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Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K
Accepted Manuscript Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K Naruki Fukushima, Satoshi Shiratori, Takeshi Makiya, Takashi Murakami, Ryo Ohmura PII: DOI: Reference:
S0021-9614(17)30268-9 http://dx.doi.org/10.1016/j.jct.2017.07.036 YJCHT 5154
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
14 December 2016 26 July 2017 27 July 2017
Please cite this article as: N. Fukushima, S. Shiratori, T. Makiya, T. Murakami, R. Ohmura, Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K, J. Chem. Thermodynamics (2017), doi: http://dx.doi.org/10.1016/j.jct. 2017.07.036
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Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K
Naruki Fukushimaa, Satoshi Shiratoria, Takeshi Makiyaa, Takashi Murakamia, Ryo Ohmura*a. a
Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku,
Yokohama 223-8522, Japan Tel: +81-45-556-1813 E-mail: [email protected]
Abstract The phase equilibrium conditions in the (propan-2-ol + carbon dioxide + water) system were measured. The measurements were performed using the batch, isochoric method at the temperatures between 250.8 K and 265.7 K. The equilibrium pressures were measured between 0.275 MPa and 0.995 MPa, and increased with increasing temperatures. Propan-2-ol is known as thermodynamic inhibitor for hydrate formation. However at the temperatures below 262 K, the equilibrium pressures in the (propan-2-ol + carbon dioxide + water) system are lower than those without propan-2-ol (carbon dioxide + water system). The measurements indicate the formation of the hydrates containing propan-2-ol and carbon dioxide in this system.
Keywords Phase equilibria, Clathrate hydrate, Propan-2-ol, carbon dioxide, Alcohol hydrate
1. Introduction 1
Clathrate hydrates are crystalline compounds trapping molecules in their cages. Water molecules are constituent part of the hydrate cages, shaping the cavities with hydrogen bonding. There are three main types of structure among hydrates: structure I, structure II, structure H, represented as sI, sII, and sH respectively. Applying their notable characteristics such as high gas storage, selectivity of trapped gases, large heat involved in formation and dissociation of hydrates, a variety of industrial technology has been proposed. Hydrate-based refrigeration system has been developed for residential air-conditioning use [1].
Application of CO2
hydrate as a refreshing cold dessert is an emerging, unique idea [2-6].
Theoretical
performance of hydrate-based heat engine was evaluated for using ocean thermal energy [7]. Capturing a compound from gaseous mixture in the form of hydrate is also one of the major examples of hydrate-based technologies [8, 9]. Alcohols have been known for changing hydrate forming condition to higher pressure and lower temperature, inhibiting hydrates from forming [10]. On the other hand, hydrate containing alcohols in their cages, alcohol hydrate, has also been reported [11]. Various alcohols such as ethanol [12-14], propan-1-ol [15-17] and propan-2-ol [18-20] with help gases have also been shown to exist recently.
Among alcohols, our interest in this study is
propan-2-ol. The systems involving propan-2-ol have been proven to be abstruse. Takeya et al. reported the existence of transitional form of CH4 + propan-2-ol hydrate at low temperatures [21].
Interestingly, the double alcohol hydrate transformed from cubic structure II to
tetragonal form with asymmetry at about 110 K. In the (fluoromethane + propan-2-ol + H2O) system, the characterization of the hydrate was not completed due to unknown peaks in the PXRD pattern [22]. These mysterious phenomena involving propan-2-ol can be attributed to an intricate interaction between propan-2-ol molecules and water molecules. Alavi et al. found strong hydrogen bonding induced by alcohol is greatly related to stabilization of hydrate 2
cage [23]. For further understanding of guest-host interaction of hydrate crystal, propan-2-ol is an intriguing compound. In this study, we performed phase equilibrium measurements for a system, (propan-2-ol + CO2 + H2O). Similar study was previously conducted by Lee et al., reporting the phase equilibrium data for 272.5 K to 282.2 K at different concentrations [24]. However, no measurement has been conducted for low temperature range below freezing point of water. This study might establish more accurate interpretation of the interaction between guest compounds including alcohol and water molecules, the mysterious structure change of hydrate containing propan-2-ol.
2. Experimental method 2.1. Materials The materials in this study are liquid reagent of propan-2-ol (0.999 mass fraction, Sigma-Aldrich Co., U.S.A.), CO2 gas (0.99995 volume fraction, Japan Fine Products Co., Japan) and water. The water was deionized and distilled (WG222, Yamato Scientific Co., Japan) in our laboratory. The specification of the materials used in this study is summarized in Table 1.
Table 1. Specifications of the compounds in this study. Sample name
Chemical Formula
Supplier
propan-2-ol
C3H7OH
Sigma-Aldrich Co. LLC.
