Ứng dụng hữu ích của Gas hydrates trong ngành công nghiệp dầu khí. Cung cấp các thông tin cần thiết cho các kỹ sư dầu khí nhằm đáp ứng cho nhu cầu năng lượng không chỉ của riêng nước ta mà còn trên thế giới.
lllll ELSEVIER Fluid Phase Equilibria 117 (1996) 168-177 F O R M A T I O N AND D E C O M P O S I T I O N OF GAS HYDRATES P Raj Bishnoi* and V Natarajan Department of Chemical and Petroleum Engineering University of Calgary Calgary, Alberta CANADA - T2N 1N4 ABSTRACT The kinetics of hydrate formation and decomposition are explained as understood to date The formation and decomposition phenomena are complex Hydrate formation is viewed as a crystallization process that includes the nucleation and growth processes Hydrate nucleation is an intrinsically stochastic process that involves the formation and growth of gas-water clusters to critical sized, stable hydrate nuclei Hydrate growth process involves the growth of stable hydrate nuclei as solid hydrates Hydrate decomposition is a sequence of lattice destruction and gas desorption processes The process of heat transfer during hydrate decomposition is analogous to nucleate boiling phenomena The focus of this work is to present the various perspectives on the kinetic processes at a conceptual level Key issues for research in this area are identified and some possible directions for future work are suggested INTRODUCTION Gas hydrates are crystalline, non-stoichiometric, clathrate compounds They are formed by certain gases when contacted with water under favourable temperature and pressure conditions Natural gas components like CH4 C2H6, C3H8, i-C4H~o, CO2 and H2S besides other gases like Ne, Ar, Kr, Xe, N2, 02 and hydrocarbons like cyclopropane form hydrates The water molecules in the hydrates form a cage-like crystal structure through hydrogen bonding around the entrapped gas molecules The gas hydrate structures ~6 are identified as I, II and the recently determined structure H 7'g Structures I and II consist of two types of cavities and structure H consists of three types of cavities Extensive information on gas hydrates is available as compiled in various sources 9'"~ and from the proceedings" of a recently concluded international conference on gas hydrates The industrial interest in gas hydrates began with the discovery that hydrate formation could plug natural gas pipelines t2 Initial interest was on the avoidance of hydrate formation in pipelines and other process equipment Hence much research was directed to understand the conditions of hydrate formation As a result of extensive thermodynamic studies, considerable hydrate phase equilibrium data and methods to predict hydrate formation conditions are available 9' 1.~327 These studies have also focused on the development of chemical agents that inhibit hydrate formation Substances which affect the colligative properties of a solution generally inhibit hydrate formation Methanol is one such commonly used inhibitor in the industry ~7,~s Electrolytes are also known to inhibit hydrate formation 2~27 As the focus of this work is on the kinetics of hydrate formation and decomposition, the studies on the thermodynamics of hydrates are not discussed Details on these studies could be obtained from reviews by Holder28 and Englezos 29 In contrast to the advances made in the thermodynamics of hydrates, the kinetics are less understood The kinetics * - Author for correspondence 0378-3812/96/$15.00 © 1996ElsevierScienceB.V All fights reserved SSDI 0378-3812(95)02950-8 P.R Bishnoi, V Natarajan / Fluid Phase Equilibria 117(1996) 168-177 169 could be broadly divided into the two categories of formation and decomposition kinetics Generally hydrate formation and decomposition processes are studied separately and only recently Bishnoi et al 3° have shown that a unified treatment of hydrate formation and decomposition is possible A good knowledge of the hydrate formation kinetics would allow the exploitation of the kinetics mechanism favourably to depress the hydrate formation rate Although hydrate formation may be unavoidable, the rate of formation could be slowed 3136 to allow gas transport in pipelines without plugging the lines Another idea to modify the hydrate particle characteristics to prevent the particles from agglomerating is being explored 37 This would enable the solid hydrates to be transported through pipelines in slurry form3am In comparison to hydrate formation there have been even fewer studies on hydrate decomposition With the depletion of conventional natural gas reserves, there would be a need in the future to exploit the vast quantities of natural gas reserves known to occur in hydrate form9'1°'4~'42.A practical and viable technology to tap this vast source of the gas would require simulation studies 43 52 of the gas recovery processes and could only be developed if hydrate decomposition kinetics are well understood For this mason it is expected that hydrate decomposition would be an area of considerable interest in the future In this work, the kinetics of hydrate formation and decomposition are explained as understood to date The formation and decomposition phenomena are complex The focus of this work is to present the various perspectives