 3(1 − X ) 3 + 2(1 − X )

/8/

f 3 ( X ) = 1 − (1 − X )

/9/

2

1

3

140

Therefore, if the sum of the conversion functions is represented versus the

141

integral of concentration over time, a straight line is obtained. In that case, the

142

parameters τ1, τ2, and τ3 of the line, which are defined by Equations 7-9, could be used

143

to estimate the mass transfer coefficient, kL, the effective diffusion coefficient, Def, and

144

the kinetic constant, k. But for the sake of simplicity it is usually better to determine

145

which of them can be neglected or which of the reaction steps of the process they are

146

controlling. When there is a single controlling step and it is well defined, Equation /6/


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147

enables the corresponding kinetics coefficient to be estimated using the slope of the plot

148

of fi(X) versus the integral of concentration over time.

149

Ion exchange systems usually show very fast chemical reactions4,5 so they tend

150

to be kinetically controlled by mixed contributions from external and internal diffusion.

151

In that case f3(X) can be neglected5, 17 and Equation /6/ can be rewritten (Equation 10) to

152

allow straightforward estimation of the characteristic parameter. The data from the

153

experiment should then be fitted into a linear relationship by plotting the left-hand term

154

of Equation /10/ versus the conversion-term in brackets, and then the parameters τ1 and

155

τ2 can be calculated from the y-intercept and the slope of the line, respectively.

156

∫  C C

t

0



 dt   = τ +τ  f2 ( X )  1 2  X  X  0

/10/

157 158

Effect of Bulk Metal Concentration on Mass Transfer

159

In the load kinetics of a single metal (monometallic system), the ion exchange

160

reaction occurs between the solid phase where the initially loaded counterion is joined

161

to the ionogenic group (a sodium ion in this case, because the resin is pre-treated with

162

sodium hydroxide), and the solution from which the divalent ions are taken. Exchange

163

assays are performed at different concentrations, with the other conditions being kept

164

constant during the reaction.



3.0

q (mmol/gDR)

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2.5

1000 mg/L

2.0

500 mg/L

1.5 1.0

100 mg/L

0.5 50 mg/L

0

165 166 167

40

80

120

160

Time (min)

Figure 1-.- Effect of the initial copper concentration in the solution on the kinetics of Cu/Na exchange ( Lewatit TP-208, pH 3 and 293 K).

168 169

As might be expected, the initial copper loading rate clearly increases with

170

concentration in bulk solution from 0.03 to 0.15 mmol g-1min-1 for 50 and 1000 mg/L,

171

respectively. Similarly, final copper uptake also increases with concentration. The

172

estimated values of this parameter are reported in Table 1. In all the cases tested, the

173

system has almost reached the equilibrium state after 3 hours. These kinetic experiment

174

results can be analyzed in terms of the Shrinking Core Model (SCM) by plotting

175

Equation 10 for the whole set of experimental results18.


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5000

∫

Ci

C0

X

1000 mg/L

dt

500 mg/L

3750

2500 100 mg/L

1250 50 mg/L

0 0.00

0.25

0.50

0.75

1.00

f (X) 2

X

176 177

Figure 2.- Fitting experimental data on copper retention to the Shrinking Core Model.

178 179

In Figure 2 it can be observed that four sets of experiment results fit closely with

180

the straight line. But it must be pointed out that the y-intercept tends to increase with

181

lower concentrations. That is, the contribution of external diffusion is noticeable at low

182

concentrations, whereas at high concentrations the kinetics can be considered to be

183

controlled entirely by internal diffusion because these straight lines show low values of

184

the intercept (τ1).

185

For the whole set of experiments τ1 and τ2 are calculated and the parameters are

186

shown in Table 1, where the Sherwood Number (Sh) defined by Equation 11 is also

187

included.



