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Ind. Eng. Chem. Res. 1998, 37, 3124-3132
Quantifying Hydrate Formation and Kinetic Inhibition E. D. Sloan,* S. Subramanian, P. N. Matthews, J. P. Lederhos, and A. A. Khokhar Center for Hydrate Research, Colorado School of Mines, Golden, Colorado 80401-1887
In the Prausnitz tradition, molecular and macroscopic evidence of hydrate formation and kinetic inhibition is presented. On the microscopic level, the first Raman spectra are presented for the formation of both uninhibited and inhibited methane hydrates with time. This method has the potential to provide a microscopic-based kinetics model. Three macroscopic aspects of natural gas hydrate kinetic inhibition are also reported: (1) The effect of hydrate dissociation residual structures was measured, which has application in decreasing the time required for subsequent formation. (2) The performance of a kinetic inhibitor (poly(N-vinylcaprolactam) or PVCap) was measured and correlated as a function of PVCap molecular weight and concentrations of PVCap, methanol, and salt in the aqueous phase. (3) Long-duration test results indicated that the use of PVCap can prevent pipeline blockage for a time exceeding the aqueous phase residence time in some gas pipelines. I. Introduction Hydrates are crystalline compounds that are composed of water and natural gas at high pressures and moderately low temperatures. Hammerschmidt (1934) first reported the presence of hydrates in oil and gas transmission lines, signaling an enduring interest in hydrates by the energy industry. Hydrate formation in pipelines is common in seasonally cold or sub-sea environments with low temperatures and high pressures. Hydrates grow from small crystals to large masses which block flowlines, resulting in costly and often hazardous hydrate dissociation procedures (Sloan, 1998). One major contribution of Professor Prausnitz has been to extend the statistical thermodynamic hydrate model (van der Waals and Platteeuw, 1959) to multicomponent gas systems via the Parrish and Prausnitz (1972) method, with an update by Anderson and Prausnitz (1986). The Parrish and Prausnitz method may be the most common industrial use of statistical thermodynamics. The statistical thermodynamic prediction has been widely used in place of hydrate phase measurements for over a quarter of a century. Recently, modern tools such as NMR spectroscopy (Ripmeester and Ratcliffe, 1989) and Raman spectroscopy (Sum et al., 1997) have provided measurement methods of hydrate molecular phenomena, as a complement to diffraction methods. Measurement of microscopic and macroscopic phenomena of hydrate formation, dissociation, and inhibition is the objective of this work. Inhibition of hydrates has traditionally been done by thermodynamic means using chemicals such as methanol, ethylene glycol, or salt that depress the hydrate formation point in a manner analogous to the freezing point depression of ice. Successful inhibition with methanol or glycols typically requires inhibitor concentrations from 15 to 50 wt % in the free water phase. Hydrate inhibition by methanol injection costs oil and gas companies around $500 million/year (Sloan, 1992). In the past few years, kinetic inhibition has been suggested as an economic alternative to thermodynamic techniques (Long et al.; 1994, Lederhos et al., 1996). In
concept, kinetic inhibition allows hydrates to form only small crystals, slowing the rate of hydrate growth for a period longer than the residence time of free water in pipelines, so that blockage is prevented. While hydrate thermodynamics are well-defined for structures I, II, and H, hydrate kinetics are not wellcharacterized. Until recently, kinetic inhibition research has focused on the discovery and qualitative description of good inhibitors rather than quantification of inhibitor performance. Lederhos et al. (1996) reported that poly(N-vinylpyrrolidone) (PVP), poly(N-vinylcaprolactam) (PVCap), and a terpolymer combination (VC-713) function as kinetic hydrate inhibitors. Larsen et al. (1996) and Makogon et al. (1997) indicated that adsorption of kinetic inhibitors on the surfaces of structure II hydrate caused changes in single-crystal morphology from threedimensional octahedra to two-dimensional plates, with complete inhibition of crystal growth at inhibitor concentrations lower than 1 wt %. This work concerns measurement of kinetic inhibitor performance on the microscopic scale via Raman spectroscopy and