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Accepted Manuscript Modeling Gas Hydrate-Containing Phase Equilibria for Carbon Dioxide-rich Mixtures using an Equation of State Ju Ho Lee, Sun Hyung Kim, Jeong Won Kang, Chul Soo Lee PII: S0378-3812(15)30131-X DOI: 10.1016/j.fluid.2015.09.026 Reference: FLUID 10768 To appear in: Fluid Phase Equilibria Received Date: 18 May 2015 Revised Date: September 2015 Accepted Date: 10 September 2015 Please cite this article as: J.H Lee, S.H Kim, J.W Kang, C.S Lee, Modeling Gas Hydrate-Containing Phase Equilibria for Carbon Dioxide-rich Mixtures using an Equation of State, Fluid Phase Equilibria (2015), doi: 10.1016/j.fluid.2015.09.026 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 ACCEPTED MANUSCRIPT Modeling Gas Hydrate-Containing Phase Equilibria SC RI PT for Carbon Dioxide-rich Mixtures using an Equation of State a M AN U Ju Ho Leea, Sun Hyung Kimb, Jeong Won Kang*b and Chul Soo Leeb Nuclear Fuel Cycle Process Development Division, Korea Atomic Energy Research Institute, TE D 111, Daedeok-daero 989beon-gil, Yuseong-gu, Daejeon, 305-353, Republic of Korea b Department of Chemical and Biological Engineering, Korea University, 145, Anam-ro, Corresponding author: Tel: 82-2-3290-3305, E-mail: jwkang@korea.ac.kr AC C * EP Seongbuk-gu, Seoul, 136-713, Republic of Korea ACCEPTED MANUSCRIPT ABSTRACT Thermodynamic modeling of phase behaviors for CO2-rich mixtures in gas hydrate forming RI PT conditions are required for the process design in the field of carbon dioxide sequestration and enhanced oil recovery With recent experimental data published for solubility of water in CO2– rich mixtures that are significantly different from those previously published, improved modeling SC studies become necessary for phase equilibria containing gas hydrates In the present study, an equation of state based on hydrogen-bonding nonrandom lattice fluid theory was applied for both M AN U vapor and liquid phases The model for hydrogen-bonding contribution is simplified and a weak hydrogen bonding between water and carbon dioxide was included for improved calculation of mutual solubility Hydrate phase was modeled by van der Waals and Platteeuw method but without guest specific parameters other than Kihara potential parameters The method was TE D applied to single and binary CO2-rich guest mixtures containing methane, ethane, propane, isobutene, nitrogen, hydrogen sulfide and methanol for temperatures above 180 K and pressures below 100 MPa Results of two- and three-phase equilibrium calculations containing gas EP hydrates were found to be comparable with those of CSMGem (Sloan and Koh, Clathrate and Hydrates of Natural Gases, 3rd ed., CRC Press, Boca Raton, FL, 2008) in general and better for AC C water contents in liquid carbon dioxide in equilibrium with gas hydrates KEYWORDS Clathrate Hydrate; Carbon Dioxide; Nonrandom Lattice Fluid with Hydrogen Boding ACCEPTED MANUSCRIPT Introduction Thermodynamic phase behaviors of CO2-rich mixtures in gas hydrate forming conditions are RI PT essential information for flow assurance in the field of carbon dioxide sequestration and enhanced oil recovery Gas hydrates are formed in water-containing mixtures and may result in line plugging depending on process conditions such as temperature, pressure and water contents when guest species are present For a given temperature incipient hydrate forming pressure is SC determined, below which no gas hydrates are formed A mixture at hydrate forming temperature M AN U and pressure conditions may form gas hydrates depending on its water content Water-containing mixtures in pipelines are often in hydrate forming temperature and pressure conditions Thus the practical