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A review on hydrate composition and capability of
thermodynamic modeling to predict hydrate pressure
and composition
Saheb Maghsoodloo Babakhani, Baptiste Bouillot, Son Ho-Van, Jérome
Douzet, Jean-Michel Herri
To cite this version:
Saheb Maghsoodloo Babakhani, Baptiste Bouillot, Son Ho-Van, Jérome Douzet, Jean-Michel Herri. A
review on hydrate composition and capability of thermodynamic modeling to predict hydrate pressure
and composition. Fluid Phase Equilibria, Elsevier, 2018, 472, pp.22-38. 10.1016/j.fluid.2018.05.007.
hal-01807219
1 A review on hydrate composition and capability of thermodynamic 2 modeling to predict hydrate pressure and composition 3 Saheb Maghsoodloo Babakhani*, Baptiste Bouillot, Son Ho-Van, Jérôme Douzet, Jean-Michel 4 Herri 5 Ecole des Mines de Saint-Etienne, SPIN, CNRS 5307, LGF, F-42023 Saint-Etienne, France 6 * Corresponding author: saheb.m@emse.fr 7 Keywords: gas hydrates, hydrate composition, thermodynamics, phase equilibria, modeling
9 Abstract 10 Gas hydrates are widely considered to be a crucial topic in oil and gas industries and attracting 11 significant research due to potential applications such as gas storage, separation as well as water 12 desalination. While the guest composition of hydrate phase is vital, due to the experimental 13 difficulties in measuring hydrate composition, very little applicable information is available in the 14 literature. Paradoxically, this is true, in spite of that; completing an experimental database on 15 hydrate composition could have a significant impact on the processes design and modeling. 16 Moreover, this should provide fundamental knowledge of kinetic effects as well as clarifying 17 thermodynamic equilibrium. Hence, this paper was planned with the intent to fill in the gaps, 18 classify and offer an overview of experimentally derived data on hydrate composition for 19 literature. In addition, a thermodynamic model based on the van der Waals and Platteeuw 20 approach and Kihara potential was utilized to simulate the hydrate composition along with 21 equilibrium pressure. 22 Previous experimental data shows that guest distribution in hydrate phase depends noticeably on 23 the guest composition in vapor phase. In addition, composition of larger molecules, such as 24 propane or butane, in the hydrate phase, is notably higher than in vapor phase. Our simulation 25 results demonstrated that the hydrate composition data from direct measurement (microscopic 26 tools) have been well evaluated by the thermodynamic model. Nevertheless, when structural 27 transition can occur in a system, the thermodynamic model is no longer accurate. In the case of 28 indirect measurements, the thermodynamic model usually predicts well the hydrate composition. 29 Nonetheless, its capability does vary with differing hydrate composition and equilibrium 30 pressure, to the extent that in some cases, it completely fails to predict hydrate composition. This 31 could be due to kinetic effects on the enclathration of guest molecules during the crystallization, 32 errors in experimental techniques to measure the hydrate composition or the model parameters 33 like Kihara potential are not properly applied. Finally, these observations show that more reliable 34 experimental database is needed to study the evolution of guest distribution in hydrate phase and 35 some enhancements are required for the standard thermodynamic model.
