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Effect of polyethylene oxide on gas hydrate phase equilibria
271
Fluid Phase Equilibria, 92 (1994) 271-288
Elsevier Science Publishers B.V., Amsterdam
Effect of polyethylene equilibria
oxide on gas hydrate phase
Peter Englezos * and Yee Tak Ngan Department of Chemical Engineering, V6T 124 (Canada)
The University of British Columbia,
Vancouver, B.C.,
(Received December 28, 1992; accepted in final form April 19, 1993)
ABSTRACT Englezos, P. and Ngan, Y.T., 1994. Effect of polyethylene equilibria. Fluid Phase Equilibria, 92: 271-288.
oxide on gas hydrate phase
Incipient phase equilibrium data for methane, ethane and propane hydrate formation in aqueous solutions of polyethylene oxide (PEO) were measured. The experiments were performed in the temperature range of 273.55-285.3 K. The range of measured incipient equilibrium hydrate formation pressures was 0.187-9.961 MPa. Aqueous polyethylene oxide solutions at 5, 15 and 25 wt.% were used. The results indicate a very weak inhibiting effect compared with the effect of electrolytes and alcohols on the equilibrium hydrate formation conditions. The measured equilibrium hydrate formation pressures were compared with the predictions from the existing gas hydrate equilibria prediction method. The data were found to be in good agreement with the predicted values. Keywords: experiments, data, phase equilibria, gas hydrates, polyethylene oxide.
INTRODUCTION
Gas hydrates are solid solutions. Hydrogen bonding among water molecules creates a three-dimensional structure (lattice) with cavities which is thermodynamically unstable (empty hydrate lattice) but can become stable with the inclusion of molecules such as natural gas components. Each cavity can be occupied by only one molecule. Therefore, gas hydrates are inclusion compounds and they are often called clathrate hydrates or water clathrates. They have been known since 18 10 (Davy, 1811) but became industrially important when it was realized that they can plug natural gas
* Corresponding
author.
0378-3812/94/$07.00 0 1994 - Elsevier Science Publishers B.V. All rights reserved
272
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
pipelines at temperatures above the normal freezing point of water (Hammerschmidt, 1934). This is a consequence of the fact that gas hydrates are solid compounds that can be formed at temperatures at which water ordinarily exists in the liquid state. Because light hydrocarbon gases, H2S and COZ are among the molecules that can form hydrates, knowledge of the natural gas-water phase diagram in the hydrating region became a necessity for rational design of oil and gas production and processing facilities. Vast quantities of naturally occurring gas hydrates, containing mostly methane, were discovered in the earth’s crust (Katz, 1971; Makogen et al., 1972; Davidson et al., 1978). The energy resource potential of these in situ hydrates is too significant to be ignored (Finlay and Krason, 1990). Kvenvolden (1988) estimated that lOI m3 of methane gas exist in hydrate form. Canada is among the regions of the world where a big portion of these in situ gas hydrates are located (Judge, 1982; Hyndman and Davis, 1992). Information on the structure, properties, technological significance and implications of gas hydrates is readily available (Davidson, 1973; Makogon, 1981; Sloan, 1990a). Gas hydrate phase equilibrium data and predictive methods are needed for the rational design of the facilities in the oil, gas and chemical industries that deal with hydrates. A large amount of data has been collected during the past five decades (Sloan, 1990a). The incipient equilibrium hydrate formation conditions for the main constituents of natural gases and for several mixtures have been determined in pure water and in the presence of alcohols and electrolytes. The word incipient is used to denote the fact that an infinitesimal amount of hydrate co-exists in equilibrium with the fluid phases at equilibrium. Alcohols and electrolytes are used for the prevention of hydrate formation because they decrease the activity of water and as a result a higher pressure is required for hydrate formation at a given temperature. Reasonably accurate thermodynamics-based prediction methods have also been developed and are used in process design and simulation. The industry has now available a large data bank of experimental data which together with prediction methods enables it to: (a) identify the conditions at which a natural gas mixture will form hydrates; and (b) compute the minimum amount of inhibitors that is required to prevent hydrate formation. Recently, hydrates research has begun to focus on the effect of substances such as water-soluble polymers and other components of drilling fluids and surfactants on gas hydrate formation (Cha et al., 1988; Sloan, 1990b; 1991; Ouar et al., 1992). This is because oil and gas exploration and production are moving to Arctic and/or deep offshore regions and the cost of conventional hydrate prevention techniques increases (Sloan, 1990b; 199 1). There is strong industrial interest in developing a new class of inhibitors which will
P. Englezas and Y.T. Ngan / Fluid Phase Equilibria 92 (i994) 211-288
273
affect both the equilibrium formation conditions and the rate of crystal growth (Hubbard, 1991; Muijs, 1991). In addition, water-based drilling fluids are preferred over oil-based ones (Bland, 1991). Hydrate fo~ation in drilling muds or decomposition during drilling through in situ hydrate zones are always taken into consideration by drilling engineers. Because there are no experimental data available in the open literature on hydrate formation from natural gas components in the presence of watersoluble polymers, the objective of this work was to provide data on the effect of a common water-soluble polymer, polyethylene oxide, on the equilibrium hydrate formation conditions of natural gas components. It should be noted, however, that Fennema and coworkers studied the formation of hydrates from CH,Br and CH3F in solutions of apple juice, orange juice, sucrose and D-glucose and found that these solutes depressed the equilibrium hydrate formation tem~rature (Huang et al., 1965). Because the effect of water-soluble polymers on the equilibrium hydrate formation conditions can be calculated (Englezos, 1992), another objective was to compare the data with the predictions and test the validity of the method. Incipient phase equilibrium data for methane, ethane and propane hydrate fo~ation are reported. EXPERIMENTAL
Apparatus All the experiments were conducted using the apparatus displayed in Fig. 1. The apparatus can use two different equilibrium cells, one at a time, for the determination of the incipient equilibrium hydrate formation conditions. One cell was used for the experiments with methane and ethane (high pressure cell) while the other was used for the experiments with propane (low pressure cell). The cells can be easily connected and disconnected from the apparatus. Each cell was in turn immersed in a temperature-controlled bath. The bath contains 118 1 of a liquid mixture of (SO-SO wt.%) water and ethylene glycol to keep a constant temperature within the system. The temperature of the glycol mixture is controlled by an external ref~gerator~heater (Forma Scientific model 2095). The ref~gerator~ heater has a capacity of 28.5 1. It utilizes a 50-50 mass% solution of ethylene glycol and water. This solution is circulated in a closed loop and exchanges heat with the solution inside the bath where the cell is immersed. Copper tubing was used for the construction of the heating/cooling coil. A motor-driven stirring mechanism is used to maintain a relatively constant temperature ( fO.10 IL) in the glycol-water mixture of the bath over a long period of time.
Fig. 1. Schematic of the experimental apparatus.