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188

Sh =

2τ2

τ1

=

k L Ro Def

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/11/

189 190 Table 1.- Kinetic parameters for copper uptake on IDA resin at pH 3 and 293 K . C0

Ceq

τ1

τ2

kL x105

qCu*

Def x10-10

(mg/L)

(mg/L)

(s)

(s)

(m/s)

(mmol/g)

(m2/s)

50

1.11

1060

640

3.89

1

0.38

125.3

100

3.00

1280

1530

3.31

2

0.78

54.3

500

267.2

950

7730

2.13

16

1.82

5.2

1000

630.0

930

10100

1.58

22

2.51

2.9

Sh

191 192

Likewise, the kinetics of simultaneous uptake of copper and cobalt from a

193

bimetallic equimolar solution (bimetallic system) is also analyzed19. The SCM is

194

applied to analyze experimental data corresponding to the bimetallic kinetics for the

195

first stage of the kinetic curve; that is, while the copper/sodium and cobalt/sodium

196

exchange occurs in parallel and almost independently. Parameters are reported in Table

197

2.


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198

Table 2.- Kinetic parameters for the bimetallic system (Cu and Co uptake on IDA resin

199

at pH 3 and 293 K).

Copper C0

Ceq

τ1

τ2

kLx105

(mg/L)

(mg/L)

(s)

(s)

(m/s)

Sh

qCu* (mmol/g)

Defx1010 (m2/s)

50

1.5

740

460

5.73

1

0.40

180.49

100

13.5

1400

2290

2.78

3

0.68

33.34

500

292.4

750

3860

2.35

10

1.55

8.98

1000

752.5

710

6080

1.95

17

2.40

4.46

Sh

qCo*

Defx1010

Cobalt C0

Ceq

τ1

τ2

kLx105

(mmol/g)

(m2/s)

6

0.31

32.14

2.78

7

0.49

15.07

2690

0.40

5

0.72

7.00

2450

0.94

9

0.93

3.93

(mg/L)

(mg/L)

(s)

(s)

(m/s)

50

19.5

680

1890

4.58

100

42.1

690

3380

500

480.1

1130

1000

944.4

520

200 201

How solute concentration affects the relative contributions of these two

202

mechanisms can be observed in Figure 3, where it is noted that for lower concentrations

203

(less than 50 mg/L) the system is controlled by the external mass transfer but for higher

204

concentrations (higher than 400 mg/L) the contribution of external diffusion becomes

205

negligible as Sh is higher than ten. At lower concentrations, the regression lines did not

206

pass through the origin, suggesting that intraparticular diffusion is not the only rate-

207

controlling step and other mechanisms may also control the metal load rate. This

208

displacement from the origin indicates that there is a boundary layer resistance between

209

phases, and its value is proportional to the boundary layer thickness. These results are 11 ACS Paragon Plus Environment


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210

similar to the findings in previous works on adsorption by Sadegh20. At higher

211

concentrations, the contribution of external diffusion, rated by τ2/τ1, is less than 10%.

212

This is clearly observed by the Figure 2, where experimental results for C0=1000 mg/L

213

fit perfectly to the pattern for internal diffusion-controlled kinetics.

214

But, as can be seen in Table 1, the contribution of external diffusion to the

215

overall process is independent of the metal concentration, because the kinetic parameter

216

τ1 is nearly constant throughout the experiments. However, τ2 increases almost

217

proportionally to the copper concentration in the initial solution. That is, as the

218

concentration increases the internal diffusion coefficient decreases, so at high

219

concentrations the internal diffusion is the controlling mechanism. As one might expect,

220

concentration does not affect the external mass transfer coefficient, but the overall

221

kinetics are largely dependent on this parameter since its relative contribution increases

222

at lower concentrations because internal mass transfer slows down.

223

This finding is in agreement with the results reported by Koh21, who conclude

224

that a parallel diffusion model is a good tool for analyzing experimental breakthrough

225

curves, but could also help to explain anomalous results at lower feed rates, which the

226

authors attribute to poor distribution. As evaluated, the effective diffusion coefficient

227

depends strongly on the concentration (Table 1 and 2), a fact noted by some authors.

228

Nestlé22 examines the physical meaning of the dependence of the diffusion coefficients

229

on the concentration from the derivatives of different isotherms in a copper exchange

230

system on calcium alginate tubes. The expressions obtained for the effective diffusion

231

coefficient derived from them represent an approximation of the description of ion

232

exchange systems where there is competition between two ions.

233


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Sh 20

15 Sh>10

10

5 Sh>1

0 0

300

900

1200

C (mg/L) 0

234 235

600

Figure 3.- Relative contribution of the external and internal diffusion mechanisms with

236

concentration at pH 3 and 293 K (Data from Table 3).