70 Table 1. The differences between three structures of gas hydrates [12]
Hydrate structures sI sII sH
Shape Cavity (^) Small Large Small Large Small Medium Large Description (^) 512 51262 512 51264 512 435663 51268 Number per unit cell (mi) 2 6 16 8 3 2 1 Average cavity radius (Å) (^) 3.95 4.33 3.91 4.73 3.91 4.06 5. Coordination number a^ 20 24 20 28 20 20 36 (a) The number of oxygen atom per cavity
72 3. Thermodynamic modeling 73 At thermodynamic equilibrium, the chemical potential of each phase must be the same. In the 74 case of gas hydrates, based on the classical van der Waals and Platteeuw model [55], liquid- 75 hydrate equilibrium is expressed by defining a metastable phase β, corresponding to the empty 76 hydrate: ∆𝜇𝑊 𝐿−𝛽 = ∆𝜇𝑊 𝐻−𝛽 77 (1) 78 The left hand side of equation 1 is the difference between chemical potential of water in liquid 79 and β phase and the right hand side is the difference between chemical potential of water in 80 hydrate and β phase. 3.1. Description of ∆𝝁𝑾 𝑳−𝜷
82 The difference between chemical potential of water in liquid phase and β phase can be described 83 by classical thermodynamic using Gibbs-Duhem equation. It can be rewritten as follow [14]: ∆𝜇𝑊 𝐿−𝛽 84 = 𝑇 ∆𝜇𝑊𝐿−𝛽| 𝑇^0 𝑃^0 𝑇^0
- (𝑏𝑃,𝑊 𝐿−𝛽 𝑇^0 − ∆𝐶𝑝,𝑤 𝐿−𝛽 | 𝑃^0 𝑇^0 ) − 𝑇𝑙𝑛 𝑇 𝑇^0
1 2 𝑏𝑃,𝑊 𝐿−𝛽 𝑇(𝑇 − 𝑇^0 ) + (∆ℎ𝑊,𝑚 𝐿−𝛽 | 𝑃^0 𝑇^0 85 + 𝑇^0 (𝑏𝑃,𝑊 𝐿−𝛽 𝑇^0 − ∆𝐶𝑝,𝑤 𝐿−𝛽 | 𝑃^0 𝑇^0 ) − 1 2 𝑏𝑃,𝑊 𝐿−𝛽 𝑇^0 2 ) (1 − 𝑇 𝑇^0 ) + ∆𝑣𝑊,𝑚 𝐿−𝛽 | 𝑇^0 86 (𝑃 − 𝑃^0 ) − 𝑅𝑇𝑙𝑛𝑥𝑊𝐿^ (2) where T^0 =273.15K and P^0 =0 are the reference temperature and pressure, respectively. ∆𝑣𝑊,𝑚 𝐿−𝛽 87 , ∆𝐶𝑝,𝑤 𝐿−𝛽 and 𝑏𝑃,𝑊 𝐿−𝛽 88 are thermodynamic properties of water in liquid phase and β phase and they were calculated by Sloan and Koh [12]. ∆ℎ𝑊,𝑚 𝐿−𝛽 and ∆𝜇𝑊 𝐿−𝛽 89 are microscopic parameters of 90 hydrates and regrettably there are different values correspond to each author. Based on a previous 91 study of our team, it was concluded that the values from Handa and Tse are the best set for
92 modeling gas hydrates equilibrium [14,56]. All parameters are listed in Table 2. More details can 93 be found in the previous works of our group [14,47,57,58].
94 Table 2. Thermodynamic properties of hydrates
Parameters Unit Structure I Structure II ∆ℎ𝑊^ 𝐿−,𝑚𝛽^ J/mol - 5080 - 5247 ∆𝑣𝑊^ 𝐿−,𝑚𝛽^10 -^6 m^3 /mol 4.5959 4. ∆𝐶𝑝^ 𝐿,𝑤−𝛽^ J/mol/K^ - 38.12^ - 38. 𝑏𝑃^ 𝐿,−𝑊𝛽^ J/mol/K^2 0.141^ 0. ∆𝜇𝑊^ 𝐿−𝛽^ J/mol^1287
3.2. Description of ∆𝝁𝑾 𝑯−𝜷
97 From van der Waals and Platteeuw approach, statistical thermodynamics is used to express ∆𝜇𝑊 𝐻−𝛽 98 : ∆𝜇𝑊 𝐻−𝛽 99 = 𝑅𝑇 ∑ 𝑣𝑖 𝑖ln(1 − ∑ 𝜃𝑗 (^) 𝑗𝑖) (3) 100 where 𝑣𝑖 is the number of cavities type i per mole of water. 𝜃𝑗𝑖^ is the occupancy factor of 101 molecule j in the cavity i. The occupancy factor can be described by considering the analogy 102 between gas adsorption in the three dimensional hydrate structures and two-dimensional 103 Langmuir adsorption [12,59]. 𝜃𝑗𝑖^ = 𝐶𝑗𝑖𝑓𝑗(𝑇,𝑃) 1+∑ 𝐶𝑗 𝑗𝑖𝑓𝑗(𝑇,𝑃) 104 (4) 105 where 𝑓𝑗 (𝑇, 𝑃) is the fugacity of guest molecule j at desire temperature and pressure. The value of 106 fugacity can be calculated by assuming equilibrium with a gas phase. Therefore, a standard 107 equation of state, such as Soave-Redlich-Kwong (SRK), can be used as fugacities are similar in 108 all phases, including vapor phase. 𝐶𝑗𝑖^ is the Langmuir constant of guest molecule j in the cavity 109 type i. The Langmuir constant depends on the interaction potential between the trapped guest 110 molecules and the surrounding water molecules cage, and for spherical guest-cages potentials can 111 be expressed as follows: 𝐶𝑗𝑖^ = 4𝜋 𝑘𝑇 ∫ exp(− 𝑤(𝑟) 𝑘𝑇 )𝑟^2 𝑑𝑟 ∞ 112 0 (5) 113 where w(r) is the potential interaction between the guest molecule and the cavity based on the 114 distance between the gas and water molecule in the structure ( r ). In our study, the potential 115 interaction was calculated based on the Kihara parameters as following: 𝑤(𝑟) = 2𝑧𝜀 [ 𝜎^12 𝑅^11 𝑟 (∆^10 + 𝑎 𝑅 ∆^11 ) − 𝜎^6 𝑅^5 𝑟 (∆^4 + 𝑎 𝑅 116 ∆^5 )] (6)
