Investigation of Volume Changes in Carbon Dioxide Hydrate Formation Process

Gas hydrate formation is a new technology to uptake carbon dioxide. In the present work, the kinetics of changes in the volume of unreacted water, the formed carbon dioxide hydrate, and also the unreacted gas inside the reactor were investigated with the passage of time. Experiments were performed in a stagnant 169 cm 3 double-walled reactor at a temperature of 275.15 K and a pressure of 3 MPa. The tests were done by using the isochoric-isothermal method. The results of the experiments showed that the volume of unreacted water decreased with respect to time and the volume of hydrate formed increased. Taking into account the different molar volumes of hydrate formed and the molar volume of reacted water in the test conditions, the changes in gas volume inside the reactor were calculated with the passage of time. The gas volume inside the reactor decreased from 144 cm 3 at the beginning of the process to 141.62 cm 3 at the end of the reaction. By decreasing the pressure during carbon dioxide hydrate formation process, the amount of hydration number increased from 6.047 mol/mol to 6.109 mol/mol. doi : 10.5829/ijee.2024


A B S T R A C T
Gas hydrate formation is a new technology to uptake carbon dioxide.In the present work, the kinetics of changes in the volume of unreacted water, the formed carbon dioxide hydrate, and also the unreacted gas inside the reactor were investigated with the passage of time.Experiments were performed in a stagnant 169 cm 3 double-walled reactor at a temperature of 275.15K and a pressure of 3 MPa.The tests were done by using the isochoric-isothermal method.The results of the experiments showed that the volume of unreacted water decreased with respect to time and the volume of hydrate formed increased.Taking into account the different molar volumes of hydrate formed and the molar volume of reacted water in the test conditions, the changes in gas volume inside the reactor were calculated with the passage of time.The gas volume inside the reactor decreased from 144 cm 3 at the beginning of the process to 141.62 cm 3 at the end of the reaction.By decreasing the pressure during carbon dioxide hydrate formation process, the amount of hydration number increased from 6.047 mol/mol to measurements indicate an increase in the average annual surface temperature of 0.3 to 0.6°C over the past 159 years [1].If this upward trend in temperatures continues, the detrimental effects of global warming on the world's population will become unavoidable.Consequently, concerns about the escalating levels of carbon dioxide and other greenhouse gases in the atmosphere have prompted global apprehension, leading to international initiatives such as the Kyoto Protocol and the Paris Agreement.The primary sources of carbon dioxide emissions in the atmosphere include thermal power generation, oil and natural gas refining and processing, cement production, the iron and steel industries, and petrochemical industries [2].Therefore, it is crucial to remove this gas from the emissions of industrial complexes to mitigate the negative impacts of climate change.The hydrate formation process is among the latest methods used for carbon dioxide absorption.Gas hydrates are crystal structures resembling ice, which form when they encounter low-density gases like methane, ethane, or carbon dioxide at low temperatures and high pressures [3][4][5][6][7][8].Figure 1 illustrates the hydrogen bonding between water molecules.
In recent years, the potential benefits of gas hydrates have garnered attention, leading to numerous studies in the field [9][10][11][12][13][14][15][16][17][18][19][20][21].However, due to the high costs and timeconsuming nature of the hydrate formation process, none of the proposed processes utilizing hydrate formation have been implemented on an industrial scale [22][23][24][25][26][27]. Figure 2 presents a real image of methane hydrate formed in a laboratory reactor.SI, SII, and SH are three prevalent structures of gas hydrates.These structures exhibit distinct shapes, including variations in the types and numbers of cavities they possess.The SI structure, also known as structure I, is the most common type of gas hydrate.It consists of cages formed by interconnected water molecules, which enclose the guest gas molecules.These cages can be further classified into large, small, and intermediate sizes, depending on the number of water molecules they comprise.The SII structure, or structure II, is characterized by a more complex arrangement.It contains two types of cages: large and small.The large cages are similar to those in the SI structure, while the small cages are formed by linking water molecules through facesharing.The SH structure, or structure H, is relatively less common but still significant.It consists of hexagonalshaped cages, unlike the cubic cages found in SI and SII structures.These hexagonal cages offer a unique configuration for hosting gas molecules.Figure 3 provides a visual representation of these structures, highlighting their unique characteristics.
Due to the difference between the molar volume of the formed hydrate and the molar volume of the reacted water, the volume of gas inside the reactor changes by time in the process of gas hydrate formation.In this research, we calculate the volume of unreacted water and volume of hydrate formation versus the time and gas volume changes inside the reactor, in the process of carbon dioxide hydrate formation.

Materials
To prepare the solutions, distilled water was used.Carbon dioxide, with a purity of 99.99 mol%, was supplied by Sepehr Kavian Gas company.

Apparatus
Figure 4 shows the schematic diagram illustrating the apparatus utilized in the current study.The used appartus  in this research is fully described in our previous research [10].Th used apparaus is equipped with a thermometer (PT100) and a pressure transducer.The standard uncertainties, u, of measured temperature and pressure are u(T) = 0.1 K and u(P) = 5 kPa, respectively.

