Renewed Measurements of Carbon Dioxide Hydrate Phase Equilibrium

This paper investigates the phase equilibrium conditions in the carbon dioxide hydrate forming system. Carbon dioxide hydrate can be utilized for carbon capture, salt manufacture, carbonated solid foods and tritium water concentration, so the phase equilibrium conditions have been substantially reported so far. However, the data from previous studies were inconsistent with each other, such as there is a difference of 1.0 K in the phase equilibrium temperature at 2 MPa. In this study, the newly three-phase (water rich liquid + hydrate + guest rich vapor) equilibrium conditions in the carbon dioxide hydrate forming system were measured at twenty different temperature conditions within the range of (271.9-282.7) K in the two different laboratories. The six pairs of the three-phase equilibrium condition data measured under equivalent pressure conditions were consistent within mutual uncertainties. The internal consistency of the data measured in this study was evaluated by the Clausius-Clapeyron equation. The data measured in this study existed within the uncertainty range of the data from several previous studies.


Introduction
Clathrate hydrates (hydrates) are ice-like crystalline compounds formed when molecules are encapsulated in a cage-like structures composed of hydrogen-bonded water molecules. Water is called "host" because it constitutes the cage structures. The molecules encapsulated into the cage-like structures are called "guest molecules". Hydrates are expected to be used in various applications because hydrates have unique properties, for example high gas storage capacities, large formation/decomposition heats, and guest compounds selectivity. There are several novel applications utilizing carbon dioxide hydrate such as carbon capture [1][2][3], salt manufacture [4][5][6] and carbonated solid foods [7,8]. Tritium water concentration through hydrate formation is an emerging technology that utilizes another unique property of hydrates; host compounds selectivity [9]. To determine an operation condition on these hydratebased technologies, it is necessary to know the pressure and temperature conditions at which hydrates are formed and decomposed. Hydrates form at conditions of lower temperatures and higher pressures than the L + H + V three-phase equilibrium conditions, where the three phases of water rich liquid phase (L), hydrate phase(H) and guest rich gas phase(V) are in equilibrium. The three-phase equilibrium conditions in the carbon dioxide hydrate forming system have been extensively reported in the previous studies [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] as compiled in Fig. 1, a pressure-temperature (p-T) diagram. Fig. 1 shows that there is 1 K difference in the three-phase equilibrium temperature between the data at p ~ 2 MPa. An uncertainty of temperature measurements by a platinum-wire resistance thermometer is typically 0.1 K, which means a difference of 1 K exceeds the mutual uncertainty. A difference of 1 K in the phase equilibrium conditions makes it difficult to compare with other systems. For example, the phase equilibrium temperature difference between the carbon dioxide hydrate forming system and carbon dioxide + heavy water system is 3.2 K at 2 MPa [13]. Therefore, a fluctuation of 1 K is equivalent to a 32% deviation. The reliable phase equilibrium conditions of simple carbon dioxide hydrate are necessary to evaluate equilibrium conditions in other hydrate forming systems pressurized with carbon dioxide, e.g., in the system with carbon dioxide + heavy water [13], carbon dioxide + structure H hydrate former + water [28], and so on. Fig. 2 shows the scatter of the three-phase equilibrium conditions in the carbon dioxide hydrate forming system reported in the previous studies [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This figure shows the deviations of experimental data from the regressed temperature. T calc is the average of equilibrium temperature interpolated the three-phase equilibrium data from previous studies by using the Clausius-Clapeyron equation: where p is the pressure, T is the absolute temperature, ΔH is the enthalpy change for the carbon dioxide hydrate decomposition per mol of carbon dioxide, z is the compressibility factor and R is the universal gas constant. To calculate T calc , the Clau-sius-Clapeyron equation, which has thermodynamic significance, is used. T calc is calculated separately for two cases: when the pressure is below 2 MPa and over 2 MPa.