problem of flow assurance is to determine the limit of water contents below which no gas hydrates are formed The limit turns out to be the water contents of vapor or guest-rich liquid mixtures in equilibrium with gas hydrates Thermodynamic data and models provide such Comprehensive equilibrium conditions TE D information including compositions may be conveniently calculated using CSMGem [1] in which a cubic-type EOS is used for guest-rich phase, a separate equation of state with excess Gibbs function model is used for aqueous phase EP and van der Waals-Platteeuw contribution is included with Kihara potential parameters and AC C temperature and pressure dependent molar volume of empty hydrate for hydrate phase, both of which are specific to guest species Gas hydrate containing phase equilibria involve hydrate (H), vapor (V), water-rich liquid (Lw), guest-rich liquid (Lg) and/or Ice (I) Equations of state have been used for both vapor and liquid phases in recent modeling studies of hydrate containing phase equilibria such as a lattice EOS in Yang et al [2, 3] with association contribution, SAFT in Li et al [4], cubic EOSs in Yoon et al [5] and Bandyopadhyay and Klauda [6] with GE-EOS mixing rules but without association term ACCEPTED MANUSCRIPT and CPA EOSs in Folas et al [7], Youssef et al [8], Haghighi et al [9], Chapoy et al [10, 11], and Karakatsani and Kontogeorgis [12] Yang et al [2, 3] included self-association contribution of water molecules and applied their method to single guests of CO2 [2] and methane [3] in RI PT calculating of two- and three-phase equilibria Li et al [4] included self and cross association contribution of water and alcohol inhibitors and applied their model to incipient hydrate forming conditions of single guest inhibitor systems and mixed guests Chapoy et al [10] introduced SC hydrogen-bonding of CO2 between themselves and with water to obtain good agreements with solubility data in guest-rich liquid in equilibrium with gas hydrates and incipient hydrate forming M AN U conditions over a wide range of temperature from below freezing temperature of water Chapoy et al [11] later applied similar method for CO2-rich mixtures containing impurities and compared with their data Karakatsani and Kontogeorgis [12] found that their calculation significantly underestimated water contents in CO2-rich liquid in equilibrium with gas hydrates TE D assuming no hydrogen-bonding of CO2 In modeling gas hydrate phase van der Waals and Platteeuw model [13] is used for guest inclusion contribution and properties of empty gas hydrates Langmuir constants for van der EP Waals-Platteeuw contribution were calculated using spherical core Kihara potential as done in Yoon et al [5] and Chapoy et al [10] and correlated as done in most other studies Separately AC C correlated Langmuir constants tend to increase the fitting degree of freedom Incipient hydrate forming conditions were modeled in all these studies but limited to single guest systems in some studies [2, 8] Water contents were calculated in Yang et al [2], Folas et al [7], Chapoy et al [11] and Karakatsni and Kontogeorgis [12] Modeling studies rely on consistency of data as well as soundness of model Large uncertainties are suspected in some data sets for hydrate containing H-Lg and Lw-H-Lg phase ACCEPTED MANUSCRIPT equilibrium and became major difficulties in developing a reliable method of calculation Water contents in guest-rich phase provide key information for flow assurance together with incipient hydrate formation condition For example strong pressure dependence of water contents in H-Lg RI PT equilibria for CO2-water mixtures [14] was suspected to have large uncertainties [15] Recent literature data show