Ind. Eng. Chem. Res. 1993,32, 1251-1274
1251
REVIEWS Clathrate Hydrates Peter Englezos Department of Chemical Engineering, The ‘niversity of British Columbia, 2216 rain Mall, Vancouver,British Columbia V6T 124,Canada
Clathrate hydrates or gas hydrates are solid solutions. Water molecules are linked through hydrogen bonding and create cavities (host lattice) that can enclose a large variety of molecules (guests). There is no chemical bonding between the host water molecules and the enclosed guest molecule. The clathrate hydrate crystal may exist at temperatures below as well as above the normal freezing point of water. Clathrate hydrates have been a source of problems in the energy industry because the conditions a t which oil and gas are produced, transported, and processed are frequently suitable for clathrate hydrate formation. Naturally occurring clathrate hydrates in the earth, containing mostly methane, are regarded as a future energy resource. These methane hydrates, however, are potentially threatening t o the global environment if they decompose due to the greenhouse effect. Several innovative separations based on clathrate hydrate formation with applications in a variety of industrial sectors have been examined in the laboratory and pilot-plant stage. This paper reviews the status of our current knowledge on clathrate hydrates. The emphasis is on the aspects related to technological problems and opportunities that arise from the artificial or natural formation and decomposition of clathrate hydrates. However, a description of the fundamentals of formation, properties, and structure is also presented, and aspects related to the molecular simulation are discussed. Studies on calorimetric properties, orientational disorder, guest-guest interactions, and nuclear magnetic resonance are not reviewed, but literature references are made. Clathrate hydrates arouse great interest within chemical and petroleum engineering, chemistry, earth, and environmental sciences.
Q
1. Introduction
In 1810,Sir Humphry Davy discovered that a solid could be formed when an aqueoua solution of chlorine (then known as oxymuriaticacid) was cooled below 9.0“C (Davy, 1811). Faraday confirmed the existence of this solid compound and suggested that ita composition was nearly 1 part of chlorine and 10 parts of water (Faraday, 1823). It is now known that there are more than 100specieswhich can combine with water and form nonstoichiometricsolid compounds. The term “gas hydrate” has been applied to these solids (Davidson, 1973),but the correct designation is clathrate hydrates. In this study, these compounds will be referred to as clathrate hydrates or gas hydrates interchangeably. Typical examples of hydrate-forming substances include CH4, CZHB,CsHs, COz, and HzS. In Figure 1,a vessel containing water and propane is shown. One may easilyattain temperatureand pressure conditions that will cause hydrate crystals to form. In general, the crystals tend to agglomerate near the gas-liquid interface. Harmens and Sloan (1990)presented a description of the propanewater phase diagram. During the first 100 years after the discovery of gas hydrates, the interest in these compounds was academic. It was concerned with the identification of (a) the species that can form hydrates and (h) the pressuretemperature conditions at which the formation occurs. In 1934,at a time when the oil and gas industry in the United States was growing rapidly, it was recognized that the plugging of natural gas pipelines was due not to ice formation but to formation of clathrate hydrates of natural gas (Hammerschmidt, 1934). That time marked the beginning of an intense research effort on natural gas hydrates by the
-7 I Hydrate
Figure I. Propane gas hydrate formation in the laboratory.
industry, the government, and the academia. Deaton and Frost (1946)offered a good account of those research efforts. The crystal structure of gas hydrates became known through X-ray diffraction studies in the early 1950s and aided the development of a statistical thermodynamic model for the hydrate as a solid solution (van der Waals and Platteeuw, 1959). A major development occurred in the 1960s. It was then realized that clathrate hydrates of natural gas exist in vast quantities in the earth’s crust (Chersky and Makogon, 1970;Katz, 1971;Makogon et al., 1972). The large amounts of gas in hydrate form justify efforts to find economic recovery schemes (Finlay and Krason, 1990). The need to understand the clathrate hydrates of natural gas motivated most of the research efforts, but other technological considerations also stimulated research on gas hydrates. During the 1960s and
0888-5885/93/2632-1251$04.00/0 0 1993 American Chemical Society
1252 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
early 1970s work was done to develop a process for the desalination of seawater via gas hydrate formation (Knox et al., 1961; Barduhn et al., 1962; Vlahakis et al., 1972). The feasibility of the process was demonstrated on a pilotplant scale. However, it was not developed industrially since it was not as economical as other processes. Other separation processes through hydrate formation are now approaching commercial stage (Douglas, 1989). In addition to an overwhelming number of research papers, several reviews, symposium proceedings, and three monographs on clathrate hydrates have been published during the past 40 years. Mandelcorn (1959) reviewed the structure, molecular and thermodynamic properties, and uses of clathrates. van der Waals and Platteeuw (1959) reviewed the knowledge on clathrate hydrates and presented a model to describe the chemical potential of water in the hydrate. Byk and Fomina (1968) reviewed the structure and properties. Hand et al. (1974) presented a general view of gas hydrates. Davidson (1973)offered the most comprehensive review on the properties and structures. Jeffrey also reviewed the structures (Jeffrey and McMullan, 1967; Jeffrey, 1984a). Holder et al. (1988) reviewed the gas hydrate equilibrium predictive methods. In his monograph, Makogon (1981) described much of the work in the Soviet Union on the thermodynamics and kinetics of hydrate formation and the formation of hydrates in porous media. Berecz and Balla-Achs (1983) reviewed the literature up to 1980. Cox (1983) edited a volume with eight papers on the properties, phase equilibria, kinetics, and in-situ natural gas hydrates. Sloan (1990a) offered the most comprehensive treatment on the subject. The emphasis was on the clathrate hydrates of natural gas. The structure and properties were discussed. A list of all the phase equilibrium data together with the experimental and predictive methods was also included. The treatment of the subject of in-situ gas hydrates included geological,geophysical,and reservoir engineering aspects. The kinetics of formation and the hydrate prevention methods in the hydrocarbon industry were also discussed. The thermodynamics and kinetics of gas hydrates were also reviewed separately by Sloan (1990b). Englezos et al. (1990) reviewed the work at Bishnoi’s laboratory on the kinetics of hydrate formation. Belosludov et al. (1991) and Zubkus et al. (1992) reviewed the efforts to formulate a theory of nonideal clathrate solutions. Yamamuro and Suga (1989) and Suga et al. (1992) discussed orientational ordering phenomena. The review papers and the monographs dealt primarily with the clathrate hydrates of natural gas and the fundamentals. Less emphasis was given to the technologicalaspects outside the oil and gas industry. The subject of clathrate hydrates is broad, and lately, rapid developments are taking place. The scope of this review is to present the current knowledge on clathrate hydrates. The objectives of the study are to review the fundamentals, the technological developments, and the energy and environmental implications. Historical aspects are presented when they are essential in understanding the developments and the current status. Following the introduction, information on the structure and properties of clathrate hydrates is presented in the second section. The subject of phase equilibrium is discussed in the third section. In the fourth section, the kinetics of hydrate formation and decomposition are reviewed. The technological aspects are presented in the fifth section, while the environmental implications are discussed in the last section of the paper.
2. Clathrate Hydrates
The clathrate hydrates are a special type of inclusion compound. In this section, the inclusion compounds are classified. The structure of the clathrate hydrate crystals is described, and a brief reference to the physical and thermodynamic properties is made. 2.1. Inclusion Compounds. Inclusion compounds generally consist of two molecular species that arrange themselves in space so that one (host) physically entraps the other (guest). The geometrical relationship between the host and the guest is the basis for the classification of the inclusion compounds into (i) clathrate or cage; (ii) channel or canal, and (c) layer (Mandelcorn, 1959;Huang et al., 1965). Hitchon (1974)adopted Brown’sclassification (Brown, 1962)of inclusion compounds and included three more types. Powell (1948) at the University of Oxford was the first to describe the clathrate structure and named clathrate compounds those inclusion compounds in which two or more components are associated without ordinary chemical union but through complete enclosure of one set of molecules in a suitablestructure formed by another. In clathrates, the host molecules arrange themselves in hollow polyhedra. The cavities of these polyhedra accommodate the guest molecules. Hagan (1962) and Atwood et al. (1984) offered comprehensive coverage of the subject of inclusion compounds. The clathrate compounds are divided into two categories. Those having water as the host species are called aqueous (water) clathrates or simply clathrate hydrates. They are also commonly known as gas hydrates. The other category includes the clathrates in which the host is not water (nonaqueous clathrates). This work is concerned with the clathrate hydrates. 2.2. Formation and Structures. Palin and Powell (1945) reported the results of the X-ray analysis of the crystalline compound formed between quinol (hydroquinone) and sulfur dioxide. In 1948,they discussed and revealed the structure of the clathrate compound of quinol with methanol and other compounds (Palin and Powell, 1948a,b). Later, X-ray analysis revealed that gas hydrates could be recognized as clathrates and crystallize in two distinct cubic structures. von Stackelberg (1949a,b) reported the first results of his group’s investigations over 20 years at the University of Bonn. The conclusion of the work was that all crystals crystallize in the cubic class. Claussen (1951a-c) at the University of Illinois constructed a cubic unit cell containing 136 water molecules and proposed structure I1 hydrates. His results were immediately confirmed by von Stackelberg and Muller (1951a,b). Structure I gas hydrates were determined simultaneously by Pauling and Marsh (1952) at the California Institute of Technology and by Muller and von Stackelberg (1952). Davidson and his co-workers at the National Research Council (NRC) of Canada carried out many structural, calorimetric, and molecular simulation studies. Their structural work led to (a) the elucidation of the type of hydrate structure (11)that the small molecules of argon, krypton, oxygen, and nitrogen form (Davidson et al., 1984a,b; Tse et al., 198f3), as it was previously suggested on a purely theoretical basis by Holder and Manganiello (1982), and (b) the identification of a third hydrate structure (Ripmeester et al., 1987; Ripmeester and Ratcliffe, 1990). Clathrates are solid solutions of a volatile solute in a host lattice (van der Waals, 1956). The solvent is known as the empty hydrate lattice. It is thermodynamically
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1253
Figure 2. Pentagonaldodecahedral cavity with a methane molecule. The hydrogen atoms of the water molecules are not shown. Linkage of the cavities through their vertices creates structure I hydrate. A unit cellcontains two such cavities plus six tetrakaidecahedral, which are formed as a result of the packing of the pentagonal dodecahedra. Methane forma structure I hydrate. When the dodecahedraare linked throughtheirfaces, hydrateshctureIIisformed. Aunitcellcontains 16 dodecahedral cavities plus 8 hexakaidecahedral ones formed as a result of the packing. Propane forms structure I1 hydrate.
unstable. It owes its existence to the fact that the water molecules are linked through hydrogen bonding and form a lattice-like structure with cavities. The diameter of the cavities is between 780 and 920 pm. Molecules which do not interfere with the hydrogen bonding of water molecules and have a diameter that is smaller than the diameter of the cavity can render the structure stable under suitable pressure and temperature conditions (Jeffrey, 1984a).This stable structure is the gas hydrate. The basic cavity formed by hydrogen-bonded water molecules is the pentagonal dodecahedron. It is a polyhedron with 12 pentagonal faces and can accommodate only one guest molecule. Such a cavity with a methane molecule inside is shown in Figure 2. Structure I gas hydrates are formed when these cavities arrange themselves in space in amanner that they link together through their vertices. Because dodecahedra are not able to pack together precisely, a tetrakaidecahedron, a polyhedron with 12 pentagonal and 2 hexagonal faces, is created. The unit cell of structure I gas hydrate is a cube with a 1200pm side length and contains 46 water molecules. The oxygen atoms of these water molecules are arranged in such a manner that two pentagonal dodecahedra and six tetrakaidecahedra are formed. Molecules that form structure I gas hydrates have diameters in the range 410580 pm (Handa and Tse, 1986). Structure I1 gas hydrates are formed when the pentagonal dodecahedron cavities arrange themselves in space in a manner that they link together through face sharing. As a result of this arrangement, a hexakaidecahedron, a polyhedron with 12 pentagonal and 4 hexagonal faces, is created. A unit cell of gas hydrate of structure I1 is a cube of side length close to 1730 pm, contains 136 water molecules, and consists of 8 hexakaidecahedron and 16 pentagonal dodecahedron cavities. Molecules that form structure I1 hydrates have diameters of less than 410 pm or greater than about 550 pm (Handa and Tse, 1986). Davidson (1973) listed structural and stability characteristics of individual clathrate hydrates. That list should be modified to reflect the fact that Ar, Kr, 0 2 , and NZare now known to form structure I1 hydrates. The positions of the water molecules in the unit cells are well-defined. Their orientation, however, is not. The reviews by Jeffrey andMcMullan (1967),Davidson (1973),Jeffrey (1984a,b), and Sloan (1990a) should be consulted for additional information on structures I and 11. Recently, on the basis of NMR and powder diffraction data, the existence of a third structure was reported
(Ripmeester et al., 1987). This is now known as structure H and can occur naturally. Ripmeester and Ratcliffe (1990) defined the guest size range which will promote structure H hydrates and identified 24 structure H guests. Lederhos et al. (1992)presented the first phase equilibrium data for structure H hydrates. In particular, they studied the formation of hydrates from methane and adamantane. Adamantane (CloH16) is a major component of diamondoids found in hydrocarbon reservoirs in the Gulf of Mexico. The importance of the new structure to the hydrocarbon industry is significant, and further structural investigations and phase equilibrium data are needed. Another recent development came from the infrared spectroscopic investigations of Fleyfel and Devlin (1991). They claim that C02 may be the "largest" small molecule, like Ar, Kr, 0 2 , and N2, able to form structure I1 hydrate. They studied the growth of COz hydrate on ethylene oxide hydrate and on tetrahydrofuran (THF) hydrate. Structure I hydrate was formed with ethylene oxide and COzoccupied both the small and the large cavities. When C02 hydrate was grown epitaxially to the THF hydrate, structure I1 was formed and C02 occupied the small cavities only. Spectroscopic studies involving H2S and THF had been reported previously by Devlin and co-workers (Richardson et al., 1985). In the structure I1 double hydrate of THF and H2S, THF molecules occupy the large cavities while those of H2S occupy the small ones. It should be noted that Sloan (1990a) had expressed the opinion that H2S and N2 might undergo structural changes similar to those of methane in the presence of larger molecules. 2.3. Properties. Davidson and his co-workers reviewed the spectroscopic properties of ice and gas hydrates (Davidson, 1973; 1983; Davidson and Ripmeester, 1984). On the basis of these studies, Sloan (1990a) reported the spectroscopic, mechanical, and transport properties of gas hydrates and compared them with those of ice. The dielectric and nuclear magnetic resonance properties are affected by the orientational disorder of the water molecules in the hydrate lattice. Parsonage and Staveley (1984) reviewed the calorimetric studies. Handa and his co-workers at NRC carried out calorimetric studies at ambient and high pressures (Handa et al., 1984; Handa, 1986a-c, 1988). Sloan (1990a) reported his and Kobayashi's work. He also reviewed the experimental methods for the measurement of heat capacity, enthalpy, and thermal conductivity of clathrate hydrates. Sloan and Fleyfel(l992) proposed a method to estimate the heat of hydrate decomposition at temperatures above 0 "C. Dharma-wardana (1983) demonstrated how to predict the thermal conductivity of ice and clathrate hydrates using the mean-free path formula. Cady (1983) reviewed the issues related to the composition of gas hydrates. The density of gas hydrate crystals varies from 0.8 to 1.2 g/cm3. 3. Clathrate Hydrate Phase Equilibrium
The studies on clathrate hydrate equilibrium focused on gathering incipient equilibrium hydrate formation data and on developing predictive methods for the calculation of phase equilibria. The incipient formation conditions refer to the situation in which an infinitesimal amount of the hydrate phase is present in equilibrium with fluid phases. Knowledge of the equilibrium hydrate-forming conditions is necessary for the rational and economicdesign of processes in the chemical, oil, gas, and other industries where hydrate formation is encountered. A thorough account of the experimental work and the computational methods on hydrate equilibria is available (Holder et al., 1988; Sloan, 1990a). In this section, some historical
1254 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1.o
Hydrale-Vapor-Aqueous Liquid ( K u b l a el ai. 1984) 0
0.8 A
Vapor Pressure (Kubola et .I. 1984)
Hydrate-Liqutd-Aqueous Liquid (Kubola et ai. 1984)
where C,, are the Langmuir constants, urn are the number of cavities of type m per water molecule in the hydrate lattice ( V I = 1/23 and u2 = 3/23), and f j is the fugacity of component j in the fluid phase with which hydrate is in equilibrium. The fugacity of water in the empty hydrate lattice, is computed by the equation
A
0
n 0.6
2
3 2
1 K2 42
a
0.4
ftT,
n 0.2
A 0.0' 269
Q1
' 271
.
273
.
I
275
'
I
277
.
I
279
'
281
Temperature (K) Figure 3. Propane-water partial phase diagram in the hydrating region. The continuous lines are interpolationsof the experimental data.