237 238

Since the observed Sherwood number depends on solute concentration through

239

the term Def, it can be substituted using Equation 11, where the pore diffusion

240

coefficient is assumed to be constant for a large range of conditions and the factor f(C)

241

considers solution concentration contribution and interactions on diffusion. The

242

Sherwood number (Sho) defined on the basis of the pore diffusion coefficient is assumed

243

to be independent of the solution concentration and dependent only on hydrodynamic

244

conditions for a given system.

245

Def = Dp ⋅ f (C )

246

Sh0 =

/12/

k L Ro = Sh ⋅ f (C ) Dp

/13/

247

The effect of concentration on pore diffusion can be assessed through Equation

248

14. This correlation shows the influence of solute activity on diffusivity in the pore, 13 ACS Paragon Plus Environment


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249

Dp23, where Do is the diffusion coefficient at infinite dilution and the term between

250

brackets accounts for activity changes in the diffusing ion. Although chemical

251

interactions within the pore are almost unpredictable, to the extent that the pore

252

environment is invariable because of fixed charges that must be balanced by free ions

253

one can conclude that the contribution of activity inside the pore does not change over a

254

wide range of solution concentrations.


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255

 ∂ ln γ  D p = Do ⋅ 1 +   ∂ ln C 

256

Moreover, many authors24 have successfully proposed the hypothesis of parallel

257

diffusion and local phase equilibrium to establish the relationship with solute

258

concentration proposed by Equation /8/ using a single diffusion coefficient because the

259

diffusion potential slows down the faster ion to balance the fluxes and gradients in the

260

pore and microsphere. Thus, the effective diffusion coefficient would depend only on

261

the pore structure and equilibrium ratio according to Equation 15. The distribution

262

coefficient, Γ (Eq. 5), is the slope of the sorption isotherm at the concentration range

263

used in the experiment. It should therefore depend on the metal load in the solid phase.

264

Figure 4 shows an inverse relationship between the two parameters which, curiously, fit

265

better into the Freundlich-type (for n=2) than the Langmuir isotherm.

/14/

0.8

Γ 0.6

0.4

0.2

0.0

266 267 268

0.5

1.0

1.5 1/q*

2.0

2.5

3.0

Figure 4.- Dependence of the equilibrium parameter Γ on metal concentration in the resin phase ( q*) at equilibrium.

269



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Page 16 of 33

270

From Figure 4 it can clearly be concluded that the parameter Γ is inversely

271

proportional to metal concentration in the solid phase for the whole range of

272

concentrations tested here. Consequently, the effective diffusion coefficient depends on

273

solid phase concentration (q*) in the same way. Provided that the isotherm is favorable,

274

that is (ρpΓ/εp)>> εp,, then from Equations 11-15 it can be concluded that the Sherwood

275

number measured in the experiment should show a linear relationship with the metal

276

load at equilibrium.

277

 ε p + (1 − ε p )ρ p ⋅ Γ  (1 − ε p )ρ p ⋅ D Def =   ⋅ Dp ≈ p εp ε p ⋅q*  

/15/

278

To validate the above argument, the observed Sherwood numbers reported in

279

Tables 1-2 are depicted in Figure 5 against the metal load at equilibrium, where the

280

linear relationship can be clearly observed. 20 Sh 15

10

5

0 0.0

281

0.5

1.0

1.5

2.0

2.5

3.0

q* (mmol/gRS)

282

Figure 5.- Linear relationship of the Sherwood number in the experiment with the metal

283

concentration in the resin at equilibrium. Reported data are aggregated

284

experiment results for monometallic and bimetallic systems.


Page 17 of 33

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285 286

It should also be noted that there is no noticeable difference between the values

287

calculated from single metal uptake and those from bimetallic solution where copper is

288

competing against cobalt for the binding sites. Therefore, regardless of the metal or the

289

system, there is a clear dependence of the effective diffusion coefficient, Def, with the

290

metal concentration in the resin at equilibrium, q*. This effect means that the observed

291

Sherwood number changes with the metal load – i.e. with solution metal concentration –

292

in spite of the fact that hydrodynamic conditions remain unchanged throughout the

293

experiments.

