Building and Verifying a Model for Mass Transfer and Reaction

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Kinetics, Catalysis, and Reaction Engineering

Building and Verifying of a Model for Mass Transfer and Reaction Kinetics of the Bunsen Reaction in the Iodine-Sulfur Process Chenglin Zhou, Songzhe Chen, Laijun Wang, and Ping Zhang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00930 • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

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Industrial & Engineering Chemistry Research

1

Building and Verifying of a Model for Mass Transfer and Reaction Kinetics of

2

the Bunsen Reaction in the Iodine-Sulfur Process

3

Chenglin Zhou, Songzhe Chen, Laijun Wang, Ping Zhang *

4

Institute of Nuclear and New Energy Technology, Tsinghua University

5

Collaborative Innovation Center of Advanced Nuclear Energy Technology

6

Beijing, 100084, China

7

* E-mail: [email protected]

8 9

Abstract

10

Iodine-sulfur (IS) process is one of the most promising thermochemical water splitting process

11

for nuclear hydrogen production. The Bunsen reaction, which produces sulfuric and hydriodic

12

acids for two decomposition reactions, plays a crucial role in the IS process. Insufficient kinetics

13

data and models of the Bunsen reaction caused difficulties for designing a Bunsen reactor, and

14

optimizing and improving the efficiency of the process. The mass transfer and kinetics

15

mechanism of the Bunsen reaction, which is a complicated gas-liquid-slurry process, were first

16

analyzed and proposed on the basis of double-film theory and thermodynamics calculation, and

17

intrinsic reaction rate equation models were deduced with different hypothesized reaction

18

mechanisms. Then, the models were further improved, and the experimental kinetics data were

19

used to verify the models. Finally, a set of reaction rate equations was developed, thereby

20

confirming its reliability for calculating the reaction kinetics data. The built models for mass

21

transfer and reaction kinetics provide crucial information for the thorough understanding of the

22

Bunsen reaction mechanism, selecting the reactor type, and designing the Bunsen reactor.

23 24

Keywords: nuclear hydrogen production, iodine-sulfur process, Bunsen reaction, mass transfer,

25

reaction mechanism, kinetics model.

26 27

1. Introduction

28

Hydrogen has received increasing attention in recent years, as a potential fuel of fuel cell

29

vehicles (FCV), and the demand for hydrogen will dramatically increase with the maturity of the

30

FCV technology1. However, most of the currently used hydrogen are produced from fossil fuel

31

by reforming accompanying emission of large amounts of CO2, which is assumed to be

32

responsible for global warming. Hydrogen can be produced in an efficient, CO2 free, and

33

large-scale manner through thermochemical water-splitting process using nuclear energy,

34

specifically, using the process heat of high-temperature gas-cooled nuclear reactor (HTGR)2-3.

35

Iodine–sulfur (IS) process is considered the most promising thermochemical technique for 1

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Industrial & Engineering Chemistry Research 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

36

nuclear hydrogen production4.

37

The IS process consists of the following three chemical reactions5:

38

Bunsen reaction: I2 + SO2 + H2O = H2SO4 + 2HI

39

HI decomposition: 2HI = H2 + I2

40

Sulfuric acid decomposition: H2SO4 = SO2 + 1/2 O2 + H2O

41

The net reaction of the abovementioned chemical reactions is water decomposition (H2O =

42

H2 + 1/2O2).

43

The IS process has been widely investigated in many institutes worldwide6-7. Thus far,

44

several integrated laboratory-scale IS facilities have been constructed and operated8-9 to verify the

45

feasibility and controllability of the IS process. Other engineering-related issues, including

46

screening engineering materials, developing the key reactors and components, and coupling

47

nuclear reactor with hydrogen plant, have become the main topics for further developing the

48

technology. Reaction kinetics will provide crucial references and data for developing chemical

49

reactors and scaling up of the process10.

50

In the IS process, H2SO4 and HI are produced by the Bunsen reaction among SO2, I2, and

51

H2O, thereby inducing the decomposition reactions of H2SO4 and HI acids. The decomposition

52

products of HI and H2SO4 (i.e., SO2, I2, and H2O) are recycled for the Bunsen reaction. At the

53

initial stage of the IS process, the Bunsen reaction is a three-phase heterogeneous reaction; that is,

54

the gaseous SO2 reacts with solid I2 and liquid H2O. The Bunsen reaction becomes a gas–liquid

55

slurry reaction, in which the recycled gases react with I2 in the HI solution when the IS process is

56

continuously operated under cycling conditions. Most studies on the Bunsen reaction have

57

focused on thermodynamics, including phase separation characteristics, side reactions, and

58

optimization of operational parameters11-14. The results guarantee that the Bunsen reaction favors

59

thermodynamic conditions and spontaneous product separation. Kinetics data are crucial to

60

reactor design and non-steady-state operation. However, few studies involved the kinetics of the

61

Bunsen reaction. Zhang15-16 and Ying17 studied the kinetics of the Bunsen reaction in a semi-batch

62

continuous stirring reactor by determining the concentration variations in the H2SO4 phase with a

63

reaction time and proposed the multistage reaction mechanism. Rao18 studied the kinetics features

64

of the Bunsen reaction in a metallic tubular static mixer reactor in a semi-batch mode and

65

investigated the effects of pressure and temperature on reaction rate. Li19 studied the apparent

66

reaction rate of a gas–liquid–liquid multiphase system in toluene of a closed, ﬁxed volume batch

67

reactor through the initial rate analysis method; total reaction rate was calculated by measuring

68

changes in SO2 pressure with time. We20-21 studied the apparent kinetics of a reverse Bunsen

69

reaction through the initial rate method, determined the apparent reaction orders and rate constant,

70

and proposed the reaction rate expression. In addition, the gas-liquid apparent kinetics under 2


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71

homogeneous conditions was studied, and kinetics parameters such as reaction orders and

72

activated energy, were determined. The kinetics models are scarce, and the reaction mechanism

73

remains unclear, although these works present certain information on the Bunsen reaction

74

kinetics. These results should be attributed to the complicated circumstance of the Bunsen

75

reaction. The knowledge of the kinetics model is crucial to designing the reactors, optimizing the

76

reaction conditions and improving the process efficiency.

