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Measurement and prediction of gas hydrate equilibrium conditions in the presence of inhibitors Wu, Huijie 2005

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M E A S U R E M E N T A N D PREDICTION OF GAS H Y D R A T E EQUILIBRIUM CONDITIONS I N T H E PRESENCE OF INHIBITORS By  HUIJIEWU  B.Sc, Inner Mongolia Polytechnic University, 1994 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF  MASTER OF APPLIED  SCIENCE  in  T H E F A C U L T Y O F G R A D U A T E STUDIES (CHEMICAL A N D BIOLOGICAL  ENGINEERING)  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A  October 2005  © H u i j i e W u , 2005  ABSTRACT Gas hydrates are crystals which are formed by water and small gas molecules at low temperature and high pressure. Hydrate for many years have been a problem in o i l and gas industries because hydrate formation may plug the pipelines or valves and might also cause blowout i n the drilling operations. In order to avoid hydrate formation, inhibitors are introduced to increase the pressure needed at a given temperature for hydrates formation. Generally used inhibitors i n o i l and gas industries are methanol, glycerol, ethylence glycol and triethylene glycol.  Knowledge o f the equilibrium hydrate-forming conditions is necessary for the rational and economic design o f processes in the chemical, o i l , gas, and other industries where hydrate formation is encountered. It is important to measure the incipient hydrate formation conditions for the systems containing different inhibitors, and also it is important to have available reliable methods for calculating the impact o f the addition o f these chemicals into the aqueous phase on the equilibrium hydrate formation conditions (inhibiting effect).  In this work, the inhibiting effects o f triethylene glycol ( T E G ) and glycerol i n methane-ethane and methane-propane gas mixture hydrate formation systems were measured. The data showed that T E G (20.0wt% and 30.0wt %) and glycerol (20.0wt %) have considerable inhibiting effect on hydrate formation.  These data are also valuable for validating the hydrate prediction models. Several models have been published based on cubic equations o f state. In this work the Trebble-Bishnoi equation was used. The results were found to be in very good agreement with the data. The statistical associating fluid theory ( S A F T ) equation o f state was also employed for the prediction o f the thermodynamic inhibiting effect o f methanol, glycerol, ethylene glycol and triethylene glycol on single gas hydrate formation. The results were found to be in satisfactory to excellent agreement with the experimental data. The S A F T equation takes into account hard sphere repulsion, hard chain formation, dispersion and association. This enables this model to be able to correlate and predict successfully systems containing water, alcohols and hydrocarbons.  ii  TABLE OF CONTENTS ABSTRACT T A B L E OF CONTENTS LIST OF T A B L E S  ii iii v  LIST OF FIGURES LIST OF S Y M B O L S ACKNOWLEDGEMENTS  vi vii ix  :  1. INTRODUCTION 2. LITERATURE REVIEW AND RESEARCH OBJECTIVES 2.1 2.2 2.3 2.4  Structure o f Gas Hydrate Thermodynamic Experimental Studies Thermodynamic Models Research Objectives  3. MATERIAL, APPARATUS AND METHODS 3.1. Materials 3.2. Apparatus 3.3. Isothermal pressure search method 3.3.1 Estimation ofthe hydrate formation pressure 3.3.2 Solution preparation 3.3.3 Elimination o f hysteresis phenomena 3.3.4 Hydrate formation condition measurement  4. EXPERIMENTAL RESULTS AND DISCUSSION 4.1. Validation o f the Experimental Apparatus and Procedure 4.2. Incipient Equilibrium Data on Methane (Cl)-Ethane (C2) Hydrate Formation in Aqueous T E G Solutions 4.3. Incipient Equilibrium Data on Methane (Cl)-Propane (C3) Hydrate Formation in Aqueous T E G Solutions 4.4. Incipient Equilibrium Data on Methane (Cl)-Ethane (C2) Hydrate Formation in Aqueous Glycerol Solutions 4.5. Incipient Equilibrium Data on Methane (Cl)-Propane (C3) Hydrate Formation in Aqueous Glycerol Solutions  5. HYDRATE FORMATION PREDICTION USING TREBBLE-BISHNOI EQUATION OF STATE 5.1. Prediction o f Methane (Cl)-Ethane (C2) Hydrate formation i n aqueous T E G solutions 5.2. Prediction o f Methane (Cl)-Ethane (C3) Hydrate formation in aqueous T E G solutions 5.3. Prediction o f Methane (Cl)-Ethane (C2) Hydrate formation i n 20.0wt% aqueous Glycerol Solutions  1 4 4 ....5 6 8  9 9 9 14 15 15 16 16  17 17 18 21 24 26  29 30 32 33 in  5.4. Prediction o f Methane (Cl)-Ethane (C3) Hydrate formation i n 20.0wt% aqueous Glycerol Solutions '.  34  6. HYDRATE FORMATION PREDICTION USING SAFT EQUATION OF STATE  36  6.1. Thermodynamic Framework 6.2. Equation o f State for Vapor and L i q u i d Phases 6.2.1 Hard-sphere repulsion term 6.2.2 Hard chain formation term 6.2.3 Dispersion term 6.2.4 Association term 6.3. M o d e l for Hydrate Phase 6.4. Parameters for S A F T 6.5. Prediction o f hydrate formation 6.5.1 Inhibiting effect o f Methanol 6.5.2 Inhibiting effect o f Ethylene G l y c o l 6.5.3 Inhibiting effect o f Glycerol 6.5.4. Inhibiting effect o f Triethylene G l y c o l 6.5.5. Discussion  36 36 36 37 37 38 39 40 41 42 44 45 46 47  7. CONCLUSIONS AND RECOMENDATIONS  48  7.1 Conclusions 7.2 Recommendations  48 48  8. REFERENCE APPENDIX  49 ,  54  A P P E N D I X A : Pressure calibration curve  54  A P P E N D I X B : Thermocouple calibration curve A P P E N D I X C : The sample o f calibrating gas composition from gas cylinder A P P E N D I X D : The sample o f calculating gas composition in hydrate equilibrium condition A P P E N D I X E : Original data for calibrating gas composition form C 1 - C 3 gas cylinder A P P E N D I X F : Original G C analysis data i n hydrate equilibrium conditions for the C l - C 2 - T E G (20.2%) systems A P P E N D I X G : Original G C analysis data in hydrate equilibrium condition for the C 1 - C 3 - T E G (0%, 20.0%, 30.0%) systems A P P E N D I X H : Original G C analysis data i n hydrate equilibrium condition for the C l - C 2 - G l y c e r o l (20.0%) and C1-C3-Glycerol (20.0%) systems A P P E N D I X I: Calculation o f hydrate point depression ( A T )  55 56  H  58 59 60 61 62 63  IV  LIST OF T A B L E S Table 1: Structural properties o f hydrates (Sloan, 1998) 4 Table 2: Experimental data from this work and literature on methane hydrate formation in pure water solution (Adisasmito. et al., 1991) 17 Table 3: Incipient equilibrium hydrate formation conditions and gas phase molar composition for the C i - C (9.0%)-TEG (20.2% and 30.0%)-H O system 19 Table 4: Incipient equilibrium hydrate formation conditions data for the C1-C2 (9.0%)-H2O system 19 Table 5: Hydrate point depression ( A T ) , and change in hydrate point depression at 2500 kPa 2  2  H  (AT ,250o) i n TEG-water 20 Table 6: Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C1-C3 ( 9 . 5 % ) - H 0 and C1-C3 (9.5%)-TEG (20.0% and 3 0 % ) - H O system 22 Table 7: Hydrate point depression ( A T ) , and change in hydrate point depression at 1000 kPa H  2  2  H  ( A T , 1000) in TEG-water Table 8: Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C , - C ( 9 . 0 % ) ~ H O and C , - C (9.5%)-Glycerol (20.0%)-H O system Table 9: Hydrate point depression ( A T ) o f Glycerol-water system Table 10: Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C1-C3 ( 9 . 5 % ) - H 0 and C1-C3 (9.5%)-Glycerol (20.0%)-H O system Tablel 1: Hydrate point depression ( A T ) o f Glycerol-water system T a b l e l 2 : Set o f binary interaction parameters for each system Tablel 3: Experimental data and prediction o f Methane (Cl)-Ethane (C2) hydrate formation i n aqueous T E G solutions Tablel4: Experimental data and predictions on C 1 - C 3 hydrate formation in aqueous T E G solutions T a b l e l 5 : Experimental data and predictions on C 1 - C 2 hydrate formation in 20.0wt% glycerol solution Tablel6: Experimental data and prediction on C 1 - C 3 hydrate formation in 20.0wt% glycerol solution Tablel7: Segment Parameters for Pure Fluids for the S A F T equation Tablel 8: Binary Interaction Parameters for the S A F T equation Tablel 9: Predictions o f the hydrate formation pressures H  2  2  2  2  H  2  H  23  25 25  2  27 27 29 31 32 34 35 41 41 43  LIST OF FIGURES Figure 1: Diagram o f gas hydrate structure 1 1 Figure 2: Schematic o f the experimental apparatus 10 Figure 3: Photo of the equilibrium cell used in the experiments 11 Figure 4: Photo o f the CP-3800 Gas Chromatograph used in the experiments 12 Figure 5: Water purifier E L G A U H Q II 13 Figure 6: Magnetic stirring system ( M O D E L 200 M I N I - S T I R R E R ) •. 13 Figure 7: Sampling tube 14 Figure 8: Roughly equilibrium pressure estimation for the system Ci-C2-20.2%TEG-H2O 15 Figure 9: Comparison o f experimental data obtained in this work and data from Adisasmito... 18 Figure 10: Equilibrium data on C 1 - C 2 hydrate formation in water-triethylene glycol solution 20 Figure 11: C 2 mole fraction at each equilibrium condition 21 Figure 12: Equilibrium data on C 1 - C 3 hydrate formation i n water-triethylene glycol solution.23 Figure 13: C3 mole fraction at each equilibrium condition 24 Figure 14: Equilibrium data on C 1 - C 2 hydrate formation in water-Glycerol solution 25 Figure 15: C 2 mole fraction at each equilibrium condition in water-glycerol solution 26 Figure 16: Equilibrium data on C 1 - C 3 hydrate formation in water-Glycerol solution 28 Figure 17: C3 mole fraction at each equilibrium condition in water-glycerol solution 28 Figure 18: Computational hydrate formation P (or T) 30 Figure 19: Experimental data and predictions on C 1 - C 2 hydrate formation i n water-triethylene glycol solution 31 Figure20: Experimental data and predictions on C 1 - C 3 hydrate formation in water-triethylene glycerol solution 33 Figure 21 Experimental data and predictions on C 1 - C 2 hydrate formatioin in water-glycerol solution 34 Figure 22Experimental data and predictions on C 1 - C 3 hydrate formation in water-glycerol solution 35 Figure 23: Methane hydrate formation in the presence of methanol: data and predictions based on S A F T 44 Figure 24: Ethane hydrate formation in the presence o f methanol: data and predictions based on S A F T 44 Figure 25: CO2 hydrate formation i n the presence o f methanol: date and predictions based on S A F T 44 Figure 26:Methane hydrate formation in the presence o f ethylene glycol: data and predictions based on S A F T 45 Figure 27: Methane hydrate formation in the presence of glycerol: data and predictions based on S A F T 45 Figure 28: CO2 hydrate formation in the presence of glycerol: data and predictions based on S A F T 46 Figure 29: Methane hydrate formation in the presence of T E G : data and predictions based on S A F T 46 Figure 30: Ethane hydrate formation i n the presence of T E G : data and predictions based on S A F T 46 Figure 31: Propane hydrate formation in the presence o f T E G : data and predictions based on S A F T 46 vi  LIST O F S Y M B O L S A = Helmholtz free energy, J C = Langmuir constant, 1/MPa Cp = heat capacity, .