294 295

Effect of temperature

296

It is clear and well established that temperature affects diffusion processes,

297

reaction rates and the chemical equilibrium of the ion exchange process11, 25, 26. As a

298

rule, all ion exchange processes take place at room temperatures, i.e. within the 18-25

299

°C range, so the influence of temperature is usually negligible. Nevertheless, a wider

300

range (274-333 K) of temperatures is studied here to clarify the mechanisms that

301

determine the overall rate of the process. These experiments were run at two copper

302

concentrations (500 and 1000 mg/L) and two solution pHs (3 and 4).

303

Figure 6 clearly shows that copper uptake, qCu(t), increases with temperature. In

304

fact there are noticeable differences between the results at different temperatures, with

305

the process being faster and the copper retention capacity greater at higher temperatures.

306

The corresponding equilibrium load (q*) is estimated by extrapolation of the copper

307

uptake kinetics. The whole set of experimental data fits neatly into Equation 6 for

308

internal diffusion control as a single controlling mechanism. Kinetics and equilibrium

309

parameters and the main results of the experiment are summarized in Table 3.



310 4.0 333 K

3.0 q (mmol/gRS)

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 18 of 33

313 K

2.0

293 K

1.0

274 K

0

15

45

60

Time (min)

311 312

30

Figure 6.- Temperature effect on the kinetics of copper uptake at pH 3 and 1000 mg/L.

313 314

From these results it can be clearly stated that temperature strongly promotes

315

mass transfer. This may be due to higher effective diffusion, as studied by Cussler23 and

316

Sirola27, who analyzed the effect of temperature on sorption of metals by silica-

317

supported composite coefficients on the basis of the Arrhenius relationship. But this

318

single assertion does not explain the large differences observed for the equilibrium load

319

of copper reported in Table 3.

320

These results are surprising, as sorption phenomena usually run exothermically

321

because of the associative nature of these processes, which involve a decrement of

322

entropy (∆S0).

348

To calculate the equilibrium constant, we assume that this is a heterogeneous

349

electrochemical process and that the retention of copper within a macroporous chelating

350

resin can be simplified, as a first approximation, by Equation 16:

351

Cu 2+ + RNa2 ⇔ RM + 2 Na+

352

where the barrel symbols represent the resin phase. The thermodynamic equilibrium

353

constant would be:

/16/

[RCu ]⋅ [Na] ⋅ f (γ ) [RNa ]⋅ [Cu ] 2

354

o K Cu =

/17/

i

2

355

Taking into account charge balances in the solution and resin phases, using

356

dimensionless variables for solid and liquid phase concentration and considering that

357

activity interactions, which are grouped in the term f(γi), do not change within the range

358

used in the experiment, we are able to define the apparent equilibrium constant

359

(reported in Table 3) on the basis of the experiment variables as:

360

K Cu =

o 2 K Cu qCu = 2 f (γ i ) C Na (Q − qCu ) ⋅ C

/18/

361

Thermodynamic parameters can then be estimated from Equation 20 by

362

representing the logarithm of the equilibrium constant versus the inverse of temperature

363

that is, using the Vant´Hoff plot shown in Figure 7.

364

∆G o = ∆H o − T∆S o = − RT ln K

365

ln K Cu = −

 Co ∆H o 1  ∆S o + − ln f (γ i ) − 2 ln Na R T  R  2 21

/19/

 ∆H o 1 ∆S ′  = − + R T R 

ACS Paragon Plus Environment

/20/


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Page 22 of 33

366

As true thermodynamic constants are not used for these calculations, the value of

367

entropy is modified by the contribution of the activity coefficients and the solution

368

concentration of the counterion. Consequently, the observed entropy (∆S´) value

369

depends on the conditions of the experiment. 7.0 ln K

Cu

6.0

5.0

4.0

3.0 7.0

6.0

370 371 372

5.0 1000/T

4.0

3.0

Figure 7.- Vant´Hoff plot of the apparent equilibrium constant for copper uptake onto IDA resin in Na-form at pH 4.

373 374

Figure 7 shows that the results of the experiment fit into a straight line and

375

thermodynamic parameters can be calculated from the slope and y-intercept (Eq. 20),

376

resulting in ∆Hº=+4.14 kcal/mol and ∆S´=+24.1 kcal/mol K. These values of entropy

377

and enthalpy reflect the complexity of this ion exchange process because both

378

parameters tend to adopt negative values aimed at single adsorption processes. Certain

379

factors that must be considered for appropriate interpretation are discussed below.