134 Figure 1. Procedure for calculating gas hydrate equilibrium pressure and composition
135 The average deviations for pressure and hydrate composition have been calculated based on 136 equations 9 and 10, respectively. 𝐴𝐴𝐷𝑝% = 100 𝑁 ∑ (^) (| 𝑃𝑖𝑒𝑥𝑝−𝑃𝑖𝑝𝑟𝑒 𝑃𝑖𝑒𝑥𝑝^ 137 𝑁𝑖 |) (9) 𝐴𝐴𝐷𝑐 = 1 𝑁 ∑ (|𝑥𝑖 𝑒𝑥𝑝 − 𝑥𝑖 𝑝𝑟𝑒 138 𝑁𝑖 |) (10) 139 where i is equilibrium point, N total number of equilibrium points, P pressure, x hydrate 140 composition, exp experimental data and pre prediction results. AADp and AADc are average 141 absolute deviation for pressure and composition, respectively.
142 All the thermodynamic modelling section has been implemented in our in-house software, 143 GasHyDyn. This software has shown a very good capability of liquid-hydrate equilibrium 144 predictions [14,57], and will be used to discuss the experimental results for both pressure and 145 hydrate composition. A photo from GasHyDyn environment with complementary information 146 summarizing the procedure of submitting a calculation has been added to the Supporting 147 Information document (Appendix A). 148 Nota Bene: the hydrate structure for modeling was chosen based on the statement of each 149 research. Unfortunately, there were some cases that the authors did not provide the structure. 150 Therefore, we simulated their experimental data for both structures I and II. Consequently, the 151 structure which agreed better with the simulation results was chosen. 152 4. Hydrate composition in literature and model comparison 153 Despite countless works on equilibrium pressure and temperature of mixed gas hydrates, to the 154 best of our knowledge, there are still few studies on the hydrate composition which depends on 155 the pressure, temperature and gas phase composition. Thanks to gas chromatography, the 156 composition of the gas phase can be easily measured, but solid phase analysis is still challenging, 157 often leading to experimental errors. In addition, some researchers studied the hydrate 158 composition of gas mixtures by different methods making them exceedingly difficult to compare. 159 Hence, in the present work, studies providing hydrate composition in open literature were 160 collected and presented. Moreover, the capability of a thermodynamic model to predict hydrate 161 pressure and composition was evaluated. This should be noted that there were some studies on 162 the hydrate composition of gas mixtures that do not furnish exact values of hydrate composition. 163 Sometimes, only figures were shown and quantitative data were not available. In this section, the 164 collected data from open literature is categorized based on their methods of hydrate composition 165 measurements. 