The dash line represents T = ± 0.2 K. In other words, the points that exist outside of these two dash lines differ from T calc by more than 0.2 K. Fig. 2 reveals that these three-phase equilibrium data from previous studies have the deviation over 0.2 K. A typical uncertainty of temperature measurements by a platinum resistance thermometer is 0.1 K. The deviation over 0.2 K means a difference of the phase equilibrium temperature data surpass the mutual temperature uncertainty. Furthermore, the average absolute deviation (AAD) was found to be 0.144 K, indicating that there is still variability in the data.
There are three known methods for measuring the phase equilibrium conditions of hydrates: the isothermal method, the isobaric method, and the isochoric method.  [10]. Empty triangle: Yasuda et al. [11]. Empty square: Nema et al. [12]. Empty rhombus: Chun et al. [13]. Filled circle: Ohgaki et al. [14]. Filled triangle: Mooijer-van den Heuvel [15]. Filled square: Fan and Guo [16]. Filled rhombus: Ng and Robinson [17]. Stripe circle: Maekawa [18]. Stripe triangle: Seo et al. [19]. Stripe square: Wang et al. [20]. Stripe rhombus: Dai et al. [21]. Half circle: Fan et al. [22]. Half triangle: Mohanmmadi et al. [23]. Half square: Unruh & Katz [24]. Half rhombus: Ferrari et al. [25]. Star: Sebil et al. [26]. Plus: Englezos & Hall [27] The isothermal method is measuring method by releasing or injecting gas under constant temperature conditions. Due to the nature of the measurement method, there is a difference between the true phase equilibrium pressure and the measured phase equilibrium pressure beyond the uncertainties of the measurements by the pressure sensor. The isobaric method is measuring method by decreasing or increasing the temperature under constant pressure conditions. This method relies on visual observation of the presence or absence of hydrates in the reactor, making the measurement results unstable. The isochoric method is measuring method decreasing or increasing the temperature within a constant-volume vessel and determining the phase equilibrium conditions based on the trend in the p-T diagram. Table 1 shows the measurement methods and the equilibrium temperature diffrence from calculated values (ΔT) of previous studies. Upon Fig. 1, it is observed that the reliability does not significantly vary depending on the measurement method. However, concerning the Fig. 2 The scatter of the L + H + V three-phase equilibrium conditions in the carbon dioxide hydrate forming system reported in the previous studies. Empty circle: Adisasmito et al. [10]. Empty triangle: Yasuda et al. [11]. Empty square: Nema et al. [12]. Empty rhombus: Chun et al. [13]. Filled circle: Ohgaki et al. [14]. Filled triangle: Mooijer-van den Heuvel [15]. Filled square: Fan and Guo [16]. Filled rhombus: Ng and Robinson [17]. Stripe circle: Maekawa [18]. Stripe triangle: Seo et al. [19]. Stripe square: Wang et al. [20]. Stripe rhombus: Dai et al. [21]. Half circle: Fan et al. [22]. Half triangle: Mohanmmadi et al. [23]. Half square: Unruh & Katz [24]. Half rhombus: Ferrari et al. [25]. Star: Sebil et al. [26]. Plus: Englezos & Hall [27]. Dash line: Double of uncertainty of the temperature measurements (± 0.2 K) heating method, the following findings are known. Tohidi et al. reported that stepwise heating results in generating reliable experimental data, as compared with continuous heating [29]. Stepwise heating is a method of increasing temperature after temperature and pressure reach a steady state, so that highly accurate phase equilibrium temperature can be obtained. On the other hand, continuous heating is a method of increasing condition at a constant rate (heating rate). Cooling rate does not affect the reliability of measured data. However, the heating rate causes reliability deterioration because it may increase the temperature before reaching a steady state.
Based on the aforementioned review, the isochoric method with stepwise heating has been identified as a reliable approach for measuring the phase equilibrium conditions. The purpose of this study is to utilize this method to measure new data of the phase equilibrium conditions in the carbon dioxide formation system. To ensure the reliability, the measurements were performed in the two different laboratories. One is at Keio University, Yokohama. While the other is at University of the Ryukyus, Okinawa, Japan. Additionaly, pairs of the phase equilibrium conditions were measured under equivalent pressure conditions in the two different laboratories. The reason for obtaining the pairs of data is to enable a direct comparison without using interpolation or extrapolation.

