Kinetics of hydrate formation using gas bubble suspended in water

Vol 45 No. 2SCIENCE IN CHINA(Series B)April 2002Kinetics of hydrate formation using gas bubble suspended inwaterMA Changfeng(马昌峰), CHEN Guangjin(陈光进)& GUO Tianmin(郭天民)High Pressure Fluid Phase Behavior& Property Research Laboratory. School of Chemical Engineering. University ofPetroleum, Beijing 102200, ChinaCorrespondence should be addressed to Ma Changfeng(email: machangfenge petrochina com.cn)Abstract An innovative experimental technique, which was devised to study the effects of tem-perature and pressure on the rate of hydrate formation at the surace of a gas bubble suspendedin a stagnant water phase, was adapted in this work. Under such conditions, the hydrate-growthprocess is free from dynamic mass transfer factors. the rate of hydrate formation of methane andcarbon dioxide has been systematically studied. The measured hydrate-growth data were corre-lated by using the molar Gibbs free energy as driving force. In the course of the experiments,Keywords: hydrate fornation, kineties, suspended gas bubble, methane, carbon dioxide.Hydrates are crystalline solid formed when water molecules link to form a clathrate structureunder suitable temperature and pressure conditions. The clathrate structure is thermodynamicallyunstable, but could be rendered stable by filling the cavities with small guest molecules( suchN2, CO2, CH, C2H and C3 Hg). At present, we have good knowledge about the thermodynamicsof hydrate formation, and abundant experimental data and extensively tested thermodynamic hydrate models are available!l-6l. Such models are, in general, capable of predicting the hydrate fornation texpressumwithOn the other hand, our knowledge of the kinetics of hydrate formation is still far from mature.The experimental data and kinetic models reported in the literature are often inconsistent. Hence,for obtaining a more comprehensive understanding of hydrate formation, the kinetics aspectshould be emphasized. Two consecutive phases are generally involved in the kinetics of hydrateformation. The first phase is the formation of the initial hydrate nuclei, and the second phase is thehydrate-growth process initiated from the formed nuclei. The first phase which is often called theinduction period, has been studied carefully only by few investigators 9. More attention wasgiven to the second phase-4. The experimental data and kinetic models presented by Englezoet al. 12. 13l and Skovborg 4l represent the most comprehensive studies on the kinetics of hydrate-growthMost of the reported experiments on hydrate-growth kinetics were performed under isother-mal and isobaric conditions in a semi-batch stied tank reactor with constant gas supply formaintaining the desired pressure. Since the geometric factors and agitation conditions of the reac-中国煤化工CNMHGNo. 2KINETICS OF HY DRATE FORMATION USING GAS BUBBLE SUSPENDED IN WATERtor affect the rate of hydrate formation, the data obtained are apparatus-dependent. We cannot expect consistent kinetic data to be obtained from different reactors used in various laboratoriesThis work was focused on the second phase. An innovative method was proposed to measurehe rate of hydrate-growth, which is independent of the factors aforementioned. The hydrate wasallowed to form at the gas-liquid interface of a gas bubble suspended in a stagnant water phase. Asthe surface area of a gas bubble can be calculated readily and the incipient point as well as the endpoint(when the bubble surface is fully covered by hydrates)of hydrate formation can be observedsharply, reliable hydrate-growth rate can thus be determined. The rate of methane and carbon dioxide hydrates formation has been systematically studied and the measured rate data were successfully correlated using the molar Gibbs free energy as driving force. Some interesting surfacephenomena were also observed in the course of our experiments1 Experimental1. 