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HI solution for the iodine–sulfur hydrogen production process
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 2 ( 2 0 1 7 ) 1 4 9 1 6 e1 4 9 2 5
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Apparent kinetics of the Bunsen reaction in I2/HI solution for the iodineesulfur hydrogen production process Chenglin Zhou, Ping Zhang*, Laijun Wang, Songzhe Chen Institute of Nuclear and New Energy Technology, Tsinghua University, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Beijing 100084, China
article info
abstract
Article history:
Massive hydrogen production featuring high efficiency, CO2 free, and cost effectiveness is a
Received 21 January 2017
crucial challenge for the hydrogen economy. Nuclear hydrogen production through ther-
Received in revised form
mochemical iodineesulfur (IS) process is a potential candidate for this purpose. Chemical
20 March 2017
reaction kinetics data are indispensable for developing a high-performance reactor as well
Accepted 17 April 2017
as the scaling up of the process. The apparent kinetics of the reaction under simulated
Available online 18 May 2017
recycling conditions of IS closed cycle operation was studied by initial rate method. The
Keywords:
and reaction temperature, on reaction rate, were systematically investigated by measuring
effects of key parameters, including agitation speed, SO2 partial pressure, I2 concentration, Nuclear hydrogen production
the variation in SO2 pressure with reaction time. Initial rate analysis method indicated that
Iodineesulfur cycle
the Bunsen reaction rates were 0.23 ± 0.01 and 0.77 ± 0.01 order with respect to SO2
Gaseliquid Bunsen reaction
pressure and I2 concentration. The apparent activation energy was 5.86 ± 0.21 kJ/mol.
Apparent kinetics
Based on these results, an exponential rate expression of the Bunsen reaction was estab-
Reaction order
lished. In addition, a simplified method for calculation of kinetics parameters was pro-
Activation energy
posed and compared with conventional techniques. Experimental results provide theoretical basis for design and development of Bunsen reactors and for elucidating the reaction process. © 2017 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Introduction As an important industrial raw material and potential energy carrier, hydrogen has received increasing attention in recent years. Hydrogen is dominantly produced from fossil fuel and emits large amounts of CO2, resulting in global warming. Hydrogen can be produced in highly efficient, CO2 free, and large-scale manner through thermochemical water splitting process using nuclear or solar energy. The iodineesulfur thermochemical cycle is considered the most promising
technique for hydrogen production using the process heat of high-temperature gas-cooled nuclear reactor (HTGR) [1,2]. IS process is initially proposed by General Atomics Corp. and considered the most suitable for hydrogen production coupled to HTGR. This process consists of the following three chemical reactions: Bunsen reaction: I2 þ SO2 þ 2H2O ¼ H2SO4 þ 2HI
(1)
HI decomposition: 2HI ¼ H2 þ I2
(2)
* Corresponding author. E-mail address: [email protected] (P. Zhang). http://dx.doi.org/10.1016/j.ijhydene.2017.04.117 0360-3199/© 2017 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 2 ( 2 0 1 7 ) 1 4 9 1 6 e1 4 9 2 5
Sulfuric acid decomposition: H2SO4 ¼ SO2 þ 1/2O2 þ H2O
(3)
The net reaction of the above reactions is water decomposition, i.e., H2O ¼ H2 þ 1/2O2. IS process has been widely investigated in many institutes worldwide, including Japan Atomic Energy Agency, General Atomics, Sandia National Laboratory, French Commissariat a l'Energie Atomique, Korean Atomic Energy Research Institute, and Tsinghua university of China [3e8]. Thus far, some integrated laboratories with improved IS facilities have been constructed and operated; studies have verified the feasibility and controllability of the process [9,10]. Therefore, engineering-related issues, such as engineering materials, reactors, components, and scaling up, are becoming the main topics of the technology. Reaction kinetics will provide crucial references and data for development of chemical reactors and scaling up of the process. In IS process, H2SO4 and HI are produced by Bunsen reaction through the reaction among SO2, I2, and H2O, thereby inducing the two decomposition reactions of H2SO4 and HI acids. The decomposition products of HI and H2SO4, e.g., SO2, I2, and H2O, are recycled for the Bunsen reaction. In the initial stage of IS process, the Bunsen reaction is a three-phase heterogeneous reaction, and the gaseous SO2 reacts with solid I2 and liquid H2O. When the IS process is continuously operated under cycling conditions, the Bunsen reaction becomes a gaseliquid slurry, i.e., the recycled gases react with I2 in HI solution. Most studies on the Bunsen reaction have focused on thermodynamics, including phase separation characteristics, side reactions, and optimization of the operational parameters [11e16]. Results ensure that the Bunsen reaction favors thermodynamic conditions and spontaneously the separation of the products. Kinetics data are crucial for reactor design and non-steady-state operation. Kinetics of HI and H2SO4 decomposition reactions have been studied [17,18]. However, few studies have investigated the kinetics of the Bunsen reaction. Zhang et al. [19,20] studied the kinetics of the Bunsen reaction in a semi-batch continuous stirring reactor by determining the concentration variations in H2SO4 phase with reaction time; the effects of temperature, SO2 flow rate, iodine content, and water content on the reaction rate were also investigated, and a multistage reaction mechanism was hypothesized and a kinetics model was proposed to fit the data obtained in a semi-batch reactor. However, the kinetics data acquired at ambient pressure could not be extrapolated to elevated pressure which is common for gas liquid reaction. Rao et al. [21] studied the kinetics features of the Bunsen reaction in a metallic tubular static mixer reactor in semi-batch mode and investigated the effects of pressure and temperature on reaction rate, but there is no kinetics equation or mathematical expression were proposed. Ying et al. [22] studied the kinetics of the electrochemical Bunsen reaction using polarization curves measurement, which was quite different from the common Bunsen reaction. Wang et al. [23] studied the apparent reaction rate in a gaseliquideliquid multiphase system in toluene in a closed, fixed volume batch reactor by using initial rate analysis method; total reaction rate was calculated by measuring changes in SO2 pressure with time. The results indicate that
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the absorption of SO2 by the liquid phase is the ratecontrolling step of the reaction. However, the transfer mechanism as well as kinetics features are different in toluene system and typical aqueous system. Li et al. [24] studied the apparent kinetics of reverse Bunsen reaction using initial rate method; the apparent reaction orders and rate constant were determined, and the reaction rate expression was proposed. Although these results were published, the kinetics study and data on the Bunsen reaction, particularly under cycling conditions, remain limited. Thus far, a definite mathematical expression has not been established for the Bunsen reaction kinetics in the presence of HI solution. The available data are insufficient for providing a theoretical basis for reactor design. Various reactors including continuous stirred tank reactor, continuous reverser flow tubular reactor, and column reactor, have been used considering the lack of principle for choosing reactor type because of insufficient reaction kinetics data. Considering the importance of the reaction kinetics on reactor design, process parameter optimization, process control, and scaling up, this study investigates the apparent kinetics of the Bunsen reaction under continuous cycling operation of IS process to obtain the appropriate rate expression, reaction orders, apparent activation energy, preexponential factor, and other kinetic parameters.
Experimental section Research method The main purpose of this work is to acquire the apparent reaction orders and activation energy of the Bunsen reaction under given conditions, and then deduce the mathematical expression of the reaction rate equation. The initial rate method was used to determine the kinetic parameters, and the concentrations of the reactants or products at different time should be determined. However, as Bunsen reaction is a “fast” one, rapid sampling or online determination of the concentration of other reactants or products at elevated temperatures and pressures are difficult or impossible. Therefore, the reaction rate is obtained by online measurement of the variation of pressure of SO2 gas with time. The amount of SO2 was calculated by the Virial equation of state. The second Virial coefficient was cited from the published results [25]. pSO2 ¼ p p0 nSO2 ¼
(4)
pSO2 V zRT
(5)
BpSO2 RT
(6)
z¼1þ
pSO2 , pressure of SO2 gas (kPa); p0, vacuum pressure of the system before feeding SO2 (kPa); p, gas pressure measured during the reaction (kPa); nSO2 , moles of SO2 gas (mol); V, gas volume (L); z, compressibility factor; B, second virial coefficient (L mol1); T, temperature (K); R, ideal gas constant (8.314 J K1 mol1).
