Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution

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 x x x ( 2 0 1 8 ) 1 e9

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Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution Songzhe Chen*, Ping Zhang, Laijun Wang, Jingming Xu Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing 100084, China

article info

abstract

Article history:

In thermochemical water-splitting iodine-sulfur cycle for hydrogen production, basic

Received 30 October 2017

physico-chemical data of HI-H2O-I2 (HIx) solution are very important. Detailed and sys-

Received in revised form

tematic studies on density/coefficient of thermal expansion (CTE) are in great need. In this

5 January 2018

work, the density values of 53 HIx samples with different compositions are measured at

Accepted 7 January 2018

atmospheric pressure and temperatures ranging from 20 to 90
C. HIx solution's density

Available online xxx

varies dramatically when changing HI or I2 contents. Increasing either HI or I2 concentration will cause increase of density. When heated, HIx's density decreases because of

Keywords:

thermal expansion. With the help of density-temperature curves, the CTE values are

HI-I2-H2O solution

calculated for HIx solutions of different compositions. It is found that increase of either I2/

Density

HI or H2O/HI will bring rise of HIx's CTE. Although the CTE value is relatively small, it is very

Coefficient of thermal expansion

sensitive to the change of composition. In the range of this work, the HIx's CTE value

Hydrogen production

changes within 5.45E-4/ºC to 9.17E-4/ºC. Polynomial regression is conducted to model the

Iodine-sulfur cycle

relationship between CTE and the composition. The obtained approximate quadratic polynomial model has good accuracy to reproduce most of the experimental CTE values within a deviation of ±5%. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction

H2SO4 / SO2 þ H2O þ 1/2O2

(2)

As a clean energy carrier, hydrogen and its clean production have attracted great attention [1e3]. The IodineeSulfur thermochemical cycle (IS-cycle) is one of the most promising massive hydrogen producing methods [4e6]. It consists of three main reactions (three sections), i.e. Bunsen reaction (Bunsen section), sulfuric acid decomposition (sulfuric acid section) and hydriodic acid decomposition (HIx section), as described by Eqs. (1)e(3):

2HI / H2 þ I2

(3)

I2 þ SO2 þ 2H2O / 2HI þ H2SO4

(1)

In Bunsen section, two kinds of acids, i.e. sulfuric acid and hydriodic acid are produced. With the existence excess I2, Bunsen reaction products form two phases spontaneously. One phase is aqueous sulfuric acid and the other is so-called HIx, a mixture of hydrogen iodide, iodine and water. In sulfuric acid section, sulfuric acid phase is purified first and then H2SO4 is concentrated and decomposed to produce O2, while other products, SO2 and H2O should be recycled to Bunsen

* Corresponding author. E-mail address: [email protected] (S. Chen). https://doi.org/10.1016/j.ijhydene.2018.01.025 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

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Nomenclature r t V g k p R2 CH2O/HI CI2/HI

density, g/mL temperature, ºC volume of HIx solution, ml volume thermal expansion coefficient (CTE), ºCe1 slope of the r-t curve, g/(ml ºC) significance level of variance analysis, dimensionless correlation coefficient, dimensionless H2O/HI molar ratio, dimensionless I2/HI molar ratio, dimensionless