1 ApparatusThe JEFFRI pendant drop high-pressureinterfacial tension (IFT) apparatus manufactured by DBR Corporation (Canada)wasmodified and adapted for our purpose. Theschematic diagram of the experimental unit is12shown in fig. 1The revised optical system consists of azoom stereo microscope installed perpendicupressure cell, a high resolution Panasonicvideo camera and a PC computer. the recorded photographic data were processed us-This modification significantly improved the 13, Valves: 2, liquid sample cylinder: 3 and 8.presureS.9 anding the software developed by this laboratory. Fig. I. Schematic of the apparatus used in this study. Idata acquisition and processinI1, high-pressure cell: 12, video camera: 14, gas supply,The operating temperature was con- 15, computer and signal receiver.trolled by three Eurothermrature con-trollers with an average uncertainty of +O 1 K. All the pressure gauges were calibrated using astandard RUSKA dead-weight pressure gauge with an uncertainty of # 0. 25%The hydrate formation features observed in the high-pressure cell are schematically illustrated in fig. 2.1.2 ChemicalsChemical grade methane (99.99%)and carbon dioxide(99.9%)purchased from Beifen Gas中国煤化工CNMHGSCIENCE IN CHINA (Series BIndustry Corporation were used in the experiments1.3 Experimental procedure(i) Sweep the whole experimental system anddraw vacuumii)Charge water into the high-pressure win-dowed cell until- 3/4 volume of the cell is filled andmaintain the system at a desired temper(ii) Introduce a certain amount of gas into the celland raise the system pressure significantly higher thathe equilibrium hydrate formation pressure and allow aquantity of gas hydrate to be formed atop the waterFig. 2. Schematic of hydrate formation on thesurface of a gas bubble. 1, Water inlet: 2, hy(iv Discharge the gas and dissociate the hydratedrate-covered gas bubble atop the gas injection formed in step(iii), but keep the water with residualneedle:3. hydrate-covered hemisphere formed by astructure remaining in the cellwindowed cell; 6. gas phase: 7, hydrate layer float(v)Aiming at eliminating the induction perioding atop the water phase: & water phase: 9, gas our experiments, repeat steps(ii)and(iv)three timesfor ensuring the full activation of the water phase(vi)Inject gas into the cell and maintain a pressure higher than the equilibrium pressure ofhydrate formation at a given temperature. a hydrate layer with non-smooth surface will be formedatop the water surface.(vi) Inject a gas bubble into the cell. When the bubble rises to the hydrate layer, a hydrate-covered hemisphere will be formed undeneath the hydrate layer(vii) Inject a second gas bubble into the cell and keep it close to the hemisphere without con-t(see fig. 2)(ix)Keep the system in stable conditions for about 3 min, and the tip of the gas bubble isarefully managed to contact with the bottom of the hemisphere to realize a point-contact. Starttime recording at this moment(as the water phase has been fully activated, nucleation happensimmediately without induction period)and terminate the time recording when the surface of sus-pended bubble is fully covered with hydrate. This time period is denoted by fF subsequently1.4 Data processing and experimental resultsThe whole hydrate formation process was recorded by the video camera and transmitted to aPC computer. The photographic data were stored in the hard disk for further processing. The sur-face area(ab)of a gas bubble recorded was calculated by in-house image software. Based on themeasured f, the average hydrate-growth rate(r) on the bubble surface is simply calculated as(1)中国煤化工CNMHGNo. 