Materials
The sample materials used in the experiments were water and carbon dioxide gas. The suppliers and the purities of the materials are as follows:

Keio University
The carbon dioxide cylinder was supplied by Japan Fine Products Co., Ltd. and used as received from the supplier. The certified purity of the gas was 0.99995 in volume fraction. Water used in the experiments was deionized and distilled water in our laboratory (model WG222, Yamato Scientific Co., Ltd.). The electrical conductivity of the water was less than 0.100 µS/cm.
University of the Ryukyus Carbon dioxide gas was supplied from Japan Fine Products Co., Ltd. and used as received. The certified purity of the gas was 0.99995 in volume fraction. Water was prepared in our laboratory by treating tap water with a reverse osmosis membrane pure water generator (model RFP742HA, Toyo Roshi Kaisha, Ltd.). The water generator is comprised of an ion exchange device and a membrane unit. The electrical conductivity of the water was less than 0.100 µS/cm.

Apparatus
Keio University A schematic diagram of the experimental apparatus used to measure the three-phase equilibrium data is shown in Fig. 3. The main part of the experimental apparatus was a withstand pressure vessel made of stainless steel. The threephase equilibrium data were measured by allowing hydrate to form in this vessel. The vessel was equipped with an electromagnetic stirrer which can be connected to an external motor to agitate inside the vessel. The vessel was submerged in a bath containing ethylene glycol aqueous solution of which temperature is controlled by a PID controlled heater (model BF400, Yamato Scientific Co., Ltd.) and an immersion cooler (ECS-30, Tokyo Rikakikai Co., Ltd.). The temperature inside the vessel was measured by a platinum-wire resistance thermometer (RF-100, Electronic

Procedure
Keio University In this study, the isochoric method [29] was used to measure the three-phase equilibrium conditions of the carbon dioxide hydrate forming system. The isochoric method is illustrated in Fig. 5. In this method, the three-phase equilibrium conditions are determined through the formation and decomposition of hydrate in a constant volume vessel. The detailed measurement method for the isochoric method is described below. The temperature and pressure in the vessel are set at conditions that will not form hydrate. The vessel is cooled to form hydrate. During hydrate formation, the pressure in the vessel drops rapidly and the temperature in the vessel rises temporarily due to the formation heat of hydrate. The temperature in Fig. 5 Method of measuring the phase equilibrium conditions in hydrate forming systems using the isochoric method the vessel is then increased to decompose hydrate. As the temperature is raised, the hydrate is decomposed and the carbon dioxide gas stored in the hydrate is released, causing the pressure in the vessel to increase. After the pressure rise calms down and the pressure becomes steady, the temperature is increased again. The temperature increase is repeated until all hydrates in the vessel have been decomposed. When all the hydrate is decomposed, the pressure in the vessel rises only slightly, depending on the phase equilibrium of the fluids. The temperature and pressure just before the slope changes on the pressure-temperature diagram is the condition where the infinitesimal amount of hydrate exists, that is, the L + H + V three-phase equilibrium conditions. At the point just where the slope changes (the inflection point), all hydrates may have dissociated. In this study, the data were measured at step of 0.1 K with 0.1 K uncertainties. Therefore, the differences between the measured conditions just before the slope changes and the calculated conditions of the inflection points are small relative the measurement uncertainties. The inflection points include the uncertainties caused by the calculation while the measured conditions have uncertainties just caused by the measurements. Accordingly, the measured conditions just before the slope changes are suitable as the equilibrium conditions determined by the p-T trajectory obtained in the measurements. First, 30 g of water was placed in the vessel and the lid was closed. After the vessel was evacuated by a vacuum pump, carbon dioxide gas was supplied to the vessel up to a pressure at which hydrate was not formed. When the carbon dioxide was dissolved to saturation in water and the pressure became steady, the temperature and pressure were noted as the initial conditions. The system was then cooled to produce carbon dioxide hydrate. Hydrate formation was confirmed by observing the pressure drop and temperature increase on a data logger tracking temperature and pressure in the vessel. During the temperature increase process, after confirming that temperature and pressure have reached a steady state, they were recorded and the temperature was increased in steps of 0.1 K. Using the method described above, the L + H + V three-phase equilibrium conditions were measured from various initial conditions.

University of the Ryukyus
The procedure used to measure the three-phase equilibrium conditions was mostly the same as that performed at Keio University. The difference in the experimental procedure was the method of stirring inside the vessel. The experimental setup used at University of the Ryukyus was not equipped with electromagnetic stirrer that enables the steady stirring. Alternatively, the fluids and solid inside the vessel were intermittently agitated by the magnet at 4-12 h intervals. Although the time required for reaching the steady state condition was longer due to the intermittent rather than continuous agitation, the steady state conditions were certainly established by carefully checking the pressure change during the experiments. During the hydrate formation and decomposition, the occurrence of the hydrate crystals was visually confirmed to support the experimental results obtained by the temperature-pressure measurements.