Purity 0.999 mass fraction is certificated 0.99995 volume fraction
Carbon dioxide
CO2
Japan Fine Products Co. is certificated 3
Deionized and
Electrical conductivity H2O
Laboratory made
distilled water
was less than 0.1 µS/cm
2.2. Apparatus The overall configuration of experimental apparatus is shown in Figure 1. The stainless steel vessel is immersed in a temperature controlled bath. A platinum resistance thermometer (Ichimura Metal Co., Japan) and a strain-gauge pressure transducer (PAB-A-500KP, PG-10KU and PH-20KB, Kyowa Electronic Instruments Co., Japan) are inserted inside the vessel, measuring the temperature and pressure in the system. The expanded uncertainty of temperature measurement, U(T), is 0.1 K with a coverage factor of k = 2 and those for pressure measurement, U(P), was estimated to be 0.010 MPa. More details of the expanded uncertainty of pressure measurement would be shown in section 3 Results and Discussion.
Figure 1. Schematic of the experimental apparatus. 2.3. Phase equilibrium measurements Isochoric procedure [25] was employed for measuring the phase equilibrium conditions in (propan-2-ol + CO2 + H2O) system. Before starting experimental runs, 30.0 g of ground ice powder and 5.9 g of liquid propan-2-ol were supplied into the reactor. The approximate diameter of ice powder was 1 mm and was made from laboratory-made water mentioned in 4
Materials section. The molar ratio of H2O (ice) to propan-2-ol was 17:1, stoichiometric composition of propan-2-ol assuming the propan-2-ol molecules occupying all large cages in sII hydrate. The experimental run begins with removal of the air in the vessel by vacuum pump and pressurization with CO2 gas. Initial pressure-temperature condition was set free from hydrate formation in each experimental run. After lowering the temperature, sharp pressure drop was observed due to formation of hydrate, trapping the gas inside the cavities. The pressure decrease in the hydrate forming process was typically very rapid. For example, the pressure drastically decreased from 0.449 MPa to 0.431 MPa at 255.8 K as shown in Figure 2. Then the temperature was repeatedly increased by 0.1 K.
Here, the pressure increase
occurred mainly because of the hydrate dissociation. In each temperature increment step, we kept T in the reactor constant for 6 h to 24 h to ensure the establishment of the steady state. After the pressure increase became subtle due to the complete dissociation of hydrate, the phase equilibrium condition was determined at the point just before the P-T slope changed because it is the most reliable condition where a small amount of hydrate was left in the vessel. The trajectory of pressure and temperature data in an experimental run is shown in Figure 2. This sequential stepwise temperature increase process was repeated for different initial conditions to obtain the four-phase/three-phase equilibrium data between 250.8 K and 265.7 K.
5
Figure2. Pressure and temperature values obtained during the isochoric procedure.
:
initial condition; □: unsteady conditions recorded during lowering temperature and pressure drop; ○: conditions recorded during temperature increase; ●: the phase equilibrium point determined in temperature-increase steps.
2.4. Sample preparation To confirm the hydrate formation at P, T conditions measured in the present study, solid sample was prepared. The experimental equipment, materials and chemical composition in the vessel were the same as described in Apparatus and Procedure sections. After removing the air, the initial condition in the vessel was set at 255.2 K and 0.56 MPa by pressurization of CO2 gas. As pressure stabilized around the phase equilibrium condition, 0.42 MPa, CO2 gas was refilled again up to 0.55 MPa (the condition where CO2 simple hydrate does not form.). The same way of pressurization was repeated until no more pressure drop was observed. The vessel was dismantled at 241.2 K after it was moved to a low temperature room cooled at 6
239.2 K and we confirmed dry mass of ice-like solid in the vessel. The portion of the solid was put in water to observe the dissociation of the solid.
3. Results and discussion The solid sample synthesized as described in the section “2.4. Sample preparation” was dissociated in water. The bubble formation was observed on the surface of the dissociating solid particles. The characteristic odour of propan-2-ol was also confirmed upon the dissociation. Because the solid sample was apparently dry and not wet, liquid propan-2-ol was likely to be converted to the hydrate that encapsulates the alcohol molecules. The phase equilibrium data measured in (propan-2-ol + CO2 + H2O) system at the temperatures between 250.8 K and 265.7 K are shown in Table 2 and Figure 3. The expanded uncertainty U(P) with coverage factor of k = 2 in this study was estimated to be 0.010 MPa from the deviations of the equilibrium pressures obtained in the two different duplicated measurements at 252.6 K and 255.8 K indicated in Table 2. In addition to the plots obtained in the present measurements, the phase equilibrium data in the (CO2 + H2O) system [26, 27] are also plotted for comparison in Figure 3. The phase equilibrium pressures in the (propan-2-ol + CO2 + H2O) system were higher than those (in CO2 + H2O) system. This indicates that the hydrate formation was inhibited above 264 K. The hydrate equilibrium conditions in the system at lower temperature and higher pressure than those in the (CO2 + H2O) system is ascribed to the dissolved propan-2-ol in water. Dissolution of propan-2-ol in water decreases the chemical potential of water in the aqueous phase. Therefore, the equilibrium temperature in the system is lower than that in the simple CO2 hydrate forming system, which is the phenomenon similar to the freezing point depression in water. The estimated phases in equilibrium above 264 K are propan-2-ol aqueous {liquid (L) + CO2-rich vapour (V) + CO2} 7
simple hydrate (HCO2). As for the temperatures below 264 K, we put ice powder and liquid propan-2-ol in the vessel and pressurize it with CO2 gas before we began the experimental run. From the sharp pressure drop in Figure 2, it is obvious that the hydrate once formed and the gas was rapidly consumed in the vessel. Also, from the P-T slope change around 255.9 K in Figure2, the portion of hydrate would gradually dissociate along with the stepwise increase of temperature from 255.4 K to 255.8 K, and the dissociation of hydrate would complete around 255.9 K. When we dismantled the vessel after the sequential procedures in the isochoric method, there was the mixture of ice and propan-2-ol-rich liquid in the vessel. Therefore, it is reasonable to consider that ice and hydrate coexisted during stepwise temperature increase in the experimental run, from 255.4 K to 255.8 K, in Figure 2. Ice and hydrate existed at the equilibrium conditions we obtained below 264 K in Figure 3. From 262 K to 264 K, the equilibrium conditions in the (propan-2-ol + CO2 + H2O) system were the same as those in the (CO2 + H2O) system. This means that chemical potential of water is the same in the both systems, in contrast to the one above 264 K as described above. Thus, ice should exist at these temperatures since propan-2-ol does not dissolve in ice. Also, the hydrate formed in the system would be the same as the one formed in the (CO2 + H2O) system in this region. This is why the equilibrium conditions remained the same as the (CO2 + H2O) system.