on the kinetic processes at a conceptual level Key issues for research in this area are identified and some possible directions for future work are suggested KINETICS OF HYDRATE FORMATION The hydrate formation process is analogous to the crystallization process 9'1°'53"57.As in crystallization, the hydrate formation process could be sub-divided into nucleation and growth processes Hydrate nucleation is the process of forming critical sized, stable hydrate nuclei, and hydrate growth is the process of growth of these stable nuclei The available information on hydrate nucleation and growth have primarily come from the laboratories of Profs Bishnoi 3°'32"~3~5'57"67and Sloan 1°'33"56'6s'7°.The nucleation processes are discussed below Hydrate Nucleation The hydrate nucleation process refers to the formation and growth of hydrate nuclei to critical size The growing clusters of gas and water molecules could be regarded as precursors to hydrate nuclei formation5.59 If the size of growing nuclei is less than the critical size then the nuclei are unstable and may grow or break in the aqueous solution A growing hydrate nucleus that attains the critical size is a stable nucleus and immediately leads to the formation of crystal hydrate The induction period is the time elapsed during the nucleation processes which include formation of gas-water clusters and their growth to critical sized stable nuclei Although the view that hydrate nucleation processes involve the formation and growth of gas-water clusters to critical sized nuclei enjoys considerable support, the precise nature of the clusters and the mechanisms of their formation and growth are still not understood Phenomena that affect the gas-water cluster formation are of interest to understand the hydrate nucleation process In particular the structure of water has an important role in the nucleation process Because of the hydrogen bonding ability of water there exist hydrogen-bonded structures among the water molecules that connect some of these molecules The structure of water7~8grefers to the arrangement of water molecules connected through hydrogen bonds to form these structures For example, ice represents a highly structured water with the positions of water molecules fixed in a tetragonal hydrogen bonded structure As the temperature increases above the freezing point the structure of water becomes more loose and disordered compared to the highly organized structure of ice Hydrate formation experiments using water from 170 P.R Bishnoi, V Natarajan / Fluid Phase Equilibria 117 (1996) 168-177 different sources by Vysniauskas and Bishnoi 5~ showed that the mean induction period varied with the source of water used In these experiments a lower mean induction period was observed when water obtained from thawed ice was used as compared to the induction period obtained when hot tap water was used The mean induction period was also lower when water obtained from dissociated hydrates was used as compared to the induction period observed when hot tap water was used 58 This is known as the "memory effect" and has been observed in a number of studies 8993 besides Vysniauskas and Bishnoi 5s In addition, studies have found that the structure of water is enhanced around a dissolved gas molecule This effect on the water structure around a dissolved solute molecule is referred as the "hydrophobic hydration" phenomenon as suggested by Frank and Co-workers94'95 The hydrophobic hydration was supported later by Glew 96 who showed the similarities in the thermodynamic properties of methane hydrates and aqueous methane solutions Molecular simulation studies 97'98for the methane-water system indicated that the average co-ordination number of water molecules around the methane molecule was closer to the co-ordination number of 21 for a structure I smaller cavity Rahman and Stillinger 99 have identified the water network around the dissolved solute molecule to be similar to that of a hydrate type cavity In addition, thermodynamic analysis shows a large negative entropy of solution which is an evidence of the creation of a structure within the body of the water ~6 ucleation Processes eq time As mentioned above the gas-water clusters play an important role in the hydrate nucleation process The nucleation process occurs when the solution is in a supercooled or supersaturated state The study of nucleation using the supersaturation and the supercooling approaches are schematically illustrated in Figures and respectively The supersaturation approach is adopted by Bishnoi and Co-workers and the supercooling approach is adopted by Kobayashi and Co-workers 92'1°°and Sloan and Co-workers tb The hydrate formation experiments were conducted by Bishnoi and Co-workers at constant temperature and pressure The experimental pressure was Figure 1: Typical Gas Consumption Plot higher than the three phase hydrate equilibrium pressure at the experimental temperature They used a stirred reactor in which the hydrate forming gas was contacted in a semi-batch manner with a known volume of water Figure shows the cumulative moles of gas consumed due to its dissolution or hydrate formation with time during an experiment The moles of gas consumed at point