//mol K d = hard-sphere diameter, l x l 0 " m 1 0  / = fugacity, M P a g. = radius distribution function k = Boltzmann constant, J K"  1  K = Boltzman's constant, J / K m = effective number o f segments M = number o f associate sites n = number o f components nc = number o f hydrate forming substances N = number o f molecules = Avogadro constant, 6.02217*10 mol" 23  1  r = radial distance from center o f hydrate cavity, m R = gas constant, 8.3143 J mol" K " 1  1  R = type m spherical cavity radius, m m  P = pressure, M P a T = absolute temperature, K v= molar volume, m /mole W(r) = cell potential function, J x = mole fraction i n liquid phase Xj = mole fraction o f component i Xf  = mole fraction o f molecule / not bonded at site A  y = mole fraction in v a p o r phase Z = compressibility factor Greek letters  P = 1/kT e/k  = energy parameter o f dispersion, K vii  s  AB  K  AB  A  AB  jk = energy parameter o f association between sites A and B , K = bonding volume = association strength between sites A and B  ju - chemical potential p = molar density, mol/m" p  n  = number density, m"  3  3  a = soft-sphere diameter,. I x l 0 ' m 1 0  v„, = number o f cavities o f type m  Subscripts i, j, k = components m = type o f cavity w = water  Superscripts assoc = association interaction A, B = association site chain = hard-sphere chain disp = dispersion interaction hs = hard-sphere res = residual term H = hydrate L = liquid L° = pure liquid water MT = empty lattice o = reference conditions of 273.15 K and zero absolute pressure V= vapor  viii  ACKNOWLEDGEMENTS I extend m y sincere gratitude to m y supervisor D r . Peter Englezos, for giving me this research opportunity and for providing me with invaluable guidance, excellent suggestions, encouragement, care and attention throughout the study. I am very grateful to m y husband Dr. Xiaosen L i for his great support and help. I would also like to thank m y research group Dr. Ju Dong Lee, Robin, Rajnish, Shivamurfhy and Praveen for their invaluable discussions, help and suggestions. I would like to thank the excellent staff members o f Chemical Engineering department for providing necessary help whenever required. M y deepest love and gratitude is felt for my parents and family members for their never ending encouragement and support. This would have been impossible without them. Last but not the least, I would like to thank all m y friends who are directly or indirectly involved in making this dream come true.  ix  1. Introduction Gas  hydrates  are nonstoichometric crystalline inclusion compounds.  A t a low  temperature and high pressure, water molecules linked together through hydrogen bonding create a lattice-like structure with cavities (host lattice) that can enclose a large variety o f molecules (guests). The interaction between the water molecules and the guests molecules are just V a n der Waals forces. Molecules which do not interfere with the hydrogen bonding o f water molecules and have a diameter that is smaller than the diameter o f the cavity can render the structure stable under suitable pressure and temperature conditions (Davidson, 1973; Sloan, 1990).Typical hydrate-forming substances include C H , C2H6, C3H8, C 0 , and H S . Naturally occurring 4  2  2  clathrate hydrates in the earth contain mostly methane and which are regarded as a future energy resource (Englezos, 1993). Sir Humphry D a v y was the first person to report clathrate hydrate formation in 1810. This was chlorine hydrate and this was confirmed by Farady in 1823. Gas hydrates crystallize in three different structures: cubic structure I (si), cubic structure II (sil), or hexagonal structure H (sH) (Ripmeester et al. 1987; Ripmeester and Ratcliffe, 1990; Ripmeester et al. 1994).  The basic  cavity formed by hydrogen-bonded water molecules is the pentagonal dodecahedron (5 ). A unit 12  cell o f gas hydrate structure I is shown in figure 1  motecutet F i g u r e 1: D i a g r a m o f gas hydrate structure 1.  1  Vast quantities o f naturally occurring gas hydrates, containing mostly methane, were discovered in the earth's crust (Katz, 1971; Makogon et al. 1972). Kvenvolden (1988) estimated that 1 0 m o f methane gas exist in hydrate. The hydrates are distributed in the deep oceans and 16  3  permafrost regions. One volume o f hydrate contains as much as 164 volumes o f gas at standard temperature and pressure condition (STP). Thus the amount o f methane in hydrate state exceeds the total combined fossil fuel and it is a great potential energy resource for the future.  Hydrates also generally are a serious problem in the gas and o i l industry. Hydrate formation may plug the pipelines or valves and also erode equipment surfaces (Sloan, 1998). Viscosity o f crude o i l may change due to the formation o f hydrates. A t drilling sites, dissociation o f solid hydrates present in natural formations may cause damage and leakage due to uncontrolled gas release, blowouts o f the wellhead, etc. The released methane contributes to greenhouse effect. Because o f these devastating and often costly consequences o f hydrate formation, methods o f slowing hydrate solids development in gas and o i l streams have been an attractive research project for a number o f years.  Hydrate formation can be prevented by using any o f the following methods. •  Adjusting the temperature and pressure until hydrate formation is not favored.  •  Dehydrating a gas stream to prevent a free water phase.  •  Inhibiting hydrate formation by the addition o f chemicals i n the water phase.  Hydrate inhibition is typically employed when it is not cost effective to install a full dehydration unit, or when an operating dehydration unit cannot obtain the desired dew point depressions. Inhibition utilizes the injection o f a known hydrate inhibitor into the process upstream o f the location where solids formation is predicted to occur. Thermodynamic inhibitors prevent hydrate formation by shifting the equilibrium conditions so that lower temperatures and higher pressures are required to form hydrates.  The hydrate suppression  ability o f the inhibitors is a consequence o f their ability to reduce the activity o f water. Commonly used thermodynamic inhibitors are methanol, ethylene glycol ( E G ) , glycerol and triethylene glycol ( T E G ) .  2  To avoid the problems associated with hydrate formation, to exploit the hydrates as an energy resource or to utilize hydrates to develop new technologies, there is a need to obtain phase equilibrium data and develop prediction methods for pure water as well as for aqueous systems containing inhibitors.  The studies on clathrate hydrate equilibrium focus on gathering incipient equilibrium hydrate formation data and on developing predictive methods for the calculation o f phase equilibria. The incipient formation conditions refer to the situation i n which an infinitesimal amount o f the hydrate phase is present in equilibrium with fluid phases. Knowledge o f the equilibrium hydrate-forming conditions is necessary for the rational and economic design o f processes in the chemical, o i l , and other industries where hydrate formation is encountered. (Englezos, 1993). The thermodynamics of hydrate formation has been studied extensively over the years and data for several thermodynamic inhibitors have been obtained. However, the data for some specific inhibitors, such as triethylene glycol, are not adequate. Such data are useful in industrial design applications as w e l l as for testing predictive models. Several methods have been published which predict hydrate formation in the presence o f inhibitors and especially methanol. The methods are usually based on using cubic equations o f state for the fluid phases. Statistical associated fluid theory ( S A F T ) has been investigated extensively since proposed, and is very advantageous over traditional cubic equations o f state. The theory is quite appropriate for associating fluids. Hence, it is suitable for alcohol-water systems. This work w i l l try to obtain more incipient equilibrium hydrate formation data for the systems containing the inhibitor o f triethylene glycol and glycerol to detect their inhibiting abilities and then make predictions using the Trebble-Bishnoi and S A F T equations o f state.  3  2. L i t e r a t u r e Review a n d Research Objectives 2.1 Structure o f gas hydrate Clathrates are solid solutions o f a volatile solute i n a host lattice (van der Waals, 1956). The solvent is known as the empty hydrate lattice formed by water molecules that are linked together with hydrogen bonds and form a three-dimensional structure with cavities. Gas molecules, which do not interfere with the hydrogen bonding o f water molecules and have a diameter that is smaller than the diameter o f the cavity, can be enclosed i n the lattices.  In a hydrate, the species forming the lattice is commonly called the host, while the caged component is called the guest. The host-lattice is thermodynamically unstable without the presence o f a guest molecule in the cavity. The guest molecule, which stabilizes the lattice, is held in place inside the lattice by weak van der Waals forces.  There are three known gas hydrate structures: Structure I; Structure II; Structure H (Ripmesster et al. 1987). Structure I consists o f two different types o f cavities. The first cavity is called a pentagonal dodecahedron (5 ) which is present in all the gas hydrate structures. Second 12  type o f cavity is called tetrakaidecahedron ( 5 6 ) , which is larger than the dodecahedron. A unit 12  2  cell o f this structure consists o f six large 5 6 cavities, and two small 5 ! 2  2  1 2  cavities created by 46  water molecules. C o m m o n structure I forming gases are methane, ethane and carbon dioxide. Structure II hydrate consists o f 16 small ( 5 ) and 8 large cavities ( 5 6 ) made up by 136 water 12  molecules. Structure H has the basic 5  1 2  12  4  cage and the two other cavities consist o f a 4 5 6 cage 3  6  3  and a 5 6 . Table L i s the Structural properties o f hydrates (Sloan, 1998) 12  8  Table 1. Structural properties of hydrates (Sloan, 1998) Structure I  Structure II  Cavity types  5", 5 "6*  5 ,5 6*  Cages/unit cell  2,6  16, 8  3,2, 1  Crystal type  Cubic  Cubic  Hexagonal  li  Structure H  ll  4  2.2. Thermodynamic experimental studies One o f the traditional methods for preventing the hydrate formation is to use inhibiting substances (methanol, glycols and glycerol) during the industrial operation. Electrolytes are also known to be strong thermodynamic inhibitors. Measurement o f the effect o f the inhibitors on the incipient equilibrium gas hydrate formation conditions is necessary for process design. For example, these thermodynamic data can be used directly in the design o f operations in the o i l and gas industry involving the search, recovery, transport, or processing o f hydrocarbon fluids. Moreover, the thermodynamic data are needed to test hydrate formation prediction methods.  