section. Similarly in HIx section, HIx phase is purified and then HI is concentrated and decomposed to produce H2, with I2 recycled to Bunsen section. Since proposed by General Atomics in mid 1970s, IS-cycle attracted considerable theoretical and experimental research for the process feasibility. Japan Atomic Energy Agency (JAEA) accomplished a demonstration of bench-scale IS process involving glassware at atmospheric pressure in 2004 [7]. Now it is in a process engineering stage in JAEA to use industrial materials for components [8]. Sandia National Laboratories (SNL), General Atomics Corporation (GA) and the French  l'Energie Atomique (CEA) conducted Commissariat a laboratory-scale experiments to investigate IS-process as an International Nuclear Energy Research Initiative (INERI) project supported by the CEA and US DOE Nuclear Hydrogen Initiative [9]. In China, a 10NL-H2/h IS-cycle facility was constructed in 2007 at INET (Institute of Nuclear and New Energy Technology) of Tsinghua University, and the close cycle demonstration were completed in 2009 [10,11]. In 2014, a bench scale IS-cycle facility with hydrogen production rate of 60NL/h was demonstrated at INET [12]. Research on IS-cycle are also very active in Korea. In 2013, a demonstration of electro-dialysis stack embedded HIx section was reported by Korea Institute of Energy Research (KIER) to be accomplished at H2 producing rate of 10 L/h under pressurized conditions [13]. In the year of 2016, the H2 producing rate of above HIx section was increased to the range of 18.3e50 L/h, depending on the operating conditions and HIx feed composition [14]. In spite of the simple principle, IS-cycle is a complicated close process. It is very difficult to realize closed-loop continuous hydrogen production. Recent years, great efforts have been devoted to the kinetics of the three main reactions [15e19], catalyst development [20e22], flowsheet/modelling studies [23], performance assessment [24], and so on. By now, one of the challenges is that lots of separating units such as gas separator, liquid-liquid phase separator, distillation column and electrodialysis cell etc. are required for the streams in the process. The streams are especially complex in the HIx section [25]. Basic physico-chemical data of HI-I2-H2O solution (HIx) in the HIx section are found to be very important, though this solution involves mainly three components, i.e., HI, I2, and H2O. These three substances make up a highly non-ideal system. In our previous work, thermodynamic properties of

HIx are estimated and applied in the process simulation & design [26]. Density data, together with coefficient of thermal expansion (CTE) of HIx, are not only necessary for CFD, and also found to be very useful in the case where volume of the solution must be appointed. For example, volume flow rates must be calculated using density data, when setting a diaphragm pump to transport HIx. Additionally, the design and arrangement of HIx's containers such as tanks, pipes are in great need of CTE data. Because of the high corrosiveness of HIx solution, coated or lined materials are often used in the containers. For the selection of all above materials, including structure materials, coating or lining layers, the CTE data are necessary. Like other physico-chemical data, density data have further uses. Kubo et al. [27] proposed a novel estimation technique for compositions of Bunsen reaction solutions in IS cycle, using the density values measured from the diphase equilibrium reaction products as inputs, including the density of HI-I2-H2O phase (containing a small amount of H2SO4). In our previous research [28], density data coupled with voltage signals were used for the composition determination of HIx solution, applying Gibbs phase rule. As mentioned above, density and CTE are of great importance for the IS-cycle research and operation. Unfortunately, to the best of our knowledge, there is no detailed and systematic report on density and CTE data for HIx solutions. Furthermore, there are especially no related data reported for hyper-azeotropic HIx solutions shown in documents. This study is aiming at establishing a density/CTE databank of HIx solutions. HIx samples of different compositions are prepared in this work. With the help of electro-electrodialysis (EED) technique [29,30], hyper-azeotropic HIx samples, i.e. HI-I2-H2O solutions with HI concentration higher than that in the azeotropic HI-H2O solution, are also secured. Density values of the samples are measured using an oscillating U-tube density meter at atmospheric pressure and temperatures ranging from 20 to 90
C. Consequently, the CTE values are calculated. The relationship among density/CTE, composition and temperature of HIx solution is discussed.

Experimental Chemicals Hypo-azeotropic hydriodic acid (~56 wt%) and iodine (>99.9 wt %) were purchased from Beijing Leadersh Chemical Co. Ltd. Analytical pure Sodium thiosulfate, sodium hydroxide and potassium iodide (all from Guangdong Xilong Chemical Co. Ltd.) are used as received for titration methods to analyze the HI and I2 contents in certain HI-I2-H2O solutions.