developments will be presented together with recent advances on the computational methods. The emphasis will be on the thermodynamic models that describe the hydrate and the fluid phases. In a multicomponent system with N substances from which only N h can be present in the hydrate crystal, the following phases might be present at incipient equilibrium: solid hydrate structure I (Hl) or solid hydrate structure I1 (H2), aqueous liquid (La),nonaqueous liquid (Ln), gas (V), and ice (I). Only one hydrate phase will form because the other requires a higher pressure. In Figure 3, the propane-water partial phase diagram in the hydrating region is shown. It is based on experimental data and indicates the loci of the various types of equilibria. Point Q1 denotes equilibria among hydrate-ice-vapor rich in propane and liquid water and point Q2 equilibria among hydrate-liquid water-vapor and liquid propane. The line KL is the vapor pressure of propane. Calculation of the incipient equilibrium conditions requires models that allow the calculation of the fugacities of all substances in every phase where they are present. 3.1. Thermodynamic Models. In the previously described multicomponent hydrate-forming system there were three fluid and two solid phases. The ice phase is considered to be pure water. The fugacity of water in the ice phase can be calculated according to a method outlined by Anderson and Prausnitz (1986). Next, the models for the other phases are described. 3.1.1. Hydrate Phase (H). The elucidation of the structures of clathrate hydrates facilitated the development of a statistical thermodynamics model for the description of the hydrate phase. van der Waals (1956) gave a statistical mechanical treatment of the nonaqueous clathrates by considering those with one type of cavity and one type of guest. The theory was subsequently extended to the clathrate hydrates (Platteeuw and van der Waals, 1958). Barrer and Stuart (1957) considered two types of cavities and different types of guests. Finally, van der Waals and Platteeuw (1959) extended these views and formulated a model for clathrates with different types of cavities and different types of guests. In a thorough discussion of the clathrate solutions, they presented a rigorous analysis of the thermodynamic behavior of clathrates on the basis of statistical mechanics. Their model is the basis of all the gas hydrate equilibrium predictive methods. It gives the fugacity of water in the hydrate by the equation
where the quantity inside the parentheses is given by a correlation proposed by Holder et al. (1980) and fL,' is the fugacity of pure liquid water. 3.1.1.1. Langmuir Constants. The Langmuir constants account for the guest molecule-water interactions in the clathrate hydrate lattice. They can be computed if a potential function for the interaction between a guest and a water molecule in a cavity is available (van der Waals, 1956). Because the location of the water molecules in the cavity is known from crystallographic studies, it is possible to add all of the binary interactions and calculate the cell potential function at a radial distance, r, from the center of the cavity. The equation that relates the Langmuir constant with the spherically averaged cell potential function, W ,at a distance, r, from the center of the cavity is given by (3) The potential, W ,arises from the host molecules located on the surface of a cavity of radius Ri. van der Waals (1956), Platteeuw and van der Waals (1958), Barrer and Stuart (1957), and van der Waals and Platteeuw (1959) used the Lennard-Jones 12-6 spherically symmetric potential to represent the binary interaction between a guest molecule and a water molecule of the cavity. They applied the Lennard-Jones and Devonshire cell theory (Hill, 1956) for the evaluation of the partition function of a hydrateforming molecule within the cavity. The calculated incipient hydrate formation pressures were very close to those experimentally obtained for monatomic gases and quasispherical molecules. However, the values for CO2 and CzHs were not as good. McKoy and Sinanoglu (1963) found that better results could be obtained for calculating the incipient hydrate formation pressures by using the Kihara potential function. This potential assigns a linear or spherical core to each molecule and therefore includes the effect of the finite size of the molecules on their interaction. The Kihara parameters were calculated from second virial coefficient data. Instead of using these data to calculate the potential parameters, Kobayashi and co-workers estimated them by fitting experimental data for CHI, Nz, and Ar hydrates obtained in his laboratory (Marshall et al., 1964; Saito et al., 1964; Nagata and Kobayashi, 1966a). The estimated parameters were then used to predict hydrate formation pressures of ternary mixtures (Saito and Kobayashi, 1965; Nagata and Kobayashi, 1966a,b). Parrish and Prausnitz (1972) used the Kihara potential and fitted parameters for 15 different gases. They presented the first algorithm for the calculation of incipient gas hydrate formation conditions from multicomponent mixtures. Holder and his co-workers attempted to remove some of the assumptions in the van der Waals-Platteeuw theory (John and Holder, 1981, 1982, 1985; Holder and Hand,
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1255 1982; Holder and John, 1983; John et al., 1985). They introduced two corrections to account for all nonidealities in the molecular interaction between the enclathrated gas and the hydrate lattice water molecules. In their modifications they also tried to keep the Kihara parameters very similar to those obtained by second virial coefficient data. This work is summarized by Holder et al. (1988). The above corrections were considered promising toward improving the prediction of hydrate formation conditions. The improvements, however, were not found to be dramatic, and according to Avlonitis et al. (1991a,b), the effect of nonidealities had been overestimated. Because the Kihara potential is not giving a fundamentally accurate description of the potential field in the cavities (Rodger, 1989),it is reasonable to attribute the inaccuracies of the predictive methods to the solid solution theory approximations. It should not be neglected, however, that the accuracy of the fluid phase equilibria calculations may affect the results significantly. Lundgaard and Mollerup (1991) have fitted Kihara parameters to a three-phase hydrate-ice-vapor equilibrium line. By using only these data for parameter estimation, they avoided the influence of uncertainties in the calculation of gas-phase fugacities and hydrocarbon solubility. The efforts to develop a nonideal solid solution model for the clathrate hydrates continue. Istomin (1987) considers guest-guest interactions in the calculation of the Langmuir constants. Belosludov et al. (1991) and Zubkus et al. (1992) discussed the revision of the van der Waals theory to include such interactions. Langmuir constants can also be calculated by Monte Carlo simulation (Tester et al., 1972). Molecular simulation techniques such as Monte Carlo (MC) and molecular dynamics (MD) are powerful tools to study the potential energy fields in the cavities and investigate the importance of the assumptions on which the ideal solid solution thermodynamic model of gas hydrates is based (Rodger, 1990a). Tse and coworkers at the National Research Council in Canada have performed MD simulations to study the vibrational properties of ice (Tse et al., 1984a) and structure I and I1 gas hydrates (Plummer and Chen, 1983;Tse et al., 1983a,b, 1984,1986; Davidson et al., 1986; Tse and Klein, 1987). Rodger (1989) performed MD simulations using the same intermolecular potentials as those employed by Tse and co-workers. He examined the factors that influence the potential energy field in the small cavities of structure I gas hydrates. Rodger also examined and tested basic assumptions of the cell theory (Rodger, 1990b, 1991a,b). It was found that the assumption that the free energy of the host lattice is not perturbed by the presence of guest molecules is not appropriate for gas hydrates. The implications to the thermodynamic stability of gas hydrates were discussed. The assumption that the free energy of the water lattice is not affected by the nature or number of guest molecules was also tested and its validity challenged. Sparks and Tester (1992) presented a numerical model for calculating guest-host and guestguest intermolecular potential energy contributions for an infinite water clathrate lattice. It was found that guestguest interactions and the subsequent water shell interactions affect the calculation of the Langmuir constants. Wallqvist (1992) performed MD simulations to study the stability of methane hydrates (structure I) in the presence of methanol. Surprisingly, it was found that it is possible to include small amounts of methanol in the lattice structure without melting the crystal. Earlier, however, Davidson et al. (1981) reported that methanol is not incorporated in the hydrate lattice. The results
were based on NMR and dielectric studies of hydrates of ethylene oxide and tetrahydrofuran formed in the presence of methanol. Tanaka et al. (1992) investigated the role of water-water interactions in the structure of methanolwater solutions by computer simulations. The structure and thermodynamic properties were also studied by Tanaka and Gubbins (1992). 3.1.2. Vapor Phase (V). The fugacity of a component in a mixture is computed by
fy = yi$;P
i = 1, ...,N
(4)
where yi and 4; denote the mole fraction and the fugacity coefficient for component i at a pressure P. The fugacity coefficient is computed from an equation of state (EoS). Any EoS can be used. Examples include the PengRobinson EoS (Peng and Robinson, 1976), the RedlichKwong EoS (Redlich and Kwong, 19481,and the TrebbleBishnoi EoS (Trebble and Bishnoi, 1988). 3.1.3. Aqueous Liquid Phase (La). The modeling of a liquid phase that contains molecular, ionic, and macromolecular solutes dissolved in water is a challenging problem. Progress, however, has been made, and models are available for the calculation of the fugacities. Liquid phases that do not contain electrolytes can be modeled by an EoS or an activity coefficient model (Prausnitz et al., 1986; Model1 and Reid, 1983). When an EoS is used, the fugacity of component i is given by
f? = x""pp
(5)
where X? and (b? are the mole fraction and the fugacity coefficient of component i in the aqueous liquid phase at pressure P. Using activity coefficients, the fugacities are given by
where yi is the activity coefficient of component i and
6is a standard-statefugacity. The EoS approach has the advantage of providing a consistent representation of vapor-liquid equilibria up to high pressures, whereas the activity coefficient approach is suitable for liquid phases at low to moderate pressures. Recent advances in mixing rule development include models that combine the benefits of both approaches (Heidemann and Fredenslund, 1989). 3.1.3.1. Effect of Electrolytes, Alcohols, and Polymers. Some of the dissolved solutes such as electrolytes, alcohols, and water-soluble polymers alter the state of the liquid phase and cause inhibition of the hydrate formation conditions. This change is manifested in the activity of water, which is reduced. Figure 4 indicates the effect of these solutes on the locus of propane hydrate-vapor-liquid water equilibria. Because of this action, methanol and ethylene glycol have been widely used for the prevention of natural gas hydrate formation. In this work, the models available for the description of the aqueous liquid phase will be discussed. An aqueous liquid phase that contains molecular compounds such as methanol but not electrolytes or macromolecular solutes can be described by an EoS. As the results by Avlonites et al. (1991a,b) and Englezos et al. (1991) have shown, an EoS describing all fluid phases can be combined with the van der Waals theory and provide a satisfactory hydrate equilibria predictive method. An aqueous liquid phase that contains water and electrolytes and other materials whose solubility can be ignored, such as light hydrocarbons, can be rigorously described by an electrolyte activity coefficientmodel. Such models are available (Zemaitis et al., 1986). Englezos and
1256 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Om8 0.7
.
-.
Plrre Water (Kubotn et 4.1984)
Vapor Rersm (Kutatact al. 1984) 0 2.5 wt % NCI (Kubotaet 4.1984) 0 5 wt 96 Methanol (Ng and Robinson, 1983) 0
0
n
E
0.5
m
0.1: 270
'
I
272
.
'
274
'
I
276
'
1
278
.
' 280
" 282
Temperature (K) Figure 4. Effect of sodium chloride, methanol, and poly(ethy1ene oxide) (PEO) on the hydrateaqueous liquid-vapor phase equilibria. This graph shows the basis of the thermodynamics based methods for the inhibition of hydrate formation.
Bishnoi (1988a) demonstrated the use of Pitzer's model (Pitzer, 1973; Pitzer and Mayorga, 1973) in hydrate equilibria predictions for systems containing single and mixed electrolytes. When the solubility of the other materials cannot be neglected, as is the case with carbon dioxide, another approach is needed. Recently, a model for the calculation of the solubility of gases in aqueous electrolyte solutions at high pressures was proposed (Aasberg-Petersen et al., 1991). This model was successfully utilized for the prediction of hydrate formation in hydrate-forming systems containing carbon dioxide and electrolytes (Englezos, 1992a). Solutions of water-soluble polymers can be described by the UNIFAC activity coefficient method (Oishi and Prausnitz, 1978; Rasmussen and Rasmussen, 1989). On the basis of this work, Englezos (1992b) developed a method for the prediction of the incipient hydrate formation conditions in aqueous polymer solutions. The polymers were found to be weak inhibitors. 3.1.4. Nonaqueous Liquid Phase (Ln). The nonaqueous liquid phase usually contains mainly the condensed hydrate former(s). For example, in natural gas hydrates it is a hydrocarbon-rich liquid phase. This phase can be described by an EoS using eq 5. 3.2. Computation of Phase Equilibrium. van der Waals and Platteeuw (1959) proposed a model for the chemical potential of water in the hydrate phase and computed incipient hydrate formation pressures for nine gases. McKoy and Sinanoglu (1963) also calculated incipient hydrate formation pressures and found better results when they employed the Kihara intermolecular potential. Kobayashi and co-workers also used the van der Waals-Platteeuw theory and classical thermodynamics for the calculation of the incipient hydrate formation conditions (Saito et al., 1964; Saito and Kobayashi, 1965; Nagata and Kobayashi, 1966a,b). On the basis of the van der Waals-Platteeuw model, Parrish and Prausnitz (1972) presented an algorithm for the prediction of hydrate equilibria in multicomponent mixtures. In the above methods, aqueous solutions of light hydrocarbons were considered. In such cases, the solubility of the hydrate-forming gases can be ignored. As a result, the set of phase equilibrium equations is simplified. Ng and Robinson (1976, 1977) and Holder et al. (1980) improved the method of Parrish and Prausnitz (1972). They also included corrections for the solubility of gases such as carbon dioxide. Ng and Robinson (1976, 1977)
measured condensed phase equilibrium and suggested a Clapeyron-type equation to obtain the pressure-temperature locus. The influence of the uncertainty of the lattice cavity size on the hydrate phase diagram calculations was recently investigated by Lundgaard and Mollerup (1992). The method of Parrish and Prausnitz was extended to compute the effect of alcohols (Anderson and Prausnitz, 1986; Munck et al., 1988; Du and Guo, 1990; Englezos et al., 1991; Avlonites et al., 1991a,b). Menten et al. (1981) were the first to present an empirical method, based on freezing point depression data, for computing light hydrocarbon hydrate formation conditions in single electrolyte solutions. Englezos and Bishnoi (1988a)presented a rigorous method with no adjustable parameters which was used to compute hydrate formation in aqueous solutions of single or mixed electrolytes. This method produced excellent results for systems with substances sparingly soluble in water (e.g., light hydrocarbons). Recently, Englezos (1992a) presented a method suitable for the calculation of hydrate equilibria in aqueous electrolyte solutions containing carbon dioxide whose solubility in water is significant. He also presented a method to compute the hydrate formation conditions in aqueous polymer solutions (Englezos, 1992b). It is still not possible to compute hydrate formation conditions in very complex mixtures such as drilling fluids. Process design in these cases should rely on experimental data such as those by Cha et al. (1988), Ouar et al. (1992),and Kotkoskie et al. (1992). Another type of equilibria that was studied because of its importance in the natural gas industry is between hydrate and a vapor or liquid hydrocarbon phase. In this case, a bulk water phase is absent and hydrates may be formed from the water content of the hydrocarbon phase. Due to the long induction time for hydrate formation and the difficulties in measuring small water concentrations, measurement of this type of equilibrium is difficult. However, experimental data and computational methods have been presented by Kobayashi, Sloan, and co-workers (Sloan et al., 1976, 1987; Sloan, 1982, 1990a; Song and Kobayashi, 1982, 1987). Ng and Robinson (1980) also presented a method for the determination of the water content of a gas. 3.2.1. Flash Calculations. The amount of hydrates that are formed from a given mixture can be computed if the mass balance equations, including the hydrate phases, are solved together with the phase equilibrium equations. Bishnoi et al. (1989) were the first to formulate and solve this problem in its general form by including all possible fluid and solid phases. The solution of the problem was based on an elegant algorithm that solves simultaneously the phase equilibria and stability equations in a multicomponent system (Guptaet al., 1991). Cole and Goodwin (1990) also performed flash calculations with systems containing hydrates. 3.3. Recent Experimental Studies. Experimental data continue to appear in the literature. Song and Kobayashi (1989) measured the inhibiting effect of methanol and ethylene glycol on the incipient hydrate formation conditions from a mixture of methane and propane. Avlonitis et al. (1989) measured hydrate formation in oilwater systems. Dholabhai et al. (1991a) and Englezos and Bishnoi (1991) presented the first experimental data on methane and ethane hydrate formation in aqueous mixed electrolyte solutions. Carroll and Mather (1991) reported hydrate-forming conditions for the hydrogen sulfidewater system. Ouar et al. (1992) and Kotkoskie et al. (1992) measured hydrate-forming conditions in systems con-
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1257 taining water-based drilling fluids. Grigg and Lynes (1992) measured hydrate formation in oil-based drilling mud. Svartas and Fadnes (1992)presented data on the inhibition of methanol. It was found that methanoldoes not promote hydrate formation at concentrations for which Makogon (1981) and Berecz and Balla-Achs (1983) reported the opposite effect. Adisasmito et al. (1991) and Adisasmito and Sloan (1992) presented data on carbon dioxide containing hydrocarbon mixtures. Ross and Toczylkin (1992)presented data on the inhibiting effect of triethylene glycol on gas hydrates from methane or ethane. Englezos and Ngan (1993a,b)measured incipient hydrate formation conditions for propane in aqueous mixed electrolyte solutions and for methane, ethane, and propane in aqueous polyethylene oxide solutions.
4. Nucleation, Growth, and Decomposition of Gas Hydrates There are two fundamental questions that have to be answered when time is a factor to be considered in hydrate formation. First, how much time will it take to begin forming hydrate crystals from a given hydrate-forming mixture at certain temperature and pressure conditions in the hydrating region of the partial phase diagram? This time is known as induction time. Second, what will be the rate of growth of hydrate crystals? Both questions are challenges to experimentalists and important from a technological viewpoint. One may pose similar questions for the gas hydrate decomposition. 4.1. Kinetics of Formation. Hammerschmidt (1934) first indicated that there could be an induction period associated with the appearance of the first crystals from a hydrocarbon-water mixture which has a suitable composition and ita pressure and temperature are such that, thermodynamically, hydrates could form. Knox et al. (1961)identified the degree of supercoolingas an important factor of the rate of hydrate formation. The degree of supercooling is defined as AT = Tes- Texp,where Tesis the equilibrium hydrate formation temperature a t a given is the experimental temperature. Barrer pressure and Texp and Ruzicka (1962a-c) carried out experimental and theoretical work on gas hydrate formation. Part of that work was a kinetic investigation of Ar, Kr, and Xe hydrate formation from ice. Mixed hydrates were also considered. Pinder’s work with the tetrahydrofuran hydrate (Pinder, 1964) illustrated the tremendous difficulties in studying the kinetics of gas hydrate formation. The author wanted to avoid the problems caused by the diffusional barrier created by the hydrate crystals in gas-liquid systems and studied the kinetics with a soluble hydrate former. The rate was found to depend on diffusion. Qualitative observations on the rate of formation were presented by Huang et al. (1965) and Williams et al. (1965). Glew and Hagget (1968a,b) studied the kinetics of ethylene oxide (EO) hydrate formation. Ethylene oxide is miscible with water, and diffusional limitations encountered with sparingly soluble hydrate formers could be avoided. They correlated their results and found the EO hydrate growth was limited by heat transfer from the hydrate slurry. Different dependence, however, was found by Pangborn and Barduhn (1970),who studied the kinetics of methyl bromide hydrate formation in a continuous stirred tank reactor. According to this study the hydrate formation rate appears to be controlled mainly by the kinetics of the interfacial reaction to form crystals. Graauw and Rutten (1970) proposed a mass-transfer-based model for the kinetics of hydrate formation. They used chlorine and propane as the hydrate-forming substances. Their