A represents the amount of gas dissolved corresponding to the three phase hydrate equilibrium pressure at the experimental temperature The metastable region between the points A and B is characterized by the hydrate nucleation processes The point B in the figure represents the point at which stable critical sized hydrate nuclei appear in a catastrophic manner Englezos and Bishnoi 54 found that the moles of gas dissolved just prior to the nucleation point, B, was substantially higher than the computed two phase (vapor-liquid) metastable equilibrium The computed value was obtained by extrapolating in the metastable region They suggested that the gas-water cluster formation could deplete the hydrate forming gas in the bulk liquid phase and thus cause the gas to dissolve beyond the two phase value The critical size of a hydrate nuclei could be calculated as suggested by Englezos et al 53'67 The hydrate growth process begins at point B and proceeds along the line B-C shown in Figure A schematic of the pressure and temperature trace of hydrate forming experiments conducted by Kobayashi and Co-workers and Sloan and Co-workers at constant volume is shown in Figure The point A in Figure could be identified with the point A in Figure At point B a catastrophic formation of stable hydrate particles occurs leading to a sudden fall in the pressure Hence the point B in Figure is equivalent to the point B in Figure The metastable state characterized by the nucleation processes is represented between points A and B The similarities between the P.R Bishnoi V Natarajan / Fluid Phase Equilibria 117(1996) 168-177 Nucleation Temperature * 171 supersaturation and the supercooling approaches as illustrated in the Figures and are readily apparent The metastable hydrate nucleation region of cluster formation and growth is represented between the point corresponding to three phase hydrate equilibrium, A, and the point of stable hydrate particle formation, B, in both the figures The appearance of hydrates at point B is sudden and has been described as catastrophic by Kobayashi and Coworkers92 Although the size of the hydrate particles is small, their number is sufficiently large to make the solution appear turbid in the experiments of Bishnoi and Co-workers In the same way the sudden appearance of hydrates results in the consumption of supersaturation leading to the dramatic pressure drop in the experiments by Kobayashi and Co-workers and Sloan and Co-workers Figure 2: Experimental Pressure-Temperature Trace From the above discussion it is clear that supersaturation and supercooling are equivalent They are essential for the hydrate nucleation processes Many researchers have modelled the induction period as a function of =o supercooling9"1°'1°H°4 The supersaturation could also be translated in terms of the degrees of supercooling 1°5 The supersaturation at any point in the solution is the excess dissolved gas concentration over the saturation concentration value at that point.The availability of supersaturation at a point -l in the solution dictates the location where stable nuclei of solid hydrates first appear For stagnant systems the hydrate formation Figure 3: Induction Period vs Supersaturation could begin at the gas-liquid interface first since the dissolved gas concentration would be the highest near the interface For stirred systems, the hydrate formation could begin anywhere in the solution depending on the dissolved gas concentration at that location Hence the hydrodynamics of the solution and the rate of gas dissolution in solution could be expected to affect the induction period The induction period of hydrate nucleation has been related to supersaturation by Bishnoi and Co-workers 3°'57 From their analysis supported by experimental data on methane, ethane and carbon dioxide hydrates57 the following points could be made The dependence of the induction periods on the supersaturation is observed as shown schematically in Figure In the figure fm is the fugacity of the gas at the experimental temperature and at hydrate equilibrium pressure The fugacity of the gas, fgv, in the figure is at the experimental temperature and pressure The supersaturation in the figure is expressed as the excess of the fugacity ratio over unity The induction periods increase as the supersaturation is decreased, tending to very large values at low supersaturations As the supersaturation is increased the induction periods generally decrease to a small value The scatter in the induction period data is high at very low supersaturations which decreases as the supersaturation is increased The induction period data exhibit random behaviour at lower supersaturations and increasingly exhibit deterministic behaviour as the supersaturation is increased Hydrate nucleation is intrinsically random in nature3°'34"~7'66"1°~.High supersaturations could mask this random nature of the nucleation phenomena thereby making the observance of the induction periods appear deterministic In addition, the random nature of the hydrate nucleation could be masked by the presence of any heterogeneities in the experimental system used for the nucleation study The randomness in the induction period data was observed