Preparation and density measurement of the HI-I2-H2O solutions Azeotropic hydriodic acid is prepared in lab by distillation of above commercial hypo-azeotropic hydriodic acid. This azeotropic hydriodic acid (HI-H2O) is titrated to determine the composition at the molar ratio HI: H2O ¼ 1:5.360. Consequently, a series of HIx, i.e. HI-I2-H2O solutions of certain

Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

No. 1

2

3

4

5

6

HI:I2: H2O 1: 0: 5.360

1: 0: 5.690

1: 0: 6.485

1: 0: 7.484

1: 0: 8.982

1: 0: 10.479

t/ºC

r/(g/ml)

20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60

1.6999 1.6904 1.6809 1.6715 1.6622 1.6529 1.6436 1.6343 1.6744 1.6651 1.6558 1.6466 1.6374 1.6282 1.6191 1.6099 1.6053 1.5964 1.5877 1.5789 1.5701 1.5614 1.5526 1.5437 1.5400 1.5318 1.5234 1.5153 1.5069 1.4985 1.4901 1.4815 1.4645 1.4571 1.4495 1.4418 1.4339 1.4260 1.4179 1.4097 1.4078 1.4009 1.3938 1.3865 1.3791

No

11

12

13

14

15

16

HI:I2: H2O

1: 0.506: 4.337

1: 0.500: 5.360

1: 0.500: 6.490

1: 0.500: 7.489

1: 0.500: 9.036

1: 0.501: 10.501

t/ºC

r/(g/ml)

80 90 15 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 25 30

2.1857 2.1718 2.3412 2.3349 2.3196 2.3046 2.2899 2.2753 2.2610 2.2467 2.2325 2.1714 2.1591 2.1460 2.1321 2.1174 2.1042 2.0906 2.0766 2.0913 2.0774 2.0639 2.0505 2.0373 2.0240 2.0107 1.9975 1.9416 1.9301 1.9177 1.9054 1.8927 1.8799 1.8667 1.8527 1.8286 1.8174 1.8062 1.7947 1.7834 1.7719 1.7603 1.7486 1.7370 1.7320

No.

21

22

23

24

25

26

HI:I2: H2O

1: 1.000: 9.000

1: 1.000: 10.485

1: 1.002: 11.977

1: 1.496: 4.337

1: 1.498: 4.724

1: 1.503: 5.360

t/ºC

r/(g/ml)

80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 30 40 50 60 70 80 90 30 40 50 60 70 80 90 20 30 40 50 60

2.1611 2.1457 2.1113 2.0970 2.0820 2.0680 2.0530 2.0390 2.0240 2.0090 2.0071 1.9938 1.9803 1.9667 1.9529 1.9390 1.9251 1.9110 1.9846 1.9714 1.9580 1.9445 1.9308 1.9172 1.9032 1.8891 2.8866 2.8671 2.8478 2.8288 2.8101 2.7916 2.7731 2.8233 2.8038 2.7847 2.7659 2.7472 2.7288 2.7106 2.7289 2.7095 2.6903 2.6715 2.6529

No.

HI:I2: H2O

32

1: 1.999: 5.360

33

1: 1.999: 5.491

34

1: 2.006:6.489

35

1: 2.008: 6.671

36

1: 2.001: 7.484

37

1: 2.026: 9.188

38

1: 2.499: 4.337

39

1: 2.496: 4.724

40

1: 2.539: 5.360

t/ºC

r/(g/ml)

80 90 40 50 60 70 80 90 40 50 60 70 80 90 40 50 60 70 80 90 50 60 70 80 90 40 50 60 70 80 90 50 60 70 80 90 60 70 80 90 60 70 80 90 50

2.0300 2.0142 2.8816 2.8614 2.8415 2.8218 2.8023 2.7831 2.8603 2.8401 2.8202 2.8005 2.7810 2.7619 2.7727 2.7526 2.7327 2.7130 2.6934 2.6743 2.7006 2.6811 2.6617 2.6424 2.6233 2.6097 2.5904 2.5710 2.5518 2.5329 2.5143 2.4851 2.4678 2.4504 2.4331 2.4150 3.1193 3.0988 3.0785 3.0582 3.0684 3.0479 3.0275 3.0073 3.0270

3

(continued on next page)

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Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

Table 1 e Density values of the HI-H2O-I2 solution samples at different temperatures.