Results and Discussion
The L + H + V three-phase equilibrium condition data in the carbon dioxide hydrate forming system measured in this study are shown in Table 2. To ensure the reliability of the measurement results, six pairs of the phase equilibrium conditions were measured under equivalent pressure conditions in the two different laboratories. Table 3 shows that six pairs are consistent within mutual uncertainties of measurements. Fig. 6 shows the phase equilibrium data measured in this study on a p-T diagram with the data reported in the previous studies. Approximation according to the Clausius-Clapeyron equation was employed to evaluate the internal consistency of the measured data and more accurate external consistency with the data from the previous studies. The phase equilibrium p-T conditions in the hydrate formation systems may be generally reproduced by the regression procedure using Clausius-Clapeyron equation shown in Eq. (1). If the right-hand side of Eq. (1) is constant, Eq. (1) can be transformed as follows: where a and b are dimensionless fitting parameters. Equation (2) means that the p-T data of the phase equilibrium conditions are linearly aligned on the lnp-1/T diagram. Values of a and b can be obtained by plotting the experimental data on the lnp-1/T diagram.
To verify the internal consistency of the phase equilibrium p-T condition data measured in this study, these data were plotted on a lnp-1/T diagram as shown in Fig. 7. The values of a, b and the correlation coefficient R 2 obtained by the linear approximation of the measured data on the lnp-1/T diagram are then shown in Table 4. In Fig. 7, the measured data are aligned along the approximate line. Fig. 8 shows the deviation of measured temperature data in this study from calculated temperature by Clausius-Clapeyron equation. In the calculations, different fitting parameters are used according to the pressure (p < 2 MPa or not). The average Fig. 6 p-T diagram of the L + H + V three-phase equilibrium conditions in the carbon dioxide hydrate forming system. Empty circle: Adisasmito et al. [10]. Empty triangle: Yasuda et al. [11]. Empty square: Nema et al. [12]. Empty rhombus: Chun et al. [13]. Filled circle: Ohgaki et al. [14]. Filled triangle: Mooijer-van den Heuvel [15]. Filled square: Fan and Guo [16]. Filled rhombus: Ng and Robinson [17]. Stripe circle: Maekawa [18]. Stripe triangle: Seo et al. [19]. Stripe square: Wang et al. [20]. Stripe rhombus: Dai et al. [21]. Half circle: Fan et al. [22]. Half triangle: Mohanmmadi et al. [23]. Half square: Unruh & Katz [24]. Half rhombus: Ferrari et al. [25]. Star: Sebil et al. [26] Table 4 Fitting parameters for Eq. (2) and the correlation coefficient absolute deviation (AAD) of measured data in this study is 0.063 K. Fig. 8 indicates that the difference between the measured data obtained in this study and the calculated values by the Clausius-Clapeyron equation is within 0.2 K. Furthermore, because the average absolute deviation (AAD) is less than 0.1 K, measured data fits well with the Clausius-Clapeyron equation. Fig. 9 shows the scatter of the three-phase equilibrium conditions in carbon dioxide + water system measured in this study with those reported in the previous studies. From this figure, we evaluated the even more precise external consistency of the measured data in this study with the data from the previous studies. T calc is calculated with the interpolation of the three-phase equilibrium condition data measured in this study by using Eq. (2). In the calculations, different fitting parameters are used depending on the pressure (p < 2 MPa or not). Dash lines represent twice the uncertainty of the temperature measurement in this study. In other words, the data that exist within the region between dash lines are consistent within uncertainty with the measured Fig. 9 The scatter of the L + H + V three-phase equilibrium conditions in the carbon dioxide hydrate forming system. Empty circle: Adisasmito et al. [10]. Empty triangle: Yasuda et al. [11]. Empty square: Nema et al. [12]. Empty rhombus: Chun et al. [13]. Filled circle: Ohgaki et al. [14]. Filled triangle: Mooijer-van den Heuvel [15]. Filled square: Fan and Guo [16]. Filled rhombus: Ng and Robinson [17]. Stripe circle: Maekawa [18]. Stripe triangle: Seo et al. [19]. Stripe square: Wang et al. [20]. Stripe rhombus: Dai et al. [21]. Half circle: Fan et al. [22]. Harf triangle: Mohanmmadi et al. [23]. Harf square: Unruh & Katz [24]. harf rhombus: Ferrari et al. [25]. Star: Sebil et al. [26]. Plus: Englezos & Hall [27]f. Dash line: twice the uncertainty of the temperature measurements (± 0.2 K) data of this study. Fig. 9 reveals that the data measured in this study (cross symbols) are consistent with data reported by Yasuda & Ohmura (empty triangle symbols) at 1 MPa < p < 1.5 MPa, Wang et al. (stripe square symbols) at 1.5 MPa < p < 2.5 MPa, Adisasmito et al. (empty circle symbols) at 2.5 MPa < p < 4 MPa, Dai et al. (stripe rhombus symbols) at 4 MPa < p < 4.5 MPa. Furthermore, the data in this study are partially consistent with the data from other previous studies. As described above, the phase equilibrium conditions measured in this study are consistent with the data from several previous studies in the pressure range of 1 MPa < p < 4.5 MPa.

Conclusion
The newly L + H + V three-phase equilibrium conditions in the carbon dioxide hydrate forming system were measured at twenty temperature conditions from 271.9 to 282.7 K. The six pairs of these data measured under equivalent conditions were consistent within mutual uncertainties. To determine fitting parameters, the Clausius-Clapeyron equation was applied to the obtained data. The differences between the calculated temperature and pressure conditions from the fitting parameters and the measured phase equilibrium conditions were within twice the uncertainty of temperature measurement. The data obtained in this study are consistent with those reported by Yasuda  Funding Not applicable.

Data Availability
The data and materials used in this study are available upon request to the corresponding author.

Declarations
Compering Interest Not applicable.