166 4.1. Dissociation of whole hydrate phase 167 One of the first systematic reports on the mixed hydrate composition was carried out by Jhaveri 168 and Robinson [62]. They studied the gas hydrate equilibrium curves of methane-nitrogen mixture 169 as well as the guest composition in gas and hydrate phases. They introduced gas mixture and 170 water inside a batch reactor at a pressure 25% more than the equilibrium pressure at a desired 171 temperature. After completion of hydrate formation, the gas phase was analyzed 172 chromatographically. The gas was then removed from the reactor and the hydrate crystals 173 dissociated. The decomposed gas was analyzed to obtain the hydrate composition. They 174 measured hydrate composition at three temperatures 273.2, 277.4 and 279.8K for various ranges 175 of pressure and gas compositions. Their results are illustrated in Figure 2. Clearly, at a constant 176 temperature, by increasing the molar composition of nitrogen in the gas phase, the equilibrium 177 pressure increased. Since the hydrate equilibrium pressure of nitrogen at a desired temperature is
277.4 5.200 6.839 I 0.440 0. 560 0. 180 0. 820 0. 138 0. 862
277.4 8.110 9.575 I 0.630 0. 370 0. 310 0. 690 0. 262 0. 738
277.4 10.340 12.286 I 0.740 0. 260 0. 470 0. 530 0. 378 0. 622
277.4 12.060 13.628 I 0.780 0. 220 0. 560 0. 440 0. 433 0. 567
277.4 13.320 21.582 I 0.925 0. 075 0. 810 0. 190 0. 734 0. 266
277.4 14.590 22.950 I 0.940 0. 060 0. 860 0. 140 0. 779 0. 221
277.4 16.210 29.486 I 1.000 0. 000 1. 000 0. 000 1. 000 0. 000
279.8 5.140 5.161 I 0.000 1. 000 0. 000 1. 000 0. 000 1. 000
279.8 7.140 7.751 I 0.350 0. 650 0. 091 0. 909 0. 102 0. 898
279.8 8.370 9.170 I 0.460 0. 540 0. 224 0. 776 0. 155 0. 845
279.8 15.550 16.516 I 0.750 0. 250 0. 550 0. 450 0. 404 0. 596
279.8 20.670 21.253 I 0.840 0. 160 0. 680 0. 320 0. 549 0. 451
279.8 25.230 27.054 I 0.914 0. 086 0. 802 0. 198 0. 715 0. 285
279.8 32.420 37.997 I 1.000 0. 000 1. 000 0. 000 1. 000 0. 000
AADp 16.32% AADc 0.
186 The results of thermodynamic simulation for hydrate pressure and composition are detailed in 187 Table 4. At 273.2 K and 279.8 K, the equilibrium pressures were successfully predicted. 188 Nonetheless, the equilibrium pressures at 277.4 K for nitrogen compositions more than 90% mole 189 fraction (in gas phase) were poorly simulated (sI). As nitrogen forms sII, we suspected a phase 190 transition in this case. Hence, the experimental data were also simulated by considering sII. The 191 results revealed that sII simulations were also unsuccessful to predict the equilibrium pressures 192 for the 277 K isotherm at high concentrations of nitrogen in the mixture of CH 4 /N 2. This might be 193 due to whether the co-existence of sI and sII at this condition (which cannot be predicted by the 194 model as it is implemented in our software) or the experimental measurement uncertainties. 195 The hydrate composition predictions were slightly different. The simulation results at low and 196 high percentages of nitrogen in the hydrate phase agreed satisfactorily with the experimental data. 197 But when there is no significant difference between the compositions of methane and nitrogen, 198 the simulation results deviated from experimental. Still, the average absolute deviation of hydrate 199 composition was less than 0.07 in mole fraction. 200 Kawasaki et al. [63] studied the guest content in hydrate phase for a gas mixture of methane, 201 ethane, propane and iso-butane with initial molar concentrations 0.885, 0.046, 0.054 and 0.015, 202 respectively. They used the same procedure as Jhaveri and Robinson [62] by removing the gas 203 and dissociating the hydrate to measure the hydrate composition at two different temperatures, 204 274.15 and 278.15 K. The experimental and simulation results are presented in Table 5.