2KINETICS OF HYDRATE FORMATION USING GAS BLBBLE SUSPENDED IN WATERThe calculated hydrate-growth rate data(expressed in terms of mm" /s)at various temperatures andpressures for methane and carbon dioxide are presented in tables I and 2, respectively.Table I The growth rate data ir] of CHy-hydrates and the calculated (-AeP RT )valuesKPwPx10°0.02794271.927660.031445.50.68028040.03385281.73.358455.80.1950280471002102281459.86496.202121280.60075350221563002323282.6653828140.0935660.325950.2546281.3594106780294328L40.147285986700463.08703.10.1457160.7827880.190196900.236620.32260.2831445.14801,402573895.0278.875.061930.4476278446.06442208164344.222774419207089277,91.8975017350.7509Correlating the hydrate-growth rate data via driving forceSince the dynamic mass transfer factors are not involved in the particular hydrate formationexperiments carried out in this work, we tried to correlate the rate of hydrate-growth with driving中国煤化工CNMHGSCIENCE IN CHINA (Seres B)Volforce. The driving force for the hydrate nucleation process has been defined differently by variousinvestigators, e.g. 7eq-texp by Vysniauskas et al. 1o. WeH-WepP by Skovborg et al Bl, inby Natarajan et al. and Ag by Christiansen et al. 6. In this work, the more general molar Gibbsfree energy difference(Ag)was chosen and extended to the description of hydrate-growth processTable 2 The growth rate data(r) of COz hydrates and calculated("/RT )valuesrimm.s△g月·mo-△g"/RT00209223.3100899527890.24724290.16400.194670.1636280.60.1883278.90952670.353627863849369277.532404266278.41.36939375984604254277.10.6298mal palforExperimental pressure, P-hydrate formation between the two end-points atWater Vapor increment l nyd aie Hydrate the operating temperature and pressure was designed by Christiansen et al. and shown in figIn this system only the gas and water con-verted to hydrate are considered as reactantsEquilibrium pressure Pwhile hydrate is the product. The final matheWater+ VaporHydratematical expression derived by Christiansen etal. for calculating the overall driving force atFig 3. Isothermal path for calculating driving force(ag" p) experimental conditions(Ag x )is given belowof hydrate forrmation from water and vapor(detailed derivation is to be referred to the origi-al article)(P-P)+Rr∑R∑f rf denote as fugacity of component i in gas phase at experimental andequilibrium conditions respectively, x; is the mole fraction of component i in gas phase, Ww Isthe molar volume of liquid water, v is the molar volume of water in clathrate hydrate and Av=wh中国煤化工CNMHGKINETICS OF HYDRATE FORMATION LSING GAS BUBBLE SUSPENDED IN WATER213In the calculation of Ag the fugacity fi was evaluated using Peng-Robinson equation ofstate7, Av was taken as 4.6 cm /mol for structure I hydrate, and the hydrate formation pressureexperimental temperature(P)was computed based on Chen-Guo hydrate modelValues of the dimensionless driving force(-Ag P/RT)evaluated for methane and carboxide corresponding to various experimental conditions are also tabulated in tables I and 23 Discussion3. 1 Correlation of hydrate growth rate dataThe ple(expressed in mm7/s)vs dimensionless driving 24.force (Ag /RT) for methane and carbon dioxide are given in fig. 4. Fig. 4 indicales that 502the molar Gibbs free energy is capable of de- 3 1.0scribing the measured hydrate-growth rate data oo oFvery well. The growth rate increases with increasing(-△g"lR), and when(-△gRT)educed drive forceapproaches zero, the growth rate approaches Fig. 4. Plot of hydrate-growth rate vs reduced driving forcezero also. Based on the plots in fig. 4, the fol- (-AgP /RT )for methane and carbon dioxidelowing correlation for hydrate-growth rate(r) is established:r=A×[e(3)The regressed coefficients A and B for methane and carbon dioxide are as followsA=2.800×10-2,B=6.132( (for methane),A= 1.210x 10 B= 6. 132(for carbon dioxinAs the values of coefficient B for methane and carbon dioxide are the same(6. 132), we could ex-pect that B is approximately a constant for various gas species.3.2 Phenomena observed during the hydrate formation processThe phenomena occurred at the surface of a suspended gas bubble during hydrate formationhave been examined carefully through the recorded video tapes. Some interesting phena areWhen the hydrate layer is initially covered the bubble surface(at tF), it looks quite coarse. Asthe hydrates continue to grow after to, the hydrate surface is becoming smoothed with the timeelapsed. The two shots taken respectively at !