results showed that mass transfer at the hydrate-forming substance-water interface can be a rate-determining factor. However, the hydrate formation reaction at the surface can also become a rate-determining step. They also found that the presence of electrolytes did not have any effect. Barrer continued the fundamental studies on the formation of gas hydrates containing Ar, Kr, and Xe (Barrer and Edge, 1967). I t was found that the induction periodvaries with the type of the hydrate former. Krypton required approximately 1 h to form hydrates, while Ar and Xe formed hydrates immediately. Falabella was able to reproduce the results for krypton (Falabella, 1975; Falabella and Vanpee, 1974). However, reproducibility of his own results was a problem. Scanlon and Fennema (1972) studied the formation of ethylene oxide hydrate (structure I) and that of tetrahydrofuran (THF) hydrate (structure 11). It was found that, a t any degree of supercooling, hydrate-forming solutions crystallized more slowly than pure water, and the THF hydrate crystallized more slowly than the hydrate of ethylene oxide. They attributed this difference to the fact that the rapidity of hydrate formation should decline as more molecules of water are required to associate in an orderly fashion with each molecule of hydrate former. However, they cautioned extension of the results to other hydrate-forming systems because their studies were based on hydrate formers readily soluble in water. Finally, it was found that polyacrylamide gel decreased the velocity of hydrate formation. Werezak (1969) examined the rate at which the solute concentration was increasing due to hydrate formation in aqueous solutions of coffee extract, sucrose, and sodium chloride. Hydrates from ethylene oxide, trichlorofluoromethane, sulfur dioxide, methyl chloride, and propylene oxide were studied. It was found that miscible hydrate formers exhibited higher rates of formation compared to the slightly soluble hydrate formers used. The rate of solution concentration was found to be a function of the initial thermal driving force and the heat-transfer capabilities of the hydrate formation vessel. Miller and Smythe (1970) reported an exponential decrease in the pressure during carbon dioxide enclathration into ice and formation of hydrates. Barduhn et al. (1976) presented the results of a kinetic study on CHzClF (R-31) and CH3CClF2 (R142b) hydrate formation in a stirred tank reactor with a 6 wt % NaCl solution. They correlated the results as a nonlinear function of the temperature difference between the equilibrium formation temperature and that in the bulk of the liquid solution. Morlat et al. (1976) studied the kinetics of ethylene hydrate formation and proposed that the growth step is a two-stage process. First, the larger cavities of the structure I hydrate are formed. At that time the small cavities are temporarily occupied. After this stage, the small cavities are filled permanently. Makogon (1981) cited work that had been carried out in Russia. He examined the morphology of hydrate crystals and described the factors which affect hydrate nucleation and growth. Supercooling, pressure, temperature, state of water, composition, and state of the gas hydrate-forming system were mentioned as factors that affect the growth. He highlighted the importance of the knowledge of the properties of water in understanding nucleation and growth. He also correlated the rate with the degree of supercooling. More than 10 years ago Bishnoi initiated a systematic study of the kinetics of gas hydrate formation and decomposition. Vysnauskas and Bishnoi (1983a,b) reported the first experimental results on methane hydrate
1258 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 formation. They also presented an empirical model that correlated the rate with the degree of supercooling, temperature, pressure, and interfacial area. A molecular mechanism was also proposed. Nucleation studies were also conducted and revealed the impact of the state of water on the induction period. These parameters were also found to influence ethane hydrate formation (Vysnauskas and Bishnoi, 1985). The experimental setup of Vysnauskas and Bishnoi was later modified to achieve homogeneous nucleation conditions and better reproducibility. The kinetic studies on methane and ethane gas hydrate formation were repeated in that improved apparatus. The data were used for the development of a mechanistic model with one adjustable parameter per hydrate former (Englezos et al., 1987a). The model was based on the homogeneous crystallization theory and described the kinetics of hydrate crystal growth. The nuclei were assumed to form instantaneously by primary nucleation. The difference in the fugacity of the dissolved gas and the three-phase equilibrium fugacity at the experimental temperature was defined as the driving force for hydrate crystal particle growth. The study revealed that formation of hydrates is not restricted to a thin layer close to the gas-liquid interface, as suggested by Makogon (1981),but could also occur throughout the liquid phase. The model was extended to the formation of hydrates from methane and ethane mixtures of various compositions (Englezoset al., 1987b). It was found that it could describe the rate of hydrate growth without any additional adjustable parameters. Similar conclusions, as far as the rate-controlling step is concerned, were reached by Smirnov (19871, who reported that hydrate formation occurs in the kinetic region. The thermodynamics of nucleation were described by Gibbs free energy analysis (Englezos et al., 1987a;Englezos and Bishnoi, 1988b),and gas hydrate particle sizes were calculated. Recently, Nerheim et al. (1992) reported the results of the investigation of hydrate kinetics in the nucleation and early growth phase by laser light scattering. Their measured nuclei sizes were found to compare well with those calculated by Englezos et al. (1987a). Dholabhai et al. (1993) presented data on the kinetics of methane hydrate formation in aqueous electrolyte solutions. The model of Englezos et al. (1987a)was adapted to predict the growth of hydrates. It was found that the model predictions matched the experimental data well. Sloan introduced the ratio of the hydrate former molecular diameter to cavity size as a nucleation parameter to explain induction period data (Sloan, 1990a,b; Sloan and Fleyfel, 1991). Furthermore, he proposed a hypothesis for the nucleation of gas hydrates from ice. The hypothesis was subsequently extended to hydrate formation from pure water (Muller-Bongartz et al., 1992). Confirmation of the hypothesis is not yet complete and requires substantial experimental evidence. The implications, however, of this work to the development of kinetic inhibitors appear to be significant. We utilized these concepts to interpret the results obtained by Scanlon and Fennema (1972). THF fills the large cavities of structure I1 and has a molecular diameter to cavity ratio of 5.916.466 = 0.9124. Ethylene oxide fits with some difficulty into smaller cavities of structure I (Davidson, 1973). It has a diameter to cavity size ratio of 5.214.92 = 1.0569 for the small cavities and 5.215.76 = 0.9028for the large cavities. The ratio of 1.0569 justifies the difficulty of the EO molecules to be included into the small cavities. Hwang et al. (1990) studied the formation of methane hydrates from melting ice and concluded that the rate depended on the rate of supply
of hydrate former to the growth surface and the rate of removal of the heat from the forming surface. Increasing the pressure was found to increase the rate of hydrate formation. Skovborg et al. (1993) reported isothermal experimental data on induction times for the formation of methane and ethane hydrates. They found the induction time to be strongly dependent on the stirring rate and the magnitude of the driving force. The driving force was expressed as the difference in the chemical potential of water in the hydrate phase and water in the water phase at the system temperature and pressure. Nucleation is characterized with variables and phenomena which are not fully understood. The induction time cannot be theoretically determined. It was experimentally found to depend on the previous history of water (Vysnauskas and Bishnoi, 1983a1, stirring rate (Englezos et al., 1987a; Skovborg et al., 1993), supercooling (Glew and Hagget, 1968a;Englezos et al., 1987a; Skovborg et al., 1993), and molecular diameter to cavity size ratio (Sloan and Fleyfel, 1991). Limited observability (particle size distribution), heat- and mass-transfer effects, and accurate measurement of the amount of hydrate former consumed (solubilityand hydrate formation) are difficultiesthat must be overcome. Progress has been made with molecular simulation (Sloan, 1990a). 4.2. Kinetics of Decomposition. Kamath et al. (1984) reported the resulta of an experimental study on the thermal decomposition of propane hydrates to gaseous propane and water. This study, an important one in the field of heat transfer, indicated that the rate of heat transfer could be correlated with an expression that incorporates the driving force for decomposition expressed as a temperature difference. The decomposition of methane hydrates was found to behave similarly and was also modeled as a heat-transfer-controlled process (Kamath and Holder, 1987). Ullerich et al. (1987) also modeled the hydrate decompositionprocess on the basis of heat-transfer considerations, but they viewed it as a moving boundary ablation process. Kim et al. (1987) suggested that the decomposition rate is proportional to a driving force that is defined as the difference between the fugacity of methane at the hydrate vapor-liquid water equilibrium conditions and the fugacity of methane in the bulk of the gas phase. This model was used by Jamalludin et al. (1989) to describe the decomposition of a methane hydrate block under thermal stimulation. It was shown that by changing the pressure we can move from a heat-transfer-controlled regime to one where both heat transfer and intrinsic kinetics are important. The formation and decomposition of oxygen hydrate was studied with a method based on differential scanning calorimetry (Hallbrucker and Mayer, 1990). It was found that dissociation of the hydrate occurs in two steps, with peaks a t 222 and 246 K approximately. Thiswas attributed to two different types of pores which differ in wall strength of the enclosing ice layers. 5. Technological Aspects The study of clathrate hydrates began in 1810 and continued to attract the interest of prominent scientists during the next 120 years. In the early 1930s, the subject entered the domain of interest to engineers. It was then realized that natural gas and water can form gas hydrates and plug pipelines, at temperatures above those at which normally water does not freeze (Hammerschmidt, 1934). Prevention of hydrate formation became a major concern and led to a large number of studies on the phase behavior
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1259 of hydrate-formingsystems. These studies continue today because the production conditions become more and more difficult. Gas hydrate formation is also an opportunity to develop useful applications. In addition, naturally occurring gas hydrates in the earth’s crust present an energy resource under proper economic circumstances. The technological problems and opportunities related to gas hydrates will be discussed in this section. 5.1. Oil and Gas Industry. Although much understanding has been gained over the years and many technologicalproblems have been successfullytackled, new issues arise and the subject continues to be investigated (Sloan,1990a,1991;Hubbard, 1991;Yakushevand Collett, 1992). One of the most significant developments was the discovery of huge quantities of hydrates in the earth’s crust (Makogon et al., 1972; Katz, 1971, 1972). Two monographs (Makogon, 1981; Sloan, 19901, several symposia (Kaplan, 1974; Bowsher, 1979; French, 1982; Cox, 1983), and reviews (Barraclough, 1980; McGuire, 1981; Pearson et al., 1983; Finlay and Krason, 1990) have appeared. Therefore, this review will briefly discuss the developments up to the late 1980s and will concentrate on the developments that occurred over the past 2-3 years. 5.1.1. Oil and Gas Production, Processing, and Drilling. Because water and hydrocarbons may coexist in many situations while we search for, produce, or process oil and gas, the possibility of gas hydrate formation should be considered. 5.1.1.1. Water Content of Natural Gas. Natural gas leaving a gas reservoir is saturated with water, and when it expands into separators or at wellheads, the temperature drops and solid gas hydrates may be formed and plug the pipelines and other processing equipment. The water content of natural gases is an important quantity to know, especially in connectionwith gas hydrate formation (Sloan et al., 1976, 1987; Ng and Robinson, 1980; Sloan, 1982, 1990a; Song and Kobayashi, 1982,1987). 5.1.1.2. Gas Hydrate Formation in Oil Reservoirs. Gas hydrates may be formed not only from a hydrocarbon vapor phase but also from a liquid one (Katz, 1972;Verma et al., 1975; Holder et al., 1976). In this case, the hydrate formation may denude the oil in the reservoir from ita light hydrocarbons. The presence of such hydrates in shallow reservoirs in Northern Canada, Alaska, and Siberia or their formation in the oil reservoirs during production adds to the complexities of the production (Davidson et al., 1978). Hydrate formation could probably be linked to the occurrence of heavy oil and tar sands (Barraclough, 1980). Ridley and Dominic (1988) mentioned such a case in the North Slope of Alaska and suggested that recovery of the heavy oil could be facilitated once the hydrates are decomposed and the light hydrocarbons dissolve back to the oil. 5.1.1.3. Prevention of Gas Hydrate Formation. The industry has developed several techniques to prevent the formation of gas hydrates. These methods together with design considerations are extensively discussed in the literature (Hammerschmidt, 1939a,b; Deaton and Frost, 1946; Bond and Russell, 1949; Bleakley, 1970; Campbell, 1976;Makogon, 1981;Nielsen and Bucklin, 1983;Robinson and Ng, 1986;Ng et al., 1987a;Sloan, 1990a;Katz and Lee, 1990; Manning and Thompson, 1991). The methods include (a) drying the natural gas, (b) heating the gas to a temperature above the equilibrium hydrate formation temperature at a given pressure, (c) reducing the pressure of the gas to a pressure below the equilibrium hydrate formation pressure at the given temperature, and (d) altering the partial phase diagram of the gas-water system
in the hydrating region by injecting methanol, glycol, or electrolytes (inhibiting substances). Electrolyte injection is not a preferred option because the aqueous salt solutions are corrosive. Methanol and glycol injection are used extensively. Systematic experimental studies on the determination of the effect of methanol and glycols on the hydrocarbon-water phase diagram have been carried out by Robinson and co-workers(Ng and Robinson, 1983,1984, 1985; Ng et al., l985,1987a,b; Robinson and Ng, 1986), by Song and Kobayashi (1989), by Istomin and Kolushev (19921, and by Svartas and Fadnes (1992). Recent developments in gas dehydration were discussed by Hubbard (1991) and by Hicks and Senules (1991). Yamanlar et al. (1991) discussed the inhibition of hydrate formation through the use of a non-hydrate former in the gas phase. It is easily noticed that the four hydrate prevention methods alter either the phase diagram (drying and injection of inhibiting chemicals) or the operating conditions by considering the phase diagram (heating and depressurization). Therefore, they are based on equilibrium thermodynamic considerations. Recently, attention has focused on inhibiting substances other than alcohols or electrolytes (Sloan, 1990b; Englezos, 1992b; Englezos and Ngan, 1993b; Ouar et al., 1992). The new substances could perhaps prevent the agglomeration of gas hydrates after they have been formed (Sloan, 1991;Hubbard, 1991; Muijs, 1991; Dholabhai et al., 1992). The search for new inhibitors is stimulated by the high cost of conventional inhibitors in offshoredevelopmentsand onshore processing facilities. It is estimated that 5-8 % of the total plant cost is capital cost required to prevent hydrate formation (Sloan, 1991). 5.1.1.4. Condensate Oil Pipelines. Bishnoi and Kalogerakis conducted a pilot plant study on gas hydrate formation and deposition from condensate oils in subsea pipelines using samples from the North Sea (Dholabhai etal., 1991b). They proposed a “hydrate deposition”factor to relate hydrate deposition to measurable quantities. Deposition occurred at water contents of 3 and 5 wt % , but very little occurred a t 0.5 wt % . The effect of fluid velocity did not have any regular trend. Subsequently, the effect of methanolon hydrate formation and deposition was studied (Dholabhai et al., 1992). The study revealed that deposition took place in the loop, but the hydrate particles did not agglomerate and they practically disappeared when methanol was added. At 4 and 11 wt % concentration of methanol, hydrates were formed but did not settle anywhere in the loop. Jamalludin et al. (1991) studied the hydrate formation conditions under emulated stagnant pipeline conditions. Gas hydrate growth was modeled by taking into account the kinetics together with the relevant heat- and masstransfer phenomena. The results indicated that hydrate plugging will not cause serious problems in an unplanned pipeline shutdown for periods of less than 48 h. The pipeline flow start-up, however, should be carried out carefully. Muijs (1991)reported that a high-pressure loop was being constructed at Shell laboratories in Amsterdam to develop chemical additives which would affect the morphology of the hydrates in a way that they would not agglomerate. Hence, a plug will probably not be formed in the pipeline. 5.1.1.5. Drilling through Hydrate Zones. Gas hydrate formation in the drilling fluids and decomposition of in-situ hydrates due to drilling through the hydrate zones are two serious problems that must be considered for safe operation and production in oil development
1260 Ind. Eng. Chem. Res., Vol. 32,No. 7, 1993 projects. The problems caused by gas hydrates become more and more frequent as the exploration and production activities are taking place in remote offshore and deep environments. Hitchon (1974)and Bily and Dick (1974) warned drilling engineers about the dangers due to the existence of hydrates in the earth. Goodman (1978) suggested that cores from reservoirs where hydrate formation is suspected should not be allowed to warm up during retrieval and storage. Hydrate decomposition testing should be conducted as soon as possible. Goodman and Franklin (1982)suggested that hydrate gas flux during Arctic drilling can be controlled by increasing the decomposition temperature through the use of higher mud weights. Gas hydrates that naturally exist in the earth may pose the following severe problems to drillingoperations: casing damage, uncontrolled gas release, blowouts, fires, and gas leakage outside the casing (Bilyand Dick, 1974;Goodman, 1978;Judge, 1982;Makogon, 1981;Franklin, 1983;Collett, 1990;Yakushev and Collett, 1992). Yakushev and Collett (1992)documented the drilling and production problems that have been attributed to the presence of gas hydrates and reviewed the techniques and proceduresto tackle these problems. To carry out drilling and completion operations in the presence of hydrates, it is important to know the hydrate distribution,volume, reservoir temperatures, pore pressures,rock porosities,and permeabilities. The actions usually taken are two: (i) prevention of hydrate decomposition and (ii) promotion of controlled hydrate dissociation. Davidson et al. (1978)reported two cases of gas kicks due to gas hydrate decomposition. Weaver and Stewart (1982)suggested the use of slow penetration rates and cool heavy mud to minimize the problems during drilling through hydrate zones. Franklin (1983)reported a procedure that permits safe drilling by proper pressure and temperature control. The characteristic of the procedure is that instead of trying to prevent the formation of hydrates, a controlled hydrate decomposition process is induced. Wooley et al. (1986) conducted a study to establish the circumstances for drilling and circulation of a gas kick which create the potential for hydrate formation. They also made recommendations on field procedures. Lowrie (1991) discussed the exploration, drilling, and production strategies in the presence of in-situ gas hydrates. 5.1.1.6. Hydrate Formation in Drilling Muds. The pressure and temperature conditions in deepwater drilling are such that in most cases hydrates may be formed easily. Barker and Gomez (1989)reported that gas hydrates were formed in two deepwater wells during drilling operations. In both cases, subsea equipment was plugged and caused difficultiesin subsequent operations. They analyzed these two occurrences and offered practical suggestions. Hale and Dewan (1990)discussed the subject of inhibition of gas hydrate formation during deepwater drilling operations. They suggested the use of a salt/glycerol-based nonflammable fluid for hydrate inhibition. The drilling fluid is a complex fluid mixture, and it is difficult to determine the effect on hydrate formation conditions. Ouar et al. (1992) reported a systematic experimental study of the hydrate formation conditions in water-based drilling muds. The study was a continuation of work initiated earlier at Sloan’s laboratory (Cha et al., 1988). It was found that electrolytes and methanol were responsible for the depression of the hydrate formation conditions. The other constituents provided minor inhibiting effects. Water-soluble polymers, for example,
are known to have minor inhibiting potential (Englezos, 1992b;Englezos and Ngan, 1993b). The surprising result of Ouar’s study was the finding that bentonite, a clay, and partially hydrolyzed polyacrylamide (PHPA), a hydrophilic polymer, appear to be thermodynamic promoters of hydrate formation. Some observations related to the kinetics of formation were also made. Clays and drill solids appear to form nucleation sites which speed up the formation conditions, while electrolytes,oils, and polysaccharide polymers appeared to decrease the rate of hydrate formation. Kotkoskie et al. (1992)also presented data on the equilibrium hydrate formation conditions in waterbased drilling muds from a natural gas mixture containing hydrocarbonsand a small amount of nitrogen. It was found that the inhibiting action was exclusively due to either the salt or the glycerol. The study also revealed that the presence of drilling mud constituents, other than salt and glycerol, tended to promote hydrate formation. The hydrates could be decomposed with the injection of methanol. Grigg and Lynes (1992)demonstrated that hydrates may be also formed in oil-based drilling muds. It is known that oil-based drilling muds are not free of water, but as much as 30 % by volume could be the aqueous phase. The study revealed that oil as a continuous phase in an oilbased drilling mud acts as an inhibitor to hydrate formation. However, when the inhibiting action is not sufficient to prevent the formation of hydrates, it was noticed that the oil promoted the rate of formation and perhaps the extent of hydrate production. Addition of calcium chloride provided inhibiting potential which was additive to that provided by the oil. 5.2. Gas Hydrates in the Earth. In the 1960s the hypothesis of natural occurrence of gas hydrates in the earth was proven by Russian researchers (Chersky and Makogon, 1970;Makogon et al., 1972). Today, it is known that gas hydrates, containing mostly methane, have been formed naturally in the earth and exist in vast quantities within and below the permafrost zone and in subsea sediment in the Arctic, the Antarctic, and tropical and subtropical oceans. Estimates of the amount of in-situ gas hydrates vary considerably. However, a reasonable figure is 10l6m3 of methane exists in solid hydrate form (Kvenvolden, 1988a). This amount exceeds the known conventional natural gas reserves and justifies the intense efforts to find economic recovery schemes. Makogon (1981),in his book, reported the efforts that led to this significant scientific discovery. Another source of the historical developments is a report by the American Gas Association (1979). It should be noted that hydrate formation in the earth’s crust continues today (Hyndman, 1992). A hydrate reservoir is shown in Figure 5. The subject of in-situ gas hydrates immediately attraded the attention of Western researchers (Katz, 1971,1972; Stoll et al., 1971)for the followingreasons: (a) the amount of gas in the form of hydrates in the earth is enormous; (b) these naturally occurring hydrates might have serious implications to the earth’s climate; and (c) the in-situ hydrates present problems to drilling and production of oil. A direct result of the work by Stoll et al. was a symposium in 1972 on “Natural Gases in Marine Sediments” (Kaplan, 1974). Claypool and Kaplan (1974), Miller (19741,Hand et al. (1974), and Hitchon (1974) discussed the aspects related to hydrates a t that symposium. It should be noted that Miller had proposed that hydrates also exist in the Antarctic (Miller, 1969) and outside the earth (Miller, 1961a,1974;Miller and Smythe, 1970).
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1261
. Pmeesfilled with hydrate
Figure 5. Hydrate reservoir in the earth's must. Such reservoir% containingmostlymethane,may befoundwithinpermafrout,within sediment below permafrost,or within the sediment benear h t he ocean floor. Suitable pressureremperature conditionsexist in many pans of the world. In such caae, ifmethane gaa and liquid wnter or ice are found in sufficient quantities, hydrate will be formed.