4

No.

7

8

9

10

HI:I2: H2O

1: 0: 11.977

1: 0.093: 4.337

1: 0.280: 4.724

1: 0.503: 4.724

t/ºC

r/(g/ml)

70 80 90 20 30 40 50 60 70 80 90 15 20 30 40 50 60 70 80 90 15 20 30 40 50 60 70 80 90 15 20 30 40 50 60 70

1.3714 1.3636 1.3556 1.3635 1.3570 1.3503 1.3434 1.3362 1.3288 1.3212 1.3134 1.9326 1.9270 1.9155 1.9043 1.8932 1.8822 1.8714 1.8605 1.8499 2.0808 2.0743 2.0614 2.0486 2.0360 2.0235 2.0112 1.9990 1.9869 2.2779 2.2720 2.2571 2.2424 2.2279 2.2137 2.1996

No

17

18

19

20

HI:I2: H2O

1: 0.500: 11.978

1: 1.004: 5.360

1: 1.001: 5.501

1: 1.000: 7.486

t/ºC

r/(g/ml)

40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 25 30 40 50 60 70 80 90 20 30 40 50 60 70

1.7210 1.7100 1.7000 1.6880 1.6770 1.6660 1.6704 1.6608 1.6510 1.6408 1.6305 1.6201 1.6094 1.5986 2.5117 2.4942 2.4769 2.4599 2.4431 2.4265 2.4106 2.3941 2.4800 2.4710 2.4540 2.4370 2.4200 2.4040 2.3870 2.3710 2.2534 2.2377 2.2221 2.2068 2.1917 2.1765

No.

27

28

29

30

31

HI:I2: H2O

1: 1.503: 5.491

1: 1.503: 6.485

1: 1.500: 7.488

1: 1.505: 10.492

1: 1.500: 11.979

t/ºC

r/(g/ml)

70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 50 60 70 80 90 40 50 60 70

2.6346 2.6164 2.5981 2.7280 2.7086 2.6894 2.6707 2.6520 2.6337 2.6155 2.5975 2.6166 2.5975 2.5786 2.5600 2.5416 2.5235 2.5054 2.4877 2.4862 2.4680 2.4498 2.4321 2.4143 2.3963 2.3781 2.3574 2.1750 2.1590 2.1430 2.1270 2.1100 2.0923 2.0772 2.0619 2.0464

No.

HI:I2: H2O

41

1: 2.534: 6.660

42

1: 2.527: 7.672

43

1: 2.527: 9.177

44

1: 2.527: 10.739

45

1: 3.039: 5.360

46

1: 3.032: 7.722

47

1: 3.032: 9.178

48

1: 3.539: 5.360

49

1: 3.539: 6.651

50 51 52

1: 3.540: 7.662 1: 3.545: 10.702 1: 4.044: 5.360

53

1: 4.052: 6.651

t/ºC

r/(g/ml)

60 70 80 90 60 70 80 90 60 70 80 90 70 80 90 75 80 90 70 80 90 70 80 90 80 90 80 90 80 90 90 90 80 90 80 90

3.0058 2.9800 2.9574 2.9355 2.8220 2.7992 2.7705 2.7545 2.7180 2.6904 2.6697 2.6494 2.5172 2.4959 2.4727 2.3770 2.3676 2.3450 3.0705 3.0434 3.0231 2.8179 2.7983 2.7754 2.6665 2.6451 3.1385 3.1136 2.9983 2.9742 2.8935 2.6554 3.2015 3.1755 3.0673 3.0417

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Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

Table 1 e (continued )