The estimated phases in equilibrium from 262 K to 264 K are ice (I),
propan-2-ol-rich liquid (L), CO2-rich vapour (V) and CO2 simple hydrate (HCO2). Below 262 K, the equilibrium pressures in the (CO2 + propan-2-ol + H2O) system were lower than in the (CO2 + H2O) system. Since chemical potential of water in ice does not change, the most plausible explanation to the phenomenon is the formation of the thermodynamically more stable hydrate than CO2 hydrate at the temperatures below 262 K. 8
What is responsible for the stable hydrate formation may be propan-2-ol trapped in the hydrate cages. The estimated phases in equilibrium below 262 K are ice (I), propan-2-ol-rich liquid (L), CO2-rich vapour (V) and binary (propan-2-ol + CO2) hydrate (HPrOH). According to Gibbs’ phase rule, the number of degrees of freedom is 1 and 2 for the four-phase and three-phase equilibrium. This means that while the four-phase equilibrium pressures (below 264 K) depend on only the temperatures, the three-phase equilibrium pressures (above 264 K) depend on the temperatures and the mole fraction of the propan-2-ol in the aqueous solution. In this study, the molar ratio of H2O to propan-2-ol is 17:1. To
consider
the
inclination of the
measured
P-T conditions,
we
applied
Clausius-Clapeyron equation to the data below 262 K. According to the equation, these slopes are expressed as follows:
d lnP ∆h = − d zR
(1)
where ∆h is the heat of hydrate formation/dissociation based on molar guest gas, z is the compressibility factor of the gas and is universal gas constant. Compressibility factor z of the phase equilibrium conditions below 261.9 K were computed in the following equation by accessing the specific volume of CO2, v, which is calculated by NIST chemistry and webbook [28]. z=
Pv TR
(2)
The plots in the Figure 4 showing lnP-T -1 correlation seems to be composed of two straight lines with different slopes, solid and dashed lines. Solid and dashed lines were determined from 6 data (250.8 K to 252.6 K) and 8 data (255.7 K to 261.2 K) in Table 2, respectively. From 250.8 K, 0.275 MPa to 252.6 K, 0.334 MPa, z gradually decreased from 0.975 to 0.971 by 0.41% with increasing temperature. Also, from 255.7 K, 0.442 MPa to 261.2 K, 0.684 MPa, z 9
gradually decreased from 0.963 to 0.945 by 1.87% with increasing temperature. On the other hand, the slopes of solid and dashed lines in Figure 4 are -6730.8 K and -5291.2 K respectively. The relative difference of the slopes is 21.4% with increasing temperature. Compared from the change of z, the change of slope in lnP-T -1 diagram is significant. Therefore, the drastic slope change in lnP-T -1 diagram may be ascribed to change in ∆h according to the equation (1). The averages of z were 0.972 and 0.956 from 6 data points (250.8 K, 0.275 MPa to 252.6 K, 0.334 MPa) and 8 data points (255.7 K, 0.442 MPa to 261.2 K, 0.684 MPa) in Table 2. Based on the assumption that z is constant, 0.972 for solid line and 0.956 for dashed line in Figure 4, ∆h for each line were calculated to be 54.4 kJ·mol-1 and 42.1 kJ·mol-1 from equation (1). The resulting difference in ∆h is 22.7% with increasing temperature. The correlation based on the single line was also performed for the 17 data points (250.8 K, 0.275 MPa to 261.2 K, 0.684 MPa in Table 2) and its slope was -5554.9 K. To evaluate the correlations, the absolute average deviation of ln(P), AAD(ln(P)), was calculated.
The
definition of the deviation is AAD (ln(P)) =
∑ln , − ln ,
(3)
where Pi,exp is the “i”th experimental equilibrium pressure and Pi,calc is the “i”th pressure calculated by the one-line and two-line correlations. The n equals 17, the number of phase equilibrium values reproduced by these correlations, from 250.8 K, 0.275 MPa to 261.2 K, 0.684 MPa in Table 2.