quantification on the macroscopic scale to simulate pipeline flow assurance. II. Experimental Section (A) Spectroscopic Apparatus and Procedure. The Raman spectrometer was a Renishaw Inc. MK III multichannel fiber optic system equipped with a 2400grooves/mm grating. Spectra were recorded with an internally mounted -70 °C Peltier-cooled CCD detector having a 600 × 400 pixel array size. The excitation source was a 30-mW Ar-ion Spectra Physics laser emitting a 514.532-nm line. The laser was delivered to an industrial-grade, high-efficiency fiber probe through bundles of 50-µm fiber optic cables. The fiber probe uses a 20× ULWD Olympus microscope objective to focus the laser on the sample. The final excitation at the sample is about 10 mW. A Hewlett-Packard Vectra 5000 series computer equipped with the Windows Raman Environment software developed by Renishaw Inc. provided experimental control. Routine calibration of the monochromator was done by using the 597.55-nm, 602.99-nm, and 607.43-
S0888-5885(97)00902-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/27/1998
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nm neon emission lines, at 2701.3 cm-1, 2852.3 cm-1, and 2973.5 cm-1 relative to the 514.532-nm green line of the Ar-ion laser. Spectra were collected sequentially on a real-time basis with 25 s of integration time/ spectrum, stored as multifiles. The analysis of the spectra was carried out using GRAMS32C spectral analysis software. Raman experiments were done in a custom-designed, high-pressure optical cell capable of operating at 40 MPa. The cell consisted of three brass plates with two 0.66-cm-thick sapphire windows on Kovar sleeves. The sample volume between the two sapphire windows was about 1.25 cm3. Slots in the top and bottom brass plates of the cell allow the tip of the 20× ULWD microscope fiber probe objective to rest against the sapphire windows enclosing the sample chamber. Coolant was circulated within the cell. Two types of experiments were carried out with the methane hydrate-forming system: (a) without kinetic inhibitor and (b) with kinetic inhibitor. Research-grade methane and double-distilled water were used in the experiments. PVCap manufactured by BASF (batch 1606/14) was used for the spectroscopic-inhibited experiment. The sample chamber was initially loaded with 1.0 cm3 of test solution (a) pure water in the uninhibited experiment and (b) a 0.02 wt % PVCap solution in the inhibited case. The cell was then connected to the gas supply line, charged with methane to 31.7 MPa, and controlled at 24 °C by circulating coolant through the cell. It was then shaken for 2 h to enable methane dissolution in the aqueous phase. All hydrate formation experiments were done by decreasing the temperature at a constant rate of 0.1 °C/ min at constant pressure and without any stirring. Raman spectra were collected on a real-time basis during the temperature ramp by focusing the laser about 1 mm below the gas-liquid interface. Hydrates first formed at the gas-liquid interface, and spectra were collected with time as the hydrate-water interface grew past the laser. Such spectra are for hydrate crystal growth, rather than nucleation. (B) Macroscopic Apparatuses and Procedures. Macroscopic experiments were conducted on two different apparatuses. Gas consumption studies were conducted on a high-pressure apparatus, while temperature ramping and induction time experiments were conducted on a multitube apparatus. Gas consumption studies measured hydrate growth via the rate of hydrated gas consumption from the vapor phase. The high-pressure apparatus shown in Figure 1 maintained constant temperature and pressure while measuring gas consumption. Hydrates were formed in a 300-cm3 autoclave, agitated at 1200 rpm. A data acquisition/control system maintained constant bath temperature with an accuracy of (0.1 °C via a refrigeration unit and two 1000-W submersible heaters. The reactor was also maintained at constant pressure to within (0.35 MPa with gas from a high-pressure reservoir, input through the dome-controlled regulator. Bath, cell, and reservoir temperature data were collected via thermistors at intervals of 30 s. Typical gas consumption experiment conditions were at 4.0 °C and a pressure of 10.3 MPa to simulate common flowline operating conditions on the deep sea floor. The rate of hydrate formation was calculated by gas depletion from the high-pressure reservoir.
Figure 1. Schematic of the high-pressure apparatus (HPA).