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The decrease of SO2 in gas phase is absorbed by the liquid reactants, and the absorption flux of SO2 gas NSO2 (mol s1) is equal to the decrease rate of SO2 in gas phase dnSO2 =dt (mol s1). So the rate r (mol s1) could be expressed as Eq. (7): r ¼ NSO2
3 2 dnSO2 d4 pSO2 V V dpSO2 5¼ 2 ¼ ¼ dt 1 þ BpSO2 RT z RT dt dt
(7)
RT
Pressure drop rate dpSO2 =dt (kPa s1) can be obtained by differentiating pressure versus time data. The rate r can be obtained by measuring the gas pressure with time. The calculation basis of the total rate and volume molar rate are unified as r ¼ VL r0
(8) 1
0
where VL, liquid volume (L); r, total rate (mol s ); r , reaction rate in per unit volume (mol s1 L1). Under appropriate experimental conditions, the liquid phase is assumed to be mixed uniformly. As such, the liquidphase mass transfer effect could be ignored. Reaction rate can then be expressed in terms of the order of reactant concentration: n2 r0 ¼ k½I2 n1 pSO2
(9)
where r0 (mol s1 L1) is the reaction rate in per unit volume, k is the reaction rate constant, [I2] (mol L1) is the concentration of iodine in solution, pSO2 (kPa) is the pressure of SO2 gas, n1 is the partial reaction order of [I2] and n2 is the partial reaction order of pSO2 . According to Arrhenius equation, the relationship among rate constant k, temperature T, pre-exponential factor A and activation energy Ea is expressed as: Ea k ¼ A exp RT
(10)
Then: n n Ea ½I2 n1 PSO2 2 ; r ¼ VL k½I2 n1 PSO2 2 ¼ VL A exp RT Ea þ ln A þ ln VL ln r ¼ n1 lnð½I2 Þ þ n2 ln PSO2 RT
(11)
Therefore, the reaction order of SO2 pressure can be obtained using initial rate method under the conditions of fixed iodine concentration, temperature, liquid volume, agitation speed, and gaseliquid contact area. A series of initial reaction rates were determined at different initial pressure levels to minimize the error. The reaction order of iodine concentration can be obtained using similar procedures. The preexponential factor and activation energy can be determined by changing the reaction temperature individually.
Experimental setup The reaction was conducted in a home-designed apparatus, which is schematically shown in Fig. 1. A gas reservoir with a capacity of 1000 mL and made of Teflon-lined stainless steel housing was heated with electric jacket to obtain the desired temperature. A reactor with 200 mL capacity, made of quartz
and jacketed by stainless steel, and equipped with mechanical stirrer and window design was also used. The pressure of the system was measured by an accurate pressure transducer connected to a computer. Changes in pressure were monitored and recorded online. The accuracy of the pressure transmitter is 0.1 kPa. All pipes were inter-twined with heater tapes to maintain the temperature. N2 was used for purging the system and testing the gas tightness. Impurity gases in the system were removed by vacuum before purging SO2. The tail gas was scrubbed using NaOH solution before discharging. Buffer bottle was used to prevent liquid back suction. The gas reservoir and reactor were designed considering the reaction system characteristics, such as high pressure, high temperature, and strong acid corrosion.
Materials and analysis Analytically pure hydroiodic acid (~57 wt%, Beijing Leadersh Chemical Co. Ltd.), iodine (>99.8 wt%, Beijing Leadersh Chemical Co. Ltd.), SO2 gas (99.9 vol%, Beijing Zhaoge Gas Co. Ltd.), N2 (99.999 vol%, Beijing Zhaoge Gas Co. Ltd.), and deionized water were used in the experiment. Hþ concentration was determined by NaOH titration. I concentration was determined by titration with KIO3. I2 concentration was determined by Na2S2O3 titration. During titration process, analytical pure sodium thiosulfate, sodium hydroxide and potassium iodate (all from Guangdong Xilong Chemical Co. Ltd.) were used as received. SO2 4 concentration was analyzed using ionic chromatography (Dionex ICX-2100).
Experimental procedure The I2/HI solution was placed in the reactor, which was purged with N2 prior to testing of the gas tightness of the system. The system was emptied by vacuum pump, and vacuum pressure was recorded, the value is about 98.0 to 100.0 kPa; repeated experiments showed that the results have no differences within the vacuum range. The connection valve between the gas reservoir and the reactor was closed, and pure SO2 gas was introduced from the cylinder into the reservoir at the set pressure. After the reservoir and reactor were preheated to the set temperature, the valve was opened and the gas was fed to the reactor. When the reaction started, pressure drop was monitored and recorded continuously. After completion of the reaction, the remaining acidic gas SO2 was removed by N2 sweeping.
Calculation of initial reaction rate The pressure in the reactor was monitored and recorded per second in real time to determine the effect of pressure on time. The dependence of pressure drop rate on time, i.e., dp/ dtet, can be obtained by numerical differentiation. The total absorption rate of SO2 can be calculated by substituting the dp/dt values into Eq. (7). The process is presented in Fig. 2. The initial rate was determined at t ¼ 0 and at different initial pressure levels. Fig. 2 shows the variation in pressure, pressure drop rate, reaction rate on reaction time, and initial rate under various initial pressure levels.
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Fig. 1 e Schematic of the experimental setup. 1 e water bath, 2 e SO2 cylinders, 3 e gas reservoir, 4 e heating jacket, 5 e reactor, 6 e buffer bottle, 7,8 e absorption bottle, 9 e vacuum pump, 10 e pressure transducer, 11 e thermocouple, 12 e computer.
350
57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa 292.6kPa
p (kPa)
250 200
0.14
(c) reaction rate 57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa
0.12 0.10 r (mol/s)
(a) pressure drop 300
150
0.08 0.06
100
0.04
50
0.02
0
0.00 0
200
400
600
800
1000
0
200
t (s) 0.00
600
800
0.14 (b) pressure drop rate
(d) initial reaction rate
-0.05
0.12
-0.10
0.10
r (mol/s)
dp/dt (kPa/s)
400 t (s)
57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa 292.6kPa
-0.15 -0.20
0.08 0.06
-0.25
0.04 0
200
400
600
800
1000
40
60
t (s)
80
100 120 140 160 180 200 220 p (kPa)
Fig. 2 e Processing approach of kinetics data by initial rate method (T ¼ 40 C, VL ¼ 70 mL, agitation speed 200 rpm, [I2] ¼ 0.65 mol/L, [HI] ¼ 1 mol/L).
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Results and discussion Effect of agitation speed on reaction rate Under the recycling conditions, the Bunsen reaction is a gaseliquid reaction, i.e., SO2 reacts with I2 resolved in HI acid solution. The overall reaction rate will be influenced by both mass transfer and chemical reaction. The effect of mass transfer should be considered to acquire an accurate reaction rate expression. The solution was mixed by agitation to reduce the mass transfer resistance. The effect of agitation speed on pressure drop was investigated with other conditions keeping the same. Variations in pressure and pressure drop rate with time under different agitation speeds were investigated considering similar analysis method introduced in the section “Calculation of initial reaction rate” (Fig. 3). Pressure drop rate is not apparently affected by agitation rate at 100e300 rpm but is apparently faster than that without agitation. Without agitation, the resistance to mass transfer, including gas diffusion and product diffusion, is high. Agitation efficiently decreases the resistance and increases the apparent reaction rate. From the figures it could be seen that the rate is almost the same in the range of 100e300 rpm, while
130
0rpm 100rpm 200rpm 300rpm 400rpm
(a) pressure drop
120
p (kPa)
110 100 90
the absorption rate increases sharply when the agitation speed increased to 400 rpm. It could be observed through the window of the reactor that the gaseliquid interface changed to a large whirlpool from a flat. The formation of the whirlpool dramatically increases the interface, and results in the increasing of the absorption rate. These results further confirm that the gaseliquid contact area is one of the most important factors influencing reaction rate. The agitation speed is set at 200 rpm in the following experiments to ensure that the solution is well mixed and the gaseliquid contact area is stable. In addition, the liquid volume is set at about 70 mL in each experiment.
Effects of SO2 pressure on reaction rate Assuming that the dependence of SO2 pressure on the Bunsen reaction kinetics conforms to the order model, the order of SO2 pressure would be obtained by measuring the reaction rate at different initial pressures of SO2 under fixed temperature, solution composition, and other parameters. To calculate the order of PSO2 with the initial rate method, it is necessary to change the initial PSO2 within a certain range. Considering the fact that SO2 is easily to be liquefied, the cylinder need heating to increase the pressure. However, the temperature could not be too high for safety concern, therefore, we set and controlled the pressure in the range of around 60e220 kPa, which was partially depends on the temperature. According to Eq. (11), the order of SO2 pressure, i.e., the slope of the straight line, would be obtained by plotting the logarithmic curve of the initial rate versus the corresponding initial pressure. As shown in Fig. 4(a), a good linear relationship exists between the logarithm of the initial pressure and the total absorption rate.
80
R2 ¼ 0:99914
ln r ¼ 0:8127 ln p 6:4364;
70
(12)
According to our previous results [26], SO2 can be absorbed by the HI solution without I2. However, assuming that all the
60 50 0
200
400
600
800
1000
1200
1400
t (s) (b) pressure drop rate
(a) total absorption rate in I2 / HI
-2.5
-0.05
ln r
dp/dt (kPa/s)
0.00
-2.0
0rpm 100rpm 200rpm 300rpm 400rpm
-0.10
-3.0 (b) total absorption rate in HI solution
-3.5
(c) Bunsen reaction rate corrected
-0.15
-4.0 -0.20
4.0 0
200
400
600
800
1000
1200
1400
t (s)
Fig. 3 e Variations in pressure and pressure drop rate with time under different agitation speeds (T ¼ 40 C, VL ¼ 70 mL, initial PSO2 ¼ 122 kPa, [I2] ¼ 0.23 mol/L, molar ratio I2/HI ¼ 0.35).