The AAD(ln(P)) was 1.63×10 -2 for the one-line correlation, whereas
the one for the previously described correlation based on the two lines was 8.68×10 -3. This indicates that the two-line correlation better reproduces the experimental data in Figure 4 than the one-line based one.
The change in ∆h, hydrate formation/dissociation heat suggests that
the stable hydrate phase transformed to another hydrate phase. Thus, the slope change is ascribed to be structural change and the hydrates generated in two straight lines in Figure 4 10
would have different crystallographic structures. Another hydrate (HPrOH’) different from the one (HPrOH) formed between 254.9 K and 261.2 K starts to form from around 254 K, the intersection of two straight lines. In the two diagrams (a) and (b) in Figure 5, we provide two experimental runs aiming to measure the same two equilibrium points above and below 254 K, the intersection in Figure 4. These points determined to be equilibrium are in consistent within the expanded uncertainty of temperature and pressure measurement with coverage factor of k = 2, ensuring reliability of the data.
Table 2. Phase equilibrium P-T conditions in propan-2-ol + CO2 + H2O system.*a T / K*b P / MPa*c
Phases
T / K*b P / MPa*c
Phases
250.8 251.6
0.275 0.303
I + L + V + HPrOH’ 257.4 I + L + V + HPrOH’ 258.1
0.500 0.525
I + L + V + HPrOH I + L + V + HPrOH
251.9 252.3
0.309 0.327
I + L + V + HPrOH’ 259.0 I + L + V + HPrOH’ 260.4
0.568 0.644
I + L + V + HPrOH I + L + V + HPrOH
252.6 252.6
0.332 0.334
I + L + V + HPrOH’ 261.2 I + L + V + HPrOH’ 261.9
0.684 0.736
I + L + V + HPrOH I + L + V + HCO2
253.6 254.0
0.376 0.399
I + L + V + HPrOH’ 262.8 I + L + V + HPrOH’ 263.6
0.753 0.775
I + L + V + HCO2 I + L + V + HCO2
254.9 255.7
0.417 0.442
I + L + V + HPrOH I + L + V + HPrOH
0.820 0.899
L + V + HCO2 L + V + HCO2
264.0 264.9
255.8 0.446 I + L + V + HPrOH 265.7 0.995 L + V + HCO2 255.8 0.445 I + L + V + HPrOH *a CO2-free mole fractions of water and propan-2-ol are xH2O = 0.9443, xPro = 0.0557 where expanded uncertainty with coverage factor, k = 2, of mole fraction is U(x) = 3.0 ×10-4. *b
U(T) = 0.1 K. The expanded uncertainty of temperature measurement with coverage factor of
k = 2 was estimated from the experimental apparatus. *c
U(P) = 0.010 MPa.
The expanded uncertainty of pressure measurement with coverage 11
factor of k = 2 was estimated from the deviation of the equilibrium pressures obtained in the two different measurements for duplication at 252.6 K and 255.8 K.
Figure 3. Phase equilibrium conditions in the propan-2-ol + CO2 + H2O system.
●, This
study; ○, CO2 + H2O system [26]; □, CO2 + H2O system [27].
Figure 4. Phase equilibrium P-T conditions in the propan-2-ol + CO2 + H2O system plotted on the lnP-T
-1
plane.
Solid and dashed lines are linear correlation lines based on 12
Clausius-Clapeyron equation.
Solid and dashed lines were determined from 6 data points
(3.99 ×10 -3 K-1 to 3.96 ×10-3 K-1 (250.8 K to 252.6 K)) and 8 data points (3.91 ×10-3 K-1 to 3.83 ×10 -3 K-1 (255.7 K to 261.2 K)) in Table 2, respectively.
(a)
(b) 13
Figure 5. P-T diagram for the experimental runs for duplication of measurements. Sequential plots in each run are (a) Run 1, , , and (b) Run 2, , , and . Phase equilibrium conditions are (a) , 252.6±0.1 K, 0.334±0.005 MPa; , 252.6±0.1 K, 0.332±0.005 MPa (b) , 255.8±0.1 K, 0.445±0.003 MPa; , 255.8±0.1 K, 0.446±0.003 MPa.
4. Conclusion Phase equilibrium measurements were performed for the (propan-2-ol + CO2 + H2O) system from 250.8 K to 265.7 K. The equilibrium pressures obtained from this study were higher than in the (CO2 + H2O) system at 264.0 K to 265.7 K and lower than in the system at 250.8 K to 261.2 K. Propan-2-ol works as a thermodynamic inhibitor above 264 K, and expanded hydrate formable conditions below 262 K.
Acknowledgement This study was supported by a Keirin-racing-based research promotion fund from the JKA Foundation.
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17
Highlights ・ Phase equilibrium measurements in propan-2-ol + CO2 + H2O system were performed. ・ Isochoric procedure was employed for determining equilibrium conditions. ・ Propan-2-ol + CO2 binary hydrate forms at temperature below 262 K. ・ Crystallographic structure of the binary hydrate may change at 254 K.