Equilibrium cells The body of each cell was machined
from solid 3 16 stainless steel cylindrical bars. A cross-sectional view of the low pressure equilibrium cell is found elsewhere (Englezos and Ngan, 1993). The cell has two viewing windows mounted on the front and back. A third viewing window is fitted at the top of the cell. Each window was machined from l/2” thick Plexiglas plates. All three windows were held in place by stainless steel bolts and were sealed with neoprene O-rings. A cross-sectional view of the high pressure cell is displayed in Fig. 2. This cell has two marine-type windows machined from Plexiglas plates. These windows are mounted on the front and back of the cell. They are sealed with silicone sealant. The cell’s lid is held in place by eight stainless steel bolts. A neoprene O-ring was used to seal the lid. It should be noted that this cell can also be used for low pressure experiments. However, the other one was used because it offers much better visibility. Stirring of the cell contents is accomplished by using a magnetic stir bar coupled to a set of magnets underneath the equilibrium cell. The set of magnets is mooted on an alumina housing which is rotated by a DC motor connected to a controller.
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288 l/4’ - 13 Thread
275
DrIU 17/3Y
l/2’ - 32 Thr
tm
316 STAINLESS
m Fig. 2. A cross-section
STEEL
PLEXIGLASS
of the high pressure
equilibrium
cell.
The temperature inside each cell is measured with copper-constantan thermocouples from Omega. In each cell, one thermocouple is positioned at the upper part of the chamber and measures the gas phase temperature, while another thermocouple is located at the lower part of the chamber to measure the temperature of the liquid phase. In the high pressure cell, an additional thermocouple is situated in the middle of the chamber. The thermocouples were calibrated with a calibrated thermometer from Fisher Scientific and a calibrated thermistor from Paso Scientific. The accuracy of the thermocouple measurements is believed to be f 0.10 K. The pressure is measured by two Bourdon tube Heisse pressure gauges from Brian Engineering. One pressure gauge was used for the low pressure cell, and the other for the high pressure cell. Their respective ranges are O-300 psi and 0- 14 000 kPa. The low pressure gauge was calibrated against an AMETEK Modcal Pressure Module (Pneumatic), traceable to NIST with a certified accuracy of 0.05% of the span. The high pressure gauge was calibrated against a hydraulic deadweight tester traceable to NBS with a
276
P. Englezos and Y. T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
certified accuracy of 0.1%. The accuracy of the pressure measurements the gauges is believed to be less than 0.25% of the span.
with
Experimental method The formation and decomposition of hydrates was observed visually through the cell windows. The experiments were performed at constant temperature. The equilibrium hydrate formation pressure was measured at several temperatures for each aqueous polymer solution. Polyethylene oxide is miscible with water in all proportions at room temperature. The appropriate amounts of laboratory grade polyethylene oxide and deionized water were weighed using two Mettler balances with readabilities of 0.1 mg and 0.01 g. Because polyethylene oxide particles absorb water and may immediately become gel-like and cohesive, the dissolution of the polymer was achieved by following a procedure described in the literature (Bailey and Koleske, 1976; Akhmetov et al., 1989). Into a thoroughly cleaned cell, 100 cm3 of the aqueous polymer solution were injected. The solution was then allowed to reach a target temperature. Flushing air from the cell was performed by charging the cell twice with the hydrate-forming gas to a pressure slightly below the vapor pressure of propane or ethane, or to 5.0 MPa when methane was used. Air in the Bourdon tube was not expected to be a problem because the amount would have been too small to disturb the gas composition. Subsequently, gas hydrates were formed by injecting hydrate-forming gas into the cell and increasing the pressure well above the hydrate formation pressure. Next, the hydrate crystals were decomposed by venting the gas out of the cell. It is necessary to form and decompose the hydrates once or twice for each solution under study because the hysteresis phenomena associated with gas hydrate formation are diminished. In addition, the structure of the liquid phase is enhanced and hydrates can form more easily. This procedure was carried out at the first experimental temperature for each polymer solution that was investigated. The cell was subsequently pressurized to an excess of approximately 0.05-0.15 MPa from the estimated equilibrium value. An estimate of the experimental hydrate formation pressure was obtained by a trial-and-error procedure. This was done once for each polymer solution concentration and the result was compared with the prediction using the method of Englezos (1992). From the comparison of this measurement and the prediction an estimate of the magnitude of the deviation between the experimental results and predictions was obtained. This deviation was used to obtain estimates of the hydrate formation pressures at other temperatures. Following the pressurization of the cell, stirring was commenced. Once the contents of the cell reached a target temperature, the pressure was
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
277
further increased by introducing more gas into the cell to induce hydrate nucleation. The pressure was set well above the hydrate point in order to have a large driving force and induce hydrate nucleation quickly. Once a small amount of hydrate was formed, the pressure was quickly decreased to the expected equilibrium value (estimated by trial and error) by venting some of the gas out of the cell. The system was left under these conditions for at least four hours. If there was a small amount of hydrate, in the form of tiny crystals, in the equilibrium cell at the end of the four-hour observation period, and the temperature and pressure were constant, then this pressure was taken as the equilibrium hydrate formation pressure at this temperature. If the hydrate was not present after the four-hour period, the pressure of the system was below the equilibrium pressure. In this case, the experiment was repeated but the new estimated equilibrium pressure was set at a higher value. The experiment was terminated when the pressure and temperature in the cell were constant and a small amount of hydrate crystals was detectable. Subsequently, a different temperature was selected and the procedure was repeated to obtain the next incipient hydrate phase equilibrium point. The above procedure was used to find equilibrium points for the 5 wt.%, and 15 wt.% polymer solutions. It is known that more concentrated solutions of polyethylene oxide tend to become elastic, reversible gels (Bailey et al., 1958). The 25 wt.% polymer solutions were more viscous and could not be mixed as well as the others at 5 and 15 wt.%, and so a small change in procedure was adopted. In order to compensate for the problem, the volume of the solution was reduced to 75 cm3 and the observation time was increased to 6 hours. The hydrate-forming gases were supplied from Medigas. The purities of methane, ethane and propane gases that were used in this study were 99.9, 99.0 and 99.5% (by volume), respectively. Polyethylene oxide with an average molecular weight of 100 000, supplied from Aldrich, was used in all the experiments. CALCULATION
OF THE INCIPIENT
HYDRATE
FORMATION
PRESSURE
A method for the calculation of the incipient equilibrium hydrate formation conditions in a hydrocarbon-water-polymer system has been presented by Englezos (1992). The method is entirely predictive. No adjustable parameters are required to compute the incipient equilibrium hydrate formation pressure at a given temperature. In the present work, that method was used to calculate the hydrate formation pressure at each experimental temperature. This enabled us to compare the predictions with the experimental data and test the validity of the predictive method. The incipient