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 x x x ( 2 0 1 8 ) 1 e9

5

3.4 3.2

No.1 HI: I2: H2O=1: 0: 5.360 No.3 HI: I2: H2O=1: 0: 6.485

3.0

No.5 HI: I2: H2O=1: 0: 8.982 No.7 HI: I2: H2O=1: 0: 11.977

Density / (g/mL)

2.8

No.11 HI: I2: H2O=1: 0.506: 4.337 No.14 HI: I2: H2O=1: 0.500: 7.489

2.6

No.24 HI: I2: H2O=1: 1.496: 4.337 No.26 HI: I2: H2O=1: 1.503: 5.360

2.4

No.28 HI: I2: H2O=1: 1.503: 6.485

2.2

No.37 HI: I2: H2O=1: 2.026: 9.188

2.0

No.40 HI: I2: H2O=1: 2.539: 5.360

No.31 HI: I2: H2O=1: 1.500: 11.979 No.38 HI: I2: H2O=1: 2.499: 4.337 No.41 HI: I2: H2O=1: 2.534: 6.660 No.43 HI: I2: H2O=1: 2.527: 9.177

1.8

No.48 HI: I2: H2O=1: 3.539: 5.360 No.49 HI: I2: H2O=1: 3.539: 6.651

1.6

No.52 HI: I2: H2O=1: 4.044: 5.360 No.53 HI: I2: H2O=1: 4.052: 6.651

1.4 1.2

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

t/ C O

Fig. 1 e Density variation of HI-H2O-I2 solution with the changing composition and temperature.

compositions are prepared, starting with above azeotropic hydriodic acid by adding iodine and deionized water. The composition of the obtained HIx solutions could be calculated easily based on the masses of the starting materials, namely, azeotropic hydriodic acid, iodine and water. The HIx solutions with HI concentration above the azeotropic equilibrium of HI-H2O, in other words, the hyperazeotropic HIx solutions are obtained by the means of electro-membrane separation technique, termed electroelectrodialysis (EED) [29]. The composition of hyperazeotropic HI-I2-H2O solutions is determined by titration methods. In this research, totally 53 HIx solutions are prepared. The HI/H2O molar ratio of these solutions ranged from 1:4.337 to 1:11.979, while the HI/I2 molar ratio from 1:0 to 1:4.052. Because of the I2 solubility's strong dependence on both I content and temperature, the precipitation of solid I2 is carefully monitored during the HIx solution preparation. The high I2 content HIx solutions are prepared and kept in glass vessels in a temperature-controlled water bath before sampling, ensuring all the samples are of homogenous HIx-H2O-I2 solution. Samples are taken from every HIx solution and the densities are measured using an oscillating U-tube density meter, DMA 4100 M (Anton Paar, Austria), at the temperature ranging from 20 to 90
C at atmospheric pressure. Each time 1 mL of a HIx solution is tested and the measurements are repeated three times to ensure reproducibility. The density meter is equipped with high-resolution built-in temperature controller. Once the temperature reaches the preset point, the density meter will collect the oscillating frequency signals of the quartz U-tube filled with a certain HIx solution, detecting the sample's density with high accuracy. After careful calibration, DMA 4100 M gives the standard uncertainty of the

temperature 0.01 K, and the standard uncertainty of the density 0.0001 g cm3. Polynomial regression is performed to obtain the mathematic model for the data, and the suitability of the fitted model is evaluated by the coefficient of determination (R2), the level of significance (p), and residual analysis. The polynomial regression and model evaluation are carried out using the statistical software package Data Processing System (DPS, version 12.01, Hangzhou Ruifeng Information Technology Co., Ltd.) [31].