in recent hydrate nucleation studies by Parent and 172 P.R Bishnoi, V Natarajan / Fluid Phase Equilibria 117 (1996) 168-177 Bishnoi 66 under pristine experimental conditions A molecular mechanism of the hydrate nucleation process has been postulated by Sloan and Co-workers 56"69'7° Their mechanism envisages the formation of intermediate structures from the gas-water clusters and the growth of these structures to stable hydrate nuclei Through the use of chemical kinetic equations for each of the species postulated in their mechanism 69'7°, they have modelled the nucleation process A reaction kinetic mechanism for hydrate formation is also proposed by Lekvam and RuoW °7'~°8 This approach uses a kinetic rate model for the nucleation and growth processes This model does not seem to impose the stability of the hydrate nuclei The available information on hydrate nucleation is at a macroscopic level and very little is known experimentally about the sub-critical nuclei in solution The mechanism of hydrate nucleation needs to be experimentally studied and understood before any modelling at a molecular level could be accomplished Hydrate Growth The hydrate growth process refers to the growth of stable hydrate nuclei as solid hydrates and has been studied by several researchers from the early sixties Knox et al z°9 studied the propane hydrate growth in a stirred slurry pilot plant reactor for a desalination process They indicated that approximate sizes of the crystals obtained by the growth depends on the degree of supercooling A higher degree of supercooling produced chiefly smaller particles and resulted in distinct crystal growth Studies by Pinder 11° on hydrate formation kinetics with a soluble hydrate former like tetrahydrofuran showed that the rate of hydrate forming reaction could be diffusion dependent The kinetics of hydrate growth from ice has been studied by Barrer and Edge m who observed a distinct induction period for krypton Later Falabella 1~2used an apparatus similar to that of Barrer and Edge, and obtained similar results in his study Falabella also observed an induction period for methane He proposed a second-order kinetic model based upon the isothermal, isobaric conversion of ice for his kinetic data and the data from Barrer and Edge Sloan and Fleyfe169 have experimentally studied the growth kinetics of cyclopropane hydrates Bishnoi and Co-workers have conducted a systematic study of hydrate formation kinetics over many years 53"55'57"67 The studies were conducted for various gases and gas mixtures in pure water, electrolyte and surfactant solutions using a semi-batch stirred reactor In these experiments at constant temperature and pressure the overall gas consumption was obtained as a function of time Earlier in their studies a semi-empirical model was proposed for the gas consumption rate by Vysniauskas and Bishnoi 5s'59 Later, an intrinsic kinetic model for Diffusion hydrate growth with only one adjustable parameter was Film formulated by Englezos et al 53 The model is a mechanistic model based on crystallization and mass transfer theories It envisages that the solid hydrate Distancealongfilm particle is surrounded by an adsorption "reaction" layer Figure 4: Fugacity profile in the diffusion and adsorption followed by a stagnant liquid diffusion layer The "reaction" film around a growing hydrate dissolved gas diffuses from the solution surrounding the particle stagnant liquid layer to the hydrate particle-water interface and then, by an adsorption process the gas molecules are incorporated into the structured water framework As the water is in excess the reaction at the interface is considered to be of first order in gas concentration The fugacity of the dissolved gas is used in place of its concentration to express the reaction rates A schematic of the dissolved gas fugacity profile in the diffusion and the adsorption layers around a Adsorption "Reaction" Film P.R Bishnoi, V Natarajan / Fluid Phase Equilibria 117 (1996) 168-177 173 growing hydrate particle, assumed spherical, in the solution is shown in Figure In the diffusion layer, the dissolved gas fugacity changes from the value, fb, to the value, f~ In the adsorption layer, the fugacity value falls to f~q, the value at the three phase hydrate equilibrium pressure and at the particle surface temperature The driving forces for the diffusion around the particle is fb-f,, whereas it is f:fm for the "reaction" step At steady state the rates of the two steps are equal Therefore f~ can be eliminated from the individual rate expressions to yield the rate of growth per particle as below () (1) The quantity fb-f~qis the difference in the fugacity of the dissolved gas and its fugacity at the three phase equilibrium It defines the overall driving force K* is the combined rate constant for the diffusion and adsorption "reaction" processes and Ap is the surface area of each particle As diffusional limitations are avoided in their well stirred system the K* values reported by them represent the intrinsic rate constant of the reaction The K* values were determined from experimental data on formation kinetics of methane and ethane hydrates This model was successfully extended to formation kinetics