205 Table 5. The gas composition in different phases at 3MPa. Uncertainties were not provided.
Gas
T=274.15 K T=278.15 K
Gas and hydrate phase compositions Gas and hydrate phase compositions
Gas (exp) Hydrate (exp) Hydrate (Pre) Gas (exp) Hydrate (exp) Hydrate (Pre) Methane 0.987 0.760 0. 827 0.979 0.702 0. 784 Ethane 0.011 0.089 0. 031 0.017 0.104 0. 034 Propane 0.002 0.117 0. 141 0.004 0.150 0. 181 iso-Butane 0.0 0.034 NA 0.0 0.044 NA
207 The authors remarked that all i-butane molecules concentrated in the hydrate phase, irrespective 208 of the temperature. They also considered that the concentration of heavier hydrocarbon in hydrate 209 phase at 278.15 K is higher at 274.15 K. Moreover, the deviation of simulation results for the 210 hydrate composition of methane, ethane and propane were 0.074, 0.064 and 0.027, respectively. 211 The deviations between the experimental and prediction values could be due to uncertainties in 212 the experimental procedure. In fact, Kawasaki et al. removed the gas mixture from the reactor 213 after hydrate formation to measure hydrate composition. Hence, the hydrate phase could be 214 dissociated during the gas removing step due to the pressure drop, leading to the measurement 215 uncertainties. 216 Kang et al. [64] measured the hydrate composition of CO 2 -N 2 mixture at three isotherms of 217 vapor-hydrate equilibrium condition. After hydrate formation, they purged the gas outside the 218 cell and dissociated the hydrate by increasing temperature. Figure 3 presents the equilibrium 219 pressure versus nitrogen composition in the gas phase at H-V equilibrium condition for three 220 isotherms. Our simulation results are also shown by dash lines in the figure. The simulation of 221 hydrate composition is detailed in Table 6 as well as the experimental results.
277. 0 5. 12 5. 40 I 0. 39 0. 61 0. 89 0. 11 0. 85 0. 15
277. 0 11. 71 11. 30 I 0. 18 0. 82 0. 54 0. 46 0. 62 0. 38
277. 0 15. 15 14. 81 I 0. 12 0. 88 0. 35 0. 65 0. 49 0. 51
277. 0 18. 74 19. 56 I 0. 07 0. 93 0. 19 0. 81 0. 31 0. 69
277. 0 23. 50 28. 37 I 0. 00 1. 00 0. 00 1. 00 0. 00 1. 00
277. 0 1. 91 1. 99 I 1. 00 0. 00 1. 00 0. 00 1. 00 0. 00
277. 0 2. 54 2. 38 I 0. 85 0. 15 0. 98 0. 02 0. 98 0. 02
280. 0 2. 74 2. 86 I 1. 00 0. 00 1. 00 0. 00 1. 00 0. 00
280. 0 3. 52 3. 57 I 0. 83 0. 17 0. 98 0. 02 0. 98 0. 02
280. 0 4. 14 4. 35 I 0. 70 0. 30 0. 96 0. 04 0. 95 0. 05
280. 0 4. 95 5. 29 I 0. 59 0. 41 0. 94 0. 06 0. 92 0. 08
280. 0 8. 09 8. 50 I 0. 39 0. 61 0. 86 0. 14 0. 83 0. 17
280. 0 14. 64 13. 50 I 0. 25 0. 75 0. 64 0. 36 0. 68 0. 32
280. 0 20. 29 18. 39 I 0. 17 0. 83 0. 45 0. 55 0. 55 0. 45
280. 0 26. 09 25. 74 I 0. 09 0. 91 0. 22 0. 78 0. 35 0. 65
280. 0 31. 58 38. 81 I 0. 00 1. 00 0. 00 1. 00 0. 00 1. 00
AADp 6.5% AADc 0.