Experimental data regarding the effect o f thermodynamic inhibitors continue to appear i n the literature. Song and Kobayashi (1989) measured the inhibiting effect o f methanol and ethylene glycol on the incipient hydrate formation conditions from a mixture o f methane and propane. Dholabhai et al. (1991a) and Englezos and Bishnoi (1991) presented experimental data on methane and ethane hydrate formation i n aqueous mixed electrolyte solutions. Svartas and Fadnes (1992) presented data on the inhibition o f methanol. It was found that methanol doesn't promote hydrate formation at concentrations for which Makogon (1981) and Berecz and Balla-Achs (1983) reported the opposite effect. Englezos and Ngan (1993a) measured incipient hydrate formation conditions for propane in aqueous mixed electrolyte solutions. Englezos and Ngan (1994) also measured incipient phase equilibrium data for methane, ethane and propane hydrate formation in aqueous solutions o f polyethylene oxide (PEO). The results indicate a very weak inhibiting effect compared with the effect o f electrolytes and alcohols on the equilibrium hydrate formation conditions. Experimental data for CO2 hydrates in aqueous solutions containing methanol and electrolytes were reported by Dholabhai at al. (1996). Breland and Englezos (1996) provided equilibrium condition data for carbon dioxide hydrate i n pure water and aqueous glycerol solutions i n order to evaluate the effectiveness o f glycerol as an inhibiting agent. It was shown that glycerol has a considerable inhibiting effect on carbon dioxide hydrate formation though it was not as effective as an inhibiting agent as sodium chloride or methanol. Bishnoi et al. (1999) measured equilibrium conditions for hydrate formation frrom a ternary mixture o f methane, propane and carbon dioxide, and from a natural gas mixture i n the presence o f electrolytes and methanol. Experimental three phase equilibrium data for two mixtures o f methane and CO2 in the presence o f methanol, ethylene glycol and electrolytes were obtained by  5  Dholabhai et al. (1997). Servio et al. (1999) measured incipient equilibrium gas hydrates formation  conditions  glycol-NaCl-H 0 2  for  systems.  the  C02-CH -neohexane-NaCl-H 0 4  Mahmodaghdam  2  and  and CH -polypropylene 4  Bishnoi.(2002) obtained  equilibrium  experimental data for methane, ethane, and propane incipient hydrae formation in the presence o f diethylene glycol and that for propane in the presence in the presence o f ethylene glycol were obtained. R o c h (2003) measured 3-phase hydrate equilibrium o f methane-rich gas mixtures in pure water and i n the presence o f different salts, methanol and glycol were investigated. Eichholz et al. (2004) provided experimental three-phase hydrate equilibrium data for methane hydrates i n aqueous solutions o f ethylene glycol and sodium chloride.  Triethylene glycol ( T E G ) and glycerol are industrially used chemicals to inhibit the formation o f gas hydrates. Ross and Toczylkin (1992) have presented data on the effect o f T E G on methane and ethane gas hydrate. Servio and Englezos (1997) measured incipient equilibrium propane hydrates formation conditions in aqueous triethylene glycol solution. T E G was shown to have considerable inhibiting effect on propane hydrate formation. Breland and Englezos measured the equilibrium hydrate formation data for carbon dioxide in aqueous glycerol solutions. It was shown that inhibiting effectiveness o f T E G is comparable to glycerol at the same weight % basis, but they are weaker than methanol. In order to obtain further knowledge about the inhibition ability o f the T E G and glycerol and provide data for developing and testing the predictive methods for hydrate equilibrium, more experiment data is required.  2.3. Thermodynamic models Several models have been proposed over the years to predict the equilibrium hydrate formation conditions. Hammerschmidt (1934) developed the first method used i n the industry for predicting the inhibiting effect o f methanol. The method is empirical and the reliability o f the calculations  is  variable  (Ng,  1985).  Anderson  and  Prausnitz  (1986)  presented  a  thermodynamics-based method for calculating the inhibiting effects o f methanol. They used van der Waals-Platteuw model for the solid hydrate phase, Redich-Kwong equation o f state for the vapour phase and the U N I Q U A C model for the liquid phase. Henry's constants were used for calculating the fugacities o f components in their supercritical state in the liquid phase. Furthermore, empirical correlations were used for calculating the molar volumes, partial molar  6  volumes at infinite dilution and the fugacity o f hypothetical liquid water below the ice-point temperature. Robinson and N g (1986) have mentioned a commercial computer program which allows the calculation o f the depression o f hydrate formation temperatures due to methanol. A thermodynamics-based computation methodology was presented by Englezos et al. (1991) for calculating the depression effects o f methanol and the amounts o f methanol required, which used the Trebble-Bishnoi equation o f state for the liquid and vapor phases and the van der Waals-Platteeuw model for the solid hydrate phase. Avlonitis et al. (1991) employed one o f the established three-parameter cubic equations o f state (EOS) for all fluid phases and developed special mixing rules for asymmetric interactions. However, it should be noted that the traditional models such as cubic equations are not suitable models for.associating fluids such as glycols which is associating fluids.  The statistical associating fluid theory ( S A F T ) is based on Wertheim's first-order thermodynamic perturbation theory (Wertheim, 1986) for associating fluids, and has been developed very rapidly i n recent years (Muller and Gubbins, 2001). Molecular-based equations o f states with salient physical meaningful parameters are generally more reliable than empirical models for extrapolation and prediction. Consequently, S A F T has been used to model successfully a wide variety o f the thermodynamic properties and phase equilibria for industrially important fluids containing n-alkane mixtures and alcohols aqueous solutions (Muller and Gubbins, 2001; Voutsas et al. 2000; Pfohl et al. 1999). Recently we successfully used the S A F T equation  to  model the  phase equilibria o f the  ternary  systems, water/alcohol/alcohol,  water/alcohol/hydrocarbon, water/alcohol/C02 and the constituent subsystems ( L i and Englezos, 2003; L i and Englezos, 2004). In this work, we applied the above S A F T for the prediction o f the thermodynamic inhibiting effect o f methanol, glycerol, ethylene glycol and triethylene glycol on gas hydrate formation. The vapor and liquid phases are described using the S A F T model. The van de Waals-Platteeuw model is used for the solid hydrate phase. In addition, the compositions o f the equilibrium phases are calculated. It is noted that there are no applications o f S A F T to gas hydrate formation so far.  7  2.4. Research objectives K n o w i n g hydrate phase equilibrium data for systems containing  thermodynamic  inhibitors also still incomplete, thus more experimental data for the systems containing inhibitors are required. A l s o a more powerful prediction model is need. M y specific research objectives are: •  Measuring the incipient equilibrium hydrate formation data for CH4-C2H6 and C H 4 - C 3 H 8 hydrates in the presence o f triethylene glycol and glycerol.  •  Predicting hydrate formation condition using Trebble-Bishnoi, and S A F T equations o f state.  8  3, M a t e r i a l s , A p p a r a t u s and Methods  3.1. Materials De-ionized water was used to avoid the contamination o f unwanted salt during the experiments. Distilled water was used as the input to the water purifier to produce de-ionized water. The purity o f de-ionized water was very important in this experiment because salts in the water such as N a C l , C a C l are inhibitors and w i l l affect the measurements. Triethylene glycol was obtained from Sigam-Aldrich Canada, L t d . The purity was 99%. Glycerol with 99.7% purity was obtained from Fisher Scientific.  The dry gas composition ofthe C H 4 - C 2 H 6 (C1-C2) mixture and the CH4-C3H8 (C1-C3) mixture from cylinders were determined by Gas Chromatography prior to starting  the  experiments. The calibration procedure is shown i n the Appendix C . The methane content found to be 91.0% and the balance ethane in the C 1 - C 2 gas cylinder. The methane content o f the C 1 - C 3 cylinder was 90.5% and the balance propane.  3.2. Apparatus A l l the experiments were carried out using the apparatus shown i n F i g . 2.  The  equilibrium cell is made o f Plexi-glass. The cell is immersed i n a temperature-controlled bath. The liquid i n the water bath is a mixture o f water and ethylene glycol (50%-50%) to maintain a constant temperature within the system. The temperature ofthe glycol mixture is controlled by an external  refrigerator/heater  ( V W R Scientific,  MODEL  1187).  The  solution  in  the  refrigerator/heater is a mixture o f glycol and water which is circulated i n a closed loop and exchanges heat with the solution inside the bath where the cell is immersed. Copper tubing was used for the construction o f the heater/cooling coil. A motor-driven stirring mechanism was used to maintain a relatively constant temperature (±0.10K) in the bath over a long period o f time.  A  digital pressure indictor ( H E I S E Digital Pressure Indictor) was connected to equilibrium cell to measure the pressure o f the system. The maximum pressure the digital indictor can measure is 10000 psi with ± 0.07% F . S . (Full scale) accuracy. The gas in the equilibrium cell can be transported using sampling tube to Gas Chromatography (Varian G C CX3400) to analyze the gas composition. The hydrate formation and decomposition process can be observed through the 9  Microscope ( N I K O N , S M Z - 2 T ) which is situated in front o f the water bath. It provides more accurate observation with 5 times magnification. sampling  Pump  C: Equilibrium cell T: Thermocouple G C : Gas chromatography V 1 , V 2 , V 3 , V 4 , V 5 : Valves Figure 2: Schematic of the apparatus  10  Figure3: photo o f the equilibrium cell used in the experiments  The equilibrium cell is made  from plexiglass with the dimensions o f 25 mm  (diameter)*44mm (height). Thickness o f the cell is 6mm. This column has stainless steel lids on both sides which are held in place by 3 stainless steel bolts. Four neoprene O-rings were used to seal the lids. Figure 3 shows the photo o f the equilibrium cell used in the experiments. Stirring o f the cell contents is accomplished by using a magnetic stir bar coupled to a set o f magnets underneath  the  equilibrium cell. The temperature  inside the cell  is measured with a  copper-constant thermocouple from Omega which is placed just below the liquid surface. The accuracy o f the thermocouple measurements is believed to be ±0.1K. The pressure is measured by H E I S E Digital Pressure Indictor which is calibrated by an accurate pressure gauge ( W I K A 27888DA). The pressure range is 0-10000psi and the accuracy o f the pressure measurements is± 0.07% F.S. A Varian gas chromatography model CX-3400 was used for measuring gas composition o f C 1 - C 2 (or C3)-(0%, 20.0%) T E G hydrate formation systems, and V a r i o n model CP-3800 for C 1 - C 2 (or C 3 ) - 3 0 . 