77

In this work, we analyzed the mass transfer and reaction mechanism based on double-film

78

theory, deduced and improved intrinsic reaction rate equation models, and verified the models

79

with experimental data. This work would also provide useful information for to thoroughly

80 81

understand the mechanism of the Bunsen reaction. 2. Theoretical analysis

82

2.1 Mass transfer and process analysis of the Bunsen reaction

83

Bunsen reaction is a typical heterogeneous process. The reaction can be divided into several

84

basic steps on the basis of double-film theory (Figure 1): 1) SO2 bulk transfer to the gas-liquid

85

interface through the gas membrane; 2) gas-liquid equilibrium; 3) gas transfer from the gas-liquid

86

interface to the liquid bulk through the liquid membrane; 4) chemical reaction; 5) I2 dissolves to

87

liquid and reaches equilibrium on the solid-liquid interface; 6) transfer of dissolved I2 from the

88

solid-liquid interface to the liquid bulk through the liquid membrane; and 7) diffusion of reaction

89

products.

90

Gas-liquid interface P Pi Cg

Reaction

ci

Cl

c

Gas bulk

Gas film

Liquid film

Liquid bulk

Liquid film

91 92

Figure 1. Gas-liquid Bunsen reaction

93 94

Dynamic behaviors of these steps are introduced as follows: 3


Solid iodine


95 96

(1) Gaseous SO2 transfers from the bulk of gas phase to the gas-liquid interface. The mass transfer flux can be calculated with Equation (1). (1)

i ) N SO2 = k g S ( p SO2 − pSO 2

97

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i If pure SO2 is used, then the resistance of the gas membrane is zero, and p SO = p SO . For the 2

2

98

convenience of calculation, pure SO2 (99.9%) was used in the follow-up experiment. The

99

variation of gas pressure with time was measured by the experiment. The mass transfer rate in gas

100

phase is calculated from the gas state equation. The calculation method is the same as that in

101

Reference21. i N SO2 = kg S ( pSO2 − pSO )=− 2

102 103

dnSO2 dt

=−

V dpSO2 z 2 RT dt

(2)

(2) SO2 reaches a gas-liquid equilibrium at the gas-liquid interface. The gas-liquid equilibrium under experimental conditions can be described by Henry’s law. (3)

i ciSO =H SO2 pSO 2 2

104

(3) The SO2 molecules transfer from the gas-liquid interface to the liquid bulk.

N SO2 = kL S (ciSO − cSO ) 2

105

(4)

2

(4) Solid iodine dissolves in the solid-liquid interface.

I2 (s) ⇌ I2 (aq)

(5)

106

(5) I2(aq) diffuses to the solution bulk . If the solid-liquid interface can reach the dissolution

107

equilibrium, and the I2 (aq) concentration on the interface is saturated, then the dissolution flux

108

of I2 can be calculated with Equation (6).

109

NI2 = kI a([I2 ]s − [I2 ]) 110 111 112

113

(6)

(6) The chemical reactions occur in the liquid bulk; the reactions consist of the following steps. (a) Dissociation of SO2 in the aqueous solution.

SO2 (a)+H2O ⇌ HSO3- + H+

(7)

HSO3− ⇌ SO32- +H+

(8)

H2O ⇌ OH- +H+

(9)

The assumption that no secondary dissociation of sulfurous acid is reasonable given the high 4


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114

H+ concentration in the solution. SO2 distribution under different acid concentrations is

115

calculated to discuss the reliability of this hypothesis. If Cs is the total concentration of SO2 in

116

the solution, then

Cs =[SO2 ]+[HSO3- ]+[SO32- ] . 117

A two-level dissociation constant of a SO2 aquo-complex can be expressed as: K S1 =

[HSO3- ][H + ] , [SO 2 ]

(11)

[SO32- ][H + ] . [HSO3- ]

(12)

KS 2 = 118

Concentrations of different species in the sulfurous acid can be expressed as:

K S1[SO2 ] , [H + ]

(13)

K S 2 [HSO 3- ] K S 1 K S 2 [SO 2 ] . = [H + ] [H + ]2

(14)

[HSO3- ] = [SO 32- ] = 119

(10)

Equations (13) and (14) are integrated into Equation (10). [SO 2 ]=

Cs [H + ]2 K S 1 K S 2 +K S 1[H + ]+[H + ]2

(15)

[HSO3- ] =

K S 1[H 2SO3 ] K S 1Cs [H + ] = K S 1 K S 2 +K S 1[H + ]+[H + ]2 [H + ]

(16)

[SO32- ] =

K S 2 [HSO3- ] K S 1 K S 2C s = + K S 1 K S 2 +K S 1[H + ]+[H + ]2 [H ]

(17)

120

The use of thermodynamics software HSC-chemistry determines that Ks1=0.0116 and

121

Ks2=5.129E-8 at 40 °C. The concentration distributions of dissociation species in the SO2 solution

122

under different pH at 40 °C are illustrated in Figure 2.

5



1.0 concentration ratio (Cs)

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

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SO2 HSO3(-) SO3(2-)

0.8 0.6 0.4 0.2 0.0 -2

0

2

4

6

8

10

12

14

pH

123 124

Figure 2. Concentration distribution of dissociation species in the SO2 solution at different pH

125

levels

126 127

Only under high pH condition can SO32- exist in the solution. Meanwhile, SO32- hardly

128

coexist with SO2. SO32- can be neglected reasonably, and only the first-level dissociation of SO2

129

is considered because the acid concentration in the Bunsen reaction is high, and pH is low.

130

(b) Complex reaction between iodine and I-.

I 2 (aq)+I - ⇌ I3131 132

(18)

(c) The Bunsen reaction among SO2, I2, and H2O; the actual reaction mechanism is complicated and remains unknown.

SO2 +I2 +2H2O → H2SO4 +2HI

(19)

133

(7) Products diffuse to solutions evenly; the solution bulk can be considered a homogeneous

134

phase under stirring because the products are liquid. Bunsen reaction rate is expressed by the

135

generation rate of sulfuric acids. Reaction rate is the function of reactant concentration and

136

temperature and can be deduced by the reaction mechanism.

r=

d [SO42- ] = f (T ,[SO2 ],[ I 2 ],L) dt

(20)

137

The Bunsen reaction occurs mainly in the solution bulk. It is assumed that the iodine and

138

sulfur dioxide in the solution are only involved in the Bunsen reaction (no side reactions occur);

139

the accumulation of reactants SO2 and I2 can be expressed by the absorptive amount minus

140

reaction consumption. d [SO 2 ] N SO2 = −r dt VL

(21) 6


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d [I 2 ] N I 2 = −r dt VL

(22)

141

The differential equation set formed by Equations (2), (3), (4), (6), (20), (21), and (22) can

142

be solved by MATLAB given the reaction temperature, initial pressure, and initial I2

143

concentration. The corresponding reactants, product concentration and reaction rate can be

144

calculated at any time. Thus the law of the reaction kinetics can be determined.