much weaker pressure dependence [11, 15, 16] Data sets on Lw-H-Lg equilibria tend to show deviations between themselves including the quadruple point data SC Considering that recent modeling studies are less comprehensive and that recent water contents data in CO2-water mixtures are significantly different from existing data, a new M AN U comprehensive modeling study for incipient hydrate forming conditions and water contents in guest mixtures is warranted for CO2-rich mixtures An equation of state approach with association contribution is expected to be applicable to both vapor and liquid phases Guest independent molar volume of empty hydrates as opposed to those used in CSMGem [1] and TE D Langmuir constants calculated from Kihara potential would simplify the nature of model The present study is intended to develop a model and parameter sets for comprehensive and improved phase equilibria of CO2-rich mixtures EP Thermodynamic Relations AC C 2.1 Van der Walls-Platteeuw Model for Gas Hydrate Phase Phase equilibrium calculation requires equality conditions of chemical potential or fugacity for each component in all stable phases When Helmholtz free energy is represented by its canonical variables, chemical potential representation is readily obtained Chemical potential and fugacity may be used interchangeably using relation for a component in fluid phase; ACCEPTED MANUSCRIPT µ − µ iig , f i = exp i RT (1) Eq (1) can be applied to fugacity of water in hydrate phase to give, µ EH − µ Wig , µ WH − µ WEH ∆µ WEH exp f WH = exp W + = RT RT RT RI PT where the second quantity in the numerator denotes chemical potential of pure ideal gas at bar ∆ µ WH exp RT (2) SC The difference of chemical potential in the first exponential term is pressure corrected Gibbs free energy change of forming empty hydrates from pure water at ideal gas state The exponential and molar volume of empty hydrates fWEH = PWEH φWEH exp RT ∫ P PWEH VWEH dP M AN U term represents the fugacity of empty hydrates that is written in terms of saturated vapor pressure (3) The change of chemical potential in the second exponential term on the right hand side of Eq (2) Platteeuw model [13]; TE D denotes the effect of guest inclusion into hydrate lattices that is represented by van der Waals and (4) EP ∆µWH = RT ∑ vi ln 1 + ∑ C j , i f jΠ i j AC C where, vi is the number of i-type cavity per water molecule, f jΠ is the fugacity of guest component j in equilibrium with fluid phase П C j ,i is the Langmuir constant of guest component j in i-type cavity vi and C j ,i depend on hydrate structure types; sI, sII and sH The Langmuir constant is obtained using the spherical core Kihara potential between water and guest molecules ACCEPTED MANUSCRIPT ∞ for r ≤ 2a j 12 σ j − 2a j U (r ) = σ j − 2a j 4ε j r − 2a − r − 2a j j (5) for r ≥ 2a j RI PT where, σ j is the core distance at zero potential, a j is the radius of the spherical core, r is the distance of the guest molecule from the cavity center and ε j represents the maximum attractive SC potential For Kihara potential, McKoy and Sinanoglou [17] obtained the cavity potential for the C j ,i = 4π kT ∫ Ri − a j W (r ) exp− r dr kT R W ( r ) = zi ε j i r = N σ j 12 a j 11 σ j δ 10 δ j − j + Ri Ri Ri a j δ j + δ j Ri −N −N r aj r aj 1 − − − − 1 + Ri Ri R Ri i (6) (7) (8) TE D δ N j M AN U interaction between water and the guest molecule in gas hydrate where, Ri is the radius and zi is the coordination number of i-type cavity All these parameters EP other than Kihara potential parameters are obtained from Sloan and Koh [1] Some investigators introduced volume expansion of gas hydrate due to the inclusion of guest AC C molecules to improve the fugacity representation of water