0 % T E G and C 1 - C 2 (or C3)-20.0% Glycerol systems. Thermal Conductivity  11  ( T C D ) and Flame Ionization detectors (FID) are available in both chromatographs. Figure 4 shows the picture o f the CP-3800 G C used in the experiments. During the experiments, the FID with a split injector was used to analyze the gas phase composition. The main parameters of G C were set as follows: •  The temperature of the injector: 150 °C  •  The temperature o f column: 40°C  •  The temperature of the FID: 250 °C  Figure 4: the photo o f the CP-3800 Gas Chromatograph used in the experiments  Water purifier ( E L G A U H Q II, Great Britain) is used to product de-ionized water. The purity o f de-ionized water was very important in this experiment because some salt in the water act as inhibitors, such as N a C l , C a C l , which affect the measurement result. The picture is shown in figure 5 as follow:  12  Figure 5: Water purifier E L G A U H Q II Stirring o f the contents of the equilibrium cell is accomplished by a magnetic stirring system ( M O D E L 2 0 0 M I N I - S T I R R E R ) and shown in figure 6.  Figure 6 : Magnetic stirring system ( M O D E L 2 0 0 M I N I - S T I R R E R )  Figure 7 shows the picture o f the sampling tube which was used i n the experiments to collect the samples under equilibrium conditions and then inject it to the G C for analysis.  Figure 7: Sampling tube  3.3. Isothermal pressure search method Incipient equilibrium conditions refer to the situation where an infinitesimal amount of hydrates is in equilibrium with the aqueous liquid phase and with the hydrocarbon-rich vapor phase. Practically, this is the situation when a small number o f very tiny crystals (visible by a microscope) coexist i n equilibrium with the fluid phases. The isothermal pressure search method is used for the determination o f the hydrate formation conditions (Englezos and Ngan, 1994). This method is used because the system can reach thermal equilibrium faster compared to the time required for an adjustment o f the temperature. It is described next.  14  3.3.1 Estimation of the hydrate formation pressure  In order to facilitate the experimental search the equilibrium pressure values were roughly estimated based on available data. The following is an example on how to estimate the equilibrium pressures for system C l (90.4%)-C2 (9.6%)-TEG (20.2%)-H2O. The phase diagram for the systems o f C 1 - H 2 0 , C l - T E G (20.2%)-H2O and C l (90.4%)-C2 (9.6%)-H20 is shown on Figure 8. For example, to estimate equilibrium pressure at 278.0 K , a vertical line is drawn through the point at T=278.0K. It goes through the phase boundary lines o f the systems C 1 - H 2 0 , C l - T E G (20.2%)-H2O and C l (90.4%)-C2 (9.6%)-H20. A s shown in the figure, the equilibrium pressure for system C l (90.4%)-C2 (9.6%)-TEG (20.2%)-H2O at T=278K is equal to the pressure at point D ( P D ) plus the pressure difference  PA-PB-  Following the same method, other equilibrium  points can be estimated. This estimation result w i l l give us an approximation o f the hydrate formation conditions to be measured and thus expedite the process.  274  276  278  280  282  284  T e m p e r a t u r e [K] Figure 8. Roughly equilibrium pressure estimation for the system C i - C - 2 0 . 2 % T E G - H 2 O 2  3.3.2 Solution preparation  During the experiments, 20.2%, 20.0 % and 30.0% (by weight) triethylene glycol solution and 20.0% glycerol solution are needed. Triethylene glycol and glycerol are a l l miscible with water in all proportions at room temperature. The appropriate amounts o f laboratory grade T E G or 15  glycerol and deionized water were weighed using Mettler P2000 balance from Bracewell Balance and Inst. Service L T D with readabilities o f O.lmg. Then the solution was stirred for 30min for complete mixing.  3.3.3 Elimination of hydrate hysteresis phenomena  Before starting the measurements o f the incipient formation pressures at different temperatures using a particular T E G or glycerol solution, hydrate formed and decomposed in order to eliminate the hysteresis phenomenon associated with hydrate formation. The procedure involves injecting 18ml ofthe aqueous T E G or glycerol solutions into a thoroughly cleaned cell. The solution was then allowed to reach a target temperature. Hydrate-forming gas at the pressure 2000KPa was then injected into the cell and removed. The magnetic stirring system is then started. Subsequently, the cell was pressurized above the hydrate formation pressure to form large amount o f hydrate. Next; the hydrate crystals were decomposed by venting the gas out o f the cell. It is necessary to repeat this procedure at least twice to eliminate the hydrate hysteresis phenomena.  3.3.4 Hydrate formation condition measurement  After eliminating the hydrate hysteresis phenomena, the cell was pressurized around the estimated hydrate formation pressure and the system was allowed to reach the target temperature. After that, the cell pressure was further increased by introducing more gas into the cell to induce hydrate nucleation. The pressure was set well above the hydrate formation point in order to have a large driving force and induce hydrate nucleation quickly. Once a small amount o f hydrate was formed, the pressure was quickly decreased to the expected equilibrium value (estimated as shown i n figure 5) by venting some ofthe gas out ofthe cell. If this small amount o f tiny hydrate in the system were still present after at least four-hour period, the pressure was recorded. Then the pressure was dropped by about 50KPa. I f the hydrate i n the cell completely decomposed, the recorded pressure is taken as the equilibrium hydrate formation pressure at this temperature. If the hydrate was not present after the four-hour period, the pressure o f the system was below the equilibrium pressure. In this case, the experiment was repeated but the new estimated equilibrium pressure was set at a higher value (50KPa above). The experiment was terminated when the  16  pressure and temperature i n the cell were constant and an infinitesimal amount o f hydrate crystals was detectable with the aid ofthe microscope.  4. E x p e r i m e n t a l Results a n d Discussion  4.1 Validation o f experimental apparatus and procedure In order to establish the validity o f the experimental apparatus, two experiments were performed with methane and water and the results were compared with the data available in the literature. The numerical values o f the measured data and those from the literature are shown in Table 2. In figure 9, the literature data together with the experimental data obtained in this work are shown. From figure 9, we can see that our measurements compare well with those from the literature.  Table 2. Experimental data from this work and literature on methane hydrate formation in pure water solution (Adisasmito. et al., 1991)  T/K 273.4 274 274.6 276.7 278.3 279.6 280.4 280.9 282.3 283.6 284.7 286.4  Experiment Pressure/MPa Adisasmito, 1991 This work 2.68 2.94 3.05 3.72 4.39 5.02 •' 5.53 5.77 6.65 7.59 8.55 10.57  17  12 A © 10  C1-H20, Adisasmito et al., 1991 C1-H20, This work  H  ro D_  3  0)  6  A ®  272  274  ©  i  276  r-  278  280  282  284  286  288  Temperature (K) F i g u r e 9. C o m p a r i s o n o f e x p e r i m e n t a l data o b t a i n e d i n this w o r k a n d data f r o m A d i s a s m i t o  4.2 Incipient equilibrium data on methane (Cl)-ethane (C2) hydrate formation in aqueous T E G solutions After the validation o f the apparatus and the procedure, the incipient hydrate formation conditions for the C 1 - C 2 - T E G - H 2 0 system were measured. The concentrations o f T E G in the aqueous solution are 20.2wt% and 30wt%. The results are shown in table 3 and plotted in figure 10. In order to obtain a measure o f the inhibition ability o f T E G , two incipient hydrate formation data for the C 1 - C 2 - H 2 0 system with the same C l and C 2 gas composition were measured, and results are given i n table 4 and shown in figure 10 as well. The solid lines shown in the figure are drawn by "best fit" to clarify the trends o f the data. A s seen from figure 10 T E G shows considerable inhibition ability on C 1 - C 2 hydrate formation. The inhibiting effect is also proportional to the concentration of the inhibitor.  Table 5 shows the hydrate point depression for each concentration at three different pressures (Appendix I gives the explanation on how to calculate the hydrate point depression).  18  However, the experimental uncertainty is greater than the differences in hydrate point depression for aqueous T E G solution at different pressures, so it was assumed that the hydrate point depression values are not significantly affected by pressure. Table 5 also shows the change in hydrate point depression for increasing concentrations o f T E G at 2500kPa. The gas composition was measured using G C , the results is also given i n table 3 and shown in figure 11. From the figure, we can see that gas composition i n equilibrium condition has changed somewhat compared with the original gas composition from the cylinder. The C l concentration increased and C 2 concentration decreased. This is consistent with the fact that C 2 is more soluble than C l in the water phase  Table 3. Incipient equilibrium hydrate formation conditions and gas phase molar composition for the C, - C (9.0%)-TEG (20.2% and 30.0%)-H O system  2  2  Concentration of T E G (mass %)  Temperature/K  Pressure/MPa  282.0  4.458  Gas mole fraction C2 Cl 91.4 8.6  280.8  3.858  91.4  8.6  279.5  3.280  276.5  2.430  91.4  8.6  274.9  2.087  91.4  8.6  272.6  1.528  91.5  8.5  280.2  4.520  279.4  4.130  90.8  9.2  277.4  3.400  90.7  9.3  275.3  2.800  90.9  9.1  273.8  2.280  90.9  9.1  20.2%  30.0%  Table 4. Incipient equilibrium hydrate formation conditions data for the  Ci-C  2  (9.0%)-H O system  Temperature/K  Pressure/MPa  279.6  2.700  276.8  1.928  2  19  Table 5. Hydrate point depression ( A T ), and change in hydrate point depression at 2500 kPa H  (  A  T 25oo) in TEG-water Concentration of H-  (AT /K)  (AT ,2500)/K H  H  T E G (mass %)  P=2500kPa  P=3000kPa  P=3500kPa  0  0  0  0  20.2  2.3  2.3  1.8  2.3  30  4.7  4.7  4.4  2.4  Figure 10: Equilibrium data on C1-C2 hydrate formation in water-triethylene glycol solutions  20  •  C1-C2(9.0%)-TEG(20.2%)-H2O C2 in gas cylinder (9.0%)  •  •  •  •  •  7  272  274  276  278  280  282  284  temperature (K) Figure 11: C 2 mole fraction at each equilibrium condition  4.3. Incipient equilibrium data on methane-propane (C3) hydrate formation i n aqueous T E G solutions  The incipient hydrate formation conditions for methane and propane mixture (methane is 90.5% and propane is 9.5% by volume) in aqueous 20.2 and 30 wt% T E G solution and in pure water were measured and the results are given i n Table 6. The data are also plotted and shown in Figure 12. The solid lines shown in the figure are drawn by "visual fit" to clarify the trends o f the data.  