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
278
equilibrium hydrate formation pressure, P, at a given temperature, computed by solving the non-linear equation A vMT-LO w
’ - t
RT
vi ln( 1 + 2
i=l
C,yj(py P ) + 11/(T) - In a, = 0
j=l
T, is
(1)
where the function, t,b(T) is easily derived from an equation that gives the difference in the chemical potential of water from that of the empty hydrate lattice (Holder et al., 1980). An analytical expression for this function is given below. G(T)
=
$!f$ +$
(To - T) +
cAcz~ BTo) In($)
Ah;-ACO,P+@‘)’ +
R
1
The values for the physical and thermodynamic parameters of the hydrate which are required in eqns. (1) and (2) are given in Table 1. In eqn. (l), C, are the Langmuir constants which at a given temperature are computed by a correlation proposed by Parrish and Prausnitz (1972). The Trebble-Bishnoi equation of state (Trebble and Bishnoi, 1988) is used for the calculation of the fugacity coefficients, 4jy in the vapor (V) phase. The hydrate equilibria prediction method requires the calculation of the activity of water, G, in aqueous polymer solutions. The calculation of cr, is based on the UNIFAC group contribution method (Oishi and Prausnitz, 1978; Rasmussen and Rasmussen, 1989). Three contributions are taken into account for the calculation of the activity of water as follows: TABLE 1 Physical and thermodynamic Property
P AC; Ahho, A& A yMT-Lo w
“I “2
To
reference properties for gas hydrates
Value Structure I
Structure II
0.141 J mol-’ K-* -38.13 J mol-’ K-’ -4860.0 J mol-’ 1264.0 J mol-’ 4.6 x 10m6m3 mol-’ l/23 3123 273.15 K
0.141 J mol-’ K-* -38.13 J mol-’ K-’ - 5203.5 J mol-’ 883 J mol-’ 5.0 x 10d6 m3 mol-’ 2117 l/17 273.15 K
P. Englezos and Y.T. Ngan / Fluid Phase Equilibria 92 (1994) 271-288
279
‘%v =
(31
‘&ombinatorial
+
&&dual
+
@-free volume
The combinatorial term attempts to describe the dominant entropic contribution. It is determined by the composition, size and shape of the molecules. The residual term is due primarily to the intermolecular forces that are responsible for the enthalpy of mixing. Because we are dealing with a polymer-solvent system with large size differences between the polymer and water molecules, free-volume effects are important and are included in the equation. RESULTS AND DISCUSSION
Prior to the experiments with aqueous polymer solutions, experiments with pure methane and pure ethane in water were conducted in order to establish the validity of the measurements. In these experiments the incipient equilibrium hydrate formation pressures were measured. The results for methane hydrate are reported in Table 2. These data and the data from TABLE 2 Incipient equilibrium (PEO) solutions Temperature (R) 214.3 278.25 281.55 285.15 274.65 276.05 278.15 280.75 283.15 285.30 273.55 275.65 277.65 279.65 281.95 273.95 276.05 278.4 280.65 282.85 285.15
data on methane hydrate formation
PEO concentration (wt.%) 0 0 0 0
5.00 5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00 25.00
in aqueous polyethylene
Experimental (MPa) 2.976 4.251 6.101 9.101 3.101 3.541 4.501 5.951 7.451 9.341 2.791 3.341 4.251 5.301 6.801 3.356 3.901 5.176 6.326 7.951 9.961
pressure
oxide
P. Englezos and Y. T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
280
273
276
277
279
261
Temperature
Fig. 3. Experimental solutions.
263
266
267
(K)
data and predicted methane hydrate formation
pressures in aqueous
Roo et al. (1983) are shown in Fig. 3 together with the incipient equilibrium hydrate formation pressures calculated at the experimental temperatures. The predictions are shown as a solid line. It is seen that there is good agreement among the data. There is also good agreement between the predicted values and the experimentally measured incipient hydrate formation pressures. The incipient hydrate formation data for ethane in pure water are reported in Table 4. These data together with other data from the literature and the predicted values are shown in Fig. 4 and indicate good agreement between the data from different sources and the predictions. Propane hydrate formation data in pure water were collected using the low pressure cell. These data were compared with others from the literature and with the predictions, and were found to be in good agreement (Englezos and Ngan, 1993). Finally, it is noted that measurements at a particular temperature TABLE 3 Comparison of the incipient equilibrium methane hydrate formation water, methanol, sodium chloride, and polyethylene oxide solutions Temperature (R)
275.41 275.87 275.87 275.87 275.87
conditions
in pure
Pressure (MPa)
Aqueous phase concentration (wt.%)
Experimental
Calculated
(0) (0) NaCl (10) CH,OH (10) PEO (10)
3.34a 5.63C -
3.17b 3.32b 5.30b 5.54d 3.37”
a Roo et al. (1983). b Englezos and Bishnoi (1988). c Ng and Robinson (1983). d Englezos et al. (1991). ’ Englezos ( 1992).
281
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
TABLE 4 Incipient equilibrium (PEO) solutions
data on ethane hydrate formation
PEO concentration (wt.%)
Temperature (K)
Experimental (MPa)
0 0
274.8 278.8 281.8 275.0 277.6 279.1 281.1 282.9 274.85 276.65 278.85 280.75 282.65 275.45 277.25 278.95 281.05 282.75
in aqueous
polyethylene
pressure
0.576 0.951 1.386 0.591 0.826 1.001 1.291 1.636 0.601 0.751 1.011 1.261 1.651 0.661 0.851 1.031 1.326 1.696
0
5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00
were easily reproducible. On the basis of these observations it cluded that the apparatus was able to provide reproducible data in agreement with data from other laboratories. All the experimental data for aqueous polymer solutions are Tables 2, 4 and 5. The results for methane at 5 and 25 wt.% are 1.8- .
n
1.6-
0 Hohier&Hmd,l982
0.44 274
oxide
was conthat were shown in shown in
Eagkms&Bishnoi.1991
1
n
276
278 Temperature
Fig. 4. Experimental solutions.
1 . 280
1
1
282
284
(K)
data and predicted ethane hydrate formation
pressures in aqueous
282
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
TABLE 5 Incipient experimental (PEO) solutions
data on propane hydrate formation
in aqueous polyethylene
Temperature (IQ
PEO concentration (wt.%)
Experimental (MPa)
273.6 273.85 274.7 275.45 276.1 277.05 277.75 278.2 273.55 274.5 275.25 275.9 276.75 277.55 277.9 273.6 274.45 275.1 275.8 276.45 277.1
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00 25.00
0.187 0.198 0.239 0.281 0.323 0.399 0.470 0.531 0.200 0.245 0.284 0.329 0.405 0.474 0.522 0.230 0.270 0.314 0.371 0.444 0.522
oxide
pressure
Fig. 5. It is seen from the figure that the polymer is a hydrate inhibitor. Its action, however, is weak. The inhibiting action of polyethylene oxide was compared with that of sodium chloride and methanol. In Table 3, the incipient methane hydrate formation pressures in pure water and in 10 wt.% methanol, sodium chloride, and polyethylene oxide solutions are shown for comparison purposes. Methanol and sodium chloride alter the hydrate formation conditions significantly. The effect of the polymer, however, is small. The hydrate formation pressure is only 0.05 MPa higher than that in pure water. Therefore the inhibiting action of polyethylene oxide is weak compared with the action of electrolytes or alcohols at the same weight percent concentration. Although the polymer reduces the activity of water, this reduction is not significant enough to cause a strong increase in the required pressure for hydrate formation at a given temperature. In Fig. 6, the calculated activity of water in aqueous solutions of NaCl and polyethylene oxide is plotted versus concentration. The electrolyte
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288 12.07
283
I 25wt%
-
9.5 T 5wt% t zl 2 t b
o 0
D 4.5 7.0! 2.0-1 273
* /
-
-
.