in gas hydrate phase, which leads to molar volume [1] or vapor pressure [6] of empty gas hydrates that depends on guest species These guest dependent corrections lead to empirical correlations and mixing rules for mixed guests In the present study molar volume and vapor pressure of empty gas hydrates are assumed to be independent on guest molecules 2.2 Hydrogen Bonding Nonrandom Lattice Fluid Equation of State (NLF-HB EOS) ACCEPTED MANUSCRIPT Lattice fluid equation of state was proposed Sanchez and Lacombe [18] for vapor and liquid phases by introducing holes in lattices, in which hard body interactions are modeled by Flory athermal lattice chain contribution and attractive interactions by van der Waals contribution The RI PT lattice model was used and improved by various authors and generalized with the addition of association contribution The present equation of state is similar to that used by Yang et al [2, 3] for phase equilibrium calculation for mixtures containing gas hydrates but with simplified SC association contribution proposed in the present study With fitted parameters the equation of state is applicable to both vapor and liquid phases When used for properties calculation the M AN U equation of state was found comparable to cubic EOSs and SAFT [19] The equation of state behaves cubic-like and density roots are readily found Its hydrogen bonding contribution term is very flexible The model equations are briefly given below Fugacity or chemical potential of a fluid phase П that contains N0 holes and Ni molecules of TE D component i with segment number ri is calculated using a hydrogen-bonding nonrandom lattice fluid equation of state used by Yang et al [2] Each molecule interacts with neighboring segment of other molecules with effective surface area qi that is defined by zqi = ( z − 2)ri + , where The EP coordination number z is normally set to 10 Molecules are in located in the stack of imaginary lattices with a unit fixed cell volume VH, which is set to 9.75 cm3/mol For mixtures, mole AC C fractions, average segment number, and average surface area parameter are defined as follows; C xi = N i / ∑ N j j =1 C rM = ∑ x j rj j =1 C qM = ∑ x j q j (9) θi = qi N i / N q (10) j =1 We also define, φi = ri Ni / N r C φ = ∑φ j j =1 where, ACCEPTED MANUSCRIPT C C N r = N + ∑ rj N j Nq = N0 + ∑ q j N j j =1 (11) j =1 For hydrogen-boding species, the numbers of k-type donor sites in a molecule of component i RI PT is denoted as d ik and the number of l-type acceptor sites for component j is denoted as a lj The total numbers of the k-type donor and l-type acceptor are obtained by the following equations, i =1 C N al = ∑ a lj N j j =1 C C ν dk = N dk / ∑ ri N i ν al = N al / ∑ ri N i i =1 (12) i =1 SC C N dk = ∑ d ik N i type acceptor is defined as N kl N ko = N dk − ∑ N kl , N 0l = N al − ∑ N kl l k C C i =1 i =1 M AN U Numbers of proton donors and acceptor sites that are not participating in hydrogen boding are defined as N k and N0l , whereas the number of association pairs between k-type donor and l- (13) C ν ko = Nk / ∑ ri Ni , ν ol = N0l / ∑ ri Ni , ν kl = Nkl / ∑ ri Ni , ν = ∑∑ν kl i =1 k (14) l TE D Then equations for pressure and chemical potential are obtained as follows; PV H z q M z φ − ln(1 − φ ) − β (ε MR + ε MNR ) − νφ = ln 1 − 1 − RT rM EP θ VH q + ri ln 1 − 1 − M φ − ri ln(1 − φ ) + ln i RT RT rM qi ν dk νl zq β r R NR k + i 1 − i (ε MR + ε MNR ) − ε Mi − ε Mi − ∑ a il ln a − ∑ d i ln qi ν k0 ν 0l k k = − ln AC C µ i − µ iigs (15) (16) where β = 1/kT (k is the Boltzmann constant) and C C ε MR = ∑∑θ kθ l ε kl (17) k = l =0 ε MNR = β ∑ ∑ ∑ ∑θ θ θ k l m θ n ε kl (ε kl + 3ε mn − 2ε km − 2ε ln ) R ε Mi = 2∑ θ k ε ki (18) (19) ACCEPTED MANUSCRIPT Table