18
S0021-9614(17)30268-9 http://dx.doi.org/10.1016/j.jct.2017.07.036 YJCHT 5154
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
14 December 2016 26 July 2017 27 July 2017
Please cite this article as: N. Fukushima, S. Shiratori, T. Makiya, T. Murakami, R. Ohmura, Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K, J. Chem. Thermodynamics (2017), doi: http://dx.doi.org/10.1016/j.jct. 2017.07.036
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Phase equilibrium condition measurements in the clathrate hydrate forming system of (propan-2-ol + carbon dioxide + water) at temperatures between 250.8 K and 265.7 K
Naruki Fukushimaa, Satoshi Shiratoria, Takeshi Makiyaa, Takashi Murakamia, Ryo Ohmura*a. a
Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku,
Yokohama 223-8522, Japan Tel: +81-45-556-1813 E-mail: [email protected]
Abstract The phase equilibrium conditions in the (propan-2-ol + carbon dioxide + water) system were measured. The measurements were performed using the batch, isochoric method at the temperatures between 250.8 K and 265.7 K. The equilibrium pressures were measured between 0.275 MPa and 0.995 MPa, and increased with increasing temperatures. Propan-2-ol is known as thermodynamic inhibitor for hydrate formation. However at the temperatures below 262 K, the equilibrium pressures in the (propan-2-ol + carbon dioxide + water) system are lower than those without propan-2-ol (carbon dioxide + water system). The measurements indicate the formation of the hydrates containing propan-2-ol and carbon dioxide in this system.
Keywords Phase equilibria, Clathrate hydrate, Propan-2-ol, carbon dioxide, Alcohol hydrate
1. Introduction 1
Clathrate hydrates are crystalline compounds trapping molecules in their cages. Water molecules are constituent part of the hydrate cages, shaping the cavities with hydrogen bonding. There are three main types of structure among hydrates: structure I, structure II, structure H, represented as sI, sII, and sH respectively. Applying their notable characteristics such as high gas storage, selectivity of trapped gases, large heat involved in formation and dissociation of hydrates, a variety of industrial technology has been proposed. Hydrate-based refrigeration system has been developed for residential air-conditioning use [1].
Application of CO2
hydrate as a refreshing cold dessert is an emerging, unique idea [2-6].
Theoretical
performance of hydrate-based heat engine was evaluated for using ocean thermal energy [7]. Capturing a compound from gaseous mixture in the form of hydrate is also one of the major examples of hydrate-based technologies [8, 9]. Alcohols have been known for changing hydrate forming condition to higher pressure and lower temperature, inhibiting hydrates from forming [10]. On the other hand, hydrate containing alcohols in their cages, alcohol hydrate, has also been reported [11]. Various alcohols such as ethanol [12-14], propan-1-ol [15-17] and propan-2-ol [18-20] with help gases have also been shown to exist recently.
Among alcohols, our interest in this study is
propan-2-ol. The systems involving propan-2-ol have been proven to be abstruse. Takeya et al. reported the existence of transitional form of CH4 + propan-2-ol hydrate at low temperatures [21].
Interestingly, the double alcohol hydrate transformed from cubic structure II to
tetragonal form with asymmetry at about 110 K. In the (fluoromethane + propan-2-ol + H2O) system, the characterization of the hydrate was not completed due to unknown peaks in the PXRD pattern [22]. These mysterious phenomena involving propan-2-ol can be attributed to an intricate interaction between propan-2-ol molecules and water molecules. Alavi et al. found strong hydrogen bonding induced by alcohol is greatly related to stabilization of hydrate 2
cage [23]. For further understanding of guest-host interaction of hydrate crystal, propan-2-ol is an intriguing compound. In this study, we performed phase equilibrium measurements for a system, (propan-2-ol + CO2 + H2O). Similar study was previously conducted by Lee et al., reporting the phase equilibrium data for 272.5 K to 282.2 K at different concentrations [24]. However, no measurement has been conducted for low temperature range below freezing point of water. This study might establish more accurate interpretation of the interaction between guest compounds including alcohol and water molecules, the mysterious structure change of hydrate containing propan-2-ol.
2. Experimental method 2.1. Materials The materials in this study are liquid reagent of propan-2-ol (0.999 mass fraction, Sigma-Aldrich Co., U.S.A.), CO2 gas (0.99995 volume fraction, Japan Fine Products Co., Japan) and water. The water was deionized and distilled (WG222, Yamato Scientific Co., Japan) in our laboratory. The specification of the materials used in this study is summarized in Table 1.
Table 1. Specifications of the compounds in this study. Sample name
Chemical Formula
Supplier
propan-2-ol
C3H7OH
Sigma-Aldrich Co. LLC.