Results and discussions Density measurements The experimental density data are listed in Table 1. Totally, there are 53 HIx samples listed in this table, where density values of every sample are listed together according to the order from low to high testing temperature. Moreover, samples with high I2/HI molar ratios are listed behind those with no I2 or low I2/HI molar ratios. In general, HI-H2O-I2 solution's density is influenced by both temperature and composition. To illustrate the effects of temperature and composition, the density-temperature data of 19 samples are selected to draw Fig. 1, by plotting linear graphs in the coordinate of density-temperature. As seen in Fig. 1, temperature's effect on density is relatively limited comparing to that of composition, but it is obvious that when the solution is heated, HIx's density decreases because of thermal expansion, i.e. the increased thermal energy of the molecules leads to the expansion of intermolecular distances. As for the composition, HI-H2O-I2 solution's density varies dramatically when changing HI or I2 contents. When I2/HI molar ratio ðCI2 =HI Þ fixed, increasing of H2O/HI ratio ðCH2 O=HI Þ

Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

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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 x x x ( 2 0 1 8 ) 1 e9

decreases the density; while when CH2 O=HI fixed, increasing CI2 =HI leads to the increase of density. In other words, increasing of either HI or I2 content will cause increase of density. Density data at 90
C of all the 53 samples are collected to draw Fig. 2, using 3D scatter plots in a r  CI2 =HI  CH2 O=HI 3D coordinate space to give much more intuitionistic illustration for above mentioned density-composition relationship. In the figures, sample sequence numbers are used as symbols of the corresponding data points, and the projections of data points on the plane of CH2 O=HI  CI2 =HI (bottom plane of the coordinate space) are also shown. Fig. 2(a) is an isometric view plot, while Fig. 2(b) is a “rotated version” of Fig. 2(a) by rotating the former to a certain angle of view. With the help of Fig. 2(b), it is easy to find out that the density data points actually fall in a three-dimension curved surface. Above result suggests the nonlinear relationship among density, H2O/HI ratio, and H2O/HI ratio.

8.0

H2O: HI

6.0

1.0 4.0

1.5

Density / (g/mL)

2.0

1.0 4.0

I

3.0

:H

10.0

2.5

2

12.0

2.0

3.0

I

52 53 48 49 a 50 45 51 38 4039 47 46 41 42 32 43 34 33 44 35 36 37 2524 26 28 27 29 31 30 18 19 20 23 22 21 1011 13 12 14 17 16 15 9 8 7 6 5 4 3 21

0.0

b

2.5

2.0

H2O : HI

12.0 10.0

Density / (g/mL)

3.0

1.5

8.0 6.0 4.0

0.0

1.0

2.0

3.0

1.0 4.0

I2 : HI Fig. 2 e Relationship among CTE, I2/HI and H2O/HI ratios in HI-H2O-I2 solution at 90
C (a): isometric view plot; (b): rotated drawing of Fig. 2(a).

Calculation of the thermal expansion coefficient According to the definition, coefficient of thermal expansion (i.e., volume CTE) of HIx could be calculated by Eq. (4). g¼

1 dV V dt

(4)

where g represents CTE, V is the volume of the solution, and dV/dt is the volume changing rate with temperature. In the case of this study, g of HIx solution with certain composition could be suggested as a constant in the temperature range from room temperature to 90
C. Thus, Eq. (4) could be transferred to Eq. (5). g ¼ ðV2  V1 Þ=ðDt$V1 Þ

(5)

Based on Eq. (5), Eq. (6) is easy to be deduced. r  r1 k ¼ g¼ 2 r2 Dt$r2

(6)

where k ¼ (r2 e r1 )/Dt, namely, the slope of the respective r-t curve. Limited by the space, data points of the 53 samples could not be all drawn in Fig. 1. While for most of the samples (except sample No. 47e53, which have less than 2 temperature points), their r-t curves are fitted using linear regression. The slopes (k) of the curves and the respective correlation coefficients (R2) of the regression process are listed in Table 2. Except that of sample No. 41, all of the R2 values are larger than 0.99, suggesting good quality of the linear regression. Adopting the density values measured at 90
C as r2 for the respective samples, and using obtained k values listed in Table 2, thermal expansion coefficients of the samples are calculated using Eq. (6). The resulted g values are also listed in Table 2 (except samples No.52 and 53, which have only one densitytemperature point). The data points are drawn in the g  CI2 =HI  CH2 O=HI 3D coordinate space, as shown in Fig. 3. CTE of HIx is influenced significantly by the composition. Increase of either CI2 =HI or CH2 O=HI will bring rise of CTE. Generally speaking, the values of HIx's CTE are relatively small, though they vary by a large margin with the change of composition. In the range of this work's experimental conditions, sample No. 44 has the largest CTE, 9.17E-4/ºC, while sample No. 7 has the smallest, 5.45 E-4/ºC.