275
277
Predictions
8 . . 279
Temperature
. . . 1
281
283
285
(K)
Fig. 5. Experimental data and predicted methane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
Fig. 6. Activity of water in sodium chloride and in polyethylene oxide solutions.
reduces the activity of water substantially compared with the small reduction caused by the polymer. Electrolytes are known to alter the thermodynamic state of the liquid water phase whereas the polymer changes the viscosity of the solution substantially but not the activity of water. The accuracy of these calculations on the activity of water was tested previously and was found to be very good (Englezos and Bishnoi, 1988; Englezos, 1992). In Fig. 5, the continuous lines represent the predicted hydrate formation pressures based on the method of Englezos (1992). The maximum percentage deviation between data and predictions at 5 wt.% was found to be 8.8. At 25 wt.%, the maximum percentage deviation is 13.9. As seen in Fig. 3, the calculated incipient equilibrium hydrate formation pressures in pure water are consistently smaller than the data. In polymer solutions the trend is the same, but the deviations are larger in magnitude. Because gas hydrate phase equilibria depend on many factors (Sloan, 1990a; 1990b), such deviations between data and purely predicted (non-fitted) values are reason-
284
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
.
0.44 274
-
.
276
.
.
u
1
270
260
262
264
Temperature
(K)
Fig. 7. Experimental data and predicted ethane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
able. Finally, it is noted that the maximum deviation between data at 15 wt.% and predicted values was found to be 8.1%. In Fig. 7, the results for ethane hydrate formed in 5 and 25 wt.% polyethylene oxide solutions are shown. The weak inhibiting effect of polyethylene oxide is also noticed. The predictions and the data agree very well. The maximum deviations between data given in Table 4 and calculated values at 5, 15 and 25 wt.% are 2.0, 3.6 and 5.4%, respectively. The results for propane hydrate formation in polyethylene oxide solutions of 5 and 25 wt.% are shown in Fig. 8. Again, the weak inhibiting effect of the polymer is evident. The calculated hydrate formation pressures are in good agreement with the measured values given in Table 5. The maximum deviation between data and predictions in Fig. 8 was found to be 6.3%. The water-soluble polymer (polyethylene oxide) that was investigated in this work was found to have a weak inhibiting effect on the equilibrium
-
Oil ‘273
Predictions
274
275
276
Temperature
277
276
279
(K)
Fig. 8. Experimental data and predicted propane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
P. Englezos and Y.T. Ngan / Fluid Phase Equilibria 92 (1994) 271-288
285
natural gas hydrate formation conditions. Therefore, it cannot be used as an effective thermodynamic inhibitor. Water-soluble polymers, however, alter the viscosity of the solution significantly (Bailey and Koleske, 1976). This may affect the nucleation conditions of the hydrate crystals, but such studies are not available in the open literature. CONCLUSIONS
Equilibrium hydrate formation data for pure methane, ethane and propane in aqueous polyethylene oxide solutions were collected and reported for the first time. Aqueous solutions of 5, 15 and 25 wt.% were used. The temperature range of the experiments was 273.55-285.3 K. The pressure range was 0.187-9.961 MPa. Compared with methanol and sodium chloride, the polyethylene oxide was found to be a weak inhibitor. The experimental data were compared with the predictions using the method of Englezos (1992) and were found to be in good agreement. LIST OF SYMBOLS
C
G h Nh P R T V Y
Langmuir constant (MPa-‘) heat capacity (J mol-’ K-r) enthalpy (J mol-‘) number of hydrate-forming components pressure (MPa) universal gas constant (J mol-’ K-l) temperature (K) volume (m’) mole fraction in vapor phase
Greek letters 2 CL z II/
activity of water difference chemical potential number of cavities of type i fugacity coefficient temperature function in eqn. (1)
Subscripts i j W
index ( 1,2) index ( 1, . . . , Nh) water
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
286
Superscripts
LO MT V 0
pure liquid water empty hydrate vapor reference conditions at 273.15 K and zero absolute pressure
ACKNOWLEDGMENTS
The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Gas Processors Association (CGPA) is greatly appreciated.
REFERENCES Akhmetov, B., Novichenko, Y. and Chapurin, V., 1989. Physical and Colloid Chemistry, translated from the Russian by G. Leib. Mir Publishers, Moscow, pp. 302-311. Bailey, F.E., Jr. and Koleske, J.V., 1976. Poly(ethylene oxide). Academic Press, New York, pp. 29-38. Bailey, F.E., Jr., Powell, G.M. and Smith, K.L., 1958. High molecular weight polymers of ethylene oxide. Ind. Eng. Chem., 50( 1): 8-16. Bland, R., 1991. Development of new water based mud formulations. In: P.H. Ogden, (Ed.), Chemicals in the Oil Industry: Developments and Applications. Royal Society of Chemistry, pp. 83-98. Cha, S.B., Quar, H., Wildemann, T.R. and Sloan, E.D., 1988. A third surface effect on ethane hydrate formation. J. Phys. Chem., 92: 6492-6494. Davidson, D.W., 1973. Gas hydrates. In: Frank, F. (Ed.), Water a Comprehensive Treatise, Vol. 2. Plenum Press, New York, pp. 115-234. Davidson, D.W., El-Defrawy, M.K., Fuglam, M.O. and Judge, A.S., 1978. Natural gas hydrates in Northern Canada. In: The Proceedings of the Third International Conference on Permafrost, lo-13 July, Edmonton, Alberta, vol. 1, pp. 938-943. Davy, H., 18 11. The Bakerian Lecture. On some of the combinations of oxymuriatic gas and oxygene, and on the chemical relations of these principles, to inflammable bodies. Philos. Trans. R. Sot. London, 101, Part I: l-35. Englezos, P., 1992. Incipient equilibrium hydrate formation conditions in aqueous polymer solutions. Chem. Eng. Res. Des., 70: 43-47. Englezos, P. and Bishnoi, P.R., 1988. Prediction of gas hydrate formation conditions in aqueous electrolyte solutions. AIChE J., 34: 1718-1721. Englezos, P. and Bishnoi, P.R., 1991. Experimental study of the equilibrium ethane hydrate formation conditions in aqueous electrolyte solutions. Ind. Eng. Chem. Res., 30: 16551659. Englezos, P., and Ngan, Y.T., 1993. Incipient equilibrium data for propane hydrate formation in aqueous solutions of NaCl, KCl, and CaCl,. J. Chem. Eng. Data, 38: 250-253. Englezos, P., Huang, Z. and Bishnoi, P.R., 1991. Prediction of natural gas hydrate formation conditions in the presence of methanol using the Trebble-Bishnoi equation of state. J. Can. Pet. Technol., 30(2): 148-155.
