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Energy & Fuels 1998, 12, 212-215
Experimental Study of Hydrate Crystal Growth from Methane, Carbon Dioxide, and Methane + Propane Mixtures S.-Y. Lee, E. McGregor, and G. D. Holder* Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15217 Received October 9, 1997. Revised Manuscript Received December 28, 1997
Gas hydrates are crystalline, icelike solids formed from water contacted with certain light hydrocarbons and other low-molecular-weight, nonpolar substances under high pressure and low temperature. In this study, methane-propane mixture hydrates were made at various conditions. The reaction rates were experimentally measured at each condition. Structure II-type hydrates were formed up to 7580 kPa at around 280 °K from methane containing 3% and 5% propane. The reaction rates for forming hydrates were proportional to the pressure difference between the system pressure and the dissociation pressure. The kinetic model was developed.
Introduction and Background Gas hydrates are crystalline inclusion compounds composed of water and natural gas in nonstoichiometric ratios varying from 5.67 to 17 water molecules per hydrated gas molecule.1,2 Hydrate crystals represent one of the few phases and perhaps the only condensed phase where water and light nonpolar gases exist together in significant proportions and are of particular interest to the petroleum and natural gas industries because of their potential as a separating agent, their potential as a storage vehicle, and their undesired ability to plug gas transportation lines.3 Gas-water mixtures will form crystals that coat the walls of and potentially plug gas transportation lines causing the cessation of gas or gas + oil flow. When producing oil or gas, one goal that industry needs is to understand the conditions under which operation is possible without plugging. One such operating condition is where the hydrates are thermodynamically unstable. Such conditions are generally present when operating at temperatures above 298 °K, although the temperature depends upon pressure, usually 50-200 MPa, and gas composition, usually 95+% methane.1,4.5 Sufficiently high temperatures are generally not present when producing gas in offshore operations because deep ocean waters are seldom warmer than 277-281 K. To prevent hydrate formation, operators will generally inject methanol, which acts as an antifreeze and desta(1) Holder, G. D.; Zetts, S. P.; Pradhan, N. Rev. Chem. Eng. 1988, 5 (1), 1. (2) Sloan, E. D. Clathrate Hydrates of Natural Gas; Mercel Dekker: New York, 1990. (3) Holder, G. D.; Enick, R. M. Solid Deposition in Hydrocarbon System-Kinetics of Waxes, Aspaltens and Diamondoids. Final Report, Gas Research Institute, GRI, 1995. (4) Lingelem, M. N.; Majeed, A. I.; Stange, E. Industrial Experience in Evaluation of Hydrate Formation, Inhibition and Dissociation in Pipeline Design and Operation. In Natural Gas Hydrates, Annals. of NY Academy of Science; Sloan, E. D., et al., Ed.; New York, 1994; p 75. (5) Holder, G. D.; Zele, S.; Enick, R.; LeBlond, C. Ann. N.Y. Acad. Sci. 1994, 715, 344.
bilizes hydrates.1,2 Effective methanol concentrations are generally 10-50%, by weight, of the water + methanol liquid.1 Sometimes, it is not desirable or possible to operate at conditions where hydrates are thermodynamically unstable. Such conditions may occur if methanol injection facilities fail or in cases where methanol injection and recovery are prohibitively expensive. In such instances it is desirable to understand for what duration is operation of a gas transportation line possible without the complete plugging of the line by hydrates. To answer this question, the rates at which hydrates form must be known. The process of line plugging includes the nucleation of hydrates on a heterogeneous surface, such as the pipe wall, and the growth of these hydrates toward the center of the pipeline. This scenario for hydrate growth is deemed most likely for two reasons. First, the pipe wall is generally the coldest part of the transportation line and hence the location where hydrates are most thermodynamically stable. Second, the formation of crystalline hydrates normally requires a solid nucleation site, and the pipe wall is generally the only source of such sites. Crystals can subsequently abraid from the pipe wall and be transported down the pipeline, but such abraided crystals are not expected to be the primary cause of initial flow constriction. For systems containing liquid hydrocarbons, hydrates may form in the bulk or at the gas-liquid interface.6 In the present study, we determine the rates at which hydrates nucleate and grow on the surface of a cold pipe wall over which gas is flowing at rates comparable to those that might exist in a pipeline. Experimental Section The apparatus for studying the precipitation and growth of solids is shown in Figure 1. The apparatus (6) Hunt, A. Uncertainties remain in predicting paraffin deposition. Oil Gas J. 1996, July, 98.