Modelling of CTE-composition relationship Basing on the above discussion and obtained data, polynomial regression is conducted to develop an approximate quadratic polynomial model, expressing the CTE-composition relationship, using CTE (g, with ºC1 as unit) as dependent variable, and H2O/HI molar ratio, I2/HI molar ratio (CH2 O=HI and CI2 =HI , respectively) as independent variables. The obtained equation is as follows: g% ¼ 0:05759 þ 0:00344CI2 =HI þ 0:0008086CH2 O=HI  0:001217CI2 =HI 2  0:00008161CH2 O=HI 2 þ 0:001102CI2 =HI CH2 O=HI

(7)

This equation's p value, i.e., significance level of variance analysis (F test) is 1.000E-7, and the correlation coefficient R2 is

Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

7

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 x x x ( 2 0 1 8 ) 1 e9

Table 2 e Slopes(k) of the r-t curves and the calculated CTE values of HI-H2O-I2 samples.

1.0000 1.0000 1.0000 1.0000 0.9997 0.9994 0.9990 0.9999 0.9999 0.9999 0.9999 0.9997 1.0000 0.9994 1.0000 0.9998 0.9996 0.9998 0.9999 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9999 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 1.0000 0.9999 0.9999 1.0000 1.0000 0.9992 0.9893 0.9939 0.9993 0.9981 0.9932 0.9980 e e e e e e e

41

0.8745. Fig. 4 is drawn to illustrate the reproducing accuracy of above model. In this figure, HIx samples' CTE values calculated with Eq. (7) are compared with the experimental values, i.e., the CTE values acquired through r-t curves. A red line and a blue line are drawn in Fig. 4, illustrating the borders of 5% and þ5% deviations respectively. According to Fig. 4, most

31

47 53 49 29 52 22 214036 4846 28 35 45 37 20 34 16 17 27 15 26 19 14 0.070 18 33 13 32 12 2425 7 1110 6 9 5 3839 0.060 8 2 3 4 1

0.080

0.0573 0.0572 0.0569 0.0563 0.0556 0.0550 0.0545 0.0597 0.0631 0.0657 0.0654 0.0657 0.0669 0.0684 0.0654 0.0657 0.0642 0.0701 0.0707 0.0715 0.0726 0.0719 0.0722 0.0682 0.0692 0.0718 0.0717 0.0740 0.0772 0.0768 0.0777 0.0708 0.0713 0.0736 0.0737 0.0760 0.0725 0.0666 0.0677 0.0788 0.0839 0.0855 0.0896 0.0917 0.0784 0.0766 0.0809 0.0800 0.0810 e e 0.0819 0.0842

42 30 23

12.0 0.0

10.0

1.0

8.0

2.0 3.0

I : 2 HI

6.0 4.0

:H I

0.9363 0.9208 0.8785 0.8346 0.7833 0.7458 0.7160 1.104 1.253 1.426 1.459 1.365 1.337 1.268 1.143 1.095 1.027 1.678 1.676 1.534 1.458 1.374 1.364 1.890 1.877 1.865 1.863 1.841 1.821 1.620 1.565 1.970 1.969 1.969 1.933 1.911 1.750 2.036 2.037 2.314 2.312 2.265 2.215 2.151 2.370 2.125 2.140 2.490 2.410 e e 2.600 2.560