The second measure of inhibitor performance was subcooling, used on the multitube apparatus, described below. Subcooling indicated how far below hydrate equilibrium temperature a system could be cooled before detectable hydrate growth began. In Figure 2 subcooling is indicated as the difference between the three-phase equilibrium temperature (Lw-H-V) and the temperature of hydrate onset, ∆Tsub ) Teq - Tonset. Lederhos and Sloan (1996) demonstrated that subcooling measurements are transferable between bench-scale and pilot-plant apparatuses. Most subcooling experiments were done on the multitube apparatus, shown in Figure 3a. This apparatus was configured two ways: (1) with 10 1.0-cm-i.d. stainless steel tubes and (2) with 10 1.0-cm-i.d. sapphire tubes. Both tube types were 15 cm long and had a volume of 11 cm3. In either configuration, the tubes were mounted in a rack, which was submerged in a temperature-controlled water bath. Temperature control was achieved in the same manner as for the above highpressure apparatus. The rack was connected to a computer-controlled step motor, which rotated the rack (30° from the horizontal position. Insertion of a 0.7cm-diameter stainless steel ball into each tube provided mixing in the tubes as the rack was rotated. In the stainless steel tube configuration, each tube was connected via a 0.16-cm-i.d. stainless steel line to a pressure transducer and a shut-off valve, to detect hydrate formation in individual tubes. Subcooling experiments were typically run at a pressure of 20.6 MPa and were ramped at 2.5 °C/h from 24.0 to 2.5 °C. Hydrate onset was indicated by a rapid decrease in pressure, because hydrate formation concentrates gas. In the sapphire tube configuration, each tube was equipped with two proximity sensors to allow hydrate onset detection (Figure 3b). Each tube acted as a rolling ball viscometer as the rack of tubes was rotated (30° from the horizontal position. The proximity sensors measured travel times of the 0.7-cm-diameter stainless steel balls in the tubes over a 2.5-cm length after the ball had reached terminal velocity in one portion of the rotation cycle. Hydrate onset was indicated by an increase in the ball travel time as the apparent viscosity of the test solution increased. The transparent sapphire tubes also allowed visual confirmation of the presence of hydrates. In this configuration, the multitube apparatus was also used to conduct temperature-ramping studies as noted above. Thirty-four statistical tests using subcooling as the response variable (fractional factorial resolution levels
3126 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 2. Measurement of subcooling. The cooling rate was 2.5 K/h in all experiments. Indicated equilibrium conditions are for a typical Green Canyon gas.
Figure 3. Multitube apparatus in (a) the steel tube configuration and (b) the sapphire tube configuration.
III (8 tests), IV (10 tests), and V (16 tests)) were done to characterize the significant variables in kinetic inhibition. The method of Box et al. (1978) was used, as detailed by Matthews (1997). While these preliminary statistical tests enabled the determination of the most significant variables, the resulting linear correlations yielded unacceptable fits of data with absolute average deviations of 18.3%, 11.0%, and 30.1%, for levels
III-V, respectively. To provide a database for improved fit, an additional 144 tests were performed over the range of PVCap polymer molecular weight and methanol, sea salt, and polymer concentrations specified in Table 1. (C) Chemicals. All Raman studies were done with 99.99% pure methane, while macroscopic experiments were conducted with a typical Gulf of Mexico gas
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3127 Table 1. Tests Summary upon Which Subcooling Correlation Is Based polymer concn range (wt %)
no. of tests
mol wt, Mn (g/gmol)
additive
additive concn (wt %)
0.02-3.50 0.5 0.5
106 11 27
900-40 000 1600-27 000 1,600-27 000
none methanol sea salt
NA 2.0-15.0 2.0-7.0
mixture (87.2 mol % CH4, 7.6% C2H6, 3.1% C3H8, 0.5% i-C4H10, 0.8% n-C4H10, 0.4% n-C5H12, 0.4% N2). Commercial samples of the kinetic inhibitor poly(N-vinylcaprolactam) (PVCap) were provided by BASF (batches 224/64/3) and ISP (batch ACP-117, Mn ) 27 000 g/gmol), while laboratory samples were synthesized by Professor Bill Brittain and Dr. Dawei Li at University of Akron. No performance distinction was observed as a function of the manufacturer. Number-averaged molecular weight (Mn) analyses were performed at University of Akron using gel permeation liquid chromatography.
Figure 4. Time-independent Raman spectra of methane in the vapor phase, dissolved in the aqueous liquid, and in both cages of structure I hydrate.