Figure 12 clearly shows the inhibiting effect o f T E G i n methane-propane  hydrate  formation conditions. The hydrate point depressions for each concentration at three different pressures are obtained and shown in the table 7. The change i n hydrate point depression for increasing concentrations o f glycerol at lOOOkPa is also shown in the table.  21  The gas composition at each equilibrium condition was also obtained and the results are shown in Table 6. The comparison between propane mole fractions at each equilibrium conditions with the propane mole fraction from the original gas cylinder is plotted in Figure 13. A s seen in the figure the gas composition changes  compared to the original gas composition from the gas  cylinder. The methane concentration increased whereas the propane one decreased because propane is more soluble than methane. Moreover, we can see that the solubility o f propane in T E G solution is more than that in the pure water. Finally the gas composition does not change compared to the original gas form the cylinder for the 30% T E G solution.  Table 6. Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C , - C ( 9 . 5 % ) - H 0 and C1-C3 (9.5%)-TEG (20.0% and 3 0 % ) - H O system. 3  Concentration of T E G (mass %)  0  20  30  2  2  Gas mole fraction C, c  Temperature/K  Pressure/KPa  280.6  1190.4  278.9  990.4  277.0  783.4  275.4  645.0  90.6 90.6  9.4 9.4  273.6  521.6  90.4  9.6  281.4  1756.0  91.6  8.4  279.5  1418.0  91.4  8.7  277.3  1142.1  275.4  915.0  91.6 90.9  8.4 9.1  273.6  750.0  281.7  2211  90.3  9.7 .  280.0  1831  277.8  1390  90.1  9.9  276.0  1120  90.5  9.5  274.2  900  3  22  Table 7: Hydrate point depression (AT ), and change in hydrate point depression at 1000 kPa H  (A'lVi, 1000) in TEG-water Concentration of  (AT ,,ooo)/K  (ATH/K)  H  T E G (mass %)  P=900kPa  P=1000kPa  P=1190kPa  0  0  0  0  20  2.7  2.8  3.0  2.8  30  3.9  4.1  4.4  1.3  C1-C3 -A-  i  272  (9.5%)-H20  C 1 - C 3 (9.5%)-TEG(20%)-H2O  1  274  1  276  1  278  1  280  1  282  Temperature [K] Figure 12: Equilibrium data on C1-C3 hydrate formation in water-triethylene glycol solution  23  16 V O 14  A S  C1-C3-0%TEG-H2O C1-C3-20%TEG-H2O gas from cylinder (9.5%) C1-C3-30%TEG-H2O  12  o  2  10  HS-  M—  o E  o"  8  6  H  1 272  274  1  276  1  1  278  280  1 282  284  Temperature (K) Figure 13: C3 mole fraction at each equilibrium condition  4.4. Incipient Equilibrium Data on Methane (Cl)-Ethane (C2) Hydrate Formation in Aqueous Glycerol Solutions The incipient hydrate formation conditions for the methane-ethane mixture (methane is 91.0% and propane is 9.0% by volume) in 0% and 20wt%> aqueous Glycerol solutions were measured and the results are given in Table 8. The data are also plotted and shown in Figure 14.  It is obvious that glycerol also has a considerable inhibiting effect in hydrate formation. The hydrate point depression for each concentration at three different pressures is shown in the table9. A s seen the hydrate point depression at a given inhibitor concentration is independent of pressure.  The gas composition at each equilibrium condition was also obtained. The results are shown in Table 8. The comparison o f C 2 mole fractions at each equilibrium condition with the C2 mole fraction in the original gas cylinder is plotted in Figure 15. A s seen the gas composition at each equilibrium condition does not change significantly compared to the cylinder gas composition.  24  Table 8: Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C C (9.0%)~H O and C , - C (9.0%)-Glycerol (20.0%)-H O system. r  2  2  2  Concentration of Glycerol (mass %) 0  20  2  Gas mole fraction C C,  Temperature/K  Pressure/KPa  279.6  2.700  276.8  1.928  274.2  2130  90.9  9.1  276.3  2620  91.1  8.9  278.8  3420  90.8  9.2  280.1  4100  281.3  4751  90.8  9.2  2  Table 9. Hydrate point depression (AT ) of Glycerol-water system. H  Concentration of  (ATH/K)  Glycerol (mass %)  P=2200kPa  P=2400kPa  P=2600kPa  0  0  0  0  20  3.3  3.2  3.0  6000 -••  C1-C2(9.0%)-20.0% Glycerol (this study) C1-C2 (9.0%)-H2O (this study)  5000  TO 0_ 4000 0  3  (/) W <D  3000  2000  272  274  276  278  280  282  Temperature (K) Figure 14: Equilibrium data on C1-C2 hydrate formation in water-Glycerol solution 25  12 C1-C2(9.0%)-Glycerol (20.0%0-H2O system C2 from gas cylinder (9.0%) 11  o 10 ro "£ (D  o o o o E  8  H  CM O  274  276  278  280  282  Temperature (K) Figure 15: C 2 mole fraction at each equilibrium condition in water-glycerol solution  4.5. Incipient Equilibrium Data on Methane (Cl)-Propane (C3) Hydrate Formation in Aqueous Glycerol Solutions.  The incipient hydrate formation conditions for the system o f C 1 - C 3 (9.5%)-20.0% glycerol-H20 were measured as well. The results are shown i n the tablel 1 and plotted in the figure 16. The hydrate point depression at three different pressures is shown in table 11. It can be assumed that the hydrate point depression values are not affected by pressure at the same concentration.  The gas composition at each equilibrium condition is obtained using G C and the results are shown i n Table 6 as well. The comparison o f C 2 mole fractions at each equilibrium conditions with the C 2 mole fraction from the original gas cylinder is plotted i n Figure 17.  26  Table 10. Incipient equilibrium hydrate formation conditions data and gas phase molar composition for the C , - C (9.5%)-H 0 and d - C (9.5%)-Glycerol (20.0%)-H O system 3  2  Concentration of Glycerol (mass %)  0  20  3  2  Gas mole fraction C, C  Temperature/K  Pressure/KPa  273.6  522  275.4  645  277  783  278.9  990  90.6 90.6  9.4 9.4  280.6  1190  90.4  9.6  274.2  870  90.0  10.0  275.7  1020  90.0  10.0  278.3  1330  280.3  1690  90.1 90.1  9.9 9.9  281.6  1990  3  Table 11: Hydrate point depression ( A T ) of Glycerol-water system H  Concentration of  (ATH/K)  Glycerol (mass %)  P=840kPa  P=1000kPa  P=1190kPa  0  0  0  0  20  3.2  3.2  3.4  27  C1-C3 (9.5%)-Glycerol (20.0%)-H O (this study) 2  2000  ro  Q_  C1-C3 (9.:  1500  Z3  in  1000  500  274  272  276  278  282  280  Temperature (K) Figure 16: Equilibrium data on C1-C3 hydrate formation in water-glycerol solution  16 •  C1-C3(9.5%)-20.0%Glycerol-H2O C3 from gas cylinder  14  c o  12  o Q. E o o  10  -*—>  H  o E CO  O  •6  H  272  274  276  278  280  282  Temperature (K) Figure 17: C 3 mole fraction in each equilibrium condition in water-glycerol solution  5.  H y d r a t e f o r m a t i o n p r e d i c t i o n u s i n g T r e b b l e - B i s h n o i e q u a t i o n o f state ( T - B E o S )  The well-known T B EoS is applied to predict the all above four-component hydrate formation systems (Trebble and Bishnoi, 1988). The methodology o f the calculation has been presented in details elsewhere (Englezos et al. 1991). The binary interaction parameters for the equation are shown in the table 12. The computational flow diagram is shown i n the figure 18 (Englezos et al. 1991). The predictions are compared to the experimental results and the absolute average deviation o f predicted pressure ( A A D (P), %) is defined as follows (Englezos et al. 1991)  P  AAD{P){%) =  -P  cat  exp  xlOO  exp  where N  p  is the number o f data points  Table 12: Set o f binary interaction parameters for each system system H20-CH4 H20-C2H6 H20-C3H8 CH4-C2H6 CH4-C3H8 TEG-CH4 TEG-C2H6 TEG-C3H8 H20-TEG  K 0.4284 0 0 -0.0052 -0.0135 -2.399 0.299 0.465 0 a  K -0.1727 0 0 0 0 0 0 0.881 0.854 b  Kd -1.2266 -0.2611 -0.2969 0 0 0.952 -0.295 1.412 0  Literature source Englezos et al. (1991) Trebble and Bishnoi (1998) (binary interaction parameter) Jou and Otto (1987) (equilibrium data) Cartays and Starling (1996) (equilibrium data)  29  Enter T (or P), feed composition and initial guess for P (or T) •  *  Perform T P Flash  Figure 18: Computational hydrate formation P (or T)  5.1. Prediction o f Methane (Cl)-Ethane (C2) Hydrate formation in aqueous T E G solutions  Predictions o f methane and ethane gas mixture hydrate formation systems with different concentrations o f T E G using T - B equation o f state were shown in the table 13 and plotted in the figure 19. It is obvious that the prediction is very good.  30  Table 13: experimental data and prediction o f Methane (Cl)-Ethane (C2) Hydrate formation in aqueous T E G solutions Concentration o f T E G (mass %) 0  20.2  30.0  1.0  -I 272  Temperature ( K )  P  279.6 276.8 282.0 280.8 279.5 276.5 274.9 272.6 280.2 279.4 277.4 275.3 273.8  e q  (experiments) (MPa) 2.700 1.928 4.458 3.858 3.280 2.430 2.087 1.528 4.520 4.130 3.400, 2.800 2.280  P  e q  (prediction) (MPa)  4.67 3.97 3.31 2.52 2.18 1.64 4.6 4.15 3.39 2.8 2.45  AADP (%)  4.0%  2.74%  1  1  1  1  1  274  276  278  280  282  1 284  Temperature (K) Figure 19: experimental data and predictions on C1-C2 hydrate formation in water-triethylene glycol solution  31  5.2. Prediction o f Methane (Cl)-Propane (C3) Hydrate formation in aqueous T E G solutions  Predictions o f methane and propane gas mixture hydrate formation systems with different concentrations o f T E G using T - B equation o f state were shown i n the table 14 and plotted in the figure 20.we can see that T B E o S gave prediction in good agreement with the experimental data. Table 14: experimental data and predictions on C1-C3 hydrate formation in aqueous T E G solution Concentration o f T E G (mass %)  0  20.0  30.0  Temperature ( K ) 280.6 278.9 27.7.0 275.4 273.6 281.4 279.5 277.3 275.4 273.6 281.7 280.0 277.8 276.0 274.2  P  e q  (experiments) (MPa) 1.19 0.99 0.78 0.65 0.52 1.76 1.42 1.14 0.91 0.75 2.21 1.83 1.39 1.12 0.9  P  e q  (prediction) (MPa) 1.18 1 0.78 0.64 0.53 1.74 1.41 1.13 0.89 0.74 2.2 1.83 1.38 1.11 0.88  A A D P (%)  1.06  1.91  0.86  32  272  274  276  278  280  282  temperature (K) Figure20: experimental data and predictions on C1-C3 hydrate formation in water-triethylene glycol solution  5.3. Prediction o f Methane (Cl)-Ethane (C2) Hydrate formation in aqueous 20.0wt% glycerol solutions  The incipient hydrate formation conditions for C 1 - C 2 (9.0%) gas mixture i n the presence o f 20.0wt% glycerol were predicted using T B E o S . The predictions were compared with the experimental data and shown in table 15 and plotted in the figure 21. From the figure, we can see that the prediction is very comparable with the experimental data. The A A D P is only 0.85%>.  33  Table 15: experimental data and predictions on C1-C2 hydrate formation in 20.0wt% glycerol solution Temperature ( K )  P  e q  274.2 276.3 278.8 280.1 281.3  (experiments) (MPa) 2.13 2.62 3.42 4.10 4.75  P  e q  A A D P (%)  (prediction) (KPa) 2.15 2.78 3.63 4.30 4.90  0.85%  1  272  274  276  278  280  282  temperature (K) Figure 21: experimental data and predictions on C1-C2 hydrate formation in water- glycerol solution  5.4. Prediction o f Methane (Cl)-Propane (C3) Hydrate formation in aqueous 20.0wt% glycerol solutions  The incipient hydrate formation conditions for C1-C3 (9.5%) gas mixture in the presence of 20.0wt% glycerol were predicted using T B E o S . Table 16 compares the experimental data with the predicted values. It can be seen from figure 22 that the experimental data matches well with the predictions. 