of mixtures of methane and ethane 67 without any additional parameters For methane hydrates, with the same K* that was obtained for hydrate formation from pure water, the model is shown to apply to hydrate formation from electrolyte solutions t ~3 A kinetic model for CO hydrate formation at the interface between liquid CO2 and water is reported by Shindo et al) 14'H5 They assume that the hydrate formation occurs mainly in the liquid CO and not in water The formation of CO2 hydrate is considered as a first order homogeneous reaction between CO2 and water Recently, Skovborg and Rasmussen t~6have formulated a model for hydrate growth kinetics using the experimental gas consumption data obtained by Bishnoi et al ~1'6~.They stated that the formation of hydrates would affect the liquid side gas-liquid mass transfer coefficient, and used the data to empirically determine the mass transfer coefficient This approach does not provide any insight on the hydrate growth process Future studies on hydrate growth kinetics should include the determination of the size distribution of the growing hydrate particles At present limited results on the size distribution of cyclopropane hydrate particles are available from Monfort and Nzihou 91 In addition, the agglomeration characteristics of the growing hydrate particles need to be studied Hydrate Decomposition The hydrate decomposition has not been as extensively studied as hydrate formation Holder and Co-workers m'1~8 have studied the heat transfer during the hydrate decomposition process and drawn its analogy with the nucleate boiling phenomena Based on this analogy, Kamath et al H7 expressed the heat transfer rate during propane hydrate decomposition to be a power function of AT, which is the temperature difference between the bulk fluid and the hydrate surface Later Kamath and Holder 118 generalized the correlation and applied it to methane hydrate decomposition Bishnoi and C o - w o r k e r s 119 have conducted experiments on methane hydrate decomposition in a semi-batch, well stirred reactor In their experiments, hydrates were formed at a pressure above the three phase hydrate equilibrium pressure at the experimental temperature Then the decomposition was initiated by a drop in the pressure to a desired pressure below the three phase equilibrium pressure maintaining the temperature constant The amount of gas evolved from the decomposing hydrates was obtained as a function of time The experiments were conducted at high enough stirring rates to avoid mass transfer effects They have suggested that the hydrate decomposition may be viewed as a two step process the destruction of the clathrate host lattice at the particle surface followed by the desorption of the guest molecule from 174 P.R Bishnoi, V Natarajan / Fluid Phase Equilibria 117(1996) 168-177 the surface An intrinsic kinetic model for hydrate decomposition was formulated by Kim et al.ll9 The decomposing hydrate particle, assumed spherical, was considered surrounded by a cloud of gas as shown schematically in Figure In the figure the decomposing particle is surrounded by a desorption "reaction" layer followed by a cloud of the evolved gas The rate of decomposition for a hydrate particle is given by, ( m a 0% -f,b, (2) Figure 5: Decomposition of Hydrate Particles where Kd is the decomposition rate constant and Ap is the surface area of a particle The three phase equilibrium fugacity of the gas, f~q, and the fugacity of the gas, fgv, are at the particle surface temperature but at the three phase equilibrium and the experimental pressure respectively The decomposition driving force was defined as the fugacity difference, f~q - fgv As mentioned earlier for the hydrate growth, the decomposition studies also should be undertaken to include the determination of the size distribution of the decomposing particles CONCLUDING REMARKS The study of the kinetics of hydrate formation and decomposition offers considerable challenges Hydrate formation is viewed as a crystallization process that includes nucleation and growth processes The nucleation is an intrinsically stochastic process that involves the formation and growth of gas-water clusters to critical sized, stable hydrate nuclei The stochastic nature of the nucleation could be masked by high nucleation driving forces and the presence of heterogeneities At present there are no molecular level measurements of the hydrate nucleation process Such measurements are needed to formulate a molecular level mechanism Hydrate growth involves the growth of stable hydrate nuclei as solid hydrates The surface area of the growing hydrate particles strongly affects the growth rate Hydrate decomposition is a sequence of lattice destruction and gas desorption processes The heat transfer rate during hydrate decomposition is analogous to nucleate boiling phenomenon The size distribution of the hydrate particles during the growth and decomposition processes should be studied for use in the modelling of these processes The agglomeration characteristics of the hydrate particles should be studied to explore the possibility of transporting the particles through pipelines in a slurry 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