III. Results and Discussion (A) Microscopic Evidence of Hydrate Growth and Inhibition. Sum et al. (1997) presented most of the constant-temperature spectra in Figure 4, identifying methane in the gas phase and in the large and small cavities of structure I hydrate. The plot shows intensity in arbitrary units (a.u.) as a function of the Raman shift (wavenumbers, cm-1) characteristic of methane molecules in various environments. Sum et al. (1997) indicated that resolution and integration of both peaks in the hydrate provided the relative occupation of methane in each cavity type. The new spectrum in Figure 4 is the peak for methane dissolved in the aqueous phase at 31.7 MPa and 298 K. All spectra in Figure 4 do not change with time and thus serve as the end points for time-dependent measurements. Figure 5 provides molecular evidence of methane hydrate formation with time. The plot ordinate shows intensity versus characteristic Raman shift on the abscissa, as a function of time on the third orthogonal axis. The Figure 4 spectrum of methane dissolved in water serves as the initial point in Figure 5, while the final condition in Figure 5 is the spectrum of methane contained in the cavities of sI shown in Figure 4. Figure 5 then represents a relatively smooth transition of methane dissolved in water to methane contained in each hydrate cavity as a function of time. The time-wise resolution and integration of the two hydrate peaks show the relative occupation of the hydrate cavities. Figure 6 shows spectra analogous to those in Figure 5, but with a liquid solution which contains 0.02 wt % PVCap as a kinetic inhibitor. The initial dissolved methane peak at 2911.3 cm-1 shows an abrupt discontinuity at about 8500 s, coincident with the sudden appearance of peaks for methane in hydrate. This abrupt transition was caused by catastrophic nucleation and growth due to the high degree of subcooling. With kinetic inhibition the hydrate signals first appeared 4 °C lower than in the uninhibited solution (9.9 °C versus 14 °C). Inspection of the methane hydrate spectra in Figure 6 suggests a significantly different rate of formation of the large to small cavities with time in the inhibited solution, relative to similar spectra in Figure 5. The inhibited hydrate interface progressed very slowly past the laser, so that the signal was in the liquid-solid interface region during the course of the measurements.
Figure 7 is a comparison of the ratio of methane in the large to small hydrate cavities with time for the uninhibited and inhibited solution, beginning with the appearance of the hydrate signals in each case. The uninhibited cavity ratio (circles) gradually surpassed 3.0 at 7000 s as equilibrium was approached. Complete occupation of all cavities yields a ratio of 3.0; values greater than 3.0 may indicate that the small cavities are incompletely filled, while the large cavities are almost completely occupied, as suggested by the Parrish and Prausnitz (1972) prediction method. The plateaus in the uninhibited cavity ratio line are not yet understood. In Figure 7 the inhibited cavity ratio (triangles) shows an abrupt change just after hydrate growth began, coincident with the abrupt disappearance of the aqueous methane peak, as discussed in Figure 6. Figure 7 also shows an apparent asymptotic ratio of about 2.5 at 7000 s. The reason for this asymptotic large-small cavity ratio is not yet understood. While the spectra in Figures 5-7 should be considered preliminary, they show the power of the experimental method to determine rate-controlling species and inhibitor affects on hydrate molecular phenomena. Future spectroscopic studies at constant temperature may enable the construction of a microscopic-based kinetic model of hydrate formation, using the ratio of methane in each cavity. (B) Macroscopic Evidence of Residual Structure. Using the multitube apparatus in the sapphire cell configuration, experiments were conducted on mixed natural gas systems without kinetic inhibitors. Prior to hydrate formation, a baseline apparent viscosity was established, as shown in Figures 8 and 9. The method is apparently insensitive to gas solubility, creating the precursory structure recently reported by Song et al. (1997). In each figure the initial pressure of 6.9 MPa was decreased during the experiment by the thermal contraction of the vapor, increased gas solubility, and inclusion of gas in hydrates or residual structure. As hydrates formed, there was a dramatic increase in the apparent viscosity of the solution, indicated by an increased ball travel time. After hydrate formation, tubes became rapidly plugged and ball travel time was infinite, causing gaps in the data in Figures 8 and 9. As the temperature was increased, the hydrates began
3128 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 5. Uninhibited kinetic Raman spectra of methane in transition from dissolved methane to methane hydrate.
Figure 6. Inhibited kinetic Raman spectra of methane in transition from dissolved methane to methane hydrate.
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3129
Figure 7. Ratio of large to small sI hydrate cavity formation with time for uninhibited (circles) and inhibited (triangles) formation kinetics.
Figure 8. Evidence of residual structure in a methane gas system with deionized water. The apparent viscosity of the solution returned to baseline only after heating to 28 °C.