Purity 0.999 mass fraction is certificated 0.99995 volume fraction
Carbon dioxide
CO2
Japan Fine Products Co. is certificated 3
Deionized and
Electrical conductivity H2O
Laboratory made
distilled water
was less than 0.1 µS/cm
2.2. Apparatus The overall configuration of experimental apparatus is shown in Figure 1. The stainless steel vessel is immersed in a temperature controlled bath. A platinum resistance thermometer (Ichimura Metal Co., Japan) and a strain-gauge pressure transducer (PAB-A-500KP, PG-10KU and PH-20KB, Kyowa Electronic Instruments Co., Japan) are inserted inside the vessel, measuring the temperature and pressure in the system. The expanded uncertainty of temperature measurement, U(T), is 0.1 K with a coverage factor of k = 2 and those for pressure measurement, U(P), was estimated to be 0.010 MPa. More details of the expanded uncertainty of pressure measurement would be shown in section 3 Results and Discussion.
Figure 1. Schematic of the experimental apparatus. 2.3. Phase equilibrium measurements Isochoric procedure [25] was employed for measuring the phase equilibrium conditions in (propan-2-ol + CO2 + H2O) system. Before starting experimental runs, 30.0 g of ground ice powder and 5.9 g of liquid propan-2-ol were supplied into the reactor. The approximate diameter of ice powder was 1 mm and was made from laboratory-made water mentioned in 4
Materials section. The molar ratio of H2O (ice) to propan-2-ol was 17:1, stoichiometric composition of propan-2-ol assuming the propan-2-ol molecules occupying all large cages in sII hydrate. The experimental run begins with removal of the air in the vessel by vacuum pump and pressurization with CO2 gas. Initial pressure-temperature condition was set free from hydrate formation in each experimental run. After lowering the temperature, sharp pressure drop was observed due to formation of hydrate, trapping the gas inside the cavities. The pressure decrease in the hydrate forming process was typically very rapid. For example, the pressure drastically decreased from 0.449 MPa to 0.431 MPa at 255.8 K as shown in Figure 2. Then the temperature was repeatedly increased by 0.1 K.
Here, the pressure increase
occurred mainly because of the hydrate dissociation. In each temperature increment step, we kept T in the reactor constant for 6 h to 24 h to ensure the establishment of the steady state. After the pressure increase became subtle due to the complete dissociation of hydrate, the phase equilibrium condition was determined at the point just before the P-T slope changed because it is the most reliable condition where a small amount of hydrate was left in the vessel. The trajectory of pressure and temperature data in an experimental run is shown in Figure 2. This sequential stepwise temperature increase process was repeated for different initial conditions to obtain the four-phase/three-phase equilibrium data between 250.8 K and 265.7 K.
5
Figure2. Pressure and temperature values obtained during the isochoric procedure.
:
initial condition; □: unsteady conditions recorded during lowering temperature and pressure drop; ○: conditions recorded during temperature increase; ●: the phase equilibrium point determined in temperature-increase steps.
2.4. Sample preparation To confirm the hydrate formation at P, T conditions measured in the present study, solid sample was prepared. The experimental equipment, materials and chemical composition in the vessel were the same as described in Apparatus and Procedure sections. After removing the air, the initial condition in the vessel was set at 255.2 K and 0.56 MPa by pressurization of CO2 gas. As pressure stabilized around the phase equilibrium condition, 0.42 MPa, CO2 gas was refilled again up to 0.55 MPa (the condition where CO2 simple hydrate does not form.). The same way of pressurization was repeated until no more pressure drop was observed. The vessel was dismantled at 241.2 K after it was moved to a low temperature room cooled at 6
239.2 K and we confirmed dry mass of ice-like solid in the vessel. The portion of the solid was put in water to observe the dissociation of the solid.
3. Results and discussion The solid sample synthesized as described in the section “2.4. Sample preparation” was dissociated in water. The bubble formation was observed on the surface of the dissociating solid particles. The characteristic odour of propan-2-ol was also confirmed upon the dissociation. Because the solid sample was apparently dry and not wet, liquid propan-2-ol was likely to be converted to the hydrate that encapsulates the alcohol molecules. The phase equilibrium data measured in (propan-2-ol + CO2 + H2O) system at the temperatures between 250.8 K and 265.7 K are shown in Table 2 and Figure 3. The expanded uncertainty U(P) with coverage factor of k = 2 in this study was estimated to be 0.010 MPa from the deviations of the equilibrium pressures obtained in the two different duplicated measurements at 252.6 K and 255.8 K indicated in Table 2. In addition to the plots obtained in the present measurements, the phase equilibrium data in the (CO2 + H2O) system [26, 27] are also plotted for comparison in Figure 3. The phase equilibrium pressures in the (propan-2-ol + CO2 + H2O) system were higher than those (in CO2 + H2O) system. This indicates that the hydrate formation was inhibited above 264 K. The hydrate equilibrium conditions in the system at lower temperature and higher pressure than those in the (CO2 + H2O) system is ascribed to the dissolved propan-2-ol in water. Dissolution of propan-2-ol in water decreases the chemical potential of water in the aqueous phase. Therefore, the equilibrium temperature in the system is lower than that in the simple CO2 hydrate forming system, which is the phenomenon similar to the freezing point depression in water. The estimated phases in equilibrium above 264 K are propan-2-ol aqueous {liquid (L) + CO2-rich vapour (V) + CO2} 7
simple hydrate (HCO2). As for the temperatures below 264 K, we put ice powder and liquid propan-2-ol in the vessel and pressurize it with CO2 gas before we began the experimental run. From the sharp pressure drop in Figure 2, it is obvious that the hydrate once formed and the gas was rapidly consumed in the vessel. Also, from the P-T slope change around 255.9 K in Figure2, the portion of hydrate would gradually dissociate along with the stepwise increase of temperature from 255.4 K to 255.8 K, and the dissociation of hydrate would complete around 255.9 K. When we dismantled the vessel after the sequential procedures in the isochoric method, there was the mixture of ice and propan-2-ol-rich liquid in the vessel. Therefore, it is reasonable to consider that ice and hydrate coexisted during stepwise temperature increase in the experimental run, from 255.4 K to 255.8 K, in Figure 2. Ice and hydrate existed at the equilibrium conditions we obtained below 264 K in Figure 3. From 262 K to 264 K, the equilibrium conditions in the (propan-2-ol + CO2 + H2O) system were the same as those in the (CO2 + H2O) system. This means that chemical potential of water is the same in the both systems, in contrast to the one above 264 K as described above. Thus, ice should exist at these temperatures since propan-2-ol does not dissolve in ice. Also, the hydrate formed in the system would be the same as the one formed in the (CO2 + H2O) system in this region. This is why the equilibrium conditions remained the same as the (CO2 + H2O) system.