4.2
4.4
4.6
4.8
5.0
5.2
5.4
ln p Fig. 4 e Logarithmic relationship between initial pressure (kPa) and rate (mol/s), (a) total absorption rate in I2/HI, molar ratio I2/HI ¼ 0.69, (b) total absorption rate in HI solution, (c) Bunsen reaction rate corrected (T ¼ 40 C, [HI] ¼ 1 mol/L).
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absorbed SO2 can react with I2, we did not consider the factor of physical absorption when calculating the order of PSO2 by using the above process, and then the total pressure drop was all attributed to the chemical reaction. A comparative experiment without I2 dissolved in the HI solution was performed to verify the reliability of the method. As shown in Fig. 4(b), the absorption rate of SO2 and SO2 pressure exhibit a good order relationship. ln r ¼ 1:0480 ln p 7:9045;
R2 ¼ 0:99837
(13)
Fig. 5 compares the total absorption rates in HI solution with and without iodine. The total absorption rates in both cases are in the same order of magnitude, so the physical absorption should not be neglected. Therefore, the reaction rate should be corrected by subtracting the physical absorption rate from the total absorption rate. The total absorption rate, which consists of chemical and physical absorption rate and expressed with the decreasing rate of SO2 in gas phase, is calculated by Eq. (7). Because rapid sampling of liquid components under elevated pressures is difficult, the chemical and physical absorption rate cannot be measured directly. The absorption rate without iodine is defined as the physical absorption rate, it is assumed that at the initial time the physical absorption rates under conditions with or without presence of iodine are same, Bunsen reaction rate (chemical absorption rate) is assumed to be the one subtracting the physical absorption rate from the total one. Though physical absorption changes with variation of the composition of the solution during continuous Bunsen reaction, at the initial time the property of the solution does not changed significantly, therefore, the initial effect of difference in physical absorption could be neglected. Fig. 4(c) shows the corrected results, i.e., the logarithmic dependence of the Bunsen reaction rate on the initial pressure, after deduction of the physical absorption rate. A good linear agreement is presented between the logarithmical initial reaction rate and the initial pressure. ln r ¼ 0:2340 ln p 4:9514;
R2 ¼ 0:99247
(14)
Therefore, the partial reaction order of SO2 pressure in the Bunsen reaction is 0.23 ± 0.01. 0.14 I2/HI=0.69 I2/HI=0
r (mol/s)
0.12
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In Fig. 4, the line of (c) Bunsen reaction rate corrected dropped quite a lot after physical absorption correction, which suggests that chemical absorption plays a minor role in the process. In our experiments, I2 is dissolved in the HI solution; and the concentration of I2 is not high enough to result in the phase separation. Compared to I2, the amount of water is excessive. Under these conditions, the physical absorption of SO2 may be dominant in the process. Although Bunsen reaction would not occur without I2, physical absorption of SO2 still occurs in the HI solution. Verhoef et al. [27e31] studied the reaction rate of the KarleFischer titration reaction and concluded that the reaction among SO2, I2, and H2O in aqueous solution is a first-order reaction with respect to SO2 and I2. Wang et al. [23] concluded that the Bunsen reaction rate in the presence of toluene is also a first order with respect to SO2 and I2. The Bunsen reaction in the I2/HI system differs from those in the KarleFischer titration system and iodineetoluene system. In the present work, a low order of SO2 pressure was obtained probably because the Bunsen reaction is heterogeneous and the mass transfer efficiency affects the reaction rate. Meanwhile, the mass transfer efficiency may vary with experimental operation conditions; therefore, the total reaction rate will be affected by both mass transfer and the reaction itself. Eqs. (12) and (13) show that SO2 absorption rate in the HI solution conforms to the first-order relationship with pressure; however, the order decreases to approximately 0.8 when iodine was added. This finding indicates that the addition of iodine changes the property of the solution, restricting the absorption of SO2 gas. This phenomenon may be attributed to the presumption that the Bunsen reaction occurs at the gaseliquid interface; the reaction heat released enhances the local temperature and further hinders the absorption of SO2 gas. This finding could be verified by the immediate increase in the temperature when feeding SO2 gas into the reactor. The dependence of temperature on SO2 absorption rate in the HI solution shows that the absorption rate decreases with increasing temperature at the same pressure. The Bunsen reaction is an exothermic reaction and thus hinders the absorption process. The reaction order measured may be subjected to various factors, such as absorption mass transfer, which should be modified under different mass transfer conditions.
Effects of I2 concentration on reaction rate
0.04
The reaction order of [I2] was measured by the initial reaction rate method. The iodine concentration is varied from 0.2 to 0.7 mol/L, solid iodine could be precipitated at higher [I2]. The results are shown in Fig. 6, and the corrected results, i.e., subtracting the physical absorption rate from total rate, are presented for comparison. After correction, a good linear dependence of the logarithmic reaction rate and the iodine concentration could be expressed by Eq. (15) and shown in Fig. 7.
0.02
ln r ¼ 0:7651 lnð½I2 Þ 3:4094;
0.10 0.08 0.06
40
60
80
100 120 140 160 180 200 220 p (kPa)
Fig. 5 e Initial total absorption rate at different corresponding initial pressure levels in cases of iodine incorporation and non-iodination.
R2 ¼ 0:99843
(15)
The slope of the fitting line is the partial reaction order of iodine concentration and has a value of 0.77 ± 0.01. The reaction order of iodine was obtained under fixed SO2 gas pressure and temperature but with different I2 concentrations in the solution. Factors affecting the absorption of SO2 gas were basically controlled at the same level. The
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Effects of temperature on Bunsen reaction rate 0.100
r (mol/s)
0.095 0.090 0.085 0.080 0.075 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
[I2] (mol/L)
Fig. 6 e Initial total absorption rate at different iodine concentrations (T ¼ 40 C, initial PSO2 ¼ 163 kPa, [HI] ¼ 1 mol/L).
To acquire the apparent activation energy of the reaction, reaction rates were measured at the different temperature ranges. Considering the possible volatilization of iodine at higher temperature, a mild temperature ranges between 25 and 50 C was chosen. Reaction rate was corrected with the similar way as previously. Fig. 8 shows the relationship between the initial absorption rate of SO2 in the HI solution and temperature, the initial absorption rate decrease with increasing temperature (Eq. (17)). The total absorption rate also decreases with increasing temperature in the range of 25e50 C when I2 was added into the HI solution. Similarly, Rao et al. [21] found that Bunsen reaction rate decreases with increase in temperature for a fixed operating pressure, however the conclusion should be opposite according to the Arrhenius equation. Actually, the corrected reaction rate increases with temperature by subtracting the physical absorption rate from the total absorption rate. Therefore, the correction of reaction rate is reliable and necessary. ln r ¼ 1:5066E þ 06ð1=TÞ2 8582:83ð1=TÞ þ 9:1841;
-3.6
R2 ¼ 0:99970 -3.8
According to the Arrhenius equation, the relationship between the logarithm of the reaction rate and the reciprocal of temperature should be linear. The regressed relationship is shown in Fig. 9 and could be expressed by Eq. (18).
-4.0
ln r
(17)
ln r ¼ 705:0556ð1=TÞ 1:5636;
-4.2
-4.4
-4.6 -1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
ln([I2])
R2 ¼ 0:99617
(18)
The fitting slope is 705.0556 ± 25.2084, and the activation energy is (705.0556 ± 25.2084) 8.314 J/mol ¼ 5.86 ± 0.21 kJ/mol. According to Eqs. (11) and (18), the pre-exponential factor A could be calculated with a value of 1:36 ðmol=L=sÞ ðmol=LÞ0:23 ðkPaÞ0:77 . Wang et al. [23] and Zhang et al. [20] reported that the activation energy values of the Bunsen reaction in the toluene system are 6.02 and 9.21 kJ/mol, respectively. In the present
Fig. 7 e Logarithmic relationship between the initial Bunsen reaction rate (mol/s) and iodine concentration (mol/L).
-2.65 -2.70
I2 þ I #I 3
(16)
-2.75 ln r
experimental results accurately reflect the influence of iodine concentration on the Bunsen reaction. The reaction order of iodine is slightly less than 1, which is probably due to the chemical equilibrium between I 3 and I2, as shown in Eq. (16). I 3 and I2 can react with SO2, and the reaction constant is changed. Calculation is based on the total iodine concentration, thus the total reaction order measured is slightly lower than 1. The regression line exhibits good linearity, indicating that the effect of the iodine concentration on the reaction rate excellently meets the order relationship under the experimental conditions. The chemical equilibrium between I 3 and I2 can be neglected considering the apparent kinetics. Additional experimental data are needed to delineate the effects of I 3 and I2 to further investigate the mechanism of the reaction.
-2.80 -2.85 -2.90 -2.95 -3.00 0.0030
0.0031
0.0032
0.0033
0.0034
1/T (K-1)
Fig. 8 e Relationship between the initial absorption rate of SO2 and the temperature in the HI solution ([I2] ¼ 0, initial PSO2 ¼ 120 kPa, [HI] ¼ 1 mol/L, unit of r is mol/s).
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Table 2 e Comparison of the kinetic results obtained from two calculation methods.