380

On the one hand, endothermic ion exchange processes are frequently found.

381

Agrawal30 study the influence of temperature on the equilibrium of several ions with 22 ACS Paragon Plus Environment

Page 23 of 33

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382

IDA resin, concluding that in most cases the enthalpy change is positive during metal

383

exchange over Amberlite IRC 718 in Na-form; hence the process is endothermic in

384

nature. Morcali31 also report an enthalpy change for the uptake of copper onto TP207 in

385

sulphate media, resulting in ∆HºCu = 35-27 kJ/mol (and ∆Sº = 131.98 J/mol K).

386

The enthalpy balance of the process considers the energy expended to break the

387

bonds, the heat generated to create the new bonds and the heat expended to restructure

388

the matrix. Furthermore, the balance must encompass the enthalpy changes

389

accompanying hydration and dehydration, which depend on the degree of saturation of

390

the resin (due to the interactions). It is thus obvious that the reaction enthalpy can be

391

positive even though copper chelate bonds are stronger than those of the sodium

392

displaced from the chelating group.

393

The observed reaction entropy may increase because of changes in the reaction

394

stoichiometry or because of water fluxes. In this sense, Biesuz32, who also report the

395

endothermic sorption of Cd and Ni, interpret the results of experiments on the basis of

396

MR and M(HR)2 complexes, concluding that the formation of those complexes is

397

slightly dependent on temperature. Previously, Mijangos34 reports two stoichiometric

398

ratios for copper uptake onto TP-207. Moreover, temperature affects the ion exchanger,

399

causing density changes associated with elastic forces in the polymeric matrix and

400

volume changes. The volume increase goes with water and electrolytes. This entry of

401

water must be understood as an entropy increase. Likewise, positive values of entropy

402

can be found when there are dissociation reactions (in this case one copper ion frees two

403

sodium ions) or when the sorbate is highly mobile.

404

In the series of kinetic experiments performed at different temperatures, it is

405

found that the Arrhenius relationship, Equation 21, provides a good fit of the

406

experiment data and can consequently be used to estimate the effective diffusion

407

coefficient over a wide range of temperatures: 23 ACS Paragon Plus Environment


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Page 24 of 33

Ea 1 +A R T

408

ln Def = −

409

Figure 8 shows an Arrhenius plot representing the effective diffusion

410

coefficients corresponding to an initial copper concentration of 500 mg/L at pH 3,

411

which clearly fits into a straight line. From the slope of the line, the value of the

412

activation energy associated with intraparticular diffusion though the macroporous

413

matrix is calculated. These values are summarized in Table 4.

/21/

-20.0

ln D

ef

-20.2

-20.5

-20.8

-21.0

-21.2

-21.5 3.0

3.2

3.5

416

4.0

1000/T

414 415

3.7

Figure 8.- Arrhenius plot for the effective diffusion coefficients calculated for copper kinetics in TP-208 resin at 500 mg/L, at pH 3.

417 418 419

Table 4.- Values of the activation energy for diffusion of copper calculated at different pH values and metal concentrations. pH=3

pH=4

C0 (mg/L)

500

1000

500

1000

Ea (kcal/mol)

3.05

3.55

3.30

3.70

420 24 ACS Paragon Plus Environment

Page 25 of 33

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421

It has been found that the Arrhenius equation provides a good fit for the effective

422

diffusion coefficient. The activation energy (3.0-3.7 kcal/mol) is in the range of the

423

characteristics for physical processes such as diffusion. This rules out any irreversible

424

chemical interaction, but solution pH and concentration clearly increase the estimated

425

activation energy. The contribution of the solid-phase and pore diffusion to effective

426

diffusion coefficient is determined by the solute distribution between internal phases

427

within the macroporous resin. This effect can be explained in terms of Equation 15

428

through parameter Γ. As solid-phase and pore diffusion are both transporting

429

mechanisms within the macroporous resin, the effective diffusion coefficient is

430

dependent on the solution parameter and equilibrium constants, so the associated

431

activation energy is also dependent on solution pH and concentration.