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287
Finlay, P. and Krason, J., 1990. Evaluation of geological relationships to gas hydrate formation and stability: summary report. Gas Energy Rev., 18: 12- 18. Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gas transmission lines. Ind. Eng. Chem., 26(8): 851-855. Holder, G.D. and Hand, J.H., 1982. Multiple-phase equilibria in hydrates from methane, ethane, propane and water mixtures. AIChE J., 28(3): 440-447. ’ Holder, G.D., Gorbin, G. and Papadopoulos, K.D., 1980. Thermodynamic and molecular properties of gas hydrates from mixtures containing methane, argon, and krypton, Ind. Eng. Chem. Fundam., 19: 282-286. Huang, C.P., Fennema, 0. and Powrie, W.D., 1965. Gas hydrates in aqueous organic systems I. Preliminary studies. Cryobiology, 2: 109-115. Hubbard, R.A. 1991. Recent developments in gas dehydration and hydrate inhibition. SPE 21507, presented at the SPE Gas Technology Symposium, Houston, Texas, 23-25 January, pp. 253-276. Hyndman, R.D. and Davis, E.E., 1992. A mechanism for the formation of methane hydrate and seafloor bottom-simulating reflectors by vertical fluid expulsion. J. Geophys. Res., 97 (B5): 7025-7041. Judge, A., 1982. Natural gas hydrates in Canada. In: French, H.M. (Ed.), The Proceedings of the Fourth Canadian Permafrost Conference, 2-6 March, 1981, Calgary, Alberta, National Research Council of Canada, pp. 320-328. Katz, D.L., 1971. Depths to which frozen gas fields (gas hydrates) may be expected. J. Pet. Technol., 419-423. Kvenvolden, K.A., 1988. Methane hydrate - a major reservoir of carbon in the shallow geosphere. Chem. Geol., 71: 41-51. Makogon, Y.F., 1981. Hydrates of Natural Gas. W.J. Cieslewicz. Penn Well Publishing, Tulsa, OK. Makogon, Y.F., Trebin, F.A., Trofimuk, A.A., Tsarev, V.P. and Cherskiy, N.V., 1972. Detection of a pool of natural gas in a solid (hydrate gas) state. Dokl. Acad. SC. USSR-Earth Sciences Sections, 196: 197-200. (Originally published in Russian, 1971). Muijs, H.M., 1991. Surfactants in oil production. In: P.H. Ogden, (Ed.), Chemicals in the Oil Industry: Developments and Applications. Royal Society of Chemistry, pp. 277297. Ng, H.-J. and Robinson, D.B., 1983. Equilibrium phase compositions and hydrating conditions in systems containing methanol, light hydrocarbons, carbon dioxide and hydrogen sulfide. Gas Processors Association, Research Rept., RR-66, Tulsa, OK. Oishi, T. and Prausnitz, J.M., 1978. Estimation of solvent activities in polymer solutions using a group-contribution method. Ind. Eng. Chem. Process Des. Dev., 17(3): 333339. Ouar, H., Cha, S.B., Wildeman, T.R. and Sloan, E.D., 1992. The formation of natural gas hydrates in water-based drilling fluids. Trans. Inst. Chem. Eng. (Chem. Eng. Res. Des.), 70: 48-54. Parrish, W.R. and Prausnitz, J.M., 1972. Dissociation pressures of gas hydrates formed by gas mixtures. Ind. Eng. Chem., Process Des. Dev., 11: 26-34. Rasmussen, D. and Rasmussen, P., 1989. Phase equilibria in aqueous polymer solutions. Chem. Eng. Prog., February, 50-59. Roo, J.L., Peters, C.J., Lichtenthaler, R.N. and Diepen, G.A.M., 1983. Occurrence of methane hydrate in saturated and unsaturated solutions of sodium chloride and water in dependence of temperature and pressure. AIChE J., 29(4): 651-657.
288
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Sloan, E.D., Jr., 1990a. Clathrate Hydrates of Natural Gases. Marcel1 Dekker, New York. Sloan, E.D., Jr., 1990b. Natural gas phase equilibria and kinetics: understanding the state of the art. Rev. Inst. Fr. Pet., 45(2): 245-266. Sloan, E.D., Jr., 1991. Natural gas hydrates. J. Pet. Technol., 43: 1414-1417. Trebble, M.A. and Bishnoi, P.R., 1988. Extension of the Trebble-Bishnoi equation of state to fluid mixtures, Fluid Phase Equilibria, 40: l-21.
Fluid Phase Equilibria, 92 (1994) 271-288
Elsevier Science Publishers B.V., Amsterdam
Effect of polyethylene equilibria
oxide on gas hydrate phase
Peter Englezos * and Yee Tak Ngan Department of Chemical Engineering, V6T 124 (Canada)
The University of British Columbia,
Vancouver, B.C.,
(Received December 28, 1992; accepted in final form April 19, 1993)
ABSTRACT Englezos, P. and Ngan, Y.T., 1994. Effect of polyethylene equilibria. Fluid Phase Equilibria, 92: 271-288.
oxide on gas hydrate phase
Incipient phase equilibrium data for methane, ethane and propane hydrate formation in aqueous solutions of polyethylene oxide (PEO) were measured. The experiments were performed in the temperature range of 273.55-285.3 K. The range of measured incipient equilibrium hydrate formation pressures was 0.187-9.961 MPa. Aqueous polyethylene oxide solutions at 5, 15 and 25 wt.% were used. The results indicate a very weak inhibiting effect compared with the effect of electrolytes and alcohols on the equilibrium hydrate formation conditions. The measured equilibrium hydrate formation pressures were compared with the predictions from the existing gas hydrate equilibria prediction method. The data were found to be in good agreement with the predicted values. Keywords: experiments, data, phase equilibria, gas hydrates, polyethylene oxide.
INTRODUCTION
Gas hydrates are solid solutions. Hydrogen bonding among water molecules creates a three-dimensional structure (lattice) with cavities which is thermodynamically unstable (empty hydrate lattice) but can become stable with the inclusion of molecules such as natural gas components. Each cavity can be occupied by only one molecule. Therefore, gas hydrates are inclusion compounds and they are often called clathrate hydrates or water clathrates. They have been known since 18 10 (Davy, 1811) but became industrially important when it was realized that they can plug natural gas
* Corresponding
author.