Figure 9. Evidence of residual structure in a methane gas system with deionized water. The apparent viscosity of the solution returned to baseline only after heating to 28 °C.
to dissociate and the ball travel time decreased, approaching the baseline. However, the ball travel time did not return to the baseline value in any experiment. In this time period, the ball travel time was significantly higher than the baseline value despite visual evidence that hydrates were no longer in the cell. Ball travel times could be restored to baseline values, but only after the solutions had been heated to 28.0 °C (a temperature well above
hydrate equilibrium) and allowed to mix for approximately 24 h. The above result indicates the existence of a persistent structure in water. While this is a quantitative indication of hydrate residual structure, Makogon (1981) first suggested residual structure, and Bishnoi and coworkers proposed that residual structure was the cause of reduced induction time (Vysniauskas and Bishnoi, 1983; Parent and Bishnoi, 1996). The industrial implication of such measurements is that once a hydrate plug has been formed and dissociated, subsequent hydrate formation will occur more readily until the water has been removed from the pipeline. (C) Subcooling of PVCap. PVCap polymer was tested in deionized water to characterize the molecular weight and concentration dependence of subcooling. A wide range of molecular weights were tested on industrial samples from ISP and BASF, as well as laboratorysynthesized samples from University of Akron. Figure 10 illustrates subcooling results of PVCap. As the molecular weight of PVCap decreased, subcooling increased before hydrate onset. The minimum molecular weight tested (900 g/gmol) showed the highest subcooling. In contrast, monomers of PVCap showed little inhibition in concentrations as high as 5.0 wt % in gas consumption testing. As shown in Figure 10, increasing the concentration of PVCap caused increased subcooling in all cases. For higher molecular weights, there appeared to be an asymptotic high concentration of PVCap, above which further increases appeared to have a minor effect on subcooling. Most tested concentrations were limited to below 1.5 wt % because industrial use at higher concentrations is uneconomical. (D) Blending Kinetic Inhibitors with Thermodynamic Inhibitors. To further investigate the nature of inhibition, PVCap was studied in blends with methanol and ASTM sea salt. It was found that methanol and salt affect the subcooling ability of PVCap significantly. Since subcooling is defined as the difference between the equilibrium temperature and the onset temperature, the thermodynamic effects of salt or methanol are accounted for in the equilibrium temperature. PVCap polymer mole fractions were too small to affect the equilibrium condition in all cases. In preliminary testing, it was verified that neither salt nor methanol by itself possesses significant subcooling kinetic ability; such inhibition is thermodynamic. However, when blended with PVCap, methanol and salt had a significant effect on subcooling. Testing with PVCap in methanol involved 0.5 wt % PVCap and concentrations of methanol from 0 to 15.0 wt %, shown in Figure 11. Subcooling decreased in linear proportion to the concentration of methanol, indicating that PVCap was less effective in the presence of methanol. Figure 11 also shows that lower molecular weights of PVCap were more negatively affected by the presence of increased methanol concentrations. Subcooling results for 0.5 wt % PVCap and salt concentrations from 0 to 7.0 wt % are shown in Figure 12. At low concentrations of salt, there was little or no effect on the high molecular weight PVCap. The lowest molecular weight of PVCap (Mn ) 900 g/gmol) showed a significant subcooling decrease at lower salt concentrations. At higher salt concentrations (above 5.0 wt % salt), all molecular weight PVCap tested showed an improved subcooling.
3130 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 10. Subcooling ability of PVCap with concentration and molecular weight.
(wt %), and methanol concentration (wt %). The equation resulting from the regression analysis was
∆Tsub (°C) ) R ln(wt % PVCap) + β + ζ (wt % sea salt)2 + γ (wt % sea salt) + µ (wt % MeOH) (1) where
Figure 11. Effect of methanol on 0.5 wt % PVCap subcooling.
Figure 12. Effect of ASME sea salt on 0.5 wt % PVCap subcooling.