Comparisons of calculated incipient hydrate forming conditions of single guests with experimental data and CSMGem [1] results I-H-V No data I-H-V 178.2-191.3 0.04-0.09 I-H-V 262.2-270.9 1.80-2.40 I-H-V 190.2-262.4 0.08-1.80 Phases T range [K] P range [MPa] 259.0 1.65 [83] 18.0 [84] 0.6 4.8 [85] 14.1 15.6 [86] 10.4 11.5 273.2-286.7 2.64-10.80 1.3 2.7 [83] Lw-H-V 11 290.2-306.7 15.93-110.80 2.1 2.2 [87] Lw-H-V 273.2-294.3 2.65-28.57 1.8 3.0 [88] Lw-H-V 283.2-288.7 7.10-13.11 3.2 1.3 [89] Lw-H-V 13 273.7-285.9 2.77-9.78 0.5 0.8 [85] Lw-H-V 295.7-302.0 33.99-77.50 5.3 6.8 [90] Lw-H-V 10 285.7-301.6 9.62-68.09 1.2 2.8 [91] Lw-H-V 274.6-291.2 1.1 1.0 [29] Lw-H-V 11 273.4-286.4 2.68-10.57 1.2 2.0 [92] Lw-H-V TE D 3.02-18.55 273.3-286.0 2.69-10.04 1.9 3.1 [93] Lw-H-V 275.4-281.2 2.87-6.10 4.7 5.3 [94] Average 1.9 2.5 EP I-H-V M AN U Lw-H-V 260.8-269.3 0.29-0.44 7.8 16.7 [83] I-H-V 263.5-272.0 0.31-0.46 2.1 6.8 [85] I-H-V 200.8-240.8 0.008-0.10 2.0 24.8 [84] Average 3.5 16.8 AC C C2H6 Ref 27.5 SC Average AAD (%) CSMGem NLF-HB 2.8 7.3 RI PT Guest comp CH4 Lw-H-V 11 273.4-287.0 0.545-3.05 5.3 5.9 [83] Lw-H-V 20 273.7-286.5 0.51-2.73 0.5 0.8 [85] Lw-H-V 279.9-287.4 0.97-3.93 5.4 6.6 [28] 40 ACCEPTED MANUSCRIPT 277.6-282.5 0.81-1.55 0.5 0.6 [89] Lw-H-V 10 277.8-287.2 0.85-2.46 2.2 2.4 [95] Lw-H-V 277.5-286.5 0.78-2.62 3.6 3.4 [96] Lw-H-V 278.8-288.2 0.95-3.36 10.1 7.7 [97] Average 287.7-288.4 4.91-6.84 Lw-H-Lg 288.0-290.6 3.33-20.34 Average 20.2 18.2 [83] 8.4 6.3 [26] 14.6 12.6 261.2-272.9 0.10-0.17 11.6 19.9b [85] I-H-V 247.9-262.1 0.05-0.10 12.5 16.0 [98] Average 12.3 17.8 M AN U 273.7-277.1 0.18-0.39 2.5 1.6 [85] Lw-H-V 274.3-277.2 0.24-0.41 9.4 5.5 [28] Lw-H-V 274.3-277.8 0.21-0.46 2.2 2.8 [99] Lw-H-V 274.2-278.4 0.21-0.54 4.3 1.0 [100] Lw-H-V 273.9-278.0 0.19-0.51 2.8 2.3 [29] Lw-H-V 273.7-278.0 0.21-0.51 9.6 5.4 [101] Lw-H-V 10 273.2-278.0 0.17-0.47 2.0 2.7 [102] 0.22-0.51 4.9 5.3 [94] Average 4.1 2.9 TE D Lw-H-V Lw-H-V 274.2-278.2 Lw-H-Lg 278.6-278.8 0.68-2.05 0.09a 0.20a [28] Lw-H-Lg 278.4-278.6 3.87-16.8 0.37a 0.05a [29] Lw-H-Lg 278.6-278.9 0.81-6.12 0.14a 0.32a [27] Average 0.20a 0.21a AC C iC4H10 3.4 I-H-V EP C3H8 3.4 SC Lw-H-Lg RI PT Lw-H-V I-H-V 271.2-272.3 0.10-0.11 2.4 13.5b [103] I-H-V 10 241.4-269.5 0.02-0.09 8.7 21.2 [98] Average 6.4 18.3 41 ACCEPTED MANUSCRIPT 0.11-0.17 4.2 9.1 [104] Lw-H-V 10 273.2-275.1 0.11-0.17 2.0 6.9 [103] Lw-H-V 274.4-274.6 0.13-0.16 7.5 7.1 [94] Average 3.8 8.4 0.27a 0.13a [105] 0.9 3.5 [106] 1.2 5.5 [87] 16.27-35.16 1.9 2.5 [88] Average 1.1 3.5 275.4-275.8 0.23-14.27 Lw-H-V 38 272.1-291.1 14.49-95.85 Lw-H-V 277.6-291.5 24.93-101.97 Lw-H-V 273.2-281.1 M AN U SC Lw-H-Lg I-H-V 256.8-271.8 0.55-1.05 2.7 7.3 [107] I-H-V 182.1-192.5 0.01-0.02 16.8 3.3 [108] Average 8.1 7.2 Lw-H-V 19 273.7-282.9 1.32-4.32 1.5 5.7 [85] Lw-H-V 277.2-281.9 2.04-3.69 1.9 3.9 [109] Lw-H-V 36 271.8-283.2 1.05-4.50 5.0 9.0 [107] Lw-H-V 273.9-282.0 1.38-3.84 1.9 5.9 [99] Lw-H-V 41 272.0-283.2 1.09-4.51 3.7 7.2 [110] Lw-H-V 279.6-282.8 2.74-4.36 1.1 2.0 [26] Lw-H-V 274.3-282.9 1.42-4.37 1.6 4.7 [92] Average 3.4 7.0 AC C H2S RI PT 273.2-275.1 EP CO2 24 TE D N2 Lw-H-V Lw-H-Lg 10 283.2-290.2 4.50-109.50 12.0 11.3 [25] Lw-H-Lg 282.9-283.9 5.03-14.36 19.1 24.5 [26] Average 14.7 16.2 Lw-H-V 283.2-302.7 0.31-2.24 22.4 3.2 [111] Lw-H-V 11 277.6-302.0 0.16-2.07 4.2 6.3 [67] Lw-H-V 13 298.7-300.9 1.61-2.07 12.9 9.1 [112] 42 ACCEPTED MANUSCRIPT ∑T exp − Tcal 3.45-35.07 8.5 5.5 (number of data points) TE D M AN U SC NLF-HB calculations give Lw-H-V above 272 K EP b AADT [K] = 302.8-305.5 7.1 AC C a 15 10.9 RI PT Lw-H-Lg Average 43 [67] ACCEPTED MANUSCRIPT Table Comparisons of calculated incipient hydrate forming conditions of binary mixed guests with experimental data, PSRK [6] and