-3.75
ln r
-3.80
-3.85
-3.90
-3.95 0.0031
0.0032
0.0033
0.0034
1/T (K-1)
Fig. 9 e Relationship between the logarithm of the reaction rate and the reciprocal of temperature ([I2] ¼ 0.65 mol/L, initial PSO2 ¼ 120 kPa, [HI] ¼ 1 mol/L, unit of r is mol/s). work, the activation energy is 5.86 kJ/mol. Although the experimental conditions and operating methods are different, the apparent activation energy values obtained by several methods are all relatively low. This finding indicates the weak effect of temperature on reaction rate.
Method
I2 order
SO2 order
Ea (kJ/mol)
A
Method 1 Method 2
0.77 ± 0.01 0.75 ± 0.01
0.23 ± 0.01 0.24 ± 0.01
5.86 ± 0.21 5.65 ± 0.56
1.36 1.18
As shown in Table 2, the results obtained by multiple regression are consistent with previously reported findings. Compared with the former method, the overall regression method is simpler; as such, all reaction parameters, such as reaction order, activation energy, and pre-exponential factor, can be calculated without plotting. Theoretically, experiment duration can be remarkably reduced under the condition of having an accurate kinetic model. If the dependence of PSO2 or [I2] on the reaction rate does not meet the order relationship but the order could be regressed by this method, the effect would be unclear. However, stepwise regression method may directly reflect the dependence of the kinetics data, including order and activation energy, on the reaction conditions including PSO2 , [I2], and temperature from the plotting curve. The overall regression was performed as verification method considering that the two approaches generate similar results.
Kinetics equation of the Bunsen reaction Regression method for kinetics data Although the apparent kinetic data of the Bunsen reaction could be acquired, the process is complicated. According to Eq. (11), kinetics data, including reaction order, activation energy, and pre-exponential factor, would be regressed by at least four sets of experimental data; thus, we attempted to develop a general method. If this method works, both the experiment and data analysis process would be simplified. Table 1 presents the 14 sets of experiment data. We used Matlab to perform multiple regression, and the calculated kinetics data are listed in the same table. The determination coefficient of the regression model is R2 ¼ 0.99732, and the probability of PROB > F is 1.00697E13. This finding indicates that the regression model is valid. The kinetics data calculated by the two approaches are compared in Table 2.
Based on the above discussion, the kinetics equation of Bunsen reaction could be expressed as follows: n n Ea ½I2 n1 PSO2 2 r0 ¼ k½I2 n1 PSO2 2 ¼ A exp RT
(19)
where n1 and n2 are the reaction order for [I2] and PSO2 , respectively. n1 ¼ 0:77 ± 0:01;
n2 ¼ 0:23 ± 0:01
The apparent activation energy is 5.86 ± 0.21 kJ/mol. The exponential form of Bunsen reaction rate expression was established: 0:23 5861:8 ½I2 0:77 PSO2 r0 ¼ 1:38 exp RT
(20)
Table 1 e Data used for kinetics multivariate regression. T ( C) 40 40 40 40 40 40 40 40 40 40 25 33 40 50
P (kPa)
[I2] (mol/L)
r (mol/s)
1/T (1/K)
ln p
ln[I2]
ln r
57.8 88.1 119.6 161.1 215.8 161.4 163.1 163.5 162.7 161.3 119.9 119.8 119.8 120.1
0.6521 0.6521 0.6521 0.6521 0.6521 0.6521 0.4934 0.3976 0.3022 0.2071 0.6521 0.6521 0.6521 0.6521
0.01809 0.02032 0.02167 0.02345 0.02464 0.02352 0.01961 0.01631 0.01323 0.00987 0.01965 0.02095 0.02207 0.02358
0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003357 0.003266 0.003183 0.003102
4.0570 4.4785 4.7842 5.0820 5.3744 5.0841 5.0942 5.0968 5.0916 5.0831 4.7868 4.7861 4.7855 4.7881
0.4276 0.4276 0.4276 0.4276 0.4276 0.4276 0.7065 0.9223 1.1965 1.5748 0.4276 0.4276 0.4276 0.4276
4.0124 3.8960 3.8317 3.7527 3.7036 3.7498 3.9317 4.1159 4.3250 4.6181 3.9296 3.8656 3.8136 3.7474
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Table 3 e Kinetic results of Bunsen reaction from different researchers. Researcher I2 order SO2 order Ea (kJ/mol) A/rate constant Rate expression Absorption consideration Characteristics
Verhoef [29e31]
Wang [23]
Zhang [19,20]
This work
1 1 e Done e e KarleFischer titration reaction, in methanol solvent, trace water
1 1 6.02 Done Done e I2 provided by iodineetoluene solution, heterogeneous
e e 9.21 e Done e SO2 þ solid I2 þ H2O, heterogeneous, phase separation
0.77 0.23 5.86 Done Done Done I2 dissolved in HI solution, homogeneous solution
where r0 is the reaction rate, mol L1 s1; [I2] is the iodine concentration, mol L1; PSO2 is SO2 pressure, kPa; T is the temperature, K; and ideal gas constant R ¼ 8.314 J mol1 K1. The kinetic data of Bunsen reaction from several researchers are compared in Table 3. Compared to other works, a classic physical chemistry method, initial rate method, was used to study the kinetics parameters, and the kinetics equation containing reaction order and activation energy was firstly established, which provides an important theoretical basis for the design of Bunsen reactor as well as optimization of the reaction conditions. As the effects of the several factors, including agitation speed, SO2 pressure, I2 concentration, and reaction temperature, on the reaction rate were explored, it is appropriate to summarize an optimum range of operating conditions for the given reactor setup based on the kinetics equation. As for the agitation speed, from the experiments results, the solution would be mixed well when the agitation speed reaches to 100 rpm and agitation with a value of 100e300 rpm presents a similar mixing effect for the given reactor, and continued increasing of agitation speed would lead to unstable operation, therefore, 100e300 rpm should be a suitable speed range for our reactor. The partial reaction order of SO2 pressure is small (0.23 ± 0.01), indicating that increasing SO2 pressure has limited effect on enhancing the reaction rate. Furthermore, according to our previous study [26], excess SO2 easily lead to side reactions. Therefore, higher SO2 gas pressure is not necessary. The partial reaction order of [I2] is 0.77, meaning that increasing of [I2] can apparently enhance the reaction rate. In addition, excess I2 is thermodynamically favorable for phase separation in real iodineesulfur process. Considering above factors, higher I2 concentration is favorable. The low activation energy indicates that the temperature has minimal effect on reaction rate, so a lower reaction temperature should be chosen for convenient operating. However, the solubility of iodine will decrease and separation characteristics would be deteriorated with lower temperature. These effects should be considered when choosing the reaction temperature. These principles may give some useful guidance for choosing and controlling of the conditions of the Bunsen reaction and separation process.
Conclusions In this work, the apparent kinetics of the Bunsen reaction in HI solution system was studied. The Bunsen reaction rate was
described by correlating the pressure drop with reaction time. The effects of key reaction conditions, including agitation speed, SO2 gas pressure, I2 concentration, and temperature, on kinetics parameters were investigated using initial rate analysis method. The reaction orders for PSO2 and [I2] of the Bunsen reaction are 0.23 ± 0.01 and 0.77 ± 0.01; the apparent activation energy is 5.86 ± 0.21 kJ/mol. Based on these data, the exponential rate expression of the Bunsen reaction was established. Analysis showed that SO2 gas absorption and mass transfer process are the rate-limiting steps in the entire reaction process. The low activation energy of Bunsen reaction indicates that the temperature has minimal effect on reaction rate. These experimental results provide some important guidance for the design of Bunsen reactor and elucidation of the reaction process.
Acknowledgment This work was supported by National Natural Science Foundation of China (Grant No. 21676153).