It is not clear why salt and methanol affect the subcooling of PVCap. However, it seems likely that the addition of salt or methanol could change PVCap’s conformation in solution and possibly decrease the ability of PVCap to adsorb to the hydrate surface. Because longer chain lengths are associated with higher molecular weight PVCap, the conformation in solution may be different for polymers of different chain lengths. (E) Empirical Correlation of Subcooling Data. The similarity in trends of the PVCap subcooling data indicates that the data can be empirically correlated. A multiple regression analysis was performed in which subcooling was correlated with PVCap molecular weight (Mn), PVCap concentration (wt %), salt concentration
R ) -5.56 × 10-6(Mn of PVCap) + 3.00
(2)
β ) 45.691(Mn of PVCap)-0.075
(3)
µ ) 0.1763 ln(Mn of PVCap) - 1.6043
(4)
ζ ) -0.047 ln(Mn of PVCap) + 0.4932
(5)
γ ) 0.268 ln(Mn of PVCap) - 2.707
(6)
The correlation of eqs 1-6 was tested against all collected data for PVCap systems in methanol, salt, or deionized water with an average absolute error of 9.7%. The above correlation only applies to systems containing PVCap with molecular weights and polymer, methanol, and salt concentrations specified in Table 1. (F) Long-Duration Experiments. The subcooling results could by used by industry for pipeline operation at conditions below the equilibrium temperature but above the predicted hydrate onset temperature. By fixing the operating pressure, the equilibrium temperature was also fixed for a given solution. The amount of subcooling predicted by eq 1 (∆Tsub) was controlled by the molecular weight and concentration of PVCap, as well as concentrations of methanol and salt. The presence of any thermodynamic inhibitor (methanol or salt) decreased the equilibrium temperature in both ∆Tsub and ∆Top. The difference between ∆Tsub and ∆Top provided a comparison of the operating temperature to the expected onset temperature:
∆Tsub - ∆Top ) (Teq - Tonset) - (Teq - Top) ) Top - Tonset (7) If Top is greater than Tonset, a delay in hydrate formation would be expected. Two types of tests were conducted using this concept. The first type was run on
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3131
Figure 13. Experiments in induction time by varying the concentration of PVCap.
the multitube apparatus at constant ∆Top. The response variable was the induction time observed from the beginning of the experiment until the first detectable onset of hydrate formation. Figure 13 shows that, for
any system in which Tonset g Top, immediate hydrate formation occurred. For experiments in which (Top Tonset) g 1.0 °C, induction times were less than 500 min. For 1 °C < (Top - Tonset) < 2.2 °C, an abrupt increase occurred in the induction time. For (Top - Tonset) g 2.2 °C, very long induction times were observed. Experiments were only allowed to run for 2.6 days, so onsets of hydrate formation were never observed for points in Figure 13 with induction times greater than 3800 min. Figure 14a,b shows results from the second type of long-duration gas consumption experimentsson the high-pressure apparatus achieved by manipulation of Tonset using a combination of thermodynamic inhibitors and PVCap, to achieve a gas consumption less than 0.2 gmol, indicating a very low amount of hydrate formation. All experiments in Figure 14a,b were run at 4.0 °C and 10.3 MPa with 0.75 wt % PVCap (Mn ) 1800 g/mol) and varying amounts of methanol and salt. In
Figure 14. Gas consumption tests with 0.75 wt % PVCap at 10.6 MPa and 277 K: (a) 0.66 wt % ASTM sea salt and various methanol concentrations, (b) 3.5 wt % sea salt and two methanol concentrations.
3132 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
two cases long times of hydrate inhibition were observed: (1) when (Top - Tonset) g 6.3 °C, the systems were inhibited for 19 days (marked ∆Top ) 5.5 °C in Figure 14a) and (2) when (Top - Tonset) g 5.5 °C, the system was inhibited for 28 days (marked ∆Top ) 8.1 °C in Figure 14b). Substantial hydrate formation was not observed in these two tests for times in excess of typical residence times of free water in an offshore pipeline. The above high-pressure tests indicate that when (Top - Tonset) g 5.5 °C, kinetic inhibition may be a viable option for flowlines. To use these results, three readily available temperatures are required: (1) the lowest operating temperature at the flowline pressure (Top), (2) the equilibrium hydrate temperature at the flowline pressure (Teq) so that ∆Top ()Teq - Top) can be calculated, and (3) the ∆Tsub value predicted by eqs 1-6, paying careful attention to the range of