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Energy & Fuels, Vol. 12, No. 2, 1998 213
Figure 2. Heat flow through the reactor. T4 is the average of Tin and Tout. Figure 1. Experimental equipment: (1) high-pressure gas, (2) gas hydrate, (4) gas cooling/heating fluid flowing in cylinder, (5) cooling fluid in coils, (6) rotating cylinder, (7) highpressure cell, (8) insulation, (T) thermocouple, (P) pressure transducer.
consists of two coaxial cylinders with the inner cylinder magnetically rotated. Water (150 mL) and gas (about 7 MPa) fill the annulus space between the fixed and rotating cylinders. Hydrates form on the cold outer wall of the annulus. The fundamental improvement of this apparatus relative to cells used in the past is that gas will flow in the annular space over the hydrate formation surface rather than remaining static. This will provide a means of investigating the effects of gas shear stress at the hydrate-forming surface in pipelines. Since gas shear stress can affect heat and mass transfer, this is an important variable. Another significant modification is that a temperature gradient between the gas and the ice can be easily established by selecting different temperatures for the gas coolant fluid and the ice coolant fluids. Temperature gradients within this vessel are established by flowing methanol-water mixtures from separate isothermal baths through the cooling coils on the outside of the vessel and the inner chamber. The rpm of the inner rotating cylinder is adjusted allowing varying gas flow rates. The temperature of the circulating fluid in the outer cooling coils is then adjusted as desired, usually in the range 270-280 K. The temperature of the inner chamber is kept in the range 275295 K. Hydrate formation was initiated by adjusting the temperature of the inner cooling chamber until the gas phase reaches the desired temperature, which is always less than the hydrate formation temperature. The rate of hydrate formation is markedly decreased when equilibrium is approached. A temperature gradient is therefore established across the hydrate layer. The surface of the hydrate was then in direct contact with the flowing methane or the methane + propane mixture at 274-275 K. Pressure decreases as the methane + propane from the gas phase enters the hydrate phase. The pressure decrease is used to calculate the amount of hydrate formed using the Peng-Robinson equation of state.7
Experiments continue until either (1) the pressure of the gas remains constant, indicating that hydrate formation has ceased, or (2) the rotation of the inner cylinder ceases because small amounts of hydrates clog the bearings and friction surfaces. The system is then depressurized, and the hydrate crystals are examined before they dissociate. The hydrates form a relatively uniform layer of frostlike solid in the annular gap. Kinetics of Hydration Formation Reaction Temperature Calculation. After setting up the heat balance equations, a convection heat transfer coefficient and reaction temperature can be calculated from the equations and the experimental data. Heat is convected from the inner cylinder through the annulus and conducted through the hydrate and pipe wall to the cooling coil. Heat is also generated at the hydrate surface due to the latent heat of hydrate formation. In this experiment, the independent variables are the inner cylinder temperature, T2, the outer cylinder temperature, T4, the distance between outer cylinder and hydrates, rs and the coolant flow rate, m. The conduction coefficients for hydrates khyd and for stainless steel kss are constants. From Figure 2, the overall heat balance is
Qcond ) Qconv + Qgen
(1)
All the heat convected into the system and generated in the system would be released by conduction. The following equations are those for each case. The heat conducted through the cylinder wall is
Qcond )
(Ts - T4)2πL r3 r4 1 1 ln + ln khyd rs kss r3
()
()
(2)
where Ts is the hydrate surface temperature. T4 is the average temperature on the outside of outer cylinder, r3, and r4 are the inside and outside radius of the outer (7) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem., Fundam. 1976, 15, 1.
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Lee et al.