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[8] Shin Y, Lee T, Lee K, Kim M. Modeling and simulation of HI and H2SO4 thermal decomposers for a 50 N L/h sulfureiodine hydrogen production test facility. Appl Energy 2016;173:460e9. [9] Kubo S, Nakajima H, Kasahara S, Higashi S, Masaki T, Abe H, et al. A demonstration study on a closed-cycle hydrogen production by the thermochemical water-splitting iodineesulfur process. Nucl Eng Des 2004;233:347e54. [10] Zhang P, Zhou CL, Guo HF, Chen SZ, Wang LJ, Xu JM. Design of integrated laboratory-scale iodine sulfur hydrogen production cycle at INET. Int J Energy Res 2016;40:1509e17. [11] Sakurai M, Nakajima H, Onuki K, Shimizu S. Investigation of 2 liquid phase separation characteristics on the iodineesulfur thermochemical hydrogen production process. Int J Hydrogen Energy 2000;25:605e11. [12] Kim Y-H, Kim H-S, Han S-J, Park C-S, Bae K-K, Lee J-G. Phase separation characteristics of pressurized Bunsen reaction for sulfureiodine thermochemical hydrogen production process. In: Liu Z, Peng F, Liu X, editors. Advances in chemical engineering II, vol. 1e4; 2012. p. 554e7. [13] Lan SR, Guo HF, Zhang P, Chen SZ, Wang LJ, Xu JM. Phase separation characteristics of HIeI2eH2SO4eH2O mixture at elevated temperatures. Fluid Phase Equilib 2013;342:1e7. [14] Lee BJ, No HC, Yoon HJ, Kim SJ, Kim ES. An optimal operating window for the Bunsen process in the IeS thermochemical cycle. Int J Hydrogen Energy 2008;33:2200e10. [15] Zhang P, Xue LL, Lan SR, Guo HF, Chen SZ, Wang LJ, et al. Reaction parameters of the Bunsen reaction under simulated recycling conditions. Int J Hydrogen Energy 2014;39:14565e73. [16] Hadj-Kali MK, Gerbaud V, Lovera P, Baudouin O, Floquet P, Joulia X, et al. Bunsen section thermodynamic model for hydrogen production by the sulfureiodine cycle. Int J Hydrogen Energy 2009;34:6625e35. [17] Nguyen TDB, Gho YK, Cho WC, Kang KS, Jeong SU, Kim CH, et al. Kinetics and modeling of hydrogen iodide decomposition for a bench-scale sulfureiodine cycle. Appl Energy 2014;115:531e9. [18] Zhang YW, Yang H, Zhou JH, Wang ZH, Liu JZ, Cen KF. Detailed kinetic modeling of homogeneous H2SO4 decomposition in the sulfureiodine cycle for hydrogen production. Appl Energy 2014;130:396e402. [19] Zhang Y, Peng P, Ying Z, Zhu Q, Zhou J, Wang Z, et al. Experimental investigation on multiphase Bunsen reaction in the thermochemical sulfureiodine cycle. Ind Eng Chem Res 2014;53:3021e8. [20] Zhu Q, Zhang Y, Ying Z, Wang S, Wang Z, Zhou J, et al. Kinetic and thermodynamic studies of the Bunsen reaction
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Apparent kinetics of the Bunsen reaction in I2/HI solution for the iodineesulfur hydrogen production process Chenglin Zhou, Ping Zhang*, Laijun Wang, Songzhe Chen Institute of Nuclear and New Energy Technology, Tsinghua University, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Beijing 100084, China
article info
abstract
Article history:
Massive hydrogen production featuring high efficiency, CO2 free, and cost effectiveness is a
Received 21 January 2017
crucial challenge for the hydrogen economy. Nuclear hydrogen production through ther-
Received in revised form
mochemical iodineesulfur (IS) process is a potential candidate for this purpose. Chemical
20 March 2017
reaction kinetics data are indispensable for developing a high-performance reactor as well
Accepted 17 April 2017
as the scaling up of the process. The apparent kinetics of the reaction under simulated
Available online 18 May 2017
recycling conditions of IS closed cycle operation was studied by initial rate method. The
Keywords:
and reaction temperature, on reaction rate, were systematically investigated by measuring
effects of key parameters, including agitation speed, SO2 partial pressure, I2 concentration, Nuclear hydrogen production
the variation in SO2 pressure with reaction time. Initial rate analysis method indicated that
Iodineesulfur cycle
the Bunsen reaction rates were 0.23 ± 0.01 and 0.77 ± 0.01 order with respect to SO2
Gaseliquid Bunsen reaction
pressure and I2 concentration. The apparent activation energy was 5.86 ± 0.21 kJ/mol.
Apparent kinetics
Based on these results, an exponential rate expression of the Bunsen reaction was estab-
Reaction order
lished. In addition, a simplified method for calculation of kinetics parameters was pro-
Activation energy
posed and compared with conventional techniques. Experimental results provide theoretical basis for design and development of Bunsen reactors and for elucidating the reaction process. © 2017 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Introduction As an important industrial raw material and potential energy carrier, hydrogen has received increasing attention in recent years. Hydrogen is dominantly produced from fossil fuel and emits large amounts of CO2, resulting in global warming. Hydrogen can be produced in highly efficient, CO2 free, and large-scale manner through thermochemical water splitting process using nuclear or solar energy. The iodineesulfur thermochemical cycle is considered the most promising
technique for hydrogen production using the process heat of high-temperature gas-cooled nuclear reactor (HTGR) [1,2]. IS process is initially proposed by General Atomics Corp. and considered the most suitable for hydrogen production coupled to HTGR. This process consists of the following three chemical reactions: Bunsen reaction: I2 þ SO2 þ 2H2O ¼ H2SO4 þ 2HI
(1)
HI decomposition: 2HI ¼ H2 þ I2
(2)
* Corresponding author. E-mail address: [email protected] (P. Zhang). http://dx.doi.org/10.1016/j.ijhydene.2017.04.117 0360-3199/© 2017 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
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Sulfuric acid decomposition: H2SO4 ¼ SO2 þ 1/2O2 þ H2O
(3)
The net reaction of the above reactions is water decomposition, i.e., H2O ¼ H2 þ 1/2O2. IS process has been widely investigated in many institutes worldwide, including Japan Atomic Energy Agency, General Atomics, Sandia National Laboratory, French Commissariat a l'Energie Atomique, Korean Atomic Energy Research Institute, and Tsinghua university of China [3e8]. Thus far, some integrated laboratories with improved IS facilities have been constructed and operated; studies have verified the feasibility and controllability of the process [9,10]. Therefore, engineering-related issues, such as engineering materials, reactors, components, and scaling up, are becoming the main topics of the technology. Reaction kinetics will provide crucial references and data for development of chemical reactors and scaling up of the process. In IS process, H2SO4 and HI are produced by Bunsen reaction through the reaction among SO2, I2, and H2O, thereby inducing the two decomposition reactions of H2SO4 and HI acids. The decomposition products of HI and H2SO4, e.g., SO2, I2, and H2O, are recycled for the Bunsen reaction. In the initial stage of IS process, the Bunsen reaction is a three-phase heterogeneous reaction, and the gaseous SO2 reacts with solid I2 and liquid H2O. When the IS process is continuously operated under cycling conditions, the Bunsen reaction becomes a gaseliquid slurry, i.e., the recycled gases react with I2 in HI solution. Most studies on the Bunsen reaction have focused on thermodynamics, including phase separation characteristics, side reactions, and optimization of the operational parameters [11e16]. Results ensure that the Bunsen reaction favors thermodynamic conditions and spontaneously the separation of the products. Kinetics data are crucial for reactor design and non-steady-state operation. Kinetics of HI and H2SO4 decomposition reactions have been studied [17,18]. However, few studies have investigated the kinetics of the Bunsen reaction. Zhang et al. [19,20] studied the kinetics of the Bunsen reaction in a semi-batch continuous stirring reactor by determining the concentration variations in H2SO4 phase with reaction time; the effects of temperature, SO2 flow rate, iodine content, and water content on the reaction rate were also investigated, and a multistage reaction mechanism was hypothesized and a kinetics model was proposed to fit the data obtained in a semi-batch reactor. However, the kinetics data acquired at ambient pressure could not be extrapolated to elevated pressure which is common for gas liquid reaction. Rao et al. [21] studied the kinetics features of the Bunsen reaction in a metallic tubular static mixer reactor in semi-batch mode and investigated the effects of pressure and temperature on reaction rate, but there is no kinetics equation or mathematical expression were proposed. Ying et al. [22] studied the kinetics of the electrochemical Bunsen reaction using polarization curves measurement, which was quite different from the common Bunsen reaction. Wang et al. [23] studied the apparent reaction rate in a gaseliquideliquid multiphase system in toluene in a closed, fixed volume batch reactor by using initial rate analysis method; total reaction rate was calculated by measuring changes in SO2 pressure with time. The results indicate that
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the absorption of SO2 by the liquid phase is the ratecontrolling step of the reaction. However, the transfer mechanism as well as kinetics features are different in toluene system and typical aqueous system. Li et al. [24] studied the apparent kinetics of reverse Bunsen reaction using initial rate method; the apparent reaction orders and rate constant were determined, and the reaction rate expression was proposed. Although these results were published, the kinetics study and data on the Bunsen reaction, particularly under cycling conditions, remain limited. Thus far, a definite mathematical expression has not been established for the Bunsen reaction kinetics in the presence of HI solution. The available data are insufficient for providing a theoretical basis for reactor design. Various reactors including continuous stirred tank reactor, continuous reverser flow tubular reactor, and column reactor, have been used considering the lack of principle for choosing reactor type because of insufficient reaction kinetics data. Considering the importance of the reaction kinetics on reactor design, process parameter optimization, process control, and scaling up, this study investigates the apparent kinetics of the Bunsen reaction under continuous cycling operation of IS process to obtain the appropriate rate expression, reaction orders, apparent activation energy, preexponential factor, and other kinetic parameters.
Experimental section Research method The main purpose of this work is to acquire the apparent reaction orders and activation energy of the Bunsen reaction under given conditions, and then deduce the mathematical expression of the reaction rate equation. The initial rate method was used to determine the kinetic parameters, and the concentrations of the reactants or products at different time should be determined. However, as Bunsen reaction is a “fast” one, rapid sampling or online determination of the concentration of other reactants or products at elevated temperatures and pressures are difficult or impossible. Therefore, the reaction rate is obtained by online measurement of the variation of pressure of SO2 gas with time. The amount of SO2 was calculated by the Virial equation of state. The second Virial coefficient was cited from the published results [25]. pSO2 ¼ p p0 nSO2 ¼
(4)
pSO2 V zRT
(5)
BpSO2 RT
(6)
z¼1þ
pSO2 , pressure of SO2 gas (kPa); p0, vacuum pressure of the system before feeding SO2 (kPa); p, gas pressure measured during the reaction (kPa); nSO2 , moles of SO2 gas (mol); V, gas volume (L); z, compressibility factor; B, second virial coefficient (L mol1); T, temperature (K); R, ideal gas constant (8.314 J K1 mol1).