5.2.1. Detection and Occurrenceof the In-SituGas Hydrates. Suitable thermodynamicconditions (pressure and temperature) for the existence of gas hydrates in the earth are encountered in many parts of the world. One can easily superimpose on a temperaturedepth diagram oftheearths crust the temperaturepressure relationship that describes the gas-hydratewater phase equilihria (Katz, 1971: Makogon et al., 1972; Bily and Dick, 1974; Makogon, 1982;Judge, 1982; Holder et al., 1987; Godbole et al., 1988). The hydrate formation pressure is easily converted to depth by considering the equivalent hydrostatic pressure. The range of depth where hydrate formation is favorable thermodynamically is called the gas hydratestability zone. Gas hydrates will indeed form if sufficient gas and water are present in the pores of the sedimentary rocks. Thedetectionoftheearthslocations wheregas hydrate deposita are found and the subsequent estimation of the quantityofgasincluded havebeen thesubject ofnumerous investigations since thediscovery of in-situ hydrates. Stoll et al. (1971) reported that the formation of natural gas hydrates can result in significant increases in the acoustic wave velocity in ocean sediments. That was the first indicationofnaturalgas hydratesoutside theSoviet Union. Bryan (1974)presented indicationsof theexistence of insitugas hydratesin the Blake-BahamaOuter Ridge based on seismic methods. Tucholke et al. (1977) employed seismic methods and reported the existence of in-situ gas hydrates beneath the Western North AtlanticOcean floor. Bily and Dick (1974) presented the results of two exploratory wells in the Mackenzie Delta on Canada. On the basis of wireline logs, it was concluded that gas hydrates were contained in shallow sand reservoirs. Geophysical (well logs and bottom-simulating reflectors) as well as geologic and geochemical detection activities continued in order to identify the extent and nature of hydrate occurrence in the earth (Kvenvolden, 1982,1983; Collett, 1983; Dillon and Paull, 1983; Weaver and Stewart, 1982). A "bottom-simulating" reflector is an anomalous seismic reflection that parallels ocean-bottom topography. Pandit and King (1982,1983) reported their experimental work on compressional and shear wave velocities in hydrates andin ice. Thiswork isimportant insuccessfullyutilizing the seismic hydrate detection methods. Kvenvolden
(1988a)reported the locations of gas hydrates in the earth. He also estimated the amount of gas hydrates and discussed their importance as a natural gas source and as afactor affecting globalclimate. Sloan (1990a)thoroughly reviewed these activities and discussed the knowledgethat was gained. In this review, the extent, location, and mechanism of the in-situ gas hydrate accumulation were reported. Current research efforts focus on advancing the detectiontechniques. Wrightetal. (1991)discussedthespectral analysis of surface waves nondestructive seismictechnique for the detection of gas hydrates in the earth. Malone and Dillon (1992) summarized the problems related to the detection of gas hydrates. It was suggested that a joint seismic-refraction and seismic-reflection experiment can provide information not only on the top and bottom of the hydrate zone but also on the vertical and lateral variations ofthe hydrate depositswithm the hydrate formation zone. Anderson (1992)also reviewed the existingremote sensing evidence for gas hydrates in marinesediments. Data from the continental slope off Peru, the southwestern Japan Nankai margin, and the Rlake-Rahama Outer Ridge, were shown to provide temperature calibrations for deep sea bottom-simulating reflectors that mark the base of the hydrate formation zone (Hyndmanetal., 1992). Hyndman and Spence (1992) reported the analysis of multichannel reflection data from off the coast of Vancouver Island. The study provided support to the idea that the hydrate is concentrated in a layer a t the base of the hydrate stability zone just above the bottom-simulating reflectors. Hyndman (1992) discussedthe distribution, amount, and nature of gas hydrates. Dillon et al. (1991) reported a method, based on seismic and sediment data, for the estimation of the amounts of gas hydrates in marine sediments. Knowledge of the amount of hydrate layers will be extremely useful in determining the amount of gas hydrate that could be released in the atmosphere as a result of the carbon dioxide induqed global atmospheric temperature rise (Kvenvolden, 1988a,b; MacDonald, 1990; Englezos, 1992~). Earlier, Pearson et al. (1983)reported that the natural gas hydrate depoaites are characterized hy high seismic velocities and electrical resistivities compared to unfrozen sediments or permafrost zones. It was suggested that high sonic velocities provide a qualitative indication of the presence of hydrates, whereas resistivities provide a quantitative indication of the amount of hydrate present. Samples from offshore gas hydrates have been recovered in the Black Sea [cited by Brooks et al. (1991)1,the Gulf of Mexico (Brooks et al., 1984), and offshore northern California (Brooks et al., 1991). Sloan (1985) measured heat capacity, heat of dissociation, and thermal conductivity using a sample from a massive hydrate collected from suboceanic sediment. Handa (1988) also measured the composition, enthalpy of dissociation, and heat capacities of in-situ gas hydrates. 5.2.2. Formation of In-Situ Gas Hydrates. In addition to the knowledge of the location and extent of in-situgas hydrates, the understanding of their formation was also an objective of several studies. Makogon (1981) described the experimental work in Russia and reviewed the knowledge on the formation conditions in porous media. He discussed the zones of stability of hydrates, thedetection of prospective areas of hydrate deposita, and the existence of gas hydratesinmarine sediments. Finally, he described a gas hydrate field in western Siberia. Evrenos e t al. (1971) were the first in the Western world to study experimentally the formation of gas hydrates in
1262 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
porous media. Their motivation, however, was irrelevant to the possible existence of hydrates in the earth. Their work was concerned with the development of a procedure to use hydrates to create impermeable gas storage reservoirs. Cheng and Pinder (1976) studied the formation of Freon 11 hydrate in sand. Their objective was to consolidate the sand formation. Wittebolle and Sego (1985) described a laboratory facility where hydrates where formed in sand. The strength and deformation behavior of the hydrate-containing sediments were examined. Baker (1974) reported the results of his exploratory experimental work on the formation and decomposition in unconsolidated sand. Stoll (1974) suggested that successful exploitation of the naturally occurring gas hydrates necessitates research in detection methods, hydrate core recovery techniques, and kinetics of formation and decomposition. The characteristics of sediments containing gas hydrates were described by Stoll and Bryan (1979). Weaver and Stewart (1982)reported that hydrate accumulations were only detected in sands beneath the permafrost in the Beaufort Sea but not in clay or silt sediments. Claypool and Kaplan (1974) suggested that not all of the methane in hydrates is from biological production. Methane originated from deeper locations in the earth was produced by thermal cracking of organic matter and migrated upward. This methane was converted into hydrates when suitable pressure-temperature conditions prevealed as a result of global climate changes. MacDonald (1983) also discussed the two possibilities for the origin of methane in gas hydrates in the earth. Kvenvolden (1982, 1983)discussed the biologicorigin of methane that resulted in the formation of two sampled marine hydrates. Significant effort was devoted in the 1980sto understand the two mechanisms of generation of gases for the formation of the in-situ gas hydrates. This work has been summarized by Sloan in his monograph (Sloan, 1990a). Sloan also summarized the knowledge about the accumulation of hydrates in sediments. Collett et al. (1988,1990) investigated the origin of gas hydrates in the North Slope of Alaska. They concluded that thermogenic gas migrated upward and mixed with biogenic gas. Concentrations of gas sufficient to cause hydrate formation were reached, and hydrates were formed when the climate changes resulted in thermodynamically favorable conditions. The phenomena of salt and isotope fractionation in pore waters associated with gas hydrate formation were described by Hesse (1990). Yousif and Sloan (1991) presented the results of their investigation of hydrate formation and decomposition in porous media. That work offered considerable insight into the formation process. It was concluded that an annealing process could help form more hydrates in a consolidated medium. In shallow water seep areas gas bubbles can be seen breaking the surface (Dando and Hovland, 1992). This submarine seeping gas makes the sea appear to “boil”. Hydrates may be formed as this gas rises and enters suitable pressure-temperature conditions. Hydrates of carbon dioxide and some methane and hydrogen sulfide have been recently reported at the sediment surface in the Okinawa trough (Sakai et al., 1990). Hyndman and Davis (1992) presented a model that describes hydrate formation beneath the continental slope. According to this theory, methane generated by biological processes below the bottom of the hydrate formation zone moves upward together with other pore fluids. When the fluids enter the hydrate formation zone, they are depleted from methane that forms hydrates. The implication of
this theory is that in-situ gas hydrate formation is an ongoing process in the earths crust. The model by Hyndman and Davis explains the regional distribution of bottom-simulating reflectors and accounts for the evidence that the hydrates are usually found at the bottom of the hydrate formation zone. However, the mechanism by which methane is depleted efficiently from the rising fluids is not entirely understood. 5.2.3. Extraction of Natural Gas from Hydrates in the Earth. The gas supply potential of the in-situ gas hydrates is too significant to ignore (Kvenvolden, 1988a; Finlay and Krason, 1990). As soon as it was realized that gas hydrates exist naturally in the earth, this possibility began to be seriously examined (Davidson et al., 1978). The resource potential in areas where research has been completed and data have been collected was discussed by Finlay and Krason (1990). Appropriate economic conditions for the commercial exploitation of this unconventional gas resource will be in place during the next century (Ridley and Dominic, 1988; Sloan, 1990a). In 1980, Barraclough from the Los Alamos National Laboratory reviewed the knowledge on the nature, evidence, occurrence, and resource potential of in-situ gas hydrates. He summarized the efforts by the Russians to exploit this unconventional gas resource. Makogon (1981, 1982) also summarized that work and discussed the exploitation of this resource. Judge (1982) discussed the developments in Russia and North America. The methods for the recovery of gas that were discussed by Barraclough are (a) injection of inhibitors (methanol and/or electrolytes), (b) thermal stimulation, and (c) decompression. Injection of inhibitors alters the phase diagram and renders the pressure-temperature conditions in the reservoir favorable for the hydrates to decompose. The inhibitors act as freezing point depressants. Thermal stimulation techniques include steam or hot gas injection, injection of hydrothermal waters, and an in-situ combustion of some of the methane gas. The objective is to raise the temperature about the equilibrium formation temperature at the given reservoir pressure. Depressurization alters the reservoir conditions to a point where gas hydrate decomposition is favored thermodynamically. Barraclough (1980) pointed out the difficulties associated with these techniques and suggested areas of research to increase the knowledge on the in-situ hydrates and enable the exploitation of these reserves. McGuire (1981, 1982) from the Los Alamos National Laboratory investigated two conventional natural gas production technologies, thermal stimulation and decompression, in order to develop models for the production of gas from methane hydrate reservoirs. I t was concluded that unless the hydrate reservoir has high in-situ permeability or is located near geothermal aquifers, the thermal stimulation technique does not appear to be economical. On the other hand, the decompression technique should be viable if a high-permeability fracture can be maintained at temperatures below the normal freezing point of water. For that purpose, electrolytes such as CaC12 are used together with polymers that are compatible with the brines and have a desirable shear-thinning rheology. Weaver and Stewart (1982) described the evidence for hydrate occurrence at four locations under the Beaufort Sea shelf. Holder and his colleaguesstudied the factors that would enable a gas hydrate reservoir to produce gas in an energyefficient manner (Holder et al., 1982). Reservoir porosity and the thermal properties of the hydrates and the reservoir were found t o be determining factors. Subsequently, Holder et al. (1983) presented a model for gas
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1263 production from a hydrate reservoir that is located immediately above a gas reservoir. Depletion of the gas reservoir will result in a pressure reduction which in turn will cause the decomposition of the in-situ gas hydrates. Pearson et al. (1983) described the physical properties of gas hydrate reservoirs. A steam injection process for the decomposition of the in-situ hydrates and the subsequent gas recovery was modeled by Bayles et al. (1986). Their model was based on heat-transfer considerations alone to determine the bounds of the energy efficiency (combustible energy of the produced gaslenthalpy of the injected steam) and recovery potential of a hydrate reservoir. The effects of various reservoir parameters were investigated. Kamath and Godbole (1987) examined a production technique based on the injection of a hot brine solution to decompose the hydrates. On the basis of a mathematical model of the process, it was found that brine injection compared to steam or hot water injection has lower energy requirements and losses and higher gas production. Ridley and Dominic (1988) described the implications of natural gas hydrates and discussed the principles of the decompression and the thermal processes for the recovery of gas from hydrate reservoirs. Sloan (1990a), in his monograph, reviewed the work that was carried out in the 1980sand described the experience from the Messoyakha reservoir, which is the only producing reservoir. Furthermore, he explained why a comprehensive reservoir simulation model is needed. Recently, Kamath et al. (1991) presented the results of an experimental investigation of the decompression and the brine injection methods. Sharma et al. (1992)reviewed the merits and drawbacks of the various hydrate reservoir exploitation techniques. Experimental data on the decompression and brine, methanol, glycol, hot water, and steam injection were presented together with correlations for the rates of decomposition. It was concluded that for hydrate reservoirs located above a free gas zone the decompression technique is the most suitable. However, thermal techniques were found to be more appropriate for reservoirs in the absence of a free gas zone. 5.2.3.1. Decomposition of In-Situ Gas Hydrates. Successful design of gas recovery schemes from hydrate reservoirs requires knowledge of the rate of hydrate decomposition. This need motivated several studies on the modeling of the decomposition process. Initially, laboratory-prepared hydrate slurries or blocks were used (Kamath et al., 1984; Kamath and Holder, 1987; Ullerich et al., 1987; Kim et al., 1987). Subsequently, studies in a porous medium were carried out. Selimand Sloan (1990)were the first to describe hydrate dissociation in sediment. Thermal stimulation was used to decompose the hydrates. Their study revealed the strong dependence of the dissociation rate on the thermal properties and the porosity of the reservoir. Similar pioneering work was also reported by Sloan and his colleagues (Yousif et al., 1990). A model to describe the decomposition of hydrates by a decompression process was formulated. A more elaborate, three-phase, onedimensional decomposition model, based on the decompression technique, was presented the next year by Yousif et al. (1991). The work was accompanied by experimental data of gas and water production. It was found that the model was able (a) to describe the gasand water production data, (b) to track the decomposition boundary, and (c) to match the pressure and saturation profiles. Yousif and Sloan (1991) described formation of hydrates in Berea sandstone and subsequent decomposition. It was found that because hydrate decomposition is an endothermic
process, rapid decomposition could cause such a temperature drop that would allow hydrates to form or ice to freeze. In this case, decomposition will stop. In addition, hydrate dissociation is expected to generate considerable volumes of water. Zonenshayn et al. (1987) reported that a large pulsating gas plume in the Sea of Okhotsk is due to volcanic heating of overlying gas hydrates. The gas consists largely of methane with some hydrogen and higher hydrocarbons. Ershov and Yakushev (1992) studied experimentally the decomposition of hydrates in frozen rocks. It was found that at temperatures below the normal freezing point of water hydrates may exist at low pressures, below the equilibrium formation pressure, for a very long time. Initial hydrate decomposition leads to the formation of an ice film that coats the hydrate particles and prevents further decomposition. In permafrost hydrate-containing rocks, gas hydrates can exist for a long time after a pressure reduction. This implies that in-situ methane gas hydrates may be present at locations above their stability zones. Self-preserved hydrates were also reported to exist in nature (Yakushev and Collett, 1992). 5.3. Development of SeparationTechnology. There are two reasons that justify the efforts to exploit hydrate formation for the development of useful separation methods. First, gas hydrate crystals contain only water and the hydrate-forming substances, and second, the composition of the hydrate-forming substances in the hydrate crystal is different from that in the original mixture. Therefore, one can recover water from an aqueous solution by forming hydrate, separating the crystals from the concentrated solution, and then decomposing the hydrate. One can also separate a gas mixture by forming hydrates at conditions that will result in the desired fractionation. Such separations are discussed next. 5.3.1. Concentrationof Aqueous Organic Solutions. There is a variety of dilute aqueous solutions which can be concentrated via gas hydrate formation in a manner analogousto but more economic than freeze concentration. The term freeze concentration is often used interchangeably with the term freeze crystallization. Freeze crystallization refers to any process that removes heat from a mixture during which a component crystallizes. Freeze concentration is a type of freeze crystallization in which the crystallized substance is physically removed, leaving behind a more concentrated liquid (Heist, 1979;Englezos, 1993). Freeze concentration is based on the fact that crystallization of an aqueous solution produces crystals that do not contain any solutes present in the original solution. Because clathrate hydrates can be formed a t temperatures above the normal freezing point of water, there is an energy advantage in replacing the crystallization step of a freeze concentration system by gas hydrate formation (Parker, 1942; Findlay, 1962). Huang et al. (1965) investigated experimentally the characteristics of CH3Br and CH3F hydrates in water and in a variety of aqueous solutions. It was possible to form sizable amounts of hydrates in systems containing carbohydrates, proteins, or lipids. It was found that stirring enhances the rate of formation but has no effect on the total amount of hydrates formed. Inhibition of the equilibrium formation conditions due to the presence of various solutes was also noticed. Subsequently, they employed hydrate formation to concentrate apple, orange, and tomato juices (Huang et al., 1966). They were able to remove approximately 80% of the water. The crystals were removed by using a basket-type centrifuge. The concentration process was found to diminish the color and
1264 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
the flavor and frequently to impart a bitter aftertaste. van Hulle et al. (1966)reported the results of their experimental work on hydrate formation in polyacrylamide gels. It was found that the highly water soluble ethylene oxide and sulfur dioxide formed hydrate crystals within the gel easily. Dichlorofluoromethane, which is slightly soluble, also formed hydrates within the gel but the highly water insoluble trichloromethane formed only at the gel-hydrate former interface. Scanlon and Fennema (1972) examined the crystallization velocities of ethylene oxide and tetrahydrofuran hydrates in aqueous solutions and in polyacrylamide gels. The presence of polyacrylamide gel decreased the velocity of hydrate formation. EO hydrate formed at a velocity greater than that of tetrahydrofuran. The subject of aqueous solution concentration was investigated by Werezak (1969) to develop concentration technology for temperature sensitive and/or viscous solutions. Solutions of coffee extract, sucrose, and sodium chloride using ethylene oxide, trichlorofluoromethane, propylene oxide, sulfur dioxide, and methyl chloride as hydrate formers were examined. A process for concentrating aqueous solutions by clathrate hydrate formation was described. I t was found that the process could operate well with ethylene oxide as the hydrate former. Wilson et al. (1990) described the use of a single compound as a hydrate former and as extraction solvent for the recovery of products from solutions preconcentrated by gas hydrate formation. It was found that hydrate formation significantly increased the effective distribution coefficient and selectivity of the extraction processes. Supercritical ethylene and near-critical carbon dioxide were utilized. The beet sugar industry is an area where formation of hydrates is examined as a concentration method instead of the energy-demanding evaporation (Heist Engineering Corp., 1988). 5.3.2. Bioengineering and Biotechnology. Lund et al. (1968,1969)investigated the effect of hydrate formation and decomposition on the activity of the enzyme invertase. The study concluded that there is very little possibility that the various enzymes in food or biological systems can be controlled by gas hydrates. van Hulle and Fennema (1971a) reported that hydrate can be formed in plant or animal tissue if a sufficient quantity of ethylene oxide is allowed to diffuse into the tissue prior to initiation of crystallization. Subsequently, van Hulle and Fennema (1971b) investigated the effects of ethylene oxide and ethylene oxide hydrate on beef muscle and rat liver tissue. It was found that (a) EO without hydrate crystals present causes muscle and liver cells to shrink, (b) slowly crystallized EO hydrate appears to form only in extracellular areas and its presence results in shrinkage of tissue cells, and (c) shrinkage increases with time and temperature of EO hydrate formation. Results b and c are also observed during freezing of animal tissue. Later, van Hulle and Fennema (1972)performed a study of hydrate formation in carrot tissue using ethylene oxide and tetrahydrofuran (THF). They concluded that (a) EO and THF without hydrate crystals present do not alter appreciably the microscopic appearance of carrot tissue, (b) slow hydrate formation resulted in extracellular crystalline areas which caused shrinkage and distortion of adjacent tissue, and (c) crystalline masses of EO hydrate tended to increase in size and become less numerous as the rate of formation was decreased and the growth period was increased. Result b is also observed during freezing of carrot tissue. Recently, John and co-workers at Tulane University have reported work on gas hydrate formation in protein
containing reversed micellar solutions. Nguyen et al. (1989) studied methane hydrate formation. It was found that the incipient equilibrium hydrate formation conditions depend on the water to surfactant molar ratio. Decreasing this ratio increases the hydrate formation pressure at constant temperature. However, increasing the surfactant concentration at constant water to surfactant ratio does not affect the hydrate formation conditions. Subsequently, they examined the effect of hydrate formation on the activity of enzymescontained in the reversed micelles (Rao et al., 1990). It was shown that hydrate formation takes place in the microaqueous environment, depletes water, and alters the size of the micelles. As a result, the enzyme activity is modified. Lipase and a-chymotrypsin encapsulated in reversed micelles formed by isooctane and the anionic surfactant bis(2-ethylhexyl) sulfosuccinate sodium salt (AOT) were studied. In a subsequent paper, Rao et al. (1992) examined the role of high-pressure, low molecular weight gases on the activity of enzymes encapsulated in liquid-phase reversed micelles. It was found that lipase activity can be reversibly switched off. However, the activity of a-chymotrypsin was found to be constant until conditions of a pressure-induced cloud point or phase split. The ability to modify the water content in reversed micelles through hydrate formation has a number of implications in enzymatic catalysis, biomembranes, and drug delivery systems. Hydrate formation can be utilized to develop a process for the recovery of proteins encapsulated in reversed micellar solutions. Such a process was described by Phillips et al. (1991). Concentration of the solutions obtained from fermentation is an area where clathrate hydrate formation could be useful. Possible applications include the production of pharmaceutical grade lactose, whey protein concentrate which has a high protein content, and could be used as a dietary supplement for humans and livestock (Douglas, 1989). 5.3.3. Desalination. Hydrate formation as a step in developing a method to produce potable water from seawater was proposed in the 1940s (Parker, 1942) and received considerable attention in the 1960s and 1970s. McDermott (1971) discussed the numerous patents that have been awarded. Several process configurations were developed and demonstrated at a pilot-plant scale but never realized at an industrial scale. This was due to the difficulty in separating the crystals from the concentrated brine solutions and the removal of dissolved hydrate former from the recovered water (Rautenbach and Seide, 1978; Tleimat, 1980; Khan, 1986). Knox et al. (1961) presented results of the work at Koppers Co. to develop a desalination process based on propane hydrate formation. Barduhn et al. (1962) discussed the general characteristics of the hydrate process for the desalination of seawater. They also discussed the use of Freon 21, Freon 31, and methyl bromide as the hydrating agents. The Koppers Co. hydrate process using refrigerant 12 was described by van Heem (1965). Sweet Water Development Co. was another company which explored the hydrate process (Williams et al., 1965). Both companies operated pilot-plant facilities with the support from the Office of Saline Water in the United States. Pavlov and Medvedev (1965) discussed the developments of the hydrate process in the Soviet Union. Barduhn (1967, 1968) reviewed the developments of the desalination process by freezing and gas hydrate formation. Sugi and Saito (1967) reported the efforts in Japan to demineralize seawater via refrigerant 21 hydrate formation. Werezak
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1265 (1969) studied the formation of ethylene oxide hydrates in aqueous solutions containing 3.5 w t % sodium chloride. Barduhn et al. (1962) and Vlahakis et al. (1972) formulated a set of diverse criteria that should be met by a hydrating agent to be successfullyutilized. Because there are more than 100 hydrate-forming substances, considerable effort was devoted in the study of the characteristics, phase equilibria, and kinetics of severalhydrates. Graauw and Rutten (1970) studied the kinetics of chlorine and propane hydrate formation. Bozzo et al. (1973) reported all of the necessary thermodynamicdata for the evaluation of the chlorine and carbon dioxide as hydrating agents in the desalination process. Barduhn et al. (1976) investigated the kinetics of refrigerant 31 and refrigerant 142b, while Morlat et al. (1976) studied the ethylene hydrate formation kinetics. Schneider et al. (1978) presented a laboratory-scale apparatus to demonstrate a continuous hydrate process for the separation of water from saline waters. Rautenbach and Seide (1978) discussed the technical problems and the economics of the hydrate process for the desalination of seawater. The majority of the work on desalination with freezing methods (freeze crystallization and hydrate freezing) has been reported in the six "Desalination Symposia Proceedings" (Udall et al., 1965;Delyannis, 1967;Delyannisand Delyannis, 1970, 1973, 1976, 1978). 5.3.4. Fractionation of Gases and Liquids. Because the composition of a hydrate-formingmixture is different from the composition of the hydrate phase, clathrate hydrate formation can be utilized to develop gas and liquid fractionation processes. Hammerschmidt (1934) reported the compositions of natural gases which then formed hydrates in a pipeline. The compositions of the gases released from the hydrate decomposition were analyzed and found to be different. Propane and isobutane were found to be concentrated in the sample of the pipeline hydrates. Byk and Fomina (1968), Davidson (19731, and Berecz and Balla-Achs (1983) reported a list of patents and papers from Russian and other researchers in the Western world who examined the fractionation of gas and liquid mixtures. The most important publications were those of Barrer and Ruzicka (1962a), Barrer and Edge (1967),andGebhartetal. (1970). Recently,Dorsett (1989) presented the low-temperature extraction (LTX) process which accomplishes dehydration, gas dew point control, and enhanced condensate recovery through hydrate formation and decomposition. It should be noted that the fractionation of gases is very important in fluid inclusion studies (Thomas and Spooner, 1988; Seitz and Pasteris, 1990; Diamond, 1992). 5.4. Storage and Transportation of Natural Gas and Other Materials. There are two advantages in employing hydrate formation as a means for storage and transportation. First, a much lower storage space is needed, and second, safety is improved (Byk and Fomina, 1968; Davidson, 1973). The question, however, is to develop economic methods for the production of hydrates. Explosive or labile materials such as C102 and OScan be safely stored and transported in the form of hydrates (McTurk and Waller, 1964; Davidson, 1973). Recently, Berner (1992) discussed the design of a preconceptual system to transport natural gas in the gas hydrate state. 5.5. Waste Minimization. Increasingly stringent environmental regulations have forced the process industries to develop innovative water management strategies that include (a) modification of the plant processes to minimize the consumption of fresh water and (b) development of cost-effective technologies that can recover clean
water from the effluent. Among the methods that are considered for the separation and recovery of water from industrial effluents are the freezing methods (freeze concentration and clathrate hydrate concentration). Freeze concentration was installed in the spring of 1992 at a mechanical pulp mill in Chetwynd, British Columbia, to concentrate the mill effluent. However, skepticism has been expressed regarding application of the freeze crystallization method, and evaporation was selected and found to perform well in another pulp mill (Fromson et al., 1992; Stevenson, 1992). In principle, freeze concentration of industrial effluents can be more energy efficient and easier from a technical viewpoint if the crystallization step is replaced by clathrate hydrate formation. Possible application areas include the recovery and recycling of water from pulp mill effluents, deep mine reject water, ammunition plants wastes, metal-plating industry wastes, and pharmaceutical waste streams. Gaarder et al. (1992) reported data toward the development of a process for the concentration and recovery of water from mechanical pulp mill effluents using clathrate hydrates. It was found that clathrate hydrates of propane or carbon dioxide can be formed in these dilute effluents. 6. Environmental Implications
The formation and decomposition of gas hydrates could have negative implications in the environment. For example, severe damage to the marine environment could be caused from an underwater oil blowout occurrence. However, the in-situ gas hydrates may pose a more serious problem should global warming in the earth to be able to raise the temperature above their equilibrium temperature and as a result cause their decomposition. 6.1. Oil Well Blowout. As the exploration, drilling, and production of oil moves to offshore areas, new dangers to the marine environment arise. A deep ocean oil well blowout could cause severe pollution. Maini and Bishnoi (1981) discussed this occurrence and performed an experimental study on gas hydrate formation from a rising bubble under conditions similar to that in deep ocean waters. They described the following pollution scenario. The oil will be depleted from its light hydrocarbons because at the local conditions they will form gas hydrates which will rise to the sea surface. However, before they reach the surface, they will decompose to gas and water because of the low hydrostatic pressure. At the same time the oil originally in place will rise slowly to the surface by itself and will be dispersed over a wide area due to the local water currents. In the absence of hydrate formation, however, the oil would rise rapidly with the help of the gas plume. Maini and Bishnoi (1981) concluded that gas hydrate formation on rising gas bubbles can take place in deep oceans during an oil well blowout and have severe impact on the marine environment. Topham (1984a) proposed a mathematical model to describe the rise of a gas bubble in seawater at conditions where gas hydrate crystals are formed. These crystals coat the bubble. The study found that the computed lifetimes of the bubbles are of the same order of magnitude with the experimentally observed. A natural gas mixture found in some Arctic oil fields was examined. Subsequently, Topham extended the model to hydrocarbon bubble plumes (Topham, 1984b). 6.2. Relationship with Global Warming. Among the consequences of the temperature rise due to the increase in the concentration of trace atmospheric gases (TAG) in the atmosphere could be the decomposition of the methane gas hydrates in the earth. Methane has a global warming
1266 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Enhancement //
gE ; ;
7 \
Release of Methane
I
Global
f
Warming
I
Methane Hydrate Decomposition
\ More ... Methane Hydrate Decomposition
-
Runawau Greenhot& Effect
Figure 6. Runaway greenhouse effect scenario.