application. Equation 7 indicates a subtraction of ∆Top from ∆Tsub yields (Top - Tonset). Inhibitor addition may be made until the desired value of Top - Tonset is achieved. IV. Conclusions Raman results indicated that it is possible to measure hydrate formation rates from the liquid phase. Raman spectra indicate that kinetically inhibited methane hydrate formation differed significantly from the uninhibited hydrate. Such results show the power of the Raman method,and may suggest a technique for understanding hydrate kinetic formation and inhibition mechanisms. Apparent viscosity measurements upon hydrate formation and dissociation provided evidence of residual hydrate structure. Water in pipelines from dissociated hydrates should be promptly removed to prevent rapid re-formation of hydrate plugs. The inhibition performance of PVCap was characterized. Increasing the concentration of PVCap gave an asymptotic increase in subcooling with increasing concentration. Lower molecular weights of PVCap were more effective. Methanol appears to impact the PVCap subcooling negatively, with lower molecular weight PVCap being the most severely affected. Salt effects on PVCap subcooling were minor at low concentrations but tended to be positive at higher salt concentrations. An empirical correlation was developed of the subcooling provided by PVCap polymer as a function of polymer molecular weight, polymer concentration, methanol concentration, and salt concentration. To verify the subcooling correlation, tests were conducted to simulate pipeline residence times. Natural gas hydrates may be inhibited in excess of 28 days at 10.6 MPa and 4 °C if (Top - Tonset) g 5.5 °C with 0.75 wt % PVCap. A method for use of the correlation was suggested. Acknowledgment BASF and ISP provided commercial samples of poly(N-vinylcaprolactam) (PVCap). Molecular weight analy-
sis and laboratory-synthesized samples of PVCap were provided by Professor Bill Brittain and Dr. Dawei Li at University of Akron. The National Science Foundation provided funding for the microscopic portions of this work under NSF Grant CTS-9634899. We are grateful to the CSM Hydrate Consortium which funded the macroscopic portions of this work: Amoco, ARCO, Chevron, Conoco, Exxon, Mobil, Oryx, Petrobras, Phillips, Shell, Statoil, and Texaco. Long-term inhibition tests were funded, and permission to publish the results was provided by ARCO Exploration and Production. Literature Cited Anderson, F. E.; Prausnitz, J. M. AIChE J. 1986, 32, 1321. Box, G. E. P.; Hunter, W. G.; Hunter, J. S. Statistics for Experimenters; John Wiley & Sons: New York, 1978. Hammerschmidt, E. G. Ind. Eng. Chem. 1934, 26, 851. Larsen, R.; Makogon, T.; Knight, C.; Sloan, E. D. Proceedings of the 2nd International Conference on Natural Gas Hydrates, Toulouse, France, June 2-6, 1996. Lederhos, J. P.; Sloan, E. D. Transferability of Kinetic Inhibitors Between Laboratory and Pilot Plant. SPE Annual Technical Conference, Denver, 1996; SPE 36588. Lederhos, J. P.; Long, J. P.; Sum, A.; Christiansen, R. L.; Sloan, E. D. Chem. Eng. Sci. 1996, 51, 1221. Long, J. P.; Lederhos, J. P.; Sum, A.; Christiansen, R. L.; Sloan, E. D. Proceedings of the 73rd Gas Processors Association Annual Convention, New Orleans, LA, March 7-9, 1994. Makogon, Y. F. Hydrates of Natural Gas; Translated from Russian by W. J. Cieslesicz; Penn Well Books: Tulsa, OK, 1981. Makogon, T. Y.; Larsen, R.; Knight, C. A.; Sloan, E. D. J. Cryst. Growth 1997, 179, 258. Matthews, P. N. Quantification of Significant Variables in Kinetic Hydrate Inhibition. M.S. Thesis, Colorado School of Mines, Golden, CO, April 1997. Parent, J. S.; Bishnoi, P. R. Chem. Eng. Commun. 1996, 144, 51. Parrish, W. P.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1972, 11, 26 Ripmeester, J. A.; Ratcliffe, C. I. Solid State NMR Studies of Inclusion Compounds; Report C1181-89S; National Research Council of Canada: Ottawa, Canada, 1989. Sloan, E. D. The State-of-the Art of Hydrates as Related to the Natural Gas Industry; Gas Research Institute Topical Report GRI-91/0302; Gas Research Institute: Chicago, IL, June 1, 1992. Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker Inc.: New York, 1998. Song, K. Y.; Feneyrou, Gl.; Fleyfel, F.; Martin, R.; Levois, J.; Kobayashi, R. Fluid Phase Equilib. 1997, 128, 249. Sum, A. K.; Burruss, R. C.; Sloan, E. D. J. Phys. Chem. B 1997, 38(101), 7371. van der Waals, J. H.; Platteeuw, J. C. Clathrate Solutions. Adv. Chem. Phys. 1959, 2, 1. Vysniauskas, A.; Bishnoi, P. R. Chem. Eng. Sci. 1983, 38, 1061.
Received for review December 10, 1997 Revised manuscript received March 31, 1998 Accepted April 3, 1998 IE970902H