229 As Figure 3 and Table 6 indicate, the thermodynamic model acceptably predicted the equilibrium 230 pressure (average deviation 6.5%). The hydrate composition simulation could be categorized in 231 two parts. The first part is when carbon dioxide was dominant in the hydrate phase. In this case, 232 the simulation results were well predicated (average absolute deviation for 13 equilibrium points 233 was 0.016 mole fraction). While nitrogen was dominant in the hydrate phase, the average 234 absolute deviation was 0.071 in mole fraction. 235 4.2. Material balance and volumetric properties evaluated from equation of state 236 Ohgaki et al. investigated the phase equilibrium of carbon dioxide-methane hydrate at 280.3 K 237 [65]. They obtained the guest composition in gas, liquid and hydrate phases at isothermal 238 conditions in a batch reactor. Their experimental procedure is briefly described as follows: They 239 injected separately carbon dioxide and methane to the reactor. Pure water was then introduced to 240 the reactor. The amount of each material was weighed. Thanks to a gas chromatograph, they 241 determined the gas composition of carbon dioxide and methane at equilibrium temperature and 242 pressure. The solubility of carbon dioxide and methane in water was calculated based on Henry 243 constants. They assumed that the general formula for mixed carbon dioxide-methane hydrate is as 244 follows: 245 𝑧𝐶𝑂 2. (1 − 𝑧). 𝑞𝐻 2 𝑂 (11) 246 where z is the mole fraction of carbon dioxide in hydrate phase and q is the hydration number at 247 ideal condition. They also hypothesized that the molar volume of hydrate is 130.1 cm^3 /mol [65]. 248 They calculated the volumetric properties from Soave-Redlich-Kwong equation of state or
249 IUPAC recommended equation of state for carbon dioxide and methane [60,65–67]. The hydrate 250 compositions were then calculated by the material balance. 251 Figure 4 shows their experimental results for hydrate phase composition and our simulation 252 results. Furthermore, Table 7 summarizes the experimental and modeling results by details for 253 carbon dioxide-methane hydrate at 280.3 K.
255 Figure 4. Carbon dioxide-methane hydrates phase equilibria at 280.3 K. Experimental [65] and simulation
256 results (sI). Error bars correspond to the standard uncertainty of experimental hydrate composition.
257 Table 7. Experimental results of Ohgaki et al. [65] for methane-carbon dioxide mixture hydrates at 280.3 K
258 and simulation results.
Pexp (MPa) (±0.005) Ppre (MPa) S Gas composition (exp) Hydrate^ composition (exp) (±5%) Hydrate composition (pre) CO 2 CH 4 CO 2 CH 4 CO 2 CH 4
- 04 2. 98 I 1. 00 0. 00 1. 00 0. 00 1. 00 0. 00
- 24 3. 46 I 0. 68 0. 32 0. 84 0. 16 0. 79 0. 21
- 38 3. 55 I 0. 59 0. 42 0. 80 0. 20 0. 72 0. 28
- 60 3. 85 I 0. 49 0. 51 0. 67 0. 33 0. 63 0. 37
- 64 3. 93 I 0. 45 0. 55 0. 69 0. 31 0. 60 0. 40
- 67 3. 93 I 0. 45 0. 55 0. 68 0. 32 0. 60 0. 40
- 71 3. 98 I 0. 43 0. 57 0. 61 0. 39 0. 58 0. 42
273 obtained, several experimental equilibrium points were poorly simulated (for instance 280 K and 274 3.54MPa). Additionally, they reported that CSMGem model was not capable to converge three 275 phase flash calculations in some cases, in comparison, the thermodynamic model had no problem 276 with three phase flash calculations [68].
277 Table 8. Experimental results of Belandria et al. [68] for methane-carbon dioxide hydrates and simulation
278 results.