145

Under the conditions of closed cycle operation, I2 is dissolved in the HI acid and Bunsen

146

reaction is recognized as a gas-liquid reaction, and the dissolution and diffusion of the solid I2 can

147

be neglected. Therefore, Equation (6) can be omitted, and Equation (22) can be simplified as

d [I 2 ] =−r . dt

(23)

148

The basic model of mass transfer-reaction kinetics is determined by the differential

149

equations formed by Equations (2), (3), (4), (20), (21), and (23). In this equation set, the specific

150

expression form of Equation (20) is unknown and cannot be solved directly. The relation between

151

reaction rate and reactant concentration is the key to solving the equation set. Generally, the

152

reaction rate equation is deduced from the reaction mechanism.

153

2.2 Deduction of reaction mechanism and the intrinsic reaction rate equation

154

Few studies have been conducted on the kinetics and mechanism of the Bunsen reaction. 22

summarized the discussions on the Karl Fischer and Bunsen reaction mechanisms.HSO3-

155

Grünke

156

is a species that is oxidized, but SO2 molecules cannot be oxidized directly. In the research by

157

Margerum23, the oxidized species are also HSO3- and SO32-. SO2 molecules can only be oxidized

158

after being dissociated by HSO3-.

159

According to the above analysis, several complicated factors can be neglected reasonably in

160

accordance with the characteristics of the Bunsen reaction system. The Bunsen reaction

161

mechanism composed of the following five reactions is proposed:

162

SO2 (a) + H2O ⇌ HSO3- + H +

(M-1)

I2 (a)+I- ⇌ I3-

(M-2)

I2 (a)+HSO3− → ISO3- +I- +H +

(M-3)

I3− +HSO3− → ISO3- +2I- +H +

(M-4)

ISO3- +H 2 O → I- + SO 4 2- +2H +

(M-5)

If reaction (M-1) is the rate control step, then the expression of reaction rate is 7



Page 8 of 27

(24)

r = k[SO2 ] . 163

This condition reflects that the Bunsen reaction rate is only related to SO2 concentration and

164

is unrelated to I2 concentration. Experiments demonstrate that I2 concentration will change the

165

reaction rate21. Therefore, the first-level dissociation reaction of SO2 is not a rate-determining

166

step. Previous studies have revealed that the oxidation rate is higher in elementary I2 than in the

167

complex iodine; therefore, complexation reaction (M-2) is not the rate-determining step.

168 169

If oxidation reactions (M-3) and (M-4) of iodine are the rate-determining steps, then the reaction rate equation is

r = k3[I2 ][HSO3− ] + k4 [I3− ][HSO3− ] , KI =

[I3- ] , [I 2 ][I- ]

[HSO3- ] = 170

(25) (26)

K S1[SO 2 ] . [H + ]

(27)

If iodine in solution exists in the forms of free I2 and complex I3- , then

[I 2 ]t = [I 2 ] + [I3- ] = [I 2 ] + K I [I2 ][I- ] , [I 2 ]t , 1 + K I [I- ]

(29)

[I 2 ]t K I [I- ] , [I2 ]t = 1 + K I [I ] 1 + 1/ ( K I [I- ])

(30)

[I2 ]t , 1 + 1/ ( K I [I- ])

(31)

[I 2 ] = [I3- ] =

[I- ]t = [I- ] + [I3- ] = [I- ] +

[I- ]=

(28)

([I 2 ]t − [I- ]t +1/ K I )2 + 4[I- ]t / K I − ([I2 ]t − [I- ]t +1/ K I ) 2

.

(32)

171

Equation (32) is complicated, considering the practical conditions of a typical reaction

172

system of the IS process that uses HI solution as the solvent of iodine. A high initial concentration

173

of I- is obtained, and the concentration increases continuously while the reaction continues. In

174

addition, the equilibrium constant K I has a high numerical value of 721 at 25 °C 23. Therefore,

175

K I [I- ] ≫ 1. The following approximate simplification is feasible:

[I- ]t = [I- ] + [I3- ] = [I- ] +

[I 2 ]t ≈ [I- ]+[I2 ]t 1 + 1/ ( K I [I- ])

[I- ]=[I- ]t − [I2 ]t

(33) (34)

8


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176

Equations (26), (27), (29), and (34) are integrated into Equation (25) and obtains the following

177

equations:

r = K S1 (

k3 1 + k4 ) + [I 2 ]t [SO2 ] , K I ([I ]t − [I2 ]t ) [H ]

(35)

k' 1 ) + [I 2 ]t [SO2 ] . [I ]t − [I 2 ]t [H ]

(36)

-

r = (k +

-

178

Reaction (M-5) is the rate-determining step, and Reference23 mentioned that reaction (M-5)

179

is the slowest step; therefore, the first four steps can handle an equilibrium hypothesis. If

180

excessive water is present, then the Bunsen reaction rate can be described by the following

181

equations:

r=

d [SO 4 2- ] = k5 [ISO3- ] , dt

[ISO3- ][I- ][H + ] , K3 = [I 2 ][HSO3− ]

(38)

[ISO3- ][H + ][I- ]2 K 3 , K4 = = [I3- ][HSO3− ] KI

(39)

r = k5 [ISO 3- ] = k5 K 3 182

(37)

[I 2 ][HSO3 − ] . [I- ][H + ]

(40)

Equations (27), (29), and (34) are integrated into Equation (40) and obtain

r = k5 K3 K S1

[I 2 ]t [SO2 ] kKK [I ] [SO 2 ] ≈ 5 3 S1 - 2 t , + 2 K I ([I ]t − [I2 ]t ) 2 [H + ]2 (1 + K I [I ])[I ][H ] r =k

[I2 ]t [SO2 ] . ([I ]t − [I 2 ]t ) 2 [H + ]2 -

(41)

(42)

183

On the basis of the above reaction mechanism, different steps were hypothesized as the

184

rate-determining steps, and three forms of rate expressions were deduced, expressed in Equations

185

(24), (36), and (42). Equation (24) can be excluded in accordance with the experimental results.

186

Verhoef et al. conducted a series of experimental studies on kinetics and reaction rate of the Karl

187

Fischer titration reactions24-28 . If the reaction is a first-order reaction for SO2 and I2/I3-, then the

188

rate constant under different conditions can be measured by the pseudo-first-order reaction. The

189

results demonstrated that rate constant is sensitive to pH, and I- concentrations indicate that the

190

intrinsic rate equation shall include items of the H+ and I- concentrations. The simple first-order

191

reaction hypothesis is inconsistent with the reaction mechanism, while the experimental results

192

are close to the calculation results by Equation (36). Margerum et al. measured the rate constant 9



23

193

of reactions (M-3), (M-4), and (M-5) at 25°C

; the rate constant is far smaller in hydrolysis

194

reaction (M-5) than in reactions (M-3) and (M-4). Therefore, reaction (M-5) is a rate-determining

195

step. Equation (42) was deduced on the basis of this hypothesis.