CSMGem [1] results Lw-H-V No data 15 T range [K] 279.4-287.8 P range [MPa] 0.99-3.08 Lw-H-V 23 274.8-283.2 0.95-6.09 - Lw-H-V 274.2 0.88-1.45 - Lw-H-V 16 284.9-304.1 6.93-68.57 - Average 0.27-4.36 AAD (%) CSMGem NLF-HB 3.4 3.6 Ref [96] 2.3 3.0 [85] 9.7 1.1 [34] 4.4 11.8 [91] 7.0 3.9 5.3 - 4.6 5.7 [85] Lw-H-V 25 274.8-283.2 Lw-H-V 11 274.5-282.3 0.26-0.95 - 2.3 5.8 [113] Lw-H-V 17 290.5-304.9 6.93-68.98 - 15.1 3.8 [91] Average 3.6 7.5 5.1 M AN U CH4-C3H8 PSRK - RI PT Phases SC Binary guest CH4-C2H6 Lw-H-V 63 273.2-295.2 3.62-35.96 10.9 13.4 14.3 [88] CH4-CO2 Lw-H-V 42 273.7-287.6 1.45-10.95 - 2.2 5.4 [92] Lw-H-V 17 275.5-285.7 1.99-7.00 - 10.2 5.4 [109] Average 4.9 4.5 5.4 274.8-277.6 1.32-1.84 - 13.2 9.7 [85] Lw-H-V 46 273.8-293.6 0.16-10.1 - 10.7 18.7 [105] Average - 10.8 18.3 EP Lw-H-V AC C CH4-iC4H10 TE D CH4-N2 CH4-H2S Lw-H-V 20 276.5-295.4 1.03-6.79 - 14.4 8.5 [114] C2H6-C3H8 Lw-H-V 59 273.1-283.3 0.44-2.03 5.7 4.3 4.5 [97] C2H6-CO2 Lw-H-V 40 273.5-287.8 0.57-4.08 4.7 3.0 6.4 [115] C3H8-N2 Lw-H-V 29 274.2-289.2 0.26-18.09 - 7.7 14.7 [116] C3H8-CO2 Lw-H-V 35 273.8-286.2 0.30-3.38 - 9.7 5.7 [99] 44 ACCEPTED MANUSCRIPT Lw-H-V 56 273.7-284.8 0.22-4.27 - 12.0 14.0 Average 18.8 11.1 10.8 [115] Lw-H-V 53 273.7-280.9 0.14-3.18 - 12.0 9.1 [115] CO2-N2 Lw-H-V 16 276.9-285.4 5.00-20.00 - 11.9 9.7 [117] AC C EP TE D M AN U SC RI PT iC4H10-CO2 45 ACCEPTED MANUSCRIPT Table Comparisons of calculated incipient hydrate forming conditions of inhibitor containing systems with experimental data and CSMGem [1] results Lw-H-Lg 271.0-273.2 5.00-20.00 20.0 Lw-H-V 269.5-268.9 1.59-3.48 10.0 Lw-H-V 263.9-268.9 1.59-2.94 20.0 Lw-H-Lg 276.0-278.1 4.60-13.98 Lw-H-Lg 269.1-271.8 3.34-16.09 Lw-H-V 266.7-274.7 1.01-2.56 Lw-H-V 260.3-270.7 Lw-H-V Lw-H-V AAD(%) CSMGem NLF-HB 21.8a 22.0 RI PT wt% MeOH 10.0 Ref [24] 40.9 47.9 [24] 17.5 12.2 [26] 19.0 10.2 [26] SC P range [MPa] 5.00-20.00 10.0 41.1b 39.8 [26] 20.0 54.5 35.2 [26] 10.0 4.2 5.2 [35] 0.90-3.16 20.0 5.5 6.9 [35] 269.3-277.3 1.35-3.72 10.0 2.3 6.2 [36] 265.6-270.4 1.67-3.10 20.0 5.3 5.5 [36] EP CSMGem failed to give convergent solution at point, bat points AC C a T range [K] 277.5-280.0 TE D CO2MeOH Lw-H-Lg No data Phases M AN U GuestInhibitor 46 ACCEPTED MANUSCRIPT Table 10 Comparisons of calculated solubility in guest-rich or aqueous phase with experimental data and CSMGem [1] results T range [K] P range [MPa] H-V 238.2-273.0 3.45-13.79 H-V 19 250.6-279.2 3.44-6.89 5.7 5.3 [119] H-V 12 240.0-270.0 3.4-10.34 17.7 18.3 [120, 121] H-V 13 196.0-270.0 3.45-6.9 15.0 16.3 [122] H-V 271.8-278.4 3.00-5.00 13.0 10.4 [8] H-V 12 249.3-280.0 6.90-10.40 14.3 19.0 [123] H-V 10 253.2-283.2 1.50-18.00 9.5 10.4 [7] Lw-H 16 276.2-281.7 5.00-14.30 11.0 21.0 [124] Lw-H 274.2-280.2 3.50-6.50 3.8 16.0 [125] Lw-H 13 274.2-286.2 6.00-20.00 8.1 16.0 [126] Lw-H 19 Lw-H 16 Lw-H 44 H-V [118] RI PT SC M AN U TE D Ref 273.1-278.2 4.98-19.35 31.6 10.7 [3] 276.2-281.7 5.00-14.36 5.5 16.2 [127] 276.5-294.6 10.00-40.00 3.6 12.3 [128] 271.3-275.6 1.50 15.4 14.0 [8] 276.2-283.7 2.48 17.0 18.1 [76] H-Lg 240.1-281.2 3.45 18.1a 4.1 [76] H-Lg 259.1-270.5 3.45 46.3a 34.4 [37] H-Lg 3/7d 201.7-271.0 3.45 19.4a,b 9.3 [122] Lw-H 277.3-278.5 10.10-20.10 11.6 16.6 [124] Lw-H 277.3-278.5 5.10-15.10 1.9 7.2 [129] H-V AC C C2H6 AAD (%) CSMGem NLF-HB 14.5 15.7 No data 32 Phases EP Guest comp CH4 47 ACCEPTED MANUSCRIPT a 246.7-276.4 0.77-3.45 44.2a 37.7 [37] H-Lg 6/7d 235.7-276.2 1.10 12.3a,c 4.2 [76] H-Lg 3/7d 211.2-270.9 0.86-1.10 13.9c 8.0 [122] Lw-H 0/6d 274.2-276.2 0.25-0.36 -c 14.4 [130] H-V 13 251.8-278.7 0.69-3.45 10.5 12.7 [14] H-V 271.1-276.3 2.00 28.8 39.4 [8] H-Lg 19/22d 245.2-280.2 2.07-13.79 48.6a,c 80.0 [14] H-Lg 20 274.3-282.3 6.10-10.10 44.0a 16.8 [15] H-Lg 13 253.2-277.2 