The estimated phases in equilibrium from 262 K to 264 K are ice (I),
propan-2-ol-rich liquid (L), CO2-rich vapour (V) and CO2 simple hydrate (HCO2). Below 262 K, the equilibrium pressures in the (CO2 + propan-2-ol + H2O) system were lower than in the (CO2 + H2O) system. Since chemical potential of water in ice does not change, the most plausible explanation to the phenomenon is the formation of the thermodynamically more stable hydrate than CO2 hydrate at the temperatures below 262 K. 8
What is responsible for the stable hydrate formation may be propan-2-ol trapped in the hydrate cages. The estimated phases in equilibrium below 262 K are ice (I), propan-2-ol-rich liquid (L), CO2-rich vapour (V) and binary (propan-2-ol + CO2) hydrate (HPrOH). According to Gibbs’ phase rule, the number of degrees of freedom is 1 and 2 for the four-phase and three-phase equilibrium. This means that while the four-phase equilibrium pressures (below 264 K) depend on only the temperatures, the three-phase equilibrium pressures (above 264 K) depend on the temperatures and the mole fraction of the propan-2-ol in the aqueous solution. In this study, the molar ratio of H2O to propan-2-ol is 17:1. To
consider
the
inclination of the
measured
P-T conditions,
we
applied
Clausius-Clapeyron equation to the data below 262 K. According to the equation, these slopes are expressed as follows:
d lnP ∆h = − d zR
(1)
where ∆h is the heat of hydrate formation/dissociation based on molar guest gas, z is the compressibility factor of the gas and is universal gas constant. Compressibility factor z of the phase equilibrium conditions below 261.9 K were computed in the following equation by accessing the specific volume of CO2, v, which is calculated by NIST chemistry and webbook [28]. z=
Pv TR
(2)
The plots in the Figure 4 showing lnP-T -1 correlation seems to be composed of two straight lines with different slopes, solid and dashed lines. Solid and dashed lines were determined from 6 data (250.8 K to 252.6 K) and 8 data (255.7 K to 261.2 K) in Table 2, respectively. From 250.8 K, 0.275 MPa to 252.6 K, 0.334 MPa, z gradually decreased from 0.975 to 0.971 by 0.41% with increasing temperature. Also, from 255.7 K, 0.442 MPa to 261.2 K, 0.684 MPa, z 9
gradually decreased from 0.963 to 0.945 by 1.87% with increasing temperature. On the other hand, the slopes of solid and dashed lines in Figure 4 are -6730.8 K and -5291.2 K respectively. The relative difference of the slopes is 21.4% with increasing temperature. Compared from the change of z, the change of slope in lnP-T -1 diagram is significant. Therefore, the drastic slope change in lnP-T -1 diagram may be ascribed to change in ∆h according to the equation (1). The averages of z were 0.972 and 0.956 from 6 data points (250.8 K, 0.275 MPa to 252.6 K, 0.334 MPa) and 8 data points (255.7 K, 0.442 MPa to 261.2 K, 0.684 MPa) in Table 2. Based on the assumption that z is constant, 0.972 for solid line and 0.956 for dashed line in Figure 4, ∆h for each line were calculated to be 54.4 kJ·mol-1 and 42.1 kJ·mol-1 from equation (1). The resulting difference in ∆h is 22.7% with increasing temperature. The correlation based on the single line was also performed for the 17 data points (250.8 K, 0.275 MPa to 261.2 K, 0.684 MPa in Table 2) and its slope was -5554.9 K. To evaluate the correlations, the absolute average deviation of ln(P), AAD(ln(P)), was calculated.
The
definition of the deviation is AAD (ln(P)) =
∑ln , − ln ,
(3)
where Pi,exp is the “i”th experimental equilibrium pressure and Pi,calc is the “i”th pressure calculated by the one-line and two-line correlations. The n equals 17, the number of phase equilibrium values reproduced by these correlations, from 250.8 K, 0.275 MPa to 261.2 K, 0.684 MPa in Table 2.