T (K)
Pexp (MPa) (±0.002) Ppre (MPa)
S
Gas composition (exp) Hydrate composition (exp) (±1%) Hydrate composition (pre) CO 2 CH 4 CO 2 CH 4 CO 2 CH 4
- 6 2. 44 2. 55 I 0. 08 0. 92 0. 10 0. 90 0. 16 0. 84
- 6 1. 84 2. 03 I 0. 35 0. 66 0. 55 0. 45 0. 52 0. 48
- 6 1. 94 2. 12 I 0. 29 0. 71 0. 39 0. 61 0. 46 0. 54
- 6 2. 05 2. 24 I 0. 22 0. 78 0. 29 0. 71 0. 37 0. 63
- 6 1. 51 1. 67 I 0. 63 0. 37 0. 88 0. 12 0. 77 0. 23
- 6 1. 61 1. 77 I 0. 55 0. 46 0. 80 0. 20 0. 71 0. 29
- 2 2. 58 2. 77 I 0. 17 0. 83 0. 34 0. 66 0. 29 0. 71
- 2 2. 77 2. 98 I 0. 09 0. 91 0. 18 0. 82 0. 16 0. 84
- 2 2. 12 2. 33 I 0. 38 0. 62 0. 65 0. 35 0. 56 0. 44
- 2 2. 22 2. 48 I 0. 30 0. 70 0. 59 0. 41 0. 47 0. 53
- 2 2. 40 2. 63 I 0. 23 0. 77 0. 37 0. 63 0. 38 0. 62
- 2 1. 79 1. 96 I 0. 66 0. 34 0. 83 0. 17 0. 79 0. 21
- 2 1. 87 2. 07 I 0. 57 0. 44 0. 75 0. 25 0. 72 0. 28
- 1 2. 81 3. 00 I 0. 18 0. 82 0. 26 0. 74 0. 31 0. 69
- 1 3. 03 3. 12 I 0. 13 0. 87 0. 24 0. 76 0. 24 0. 76
- 1 3. 03 3. 23 I 0. 10 0. 90 0. 24 0. 76 0. 18 0. 82
- 1 2. 32 2. 43 I 0. 41 0. 60 0. 64 0. 36 0. 57 0. 43
- 1 2. 50 2. 70 I 0. 32 0. 69 0. 40 0. 60 0. 48 0. 52
- 1 2. 69 2. 88 I 0. 23 0. 77 0. 31 0. 69 0. 38 0. 62
- 1 1. 99 2. 14 I 0. 67 0. 33 0. 88 0. 12 0. 80 0. 20
- 1 2. 17 2. 26 I 0. 58 0. 42 0. 78 0. 22 0. 73 0. 27
- 1 3. 42 3. 64 I 0. 20 0. 80 0. 23 0. 77 0. 33 0. 67
- 1 3. 63 3. 83 I 0. 14 0. 86 0. 23 0. 78 0. 24 0. 76
- 1 3. 80 3. 95 I 0. 10 0. 90 0. 15 0. 85 0. 19 0. 81
- 1 3. 04 3. 33 I 0. 32 0. 68 0. 46 0. 54 0. 48 0. 52
- 1 3. 32 3. 55 I 0. 23 0. 77 0. 27 0. 73 0. 37 0. 63
- 1 2. 58 2. 77 I 0. 61 0. 39 0. 79 0. 21 0. 74 0. 26
- 2 3. 57 4. 09 I 0. 20 0. 80 0. 27 0. 73 0. 33 0. 67
- 2 4. 49 4. 76 I 0. 15 0. 85 0. 31 0. 69 0. 25 0. 75
- 2 4. 66 4. 90 I 0. 11 0. 89 0. 25 0. 76 0. 19 0. 81
- 2 3. 54 4. 14 I 0. 34 0. 66 0. 73 0. 27 0. 49 0. 51
- 2 4. 11 4. 46 I 0. 24 0. 77 0. 34 0. 66 0. 37 0. 63
280. 2 3. 14 3. 53 I 0. 62 0. 38 0. 86 0. 14 0. 74 0. 26
280. 2 3. 48 3. 75 I 0. 49 0. 51 0. 79 0. 21 0. 64 0. 36
282. 2 5. 77 6. 08 I 0. 11 0. 89 0. 28 0. 72 0. 19 0. 81
284. 2 7. 19 7. 65 I 0. 12 0. 89 0. 11 0. 89 0. 18 0. 82
AADp 7.8% AADc 0.
281 Figure 5. Hydrate composition for methane-carbon dioxide hydrates. Experimental data [68] and simulation
282 results (sI).