13.79 40.6a 7.6 [10] H-Lg 233.2-288.2 15.00 36.5a 4.8 [11] H-Lg 16 223.2-263.2 2.00-10.00 47.5a 6.4 [16] Lw-H 10 279.1-281.5 10.10-20.10 3.1 2.0 [131] Lw-H 274.0-279.3 6.65-50.58 9.1 5.8 [132] Lw-H 12 Lw-H 32 Lw-H 30 M AN U SC RI PT 11 274.0-283.0 2.00-6.00 3.6 6.2 [133] 277.8-281.0 4.99-14.2 7.6 3.3 [2] 274.1-281.1 1.87-23.60 2.7 3.7 [134] EP CO2 H-Lg TE D C3H8 b c AC C Phase identification problem; guest-rich liquid phases reported as vapor phase in CSMGem (included for AAD%) Zero value due to very small solubility (not included for AAD%) CSMGem failed to give convergence solutions at some data points (not included for AAD%) d The number of data used for AAD% of CSMGem/NLF-HB 48 ACCEPTED MANUSCRIPT 60 RI PT 50 SC 30 20 10 0.02 0.04 1.00 TE D 0.00 M AN U P [MPa] 40 Mole fraction of CO2 Figure Comparisons of calculated phase compositions for vapor-liquid and liquid-liquid EP equilibria of CO2-water mixtures with experimental data at 298.15K in the absence of gas hydrates; △, ref [56]; ○, ref [61]; □, ref [62]; ▽, ref [74]; ◇, [82]; solid line, NLF-HB; dash line, AC C CSMGem [1] 49 ACCEPTED MANUSCRIPT RI PT 25 15 SC P [MPa] 20 M AN U 10 0.02 0.04 TE D 0.00 1.00 Mole fraction of H2S Figure Comparisons of calculated phase compositions for vapor-liquid and liquid-liquid EP equilibria of H2S-water mixtures with experimental data at 310.93 K in the absence of gas AC C hydrates; △, ref [47]; ○, ref [56]; solid line, NLF-HB; dash line, CSMGem [1] 50 ACCEPTED MANUSCRIPT 100 sI RI PT sII SC P [MPa] 10 M AN U 0.1 260 270 280 290 300 310 TE D T [K] EP Figure Comparisons of calculated incipient hydrate forming conditions for structure I hydrate forming single guests; △, ref [86] for CH4; ▲, ref [92] for CH4; ▲, ref [87] for CH4; ○, ref [85] AC C for C2H6 ; ●, ref [26] for C2H6; □, ref [106] for N2; ▽, ref [107] for CO2;▼, ref [92] for CO2; ▼, ref [25] for CO2; ◇ and ◆, ref [67] for H2S; solid line, NLF-HB; dash line, CSMGem [1] 51 ACCEPTED MANUSCRIPT RI PT SC 0.1 266 268 270 M AN U P [MPa] 10 272 274 276 278 280 T [K] TE D Figure Comparisons of calculated incipient hydrate forming conditions for structure II hydrate forming guests with experimental data; ×, ref [85] for C3H8; △, ref [102] for C3H8; ▲, ref [28] for C3H8; ▲, ref [29] for C3H8; ○, ref [98] for iC4H10; ●, ref [103] for iC4H10; ●, ref [105] for iC4H10; AC C EP solid line, NLF-HB; dash line, CSMGem [1] 52 ACCEPTED MANUSCRIPT 25 10 wt% MeOH 20 wt% MeOH RI PT P [MPa] 20 15 SC 10 265 M AN U 270 275 280 T [K] Figure Comparisons of calculated incipient hydrate forming conditions for CO2 + water + TE D MeOH system with experimental data; × and +, ref [35]; △ and ○, ref [36]; ▲ and ●, ref [26]; ▲ (zCO2 = 0.8394) and ▼ (zCO2 = 0.3349), ref [24]; ● (zCO2 = 0.7566) and ■ (zCO2 = 0.3548), ref AC C EP [24]; solid line, NLF-HB; dash line, CSMGem [1] 53 ACCEPTED MANUSCRIPT 3.0 RI PT 2.0 SC 1.5 1.0 0.5 0.0 220 230 240 M AN U Water solubility/10 -3 2.5 250 260 270 280 290 TE D T [K] Figure Comparisons of calculated water solubility in CO2-rich liquid phase in equilibrium with gas hydrates with experimental data; △ (6.21 MPa), ○ (10.34 MPa) and □ (13.79 MPa), ref [15]; ▲ (6.10 MPa) and ● (10.10 MPa), ref [16]; ▲ (6.00 MPa) and ● (10.10 MPa), ref [17]; ■ (13.79 MPa), ref [12]; solid line (6.1 MPa), dash line (10.1 MPa) and dotted line (13.79 MPa), NLF-HB AC C EP (black); CSMGem [1] (grey) 54 [...]