The AAD(ln(P)) was 1.63×10 -2 for the one-line correlation, whereas
the one for the previously described correlation based on the two lines was 8.68×10 -3. This indicates that the two-line correlation better reproduces the experimental data in Figure 4 than the one-line based one.
The change in ∆h, hydrate formation/dissociation heat suggests that
the stable hydrate phase transformed to another hydrate phase. Thus, the slope change is ascribed to be structural change and the hydrates generated in two straight lines in Figure 4 10
would have different crystallographic structures. Another hydrate (HPrOH’) different from the one (HPrOH) formed between 254.9 K and 261.2 K starts to form from around 254 K, the intersection of two straight lines. In the two diagrams (a) and (b) in Figure 5, we provide two experimental runs aiming to measure the same two equilibrium points above and below 254 K, the intersection in Figure 4. These points determined to be equilibrium are in consistent within the expanded uncertainty of temperature and pressure measurement with coverage factor of k = 2, ensuring reliability of the data.
Table 2. Phase equilibrium P-T conditions in propan-2-ol + CO2 + H2O system.*a T / K*b P / MPa*c
Phases
T / K*b P / MPa*c
Phases
250.8 251.6
0.275 0.303
I + L + V + HPrOH’ 257.4 I + L + V + HPrOH’ 258.1
0.500 0.525
I + L + V + HPrOH I + L + V + HPrOH
251.9 252.3
0.309 0.327
I + L + V + HPrOH’ 259.0 I + L + V + HPrOH’ 260.4
0.568 0.644
I + L + V + HPrOH I + L + V + HPrOH
252.6 252.6
0.332 0.334
I + L + V + HPrOH’ 261.2 I + L + V + HPrOH’ 261.9
0.684 0.736
I + L + V + HPrOH I + L + V + HCO2
253.6 254.0
0.376 0.399
I + L + V + HPrOH’ 262.8 I + L + V + HPrOH’ 263.6
0.753 0.775
I + L + V + HCO2 I + L + V + HCO2
254.9 255.7
0.417 0.442
I + L + V + HPrOH I + L + V + HPrOH
0.820 0.899
L + V + HCO2 L + V + HCO2
264.0 264.9
255.8 0.446 I + L + V + HPrOH 265.7 0.995 L + V + HCO2 255.8 0.445 I + L + V + HPrOH *a CO2-free mole fractions of water and propan-2-ol are xH2O = 0.9443, xPro = 0.0557 where expanded uncertainty with coverage factor, k = 2, of mole fraction is U(x) = 3.0 ×10-4. *b
U(T) = 0.1 K. The expanded uncertainty of temperature measurement with coverage factor of
k = 2 was estimated from the experimental apparatus. *c
U(P) = 0.010 MPa.
The expanded uncertainty of pressure measurement with coverage 11
factor of k = 2 was estimated from the deviation of the equilibrium pressures obtained in the two different measurements for duplication at 252.6 K and 255.8 K.
Figure 3. Phase equilibrium conditions in the propan-2-ol + CO2 + H2O system.
●, This
study; ○, CO2 + H2O system [26]; □, CO2 + H2O system [27].
Figure 4. Phase equilibrium P-T conditions in the propan-2-ol + CO2 + H2O system plotted on the lnP-T
-1
plane.
Solid and dashed lines are linear correlation lines based on 12
Clausius-Clapeyron equation.
Solid and dashed lines were determined from 6 data points
(3.99 ×10 -3 K-1 to 3.96 ×10-3 K-1 (250.8 K to 252.6 K)) and 8 data points (3.91 ×10-3 K-1 to 3.83 ×10 -3 K-1 (255.7 K to 261.2 K)) in Table 2, respectively.
(a)
(b) 13
Figure 5. P-T diagram for the experimental runs for duplication of measurements. Sequential plots in each run are (a) Run 1, , , and (b) Run 2, , , and . Phase equilibrium conditions are (a) , 252.6±0.1 K, 0.334±0.005 MPa; , 252.6±0.1 K, 0.332±0.005 MPa (b) , 255.8±0.1 K, 0.445±0.003 MPa; , 255.8±0.1 K, 0.446±0.003 MPa.
4. Conclusion Phase equilibrium measurements were performed for the (propan-2-ol + CO2 + H2O) system from 250.8 K to 265.7 K. The equilibrium pressures obtained from this study were higher than in the (CO2 + H2O) system at 264.0 K to 265.7 K and lower than in the system at 250.8 K to 261.2 K. Propan-2-ol works as a thermodynamic inhibitor above 264 K, and expanded hydrate formable conditions below 262 K.
Acknowledgement This study was supported by a Keirin-racing-based research promotion fund from the JKA Foundation.
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Highlights ・ Phase equilibrium measurements in propan-2-ol + CO2 + H2O system were performed. ・ Isochoric procedure was employed for determining equilibrium conditions. ・ Propan-2-ol + CO2 binary hydrate forms at temperature below 262 K. ・ Crystallographic structure of the binary hydrate may change at 254 K.
18