196

may be accurate and shall be further verified by the experimental data.

197

3. Experimental verification of the rate equation model

Therefore, both expressions

198

An experiment was designed and conducted to verify the reliability of the built Bunsen

199

reaction model and the corresponding reaction rate equation. First, a series of gas-liquid Bunsen

200

reactions were was performed under different experimental conditions. The variations in pressure

201

with time are recorded in-time. The experimental process and method are the same as those used

202

in Reference21.

203

As mentioned previously, I2 dissolves in HI under gas-liquid reaction conditions; dissolution

204

and diffusion of solid I2 can be neglected. The mass transfer-reaction kinetics model deduced by

205

double-film theory is expressed by a differential equation set composed of Equations (2), (3), (4),

206

(20), (21), and (23). The deduced reaction rate (Equation [36] or [42]) is integrated into the

207

equation set as the specific expression form of Equation (20) to solve the model. The accuracy of

208

the model can be verified by comparing the solving and experimental results. However, the

209

model cannot be dissolved directly because the reaction rate constant and liquid-phase mass

210

transfer coefficient in the equation set are unknown, and Henry’s constant is different in various

211

references. Thus, the dependence curves between pressure and time under various conditions in

212

the Bunsen reaction are acquired through the experiment. If the model is accurate, then the

213

relation curve shall conform to the experimental results. Therefore, unknown parameters in the

214

model can be acquired by a regression of differential equation parameters based on experimental

215

data and then integrated into the model to compare the calculated and experimental results.

216

Equation (36) is substituted to the Bunsen reaction model. A parameter regression of the

217

differential equation set was conducted by using MATLAB in accordance with the experimental

218

data. The regression results of the experimental data under different conditions are summarized in

219

Table 1. Under these conditions, the regressed rate constant k is a negative number, which is

220

inconsistent with its theoretical significance. The rate constants and the complexing equilibrium

221

constant of I2 and I- for reactions (M-3), (M-4), and (M-5) at 25°C are introduced in Reference23,

222

and the values of k and k ' in the rate equations can be estimated in accordance with

223

Equations (35) and (36). These equations are in the 10^5 order of magnitude, which is

224

inconsistent with a theoretical value. Therefore, Equation (36) is unreliable, and the hypotheses

225

that (M-3) and (M-4) are rate-determining steps are false.

226 10


Page 10 of 27

Page 11 of 27

227

Table 1. Regression results of the experimental data with Equation (36) under different conditions T

P

[I2]

k

kL

H

k’

SD

°C

kPa

mol/L

1/s

mm/s

mol/L/kPa

mol/L/s

kPa

40.0

162.7

0.0000

-0.0019

0.0628

0.0060

0.0033

0.1383

40.0

162.7

0.1103

-0.0031

0.0630

0.0064

0.0048

0.0514

40.0

161.3

0.2071

-0.0077

0.0547

0.0076

0.0063

0.0519

40.0

162.7

0.3022

-0.0081

0.0537

0.0083

0.0069

0.0316

40.0

163.5

0.3976

-0.0028

0.0478

0.0096

0.0006

0.0270

40.0

163.1

0.4933

-0.0036

0.0387

0.0126

0.0022

0.0533

40.0

161.4

0.6521

-0.0048

0.0401

0.0125

0.0036

0.0481

40.0

57.7

0.6521

-0.0353

0.1348

0.0045

0.0276

0.0463

40.0

88.3

0.6521

-0.0151

0.0397

0.0140

0.0128

0.0633

40.0

119.6

0.6521

-0.0029

0.0800

0.0066

0.0138

0.0617

40.0

161.4

0.6521

-0.0038

0.0348

0.0144

0.0019

0.0537

40.0

215.8

0.6521

-0.0003

0.0315

0.0148

0.0002

0.1291

40.0

292.6

0.6521

-19.500

0.0291

0.0132

13.2514

0.1525

228 229

The reliability of the Equation (42) is verified by the same method. The model regression

230

curves under two conditions and the experimental curve are compared (Figure 3); two curves

231

nearly overlapped, and similar results are observed under other conditions.

232 180

180

160

160 exp fit

120 100

120 100

a)

b)

80

80

60

60

40

0

exp fit

140

p (kPa)

140

p (kPa)

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


500

1000

1500

40

2000

0

t (s)

500

1000

1500

2000

t (s)

233

Figure 3. Comparison between the model results using Equation (42) and the experimental results:

234

a) 161kPa, [I2] =0.6521 mol/L, 40°C; b) 163kPa, [I2] =0.4933 mol/L, 40°C

235 11



Page 12 of 27

236

The regression results of the experimental data under different experimental conditions are

237

presented in Table 2. The liquid-phase mass transfer coefficient and Henry’s constant in the

238

regression analysis conform to the theoretical values. The estimation of the theoretical value of a

239

rate constant is infeasible given the lack of reference data for the equilibrium constant (K3) in

240

reaction (M-3). Table 2 displays that the regression parameters of the experimental data under

241

different conditions fluctuate aggressively in a large scale, although the regression curves under

242

different experimental conditions nearly agree with the experimental curves. Based on previous

243

theoretical hypothesis, these parameters are consistent under different experimental conditions.

244

Therefore, the model parameters must be further revised.