283 Belandria et al. also studied the hydrate composition of carbon dioxide-nitrogen mixture using 284 the same method [65,69]. They calculated the guest composition in gas, liquid and hydrate phases 285 based on the material balance and volumetric properties evaluated from equation of state. Table 9 286 details their experimental data and our simulation results. Moreover, Figure 6 illustrates the 287 experimental [69] and simulation results for two isotherms of N 2 /CO 2 binary hydrates.
288 Table 9. Experimental results of Belandria et al. [69] for nitrogen-carbon dioxide mixture hydrates and
289 simulation results.
T (K)
Pexp (MPa) (±0.002) Ppre (MPa) S Gas composition (exp) Hydrate composition (exp) (±1%) Hydrate composition (pre) CO 2 N 2 CO 2 N 2 CO 2 N 2
- 6 2. 03 2. 22 I 0. 62 0. 38 0. 97 0. 03 0. 95 0. 05
298 Figure 6. Hydrate composition for nitrogen-carbon dioxide hydrates at two isotherms. Experimental data [69]
299 and simulation results (sI).
301 4.3. Gas uptake at isobaric equilibrium condition 302 Seo et al. studied the vapor-liquid-hydrate equilibrium conditions of nitrogen-carbon dioxide and 303 methane-carbon dioxide mixtures at isobaric condition [70]. They performed their experiments in 304 a batch reactor by injecting gas mixtures and water by a syringe pump at a desired pressure. Then 305 they decreased the temperature to 5 degrees Kelvin below the hydrate formation temperature. 306 Hydrate formation led to a decrease in hydrate pressure. In order to keep constant the pressure, 307 they recharged reactor by the gas mixtures. Then, they increased the temperature by the rate of 1- 308 2 K per hour. The pressure increased due to hydrate dissociation. Then, the dissociated gases 309 were vented. When only a small amount of hydrate crystals remained in the cell and the pressure 310 was constant, this was considered as the three phase equilibrium [70]. Both their experimental 311 and our simulation results for nitrogen-carbon dioxide mixture are listed and presented in Table 312 10 and Figure 7. Moreover, the results of methane-carbon dioxide mixture are presented in Table 313 11.
315 Figure 7. Pressure-gas composition diagram for nitrogen-carbon dioxide at three isotherms (sI). Experimental
316 data from Seo et al. [70] and our prediction results
317 Table 10. Experimental results of carbon dioxide-nitrogen hydrate equilibrium pressure and composition
318 from Seo et al. [70] and our simulation results. Composition uncertainties were not provided.
T (K)
Pexp (MPa) (±0.01) Ppre (MPa)
S
Gas composition (exp) Hydrate composition (exp) Hydrate composition (pre) CO 2 N 2 CO 2 N 2 CO 2 N 2 274 1. 39 1. 42 I 1. 00 0. 00 1. 00 0. 00 1. 00 0. 00 274 1. 77 1. 74 I 0. 82 0. 18 0. 99 0. 02 0. 98 0. 02 274 2. 35 2. 39 I 0. 60 0. 40 0. 95 0. 05 0. 94 0. 06 274 2. 84 2. 84 I 0. 50 0. 50 0. 93 0. 07 0. 92 0. 08 274 3. 46 3. 57 I 0. 40 0. 60 0. 90 0. 10 0. 87 0. 13 274 7. 24 6. 55 I 0. 21 0. 79 0. 58 0. 42 0. 71 0. 29 274 11. 20 10. 03 I 0. 12 0. 88 0. 34 0. 66 0. 53 0. 47 274 14. 93 14. 91 I 0. 05 0. 95 0. 18 0. 82 0. 28 0. 72 274 17. 93 20. 81 I 0. 00 1. 00 0. 00 1. 00 0. 00 1. 00 277 1. 95 1. 99 I 1. 00 0. 00 1. 00 0. 00 1. 00 0. 00 277 2. 60 2. 38 I 0. 85 0. 15 0. 98 0. 02 0. 98 0. 02 277 3. 38 3. 52 I 0. 59 0. 41 0. 95 0. 05 0. 93 0. 07 277 5. 23 5. 40 I 0. 39 0. 61 0. 89 0. 11 0. 85 0. 15 277 11. 98 11. 30 I 0. 18 0. 82 0. 54 0. 46 0. 62 0. 38