potential 21 times greater than that of carbon dioxide (Taylor, 1991). Because methane is such a strong greenhouse gas, a continuous increase of its concentration in the atmosphere from the decomposition of hydrates would enhance global warming and create a Yrunawayngreenhouse effect (Bell, 1982; Revelle, 1983). This scenario is illustrated in Figure 6. Because the greatest temperature increases due to global warming are expected to occur in the Arctic (Quadfasel et al., 1991) hydrates in shallow, nearshore regions of the Artic Ocean are the most likely to decompose (Kvenvolden, 198813). Clarke et al. (1986) proposed that methane released from the decomposition of hydrates escapes periodically in the atmosphere in the vicinity of Bennett Island in the Soviet far Arctic. MacDonald (1990) investigated the role of hydrates in past and future climates and found that it will take several hundred to a thousand years for changes in the earth’s surface temperature and pressure to affect the stability of the in-situ hydrates. The above studies assumed instantaneous hydrate decomposition when the temperature in the hydrate surface begins to rise. It is well-known, however, that a finite driving force is required for hydrate formation or decomposition (Englezos et al., 1987; Kim et al., 1987). Furthermore, hydrate formation and decomposition are known to be associated with hysteresis effects (Schroeter et al., 1983). Englezos (1992~)took these considerations into account and presented a simple calculation scheme to evaluate the effect of global warming on the stability of gas hydrates in the Arctic. The three most probable global warming scenarios (Schneider, 1990) were considered. He used the one-dimensional heat conduction equation in a single medium without heat sources or sinks. The results were found to depend significantly on the driving force. Hatzikiriakos and Englezos (1993)took into account permafrost phase change, whenever applicable, and presented a general model that computes temperature profiles in the earth’s crust assuming it to consist of layers with different soil properties. A quasi-steady-state solution to the problem of hydrate stability below the ocean floor was also given (Englezos and Hatzikiriakos, 1993). In these models, hydrate decomposition is not instantaneous. The temperature in the hydrate layer is allowed to increase until it reaches an a-priori specified magnitude at the top of the hydrate layer. A critical time for the onset of hydrate decomposition was thus defined and used in the analysis and the interpretation of the results. These studies suggested that while decomposition of hydrates below permafrost may start after the next one hundred
years, suboceanic hydrates will not probably be affected within the next one thousand years. Finally, it is noted that prevention of the global warming necessitates separation of C02from the discharged sources and safe disposal (fixation). Japanese researchers have suggested the disposal of CO2 as hydrate deep in the ocean (Saji et al., 1992; Nishikawa et al., 1992). 6.3. Other Environmental Implications. In-situ gas hydrates could facilitate the elucidation of history (Barraclough, 1980; MacDonald, 1990; Nisbet, 1989, 1990, 1992). Decomposition of submarine hydrates could have contributed to the rapid warming at the end of the last glaciation. Another environmental implication related to gas hydrates arises from the need to suppress hydrate formation from natural gas (Hubbard, 1991). The water dew point of the gas is controlled, frequently using glycol in a contacting tower. The glycol is normally recovered by boiling off the water. Benzene, toluene, and xylene, the main aromatic components in the gas, tend to dissolve in glycol and are boiled off with the water. This may create an air pollution problem or a water pollution one in the case where the vapor is condensed. Finally, gas hydrates within the foundation sediments of deepwater offshore structures may present a hazard to the foundation of pipelines and other production facilities (Makogon, 1988; Tzirita et al., 1991; Hooper, 1992). 7. Other Applications and Implications Makogon (1981) and Berecz and Balla-Achs (1983) related hydrate decomposition with coal mine gas blowouts. Another possible application that they mentioned is the elimination of fogs and clouds. Among many of the gases that form gas hydrates are substances which are used as anesthetics. Pauling (1961) proposed the gas hydrate-microcrystal theory of anesthesia. He postulated the formation of hydrate microcrystals with structure similar to that known for each hydrate substance on the basis of the correlation of the partial pressure of the anesthetic substances and the partial pressure necessary to cause hydrate formation. However, Miller (1961b) suggested that gas hydrates are not formed in the body with the pressures of anesthetics used. Pauling suggested that the catalytic activity of enzymes may be decreased by the formation of microcrystals in the neighborhood of their active sites. Lund et al. (1969) studied the effect of hydrate formation on invertase but did not find any effect on its activity. Miller (1961a) and Miller and Smythe (1970) suggested the occurrence ofgas hydrates in the solar system. Miller also reported hydrates of air in Antarctic ice (Miller, 1969). Makogon (1987) also discussed the occurrence of gas hydrates outside the earth. He suggested that hydrate decomposition takes place in Halley’s comet. Recently, Davidson’s explanation of the Bermuda Triangle secrets in 1984gained support (Canadian Chemical News,1990). Davidson suggested that methane gas rising from the bottom of the ocean where it was in the form of hydrates can turn the sea into a mass of froth which could sink any ship. The structure of water and the relationship to clathrate hydrate formation has also been discussed (Pauling, 1970; Davidson, 1973). Gas hydrate formation can serve as a cool storage process for residential air conditioning (Carbajo, 1985; Akiya et al., 1987; Mori and Mori, 1989a,b;Mori and Isobe, 1991;Najafi and Schaetzle, 1991). 8. Concluding Remarks
An overwhelmingnumber of papers have appeared since hydrates were first discovered in 1810. This is because
Ind. Eng. Chem. Res., Vol. 32,No. 7,1993 1267 they arouse great interest in many fields such as physics, chemistry, earth sciences, environmental sciences, and engineering. In this review,the current status of knowledge on clathrate hydrates from the point of view and interest of an engineer and an industrial chemist was presented. Some concluding remarks can be made. The area of clathrate hydrate phase equilibrium has reached ahighlevel of maturity. However, data for hydrate formation in the presence of substances that alter the phase diagram are always needed for particular applications such as drilling operations, inhibition of gas hydrate formation, and separation and recovery of water from industrial effluents. Structural investigations are needed to elucidate the new structure H hydrate crystals. Phase equilibrium and predictive methods are also needed for the hydrates of the new structure. A challenging problem is to understand and model the factors that influence the induction time for the nucleation. The problem requires experiments, phenomenological modeling, as well as molecular simulation studies. In the area of technological applications, development work is required to enable the commercial application of the various separation methods and other applications of clathrate hydrate formation and decomposition. Decomposition of hydrates in porous media is a subject that requires further study because of its importance in exploiting the naturally occurring gas hydrate reserves and investigating the possibility of occurrence of a runaway greenhouse effect.
Acknowledgment The financial assistance provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is greatly appreciated.
Nomenclature C = Langmuir constant, 1/MPa f = fugacity, MPa N = number of components Nh = number of hydrate-forming substances P = pressure, MPa R = universal gas constant, J/mol Ri = type i spherical radius, m r = radial distance from center of cavity, m T = temperature, K W(r)= cell potential function, J x = liquid-phase mole fraction y = vapor-phase mole fraction Greek Letters y = activity coefficient K = Boltzman’a constant, J/K p = chemical potential urn = number of cavities of type m I$ = fugacity coefficient Subscripts i = component i j = component j m = cavity type w = water Superscripts H = hydrate La = aqueous liquid Lo = pure liquid water MT = empty O = standard state
V = vapor
Literature Cited Aasberg-Petersen,K.; Stenby, E.; Fredenslund, A. Prediction of HighPressure Gas Solubilities in Aqueous Mixtures of Electrolytes. Znd. Eng. Chem. Res. 1991,30, 2180-2185. Adisasmito, S.; Sloan, E. D. Hydrates of Hydrocarbon Gases Containing Carbon Dioxide. J. Chem. Eng. Data 1992,37,343349. Adisasmito,S.;Frank, R. J.; Sloan, E. D. Hydrates of Carbon Dioxide and Methane Mixtures. J. Chem. Eng. Data 1991,36,68-71. Akiya, T.; Owa, M.; Nakaiwa,M.; Kawasaki,S.; Ninemoto,M.; Ando, Y. Cool Storage Using Gas Hydrate. Znt. Congr. Refrig. Proc. E 1987,166-170. American Gas Association. Gas from Natural Gas Hydrates. Gas Energy Rev. 1979, 7 (lo), 1-5. Anderson, A. L. Remote Acoustic Characterization of the Seafloor Including Gassy and Hydrated Sediment Regions. Proceedings, Second (1992) Znternational Offshore and Polar Engineering Conference,San Francisco,June 14-19,1992; Chung, J. S., Natvig, B. J., Li, Y.-C., Das, B. M., Eds.; International Societyof Offshore and Polar Engineers (ISOPE): Golden, CO, 1992; pp 674-683. Anderson, F. E.; Prawnitz, J. M. Inhibition of Gas Hydrates by Methanol. MChE J. 1986,32,1321-1333. Atwood, J. L.;Davies,J. E. D.; MacNico1,D.D.Znclusion Compounds; Academic Press: New York, 1984; Vol. 1-3. Avlonitis, D.; Danesh, A.; Todd, A. C.; Baxter, T. The Formation of Hydrates in Oil-Water Systems. BHRA 1989, Multiphase Flow-Proceedings, Fourthznternational Conference;The Fluid Engineering Centre: Cranfield, Bedford, UK, 1989; pp 15-34. Avlonitis, D.; Danesh, A,; Todd, A. C. Heterogeneous Equilibria Calculations for Multicomponent Hydrate Forming Mixtures. Presented at thespring AIChEMeeting, Houston, TX, April7-11, 1991a. Avlonitis, D.; Todd, A. C.; Danesh, A. A Rigorous Method for the Prediction of Gas Hydrate Inhibition by Methanol in Multicomponent Systems. Proceedings, First (1991)Zntemutional Offshore and Polar Engineering Conference, Edinburg, U.K., Aug 11-16; International Society of Offshore and Polar Engineers (ISOPE): 1991b; pp 454-460. Baker, P. E. Experiments on Hydrocarbon Gas Hydrates in Unconsolidated Sand. In Natural Gases in Marine Sediments; Kaplan, 1. R., Ed.; Plenum: New York, 1974; pp 227-234. Barduhn, A. J. Desalination by Crystallization Processes. Chem. Eng. Prog. 1967,63,98-103. Barduhn,A. J. Thestateof the CrystallizationProcessesforDesalting Saline Waters. Desalination 1968, 5, 173-184. Barduhn, A. J. The Status of Freeze Desalination. Chem.Eng. Proc. 1975, 71, 80-87. Barduhn, A. J.; Towlson, H. E.; Hu, Y. C. The Properties of Some New Gas Hydrates and Their Use in Demineralizing Seawater. AIChE J. 1962,22,176-183. Barduhn, A. J.; Roux, G. M.; Richard, H. A. The Rate of Formation of the Hydrates of F-31 (CHzClF) and F-142b (CHSCC~F~) in a Stirred Tank Reactor. Proc. Int. Symp. Fresh Water Sea 1976, 3, 253-261. Barker, J. W.; Gomez, R. K. Formation of Hydrates During Deepwater Drilling Operations. J. Pet. Technol. 1989,297-301. Barraclough, B. L. Methane Hydrate as an Energy Resource? A Review with Recommended Future Research. Los Alamos Natl. Lab. [Rep.] 1980, LA-8368-MS (June). Barrer, R. M.; Stuart, W. I. Non-stoichiometricClathrate Compounds of Water. Proc. R. SOC.London 1957,243, 172-189. Barrer, R. M.; Ruzicka, D. J. Non-Stoichiometric Clathrate Compounds of Water. Part 2. Formation and Properties of Double Hydrates. Trans. Faraday SOC.1962a, 58, 2239-2252. Barrer, R. M.; Ruzicka, D. J. Non-Stoichiometric Clathrate Compounds of Water. Part 3. Inclusion Energies and Constants in the Small Cavities of Structure 11. Trans. Faradav SOC.1962b. 58, 2253-2261. Barrer, R. M.; Ruzicka, D. J. Non-Stoichiometric Clathrate Compounds of Water. Part 4. Kinetics of Formation of Clathrate Phases. Trans. Faraday SOC.1962c, 58, 2262-2271. Barrer, R. M.; Edge,A. V. J. Gas Hydrates ContainingArgon, Krypton and Xenon: Kinetics and Energetics of Formation and Equilibria. Proc. R. SOC.London 1967, A300, 1-24. Bayles, G. A.; Sawer,W. K.; Anada, H. R.; Reddy, S. A Steam Cycling Model for Gas Production from a Hydrate Reservoir. Chem. Eng. Commun. 1986,47, 225-245.
1268 Ind. Eng. Chem.Res.,Vol. 32, No. 7, 1993 Bell, P. R. Methane Hydrate and the Carbon Dioxide Question. In Carbon Dioxide Review; Clark, W. C., Ed.; Oxford University Press: New York, 1982; pp 401-406. Belosludov, V. R.; Lavrentief, M. Y.; Dyadin, Y. A. Dynamic and Thermodynamic Properties of Clathrate Hydrates. J. Inclusion Phenom. Mol. Recognit. Chem. 1990,8,59-69. Belosludov, V. R.; Lavrentief, M. Y.; Dyadin, Y. A. Theory of Clathrates. J.Inclusion Phenom. Mol. Recognit. Chem. 1991,10, 399-422. Berecz, E.; Balla-Achs, M. Studies in Inorganic Chemistry 4: Gas Hydrates; Elsevier: Amsterdam, 1983; pp 184-188. Berner, D. The Marine Transport of Natural Gas in Hydrate Form. Proceedings, Second (1992) International Offshore and Polar Engineering Conference,San Francisco, June 14-19,1992; Chung, J. S., Natvig,B. J., Li, Y.-C., Das, B. M., Eds.; InternationalSociety of Offshore and Polar Engineers (ISOPE): 1992; pp 636-643. Bily, C.; Dick, J. W. L. Naturally Occurring Gas Hydrates in the MacKenzie Delta, N.W.T. Bull. Can. Pet. Geol. 1974,22,340352. Bishnoi, P. R.; Gupta, A. K.; Englezos, P.; Kalogerakis, N. E. Multiphase Equilibrium Flash Calculationsin Systems Containing Gas Hydrates. Fluid Phase Equilib. 1989,53,97-104. Bleakley, W. B. Mobil's Methanol-Injection System Prevents Gulf Hydrate Formation. Oil Gas J. 1970, Dec 7, 65-67. Bond, D. C.; Russell, N. R. Effect of Antifreeze Agents on the Formation of Hydrogen Sulfide Hydrate. Pet. Trans. AIME 1949, 179,192-198. Bowsher, A. L. Proceedings of Q Workshop on Clathrates (Gas Hydrates) in the National Petroleum Reserve in Alaska, July 16-17, 1979, Menlo Park, CA, U.S. Department of Interior, Geological Survey: Washington, DC, 1979. Bozzo, A. T.; Chen, H.-S.; Kass,J. R.; Barduhn, A. J. The Properties of the Hydrates ofchlorine and Carbon Dioxide. Proc.Int. Symp. Fresh Water Sea 1973,3,437-451. Brooks,J. M.; Field, M. E.; Kennicutt, M. C., II; Fay, R. R.; McDonald, T. J. Thermogenic Gas Hydrates in the Gulf of Mexico. Science 1984,225,409-411. Brooks, J. M.; Field, M. E.; Kennicutt, M. C., 11. Observations of Gas Hydrates in Marine Sediments, Offshore Northern California. Mar. Geol. 1991, 96,103-109. Brown, J. F. Inclusion Compounds. Sci. Am. 1962,207,82-92. Bryan, G. M. In Situ Indications of Gas Hydrate. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; pp 299-308. Byk, S. S.; Fomina, V. J. Gas Hydrates. Russ. Chemical Rev. 1968, 37 (6), 469-491. Cady, G. H. Composition of Gas Hydrates. J. Chem. Educ. 1983,60, 915-918. Campbell, J. M. Water-Hydrocarbon System Behavior. In Gas Conditioning and Processing; Campbell Petroleum Series Inc.: Norman, OK, 1976; Vol. 2, Chapter 17, pp 130-160. Can. Chem. News. The Bermuda Question Answered? 1990, May, 5. Carbajo, J. J. A Direct-Contact-Charged Direct-Contact-Discharged Cool Storage System Using Gas Hydrate. ASHRAE Trans. 1985, 91 (Part 2A), 258-266. Carroll, J. J.; Mather, A. E. Phase Equilibrium in the System WaterHydrogen Sulfide: Hydrate-Forming Conditions. Can. J. Chem. Eng. 1991,69, 1206-1212. Cha, S. B.; Ouar, H.; Wildeman, T. R.; Sloan, E. D. A Third-Surface Effect on Hydrate Formation. J. Phys. Chem. 1988, 92, 64926494. Chamberlin, J. W.; Foley, H. M.; MacDonald, G. J.; Ruderman, M. A. Climate Effecta of Minor Atmospheric Constituents. In Carbon Dioxide Review: Clarke, W. C.,. Ed.:. Oxford University Press: New York, 1982; pp 255-27j. Chene. W. K.: Pinder. K. L. Consolidation of Sand Formation Using Freon-11 Gas Hydrate. Can. J. Chem. Eng. 1976, 54, 377-381: Chersky, N. J.; Makogon, Y. F. Solid Gas World Reserves are Enormous. Oil Gas Int. 1970,lO (8),82-84 [cited by Davidson et al. (197811. Cicerone, R. J.; Oremland, R. S. Biogeochemical Aspects of Atmospheric Methane. Global Biogeochem. Cycles 1988, 2, 299-327. Clarke, J. W.; Amand, P. S.; Matson, M. Possible Cause of Plumes from Bennett Island, Soviet Far Arctic. Am. Assoc. Pet. Geol. Bull. 1986, 70 (51, 574. Claueaen,W. F. SuggestedStructuresof Water in Inert Gas Hydrates. J. Chem. Phys. 1951a, 19,259-260. Claussen, W. F. A Second Water Structure for Inert Gas Hydrates. J. Chem. Phys. 1951b, 19, 1425-1426.