432 433

Conclusions

434

The heterogeneous shrinking core model (SCM) derived for parallel porous-gel

435

intraparticular diffusion is successfully applied to the analysis of the kinetics of copper

436

load onto an iminodiacetic-type commercial resin, and thus to the estimation of the mass

437

transfer coefficient and the effective diffusion coefficient in different experimental

438

conditions.

439

In spite of the fact that the ion concentration in bulk solutions does not directly affect to

440

the contribution of the external mass transfer rate, the overall kinetics are largely

441

dependent since at lower concentrations internal mass transfer speeds up and kinetics

442

can be entirely controlled by the external diffusion rate. Regardless of the metal or the

443

system, there is a clear dependence of the effective diffusion coefficient, Def, on the

444

metal concentration in the resin at equilibrium, q*. This effect means that the observed

445

Sherwood number changes with metal load even though the hydrodynamic conditions

446

remain unchanged throughout the experiments. There is a linear relationship between 25 ACS Paragon Plus Environment


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

447

the Sherwood number and the experiment data for metal load at equilibrium. There are

448

no noticeable differences between the values calculated from single metal uptake and

449

those from a bimetallic solution.

450

The process is faster and the uptake capacity is greater at higher temperatures.

451

Temperature improves the mobility of ions and therefore diffusion, which manifests as

452

an increase in metal retention. This is probably because temperature increments make

453

the matrix structure more open and flexible, which facilitates access to the active

454

centers. The positive values obtained for entropy (∆S´=+24.1 kcal/mol K) and enthalpy

455

(∆Hº=+4.14 kcal/mol) reflect the complexity of the process. Ion exchange within IDA

456

resins is a complex set of physical and chemical reactions, and a simplified

457

representation with a single chemical equilibrium does not accurately reflect the

458

phenomenon. The enthalpy change is positive even though copper chelate bonds are

459

stronger than those of sodium displaced from the chelating group because the energy

460

balance must consider the main chemical reaction, but the enthalpy also changes

461

accompanying hydration and dehydration of species, and over all the heat expended in

462

restructuring the matrix. These volume changes go with water and electrolytes. The

463

entry of free water must be understood as an entropy increase that is favored by reaction

464

stoichiometry, so that in this case one copper ion releases two high-mobility sodium

465

ions.

466

It has been found that the Arrhenius equation provides a good fit for the effective

467

diffusion coefficient. The activation energy (3.0-3.7 kcal/mol) is in the range of the

468

characteristics for physical processes such as diffusion. This rules out any irreversible

469

chemical interaction, but solution pH and concentration clearly increase the estimated

470

activation energy because the contribution of the solid-phase and pore diffusion to

471

effective diffusion coefficient is determined by the solute distribution between internal

472

phases within the macroporous resin. 26 ACS Paragon Plus Environment

Page 26 of 33

Page 27 of 33

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473 474

Notation

475

A

Parameter of the Arrhenius equation

476

C

External solution concentration (mmol/L)

477

C

Internal solution concentration or pore solution concentration (mmol/L)

478

Co

Initial concentration (mmol/L)

479

Def

Effective diffusion coefficient (m2/s)

480

Dp

Pore diffusion coefficient (m2/s)

481

Do

Diffusion coefficient at infinite dilution (m2/s)

482

Ea

Activation energy (kcal/mol)

483

f(γ)

Activity function

484

f(X)

Conversion function for SCM

485

k

Kinetic constant (s-1)

486

KCu

Ion exchange equilibrium constant for copper

487

kL

Diffusion coefficient across the liquid film (m/s)

488

n

Mean resin phase concentration, (mmol/L WR)

489

q*

Metal load of the resin at equilibrium (mmol/g DR)

490

Q

Total capacity of the resin (mmol/g DR)

491

r

Radial position (m)

492

R0

Particle radius (m)

493

R

Functional group attached to the polymeric matrix (Eq. 16)

494

R

Gas constant

495

Sh

Sherwood number (dimensionless)

496

T

Temperature (K)

497

t

Time (s) 27 ACS Paragon Plus Environment


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

498

Fractional attainment of equilibrium, X = 1 −

X

n(t ) q (t ) ≈1− n* q*

499 500

Greek symbols

501

εp

Pore volume per volume of wet resin (dimensionless)

502

Γ

Distribution coefficient (L/kg)

503

χ

Density coefficient of the resin (g DR/L)

504

ρp

Solid phase density (kg DR/m3 WR)