34  Table 16: experimental data and predictions on C1-C3 hydrate formation in 20.0wt% glycerol solution Temperature ( K )  P  e q  274.2 275.7 278.3 280.3 281.6  (experiments) (MPa) 0.87 1.02 1.33 1.69 1.99  P  e q  A A D P (%)  (prediction) (KPa) 0.93 1.10 1.48 1.82 2.11  1.6%  0.8 4 0.6 0.4 272  274  276  278  280  282  temperature (K) Figure 22: experimental data and predictions on C1-C3 hydrate formation in water- glycerol solution  35  6. Hydrate Formation Prediction using SAFT Equation of State 6.1. Thermodynamic Framework In a system o f N components containing solid hydrate (H), vapor (V) and liquid (X), the thermodynamic equilibrium is represented by, 0'=i //=//  AO  (1)  (j=l...,n )  (2)  c  where /  is the fiigacity o f component i or j; N is all the components; n is the hydrate forming c  components including water. In the above equations, the fugacities in vapor, liquid and solid phases may be calculated using a suitable thermodynamic model.  6.2. Equation o f State for Vapor and Liquid Phases In this work, the S A F T Equation o f State is employed to predict the high-pressure vapor-liquid phase equilibrium ( V L E ) o f water/gas/inhibitor systems. The residual Helmholtz free energy for an n-component mixture o f associating chain molecules can be expressed as the sum o f hard sphere repulsion, hard chain formation, dispersion and association terms as follows A  res  =A-  A  id  =A  hs  +A  chain  +A  disp  +A  (3)  assoc  where A' is the free energy o f an ideal gas with the same density and temperature as the system, d  A  hs  is the free energy o f a hard-sphere fluid relative to the idea gas, A  cham  when chains are formed from hard spheres, A  and A  d,sp  assoc  is the free energy  are the contributions to the free  energy o f dispersion and association interactions, respectively. The molecules are described as homonuclear and chainlike. They are considered to be composed o f spherical segments o f equal-size and equal-interaction parameters with Lennard-Jones potential.  6.2.1 Hard-sphere repulsion term  The  hard  sphere  term  A  hs  is  calculated  with  the  Boublik-Mansoori-Carnahan-Starling-Leland equation as follows (Boublik, 1970; Mansoori et al. 1971). 36  i hs  -£x,.m,.ln(l-C )  7=1  NkT  3  np  (4)  (=1  s  where  (5)  o  (6) In the above equations, p  is the total number density o f molecules i n the solution, and  n  d  is the hard-sphere diameter o f segment i. Its relationship with the soft-sphere diameter (cr..)  u  is based on the Barker-Henderson perturbation theory and is expressed by Cotterman (Cotterman et al. 1986) as follows  d,  \ + 0.2977kT/e,  o~  a  1 + 0.33163yt77£„. + 0.001047(,W7£,.)  where s  (V)  2  is the energy parameter o f the L - J potential.  u  6.2.2. Hard Chain Formation Term The chain term A "  was derived by Chapman (Chapman et al. 1989)  chm  4 chain  NkT  (8) i=I  where 1  ,  a jj  M  C  2  c  d  2  | 2 I  2  (1-C3)  3  (9)  Eq.(9) for like segments becomes g  1-<T,  2(l-^f  2(l-Cj  (10)  6.2.3. Dispersion Term This term is calculated by using an expression based on the Lennard-Jones potential (Cotterman et al. 1986) 37  ^—  . _ L U?  = Y .m  s  x  +  ai)  A?/T ) R  where ^»  (12)  = p (- 8.5959 - 4 . 5 4 2 4 p - 2 . 1 2 6 8 p * + 10.285/^) R  R  ^2" =  (13)  (-1-9075 + 9.9724/^ -22.216/?* + 15.904/^)  (14) 6 (15)  < 3  4ln n  n  1=1  y=l  (16)  (17) 7=1  (=1  (18)  In the above equations, cr. and £  i}  are the cross parameters between different segments  and are calculated b y the following combining rules  ^.=h+o-J/2  .(19)  ^=(1-^)V^7 where k  () 20  is binary interaction parameter.  u  6.2.4 Association term  The Helmhotz energy due to association is calculated b y the expression o f Chapman (Champmanet al. 1990) assoc  NkT  = 1-  where M  (21) 4.  ±-  is number o f associating sites on molecule i. The term X ' is defined as the mole A  i  fraction o f molecules i not bonded at site A , i n mixtures with other components, and is given by:  38  (22)  1+ J  where ^  i  B  means summation over all sites on molecule j, Aj, B ,, Cj, • •  ^  ]  m  e  a  n  s  j  summation over all components, p is the total molar density o f molecules i n the solution, and A'  is associating strength and is given by:  A Bj  A"'  BJ  = dlg^idJ^K^lexpis^'  In Eq.(23),  K  AB  lkT)-\]  (23)  is the bonding volume and s  AB  Ik  as the associating  energy. For  cross-associating mixtures, we have the mixing rules K''  =  =K >  A B  A,B  +K ' ')I2  s ' ' = s < > = (1 - k A B  A  B  AB  where k  (24)  A B  )4(e - >s ' ') A  B  (25)  A B  is binary associating interaction parameter.  AB  6.3. M o d e l for hydrate Phases The introduction o f inhibitor (alcohol) i n a liquid water-hydrocarbon mixture alters the prevailing structure i n the aqueous phase. Alcohol-water and alcohol-hydrocarbon molecular interactions result i n a "less structured" organization o f water molecules, thus reducing the possibility o f forming stable hydrate. It is noted, however, that alcohol is not incorporated in the hydrate lattice (Davidson et al. 1977). Hence, the model o f van der Waals and Platteeuw (van der Waals and Platteeuw, 1959), based on statistical mechanics, is valid and used i n the work for the fugacity o f water i n the hydrate phase. It is expressed as follows:  '-A/C^  (26)  RT where  = E(v.lna IC,./,))  (27)  +  -K-*  m=l  here Ap^ ~ T  H  -  y'=l  - p£ >  a n Q l  i * represents the difference between the chemical potential o f  water i n the empty lattice (MT) and that in the hydrate lattice (H). C  mj  is the Langmuir  39  constants and presents the gas-water interactions. It is given by John and Holder (John and Holder, 1982)-check:  -W {r)^  r  mi  KT  Vdr  (28)  here W (r) is the function for the cell potential, obtained from M c k o y and Sinanoglu (Mckoy mj  and Sinanoglu, 1963).For temperatures above 260 K , the Langmuir constants are obtained from the expression o f Parrish and Prausnitz (Parrish and Prausnitz, 1972) The fugacity o f water i n the empty hydrate lattice, f^  T  chemical AjU™ ~ ° T  L  potential = /u^  -  T  zr=ft exp v  where f£'  o f water  in  the  empty  lattice  is obtained from the difference in the and  that  o f pure  liquid  water,  , using the following equation (Holder et al. 1980): (29)  RT  is the fugacity o f pure water, and it can be calculated from the S A F T equation state.  The calculation o f Aju% ° is given elsewhere (Holder et al. 1980) T L  6.4. Parameters for S A F T The S A F T equation requires three pure-component parameters for non-associating fluids and five parameters for associating fluids. These parameters are the L - J potential well depth (  e  Ik), the soft sphere diameter o f segments ( ) , the number o f segments o f the molecule ( ) , a  m  AB  the bonding volume {  K  ) and the association energy between sites A and B (  8  ). In the case o f  mixtures, the S A F T equation uses van der Waals one-fluid mixing rules with the binary interaction parameter, k , for the dispersion interactions and the parameter, kf tj  B  , for the  associating interactions. In this work, these parameters required in the S A F T are taken from L i and Englezos and are shown i n Table 17 and 18. A s described in that work the four-site model are used for the hydrogen bonds o f the water molecule and the two-site model for the hydrogen bonds of each hydroxyl group on the alcohol. It is noted that the binary interaction parameter, k  tj  for the  systems with E G , T E G or glycerol was taken equal to 0 since it was adequate to give satisfactory results 40  Table 17: Segment Parameters for Pure Fluids for the SAFT equation Fluid  cr  m  elk  s lk AB  K  (10- m )  (k)  (K)  ,o  A  B  Water  0.982  2.985  433.91  1195.20  0.038  Methanol  1.124  3.642  309.90  2320.77  0.019  EG  1.043  4.232  354.65  2375.26  0.020  Glycerol  2.180  4.194  405.08  2195.15  0.004  TEG  3.204  3.805  252.03  2470.02  0.061  Methane  1.186  2.990  160.84  Ethane  1.437  3.1.93  199.73  Propane  2.367  3.078  174.07  C0  1.833  2.654  165.80  2  Table 18: Binary interaction Parameters for the SAFT equation Systems  K  Systems  **  Methane/water  0.0291  Ethane/methanol  0.0641  Ethane/water  0.0068  C0 /methanol  0.2025  C0 /water  -0.0452  Methane/methanol  0.2204  Methanol/water  -0.1043  2  2  6.5. Hydrate Formation Prediction W i t h the binary interaction parameters o f the constituent binary subsystems and the molecular parameters ofthe pure components from L i and Englezos, the S A F T incorporated with the model o f van der Waals and Platteeuw is employed to predict the hydrate formation conditions for  the  following  COi/water/mefhanol, glycol  nine  systems:  methane/water/methanol,  methane/water/glycerol,  ( E G ) , methane/water/triethylene  CCVwater/glycerol,  glycol  (TEG),  ethane/water/methanol, methane/water/ethyl ene  ethane/water/triethylene  glycol,  propane/water/triethylene glycol. The incipient equilibrium hydrate formation pressure was calculated at a given temperature and at a given overall concentration ofthe inhibitor (methanol, E G , T E G and glycerol). The inhibitor concentration is usually reported as the water phase concentration possibly because when an experiment is conducted water is mixed with an amount of the inhibitor and the resulting concentration is reported. That concentration is considered the 41  overallconcentation i n our calculation. It is noted that the overall concentrations must be specified in the isothermal isobaric flash calculation procedure. Table 19 summarizes the results. The absolute average deviation o f predicted pressure ( A A D (P), %) is defined as follows: cal  l  AAD(P)(%)  =  exp  xlOO  exp  where N  p  is the number o f data points.  6.51. Inhibiting effect of Methanol  The experimental data along with predictions are given in figure 23, 24, 25 for methane, ethane and carbon dioxide hydrate. Table 19 also provides information about the A A D ( P ) % . A s seen reasonably good predictions are obtained even at high pressures and at high methanol concentrations, it should be noted that the parameters required by the van der Waals model also play a role i n the quality ofthe predictions.  42  Table 19 Predictions of the hydrate formation pressures Gas  Concentration  T-range  P-range  A A D (P) (%)  o f inhibitor i n  (K)  (MPa)  This work  aqueous phasse  Data source Sloan  Englezos et  (1998)  al.