Claussen, W. F. Erratum: Suggested Structures of Water in Inert Gas Hydrates. J. Chem. Phys. 1961c, 19,662. Claypool,G. E.; Kaplan, I. R. The Origin and Distribution of Methane in Marine Sediments. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; pp 99-139. Cole, W. A.; Goodwin, S. P. Flash Calculations for Gas Hydrates: A Rigorous Approach. Chem. Eng. Sci. 1990,45,569-573. Collett, T. S. Detection and Evaluation of Natural Gas Hydrates from Well Logs, Prudhoe Bay, Alaska. Proceedings, Fourth International Conference on Permafrost, July 17-22, 1983, Fairbanks, AK; National Academy Press: Washington, DC, 1983; pp 169-174. Collett, T. S. Potential Geologic Hazards of Arctic Gas Hydratee. Am. Assoc. Pet. Geol. Bull. 1990, 74 (5), 631-632. Collett, T. S.; Bird, K. J.; Kvenvolden, K. A.; Magoon, L. B. The Origin of Natural Gas Hydrates on the North Slope of Alaska. U.S. Geol. Suru. Bull. 1988, No. 1903, 3-9. Collett, T. S.;Kvenvolden, K. A.; Magoon, L.B. Characterization of Hydrocarbon Gas Within the StratigraphicInterval of Gas-Hydrate Stability on the North Slope of Alaska, U.S.A. Appl. Geochem. 1990,5,279-287. Cox, J. L. Natural Gas Hydrates: Properties, Occurrence and Recovery; Butterworth Publiehere: Woburn, MA, 1983. Crutzen, P. J. Methane's Sinks and Sources. Nature 1991,350,380381. Dando, P. R.; Hovland, M. Environmental Effects of Submarine Seeping Natural Gas. Cont. Shelf Res. 1992,12 (lo), 1197-1207. Davidson, D. W. Gas Hydrates. In Water: A Comprehensive Treatise; Frank F., Ed.; Plenum Press: New York, 1973; Vol. 2, Chapter 3, pp 115-234. Davidson, D. W. Gas Hydrates as Clathrate Ices. In Natural COS Hydrates: Properties, Occurrence and Recouery; Cox, J. L., Ed.; Butterworth: Woburn, MA, 1983; pp 1-15. Davidson, D. W.; Ripmeester, J. A. NMR, NQR and Dielectric Properties of Clathrates. In Inclusion Compounds: Physical Properties and Applications; AcademicPress: London, 19W,Vol. 3, pp 69-127. Davidson, D. W.; El-Defrawy, M. K.; Fuglam, M. 0.; Judge, A. S. Natural Gas Hydrates in Northern Canada. Proceedings, Third International Conference on Permafrost, July 10-13, 1978; Edmonton, AB; National Research Council of Canada: Ottawa, Ontario, 1978; Vol. 1, pp 938-943. Davidson, D. W.; Gough, S. R.; Ripmeester, J. A,; Nakayama, H. The Effect of Methanol on the Stability of Clathrate Hydrates. Can. J. Chem. 1981,59,2587-2590. Davidson, D. W.; Garg, S. K.; Gough, S. R.; Handa, Y. P. Some Structural and Thermodynamic Studies of Clathrate Hydrates. J. Inclusion Phenom. 1984a, 2,231-238. Davidson, D. W.; Handa, Y. P.; Ratcliffe, C. I.; Tee, J. S. The Ability of Small Molecules to Form Clathrate Hydrates of Structure 11. Nature 1984b, 311, 142-143. Davidson, D. W.; Handa, Y. P.; Ripmeester, J. A. Xenon-129 NMR and the Thermodynamic Parameters of Xenon Hydrate. J.Phys. Chem. 1986,90,6549-6552. Davies, J. E. D.; Kemula, W.; Powell, H. M.; Smith, N. 0. Inclusion Compounds-Past, Present, and Future. J.Znclwion Phenom. 1983,1, 3-44. Davis, A. M. Shallow Gas: An Overview. Cont. Shelf Res. 1992,lZ (lo), 1077-1079. Davis, E. E.; Hyndman, R. D.; Villinger, H. Rates of Fluid Expulsion Across the Northern Cascadia Accretionary Prism: Constraints From New Heat Flow and Multichannel Seismic Reflection Data. J. Geophys. Res. 1990,96 (B6), 8869-8889. Davy, H. The Bakerian Lecture. On Some of the Combinations of Oxymuriatic Gas and Oxygene, and on the Chemical Relations of these Principles to Inflammable Bodies. Philos. Trans. R. SOC. London 1811,101, (Part I), 1-35. Deaton, W. M.; Frost, E. M., Jr. U.S. Bur. Mines Monogr. 8, 1946, No. 8. Delyannis, A. Proc. Eur. Symp. Fresh Water Sea 1967,2nd. Delyannis, A.; Delyannis, E. Proc. Int. Symp. Fresh Water Sea 1970, 3rd. Delyannis, A,; Delyannis, E. Proc. Int. Symp. Fresh Water Sea 1973, 4th. Delyannis, A,; Delyannis, E. Proc. Int. Symp. Fresh Water Sea 1976, 5th. Delyannis, A.; Delyannis, E. Proc. Int. Symp. Fresh Water Sea 1978, 6th.
Dharma-wardana, M. W. C. Thermal Conductivity of the Ice Polymorphs and the Ice Clathrates. J. Phys. Chem. 1983,87, 4185-4190. Dholabhai, P. D.; Englezos, P.; Kalogerakis, N. E.; Bishnoi, P. R. Equilibrium Conditions for Methane Hydrate Formation in Aqueous MixedElectrolyte Solutions. Can.J.Chem.Eng. 1991a, 69,800-805. Dholabhai, P. D.; Kalogerakis, N. E.; Bishnoi, P. R. Evaluation of Gas Hydrate Formation and Deposition in Condensate Pipelines: Pilot Plant Studies. SPE 22829. Presented at the 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas, TX, Oct 69,1991b. Dholabhai, P. D.; Kalogerakis, N. E.; Bishnoi, P. R. Inhibition of Gas Hydrate Deposition in Offshore Condensate Pipelines: Effect of Methanol. Presented at the CIM 1992 Annual Technical Conference, Calgary, AB, June 7-10,1992. Dholabhai, P. D.; Kalogerakis, N. E.; Bishnoi, P. R. Kinetics of Methane Hydrate Formation in Aqueous Electrolyte Solutions. Can. J. Chem. Eng. 1993,71, 68-74. Diamond, L. W. Stability of COz Clathrate Hydrate + COa Liquid + COa Vapour + Aqueous KCL-NaC1 Solutions: Experimental Determination and Application to Salinity Estimates of Fluid Inclusions. Geochim. Cosmochim. Acta 1992,56,273-280. Dillon, W. P.; Paull, C. K. Marine Gas Hydrates 11: Geophysical Evidence. In Natural Gas Hydrates: Properties, Occurrence and Recovery; Cox, J. L., Ed.; Butterworth Woburn, MA, 1983;pp 73-90. Dillon, W. P.; Lee, M. W.; Fehlaber, K.; Hutchinson, D. R. Estimation of Amounts of Gas Hydrate in Marine Sediments Using Amplitude Reduction of Seismic Reflections. J. Acoustic. SOC.Am. 1991,89 (4,Part 21, 1853. Dorsett, L. R. L T X Reapplication of Proven Technology. Presented at the SPE Gas Technology Symposium, Dallas, TX, June 7-9, 1989; pp 239-246. Douglas, J. Freeze Concentration: An Energy Efficient Separation Process. EPRZ J. 1989,Jan/Feb, 1621. Du, Y.; Guo, T.-M. Prediction of Hydrate Formation for Systems Containing Methanol. Chem. Eng. Sci. 1990,45 (4),893-900. Englezos, P. Computation of the Incipient Equilibrium Carbon Dioxide Hydrate Formation Conditions in Aqueous Electrolyte Solutions. Znd. Eng. Chem. Res. 1992s,31,2232-2237. Englezos, P. Incipient Equilibrium Hydrate Formation Conditions in Aqueous Polymer Solutions. Chem. Eng. Res. Des. 1992b,70, 43-47. Englem, P. Atmospheric Climate Changes and the Stability of the In-Situ Methane Hydrates in the Arctic. Proceedings, Second (1992)International OffshoreandPolarEngineering Conference, San Francisco, June 14-19,1992;Chung, J. S.,Natvig, B. J., Li, Y.-C., Das, B. M., Eds.; ISOPE: Golden, CO, 1992c;pp 644-652. Englezos, P. The Freeze Concentration Process and its Applications. Dev. Chem. Eng. Min. Roc. 1993,in press. Englezos, P.; Bishnoi, P. R. Prediction of Gas Hydrate Formation Conditions in Aqueous Electrolyte Solutions. AZChE J. 1988a, 34 (lo), 1718-1721. Englezos, P.; Bishnoi, P. R. Gibbs Free Energy Analysis for the Supersaturation Limits of Methane in Liquid Water and the Hydrate-Gas-Liquid Water Phase Behavior. Fluid Phase Equilib. 1988b,42, 129-140. Englezos, P.; Bishnoi, P. R. Experimental Study of the Equilibrium Ethane Hydrate Formation Conditions in Aqueous Electrolyte Solutions. Znd. Eng. Chem. Res. 1991,30,1655-1659. Englezos, P.; Hatzikiriakos, S. G. The Stability of Permafrost and Gas Hydrates Subject to Global Warming. Proceedings, Third (1993)Znternational Offshoreand PolarEngineering Conference, Singapore, June 611,1993;ISOPE: Golden, CO, 1993. Englezos, P.; Ngan, Y. T. Incipient Equilibrium Propane Hydrate Formation Conditions in Aqueous Solutions of NaC1, KCl and CaClr. J. Chem. Eng. Data 1993a 38, 250-253. Englezrm,P.; Ngan, Y. T. Effect of Polyethylene Oxide on Gas Hydrate Phase Equilibria. Fluid Phase Equilib. 1993b,in press. Englezos, P.; Kalogerakis, N. E.; Dholabhai, P. D.; Bishnoi, P. R. Kinetics of Formation of Methane and Ethane Gas Hydrates. Chem. Eng. Sci. 1987a,42,2647-2658. Englezos, P.; Kalogerakis, N. E.; Dholabhai, P. D.; Bishnoi, P. R. Kinetics of Gas Hydrate Formation from Mixtures of Methane and Ethane. Chem. Eng. Sci. 1987b,42,2659-2666. Englezos, P.; Kalogerakis, N. E.; Bishnoi, P. R. Formation and Decomposition of Gas Hydrates of Natural Gas Components. J. Inclusion Phenom. Mol. Recognit. Chem. 1990,8,89-101.
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1269 Englezos, P.; Huang, Z.;Bishnoi, P. R. Prediction of Natural Gas Hydrate Formation Conditions in the Presence of Methanol Using the Trebble-Bishnoi Equation of State. J . Can. Pet. Technol. 1991,30,148-155. Ershov, E. D.; Yakushev, V. S.Experimental Research on Gas Hydrate Decomposition in Frozen Rocks. Cold Reg. Sci. Technol. 1992, 20,147-156. Evrenos, A. I.; Heathman, J.; Ralstin, J. Impermeation of Porous Media by Forming Hydrates In-situ. J.Pet. Technol. 1971,10591066. Falabella, B. J. A Study of Natural Gas Hydrates. Ph.D. Thesis, University of Massachusetts, 1975 [cited by Sloan (1990a)l. Falabella, B. J.; Vanpee, M. Experimental Determination of Gas Hydrate Equilibrium Below the Ice Point. Znd. Eng. Chem. Fundam. 1974,13,228-231. Faraday, M. On Fluid Chlorine. Philos. Trans. R. SOC.London 1823, 113,160-165. Findlay, R. A. Adductive Crystallization. In New Chemical Engineering Separation Techniques; Schoen, H. M., Ed.; Interscience Publishers: New York, 1962;pp 257-318. Finlay, P.; Krason, J. Evaluation of Geological Relationships to Gas Hydrate Formation and Stability: Summary Report. Gas Energy Rev. 1990,18,12-18. Fleyfel, F.; Devlin,J. P. Carbon Dioxide Clathrate Hydrate Epitaxial Growth Spectroscopic Evidence for Formation of the Simple Type-I1 COz Hydrate. J. Phys. Chem. 1991,95,3811-3815. Franklin, L. J. In Situ Hydrates-A Potential Gas Source. In Natural Gas Hydrates: Properties, Occurrence and Recovery; Cox, J. L., Ed.; Butterworth Woburn, MA, 1983;pp 115-122. French, H. M.Proceedings Fourth Canadian Permafrost Conference, Calgary, AB, March 2-6, 1981; National Research Council of Canada: Ottawa, ON, 1982;pp 299-362. Fromson, D. A.; Manolescu, D. R.; Mason, J. C. Zero effluent for CTMP mills. 45th Appita Annual General Conference (APPITA'91), May 2-3,1991;APPITA Parkville, Australia, 1992;Vol. 2,pp 249-255. Gaarder, C.; Ngan, Y. T.; Englezos, P. Crystallization of Mechanical Pulp Mill Effluents Through Hydrate Formation for the Recovery of Water. Abstracts of Papers; ACS Symposium on Emerging Technologies for Hazardous Waste Management, Atlanta, GA, Sept 21-23,1992;American Chemical Society: Washington, DC, 1992. Gebhart, H. J., Jr.; Makin, E. C.; Pierron, E. D. C4 Separation with Gas Hydrates. Chem. Eng. Symp. Ser. 1970,66,105-115. Glew, D. N.; Hagget, M. L. Kinetics of Formation of Ethylene Oxide Hydrate. Part I. Experimental Method and Congruent Solutions. Can. J. Chem. 1968a,46,3857-3865. Glew, D. N.; Hagget, M. L. Kinetics of Formation of Ethylene Oxide Hydrate. Part 11. Incongruent Solutions and Discussion. Can. J. Chem. 1968b,46,3867-3877. Godbole, S.P.; Kamath, V. A.; Ehlig-Economides, C. Natural Gas Hydrates in the Alaskan Arctic. SPE Form. Eval. 1988,March, 263-288. Goodman, M. A. Logging, Coring and Testing for Permafrost Evaluation. World Oil 1978,Jan, 93-99. Goodman, M. A.; Franklin, L. Thermal Model of a New Concept for Hydrate Control During Drilling. Proceedings, Fourth Canadian Permafrost Conference,March 2-6, 1981,Calgary, AB; French, H. M., Ed.; National Research Council of Canada: Ottawa, ON, 1982;pp 349-355. Graauw, J. D.; Rutten, J. J. The Mechanism and the Rate of Hydrate Formation. Proc. Znt. Symp. Fresh Water Sea 1970, 103-116. Grigg, R. B.; Lynes, G. L. Oil-Based Drilling Mud as Gas Hydrates Inhibitor. SPE Drill. Eng. 1992,32-38. Gupta, A. K.; Bishnoi, P. R.; Kalogerakis, N. A Method for the Simultaneous Phase Equilibria and Stability Calculations for Multiphase Reacting and Non-reacting Systems. Fluid Phase Equilib. 1991,63,65-89. Hagan, S. M. Clathrate Inclusion Compounds; Reinhold Publishing: New York, 1962. Hale, A. H.; Dewan, A. K. R. Inhibition of Gas Hydrates in Deepwater Drilling. SPE Drill. Eng. 1990,109-115. Hallbrucker, A.; Mayer, E. Formation and Decomposition of Oxygen Clathrate Hydrate as Seen by Two-step Differential Scanning Calorimetry; Novel Method for Investigating Reactions Accompanied by Gas Release. J. Chem. SOC.,Chem. Commun. 1990,12, 873-874. Hammerschmidt, E. G. Formation of Gas Hydrates in Natural Gas Transmission Lines. Znd. Eng. Chem. 1934,26(8),851-855.
1270 Ind. Eng. Chem. Res., Vol. 32, No.7, 1993 Hammerschmidt, E. G. Preventing and Removing Hydrates in 30-34,94 [cited by Natural Gas Pipe Lines. Gas 1939a,15 (9, Deaton and Frost (1946)l. Hammerschmidt, E. G. Preventing and Removing Gas Hydrate Formations in Natural Gas Pipe Lines. Oil Gas J. 1939b,37,66, 69,71,72 [cited by Hulle et al. (1966)l. Hand, J. H.; Katz, D. L.; Verma, V. K. Review of Gas Hydrates with Implication for Ocean Sediments. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974;pp 179194. Handa, Y. P. CompositionDependence of Thermodynamic Properties of Xenon Hydrate. J. Phys. Chem. 1986a,90,5497-5498. Handa, Y. P. Calorimetric Determinations of the Compositions, Enthalpies of Dissociation, and Heat Capacities in the Range 85 to 270 K for Clathrate Hydrates of Xenon and Krypton. J. Chem. Thermodyn. 198613,18,891-902. Handa, Y. P. Compositions, Enthalpies of Dissociation, and Heat Capacities in the Range 85 to 270 K for Clathrate Hydrates of Methane, Ethane, and Propane, and Enthalpy of Dissociation of Isobutane Hydrate, as Determined by Heat-Flow Calorimeter. J. Chem. Thermodyn. 1986c,18,915-921. Handa, Y. P. A Calorimetric Study of Naturally Occurring Gas Hydrates. Ind. Eng. Chem. Res. 1988,27,872-874. Handa, Y.P.; Tse, J. S. Thermodynamic Properties of Empty Lattices of Structure I and Structure I1Clathrate Hydrates. J.Phys. Chem. 1986,90,5917-5921. Handa, Y.P.; Hawkins, R. E.; Murray, J. J. Calibration and Testing of a Tian-Calvet Heat-Flow Calorimeter. Enthalpies of Fusion and Heat Capacities for Ice and Tetrahydrofuran Hydrate in the Range 85 to 270 K. J. Chem. Thermodyn. 1984,16,623-632. Harmens, A.; Sloan, E. D. The Phase Behaviour of the PropaneWater System: A Review. Can. J. Chem.Eng. 1990,68,151-158. Hatzikirioikos,S . G.; Englezos,P. On the RelationshipBetween Global Warming and Methane Gas Hydrates in the Earth. Chem. Eng. Sci. 1993,in press. Heidemann, R. A,; Fredenslund, A. Vapour-Liquid Equilibria in Complex Mixtures. Chem. Eng. Res. Des. 1989,67,145-158. Heist, J. A. Freeze Crystallization. Chem. Eng. 1979,May 7,72-82. Heist, J. A. Freeze Crystallization Applications for Waste Water Recycle and Reuse. AIChE Symp. Ser. 1981, 77 (209),259-272. Heist Engineering Corp. 1988. “Beet sugar refining applications”; final report for the US. Department of Energy, available from the National Technical Information Service, U.S. Department of Commerce, Springfield, VA 22161. Hesse, R. Pore Water Anomalies in Gas-Bearing Sediments of the Deeper Continental Margins: Facts and Problems. J. Inclusion Phenom. Mol. Recognit. Chem. 1990,8,117-138. Hicks, R. L.; Senules, E. A. New Gas-Water-TEG Equilibria. Hydrocarbon Process. 1991,April, 55-58. Hill, T. L. Statistical Mechanics; Dover: New York, 1987 (republication of the original McGraw-Hill ed., 1956);pp 376-379. Hitchon, B. Occurrence of Natural Gas Hydrates in Sedimentary Basins. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; pp 195-225. Holder, G. D.; Hand, J. H. Multiple-Phase Equilibria in Hydrates from Methane, Ethane, Propane and Water Mixtures. AIChE J. 1982,28,440-447. Holder, G. D.; Manganiello, D. J. Hydrate Dissociation Pressure Minima in Multicomponent Systems. Chem. Eng. Sci. 1982,37 (l),9-16. Holder, G. D.; John, V. T. Thermodynamics of Multicomponent Hydrate Forming Mixtures. Fluid Phase Equilib. 1983,14,353361. Holder, G. D.;Katz, D. L.; Hand, J. H. Hydrate Formation in Subsurface Environments. Am. Assoc. Pet. Geol. Bull. 1976,60, 981-994. Holder, G. D.; Gorbin, G.; Papadopoulos, K. D. Thermodynamic and Molecular Properties of Gas Hydrates from Mixtures Containing Methane. Areon. ” . and K m - _t o n . Ind. Enz. Chem. Fundam. 1980, 19,282-286. Holder, G. D.; Angert, P. F.; John, V. T.; Yen, S. A. Thermodynamic Evaluation of Thermal Recovery of Gas From Hydrates in the Earth. J. Pet. Technol. 1982,May, 1127-1132. Holder, G. D.; Angert, P. F.; Pereira, V. Implications of Gas Hydrates Associated with Gas Reserves. In Natural Gas Hydrates: Properties, Occurrence and Recovery; Cox, J. L., Ed.; Butterworth: Woburn, MA, 1983;pp 91-114. Holder, G. D.; Malekar, S. T.; Sloan, E. D. Determination of Hydrate ThermodynamicReferenceProperties from Experimental Hydrate Composition Data. Ind. Eng. Chem.Fundam. 1984,23,123-126. I
Holder, G. D.; Malone, R. D.; Lawson, W. F. Effects of Gas Composition and Geothermal Properties on the Thickness and Depthof Natural-Gas-Hydrate Zones. J.Pet. Technol.1987,11471152. Holder, G. D.; Zetts, S. P.; Pradham, N. Phase Behavior in Systems Containing ClathrateHydrates. Rev. Chem.Eng. 1988,5(l),1-69. Hooper, J. Gas Hydrate Influence on Deep Ocean Foundation Design. Presented at the Second (1992)International Offshore and Polar Engineering Conference, San Francisco, June 14-19,1992(paper not included in the proceedings). Huang, C. P.; Fennema, 0.;Powrie, W. D. Gas Hydrates in Aqueous Organic Systems I. Preliminary Studies. Cryobiology 1966,2, 109-115. Huang, C. P.; Fennema, 0.;Powrie, W. D. Gas Hydrates in Aqueous Organic Systems 11. Concentration by Gas Hydrate Formation. Cryobiology 1966,2,240-245. Hubbard, R. A. Recent Developments in Gas Dehydration and Hydrate Inhibition. SPE Gas Technol. Symp. 1991,263-276. Hwang, M. J.; Wright,D.A.;Kapur,A.;Holder,G. D.AnExperimental Study of Crystallization and Crystal Growth of Methane Hydrates from Melting Ice. J. Inclusion Phenom. Mol. Recognit. Chem. 1990,8,103-116. Hyndman, R. D. “Ice” Beneath the Deep Sea: Studies of Methane Hydrate Layers Beneath the Continental Slope off Vancouver Island. Geosci. Can. 1992,19,21-26. Hyndman, R. D.; Davis, E. E. A mechanism for the Formation of Methane Hydrate and Seafloor Bottom-Simulating Reflectors by vertical Fluid Expulsion. J. Geophys. Res. 1992,97(B5), 70257041. Hyndman, R. D.; Spence, G. D. A Seismic Study of Methane Marine Bottom Simulating Reflectors. J. Geophys. Res. 1992,97 (B5), 6683-6698. Hyndman, R. D.; Foucher, J. P.; Yamano, M.; Fisher, A.; Scientific Team of Ocean Drilling Program Leg 131. Deep Sea Bottom Simulating Reflectors: Calibration of the Base of the Hydrate Stability Field as Used for Heat Flow Estimates. Earth Planet Sci. Lett. 1992,109,289-301. Istomin, V. A. A Model of Gas Hydrates Taking into Account the Guest-Guest Interactions. J.Phys. Chem. 1987,91,1404-1407. Istomin, V. A.; Kolushev, N. R. Hydrate Control at Russian Northern Gas Field. Proceedings, Second (1992)International Offshore and Polar Engineering Conference,San Francisco, June 14-19, 1992; Chung, J. S.,Natvig, B. J., Li, Y.-C., Das, B. M., Eds.; ISOPE: Golden, CO, 1992;pp 684-687. Jamaluddin, A. K. M.; Kalogerakis, N.; Bishnoi, P. R. Modelling of Decomposition of a Synthetic Core of Methane Gas Hydrate by Coupling Intrinsic Kinetics with Heat Transfer Rates. Can. J. Chem. Eng. 1989,67,948-954. Jamaluddin, A. K. M.; Kalogerakis, N.; Bishnoi, P. R. Hydrate Plugging Problems in Undersea Natural Gas Pipelines Under Shutdown Conditions. J. Pet. Sci. Eng. 1991,5,323-335. Jeffrey, G. A. Hydrate Inclusion Compounds. J.Inclusion Phenom. Mol. Recognit. Chem. 1984a,I, 211-222. Jeffrey, G. A. Hydrate Inclusion Compounds. In Inclusion Compounds: Structural Aspects of InclusionCompoundsFormed by Inorganic and OrganometallicHost Lattices; Academic Press: London, 198413;Vol. 1, pp 135-190. Jeffrey, G. A.; McMullan, R. K. The Clathrate Hydrates. In Prog. Inorg. Chem. 1967,8,43-108. John, V. T.; Holder, G. D. Choice of Cell Size in the Cell Theory of Hydrate Phase Gas-Water Interactions. J. Chem. Phys. 1981,85, 1811-1814. John, V. T.; Holder, G. D. Contribution of Second and Subsequent Water Shells to the Potential Energy of Guest-Host Interactions in Clathrate Hydrates. J. Chem. Phys. 1982,86,455-459. John, V. T.; Holder, G. D. Langmuir Constants for Spherical and Linear Molecules in Clathrate Hydrates. Validity of the Cell Theory. J. Phys. Chem. 1985,89,3279-3285. John, V. T.; Papadopoulos, K. D.; Holder, G. D. AGeneralized Model for Predicting Equilibrium Conditions for Gas Hydrates. AIChE J. 1986,31,252-259. Judge, A. Natural Gas Hydrates in Canada. Proceedings, Fourth CanadianPermafrost Conference,March 26,1981,Calgary, AB, French, H. M., Ed.; National Research Councilof Canada: Ottawa, ON, 1982;pp 320-328. Kamath, V. A.; Godbole, S. P. Evaluation of Hot-Brine Stimulation Technique for Gas Production From Natural Gas Hydrates. J. Pet. Technol. 1987,1379-1388. Kamath, V. A,; Holder, G. D. Dissociation Heat Transfer Characteristics of Methane Hydrates. AIChE J. 1987,33,347-350.