505

τ

Kinetic parameter for SCM (s-1)

506

γ

Activity coefficient of species

507 508

Subscripts and superscripts

509

o

Thermodynamic Standard conditions

510

DR

Dry resin

511

WR

Wet resin

512

i

Reaction step (Eq. 6), species i (Eq.17 )

513

est

Estimated

514

exp

Experimental

515

teo

Obtained from theoretic considerations

516 517

References

518 519

1. Rao, K. S.; Sarangi, D.; Dash, P. K.; Chandhury, G. R.. Treatment of wastewater

520

containing copper, zinc, nickel and cobalt using duolite ES-467. J. Chem.

521

Technol. Biotechnol. 2002, 77, 1107-1113.


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522

2. Kim, J. S.; Keane, M. A.. The removal of iron and cobalt from aqueous solutions

523

by ion exchange with na-Y zeolite: Batch, semi-batch and continuous operation.

524

J. Chem. Technol. Biotechnol. 2002, 77, 633-640.

525

3. Rengaraj, S.; Joo, C. K.; Kim, Y.; Yi, J.. Kinetics of removal of chromium from

526

water and electronic process wastewater by ion exchange resins: 122H, 1500H

527

and IRN97H. J. Hazard. Mater. 2003, 102, 257-275.

528

4. Höll, W.H. Ion Exchange for water: Challenges, solutions and developments. In

529

IEX 2008. Recent advances in ion exchange theory & practice; M. Cox Ed.;

530

Cambridge 2008, pp. 1-10.

531 532

5. Zagorodni, A. A. In Ion exchange materials: Properties and applications;. Elsevier: Oxford, U.K.; 2007, pp.221-238.

533

6. McKevitt, B.; Dreisinger, D. Development of an engineering model for nickel

534

loading onto an iminodiacetic resin for resin-in-pulp applications: Part II –

535

Evaluation of existing models and their extension into a hybrid correlation.

536

Hydrometallurgy. 2012, 125-126, 1-7.

537

7. Sud, D. Chelating ion exchangers: Theory and applications. In Ion Exchange

538

technology I: Theory and materials; Innamudin , Luqman, M., Eds.; Springer

539

2012; pp 373-400.

540 541

8. Harland, C.E., Ion Exchange. Theory and Practice; The Royal Society of Chemistry, Cambridge, U.K., 1994.

542

9. Ko, D. C. K.; Porter, J.F.;McKay, G. Film-pore diffusion model for the fixed-

543

bed sorption of copper and cadmium ions onto bone char. Wat. Res. 2001, 35

544

(16), 3876–3886.

545 546

10. Andersson, M.; Axelson, A; Zacci, G. Swelling kinetics of poly(Nisopropylacrylamide) gel. J. Controlled Release. 1998, 50 (1-3), 273-281.



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547

11. Ortueta, M. Efectos estructurales, hinchamiento y microcinética durante el

548

intercambio iónico de cobre y cobalto sobre resinas quelantes. Ph.D,

549

dissertation, UPV-EHU, Leioa, P.V., 2002.

550 551 552 553

12. Rudnicki, P.; Hubicki, Z.; Kolodynska, D. Evaluation of heavy metal ions removal from acidic waste water. Chem. Eng. J. 2014, 252, 362-373.

13. Mijangos, F., Díaz, M. Kinetic of copper-ion exchange onto iminodiacetic resin. Can. J. Chem. Eng., 1994, 72(6), 1028-1035.

554

14. Mijangos, F.; Bilbao, L. Application of microanalytical techniques to ion

555

exchange processes of heavy metals involving chelating resins. Progress in Ion

556

Exchange: Advances and Applications, Ion Ex'95. 1997, I, 341-348.

557

15. Tikhonov, N.; Mijangos, F.; Dautov, A.; Ortueta, M. Simulation of Internal

558

Concentration Profiles in a Multimetallic Ion Exchange Process. Ind. Eng.

559

Chem. Res. 2008., 47 (23), 9297-9303.

560

16. Alguacil, F.J.; García-Díaz, I.; Lopez, F. The removal of chromium (III) from

561

aqueous solution by ion Exchange on Amberlite 200 resin: Batch and continuous

562

ion exchange modelling. Desal. Water Treat. 2012, 45(1-3), 55-60.