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The decrease of SO2 in gas phase is absorbed by the liquid reactants, and the absorption flux of SO2 gas NSO2 (mol s1) is equal to the decrease rate of SO2 in gas phase dnSO2 =dt (mol s1). So the rate r (mol s1) could be expressed as Eq. (7): r ¼ NSO2
3 2 dnSO2 d4 pSO2 V V dpSO2 5¼ 2 ¼ ¼ dt 1 þ BpSO2 RT z RT dt dt
(7)
RT
Pressure drop rate dpSO2 =dt (kPa s1) can be obtained by differentiating pressure versus time data. The rate r can be obtained by measuring the gas pressure with time. The calculation basis of the total rate and volume molar rate are unified as r ¼ VL r0
(8) 1
0
where VL, liquid volume (L); r, total rate (mol s ); r , reaction rate in per unit volume (mol s1 L1). Under appropriate experimental conditions, the liquid phase is assumed to be mixed uniformly. As such, the liquidphase mass transfer effect could be ignored. Reaction rate can then be expressed in terms of the order of reactant concentration: n2 r0 ¼ k½I2 n1 pSO2
(9)
where r0 (mol s1 L1) is the reaction rate in per unit volume, k is the reaction rate constant, [I2] (mol L1) is the concentration of iodine in solution, pSO2 (kPa) is the pressure of SO2 gas, n1 is the partial reaction order of [I2] and n2 is the partial reaction order of pSO2 . According to Arrhenius equation, the relationship among rate constant k, temperature T, pre-exponential factor A and activation energy Ea is expressed as: Ea k ¼ A exp RT
(10)
Then: n n Ea ½I2 n1 PSO2 2 ; r ¼ VL k½I2 n1 PSO2 2 ¼ VL A exp RT Ea þ ln A þ ln VL ln r ¼ n1 lnð½I2 Þ þ n2 ln PSO2 RT
(11)
Therefore, the reaction order of SO2 pressure can be obtained using initial rate method under the conditions of fixed iodine concentration, temperature, liquid volume, agitation speed, and gaseliquid contact area. A series of initial reaction rates were determined at different initial pressure levels to minimize the error. The reaction order of iodine concentration can be obtained using similar procedures. The preexponential factor and activation energy can be determined by changing the reaction temperature individually.
Experimental setup The reaction was conducted in a home-designed apparatus, which is schematically shown in Fig. 1. A gas reservoir with a capacity of 1000 mL and made of Teflon-lined stainless steel housing was heated with electric jacket to obtain the desired temperature. A reactor with 200 mL capacity, made of quartz
and jacketed by stainless steel, and equipped with mechanical stirrer and window design was also used. The pressure of the system was measured by an accurate pressure transducer connected to a computer. Changes in pressure were monitored and recorded online. The accuracy of the pressure transmitter is 0.1 kPa. All pipes were inter-twined with heater tapes to maintain the temperature. N2 was used for purging the system and testing the gas tightness. Impurity gases in the system were removed by vacuum before purging SO2. The tail gas was scrubbed using NaOH solution before discharging. Buffer bottle was used to prevent liquid back suction. The gas reservoir and reactor were designed considering the reaction system characteristics, such as high pressure, high temperature, and strong acid corrosion.
Materials and analysis Analytically pure hydroiodic acid (~57 wt%, Beijing Leadersh Chemical Co. Ltd.), iodine (>99.8 wt%, Beijing Leadersh Chemical Co. Ltd.), SO2 gas (99.9 vol%, Beijing Zhaoge Gas Co. Ltd.), N2 (99.999 vol%, Beijing Zhaoge Gas Co. Ltd.), and deionized water were used in the experiment. Hþ concentration was determined by NaOH titration. I concentration was determined by titration with KIO3. I2 concentration was determined by Na2S2O3 titration. During titration process, analytical pure sodium thiosulfate, sodium hydroxide and potassium iodate (all from Guangdong Xilong Chemical Co. Ltd.) were used as received. SO2 4 concentration was analyzed using ionic chromatography (Dionex ICX-2100).
Experimental procedure The I2/HI solution was placed in the reactor, which was purged with N2 prior to testing of the gas tightness of the system. The system was emptied by vacuum pump, and vacuum pressure was recorded, the value is about 98.0 to 100.0 kPa; repeated experiments showed that the results have no differences within the vacuum range. The connection valve between the gas reservoir and the reactor was closed, and pure SO2 gas was introduced from the cylinder into the reservoir at the set pressure. After the reservoir and reactor were preheated to the set temperature, the valve was opened and the gas was fed to the reactor. When the reaction started, pressure drop was monitored and recorded continuously. After completion of the reaction, the remaining acidic gas SO2 was removed by N2 sweeping.
Calculation of initial reaction rate The pressure in the reactor was monitored and recorded per second in real time to determine the effect of pressure on time. The dependence of pressure drop rate on time, i.e., dp/ dtet, can be obtained by numerical differentiation. The total absorption rate of SO2 can be calculated by substituting the dp/dt values into Eq. (7). The process is presented in Fig. 2. The initial rate was determined at t ¼ 0 and at different initial pressure levels. Fig. 2 shows the variation in pressure, pressure drop rate, reaction rate on reaction time, and initial rate under various initial pressure levels.
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Fig. 1 e Schematic of the experimental setup. 1 e water bath, 2 e SO2 cylinders, 3 e gas reservoir, 4 e heating jacket, 5 e reactor, 6 e buffer bottle, 7,8 e absorption bottle, 9 e vacuum pump, 10 e pressure transducer, 11 e thermocouple, 12 e computer.
350
57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa 292.6kPa
p (kPa)
250 200
0.14
(c) reaction rate 57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa
0.12 0.10 r (mol/s)
(a) pressure drop 300
150
0.08 0.06
100
0.04
50
0.02
0
0.00 0
200
400
600
800
1000
0
200
t (s) 0.00
600
800
0.14 (b) pressure drop rate
(d) initial reaction rate
-0.05
0.12
-0.10
0.10
r (mol/s)
dp/dt (kPa/s)
400 t (s)
57.8kPa 88.1kPa 119.6kPa 161.1kPa 215.8kPa 292.6kPa
-0.15 -0.20
0.08 0.06
-0.25
0.04 0
200
400
600
800
1000
40
60
t (s)
80
100 120 140 160 180 200 220 p (kPa)
Fig. 2 e Processing approach of kinetics data by initial rate method (T ¼ 40 C, VL ¼ 70 mL, agitation speed 200 rpm, [I2] ¼ 0.65 mol/L, [HI] ¼ 1 mol/L).
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 2 ( 2 0 1 7 ) 1 4 9 1 6 e1 4 9 2 5
Results and discussion Effect of agitation speed on reaction rate Under the recycling conditions, the Bunsen reaction is a gaseliquid reaction, i.e., SO2 reacts with I2 resolved in HI acid solution. The overall reaction rate will be influenced by both mass transfer and chemical reaction. The effect of mass transfer should be considered to acquire an accurate reaction rate expression. The solution was mixed by agitation to reduce the mass transfer resistance. The effect of agitation speed on pressure drop was investigated with other conditions keeping the same. Variations in pressure and pressure drop rate with time under different agitation speeds were investigated considering similar analysis method introduced in the section “Calculation of initial reaction rate” (Fig. 3). Pressure drop rate is not apparently affected by agitation rate at 100e300 rpm but is apparently faster than that without agitation. Without agitation, the resistance to mass transfer, including gas diffusion and product diffusion, is high. Agitation efficiently decreases the resistance and increases the apparent reaction rate. From the figures it could be seen that the rate is almost the same in the range of 100e300 rpm, while
130
0rpm 100rpm 200rpm 300rpm 400rpm
(a) pressure drop
120
p (kPa)
110 100 90
the absorption rate increases sharply when the agitation speed increased to 400 rpm. It could be observed through the window of the reactor that the gaseliquid interface changed to a large whirlpool from a flat. The formation of the whirlpool dramatically increases the interface, and results in the increasing of the absorption rate. These results further confirm that the gaseliquid contact area is one of the most important factors influencing reaction rate. The agitation speed is set at 200 rpm in the following experiments to ensure that the solution is well mixed and the gaseliquid contact area is stable. In addition, the liquid volume is set at about 70 mL in each experiment.
Effects of SO2 pressure on reaction rate Assuming that the dependence of SO2 pressure on the Bunsen reaction kinetics conforms to the order model, the order of SO2 pressure would be obtained by measuring the reaction rate at different initial pressures of SO2 under fixed temperature, solution composition, and other parameters. To calculate the order of PSO2 with the initial rate method, it is necessary to change the initial PSO2 within a certain range. Considering the fact that SO2 is easily to be liquefied, the cylinder need heating to increase the pressure. However, the temperature could not be too high for safety concern, therefore, we set and controlled the pressure in the range of around 60e220 kPa, which was partially depends on the temperature. According to Eq. (11), the order of SO2 pressure, i.e., the slope of the straight line, would be obtained by plotting the logarithmic curve of the initial rate versus the corresponding initial pressure. As shown in Fig. 4(a), a good linear relationship exists between the logarithm of the initial pressure and the total absorption rate.