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1271 Kamath, V. A,; Holder, G. D.; Angert, P. F. Three Phase Interfacial Heat Transfer During the Dissociation of Propane Hydrates. Chem. Eng. Sci. 1984,39, 1435-1442. Kamath, V. A,; Mutalik, P. N.; Sira, J. H.; Patil, S. L. Experimental Study of Brine Injection and Depressurization of Methods for Dissociation of Gas Hydrates. SPE Form. Eval. 1991, Dec, 477484. Kaplan, I. R. Natural Gases in Marine Sediments; Plenum: New York, 1974; pp 1-320. Katz, D. L. Depths to Which Frozen Gas Fields (Gas Hydrates) May Be Expected. J.Pet. Technol. 1971, 419-423. Katz, D. L. Depths To Which Frozen Gas Fields (Gas Hydrates) May Be Expected-Footnotes. J. Pet. Technol. 1972, 557-558. Katz, D. L.; Lee,R. L. Gas Hydrates and Their Prevention. InNatural Gas Engineering: Production and Storage; McGraw-Hill: New York, 1990; pp 197-230. Khan, A. H. Freezing. In Desalination Processes and Multistage Flash Distillation Practice; Elsevier: Amsterdam, 1986; Chapter 5, pp 55-68. Kim, H. C.; Bishnoi, P. R.; Heidemann, R. A.; Rizvi, S. S. Kinetics of Methane Hydrate Decomposition. Chem. Eng. Sci. 1987,42, 1645-1653. Knox, W. G.; Hess, M.; Jones, G. E.; Smith, H. B. The Clathrate Process. Chem. Eng. Prog. 1961,57,66-71. Kotkoskie, T. S.; Al-Ubaldi, B.; Wildeman, T. R.; Sloan, E. D., Jr. Inhibition of Gas Hydrates in Water-Based Drilling Muds. SPE Drill. Eng. 1992, 130-136. Kubota, H.; Shimizu, K.; Tanaka, Y.; Makita, T. Thermodyanic Properties of R13 (CClFB), R23 (CHFs), R152a (C~Hflz),and Propane Hydrates for Desalination of Seawater. J. Chem. Eng. Jpn. 1984, 17 (4), 423-429. Kvenvolden, K. A. Occurrence and Origin of Marine Gas Hydrates. Proceedings, Fourth Canadian Permafrost Conference; March 2-6, 1981, Calgary, AB; French, H. M. Ed.; National Research Council of Canada; Ottawa, ON, 1982; pp 305-311. Kvenvolden, K. A. Marine Gas Hydrates. I 1 Geomchemical Evidence. In Natural Gas Hydrates: Properties, Occurrenceand Recovery; Cox, J. L., Ed.; Butterworth Woburn, MA, 1983; pp 63-72. Kvenvolden, K. A. Methane Hydrate-A Major Reservoir of Carbon in the Shallow Geosphere. Chem. Geol. 1988a, 41-51. Kvenvolden, K. A. Methane Hydrates and Global Climate. Global Biogeochem. Cycles 1988b, 2,221-229. Lederhos, J. P.; Mehta, A. P.; Nyberg, G. B.; Warn, K. J.; Sloan, E. D. Structure H Clathrate Hydrate Equilibria of Methane and Adamantane. AZChE J. 1992,38,1045-1048. Lowrie, A. Massive Gas Deposita in the Deep Sea. Proceedings,23rd Annual Offshore TechnologyConference, Houston, TX, May 6-9, 1991: Offshore Technology -_ Conference: Richardson,. TX,. 1991: pp 309-316. Lund, D. B.; Fennema, 0.; Powrie, W. D. Rotation Apparatus for Shell Freezing. Cryobiology 1968, 5, 26-28. Lund, D. B.; Fennema, 0.; pbwrie, W: D. Effect of Gas Hydrate Formers on Invertase Activity. Arch. Biochem. Biophys. 1969, 129,181-188. Lundgaard, L.; Mollerup, J. M. The Influence of Gas Phase Fugacity and Solubility on Correlation of Gas Hydrate Formation Pressure. Fluid Phase Equilib. 1991, 70, 199-213. Lundgaard, L.; Mollerup, J. M. Calculation of Phase Diagrams of Gas Hydrates. Fluid Phase Equilib. 1992, 76, 141-149. MacDonald, G. J. The Many Origins of Natural Gas. J.Pet. Geol. 1983, 5 (4), 341-362. MacDonald, G. J. Role of Methane Clathrates in Past and Future Climates. Climatic Change 1990, 16,247-281. Maini, B. B.; Bishnoi, P. R. Experimental Investigation of Hydrate Formation Behaviour of a Natural Gas Bubble in a Simulated Deep Sea Environment. Chem. Eng. Sci. 1981,36,183-189. Makogon, Y. F. Hydrates of Natural Gas; Penn Well Publishing: Tulsa, OK, 1981 (translated by W. J. Cieslewicz). Makogon, Y. F. Perspectives for the Development of Gas Hydrate Deposita. Proceedings, Fourth Canadian Permafrost Conference; March 2-6, 1981, Calgary, AB, French, H. M. Ed.; National Research Council of Canada: Ottawa, ON, 1982; pp 299-304. Makogon, Y. F. Les Hydrates de Gaz: de l’energie Congelee: Recherche 1987,18 (192), 1192. Makogon, Y. F. Gas Hydrate Accumulations and Permafrost Development. Proceedings, FifthZnt. Conf. Permafrost, Trondheim, Norway, Aug 2-5; TAPIR Publishers: 1988; Vol. 1, pp 95-101. Makogon, Y. F.; Trebin, F. A.; Trofimuk, A. A.; Tsarev, V. P.; Chersky, N. V. Detection of a Pool of Natural Gas in a Solid (Hydrate Gas)
State. Dokl. Acad. Sci. USSR-Earth Sci. Sect. 1972,196,197200 (originally published in Russian, 1971). Malone, R. D.; Dillon, W. Detection Development Needs for Gas Hydrates in Sediments. Proceedings, Second (1992)International Offshore and Polar Engineering Conference; San Francisco, June 14-19,1992, Chung, J. S., Natvig, B. J., Li, Y.-C., Das, B. M., Eds.; ISOPE: Golden, CO, 1992; pp 660-668. Mandelcorn, L. Clathrates. Chem. Rev. 1959,59,827-839. Manning, F. S.; Thompson, R. E. Prevention of Hydrate Formation. In Oil Field Processing of Petroleum, Vol. 1: Natural Gas; PennWell Books: Tulsa, OK, 1991; pp 85-98. Marshal, D. R.; Saito, S.; Kobayashi, R. Hydrates at High Pressures: Part I. Methane-Water, Argon-Water, and Nitrogen-Water Systems. AZChE J. 1964,10,202-205. McDermott, J. Desalination by Freeze Concentration; Noyes Data Corp.: Park Ridge, NJ, 1971. McGuire, P. L. Methane Hydrate Gas production: An Assessment of Conventional Production Technology as Applied to Hydrate Gas Recovery. Los Alamos Natl. Lab. [Rep.] 1981, LA-9102-MS (Nov). McGuire, P. L. Methane Hydrate Gas Production by Thermal Stimulation. In Proceedings, Fourth Canadian Permafrost Conference, March 2-6,1981,Calgary,AB, French, H. M., Ed.; National Research Council of Canada: Ottawa, ON, 1982; pp 356-362. McKoy, V.; Sinanoglu, 0. Theory of Dissociation Pressures of Some Gas Hydrates. J. Chem. Phys. 1963,38 (3), 2946-2956. McTurk, G.;Waller, J. G. Ozone-Carbon Tetrachloride Double Hydrate. Nature 1964,202, 1107. Menten, P. D.; Parrish, W. R.; Sloan, E. D., Jr. Effect of Inhibitors on Hydrate Formation. Znd. Eng. Chem. Process Des. Dev. 1981, 20 (2), 399-401. Miller, S. L. The Occurrence of Gas Hydrates in the Solar System. Proc. Natl. Acad. Sci. U.S.A. 1961a, 47, 1798-1808. Miller, S. L. Theory of Gaseous Anesthetics. Proc. Natl. Acad. Sci. U.S.A. 1961b, 47, 1515-1524. Miller, S. L. Clathrate Hydrates of Air in Antarctic Ice. Science 1969,165,489-490. Miller, S. L. The Nature and Occurrence of Clathrate Hydrates. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; pp 151-170. Miller, S. L.; Smythe, W. D. Carbon Dioxide Clathratein the Martian Ice Cap. Science 1970,170,531-533. Modell, M.; Reid, R. C. Thermodynamics and Its Applications, 2nd ed.; Prentice-Halk Englewood Cliffs, NJ, 1983. Mori, Y. H.; Mori, T. Characterization of Gas Hydrate Formation in Direct-Contact Cool Storage Process. Znt. J. Refrig. 1989a, 12, 259-265 [cited by Mori and Mori (1989b)l. Mori, Y. H.; Mori,T. Formation of Gas Hydrate with CFC Alternative R-134a. AZChE J. 1989b,35, 1227-1228. Mori, Y. H.; Isobe, F. A. Model for Gas Hydrate Formation AccompanyingDirect-Contact Evaporation of Refrigerant Drops In Water. Znt. Commun. Heat Mass Transfer 1991,18,599-608. Morlat, M.; Pernolet, R.; Gerard, N. Formation Process of Ethylene Hydrate. Proc. Int. Symp. Fresh Water Sea 1976, 3, 263-269. Muijs, H. M. Surfactants in Oil Production. In Chemicals in the Oil Industry: Developments and Applications; Ogden, P. H., Ed.; Royal Society of Chemistry: London, 1991; pp 277-297. Muller, H. R.; von Stackelberg, M. Naturwissenschaften 1952,2021. Muller-Bongartz, B.; Wildeman, T. R.; Sloan, E. D., Jr. A Hypothesis for Hydrate Nucleation Phenomena. Proceedings, Second (1992) International Offshore and Polar Engineering Conference, San Francisco, June 14-19, 1992; Chung, J. S., Natvig, B. J., Li, Y-C., Das, B. M., Eds.; ISOPE Golden, CO, 1992; pp 628435. Munck, J.; Jorgensen, S. S.; Rasmussen, P. Computations of the Formation of Gas Hydrates. Chem. Eng. Sci. 1988,43 (lo),26612672. Nagata, I.; Kobayashi, R. Calculation of Dissociation Pressures of Gas Hydrates Using the Kihara Model. Znd.Eng. Chem. Fundam. 1966a, 5, 344-348. Nagata, I.; Kobayashi, R. Prediction of Dissociation Pressures of Mixed Gas Hydrates from Data for Hydrates of Pure Gases with Water. Znd. Eng. Chem. Fundam. 1966b,5,466-470. Najdi, M.; Schaetzle, W. J. Cooling and Heating with Clathrate Thermal Energy Storage System. ASHRAE Trans. 1991,97 (Part l), 177-183. Nerheim, A. R.; Svartas, T. M.; Samuelsen, E. K. Investigation of Hydrate Kinetics in the Nucleation and Early Growth Phase by Laser Light Scattering. Proceedings, Second (1992)International Offshore and Polar Engineering Conference; San Francisco, June
1272 Ind. Eng. Chem. Res., Vol. 32, No.7, 1993 14-19,1992; Chung, J. S.,Natvig, B. J., Li, Y-C., Das, B. M., Eds.; ISOPE: Golden, CO, 1992; pp 620-627. Ng, H.-J.; Robinson, D. B. The Measurement and Prediction of Hydrate Formation in Liquid Hydrocarbon-Water Systems. Ind. Eng. Chem. Fundam. 1976,15,293-298. Ng, H.-J.; Robinson, D. B. The Prediction of Hydrate Formation in Condensed Systems. AIChE J. 1977,23, 477-482. Ng, H.-J.; Robinson, D. B. A Method for Predicting the Equilibrium Gas Phase Water Content in Gas-Hydrate Equilibrium. Znd.Eng. Chem. Fundam. 1980,19, 33-36. Ng, H.-J.; Robinson, D. B. “Equilibrium Phase Compositions and Hydrating Conditions in Systems Containing Methanol, Light Hydrocarbons, Carbon Dioxide and Hydrogen Sulfide”; Gas Processors Association,Research Report RR-66; Tulsa, OK, 1983. Ng, H.-J.; Robinson, D. B. ’The Influence of Methanol on Hydrate Formation at Low Temperatures”; Gas Processors Association, Research Report RR-74; Tulsa, OK, 1984. Ng, H.-J.; Robinson,D. B. Hydrate Formation Conditions in Systems Containing Methane, Ethane, Propane, Carbon Dioxide or Hydrogen Sulfide in the Presence of Methanol. Fluid Phase Equilib. 1986,21, 145-155. Ng, H.-J.; Chen, C.-J.; Robinson, D. B. ‘Hydrate Formation and Equilibrium Phase Compositions in the Presence of Methanol: Selected Systems Containing Hydrogen Sulfide, Carbon Dioxide, Ethane or Methane”; Gas Processors Association, Research Report RR-87; Tulsa, OK, 1985. Ng, H.-J.; Chen, C.-J.; Robinson, D. B. “The Influence of High Concentrations of Methanol on Hydrate Formation and the Distribution of Glycol in Liquid-Liquid Mixtures”; Gas Processors Association, Research Report RR-106; Tulsa, OK, 1987a. Ng, H.-J.; Chen, C. J.; Saeterstad, T. Hydrate Formation and Inhibition in Gas Condensate and Hydrocarbon Liquid Systems. Fluid Phase Equilib. 1987b, 36, 99-106. Nguyen, H.; Phillips, J. B.; John, V. T. Clathrate Hydrate Formation in Reversed Micellar Solutions. J. Phys. Chem. 1989,93,81238126. Nguyen, H.; John, V. T.; Reed, W. F. Characteristics of ProteinContaining Reversed Micelles Subjected to Clathrate Hydrate Formation Conditions. J. Phys. Chem. 1991, 95, 1467-1471. Nielsen, R. B.; Bucklin, R. W. Why Not Use Methanol for Hydrate Control? Hydrocarbon Process. 1983, April, 71-78. Nisbet, E. G. Some Northern Sources of Atmospheric Methane: Production, History, and Future Implications. Can.J.Earth Sci. 1989,26,1603-1611. Nisbet, E. G. The End of the Ice Age. Can. J. Earth Sci. 1990,27, 148-157. Nisbet, E. G. Sources of Atmospheric CHI in Early Postglacial Time. J. Geophys. Res. 1992,97 (D12), 12859-12867. Nishikawa, N.; Morishita, M.; Uchiyama,M.; Yamaguchi,F.; Ohtsubo, K.; Kimuro, H.; Hiraoka, R. C02 Clathrate Formation and ita Properties in the Simulated Deep Ocean. Energy Convers. Manage. 1992,33 (5-8), 651-657. Oishi, T.; Prausnitz, J. M. Estimation of Solvent Activitiesin Polymer Solutions Using a Group Contribution Method. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 333-339. Ouar, H.; Cha, S. B.; Wildeman, T. R.; Sloan, E. D. The Formation of Natural Gas Hydrates in Water-Based Drilling Fluids. Chem. Eng. Res. Des. 1992, 70, 48-54. Palin, D. E.; Powell, H. M. Hydrogen Bond Linking of Quinol Molecules. Nature 1946, 156, 334-335. Palin, D. E.; Powell, H. M. The Structure of Molecular Compounds. Part V. The Clathrate Compound of Quinol and Methanol. J. Chem. SOC.1948a, 571-574. Palin, D. E.; Powell, H. M. The Structure of Molecular Compounds. Part VI. The b-Type Clathrate Compounds of Quinol. J. Chem. SOC.194813, 571-574. Pandit, B. I.; King, M. S. Elastic Wave propagation in Propane Hydrates. Proceedings, Fourth Canudianpermufrost Conference, March 2-6, 1981, Calgary, AB, French, H. M., Ed.; National Research Council of Canada: Ottawa, ON, 1982; pp 335-342. Pandit, B. I.; King, M. S. Elastic Wave Velocitiesof Propane Hydrates. In Natural Gas Hydrates Properties, Occurrence and Recovery; Cox, J. L., Ed.; Butterworth Woburn, MA, 1983; pp 49-61. Pangborn, J. B.; Barduhn, A. J. The Kinetics of Methyl Bromide Hydrate Formation. Desalination 1970, 8, 35-68. Parker, A. Potable Water from Sea-water. Nature 1942,149, 184186. Parrish, W. R.; Prausnitz, J. M. Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures. Ind. Eng. Chem. Process Des. Deu. 1972, 11, 26-34.