Table 1. Heat Transfer Coefficient and Kinetic Coefficienta bulk gas temp (K)
hydrate surface temp (K)
cooling coil temp (K)
initial P (kPa)
rpm
Hi (W/(m K))
kinetic coefficient × 1010 mol/(kPa s)
linear growth rate (cm/h)
284.7 288.1 286.8 283.4 288.7 292.1 289.9 291.7
272.1 273.5 274.5 270.5 271.5 271.9 272.0 274.5
271.6 273.2 274.0 270.2 271.3 271.6 271.8 274.1
6964 7036 7016 7394 7073 6927 6782 7011
7 7 2 55 9 2 60 30
0.064 0.063 0.061 0.064 0.035 0.020 0.042 0.083
2 0.5 0.8 1 2 10 10 3
0.03 0.05 0.08 0.24 0.2 0.125 0.15 0.063
a
All data were obtained by using 97% methane + 3% propane mixture gas.
cylinder, rs is the position of the hydrate/gas interface, and L is the length of the cylinder. The heat convection across the gas phase is
Qconv )
(T2 - Ts)2πL rs r2 1 1 ln + ln Hi r2 kss r1
()
()
(3)
where T2 is the temperature of the inner cylinder, r1 and r2 are the inside and outside radii of the inner cylinder, and Hi is the heat transfer coefficient. The heat generated during the reaction is
Qgen ) ∆Hm
(4)
where m is the flow rate of water running through the inner cylinder. In eq 4 ∆H is the heat of formation of hydrate and is obtained from the following equation.2
∆H ) c + dT
(5)
where c and d are constants. Qconv is determined from the temperature decrease of the water circulated through the inner cylinder. This water is the source of the heat transferred through the annulus.
Qconv ) (Tin - Tout)mCp
(6)
where Tin and Tout are the temperature of the water in the pipe running around the inner cylinder, m is the flow rate of the water, and Cp is the heat capacity of the water. This equation implies that an insignificant amount of the heat is absorbed through the cylinder ends, which is reasonable since they are insulated. If eqs 1, 2, and 6 are combined, the following is obtained.
(Tin - Tout)mCp - m(c + dTs) ) (Ts - T4)2πL (7) r3 r4 1 1 ln + ln khyd rs kss r3
()
()
where Tin, Tout, T4, m, Cp, L, kss, kHyd, c, and d are the known experimental values, and Ts, the temperature at the hydrate surface, is an unknown value. This equation can be easily solved for Ts. After calculating Ts, the heat-transfer coefficient can be calculated from the combination of eqs 3 and 6
( )/ [
Hi ) ln
rs r2
(T2 - Ts)2πL
(Tin - Tout)mCp
-
( )]
1 r2 kss r1
(8)
Figure 3. Relationship between the reaction rate and pressure difference (k ) 3 × 10-10 mol/(kPa s).
where Tin, Tout, Ts, r1, r2, rs, kss, and L are known values and Hi is the only unknown value. Therefore this equation could be easily solved for Hi. Results are shown in Table 1. Kinetic Model. The following model is proposed for hydrate formation.
dMhyd ) k(Pexperiment - Pdissociate) dt
(9)
where k is the reaction rate coefficient and has different values. The dissociation pressure (Pdiss) for each case is calculated using a computer model.1 The pressure difference would be the driving force for reaction. Figure 3 shows a sample of the relationship between the rate and pressure. Results We have measured the linear growth rate of hydrates formed from pure methane, pure carbon dioxide, and two mixtures of methane + propane whose compositions were (95% methane and 5% propane) and (97% methane and 3% propane). The important variables in these studies were gas flow rate, gas composition, temperature, and pressure. Table 1 and Table 2 list the results of this and earlier studies. Gas Flow Rate. Higher gas flow rates tend to produce higher rates of hydrate formation. This is because the higher gas flow rates dissipate the consid-
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Energy & Fuels, Vol. 12, No. 2, 1998 215
Table 2. Growth Rate of Hydrates gas composition
bulk gas temp (K)
100% C1 100% C1 100% C1 100% C1 100% C1 100% C1 100% C1 100% C1 5%C3:95%C1 5%C3:95%C1 5%C3:95%C1 5%C3:95%C1 5%C3:95%C1 CO2 CH4/Wax CH4/PVP
283.7 ( 0.4 283.5 ( 0.5 282.1 ( 0.4 281.9 ( 0.3 283.0 ( 0.5 282.3 ( 0.7 279.7 ( 0.6 276.5 ( 0.2 291.1 ( 0.3 288.9 ( 0.4 288.7 ( 0.6 288.4 ( 0.7 287.0 ( 0.9 282.0 ( 0.3 277.8 ( 0.7 278.6 ( 0.6
initial linear cooling coil pressure growth temp (K) (kPa) rpm rate (cm/h) 272.7 ( 0.3 271.4 ( 0.1 271.9 ( 0.1 272.1 ( 0.1 271.8 ( 0.1 271.9 ( 0.2 271.5 ( 0.2 271.5 ( 0.2 272.9 ( 0.1 273.6 ( 0.2 270.0 ( 0.1 271.1 ( 0.1 270.0 ( 0.1 271.4 ( 0.1 271.6 ( 0.2 272.1 ( 0.2
6509 6039 6023 5987 6004 6019 6861 6618 7014 7110 6905 6940 7089 3555 5296 5482