(1991)  (wt%)  Methane  (Ng and  10% M e t h a n o l  266.2-286.4  2.14-18.8  1.87  3.48  3.31  20% Methanol  263.3-280.2  2.83-18.75  4.36  1.26  7.37  35% Methanol  250.9-267.8  2.38-13.68  11.46  7.24  22.12  50% Methanol  233.1-255.3  1.47-16.98  18.53  9.95  53.62  10% E G  270.2-287.1  2.42-15.6  0.93  (Robinson  30% E G  267.6-280.1  3.77-16.14  0.59  and  50% E G  263.4-266.5  9.89-15.24  0.50  1986)  10% T E G  274.6-293  3.17-25.57  0.78  (Ross  20% T E G  275-293  4\37-39.87  0.71  Toczylkin,  40% T E G  274.5-283  7.27-35.17  0.82  1992)  2 0 % glycerol  273.8-286.2  4.39-20.53  0.36  (Ng  5 0 % glycerol  264.2-276.2'  4.53-20.53  15.19  Robinson,  Robinson, 1985; Robinson and Ng, 1986)  Ng,  and  and  1994) 10% M e t h a n o l  268.3-281.4  0.417-2.8  0.63  3.27  10.21  (Ng  and  Robinson,  20% Methanol  263.5- 274.1  0.55-2.06  0.28  6.77  2.73  35% Methanol  252.6- 262.2  0.502-1.48  0.29  14.06  11.35  50% M e t h a n o l  237:5-249.8  0.423-1.007  0.48  -  60.09  10% T E G  277-282  1.0-1.8  1.14  (Ross  20% T E G  273.7-283  0.79-2.63  1.68  Toczylkin,  40% T E G  275-275.8  1.97-2.3  4.64  1992)  10% T E G  272.3-276.8  0.18-0.51  1.69  (Servio  20% T E G  271.7-275.2  0.25-0.50  1.88  Englezos,  30% T E G  270.2-272.4  0.29-0.425  0.31  1997)  10% M e t h a n o l  269.6-274.9  1.58-3.48  0.80  6.27  21.17  20% Methanol  264.0-268.9  1.83-2.94  2.11  15.15  26.37  35% Methanol  242.0-255.1  0.379-1.77  1.87  21.85  37.56  Carbon  50% Methanol  232.6-241.3  0.496-1.31  0.69  -  57.21  dioxide  10% glycerol  272.3-279.3  1.391-3.345  0.35  1985, Ng et al.  Ethane  Propane  1985a, 1985b)  (Ng  and  and  and  Robinson, 1985;  2 0 % glycerol  270.4-277.1  1.502-3.556  2.32  2 5 % glycerol  269.6-276.8  1.48-3.96  0.43  3 0 % glycerol  270.1-273.2  2.03-2.981  2.74  Robinson  and  Ng,1986) (Ng  and  Robinson, 1994; Breland  and  Englezos, 1996)  43  3.00  Symbols: Experimental • 10wt% * 20 wt% • 35 wt% • 50 wt% - Predicted  2.50  CL  Symbols: Experimental • 10wt% T 20 wt% * 35 wt% • 50 wt% Predicted  1.50  CL  1.00  o.oo  250.0  230.  260.0  270.0  280.0  290.0  T(K)  240.0  250.0  260.0  T(K)  F i g u r e 2 3 : M e t h a n e hydrate f o r m a t i o n i n the presence o f methanol: data and predictions based o n S A F T  I  i  i  i  i  230.0  240.0  250.0  260.0  270.0  Figure 24: Ethane hydrate formation in the presence o f methanol: data and predictions based on S A F T  T(K)  Figure 25: C 0 hydrate formation in the presence o f methanol: data and predictions based on S A F T 2  6.5.2. Inhibiting effect of Ethylene Glycol  Table 19 and Figure 26 present the prediction o f inhibiting effect o f ethylene glycol (EG) on methane hydrate formation with 10-50% o f E G using the S A F T equation. A s seen, the predictions compare quite well with the experimental data. The total A A D is 0.67%>. The maximum deviation is only 0.93%>. This demonstrates the excellent prediction function o f the S A F T . E G molecule has more functional groups for association than methanol. Thus its 44  associating behavior is expected to be stronger than that o f methanol. It can be seen from the above calculations that the stronger the associating behavior o f the fluid is, the stronger the prediction ability o f the Molecular-based S A F T . 18.00  16.00  14.00  12.00  ro Q_  10.00  /A  8.00  / •  6.00  Symbols: Experimental  4.00  •  10wt%  *  30 wt%  •  50 wt% Predicted  2.00 i  i  264.0  268.0  1 272.0  i  i  i  i  284.0  288.0  292.0  296.0  1  276.0  280.0  300.0  T (K)  Figure 26: Methane hydrate formation in the presence o f ethylene glycol: data and predictions based on S A F T  264.0  268.0  272.0  276.0  280.0  284.0  28£  T (K)  Figure 27: Methane hydrate formation in the presence o f glycerol: data and predictions based on S A F T  6.5.3. Inhibiting effect of Glycerol The S A F T equation was also employed to predict the inhibiting effect o f glycerol on the hydrate formation o f methane and CO2, respectively. The results are presented in Table 19 and Figures 27 and 28. A s seen, the prediction on methane hydrate formation is excellent and the deviation is only 0.36% at 25% o f glycerol. A t 50%> o f glycerol, a deviation of 15.19% is acceptable. Finally the calculated pressures for the CGVglycerol/ water system with S A F T are in quite good agreement with the data at low and high concentrations o f glycerol. The total A A D is 1.46%.  45  45.00  Symbols: Experimental  Symbols: Experimental • 10wt% A 20 wt% • 40 wt% Predicted  40.00 35.00 30.00  3.00 „  25.00  ra CL S. 20.00 CL 15.00 1.50 10.00  274.0  270.0  5.00 o.oo  276.0  1  265.0  270.0  T(K)  275.0  280.0  T(K)  Figure 29: Methane hydrate formation in the presence o f T E G : data and predictions based on S A F  Figure 28: C 0 hydrate formation in the presence o f glycerol: data and predictions based on S A F T 2  6.5.4 Inhibiting effect of Triethylene Glycol  The inhibiting effect o f T E G on the hydrate formation from methane, ethane and propane, was also computed using S A F T . The results are shown in Table 19 and Figures 29-31. The total predicted A D D s are 0.77%, 2.49% and 1.29% for the methane/TEG/water, ethane/TEG/water and propane/TEG/water, respectively. The agreement between predictions and data is quite good.  0.450 h  CL 0.350 °- 0.300  Symbols: Experimental • 10wt% * 20 wt% • 30 wt% Predicted  0.250 0.200 0.150 274.0  276.0  278.0  280.0  282.0  284.0  286.0  288.0  T(K)  Figure 30: Ethane hydrate formation in the presence o f T E G : data and predictions based on S A F T  290.0  _i  I—  270.0  i  272.0  T(K)  Figure 31: Propane hydrate formation in the presence o f T E G : data and predictions based on S A F T  46  6.5.5. Discussion  A s seen from the above calculations S A F T results in satisfactory to excellent predictions of the inhibiting effect o f methanol, . E G , glycerol and T E G on gas hydrate formation. The S A F T models takes into account chain formation and molecular associating interactions in addition to repulsion and dispersion. In systems containing inhibitors (methanol, E G , glycerol and T E G ) and water association interactions are expected to be strong. Accordingly, the association term i n the S A F T model is significant and plays a very important role for the prediction o f gas hydrate formation in the presence o f the inhibitors.  47  7. Conclusion and Recommendations 7.1. Conclusion  Triethylene glycol ( T E G ) and glycerol are common thermodynamic inhibitors used in the gas and o i l industries. K n o w i n g their inhibiting abilities is very important not only for in-situ guidelines but also valuable for validating the hydrate prediction models. In this work, inhibiting effects o f T E G and glycerol were determined experimentally through incipient hydrate formation measurements using a 91-9 m o l % mixture o f methane and ethane and a 90.5-9.5 m o l % mixture o f methane and propane. The concentrations o f the T E G in the water phase werr 20 and 30 wt % whereas that o f glycerol was 20 wt %. Moreover the inhibiting effects were also calculated by using the van der Waals Platteeuw model for the hydrate and two equations o f state for the fluid phases (Trebble-Bishnoi equation o f state and S A F T ) . The S A F T model was employed for the prediction o f the thermodynamic inhibiting on single gas hydrate formation only. Both models performed reasonably well for engineering-type calculations.  7.2. Recommendations  First, the use o f a direct cooling system is recommended in order to minimize temperature fluctuations. Second, it is recommend flushing the sampling tube with Helium since more than the pressure dropped by more than 3 psi after taking gas sample at equilibrium condition using gas sampling tube. Finally, the computational methodology using the S A F T model should be extended to deal with hydrate formation from gas mixtures too.  48  8. References Anderson, F . E . ; Prausnitz, J. M . Inhibition of Gas Hydrates by Methanol. AIChEJ.  1986, 32,  1321-1333. Avlonitis, D ; Todd, A . C.; Danesh, A . A Rigorous Method for the Prediction o f Gas Hydrate Inhibition by Methanol i n Multicompont Systems. Proc. First Int. Offshore and Polar Engineering Conf., Edinburgh, 11-16 August 1991, Int. Soc. O f Offshore and Polar Engineers. Berecz, E . ; Balla-Achs, M . Study in Inorganic Chemistry 4: Gas hydrates; Elsevier: Amsterdam,  1983;184-188. Bishnoi, P.R.; Pankaj D ; Dholabhai, J. 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Phys. 1971,  54, 1523.  M c k o y , V . ; Sinanoglu, O. Theory of Dissociation Pressures in Some Gas Hydrates. J. Chem. Phys. 1963,  38, 2946-2956.  Muller, E . A . ; Gubbins, K . E . Ind. Eng. Chem. Res., 2001,  40, 2193-2211.  N g , H.-J.; Robinson, D . B . Hydrate Formation in Systems Containing Methane, Ethane, Propane, Carbon Dioxide or Hydrogen Sulfide in the Presence of Methanol. Fluid Phase Equilib. 1985, 21, 145-155. N g . , H.-J.; Chen, C.-J.; Robinson, D . B . Gas Proc. Assn. Rsch. Rpt.  1985a, 87, March.  N g . , H.-J.; Chen, C.-J.; Robinson, D . B . Gas Proc. Assn. Rsch. Rpt.  1985b, 92, September.  N g . , H.-J.; Robinson, D . B . (First) International Conference on Natural Gas Hydrates, Annals of N e w Y o r k Academy of Sciences. 1994,  715, 450.  Pankaj D ; Dholabhai, J; Scott Parent ; Bishnoi, P.R.. Equilibrium Conditions for Hydrate Formation from Binary Mixtures of Methane and Carbon Dioxide in the Presence o f Electrolytes, Methanol and Ethylene G l y c o l . Fluid Phase Equilibria 1997,14, 235-246. Parrish, W . R . ; Prausnitz, J . M . Dissociation Pressures of Gas Hydrate Formed by Gas Mixtures.  Ind, Eng. Chem. Process Desigh Develop. 1972, 11,26-34. Pfohl, O.; Pagel, A . ; Brunner, G . Fluid Phase Equilib. 1999,  157, 53.  Ripmeester, J . A . ; Tse, J.S.; Ratcliffe, C.I. and Powell, B . M . A new clathrate hydrate structure, Nature. 1987,325, 135-136 Ripmeester, J . A . ; Ratcliffe, C.I. Xenon-129 N M R studies of clathrate hydrates: new guests for structure II and structure H , Journal of Physical Chemistry. 1990,  94(25), 8773-8776.  51  Ripmeester, J . A . ; Ratcliffe, C . L ; K l u g . D . D . , Tse, J.S. Molecular perspectives on structure and dynamics in clathrate hydrates, Annals of the N e w York Academy o f Sciences 715 (International conference on natural gas hydrates, 1993). 1994,  161-176.  Robinson, D . B . ; N G , H.-J. Hydrate Formation and Inliibition in Gas or Gas Condensate Streams.  Journal of Canadian Petroleum Technology. 1986, 25, 26-30. Roch, A r m i n . Experimental and Theoretical Studies o f Hydrate Formation o f as Mixtures in Inhibitor-containing Aqueous Solutions. Fortschritt-Berichte V D I , Reihe 3: Verfahrenstechnik  2003, 768 i - x i i i , 1-279. Ross, M . J.; Toczylkin, L . S. J. Chem. Eng. Data. 1992,  37, 488.  Ross, M . J ; Toczylkin, L . S . Hydrate Dissociation Pressures for Methane or Ethane in the Presence of Aqueous Solutions o f Triethylene Glycol. J. Chem, Eng. Date 1992,  37, 488-491  Servio, P; Englezos, P. Incipient Equilibrium Propane Hydrate Formation Conditions in Aqueous Triethylene G l y c o l Solution../ Chem. Eng. Data. 1997, 42, 800-801. Servio, P; Englezos, P. Incipient Equilibrium Propane Hydrates Formation Conditions in Aqueous Triethylene G l y c o l Solution. J. Chem. Eng. Data 1997, 42, 800-801 Servio,  Phillip.  Incipient  Equilibrium  C02-CH4-neohexane-NaCl-H20  and  Gas  Hydrates  Formation  CH4-polypropylene  Conditions  glycol-NaCl-H20  for  the  Systems.  International journal of the Society of Materials Engineering for Resources. 1999, 7(1), 24-28. Sloan, E . D . Cathrate Hydrates of Natural Gases. 