... of structures I and II empty hydrates were fitted to water solubility data in guest-rich phase for guest components of SC methane, ethane and propane in equilibrium with gas hydrates and incipient hydrate forming conditions in Lw-H-V and Lw-H-Lg equilibria of single guests listed in Table 7 and of binary guest M AN U mixtures listed in Table 8 Vapor pressures of empty hydrates are PWEH 6614.4 ln =... the other group Yoon et al [5] and Klauda and Sandler [30] reported that propane hydrates exhibit a retrograde behavior at the pressure above Lw-H-Lg-V quadruple point with hydrate model parameters fitted to both I- SC H-V and Lw-H-V data In model calculations, the retrograde behavior is sensitive to molar volume of empty hydrates It is noted that Yoon et al [5] and Klauda and Sandler [30] employed the... structure II As molar volume of empty hydrates of structure II increases, calculated slopes of Lw-H-Lg curve become steeper and eventually become negative showing the retrograde behavior in dissociation pressure Fig 4 also shows that Lw-H-Lg pressure curve for isobutane is very steep and does not show pressure retrograde behavior TE D The structure of nitrogen hydrates has been subject to controversy... components that form identical hydrate structures may assume different structures when mixed Such behavior is found in methane-ethane system in which sII SC hydrates are formed in limited bandwidth of methane composition although both components form sI hydrates in pure states For these mixtures Ballard and Sloan [33] proposed that the M AN U hydrate model parameters be regressed from dissociation pressure... whereas it is less wide in CSMGem 3.4 Water Solubility in Guest-rich Phase in Equilibrium with Gas Hydrates Water contents data in fluid phase for H-V and H-Lg equilibria of single guest systems of TE D methane, ethane and propane were included in determining molar volume and vapor pressure of empty hydrates as well as Kihara potential parameters for these components Thus water contents in H-V and... 29 (1941) 475-481 25 ACCEPTED MANUSCRIPT [83] O.L Roberts, E.R Brownscombe, L.S Howe, Oil Gas J 39 (1940) 37-43 [84] B.J Falabella, A study of natural gas hydrates, PhD Thesis, University of Massachusetts, 1975 RI PT [85] W.M Deaton, E.M Frost, Gas hydrates and their relation to the operation of natural-gas pipe lines, U.S Bureau of Mines Monograph 8, 1946 [86] T.Y Makogon, E.D Sloan, J Chem Eng Data... of carbon dioxide hydrate a review of properties of 51 gas hydrates, U.S Dept of Interior, Res Dev Report No 830, 1972 [111] D.C Bond, N.B Russell, Pet Trans AIME 179 (1949) 192-198 EP [112] J.J Carroll, Phase behaviour in the system water-hydrogen sulphide, PhD Thesis, University of Alberta, 1990 AC C [113] V.K Verma, J.H Hand, D.L Katz, Gas hydrates from liquid hydrocarbons methanepropane-water system,... K Y.; Kobayashi, R.; Sloan, E D.; Dharmawardhana,, P B, (I) The water content and correlation of the water content of methane in equilibrium with hydrates (II) The M AN U water content of a high carbon dioxide simulated Prudhoe Bay gas in equilibrium with hydrates, Gas Processors Association, GPA Research Report 45, 1980 [122] K.Y Song, M Yarrison, W Chapman, Fluid Phase Equilib 224 (2004) 271-277 [123]... between water molecules and between water and guest species 3.2 Incipient Hydrate Forming Conditions of Single Guests TE D Calculated incipient hydrate forming pressures or dissociation pressures of gas hydrates are compared with experimental data in Table 7 for single guest systems Calculated results are shown with typical data sets in Fig 3 for sI forming guests and in Fig 4 for sII forming guests EP... were calculated for the pressure range up to approximately 100 MPa which was about the maximum pressure in the present parameter determination It is noted that vapor pressure and molar volume of empty hydrates are guest independent in the present study 15 ACCEPTED MANUSCRIPT Lw-H-Lg equilibrium curve is very steep for propane and isobutene as shown by Fig 4 and temperature deviations are shown instead