80
R2 ¼ 0:99914
ln r ¼ 0:8127 ln p 6:4364;
70
(12)
According to our previous results [26], SO2 can be absorbed by the HI solution without I2. However, assuming that all the
60 50 0
200
400
600
800
1000
1200
1400
t (s) (b) pressure drop rate
(a) total absorption rate in I2 / HI
-2.5
-0.05
ln r
dp/dt (kPa/s)
0.00
-2.0
0rpm 100rpm 200rpm 300rpm 400rpm
-0.10
-3.0 (b) total absorption rate in HI solution
-3.5
(c) Bunsen reaction rate corrected
-0.15
-4.0 -0.20
4.0 0
200
400
600
800
1000
1200
1400
t (s)
Fig. 3 e Variations in pressure and pressure drop rate with time under different agitation speeds (T ¼ 40 C, VL ¼ 70 mL, initial PSO2 ¼ 122 kPa, [I2] ¼ 0.23 mol/L, molar ratio I2/HI ¼ 0.35).
4.2
4.4
4.6
4.8
5.0
5.2
5.4
ln p Fig. 4 e Logarithmic relationship between initial pressure (kPa) and rate (mol/s), (a) total absorption rate in I2/HI, molar ratio I2/HI ¼ 0.69, (b) total absorption rate in HI solution, (c) Bunsen reaction rate corrected (T ¼ 40 C, [HI] ¼ 1 mol/L).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 2 ( 2 0 1 7 ) 1 4 9 1 6 e1 4 9 2 5
absorbed SO2 can react with I2, we did not consider the factor of physical absorption when calculating the order of PSO2 by using the above process, and then the total pressure drop was all attributed to the chemical reaction. A comparative experiment without I2 dissolved in the HI solution was performed to verify the reliability of the method. As shown in Fig. 4(b), the absorption rate of SO2 and SO2 pressure exhibit a good order relationship. ln r ¼ 1:0480 ln p 7:9045;
R2 ¼ 0:99837
(13)
Fig. 5 compares the total absorption rates in HI solution with and without iodine. The total absorption rates in both cases are in the same order of magnitude, so the physical absorption should not be neglected. Therefore, the reaction rate should be corrected by subtracting the physical absorption rate from the total absorption rate. The total absorption rate, which consists of chemical and physical absorption rate and expressed with the decreasing rate of SO2 in gas phase, is calculated by Eq. (7). Because rapid sampling of liquid components under elevated pressures is difficult, the chemical and physical absorption rate cannot be measured directly. The absorption rate without iodine is defined as the physical absorption rate, it is assumed that at the initial time the physical absorption rates under conditions with or without presence of iodine are same, Bunsen reaction rate (chemical absorption rate) is assumed to be the one subtracting the physical absorption rate from the total one. Though physical absorption changes with variation of the composition of the solution during continuous Bunsen reaction, at the initial time the property of the solution does not changed significantly, therefore, the initial effect of difference in physical absorption could be neglected. Fig. 4(c) shows the corrected results, i.e., the logarithmic dependence of the Bunsen reaction rate on the initial pressure, after deduction of the physical absorption rate. A good linear agreement is presented between the logarithmical initial reaction rate and the initial pressure. ln r ¼ 0:2340 ln p 4:9514;
R2 ¼ 0:99247
(14)
Therefore, the partial reaction order of SO2 pressure in the Bunsen reaction is 0.23 ± 0.01. 0.14 I2/HI=0.69 I2/HI=0
r (mol/s)
0.12
14921
In Fig. 4, the line of (c) Bunsen reaction rate corrected dropped quite a lot after physical absorption correction, which suggests that chemical absorption plays a minor role in the process. In our experiments, I2 is dissolved in the HI solution; and the concentration of I2 is not high enough to result in the phase separation. Compared to I2, the amount of water is excessive. Under these conditions, the physical absorption of SO2 may be dominant in the process. Although Bunsen reaction would not occur without I2, physical absorption of SO2 still occurs in the HI solution. Verhoef et al. [27e31] studied the reaction rate of the KarleFischer titration reaction and concluded that the reaction among SO2, I2, and H2O in aqueous solution is a first-order reaction with respect to SO2 and I2. Wang et al. [23] concluded that the Bunsen reaction rate in the presence of toluene is also a first order with respect to SO2 and I2. The Bunsen reaction in the I2/HI system differs from those in the KarleFischer titration system and iodineetoluene system. In the present work, a low order of SO2 pressure was obtained probably because the Bunsen reaction is heterogeneous and the mass transfer efficiency affects the reaction rate. Meanwhile, the mass transfer efficiency may vary with experimental operation conditions; therefore, the total reaction rate will be affected by both mass transfer and the reaction itself. Eqs. (12) and (13) show that SO2 absorption rate in the HI solution conforms to the first-order relationship with pressure; however, the order decreases to approximately 0.8 when iodine was added. This finding indicates that the addition of iodine changes the property of the solution, restricting the absorption of SO2 gas. This phenomenon may be attributed to the presumption that the Bunsen reaction occurs at the gaseliquid interface; the reaction heat released enhances the local temperature and further hinders the absorption of SO2 gas. This finding could be verified by the immediate increase in the temperature when feeding SO2 gas into the reactor. The dependence of temperature on SO2 absorption rate in the HI solution shows that the absorption rate decreases with increasing temperature at the same pressure. The Bunsen reaction is an exothermic reaction and thus hinders the absorption process. The reaction order measured may be subjected to various factors, such as absorption mass transfer, which should be modified under different mass transfer conditions.
Effects of I2 concentration on reaction rate
0.04
The reaction order of [I2] was measured by the initial reaction rate method. The iodine concentration is varied from 0.2 to 0.7 mol/L, solid iodine could be precipitated at higher [I2]. The results are shown in Fig. 6, and the corrected results, i.e., subtracting the physical absorption rate from total rate, are presented for comparison. After correction, a good linear dependence of the logarithmic reaction rate and the iodine concentration could be expressed by Eq. (15) and shown in Fig. 7.
0.02
ln r ¼ 0:7651 lnð½I2 Þ 3:4094;
0.10 0.08 0.06
40
60
80
100 120 140 160 180 200 220 p (kPa)
Fig. 5 e Initial total absorption rate at different corresponding initial pressure levels in cases of iodine incorporation and non-iodination.
R2 ¼ 0:99843
(15)
The slope of the fitting line is the partial reaction order of iodine concentration and has a value of 0.77 ± 0.01. The reaction order of iodine was obtained under fixed SO2 gas pressure and temperature but with different I2 concentrations in the solution. Factors affecting the absorption of SO2 gas were basically controlled at the same level. The
14922
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Effects of temperature on Bunsen reaction rate 0.100
r (mol/s)
0.095 0.090 0.085 0.080 0.075 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
[I2] (mol/L)
Fig. 6 e Initial total absorption rate at different iodine concentrations (T ¼ 40 C, initial PSO2 ¼ 163 kPa, [HI] ¼ 1 mol/L).
To acquire the apparent activation energy of the reaction, reaction rates were measured at the different temperature ranges. Considering the possible volatilization of iodine at higher temperature, a mild temperature ranges between 25 and 50 C was chosen. Reaction rate was corrected with the similar way as previously. Fig. 8 shows the relationship between the initial absorption rate of SO2 in the HI solution and temperature, the initial absorption rate decrease with increasing temperature (Eq. (17)). The total absorption rate also decreases with increasing temperature in the range of 25e50 C when I2 was added into the HI solution. Similarly, Rao et al. [21] found that Bunsen reaction rate decreases with increase in temperature for a fixed operating pressure, however the conclusion should be opposite according to the Arrhenius equation. Actually, the corrected reaction rate increases with temperature by subtracting the physical absorption rate from the total absorption rate. Therefore, the correction of reaction rate is reliable and necessary. ln r ¼ 1:5066E þ 06ð1=TÞ2 8582:83ð1=TÞ þ 9:1841;
-3.6
R2 ¼ 0:99970 -3.8
According to the Arrhenius equation, the relationship between the logarithm of the reaction rate and the reciprocal of temperature should be linear. The regressed relationship is shown in Fig. 9 and could be expressed by Eq. (18).
-4.0
ln r
(17)
ln r ¼ 705:0556ð1=TÞ 1:5636;
-4.2
-4.4
-4.6 -1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
ln([I2])
R2 ¼ 0:99617
(18)
The fitting slope is 705.0556 ± 25.2084, and the activation energy is (705.0556 ± 25.2084) 8.314 J/mol ¼ 5.86 ± 0.21 kJ/mol. According to Eqs. (11) and (18), the pre-exponential factor A could be calculated with a value of 1:36 ðmol=L=sÞ ðmol=LÞ0:23 ðkPaÞ0:77 . Wang et al. [23] and Zhang et al. [20] reported that the activation energy values of the Bunsen reaction in the toluene system are 6.02 and 9.21 kJ/mol, respectively. In the present
Fig. 7 e Logarithmic relationship between the initial Bunsen reaction rate (mol/s) and iodine concentration (mol/L).