245 246

Table 2. Regression results of the experimental data with Equation (42) under different conditions T

P

[I2]

k 3

(mol/L) /s

kL

H

SD

mm/s

mol/L/kPa

kPa

0.0628

0.0060

0.1383

°C

kPa

mol/L

40.0

162.8

0.0000

40.0

162.7

0.1103

0.0037

0.0658

0.0061

0.0505

40.0

161.3

0.2071

0.0138

0.0775

0.0054

0.0614

40.0

162.7

0.3022

0.0111

0.0743

0.0061

0.0463

40.0

163.5

0.3976

0.0010

0.0479

0.0096

0.0370

40.0

163.1

0.4933

0.0079

0.0594

0.0081

0.0786

40.0

161.4

0.6521

0.0108

0.0601

0.0083

0.0846

40.0

57.7

0.6521

0.0064

0.1727

0.0036

0.1305

40.0

88.3

0.6521

0.0114

0.0602

0.0092

0.0798

40.0

119.6

0.6521

0.0002

0.0345

0.0153

0.0569

40.0

161.4

0.6521

0.0020

0.0464

0.0108

0.0594

40.0

215.8

0.6521

0.0000

0.0312

0.0150

0.1293

40.0

292.6

0.6521

0.0021

0.0360

0.0110

0.1726

247 248

The different regression results of experimental data under various conditions might be due

249

to the following reasons: (1) the regression of the differential equation parameters is complicated

250

and is easy to cause an error. (2) The high linearity of mass transfer equation and rate equation

251

increases the difficulty of numerical calculation. (3) Many variables must be optimized. This

252

condition increases the difficulty of optimization. (4) Experimental data have certain errors. In

253

addition, the model only considers the Bunsen reaction, whereas the other side reactions are

254

disregarded. Sulfur element in the solution is generated after I2 is consumed while reaction 12


Page 13 of 27 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


255

continues, and the side reaction may play a dominant role and the original rate model may no

256

longer be applicable.

257

The same liquid-phase mass transfer coefficient (H=0.0060) and Henry’s constant

258

(kL=0.0624) will be gained after iterations with different initial values when the initial I2

259

concentration is zero. Theoretically, adding I2 will not change the two parameters.

260

On the basis of the above analysis, the gas pressure at the time of completely consuming I2

261

was estimated. Data in a certain period before the complete consumption of I2 were selected as

262

the experimental data fitting. The initial value of parameter iteration was adjusted repeatedly to

263

approximate Henry’s constant and the liquid-phase mass transfer coefficient to 0.0060 and 0.0624

264

as much as possible. Secondary fitting was performed, and the results are summarized in Table 3.

265 266

Table 3. Regression results of the experimental data before complete consumption of I2 T

P

[I2]

[I-]

[H+]

k

kL

H

SD

°C

kPa

mol/L

mol/L

mol/L

(mol/L)3/s

mm/s

mol/L/kPa

kPa

40.0

162.8

0

0.9857

0.9857

0

0.0692

0.0055

0.0381

40.0

162.7

0.1103

0.9861

0.9861

0.0102

0.0606

0.0065

0.0374

40.0

161.3

0.2071

0.9838

0.9838

0.0101

0.0663

0.0062

0.0762

40.0

162.7

0.3022

0.9716

0.9716

0.0097

0.0662

0.0068

0.0463

40.0

163.5

0.3976

0.9717

0.9717

0.0098

0.0728

0.0064

0.0470

40.0

163.1

0.4933

0.9659

0.9659

0.0097

0.0694

0.0070

0.0415

40.0

161.4

0.6521

0.9513

0.9513

0.0099

0.0641

0.0078

0.1346

40.0

57.7

0.6521

0.9513

0.9513

0.0098

0.0765

0.0078

0.0269

40.0

88.3

0.6521

0.9513

0.9513

0.0126

0.0668

0.0084

0.0288

40.0

119.6

0.6521

0.9513

0.9513

0.0099

0.0712

0.0074

0.0885

40.0

161.4

0.6521

0.9513

0.9513

0.0107

0.0669

0.0075

0.0556

40.0

215.8

0.6521

0.9513

0.9513

0.0081

0.0529

0.0088

0.1501

40.0

292.6

0.6521

0.9513

0.9513

0.0104

0.0434

0.0090

0.2047

267 268

Three parameters fall in a relatively small range under different conditions after such processing.

269

If the parameter difference is in the error range, then the mean values were used as the common

270

parameter value under all experimental conditions. k=0.0101, kL=0.0648 and H=0.0076 are

271

integrated into the model. The model and experimental results are compared as illustrated in

272

Figure 4. The accuracy of the pressure sensor is 0.1%, and the measurement error of the entire 13



273

experimental system is approximately 1kPa. The calculation result is considered reliable when

274

the calculated deviation is less than 1 kPa. The standard deviation between the calculations based

275

on the average and regression parameters (Model 1) is depicted in Figure 5. The calculated result

276

based on the average parameter agrees with the experimental results when the initial pressure is

277

lower than 216kPa. The standard deviation is lower than 2 kPa. If the initial pressure is fixed, and

278

I2 concentration is variable, then the calculated result only conforms to the experimental result

279

when the I2 concentration is 0.5 mol/L. This condition demonstrates that the average parameter

280

cannot satisfy the calculations under all conditions. This model may have certain parameters

281

related to the I2 concentration, and the model and reaction mechanism must be improved.

282 180

300

57.8kPa

line: exp point: fit

a)

88.1kPa 119.6kPa 161.1kPa

140

215.8kPa

200

292.6kPa

150

I2/HI=0.65 I2/HI=0.49 I2/HI=0.40 I2/HI=0.30 I2/HI=0.21 I2/HI=0.11 I2/HI=0

line: exp point: fit

160

p (kPa)

p (kPa)

250

b)

120

100

100 80

50 60

0

200

400

600

0

800

200

400

600

800

1000

1200

t (s)

t (s)

a) [I2]=0.6521 mol/L, 40°C

b) p=163 kPa, 40°C

283

Figure 4. Comparison between model results based on the average parameter and experimental

284

results

285 10

10

Model 1 Average parameter

8 6

8

a)

SD (kPa)

SD (kPa)

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 14 of 27

4

6

2

0

0

100

150

200

250

300

b)

4

2

50

Model 1 Average parameter

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

[I2] (mol/L)

p (kpa)

a) Standard deviation under different

b) Standard deviation under different I2 14


Page 15 of 27 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


pressures

concentrations

286 287

Figure 5. Standard deviation between the model results based on the average parameter and the

288

experimental results

289 290

Regression parameters k, kL and H under different conditions fluctuate on a large scale, and

291

iterations based on the same experimental data may obtain significantly different outcomes by

292

using different initial values. The product of kL and H (kL*H) is relatively stable, although

293

independent changes in k, kL or H lack evident correlations with conditional variables. We

294

observed that kL*H is nearly consistent under different initial values of iteration, and the value of

295

kL*H changes regularly with [I2] and PSO2. Specifically, the product is positively correlated with

296

[I2] and is negatively correlated with PSO2. These results may be caused by the fact that the model

297

is highly nonlinear, and kL*H contributes a high overall regression accuracy.