0378-3812/94/$07.00 0 1994 - Elsevier Science Publishers B.V. All rights reserved
272
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
pipelines at temperatures above the normal freezing point of water (Hammerschmidt, 1934). This is a consequence of the fact that gas hydrates are solid compounds that can be formed at temperatures at which water ordinarily exists in the liquid state. Because light hydrocarbon gases, H2S and COZ are among the molecules that can form hydrates, knowledge of the natural gas-water phase diagram in the hydrating region became a necessity for rational design of oil and gas production and processing facilities. Vast quantities of naturally occurring gas hydrates, containing mostly methane, were discovered in the earth’s crust (Katz, 1971; Makogen et al., 1972; Davidson et al., 1978). The energy resource potential of these in situ hydrates is too significant to be ignored (Finlay and Krason, 1990). Kvenvolden (1988) estimated that lOI m3 of methane gas exist in hydrate form. Canada is among the regions of the world where a big portion of these in situ gas hydrates are located (Judge, 1982; Hyndman and Davis, 1992). Information on the structure, properties, technological significance and implications of gas hydrates is readily available (Davidson, 1973; Makogon, 1981; Sloan, 1990a). Gas hydrate phase equilibrium data and predictive methods are needed for the rational design of the facilities in the oil, gas and chemical industries that deal with hydrates. A large amount of data has been collected during the past five decades (Sloan, 1990a). The incipient equilibrium hydrate formation conditions for the main constituents of natural gases and for several mixtures have been determined in pure water and in the presence of alcohols and electrolytes. The word incipient is used to denote the fact that an infinitesimal amount of hydrate co-exists in equilibrium with the fluid phases at equilibrium. Alcohols and electrolytes are used for the prevention of hydrate formation because they decrease the activity of water and as a result a higher pressure is required for hydrate formation at a given temperature. Reasonably accurate thermodynamics-based prediction methods have also been developed and are used in process design and simulation. The industry has now available a large data bank of experimental data which together with prediction methods enables it to: (a) identify the conditions at which a natural gas mixture will form hydrates; and (b) compute the minimum amount of inhibitors that is required to prevent hydrate formation. Recently, hydrates research has begun to focus on the effect of substances such as water-soluble polymers and other components of drilling fluids and surfactants on gas hydrate formation (Cha et al., 1988; Sloan, 1990b; 1991; Ouar et al., 1992). This is because oil and gas exploration and production are moving to Arctic and/or deep offshore regions and the cost of conventional hydrate prevention techniques increases (Sloan, 1990b; 199 1). There is strong industrial interest in developing a new class of inhibitors which will
P. Englezas and Y.T. Ngan / Fluid Phase Equilibria 92 (i994) 211-288
273
affect both the equilibrium formation conditions and the rate of crystal growth (Hubbard, 1991; Muijs, 1991). In addition, water-based drilling fluids are preferred over oil-based ones (Bland, 1991). Hydrate fo~ation in drilling muds or decomposition during drilling through in situ hydrate zones are always taken into consideration by drilling engineers. Because there are no experimental data available in the open literature on hydrate formation from natural gas components in the presence of watersoluble polymers, the objective of this work was to provide data on the effect of a common water-soluble polymer, polyethylene oxide, on the equilibrium hydrate formation conditions of natural gas components. It should be noted, however, that Fennema and coworkers studied the formation of hydrates from CH,Br and CH3F in solutions of apple juice, orange juice, sucrose and D-glucose and found that these solutes depressed the equilibrium hydrate formation tem~rature (Huang et al., 1965). Because the effect of water-soluble polymers on the equilibrium hydrate formation conditions can be calculated (Englezos, 1992), another objective was to compare the data with the predictions and test the validity of the method. Incipient phase equilibrium data for methane, ethane and propane hydrate fo~ation are reported. EXPERIMENTAL
Apparatus All the experiments were conducted using the apparatus displayed in Fig. 1. The apparatus can use two different equilibrium cells, one at a time, for the determination of the incipient equilibrium hydrate formation conditions. One cell was used for the experiments with methane and ethane (high pressure cell) while the other was used for the experiments with propane (low pressure cell). The cells can be easily connected and disconnected from the apparatus. Each cell was in turn immersed in a temperature-controlled bath. The bath contains 118 1 of a liquid mixture of (SO-SO wt.%) water and ethylene glycol to keep a constant temperature within the system. The temperature of the glycol mixture is controlled by an external ref~gerator~heater (Forma Scientific model 2095). The ref~gerator~ heater has a capacity of 28.5 1. It utilizes a 50-50 mass% solution of ethylene glycol and water. This solution is circulated in a closed loop and exchanges heat with the solution inside the bath where the cell is immersed. Copper tubing was used for the construction of the heating/cooling coil. A motor-driven stirring mechanism is used to maintain a relatively constant temperature ( fO.10 IL) in the glycol-water mixture of the bath over a long period of time.
Fig. 1. Schematic of the experimental apparatus.
Equilibrium cells The body of each cell was machined
from solid 3 16 stainless steel cylindrical bars. A cross-sectional view of the low pressure equilibrium cell is found elsewhere (Englezos and Ngan, 1993). The cell has two viewing windows mounted on the front and back. A third viewing window is fitted at the top of the cell. Each window was machined from l/2” thick Plexiglas plates. All three windows were held in place by stainless steel bolts and were sealed with neoprene O-rings. A cross-sectional view of the high pressure cell is displayed in Fig. 2. This cell has two marine-type windows machined from Plexiglas plates. These windows are mounted on the front and back of the cell. They are sealed with silicone sealant. The cell’s lid is held in place by eight stainless steel bolts. A neoprene O-ring was used to seal the lid. It should be noted that this cell can also be used for low pressure experiments. However, the other one was used because it offers much better visibility. Stirring of the cell contents is accomplished by using a magnetic stir bar coupled to a set of magnets underneath the equilibrium cell. The set of magnets is mooted on an alumina housing which is rotated by a DC motor connected to a controller.
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288 l/4’ - 13 Thread
275
DrIU 17/3Y
l/2’ - 32 Thr
tm
316 STAINLESS
m Fig. 2. A cross-section
STEEL
PLEXIGLASS
of the high pressure
equilibrium
cell.
The temperature inside each cell is measured with copper-constantan thermocouples from Omega. In each cell, one thermocouple is positioned at the upper part of the chamber and measures the gas phase temperature, while another thermocouple is located at the lower part of the chamber to measure the temperature of the liquid phase. In the high pressure cell, an additional thermocouple is situated in the middle of the chamber. The thermocouples were calibrated with a calibrated thermometer from Fisher Scientific and a calibrated thermistor from Paso Scientific. The accuracy of the thermocouple measurements is believed to be f 0.10 K. The pressure is measured by two Bourdon tube Heisse pressure gauges from Brian Engineering. One pressure gauge was used for the low pressure cell, and the other for the high pressure cell. Their respective ranges are O-300 psi and 0- 14 000 kPa. The low pressure gauge was calibrated against an AMETEK Modcal Pressure Module (Pneumatic), traceable to NIST with a certified accuracy of 0.05% of the span. The high pressure gauge was calibrated against a hydraulic deadweight tester traceable to NBS with a
276
P. Englezos and Y. T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
certified accuracy of 0.1%. The accuracy of the pressure measurements the gauges is believed to be less than 0.25% of the span.