-2.65 -2.70
I2 þ I #I 3
(16)
-2.75 ln r
experimental results accurately reflect the influence of iodine concentration on the Bunsen reaction. The reaction order of iodine is slightly less than 1, which is probably due to the chemical equilibrium between I 3 and I2, as shown in Eq. (16). I 3 and I2 can react with SO2, and the reaction constant is changed. Calculation is based on the total iodine concentration, thus the total reaction order measured is slightly lower than 1. The regression line exhibits good linearity, indicating that the effect of the iodine concentration on the reaction rate excellently meets the order relationship under the experimental conditions. The chemical equilibrium between I 3 and I2 can be neglected considering the apparent kinetics. Additional experimental data are needed to delineate the effects of I 3 and I2 to further investigate the mechanism of the reaction.
-2.80 -2.85 -2.90 -2.95 -3.00 0.0030
0.0031
0.0032
0.0033
0.0034
1/T (K-1)
Fig. 8 e Relationship between the initial absorption rate of SO2 and the temperature in the HI solution ([I2] ¼ 0, initial PSO2 ¼ 120 kPa, [HI] ¼ 1 mol/L, unit of r is mol/s).
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Table 2 e Comparison of the kinetic results obtained from two calculation methods.
-3.75
ln r
-3.80
-3.85
-3.90
-3.95 0.0031
0.0032
0.0033
0.0034
1/T (K-1)
Fig. 9 e Relationship between the logarithm of the reaction rate and the reciprocal of temperature ([I2] ¼ 0.65 mol/L, initial PSO2 ¼ 120 kPa, [HI] ¼ 1 mol/L, unit of r is mol/s). work, the activation energy is 5.86 kJ/mol. Although the experimental conditions and operating methods are different, the apparent activation energy values obtained by several methods are all relatively low. This finding indicates the weak effect of temperature on reaction rate.
Method
I2 order
SO2 order
Ea (kJ/mol)
A
Method 1 Method 2
0.77 ± 0.01 0.75 ± 0.01
0.23 ± 0.01 0.24 ± 0.01
5.86 ± 0.21 5.65 ± 0.56
1.36 1.18
As shown in Table 2, the results obtained by multiple regression are consistent with previously reported findings. Compared with the former method, the overall regression method is simpler; as such, all reaction parameters, such as reaction order, activation energy, and pre-exponential factor, can be calculated without plotting. Theoretically, experiment duration can be remarkably reduced under the condition of having an accurate kinetic model. If the dependence of PSO2 or [I2] on the reaction rate does not meet the order relationship but the order could be regressed by this method, the effect would be unclear. However, stepwise regression method may directly reflect the dependence of the kinetics data, including order and activation energy, on the reaction conditions including PSO2 , [I2], and temperature from the plotting curve. The overall regression was performed as verification method considering that the two approaches generate similar results.
Kinetics equation of the Bunsen reaction Regression method for kinetics data Although the apparent kinetic data of the Bunsen reaction could be acquired, the process is complicated. According to Eq. (11), kinetics data, including reaction order, activation energy, and pre-exponential factor, would be regressed by at least four sets of experimental data; thus, we attempted to develop a general method. If this method works, both the experiment and data analysis process would be simplified. Table 1 presents the 14 sets of experiment data. We used Matlab to perform multiple regression, and the calculated kinetics data are listed in the same table. The determination coefficient of the regression model is R2 ¼ 0.99732, and the probability of PROB > F is 1.00697E13. This finding indicates that the regression model is valid. The kinetics data calculated by the two approaches are compared in Table 2.
Based on the above discussion, the kinetics equation of Bunsen reaction could be expressed as follows: n n Ea ½I2 n1 PSO2 2 r0 ¼ k½I2 n1 PSO2 2 ¼ A exp RT
(19)
where n1 and n2 are the reaction order for [I2] and PSO2 , respectively. n1 ¼ 0:77 ± 0:01;
n2 ¼ 0:23 ± 0:01
The apparent activation energy is 5.86 ± 0.21 kJ/mol. The exponential form of Bunsen reaction rate expression was established: 0:23 5861:8 ½I2 0:77 PSO2 r0 ¼ 1:38 exp RT
(20)
Table 1 e Data used for kinetics multivariate regression. T ( C) 40 40 40 40 40 40 40 40 40 40 25 33 40 50
P (kPa)
[I2] (mol/L)
r (mol/s)
1/T (1/K)
ln p
ln[I2]
ln r
57.8 88.1 119.6 161.1 215.8 161.4 163.1 163.5 162.7 161.3 119.9 119.8 119.8 120.1
0.6521 0.6521 0.6521 0.6521 0.6521 0.6521 0.4934 0.3976 0.3022 0.2071 0.6521 0.6521 0.6521 0.6521
0.01809 0.02032 0.02167 0.02345 0.02464 0.02352 0.01961 0.01631 0.01323 0.00987 0.01965 0.02095 0.02207 0.02358
0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003193 0.003357 0.003266 0.003183 0.003102
4.0570 4.4785 4.7842 5.0820 5.3744 5.0841 5.0942 5.0968 5.0916 5.0831 4.7868 4.7861 4.7855 4.7881
0.4276 0.4276 0.4276 0.4276 0.4276 0.4276 0.7065 0.9223 1.1965 1.5748 0.4276 0.4276 0.4276 0.4276
4.0124 3.8960 3.8317 3.7527 3.7036 3.7498 3.9317 4.1159 4.3250 4.6181 3.9296 3.8656 3.8136 3.7474
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Table 3 e Kinetic results of Bunsen reaction from different researchers. Researcher I2 order SO2 order Ea (kJ/mol) A/rate constant Rate expression Absorption consideration Characteristics
Verhoef [29e31]
Wang [23]
Zhang [19,20]
This work
1 1 e Done e e KarleFischer titration reaction, in methanol solvent, trace water
1 1 6.02 Done Done e I2 provided by iodineetoluene solution, heterogeneous
e e 9.21 e Done e SO2 þ solid I2 þ H2O, heterogeneous, phase separation
0.77 0.23 5.86 Done Done Done I2 dissolved in HI solution, homogeneous solution
where r0 is the reaction rate, mol L1 s1; [I2] is the iodine concentration, mol L1; PSO2 is SO2 pressure, kPa; T is the temperature, K; and ideal gas constant R ¼ 8.314 J mol1 K1. The kinetic data of Bunsen reaction from several researchers are compared in Table 3. Compared to other works, a classic physical chemistry method, initial rate method, was used to study the kinetics parameters, and the kinetics equation containing reaction order and activation energy was firstly established, which provides an important theoretical basis for the design of Bunsen reactor as well as optimization of the reaction conditions. As the effects of the several factors, including agitation speed, SO2 pressure, I2 concentration, and reaction temperature, on the reaction rate were explored, it is appropriate to summarize an optimum range of operating conditions for the given reactor setup based on the kinetics equation. As for the agitation speed, from the experiments results, the solution would be mixed well when the agitation speed reaches to 100 rpm and agitation with a value of 100e300 rpm presents a similar mixing effect for the given reactor, and continued increasing of agitation speed would lead to unstable operation, therefore, 100e300 rpm should be a suitable speed range for our reactor. The partial reaction order of SO2 pressure is small (0.23 ± 0.01), indicating that increasing SO2 pressure has limited effect on enhancing the reaction rate. Furthermore, according to our previous study [26], excess SO2 easily lead to side reactions. Therefore, higher SO2 gas pressure is not necessary. The partial reaction order of [I2] is 0.77, meaning that increasing of [I2] can apparently enhance the reaction rate. In addition, excess I2 is thermodynamically favorable for phase separation in real iodineesulfur process. Considering above factors, higher I2 concentration is favorable. The low activation energy indicates that the temperature has minimal effect on reaction rate, so a lower reaction temperature should be chosen for convenient operating. However, the solubility of iodine will decrease and separation characteristics would be deteriorated with lower temperature. These effects should be considered when choosing the reaction temperature. These principles may give some useful guidance for choosing and controlling of the conditions of the Bunsen reaction and separation process.
Conclusions In this work, the apparent kinetics of the Bunsen reaction in HI solution system was studied. The Bunsen reaction rate was
described by correlating the pressure drop with reaction time. The effects of key reaction conditions, including agitation speed, SO2 gas pressure, I2 concentration, and temperature, on kinetics parameters were investigated using initial rate analysis method. The reaction orders for PSO2 and [I2] of the Bunsen reaction are 0.23 ± 0.01 and 0.77 ± 0.01; the apparent activation energy is 5.86 ± 0.21 kJ/mol. Based on these data, the exponential rate expression of the Bunsen reaction was established. Analysis showed that SO2 gas absorption and mass transfer process are the rate-limiting steps in the entire reaction process. The low activation energy of Bunsen reaction indicates that the temperature has minimal effect on reaction rate. These experimental results provide some important guidance for the design of Bunsen reactor and elucidation of the reaction process.
Acknowledgment This work was supported by National Natural Science Foundation of China (Grant No. 21676153).
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