RESULTS AND DISCUSSION
To ensure the accuracy of the pressure and temperature tranducers, we measured the three-phase equilibrium data of carbon dioxide hydrate formation using an isochoric pressure-search method [29][30][31][32][33].The measured equilibrium data in this work and the data reported by Vlahakis and coworkers [34] are depicted in Figure 5.
As can be seen in Figure 5, the measured data in this work are in a good agreement with the data reported by Vlahakis and coworkers [34] that confirm the accuracy of our pressure and temperature tranducers.
The measured equilibrium data of carbon dioxide hydrate formation are tabulated in Table 2.
In each kinetic experiment, the hydrate formation cell is initially rinsed with water, followed by a rinse with distilled water.The vacuum pump is employed to remove the air from the reactor, and subsequently, 25 cm 3 of solution is injected into the cell.Using a temperature bath, the reactor is set to a temperature of 275.15 K.The hydrate-forming gas, in this case carbon dioxide, is  introduced into the cell until the desired pressure is reached.It is important to position the reactor horizontally and refrain from using the stirrer method .
The equilibrium system required sufficient time, the process of hydrate formation commences, leading to a decrease in system pressure until it reaches a stable condition where pressure changes inside the reactor are minimal (0.05 h/bar).The quantity of gas consumed during the hydrate formation process is determined through calculations using Peng-Robinson equation of state [35].Throughout the hydrate formation process, the computer records the temperature and pressure of the system at intervals of 20 seconds.
The physical reaction between water and gas molecules (for example, carbon dioxide to form hydrate can be shown as follows [36]: where M represents the hydration number.Simple gases methane and carbon dioxide form the sI hydrate structure in absence of thermodynamic additives.The hydration number is a parameter that depends on the filling of large and small cavities.The hydration number for structure sI can be calculated from the following equation [10]: In this relation, θL and θS are the occupancy fractional of large (L) and small (S) cavities, respectively, which are calculated using the Languire absorption theory as stated as follows [10].
where Ci is the Langmuir constant of carbon dioxide molecules for type i cavities and fCO2 is the fugacity of carbon dioxide in the gas phase, which is calculated using Peng-Robinson equation of state.The subscript i also represents the type i cavity.
As the solution and gas hydrate have different molar volumes, the volume of gas within the cell decreases during the formation and growth of the gas hydrate.Consequently, the instantaneous volume of gas inside the cell, denoted as Vt, can be determined using the following equation: which are Vcell and Vs0 are cell volume (169 cm 3 ) and initial volume of feed solution (25 cm 3 ), respectively.Also, VRWt and VHt represent the volume of reacted water and the volume of hydrate produced, respectively.The subscript t in the above equation indicates that these parameters are a function of time.The volume of reacted water is calculated from the following equation: The amount of calculated hydration numbe during hydrate formation are shown in Figure 6.
As shown in Figure 6, as the hydrate formation process proceeds, the amount of hydration number increases.This can be due to the pressure reduction due to the carbon dioxide hydrate growth.
Figure 7 displays the temporal variations in volume for both the unreacted solution and the hydrate formed within the reactor.It is evident that as time progresses, the volume of unreacted water within the reactor diminishes, while the volume of the formed hydrate increases.
At the onset of the process, the volume of unreacted water inside the reactor measures 25 cm 3 , which reduces to 15.8 cm 3 by the conclusion of the process.Additionally, the volume of the formed hydrate at the end of the process amounts to 11.57 cm 3 .
Figure 8 illustrates the variations in the volume of unreacted carbon dioxide gas within the reactor over time.This figure demonstrates the implementation of an advanced algorithm, as introduced by Mohammadi et al. [36], to track the changes in gas volume within the reactor as time elapses.It is evident from the figure that the volume of unreacted gas inside the reactor steadily decreases with respect to time.The observed phenomenon can be attributed to the disparity between the molar volume of the formed hydrate and the molar volume of the reacted water.As the molar volume of the formed hydrate exceeds that of water, the growth of the hydrate with respect to time leads to a reduction in the volume of the gaseous space within the reactor.Experimental results from a fixed horizontal reactor support this observation, revealing a decrease in gas volume from 144 cm 3 at the start of the process to 141.62 cm 3 .

CONCLUSION
This study aimed to investigate the kinetics of volume changes in unreacted water, formed hydrate, and unreacted gas within the reactor with respect to time.Experimental results indicated a decrease in the volume of unreacted water and an increase in the volume of formed hydrate as time progressed.Considering the varying molar volumes of the formed hydrate and reacted water under the experimental conditions, changes in gas volume within the reactor were calculated with respect to time.The gas volume inside the reactor decreased from an initial value of 144 cm 3 to 141.62 cm 3 at the end of the reaction.

Figure 3 .
Figure 3.The shape of the conventional structures of gas hydrates

Figure 4 .
Figure 4. Schematic diagram of the experimental apparatus used for the kinetic studies

Figure 5 .
Figure 5.The three-phase equilibrium data of carbon dioxide hydrate formation: ◆, this work; □, pure carbon dioxide

Figure 6 .Figure 7 .
Figure 6.The amount of calculated hydration number during carbon dioxide hydrate formation process

Figure 8 .
Figure 8. Changes in the volume of unreacted carbon dioxide inside the reactor 6.109 mol/mol.

Table 2 .
The measured equilibrium data of carbon dioxide hydrate formation