7 8 8 30 2 8 25 15 7 15 60 1 30 8 15 15
0.02 0.02 0.00 0.02 0.01 0.02 0.02 0.02 0.08 0.11 0.15 0.03 0.17 0.10 0.002 0.000
erable heat release generated during hydrate formation (50-100 kJ per mole of hydrated gas) and because the higher gas flow rates (rpm) improve the mass transfer of water to the hydrate-forming surface. It is still not clear which of these factors is most significant. However, the effect of gas flow rate levels off at the highest rates. This means that mass and heat transfer are no longer limiting, and a true kinetic value for hydrate growth is obtained. The higher gas flow rates used here are comparable to pipeline Reynolds numbers in excess of 10 000, and thus these conditions are those that might be obtained in an actual gas pipeline. For methane-propane mixtures, the gas flow rate is not an important variable. Gas Composition. It is observed that no clear difference in growth rates for the 95% methane and 97% methane mixtures was observed, but rates for gas mixtures and for carbon dioxide were faster than for pure methane. The methane hydrate is the least thermodynamically stable, and it appears that the thermodynamic driving force (difference between the equilibrium pressure (or temperature) and the actual experimental pressure (or temperature) at the hydrate surface) affects the rate at which hydrates form. This thermodynamic result3 justifies a thermodynamically based model such as eq 9 represents. Another factor that may be important is the ability to stabilize the large cavity of the hydrate structure. Propane stabilizes the large cavity of structure II better than methane, and carbon dioxide stabilizes the large cavity of structure I better than methane. The ability to stabilize the large cavity may play a role in the kinetics. The current experimental evidence is not conclusive on this issue.
Another variable of interest for the methane + propane mixtures is that the gas composition changes as the hydrates form since the propane concentration in the hydrates is much higher than in the gas phase. As more hydrates form, a eutectic mixture of methane and propane containing less than 1% propane should be present. This mixture will result in the simultaneous formation of both structure I and structure II hydrate. Temperature. In general, temperature is thought to increase the rate of any kinetic process, and that is the case here. However, higher gas temperatures also decrease the thermodynamic driving force at the forced pressure and will tend to impede the rate over the temperature range used. Here, the thermodynamic force dominates. Pressure. The range of pressures used is small, but the results seem to indicate that higher pressures increase the rate of hydrate formation according to eq 9. The range of kinetic coefficients is large, but allow an order of magnitude estimate. Conclusion The rates of hydrate formation along pipe walls will likely be comparable to the rates measured in this study. Linear growth rates of 0.2 cm/h are likely to represent the maximum growth rate that could be expected in gas transportation lines operated at ocean temperatures of 275-277 °K. As the hydrates thicken, they can serve as insulators of the line, which will result in slower cooling of the produced fluids (which come out of the earth at higher temperatures than exist in the transportation line). The insulation will produce higher transportation temperatures, which would inhibit hydrate formation. On the basis of the rates measured here, transportation lines could be operated for hundreds or thousands of hours prior to their blockage by hydrates when only nucleation/growth from the pipe wall is taken into account. In other systems, the plugging time could be shorter.9 Also, with waxes or other inhibitors the rates are much slower. Acknowledgment. We would like to thank GRI for their partial support of the early stages of this research under Contract GR5091-260-2121. EF9701955 (8) Lee, S.-Y.; McGregor, E.; Holder, G. D. An Experimental Study of Hydrate Crystal Growth From Methane, Carbon Dioxide, and Methane + Propane Mixture, 213th ACS National Meeting; American Chemical Society: Washington, DC, 1997; Vol. 42, No. 2, p 512. (9) Austrik; et al. Proceedings GPA Annual Conference, March, 1997; Gas Processors Association, Tulsa, OK; p 205.