298

According to our previous studies on the absorption behavior of SO2, the variations in

299

Henry’s constant in the range of experimental pressure under the different initial pressure of SO2

300

can be neglected29. kL*H decreases with the increase in pressure possibly because of the

301

influences of pressure on the mass transfer coefficient of the liquid phase. The increasing

302

concentration of the absorption gas can reduce the mass transfer coefficient in the chemical

303

absorption process; similar conclusions such as the mass transfer coefficient decreases with the

304

increase in gas-phase SO2 concentration, and the influences of gas-phase concentration changes

305

on mass transfer are generally expressed indirectly, can be obtained in other studies30-32

306

Based on the above analysis and hypothesis, the H in the kL*H remains constant with

307

changes in pressure, whereas the reduction in kL*H with pressure growth is mainly attributed to

308

the reduction in kL. Similarly, that the changes in I2 concentration are mainly caused by the

309

changes in the mass transfer coefficient. Thus the relationships of kL* H with the initial SO2

310

pressure and I2 concentration are regressed and expressed by Equations (43) and (44) (Figure 6).

311

kL* H=0.0005 When [I2]=0.6521 mol/L and PSO2=161.4kPa. Therefore, the linear relation of kL*

312

H, initial SO2 pressure and I2 concentration can be expressed by Equation (45).

kL * H = −8*10( −7) pSO2 + 0.0006

(43)

kL * H = 0.0002 [ I2 ] + 0.0004

(44)

k L * H = 0.0005 + 0.0002([I 2 ] − 0.6521) − 8*10( −7) (pSO2 − 161.4)

(45)

313

15



0.00050

0.00054 0.00052

KL*H (mol/(s.m2.kPa))

KL*H (mol/(s.m2.kPa))

0.00056

a)

0.00050 0.00048 0.00046 0.00044 0.00042

y = -8E-07x + 0.0006 2 R = 0.9910

0.00040 0.00038 50

100

150

200

250

b)

0.00048 0.00046 0.00044

y = 0.0002x + 0.0004 R2 = 0.9709

0.00042 0.00040 0.00038 0.00036 -0.1

300

0.0

0.1

0.2

p (kPa)

0.3

0.4

0.5

0.6

0.7

[I2] (mol/L)

Figure 6. Relation curves between kL*H and (a) initial SO2 pressure and (b) I2 concentration

314 315 316

Henry’s constant uses the value calculated from the HSC-chemistry, that is, 0.0076 at 40°C to

317

reduce the regression parameters. The mass transfer coefficient of the liquid phase is calculated

318

by using Equation (45). The correction model of the mass transfer coefficient is integrated into

319

the regression rate constant k in the established Bunsen model. All results are proximate, and the

320

mean value is 0.012. The variation data of pressure with time under different conditions can be

321

gained by substituting H=0.0076, k=0.012, and Equation (45) into the model. The variation data

322

are compared with the experimental data as demonstrated in Figure 7. 180 57.7kPa 88.3kPa 119.8kPa 161.4kPa 216.3kPa 293.1kPa

250

line : exp point : fit

a)

200

0 0.11mol/L 0.21mol/L 0.30mol/L 0.40mol/L 0.49mol/L 0.65mol/L


160 140

p (kPa)

300

p (kPa)

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 16 of 27

150

120

b)

100

100

80 50

60 0

0

200

400

600

0

800

200

400

600

800

1000

1200

t (s)

t (s)

a) [I2]=0.6521 mol/L,40 °C, different

b)163 kPa, 40 °C, different I2

pressures

concentrations

323

Figure 7. Comparison of the mass transfer coefficients between the model and the experimental

324

results under different initial SO2 pressures and I2 concentrations

325 326

In Figure 7, the model results agree well with the experimental result under different pressures. 16


Page 17 of 27

327

The relative error at the late reaction stage is higher when the initial pressure is 57.7 kPa than

328

when under other initial pressure because the vapor pressure of the solution accounts for a high

329

proportion under low pressures, and measured PSO2 is slightly higher than the actual value. The

330

model result is consistent with the experimental result when the I2 concentration is high, but

331

certain error with low I2 concentration is observed. Such error increases with the decrease in I2

332

concentration; this condition further indicates that the built Bunsen model is inapplicable after

333

complete consuming iodine. The gas pressure at the complete consumption of I2 can be estimated

334

from the initial I2 content. The deviation between the model and the experimental results before

335

the complete consumption of I2 is analyzed and demonstrates favorable agreement, as exhibited

336

in Figure 8. 180

250

p (kPa)

57.7kPa 88.3kPa 119.8kPa 161.4kPa 216.3kPa 293.1kPa

line : exp point : fit a)

200

0.11mol/L 0.21mol/L 0.30mol/L 0.40mol/L 0.49mol/L 0.65mol/L


160 140

p (kPa)

300

150

120

b)

100

100 80

50 60

0

0

200

400

600

0

800

200

400

600

800

1000

t (s)

t (s)

337

Figure 8. Comparison between the model and the experimental results under different initial

338

pressures and I2 concentrations

339 340 10

10 8 6 a) 4

6 b) 4

2

2

0

0 50

100

150

200

Model 1 Average parameter kL*H modified

8

Model 1 Average parameter kL*H modified

SD (kPa)

SD (kPa)

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


250

300

0.1

0.2

0.3

0.4

0.5

0.6

[I2] (mol/L)

p (kpa)

341

Figure 9. Standard deviations between the model and the experimental results

342

Model 1: calculation based on regression parameters

343

Average parameter: calculation based on the average parameter 17


0.7


344

Page 18 of 27

kL*H modified: The mass transfer coefficient of the liquid phase is modified by the empirical correlation

345 346

Standard deviations between the model and experimental results are displayed in Figure 9.

347

The Mass transfer coefficient of the liquid phase is modified by the empirical relation. The

348

standard deviation which is generally lower than 1 kPa, decreased sharply compared with the

349

model results based on the average parameter. The standard deviation increases with time given

350

the accumulation of calculation errors. The relative error of pressure between the model results

351

and measurement at the complete consumption of iodine is analyzed and presented in Table 4.

352

The relative error is lower than 1% at a low initial pressure (except 57.7 kPa; the vapor pressure

353

of the solution accounts for a high proportion under low pressures, and the measured PSO2 is

354

slightly higher than the actual value; thus, the relative error at 57.7 kPa is relatively high), thereby

355

indicating high a favorable agreement between the model and experimental results. These results

356

also confirm the reasonability of previous deductions and hypotheses in the range of experimental

357

conditions, and the Bunsen reaction kinetics model which is built by Equations (2), (3), (4), (21),

358

(23), (42), and (45) is reliable. The mechanism hypothesis in Equation (42) is reasonable.