with
Experimental method The formation and decomposition of hydrates was observed visually through the cell windows. The experiments were performed at constant temperature. The equilibrium hydrate formation pressure was measured at several temperatures for each aqueous polymer solution. Polyethylene oxide is miscible with water in all proportions at room temperature. The appropriate amounts of laboratory grade polyethylene oxide and deionized water were weighed using two Mettler balances with readabilities of 0.1 mg and 0.01 g. Because polyethylene oxide particles absorb water and may immediately become gel-like and cohesive, the dissolution of the polymer was achieved by following a procedure described in the literature (Bailey and Koleske, 1976; Akhmetov et al., 1989). Into a thoroughly cleaned cell, 100 cm3 of the aqueous polymer solution were injected. The solution was then allowed to reach a target temperature. Flushing air from the cell was performed by charging the cell twice with the hydrate-forming gas to a pressure slightly below the vapor pressure of propane or ethane, or to 5.0 MPa when methane was used. Air in the Bourdon tube was not expected to be a problem because the amount would have been too small to disturb the gas composition. Subsequently, gas hydrates were formed by injecting hydrate-forming gas into the cell and increasing the pressure well above the hydrate formation pressure. Next, the hydrate crystals were decomposed by venting the gas out of the cell. It is necessary to form and decompose the hydrates once or twice for each solution under study because the hysteresis phenomena associated with gas hydrate formation are diminished. In addition, the structure of the liquid phase is enhanced and hydrates can form more easily. This procedure was carried out at the first experimental temperature for each polymer solution that was investigated. The cell was subsequently pressurized to an excess of approximately 0.05-0.15 MPa from the estimated equilibrium value. An estimate of the experimental hydrate formation pressure was obtained by a trial-and-error procedure. This was done once for each polymer solution concentration and the result was compared with the prediction using the method of Englezos (1992). From the comparison of this measurement and the prediction an estimate of the magnitude of the deviation between the experimental results and predictions was obtained. This deviation was used to obtain estimates of the hydrate formation pressures at other temperatures. Following the pressurization of the cell, stirring was commenced. Once the contents of the cell reached a target temperature, the pressure was
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
277
further increased by introducing more gas into the cell to induce hydrate nucleation. The pressure was set well above the hydrate point in order to have a large driving force and induce hydrate nucleation quickly. Once a small amount of hydrate was formed, the pressure was quickly decreased to the expected equilibrium value (estimated by trial and error) by venting some of the gas out of the cell. The system was left under these conditions for at least four hours. If there was a small amount of hydrate, in the form of tiny crystals, in the equilibrium cell at the end of the four-hour observation period, and the temperature and pressure were constant, then this pressure was taken as the equilibrium hydrate formation pressure at this temperature. If the hydrate was not present after the four-hour period, the pressure of the system was below the equilibrium pressure. In this case, the experiment was repeated but the new estimated equilibrium pressure was set at a higher value. The experiment was terminated when the pressure and temperature in the cell were constant and a small amount of hydrate crystals was detectable. Subsequently, a different temperature was selected and the procedure was repeated to obtain the next incipient hydrate phase equilibrium point. The above procedure was used to find equilibrium points for the 5 wt.%, and 15 wt.% polymer solutions. It is known that more concentrated solutions of polyethylene oxide tend to become elastic, reversible gels (Bailey et al., 1958). The 25 wt.% polymer solutions were more viscous and could not be mixed as well as the others at 5 and 15 wt.%, and so a small change in procedure was adopted. In order to compensate for the problem, the volume of the solution was reduced to 75 cm3 and the observation time was increased to 6 hours. The hydrate-forming gases were supplied from Medigas. The purities of methane, ethane and propane gases that were used in this study were 99.9, 99.0 and 99.5% (by volume), respectively. Polyethylene oxide with an average molecular weight of 100 000, supplied from Aldrich, was used in all the experiments. CALCULATION
OF THE INCIPIENT
HYDRATE
FORMATION
PRESSURE
A method for the calculation of the incipient equilibrium hydrate formation conditions in a hydrocarbon-water-polymer system has been presented by Englezos (1992). The method is entirely predictive. No adjustable parameters are required to compute the incipient equilibrium hydrate formation pressure at a given temperature. In the present work, that method was used to calculate the hydrate formation pressure at each experimental temperature. This enabled us to compare the predictions with the experimental data and test the validity of the predictive method. The incipient
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
278
equilibrium hydrate formation pressure, P, at a given temperature, computed by solving the non-linear equation A vMT-LO w
’ - t
RT
vi ln( 1 + 2
i=l
C,yj(py P ) + 11/(T) - In a, = 0
j=l
T, is
(1)
where the function, t,b(T) is easily derived from an equation that gives the difference in the chemical potential of water from that of the empty hydrate lattice (Holder et al., 1980). An analytical expression for this function is given below. G(T)
=
$!f$ +$
(To - T) +
cAcz~ BTo) In($)
Ah;-ACO,P+@‘)’ +
R
1
The values for the physical and thermodynamic parameters of the hydrate which are required in eqns. (1) and (2) are given in Table 1. In eqn. (l), C, are the Langmuir constants which at a given temperature are computed by a correlation proposed by Parrish and Prausnitz (1972). The Trebble-Bishnoi equation of state (Trebble and Bishnoi, 1988) is used for the calculation of the fugacity coefficients, 4jy in the vapor (V) phase. The hydrate equilibria prediction method requires the calculation of the activity of water, G, in aqueous polymer solutions. The calculation of cr, is based on the UNIFAC group contribution method (Oishi and Prausnitz, 1978; Rasmussen and Rasmussen, 1989). Three contributions are taken into account for the calculation of the activity of water as follows: TABLE 1 Physical and thermodynamic Property
P AC; Ahho, A& A yMT-Lo w
“I “2
To
reference properties for gas hydrates
Value Structure I
Structure II
0.141 J mol-’ K-* -38.13 J mol-’ K-’ -4860.0 J mol-’ 1264.0 J mol-’ 4.6 x 10m6m3 mol-’ l/23 3123 273.15 K
0.141 J mol-’ K-* -38.13 J mol-’ K-’ - 5203.5 J mol-’ 883 J mol-’ 5.0 x 10d6 m3 mol-’ 2117 l/17 273.15 K
P. Englezos and Y.T. Ngan / Fluid Phase Equilibria 92 (1994) 271-288
279
‘%v =
(31
‘&ombinatorial
+
&&dual
+
@-free volume
The combinatorial term attempts to describe the dominant entropic contribution. It is determined by the composition, size and shape of the molecules. The residual term is due primarily to the intermolecular forces that are responsible for the enthalpy of mixing. Because we are dealing with a polymer-solvent system with large size differences between the polymer and water molecules, free-volume effects are important and are included in the equation. RESULTS AND DISCUSSION
Prior to the experiments with aqueous polymer solutions, experiments with pure methane and pure ethane in water were conducted in order to establish the validity of the measurements. In these experiments the incipient equilibrium hydrate formation pressures were measured. The results for methane hydrate are reported in Table 2. These data and the data from TABLE 2 Incipient equilibrium (PEO) solutions Temperature (R) 214.3 278.25 281.55 285.15 274.65 276.05 278.15 280.75 283.15 285.30 273.55 275.65 277.65 279.65 281.95 273.95 276.05 278.4 280.65 282.85 285.15
data on methane hydrate formation
PEO concentration (wt.%) 0 0 0 0
5.00 5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00 25.00
in aqueous polyethylene
Experimental (MPa) 2.976 4.251 6.101 9.101 3.101 3.541 4.501 5.951 7.451 9.341 2.791 3.341 4.251 5.301 6.801 3.356 3.901 5.176 6.326 7.951 9.961
pressure
oxide
P. Englezos and Y. T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
280
273
276
277
279
261
Temperature
Fig. 3. Experimental solutions.
263
266
267
(K)
data and predicted methane hydrate formation
pressures in aqueous
Roo et al. (1983) are shown in Fig. 3 together with the incipient equilibrium hydrate formation pressures calculated at the experimental temperatures. The predictions are shown as a solid line. It is seen that there is good agreement among the data. There is also good agreement between the predicted values and the experimentally measured incipient hydrate formation pressures. The incipient hydrate formation data for ethane in pure water are reported in Table 4. These data together with other data from the literature and the predicted values are shown in Fig. 4 and indicate good agreement between the data from different sources and the predictions. Propane hydrate formation data in pure water were collected using the low pressure cell. These data were compared with others from the literature and with the predictions, and were found to be in good agreement (Englezos and Ngan, 1993). Finally, it is noted that measurements at a particular temperature TABLE 3 Comparison of the incipient equilibrium methane hydrate formation water, methanol, sodium chloride, and polyethylene oxide solutions Temperature (R)
275.41 275.87 275.87 275.87 275.87
conditions
in pure
Pressure (MPa)
Aqueous phase concentration (wt.%)
Experimental
Calculated
(0) (0) NaCl (10) CH,OH (10) PEO (10)
3.34a 5.63C -
3.17b 3.32b 5.30b 5.54d 3.37”
a Roo et al. (1983). b Englezos and Bishnoi (1988). c Ng and Robinson (1983). d Englezos et al. (1991). ’ Englezos ( 1992).