Parsonage, N. G.; Staveley, L. A. K. Thermodynamic Studies of Clathrates and Inclusion Compounds. In Inclueion Compounds: Physical Properties and Applications; Academic Press; London, 1984, Vol. 3, pp 1-36. Pauling, L. AMolecular Theory of General Anesthesia. Science 1961, 134,15-21. Pauling, L. General Chemistry; Dover Publications: New York, 1970; pp 420-444. Pauling, L.; Marsh, R. E. The Structure of Chlorine Hydrate. Proc. Natl. Acad. Sci. U.S.A. 1962, 38, 112-118. Pavlov, G. D.; Medvedev, I. N. Gas Hydrating Proceee of Water Desalination. Proc. Znt. Symp. Water Desalination 1966, 123127. Pearson, C. F.; Halleck, P. M.; McGuire, P. L.; Hermes, R.; Mathews, M. Natural Gas Hydrate Deposita: A Review of In-situ Properties. J. Phys. Chem. 1983,87,4180-4185. Peng, D. Y .;Robinson, D. B. A New Two-Constant Equation of State. Znd. Eng. Chem. Fundam. 1976,15,59-64. Phillips, J. B.; Nguyen, H.; John, V. T. Protein Recovery from Reversed Micellar Solutions through Contact with a Pressurized Gas Phase. Biotechnol. Prog. 1991, 7, 43-48. Pinder, K. L. Time Dependent Rheology of the Tetrahydrofuran Hydrogen Sulfide Gas Hydrate Slurry. Can.J.Chem.Eng. 1964, 132-138. Pinder, K. L. A Kinetic Study of the Formation of the Tetrahydrofuran Gas Hydrate. Can. J. Chem. Eng. 1965,271-274. Pitzer, K. S. Thermodynamics of Electrolytes I. Theroetical Basis and General Equations. J. Phys. Chem. 1973, 77,268-277. Pitzer, K. S.; Mayorga, G. Thermodynamics of Electrolytes 11. Activity and Osmotic Coefficienta for Strong Electrolytes with One or Both Ions Univalent. J.Phys. Chem. 1973,77,2300-2308. Platteeuw, J. C.; van der Waals, J. H. Thermodynamic Properties of Gas Hydrates. Mol. Phys. 1968,1, 91-96. Plummer, P. L. M.; Chen, T. S. A Molecular Dynamics Study of Water Clathrates. J.Phys. Chem. 1983,87,4190-4197. Powell, H. M. The Structure of Molecular Compounds. Part IV. Clathrate Compounds. J. Chem. SOC.1948,61-73. Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid Phase Equilibria, 2nd ed.; PrenticeHalk Englewood Cliffs, NJ, 1986. Quadfasel, D.; Sy, A.; Wells, D.; Tunk, A. Warming in the Arctic. Nature 1991,350,385. Rao, A. M.; Nguyen, H.; John, V. T. Modification of Enzyme Activity in Reversed Micelles through Clathrate Hydrate Formation, Biotechnol. Prog. 1990, 6, 465-471. Rao, A. M.; Kommareddi, N.; John, V. T. The Use of Preesure to Modify Enzyme Activity in Reversed Micelles. Biotechnol. Prog. 1992,8, 514-520. Rasmwen, D.; Rasmussen, P. Phase Equilibria in AqueousPolymer Solutions. Chem. Eng. Prog. 1989,50-59. Rautenbach, R.; Seide, A. Technical Problem and Economics of Hydrate Process. Proc. Znt. Symp. Fresh Water Sea 1978,43-51. Redlich, 0.;Kwong, J. N. S. On The Thermodynamics of Solutions. V: An Equation of State. Fugacities of Gaseous Solutions. Chem. Rev. 1949,44, 233-244. Revelle, R. R. Methane Hydrates in Continental Slope Sediments and Increasing Atmospheric Carbon Dioxide. In Changing Climates; National Academy Press: Washington, DC, 1983; pp 252-261. Richardson, H. H.; Wooldridge, P. J.; Devlin, J. P. FT-IR Spectra of Vacuum Deposited Clathrate Hydrates of Oxirane HzS, THF, and Ethane. J. Chem. Phys. 1986,83,4387-4394. Ridley, I.; Dominic, K. Gas Hydrates Keep Energy on Ice. New Sci. 1988,117,53-68. Ripmeester, J. A.; Ratcliffe, C. I. NMR Studies of Clathrate Hydrates: New Guests for Structure I1and Structure H. J. Phys. Chem. 1990,94, 8773-8776. Ripmeester, J. A.; Tee, J. S.; Ratcliffe, C. I.; Powell, B. M. A New Clathrate Hydrate Structure. Nature 1987,325, 136-136. Robinson, D. B.; Mehta, B. R. Hydrates in the Propane-Carbon Dioxide-Water System. J. Can.Pet. Technol. 1971,lO (l), 33-35. Robinson, D. B.; Ng, H.-J. Hydrate Formation and Inhibition in Gas or Gas Condensate Streams. J. Can. Pet. Technol. 1986,26 (3), 26-30. Rodger, P. M. Cavity Potential in Type I Gas Hydrates. J.Phys. Chem. 1989, 93,6850-6855. Rodger, P. M. Stability of Gas Hydrates. J.Phys. Chem. 1990a, 94, 6080-6089. Rodger, P. M. Clathrate Hydrates-Simulations. Chem. Br. 1990b, 26,1090-1092.
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1273 Rodger, P. M. Computer Simulations of Gas Hydrates. Presented at the Spring AIChE Meeting, Houston, TX, April 7-11, 1991a. Rodger, P. M. Lattice Relaxation of Type I Gas Hydrates. AZChE J. 1991b, 37,1511-1516. Row, M. J.; Toczylkin, L. S. Hydrate Dissociation Pressures for Methane or Ethane in the Presence of Aqueous Solutions of Triethylene Glycol. J. Chem. Eng. Data 1992, 37, 488-491. Saito, S.; Kobayashi, R. Hydrates at High Pressures: Part 111. Methane-Water, Argon-Water, and Nitrogen-Water Systems. AZChE J. 1965,11,96-99. Saito, S.; Marshal, D. R.; Kobayashi, R. Hydrates at High Pressures: Part II. Methane-Water, Argon-Water, and Nitrogen-Water Systems. AZChE J. 1964,10, 734-740. Saji, A.; Ymhida, H.; Sakai, M.; Tanii, T.; Kamata, T.; Kitamura, H. Fixation of Carbon Dioxide by Clathrate-Hydrate. Energy Convers. Manage. 1992, 33 (5-8),643-649. Sakai,H.;Gamo,T.;Kim,E-S.;Tsutsumi,M.;Tanaka,T.; Ishibashi, J.; Wakita, H.; Yamano, M.; Oomori,T. Venting of Carbon DioxideRich Fluid and Hydrate Formation in Mid-Okinawa Trough Backarc Basin. Science 1990,248,1093-1096. Scanlon, W. J.; Fennema, 0. Gas Hydrates in Aqueous Organic Systems VII. Linear Crystallization Velocitiesof the Hydrates of Ethylene Oxide and Tetrahydrofuran. Cryobiology 1972,8,249254.
Schneider, S. H. The Global Warming Debate: Science or Politics? Environ. Sci. Technol. 1990,24, 432-435. Schneider, W.; Seidemann; Ebert, K. H. Laboratory Experiments of aHydrateProcessinaColumnApparatus. Proc.Int. Symp.Fresh Water Sea 1978,5341. Schroeter, J. P.; Kobayashi, R.; Hildebrand, M. A. Hydrate Decomposition Conditions in the System Hydrogen Sulfide-MethanePropane. Znd. Eng. Chem. Fundam. 1983,22, 361-364. Seitz, J. C.; Pasteria, J. D. Theoretical and Practical Aepecta of Differential Partitioning of Gases by Clathrate Hydrates in Fluid Inclusions. Geochim. Cosmochim. Acta 1990,54,631439. Selim, M. S.; Sloan, E. D. Hydrate Dissociation in Sediment. SPE Reservoir Eng. 1990, May, 244-251. Sharma, G. D.; Kamath, V. A,; Patil, S. L. Natural Gas Hydrate Resources of the Alaskan Arctic and their Recovery Potential. Proceedings, Second (1992) International Offshore and Polar Engineering Conference, San Francisco, June 14-19,1992; Chung, J. S., Natvig, B. J., Li, Y-C., Das, B. M., Eds.; ISOPE: Golden, CO, 1992; pp 652459. Skovborg, P.; Ng, H. J.; Rasmussen, P.; Mohn, U. Measurement of Induction Times for the Formation of Methane and Ethane Gas Hydrates. Chem. Eng. Sci. 1993,48 (3), 445-453. Sloan, E. D. Two-Phase Natural Gas Hydrate Equilibrium. Proceedings, Fourth Canadian Permafrost Conference, March 2-6, 1981, Calgary, AB, French, H. M., Ed.; National Research Council of Canada; Ottawa, ON, 1982; pp 343-348. Sloan, E. D. Shore-Based Laboratory Experimental Measurements on a Gas Hydrate Sample Recovered at Site 570. Initial Rep. Deep Sea Drill. Proj. 1986, 84, 695-698. Sloan, E. D. Clathrate Hydrates of Natural Gases; Dekker: New York, 1990a. Sloan, E. D. Natural Gas Phase Equilibria and Kinetics: Understanding the State-of-the-Art. Rev. Zmt. Fr. Pet. 1990b, 45 (2), 245-266. Sloan, E. D. Natural Gas Hydrates. J. Pet. Technol. 1991, 14141417. Sloan, E. D.; Fleyfel, F. A Molecular Mechanism for Gas Hydrate Nucleation from Ice. AZChE J. 1991, 37, 1281-1292. Sloan, E. D.; Fleyfel, F. Hydrate Dissociation Enthalpy and Guest Size. Fluid Phase Equilib. 1992, 76,123-140. Sloan, E. D.; Khoury,F. M.; Kobayashi, R. Water Content of Methane Gas in Equilibrium with Hydrates. Znd. Eng. Chem. Fundam. 1976,15,318-323. Sloan, E. D.; Sparks, K. A,; Johnson, J. J. Two-Phase Liquid Hydrocarbon-Hydrate Equilibrium for Ethane and Propane. Ind. Eng. Chem. Res. 1987,26, 1173-1179. Smirnov, L. F. Kinetics of Gas Hydrate Formation. Theor. Found. Chem. Eng. 1987, 465-474. Song, K. Y.; Kobayashi, R. Measurement and Interpretation of the Water Content of a Methane-Propane Mixture in the Gaseous State in Equilibrium with Hydrate. Ind. Eng. Chem. Fundam. 1982,21,391-395. Song, K. Y.; Kobayashi, R. Water Content of Carbon Dioxide in EquilibriumwithLiquid Waterand/orHydrates. SPEForm. Eval. 1987,500-508.
Song, K. Y.; Kobayashi, R. Final Hydrate Stability Conditions of a Methane and Propane Mixture in the Presence of Pure Water and Aqueous Solutions of Methanol and Ethylene Glycol. Fluid Phase Equilib. 1989, 47, 295-308. Sparks, K. A.; Tester, J. W. Intermolecular Potential Energy of Water Clathrates: The Inadequacy of the Nearest-Neighbor Approximation. J. Phys. Chem. 1992,96, 11022-11029. Stevenson, S. Meadow Lake’s Zero-effluent is Good news for Millar Western. Pulp Paper Can. 1992,93 (lo), 13-20. Stoll,R. D. Effects of Gas Hydrates in Sediments. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; pp 235-248. Stoll,R. D.; Bryan, G. M. Physical Properties of Sedimenta Containing Gas Hydrates. J. Geophys. Res. 1979,84 (B4), 1629-1634. Stoll, R. D.; Ewing, J.; Bryan, G. M. Anomalous Velocities in Sediments Containing Gas Hydrates. J. Geophys. Res. 1971,76, 2090-2094. Suga, H.; Matsuo, T.; Yamamuro, 0. Thermodynamic Study of Ice and Clathrate Hydrates. Pure Appl. Chem. 1992,64,17-26. Sugi, J.; Saito, S. Concentration and Demineralization of Sea Water by the Hydrate Process. Desalination 1967,3,27-31. Svartas, T. M.; Fadnes, F. H. Methane Hydrate Equilibrium Data for the Methanewater-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., Li, Y-C., Das, B. M., Eds.;pp 614-619. Tanaka, H.; Gubbins, K. E. Structure and Thermodynamic Properties of Water-Methanol Mixtures: Role of the Water-Water Interaction. J. Chem. Phys. 1992, 97, 2634. Tanaka, H.; Walsh, J.; Gubbins, K. E. Structure of Water-Methanol Binary Mixtures: Role of Water-Water Interaction. Mol. Phys. 1992, 76,1221-1233. Taylor, F. W. The Greenhouse Effect and Climate Change. Rep. Bog. P h p . 1991,54 (6), 881-918. Tech Commentary 1988, 1 (l), 1-4 (Freeze Concentration). Tester, J. W.; Bivins, R. L.; Herrick, C. C. Use of Monte Carlo in Calculating the Thermodynamic Properties of Water Clathrates. AZChE J. 1972,18, 1220-1230. Thomas, A. V.; Spooner, E. T. C. Fluid Inclusions in the Systems H20-CH4-NaCl-CO2 from Metasomatic Tourmaline Within the Border Unit of the Tanco Zoned Granitic Pegmatite, S.E. Manitoba. Geochim. Cosmochim. Acta 1988,52, 1065-1075. Tleilmat, B. W. Freezing Methods. In Principles of Desalination, 2nd ed.; Spriengler, K. S., Ed.; Academic Press: New York, 1980; Chapter 7, pp 359-400. Topham, D. R. The Formation of Gas Hydrates on Bubbles of Hydrocarbon Gases Rising in Seawater. Chem. Eng. Sci. 1984a, 39,821-828. Topham, D. R. The Modelling of Hydrocarbon Bubble Plumes to Include Gas Hydrate Formation. Chem. Eng. Sci. 1984b,39,16131622. Trebble, M. A.; Bishnoi, P. R. Extension of the Trebble-Bishnoi Equation of State to Fluid Mixtures. Fluid Phase Equilib. 1988, 40, 1-21. Tse, J. S. Thermal Expansion of Structure H Clathrate Hydrates. J. Inclwion Phenom. Mol. Recognit. Chem. 1990,8, 25-32. Tse, J. S.;Davidson,D. W. Intermolecular Potentials in Gas Hydrates. Proceedings, Fourth Canadian Permafrost Conference; March 2-6, 1981, Calgary, AB, French, H. M., Ed.; National Research Council of Canada; Ottawa, ON, 1982; pp 329-334. Tee, J. S.; Klein, M. L. Dynamical Properties of the Structure I1 Clathrate Hydrate of Krypton. J. Phys. Chem. 1987,91,57895791. Tee, J. S.;Klein, J. S.; McDonald, I. R. Molecular Dynamics Studies of Ice IC and the Structure I Clathrate Hydrate of Methane. J. Phys. Chem. 1983a, 87,4198-4203. Tse, J. S.;Klein, J. S.; McDonald, I. R. Dynamical Properties of the Structure I Clathrate Hydrate of Xenon. J. Chem. Phys. 1983b, 78 (4), 2096-2097. Tse, J. S.; Klein, J. S.; McDonald, I. R. Computer Simulation Studies of the Structure I Clathrate Hydrates of Methane, Tetrafluoromethane, Cyclopropane, and Ethylene Oxide. J. Chem. Phys. 1984,81 (12), 6146-6153. Tse, J. S.; Handa, Y. P.; Ratcliffe, C. I.; Powell, B. M. Structure of Oxygen Clathrate Hydrate by Neutron Powder Diffraction. J. Inclusion Phenom. 1986,4,235-240. Tucholke, B. E.; Bryan,G. M.; Ewing, J. I. Gas-Hydrate Horizons Detected in SeismicProfiler Data from the Western North Atlantic. Am. Assoc. Pet. Geol. Bull. 1977, 61 (5),698-707.
1274 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Tzirita, A.; Jeanjean, P.; Briaud, J.-L.; Dunlap, W. A. Detection of Gas Hydrates by In-Situ Testing. Proceedings, 23rd Annual Offshore Technology Conference, Houston, TX, May, 6-9,1991; OffshoreTechnology Conference: Richardson, TX, 1991;pp 325334. Udall, S. L.; Holum, K.; Di Luzio, F. C. Proc. Znt. Symp. Water Desalination 1965. Ullerich, J. W.;Selim, M. S.; Sloan, E. D. Theory and Measurement of Hydrate Dissociation. AZChE J. 1987,33, 747-752. Unruh, C. H.; Katz, D. L. Gas Hydrates of Carbon Dioxide-Methane Mixtures. Pet. Trans. AZME 1949,April, 83-86. van der Heem, P. The Koppers Hydrate Process. Proc. Int. Symp. Water Desalination 1965,769-778. van der Waals, J. H. The Statistical Mechanics of Clathrate 1956,52,184-193. Compounds. Trans. Faraday SOC. van der Waals, J. H.; Platteeuw, J. C. Clathrate Solutions. Adu. Chem. Phys. 1959,2,1-57. van Hulle, G.; Fennema, 0.Gas Hydrates in Aqueous OrganicSystems IV. Formation and Detection of Ethylene Oxide Hydrate in Tissue. Cryobiology 1971a,7, 223-227. van Hulle, G.; Fennema, 0. Gas Hydrates in Aqueous OrganicSystems V. Effects of Ethylene Oxide and Ethylene Oxide Hydrate in Animal Tissue. Cryobiology 1971b, 7,228-237. van Hulle, G.; Fennema, 0.Gas Hydrates in Aqueous OrganicSystems VI. Effects of Hydrate Formers and Hydrate Crystale in Carrot Tissue. Cryobiology 1972,8,91-103. van Hulle, G.; Fennema, 0.;Powrie, W. D. Gas Hydrates in Aqueous Oreanic Svstems 111. Hvdrate Formation in Polyacrylamide Gel. Cryobiology 1966,2,246-255. Verma. V. K.: Hand. J. H.: Katz. D. L.: Holder. G. D. Denudine Hydrocarbon Liquids of 'Natural Gas' Constituents by Hydrate Formation. J. Pet. Technol. 1975,223-226. Vlahakis, J. G.; Chen, H.-S.; Suwandi, M. S.; Barduhn, A. J. "The Growth Rate of Ice Crystals: Properties of Carbon Dioxide Hydrate, A Review of Properties of 51 Gas Hydrates"; Syracuse University Research and Development Report 830;prepared for the Office of Saline Water, US. Department of the Interior, Nov 1972. von Stackelberg, M. Feste Gashydrate. Naturwissenschaften 1949a, 327-333. von Stackelberg, M. Feste Gashydrate. Naturwissenschaften 1949b, 359-363. von Stackelberg, M.; Muller, H. R. On the Structure of Gas Hydrates. J. Chem. Phys. 1951a,1319-1320. von Stackelberg, M.; Muller, H. R. Zur Struktur der Gashydrate. Naturwissenschaften 1951b,456. Vysniauskas, A.; Bishnoi, P. R. A Kinetic Study of Methane Hydrate Formation. Chem. Eng. Sci. 1983a, 38, 1061-1072. Vysniauskas, A,; Bishnoi, P. R. Thermodynamics and Kinetics of Gas Hydrate Formation. In Natural Gas Hydrates: Properties, Occurrence and Recovery; Cox, J. L., Ed.; Butterworth: Woburn, MA, 1983b;pp 35-48. Vysniauskas, A.; Bishnoi, P. R. Kinetics of Ethane Hydrate Formation. Chem. Ena. Sci. 1985,40, 299-303. Wallqvist,A. On The Stability of Type I Gas Hydrates in the Presence of Methanol. J. Chem. Phys. 1992,96,5371-5382. Weaver, J. S.;Stewart, J. M. In situ Hydrates under the Beaufort Sea shelf. Proceedings, Fourth Canadian Permafrost Conference, March 2-6, 1981, Calgary, AB; French, H. M., Ed.; National Research Council of Canada: Ottawa, ON, 1982;pp 312-319.
Werezak, G. N. Unusual Methods of Separation. AZChE Symp. Ser. 1969,65 (91),6-18. Williams, V. C.; Roy, C. L.; Williams, R. A. Hydrate Process Pilot Plant. Proc. Znt. Symp. Water Desalination 1966,605-619. Willeon, R. C.; Bulot, E.; Cooney, C. L. Clathrate Hydrate Formation Enhances Near-critical and Supercritical Extraction Equilibria. Chem. Eng. Commun. 1990,47-55. Wittebolle, R. J.; Sego, D. C. A Laboratory Facility for Testing Sediments Containing Gas Hydrates. Proceedings, Fourth Znternational Offshore Mechanics and Arctic Engineering Symposium, Dallas, TX, Feb 17-21,1985;Chung, J. S.,Lunardini, V. J., Chakrabarti, S. K., Wang, Y. S., Sodhi, D. S., Karal, K., Ede.; The American Society of Mechanical Engineers: New York, 1985; pp 52-58. Wooley, G. R.; Giussani, A. P.; Schaayk, F. V. Hydrate Formation from Gas Kick in Deep Water Offshore Well. Proceedings, Fifth International Offshore Mechanics and Arctic Engineering (OMAE) Symposium, Tokyo, April 13-18,1986;Lunardini, V. J., Wang, Y.S., Ayorinde, 0. A., Sodhi, D. V., Eds.; The American Society of Mechanical Engineers: New York, 1986;pp 35-44. Wright, S. G.; Roeeeet, J. M.; Stokoe, K. H. Analytical and Experimental Studies of Surface Wave Meaeurementa to Detect Gas Hydrates Offshore. Proceedings, 23rd Annual Offshore Technology Conference, Houston, TX, May 6-9,1991;Offshore Technology Conference: Richardson, TX, 1991;pp 317-324. Yakushev, V. S.; Collett, T. S. Gas Hydrates in Arctic Regions: Risk to Drilling and Production. Proceedings, Second (1992)Znternational Offshore and Polar Engineering Conference, San Francisco, June 14-19,1992;Chung, J. S.,Natvig, B. J., Li, Y-c., Das, B. M., E&.; ISOPE Golden, CO, 1992;pp 669-673. Yamamuro, 0.; Suga, H. Thermodynamic Studies of Clathrate Hydrates. J. Thermal Anal. 1989,36,2025-2064. Yamanlar, S.;Poettmann, F. H.; Sloan, E. D. Control Hydrate Formation. Hydrocarbon Process. 1991,Sept, 155-161. Yousif, M. H.; Sloan, E. D. Experimental and Theoretical Investigation of Methane-Gas-Hydrate D i a t i o n in Porous Media. SPE Reservoir Eng. 1991,Nov, 69-76. Yousif, M. H.; Li, P. M.; Selim, M. S.; Sloan, E. D. Depressurization of Natural Gas Hydrates in Berea Sandstone Cores. J.Inclusion Phenom. Mol. Recognit. Chem. 1990,8,71-88. Yousif, M. H.; Abase, H. H.; Selim, M. S.; Sloan, E.D. Experimental and Theoretical Investigation of Methane-Gas-Hydrate Dissociation in Porous Media. SPE Reservoir Eng. 1991,Feb, 69-76. Zemaitis, J. F.; Clark, D. M.; Mal,M.; Scriven, N. C. Handbook of Aqueous Electrolyte Thermodynamics;DIPR/AIChE: New York, 1986. Zonenshayn, L. P.; Murdmaa, I. 0.; Baranov, V.; Kuzneteov, A. P.; Kuzin, V. S.; Kuz'min, M. I.; Avdeyko, P. A.; Stunzhas, P. A.; Lukashm, V. N.; Barash, M. S.; Valyashko, G. M.; Demina, L. L. An Underwater Gas Source in the Sea of Okhotak West of Paramushir Island. Oceanology 1987,27,598-602. Zubkus, V. E.; Tornau, E. E.; Belosludov, V. R. Theoretic PhpicochemicalProblems of Clathrate Compounds. Adu. Chem.Phys. 1992,269-359. Receiued for review November 12, 1992 Accepted March 19, 1993