359 360

Table 4. Relative errors of pressure between the model results and measurement at the complete

361

consumption of I2 T

P

[I2]

°C

kPa

mol/L

%

40.0

162.7

0.1103

0.05909

40.0

161.3

0.2071

0.55151

40.0

162.7

0.3022

0.46094

40.0

163.5

0.3976

0.70346

40.0

163.1

0.4933

-0.78714

40.0

161.4

0.6521

-0.84128

40.0

57.7

0.6521

16.62477

40.0

88.3

0.6521

-0.71935

40.0

119.6

0.6521

0.59878

40.0

161.4

0.6521

-0.67437

40.0

215.8

0.6521

-0.50132

40.0

292.6

0.6521

-0.00957

362 363 18


Relative error

Page 19 of 27 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


364

Figure 10. Sensitive analysis of the model

365 366 367

The most important parameters in the model are kL, H, and k, where kL is calculated by an

368

empirical correlation, and H and k are the two parameters that must be input from the outside.

369

The influence of the change in the two parameters on the sensitivity of the model calculation was

370

investigated. The results are depicted in Figure 10. The relationship between the value of the two

371

parameters and the standard deviation is a “V”-type function. If the value is significantly high or

372

low, then this value will cause a large error. The calculated deviation is assumed to be less than 1

373

kPa, and the calculation result is reliable. Then, the rate and Henry’s constants can be changed in

374

the range of k=0.0088–0.0245(mol/L)3 s-1, H=0.0072–0.0086 mol L−1 kPa−1.

375

The model was verified on the basis of the experimental data at the same temperature in the

376

above discussion. Temperature is an important factor that affects the reaction rate. The

377

investigation of the effect of temperature on the kinetic parameters is necessary. Thus, kinetic

378

experiments were conducted at various temperatures, and the reaction rate constants and mass

379

transfer coefficients at different temperatures were regressed on the basis of the established model.

380

Henry’s constant at different temperatures was calculated using the HSC-chemistry. The results

381

are displayed in Table 5.

382 383

Table 5. Model parameters at different temperature T

P

[I2]

k

kL

H

SD

K

kPa

mol/L

(mol/L)3/s

mm/s

mol/L/kPa

kPa

298

119.9

0.6521

0.0101

0.0557

0.01201

0.0882

306

119.8

0.6521

0.0113

0.0629

0.00925

0.2274

313

119.8

0.6521

0.0124

0.0693

0.00755

0.1440

323

120.1

0.6521

0.0143

0.0850

0.00592

0.1190

19



384 385

Arrhenius equation describes the relationship between the rate constant of a chemical

386

reaction and the temperature. The activation energy and pre-exponential factor can be acquired

387

from the Arrhenius plot. In Figure 11, the relationship between the logarithm of the reaction rate

388

constant and the reciprocal of temperature (ln (k)–1/T) is favorably linear; the regressed

389

relationship can be expressed by Equation (46).

390 391

ln k = −1336.2939

1 − 0.1166 T

R2=0.9984

(46)

392

The fitting slope of the Arrhenius plot is −1336.2939 ± 31.1157, and the activation energy is

393

(1336.2939 ± 31.1157) × 8.314 J/mol ≈ 11.11 ± 0.26 kJ/mol. The pre-exponential factor A can

394

be calculated using a value of 0.8899 (mol/L)3 s−1. Thus, the detailed expression of the rate

395

constant can be obtained, as defined in Equation (47).

396 397

k =A exp(−

Ea −11109.95 ) = 0.8899exp( ) RT RT

(47)

-4.20 -4.25 -4.30 -4.35 ln(k)

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

Page 20 of 27

-4.40 -4.45 -4.50 -4.55 -4.60 0.0030

0.0031

0.0032

0.0033

0.0034

-1

1/T (K )

398 399

Figure 11.

Arrhenius plot for the equation (42)

400

The activation energy was calculated in several works. Wang19 reported that the activation

401

energy value of the Bunsen reaction in the toluene system is 6.02 kJ/mol. Zhu16, Ying17, and

402

Zhou21 reported that the activation energy values of the Bunsen reaction are 9.212, 8.536, and

403

5.86 kJ/mol, respectively. In this work, the activation energy is 11.11 kJ/mol. Notably, the rate 20


Page 21 of 27 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


404

expression in different works is different. The same conclusion can be drawn, although the

405

experimental conditions and analysis methods are different; the activation energy of the Bunsen

406

reaction is relatively low, thereby indicating the weak effect of temperature on reaction rate.

407 408

4. Discussion on the built model

409

In summary, the mass transfer–reaction kinetic model was established in this work. Owing to

410

the case that I2 is dissolved in HI acid and the feed gas is pure SO2, the model is mainly

411

composed of Equations (2), (3), (4), (21), (23), (42), (45), and (47) summarized as follows: i N SO2 = kg A( pSO2 − pSO )=− 2

dnSO2 dt

=−

V dpSO2 z RT dt 2

i ciSO =H SO2 pSO 2

(2) (3)

2

N SO2 = kL S (ciSO − cSO )

(4)

d [SO 2 ] N SO2 −r = dt VL

(21)

d [I 2 ] =−r dt

(23)

2

r =k

2

[I2 ]t [SO2 ] ([I ]t − [I 2 ]t ) 2 [H + ]2

(42)

-

k L H = 0.0005 + 0.0002([I 2 ] − 0.6521) − 8 × 10( −7) (pSO2 − 161.4)

k =A exp(−

Ea −11109.95 ) = 0.8899exp( ) RT RT

(45) (47)

412 413

The model consists of two parts, namely, establishing a mass transfer model based on

414

double-film theory and proposing a reaction mechanism and deriving the intrinsic rate equation.

415

The established mass transfer–reaction model can not only calculate the SO2 pressure change

416

over time given the initial conditions but also obtain the changes in SO2, I2, SO42−, and I−

417

concentrations in the solution over time. Figure 12 illustrates a typical calculation result.

21



2.0 Concentration (mol/L)

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

1.6

[SO2] [I2]t [SO2] 4 [I-]t

1.2 0.8 0.4 0.0 0

500

1000 1500 2000 2500 3000 3500 4000 t (s)

418 419

Figure 12. Concentration Calculation of each component using the established model

420

[I2]=0.6521 mol/L, 40 °C, 161.4 kPa, k=0.012, H=0.0076

421 422

Previous research on the Bunsen reaction mechanism for the IS process is rare; Zhu16 and

423

Ying17 proposed a SO42− production rate model based on three elementary reactions. In their

424

research, the constant concentration of SO2 was fed into the solution, and the product

425

compositions of the sulfuric acid phase were determined. The reaction kinetics was studied from

426

the viewpoint of product formation; however, an analysis of the hydroiodic acid phase remains

427

lacking. In their experiment conditions, the mass transfer and diffusion rate of SO2 were

428

negligible compared with the chemical reaction rate. Considering the difficulty of liquid sampling

429

and analysis, in this work, the volume of SO2 gas was fixed, and the reaction rate was measured

430

and expressed from the viewpoint of reactant consumption rate. For the models, the influence of

431

gas–liquid mass transfer factors was considered in the model developed in the present work, and

432

the mass transfer coefficient and Henry’s constant were added. In analyzing the reaction

433

mechanism, five elementary reactions were proposed, especially considering two reactions,

434

namely, the hydrolysis of sulfur dioxide and complex ISO3−, which was considered the

435

rate-determining step, were analyzed. Furthermore, the influence of H+ and I− on the reaction was

436

included in the final rate equation.