563 564 565 566 567 568

17. Slater, M.J. Principles of ion exchange technology. Billings and Sons Ltd. Butterworth-Heinemann Ltd (Ed), 1991.

18. Pritzker, M. Shrinking core model for multispecies uptake onto an ion exchange resin involving distinct reaction fronts. Sep. Purif. Technol., 2005, 42(1), 15-24. 19. Mijangos, F.; Díaz, M. Kinetic of copper-ion exchange onto iminodiacetic resin. Can. J. Chem. Eng. 1994, 72(6), 1028-1035.

569

20. Sadegh, H., Shahryari-ghoshekandi, R., Tyagi, I., Agarwal, S., Gupta, V. K.

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Kinetic and thermodynamic studies for alizarin removal from liquid phase using

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poly-2-ydroxyethyl methacrylate (PHEMA). J. Mol. Liq. 2015, J. 207, 21-27.


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21. Koh, J.H.; Wankat P.C.; Wang N.H.L. Pore and Surface Diffusion and Bulk-

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Phase Mass Transfer in Packed and Fluidized Beds, Ind. Eng. Chem. Res. 1998,

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37, 228-239.

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22. Nestle, N. F. E. I.; Kimmich, R. NMR imaging of heavy metal absorption in

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alginate, immobilized cells, and kombu algal biosorbents. Biotechnol. Bioeng.

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1996, 51(5), 538-543.

578

23. Cussler, E. L. Chapter 5. Values of diffusion coefficients. In Diffusion mass

579

transfer in fluid systems (pp. 105-145) Cambridge University Press: New York

580

1984.

581

24. Bilbao, L. Aplicación de microscopía SEM-EDX al estudio de la cinética de

582

intercambio iónico en resinas quelantes. Ph.D. Dissertation, UPV-EHU, Leioa,

583

P.V., 2014.

584

25. Fernandez, A.; Díaz, M.. Equilibria for metal-binding with iminodiacetic acid

585 586

resins in high salinity media. React. Polym. 1992, 17(1), 89-94. 26.

Gode, F.; Pehlivan, E. A comparative study of two chelating ion-exchange resins

587

for the removal of chromium(III) from aqueous solution. J. Hazard. Mater.

588

2003, 100(1–3), 231-243.

589

27. Sirola, K.; Laatikainen, M.; Paatero, E. Effect of temperature on sorption of

590

metals by silica-supported 2-(aminomethyl)pyridine. Part II: Sorption dynamics.

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React. Funct. Polym. 2010, 70, 56-62.

592

28. Muraviev, D.; Noguerol, J.; Valiente, M. Application of the reagentless dual-

593

temperature ion-exchange technique to a selective separation and concentration

594

of copper versus aluminum from acidic mine waters. Hydrometallurgy. 1997,

595

44(3), 331-346.

596

29. Helfferich, F. G.. Ion exchange. New York: Dover, 1995.



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597

30. Agrawal, A.; Sahu, K. K. Influence of temperature on the exchange of alkaline

598

earth and transition metals on iminodiacetate resin. Solvent Extr. Ion Exch. 2005,

599

23(2), 265-287.

600

31. Morcali, M.H.; Zeytuncu, B.; Baysal, A.; Akman, S. Adsorption of copper and

601

zinc from sulfate media on a commercial sorbent. J. Environ. Chem. Eng. 2014,

602

2, 1655-1662.

603

32. Biesuz, R.; Pesavento, M.; Gonzalo, A.; and Valiente, M. Sorption of proton and

604

heavy metal ions on a macroporous chelating resin with an iminodiacetate active

605

group as a function of temperature. Talanta. 1998., 47(1), 127-136.

606

33. Biesuz, R.; Zagorodni, A. A.; Muhammed, M. Estimation of deprotonation

607

coefficients for chelating ion exchange resins. Comparison of different

608

thermodynamic model. J. Phys. Chem. B. 2001, 105(20), 4721-4726.

609 610

34. Mijangos, F.; Díaz, M. Metal-proton equilibrium relations in a chelating iminodiacetic resin. Ind. Eng. Chem. Res. 1992, 31, 2524-2532.

611 612 613 614


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615 616

For Table of Contents Only

617


Effect of Concentration and Temperature on Mass Transfer in Metal

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