g %/ºC

H 2O

0: 5.360 0: 5.690 0: 6.485 0: 7.484 0: 8.982 0: 10.479 0: 11.977 0.093: 4.337 0.280: 4.724 0.503: 4.724 0.506: 4.337 0.500: 5.360 0.500: 6.490 0.500: 7.489 0.500: 9.036 0.501: 10.501 0.500: 11.978 1.004: 5.360 1.001: 5.501 1.000: 7.486 1.000: 9.000 1.000: 10.485 1.002: 11.977 1.496: 4.337 1.498: 4.724 1.503: 5.360 1.503: 5.491 1.503: 6.485 1.500: 7.488 1.505: 10.492 1.500: 11.979 1.999: 5.360 1.999: 5.491 2.006:6.489 2.008: 6.671 2.001: 7.484 2.026: 9.188 2.499: 4.337 2.496: 4.724 2.539: 5.360 2.534: 6.660 2.527: 7.672 2.527: 9.177 2.527: 10.739 3.039: 5.360 3.032: 7.722 3.032: 9.178 3.539: 5.360 3.539: 6.651 3.540: 7.662 3.545: 10.702 4.044: 5.360 4.052: 6.651

R2

o γ%/ C

1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1: 1:

k*(-103)/ (g/ (ml$ºC))

4.0

Fig. 3 e Variation of CTE with the change of I2/HI and H2O/ HI ratios in HI-H2O-I2 solution.

0.0900

y=x y=0.95x y=1.05x

47 46 37

0.0800 39 38

0.0700

o

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

HI: I2: H2O

γ %/ C (Fitted Value)

Sample No.

44 43

0.090

0.0600

0.0500 0.0500

0.0600

0.0700

0.0800

0.0900

o

γ % / C (Experimental Value) Fig. 4 e Comparison of experimental values and fitted values of CTE.

sample points drop in the region between the blue line and red line, except 5 samples, namely. 37, 38, 39, 46 and 47. Therefore, it could be concluded that Eq. (7) is able to reproduce most of the experimental CTE values within the deviation of ±5%.

Conclusions Aiming at establishing density/CTE databank for HI-I2-H2O solutions, i.e. HIx, a detailed and systematic study is conducted. Density values of HIx solutions with different compositions are measured, including hyper-azeotropic HIx samples, at atmospheric pressure and temperatures ranging from 20 to 90
C. The relationship among density, composition and temperature of HIx solution is discussed. Based on the

Please cite this article in press as: Chen S, et al., Experimental density-composition data and thermal expansion coefficient of HI-I2-H2O solution, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.01.025

8

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 x x x ( 2 0 1 8 ) 1 e9

density values at different temperatures, the CTE values are calculated. Polynomial regression is conducted to model the relationship between HIx's CTE and composition. This work is valuable for IS-cycle research and development, especially in the flowsheet design, CFD, pump setting, equipment or pipe material selection, and so on. The results and conclusions of this work are summarized as follows: 1) HI-H2O-I2 solution's density varies dramatically when changing HI or I2 contents, increasing of either HI or I2 content will cause increase of density. At a certain temperature, density-composition data points fall in a threedimension curved surface in the r  CI2 =HI  CH2 O=HI coordinate space, suggesting the nonlinear relationship among density, CI2 =HI and CH2 O=HI . 2) When heated, HIx's density decreases because of thermal expansion. With the help of r-t curves, the CTE values are calculated for HIx solutions with different compositions. Although the CTE values are relatively small, they vary sensitively with the change of composition. In the range of this work, the HIx's CTE value changes within 5.45 E-4/ºC to 9.17E-4/ºC. It is found that increase of either CI2 =HI or CH2 O=HI will bring rise of CTE. 3) As a result of polynomial regression, an approximate quadratic polynomial model for the g  CI2 =HI  CH2 O=HI relationship is secured, which could reproduce most of the experimental CTE values within a deviation of ±5%.

Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant no. 21376133 and 21676153), and Program for Changjiang Scholars and Innovative Research Team in University (IRT13026). This work was also conducted under the framework of Chinese National S&T Major Projects (Grant Nos. 2017ZX06901-027 and 2018ZX06901-029).

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