437

In Equation (42), the Bunsen reaction rate is related to not only the SO2 and I2

438

concentrations but also the H+ and I− concentrations. High H+ and I− concentrations are against

439

the reaction rate, which agrees with the experimental results and previous research conclusions. 22


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440

Equation (42) reflects the influences of H+ and I− concentrations on the reaction rate

441

quantitatively. The previous literature has not reported this form of rate equation.

442

The built model provides a considerable convenience for the Bunsen reaction process

443

research and kinetic calculations. The reaction mechanism, intrinsic rate equation, and mass

444

transfer process analysis based on double-film theory are of general application value. However,

445

the empirical correlation of the mass transfer coefficient only has a narrow application range, and

446

the theoretical basis must be improved. The mass transfer coefficient kL varies with the string rate,

447

equipment parameter, component concentration, and temperature; the value must be remeasured

448

under different conditions. An accurate and general correlation with mass transfer coefficient

449

must be established in the future.

450

5. Conclusions

451

An integral multi-phase Bunsen reaction model is built on the basis of double-film theory

452

and experimental results. A Bunsen reaction mechanism is proposed, and different reaction rate

453

equation models are deduced on the basis of different rate-determining steps. The parameters in

454

the reaction and mass transfer models were regressed, and the models were verified on the basis

455

of the experimental results and differential equation parameter regression approaches. The

456

empirical relation equation of the mass transfer coefficient of liquid phase with SO2 pressure and

457

iodine concentration is established. All model results agree well with the experimental results,

458

thereby indicating an error of lower than 1%. This result reflects that the established model can

459

simulate and predict the experimental process accurately. The proposed reaction mechanism and

460

deduced reaction rate equations are reliable. In the rate equations that Bunsen reaction rate is

461

related to not only the SO2 and I2 concentrations but also the H+ and I- concentrations. Such

462

relations are reflected quantitatively in Equation (42). The built model provides a considerable

463

convenience for the Bunsen reaction process research and kinetic calculations. This work provide

464

important theoretical basis for further understanding of the Bunsen reaction process, Bunsen

465

reactor design, and IS process optimization.

466

Acknowledgments

467

This work was supported by National Natural Scientific Foundation of China (Grant

468

No.21676153) and the National Science & Technology Major Project (Grant No. ZX06901).

469 470

Symbol description N SO2

The mass transfer flux of SO2 gas, mol s-1

23



kg

The mass transfer coefficient of the gas-phase SO2 , mol m-2 kPa-1 s-1

S

The gas-liquid contact area, m2

pSO2 (p)

The subject pressure of SO2 , kPa

i pSO 2

The pressure of SO2 at the gas-liquid interface, kPa

nSO2

Molar amount of SO2 in gas phase, mol

t

Reaction time, s

dnSO2 / dt

The change rate of the molar amount of SO2 in gas phase, mol s-1

V

Gas volume of SO2, L

z

Gas compressibility factor of SO2

R

Ideal gas constant, 8.314 J·K-1·mol−1

T

Temperature, K

dpSO2 / dt

The pressure change rate of SO2 gas, kPa s-1

c iSO

2

The SO2 concentration at the side of liquid membrane in the gas-liquid interface, mol L-1

H SO2 (H)

The Henry’s constant of SO2 , mol L-1 kPa-1

c SO

The concentration of liquid-phase subject SO2 , mol L-1

kL

The mass transfer coefficient of liquid-phase SO2 , mm s-1

kI

The liquid-phase mass transfer coefficient of I2 (aq) , mm s-1.

N I2

The mass transfer flux of I2 on the solid-liquid interface, mol s-1

[I2 ]s

The saturated solubility of iodine, mol L-1

[I2 ]

The I2 concentration of the liquid-phase subject, mol L-1

a

The surface area of solid iodine, m2

Cs

The total concentration of SO2 in the solution, mol L-1

K S1

The first dissociation constant of SO2 aqueous solution, mol L-1

KS 2

The second dissociation constant of SO2 aqueous solution, mol L-1

r

Reaction rate, mol L-1 s-1

[SO 4 2- ]

Concentration of SO4 2- in solution, mol L-1

[ SO2 ]

Concentration of SO2 in solution, mol L-1

2

24


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[HSO3- ]

Concentration of HSO3- in solution, mol L-1

[SO32- ]

Concentration of SO32- in solution, mol L-1

[H + ]

Concentration of H+ in solution, mol L-1

VL

The solution volume, L

d [SO4 2- ] / dt

The accumulation rate of SO4 2- in solution, mol L-1 s-1

d [SO 2 ] / dt

The accumulation rate of SO2 in solution, mol L-1 s-1

d [I 2 ] / dt

The accumulation rate of I 2 in solution, mol L-1 s-1

k, k’

The rate constant of Bunsen reaction

k3, k4, k5

The rate constant of reaction (M-3), (M-4), (M-5)

[I- ]

Concentration of I- in solution, mol L-1

[I3- ]

Concentration of I3- in solution, mol L-1

[I2 ]t

The total concentration of I 2 species in the solution, mol L-1

[I- ]t

The total concentration of I- species in the solution, mol L-1

KI

Reaction equilibrium constant of reaction (M-2)

K3, K4, K5

Reaction equilibrium constant of reaction (M-3), (M-4), (M-5)

SD

Standard deviation, kPa

A

Pre-exponential factor , (mol/L)3 s-1

Ea

Activation energy, kJ/mol

471 472

References

473 474 475 476 477 478 479 480 481 482 483 484 485 486 487

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552 553

Table of Contents (TOC) Graphic

554 555

300

57.7kPa 88.3kPa 119.8kPa 161.4kPa 216.3kPa 293.1kPa


250

p (kPa)

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


200 150 100 50 0

556

0

200

400

600

800

t (s)

27


Building and Verifying a Model for Mass Transfer and Reaction

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