281
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
TABLE 4 Incipient equilibrium (PEO) solutions
data on ethane hydrate formation
PEO concentration (wt.%)
Temperature (K)
Experimental (MPa)
0 0
274.8 278.8 281.8 275.0 277.6 279.1 281.1 282.9 274.85 276.65 278.85 280.75 282.65 275.45 277.25 278.95 281.05 282.75
in aqueous
polyethylene
pressure
0.576 0.951 1.386 0.591 0.826 1.001 1.291 1.636 0.601 0.751 1.011 1.261 1.651 0.661 0.851 1.031 1.326 1.696
0
5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00
were easily reproducible. On the basis of these observations it cluded that the apparatus was able to provide reproducible data in agreement with data from other laboratories. All the experimental data for aqueous polymer solutions are Tables 2, 4 and 5. The results for methane at 5 and 25 wt.% are 1.8- .
n
1.6-
0 Hohier&Hmd,l982
0.44 274
oxide
was conthat were shown in shown in
Eagkms&Bishnoi.1991
1
n
276
278 Temperature
Fig. 4. Experimental solutions.
1 . 280
1
1
282
284
(K)
data and predicted ethane hydrate formation
pressures in aqueous
282
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
TABLE 5 Incipient experimental (PEO) solutions
data on propane hydrate formation
in aqueous polyethylene
Temperature (IQ
PEO concentration (wt.%)
Experimental (MPa)
273.6 273.85 274.7 275.45 276.1 277.05 277.75 278.2 273.55 274.5 275.25 275.9 276.75 277.55 277.9 273.6 274.45 275.1 275.8 276.45 277.1
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00 25.00 25.00 25.00 25.00 25.00 25.00
0.187 0.198 0.239 0.281 0.323 0.399 0.470 0.531 0.200 0.245 0.284 0.329 0.405 0.474 0.522 0.230 0.270 0.314 0.371 0.444 0.522
oxide
pressure
Fig. 5. It is seen from the figure that the polymer is a hydrate inhibitor. Its action, however, is weak. The inhibiting action of polyethylene oxide was compared with that of sodium chloride and methanol. In Table 3, the incipient methane hydrate formation pressures in pure water and in 10 wt.% methanol, sodium chloride, and polyethylene oxide solutions are shown for comparison purposes. Methanol and sodium chloride alter the hydrate formation conditions significantly. The effect of the polymer, however, is small. The hydrate formation pressure is only 0.05 MPa higher than that in pure water. Therefore the inhibiting action of polyethylene oxide is weak compared with the action of electrolytes or alcohols at the same weight percent concentration. Although the polymer reduces the activity of water, this reduction is not significant enough to cause a strong increase in the required pressure for hydrate formation at a given temperature. In Fig. 6, the calculated activity of water in aqueous solutions of NaCl and polyethylene oxide is plotted versus concentration. The electrolyte
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288 12.07
283
I 25wt%
-
9.5 T 5wt% t zl 2 t b
o 0
D 4.5 7.0! 2.0-1 273
* /
-
-
.
275
277
Predictions
8 . . 279
Temperature
. . . 1
281
283
285
(K)
Fig. 5. Experimental data and predicted methane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
Fig. 6. Activity of water in sodium chloride and in polyethylene oxide solutions.
reduces the activity of water substantially compared with the small reduction caused by the polymer. Electrolytes are known to alter the thermodynamic state of the liquid water phase whereas the polymer changes the viscosity of the solution substantially but not the activity of water. The accuracy of these calculations on the activity of water was tested previously and was found to be very good (Englezos and Bishnoi, 1988; Englezos, 1992). In Fig. 5, the continuous lines represent the predicted hydrate formation pressures based on the method of Englezos (1992). The maximum percentage deviation between data and predictions at 5 wt.% was found to be 8.8. At 25 wt.%, the maximum percentage deviation is 13.9. As seen in Fig. 3, the calculated incipient equilibrium hydrate formation pressures in pure water are consistently smaller than the data. In polymer solutions the trend is the same, but the deviations are larger in magnitude. Because gas hydrate phase equilibria depend on many factors (Sloan, 1990a; 1990b), such deviations between data and purely predicted (non-fitted) values are reason-
284
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
.
0.44 274
-
.
276
.
.
u
1
270
260
262
264
Temperature
(K)
Fig. 7. Experimental data and predicted ethane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
able. Finally, it is noted that the maximum deviation between data at 15 wt.% and predicted values was found to be 8.1%. In Fig. 7, the results for ethane hydrate formed in 5 and 25 wt.% polyethylene oxide solutions are shown. The weak inhibiting effect of polyethylene oxide is also noticed. The predictions and the data agree very well. The maximum deviations between data given in Table 4 and calculated values at 5, 15 and 25 wt.% are 2.0, 3.6 and 5.4%, respectively. The results for propane hydrate formation in polyethylene oxide solutions of 5 and 25 wt.% are shown in Fig. 8. Again, the weak inhibiting effect of the polymer is evident. The calculated hydrate formation pressures are in good agreement with the measured values given in Table 5. The maximum deviation between data and predictions in Fig. 8 was found to be 6.3%. The water-soluble polymer (polyethylene oxide) that was investigated in this work was found to have a weak inhibiting effect on the equilibrium
-
Oil ‘273
Predictions
274
275
276
Temperature
277
276
279
(K)
Fig. 8. Experimental data and predicted propane hydrate formation polyethylene oxide (PEO) solutions.
pressures in aqueous
P. Englezos and Y.T. Ngan / Fluid Phase Equilibria 92 (1994) 271-288
285
natural gas hydrate formation conditions. Therefore, it cannot be used as an effective thermodynamic inhibitor. Water-soluble polymers, however, alter the viscosity of the solution significantly (Bailey and Koleske, 1976). This may affect the nucleation conditions of the hydrate crystals, but such studies are not available in the open literature. CONCLUSIONS
Equilibrium hydrate formation data for pure methane, ethane and propane in aqueous polyethylene oxide solutions were collected and reported for the first time. Aqueous solutions of 5, 15 and 25 wt.% were used. The temperature range of the experiments was 273.55-285.3 K. The pressure range was 0.187-9.961 MPa. Compared with methanol and sodium chloride, the polyethylene oxide was found to be a weak inhibitor. The experimental data were compared with the predictions using the method of Englezos (1992) and were found to be in good agreement. LIST OF SYMBOLS
C
G h Nh P R T V Y
Langmuir constant (MPa-‘) heat capacity (J mol-’ K-r) enthalpy (J mol-‘) number of hydrate-forming components pressure (MPa) universal gas constant (J mol-’ K-l) temperature (K) volume (m’) mole fraction in vapor phase
Greek letters 2 CL z II/
activity of water difference chemical potential number of cavities of type i fugacity coefficient temperature function in eqn. (1)
Subscripts i j W
index ( 1,2) index ( 1, . . . , Nh) water
P. Englezos and Y.T. Ngan 1 Fluid Phase Equilibria 92 (1994) 271-288
286
Superscripts
LO MT V 0
pure liquid water empty hydrate vapor reference conditions at 273.15 K and zero absolute pressure
ACKNOWLEDGMENTS
The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Gas Processors Association (CGPA) is greatly appreciated.
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