1998: Marcel Dekker, N e w York. Song, K . Y . ; Kobayashi, R. Final Hydrate Stability Conditions o f a Methane and Propane Mixture in the Presence o f Pure Water and Aqueous Solutions o f Methanol and Ethylene Glycol. Fluid Phase Equilib. 1989,  47, 295-308  Sloan, E . D . Jr. Clathrate Hydrates o f Natural Gases, 2  n d  edition, Marcel Dekker, New York,  1990. Sloan, E . D . Jr. Clathrate Hydrates o f Natural Gases, 1 edition, Marcel Dekker, N e w York, st  1998. Svartas, T . M . ; Fadnes, F . H . Methane Hydrate Equilibrium Date for the Methane-Water-Methanol System up to 500 bara. Proceedings, second (1992) International offshore and Polar Engineering Conference, San Francisco, June 14-19, 1992;  Chung, J.S.,Natvig, B . J . L i , Y - C , Das, B . M . ,  Eds.;pp 614-619. Trebble, M . A . ; Bishnoi, P.R. Extension of the Trebble-Bishnoi equation o f state to fluid mixtures  Fluid Phase Equilibria. 1988, 40, 1-21.  52  Voutsas, E . C ; Boulougouris G . C . ; Economou, I. G . ; Tassios, D . P. Ind. Eng. Chem. Res. 2000, 39,797-804. Wertheim, M . S. J. Chem. Phys. 1986, 87, 7323. van der Waals, J . H . The statistical mechanics of clathrate compounds. Trans. Faraday Soc. 1956, 52, 184-193. van der Waals, J . H . ; Platteeuw, J.C. Clathrate Solutions. Adv. Chem. Phys., 1959, 2, 1-57.  53  Appendix A: Pressure Calibration Curve H E I S E Digital Pressure Indictor-90 I A used in the experiment was calibrated using a pressure gauge ( W I K A 27888DA) with accuracy of 50KPa. The calibration result is shown in Table A - l and plotted in figure A - l .  Table A - l : original data for pressure calibration  Point Point Point Point Point Point Point Point  1 2 3 4 5 6 7 8  Pressure from W I K A 27888DA (KPa)  Pressure from H E I S E Digital Pressure Indictor-90 LA (KPa) 0.00 1016 2058 2995 4047 4873 5900 6632  0.00 1014 2055 2992 4047 4875 5901 6633  Pressure Calibration 7000 6000  CD  5000  C L  dj 4000 3  (/> QJ  3000  CT>  c  T3 03 CD  2000 A 1000  A  oA  1000  2000  3000  4000  5000  6000  7000  Real Pressure (KPa)  54  Appendix B: Thermocouple calibration Curve The Copper-constant thermocouple (Omega, +0.1 °C accuracy) used in the experiment was calibrated using the standard thermometer .The calibration results are shown in the table B - l and plotted i n the figure B - l  Table B - l : original data for thermocouple calibration  Point Point Point Point Point Point Point  Temperature from standard thermometer (°C) 5.33 4.44 3.44 2.61 1.50 0.22 -0.33  1 2 3 4 5 6 7  Temperature form the thermocouple (°C) 5.9 4.9 3.8 2.8 1.7 0.3 -0.2  i—:—;— —:—•—;— —:—"—'— '—:— —:—;—i—:— —~~""—'—i—'—'—\—i—;—~ —i—i J-'l'.'{).:.'• Z" ZZ: Z.\ .Z." Z."ZZZ 2 ZZ'ZZZ ZZ iZZZZZ" ZZ4ZZ ZZZZZ.5ZZ ZZ'ZZ] Ze :  r  r _ —  :  r  r  Real temperature |°C]  Figure B - l : thermocouple calibration curve  55  APPENDIX C: The sample of calibrating gas compositionfromgas cylinder The gas composition from gas cylinder always changes with the time. Before starting the experiment, the gas composition from gas cylinder was calibrated based on analysis results o f G C . The pure methane gas was used as standard gas. A sample o f calibrating the gas composition from methane-ethane cylinder is shown in the bellow (the original gas composition from the cylinder is 90.0% o f methane and 10.0% o f ethane).  1.  Injecting five gas samples o f the pure methane and methane-ethane gas mixture from gas  cylinders to G C separately. The results were shown in table C - l and C-2.  Table C - l : Peak areas o f pure methane and methane-ethane gas samples from cylinders Peak area o f pure methane Peak area o f methane i n mixture  Sample 1 1674355  Sample 2 1681198  Sample 3 1663087  Sample 4 1668086.  Sample 5 1676407  Average 1672627  1522968  1529976  1511419  1524300  1519501  1521633  Table C-2: Peak area percentages o f methane and ethane gas samples from gas cylinders. Area % o f methane i n gas mixture Area % o f ethane i n gas mixture 2.  Sample 1  Sample 2  Sample 3  Sample 4  Sample 5  Average  80.72  80.66  80.64  80.58  80.62  80.64  19.28  19.34  19.36  19.42  19.38  19.36  the real gas composition from methane-ethane gas cylinder can be calculated as follows:  Methane in mixture=peak area of pure methane/peak area of methane in mixture=l 521633/1672627=90.97% Ethane in mixture  =100%-90.97%=9.03%  56  3.  after calibrated the gas composition from the cylinder, response factor was also calculated  as follows:  Considering the response factor of methane is equal to 1, and then the response factor o f ethane is calculated as follows:  Response factor= (area percentage of ethane/real composition of ethane)/ (area percentage of mthane/real composition of methane) = (19.36/9.03)/ (80.64/90.97)=2.419  57  Appendix D: The sample of calculating gas composition in hydrate equilibrium condition. Three gas samples were taken to do G C analysis when hydrate was in equilibrium condition. The following shows how to calculate gas composition in hydrate equilibrium condition based on methane-ethane (9.03%)-TEG (20.2%)-H2O system at 276.5 K , and the related G C date are shown in the table C - l .  Table D - l : G C data for the on methane-ethane (9.03%)-TEG (20.2%)-H2O system at 276.5 K Peak percentage  Sample 1 Sample 2 Sample 3  (%) methane 81.382 81.531 81.275  Concentration (%)  Composition (%) sum  ethane methane 81.382 18.618 81.531 18.469 81.275 18.725 average  ethane 7.698 7.636 7.742  89.080 89.167 89.017  methane 91.36 91.44 91.30 91.37  ethane 8.64 8.56 8.70 8.63  The peak percentages o f three samples obtained from G C analysis are shown in the second and third columns. The gas composition o f each sample which shown i n third and forth columns is equal to the peak percentage divided by response factor. The sum ofthe composition o f methane and ethane is given i n the fifth column. Then the concentration o f methane or ethane is equal to their composition divided by sum as shown in the last two columns. Finally the average gas composition is obtained as shown in the table.  58  Appendix E: original data for calibrating gas composition from C1-C3 gas cylinder Table E - l : Peak areas o f pure methane and methane-propane gas samples from cylinder Peak area o f pure methane Peak area o f methane i n mixture  Sample 1 1674355  Sample 2 1681198  Sample 3 1663087  Sample 4 1668086  Sample 5 1676407  Average 1672627  1500568  1490058  1545065  1512791  1527514  1515199  Table E-2: Peak area percentages o f methane and propane gas samples from gas cylinder. Area % o f methane i n gas mixture Area % o f ethane i n gas mixture  Sample 1 76.24  Sample 2 76.24  Sample 3 76.22  Sample 4 76.19  Sample 5 76.20  Average 76.22  23.76  23.76  23.78  23.81  23.80  23.78  59  Appendix F: original GC analysis data in hydrate equilibrium conditions for the C1-C2-TEG (20.2%) systems. Table F - l : original G C analysis data in hydrate equilibrium conditions for the C 1 - C 2 - T E G (20.2%) systems.  Point 1 @ 2 8 2 . 0 K Point 2 @ 280.8K  Point 4 @ 2 7 6 . 5 K K  Point 5 @ 2 7 4 . 9 K  Point 6@272.6K  Area % o f methane i n gas mixture 81.62 81.43 81.51 81.44 81.36  Area %> of ethane i n gas mixture 18.38 18.57 18.49 18.56 18.64  Sample 1  81.38  18.62  Sample 2  81.27  18.73  Sample 3  81.27  18.73  Sample 1  81.56  18.44  Sample 2  81.55  18.45  Sample 3  81.44  18.56  Sample 1  81.71  18.29  Sample 2  81.53  18.47  Sample 3  81.51  18.49  Sample Sample Sample Sample Sample  1 2 3 1 2  Table F-2. Original G C analysis data for the system with 30% T E G using the CP-3800 G C  C1-C2-30%TEG  Point 1 Point 2@279.4K Point 3@277.4K Point 4@275.3K Point 5 @ 2 7 3 . 8 K  Area % of methane i n gas mixture  Area % o f ethane or in gas mixture  80.86 80.64 80.91 80.95  19.14 19.36 19.09 19.05  .  60  Appendix G: original GC analysis data in hydrate equilibrium condition for the C1-C3-TEG (0%, 20.0%, and 30.0%) systems. Table G - l . original G C analysis data for the system with 0% and 20% T E G using the CX-3400 GC. Area % o f Area % o f propane in gas methane in gas mixture mixture 28.4 Point 3 @ 277.0K Sample 1 71.6 71.21 Sample 2 28.79 0%TEG Point 4 @ 275.4 Sample 1 71.55 28.45 Point 5 @273.6K  Sample 1  71.19  28.81  Sample 2 Sample 1  72.21 74.63  28.79 25.37  Sample 2  73.69  26.31  Sample 3  73.77  26.23  Point 2 @279.5K  Sample 1  73.36  26.64  Point 3 @277.3K  Sample 1  74.06  25.94  Sample 2  73.92  26.08  Sample 1  72.27  27.73  Sample 2  72.14  27.86  Point 1@281.7K  Sample 1  73.48  26.52  Point 2@277.8K  Sample 1  73.01  26.99  Point 3@276.0K  Sample 1  74.0  26.0  Point 1 @281.4K 20% T E G  Point 4 @275.4K  30.0%TEG  61  Appendix H: original GC analysis data in hydrate equilibrium condition for Cl-C2-Glycerol (20.0%) and C1-C3-Glycerol (20.0%) systems. Table H - l : original G C analysis data i n hydrate equilibrium condition for C l - C 2 - G l y c e r o l (20.0%) and C 1 - C 3 - G l y c e r o l (20.0%) systems suing CP-3800 G C  80.71  Area % o f ethane or propane in gas mixture 19.29  80.72 81.28 80.90 73.16 73.14 72.15 72.84  19.28 18.72 19.10 26.84 26.86 27.25 27.16  Area % o f methane in gas mixture  Cl-C2-20%glycerol  Cl-C3-20%glycerol  Point Point Point Point Point Point Point Point Point  1@281.3K 2@280.IK 3@278.8K 4@276.3K 5@274.2K 1@280.3K 2@278.3K 3@275.7K 4@274.2K  62  Appendix I: Calculation of hydrate point depression (AT ) H  The method o f calculating the hydrate point depression is explained as follows based on the C 1 - C 3 - T E G (0%, 20.0%, and 30.0%) hydrate formation systems. Firstly, the experimental data which is shown in the table 1-1 is plotted on the figure 1-1, and then quadratic equation ( y - y + ax + bx ) is selected to fit the data and the fitting curves are shown 2  0  on the figure 1-1 as well. The hydrate point depression at each pressure point can be obtained roughly. For example, at lOOOKPa, a horizontal line is drawn which crosses the three equilibrium curves, and then vertical lines are drawn from interactions, so the temperature can be obtained and is shown i n the table 1-2. The hydrate point depression at lOOOKPa can be calculated and presented in the table 1-2 as well. Table 1-1: experimental data for C 1 - C 3 - T E G (0%, 20.0%, and 30.0%) hydrate formation systems Concentration o f T E G (mass %)  0  Temperature/K  Temperature/ C  Pressure/KPa  280.6  7.5  1190.4  278.9  5.8  990.4  277.0  3.9  783.4  275.4  2.3  645.0  0.5  521.6  281.4  8.3  1756.0  279.5  6.4  1418.0  277.3  4.2  1142.1  275.4  2.3  915.0  273.6  0.5  281.7  8.6  750.0 2211  280.0  6.9  1831  277.8  4.7  1390  276.0  2.9  1120  274.2  1.1  900  273.6  20  30  u  '  63  •  •  C1-C3-0%TEG  C1-C3-20.0%TEG  2  C1-C3-30.0%TEG  Poly.(Cl-C3-20.0%TEG) — - •Poly.(Cl-C3-0%TEG)  Poly. (C1-C3-30.0%TEG)  0 1  A  3  4  5  6  7  8  9  10  Temperature (°C) Figure 1-1: experimental data and fitting curves Table 1-2: temperatures of three hydrate formation systems and Hydrate point depression (ATH) at lOOOMPa  Temperature ( C) 5.8 3.0 1.8 U  C1-C3-0%TEG C1-C3-20.0%TEG C1-C3-30.0%TEG  Hydrate point depression A T 0(5.8-5.8) 2.0 (5.8-3.0) 4.0 (5.8-1.8)  H  64  

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