=fF and t= lF+ 6 min are shown in fig. 5. Fig. 6shows the comparison of surface roughness of the hydrate layer forming on the bubble surfacleft, not fully covered the surface yet)with the hydrate layer on the hemisphere(right, formed 10min long). The trend of the change of roughness of hydrate surface is clearly indicated. Theroughness of the hydrate surface is also affected by the magnitude of driving force(-Ag ), and中国煤化工CNMHG214SCIENCE IN CHINA ISenes B)Wl.45Fig.5. Comparison of the roughness of hydrate surface shot at Tr and 5 min after fF. -Ag =595.7 J/mol, and thephotos are enlarged 50 times. (a)t=tp (b)!=7F+ 5 mintypical comforce. the smoother thhydrate surthe larger the drivingcrystal grair4 ConclusionsA newFig. 6. Comparison of the roughness of hydrate surface ing the kinetic data of hydrate formation on theformed on a gas bubble (left) and the hydrate surface on the surface of a gas bubble suspended in water washemisphere formed 10 min long (right). -Ag" p=489.9 J/mol. proposed. A series of experiments have beenand the photos are enlarged 50 times.performed on the hydrate formation of methaneand carbon dioxide. Compared with the conventional experiments run in stirred-tank reactors,characteristics of the proposed experimental method are apparatus-independent and dynamic nransfer factors are not involvedyFig. 7. Effect of driving force (A")on the roughness of hydrate surface (both photeshot at the momenthen the bubble was half-covered with hydrate and enlarged 50 umes). (a)-Ag=1035.0 J/mol, (b)-Axp=577.2中国煤化工CNMHGNKINETICS OF HYDRATE FORMATION USING GAS BUBBLE SUSPENDED IN WATER215The measured hydrate-growth rate data have been successfully correlated by using the molarGibbs free energy difference as driving force. The effects of time elapsed and driving force on thecoarseness of hydrate surface were illustrated.Acknowledgements This work was supported by the National Natural Science Foundation of China( Grant No.29806009)and the China National Petroleum Natural Gas CorporationRefer1. Sloan, E D, Clathrate Hydrates of Natural Gases, 2nd ed. New York: Marcel Dekker, 1997. 227--2902. Ng. H. J, Robinson, D. B, The measurement and prediction of hydrate formation in liquid bydrocarbon-water systems,Ind Eng. Chem. Fundam. 1976. 15: 293--2983. Parish, WR.Prausnitz, J.M., Dissociation pressures of gas hydrates formed by gas mixtures. Ind. Eng. Chem. Process.Des.Dev,1972,11(1)26-35.4.Munck, I.Jorgensen. SS Rasmussen, P, Computations of the formation of gas hydrates, Chem. Eng. Sci, 1988, 43(10)5. zuo, Y.x., Guo, T.M. Extension of the Patel-Teja equation of state to the prediction of the solubility of natural gas information water, Chem Eng. Sci, 1991. 46: 3251-32586. Chen,G J, Guo, T M.A new approach to gas hydrate modeling. Chem. Eng J, 1998, 71: 145-151.an, ED Fleyfel F. A, A molecular mechanism for gas hydrate nucleation from ice, AICHE J. 1991, 37(19): 1281Skovborg, P Ng. H J.Rasmussen, P et al., Measurement of induction times for the formation of methane and ethane gasSci,1993,48:4459. Qiu, J. H, Guo, T M, Acta Petrolei Sinica(Petroleum Processing Section), A Special Issue for the 15th World Petroleum10. Vysniauskas. A, Bishnoi, P.R. A kinetics study of methane hydrate formation, Chem. Eng. Sci., 1983, 38(7): 1061l1. vysniauskas, A Bishnoi, P.R., Kinetics of ethane hydrate formation, Chem. Eng. Sci, 1985, 40: 299-30312. Englezos, P, Kalogerakis N, Dholabhai, P D et al, Kinetics of gas hydrate formation from mixtures of methane andethane,Chem Eng. Sci, 1987, 42(11): 2647--2658glezos, P, Kalogerakis, N, Dholabhai, P D. et al, Kinetics of formation of methane and ethane gas hydrates, ChemEng, Sci,1987,42:2659-266614. Skovborg. P, Rasmussen, P, Mass transport limited model for the growth of methane and ethane, Chem. Eng. Sci. 1994.49:1131-1143.15. Natarajan, V. Bishnoi P R, Kalogerakis, N Induction phenomena in gas hydrate nucleation, Chem Eng. Sei, 1994, 49:2075-208716. Christiansen, R L. Sloan, E D. 74th Ann GPA Conv San Antonio: March, 1995(cited from reference 1: 98-100)17. Peng, D. Y. Robinson, D.B., A new tow-constant equation of state. Ind. Eng. Chem. Fundam. 1976. 15: 59-6418, Makogon, Y. F, Hydrates of Natural Gas(translated from Russian by Cieslewicz, w, ) Oklahoma: Penn Well PublishingCompany, 1981: 81中国煤化工CNMHG