Environ. Sci. Technol. 2002, 36, 5192-5198
Thermodynamics of Carbon Dioxide Hydrate Formation in Media with Broad Pore-Size Distributions D U A N E H . S M I T H , †,‡ J O S E P H W . W I L D E R , * ,† A N D KAL SESHADRI§ U.S. Department of Energy, National Energy Technology Laboratory, Morgantown, West Virginia 26507-0880, Department of Physics, West Virginia University, Morgantown, West Virginia 26506, and Parsons Infrastructure and Technology Group, Morgantown, West Virginia 26505
Equilibrium pressures for the dissociation of carbon dioxide hydrates confined in silica gel pores of nominal radii 7.5, 5.0, and 3.0 nm were measured over a wide temperature range and were observed to be higher than those for bulk carbon dioxide hydrate. Models that have been previously reported in the literature are used to determine the pore radius involved in each equilibrium associated with these data, exactly reproducing the experimental equilibrium pressure. Based on these models, pore volume distributions are reconstructed and compared to those obtained from nitrogen desorption isotherms. This comparison indicates that in the nominal 7.5 nm pores the hydrate formed nearly uniformly in the available pores, while in the nominal 5.0 and 3.0 nm pores it did not.
Introduction With a reported potential to induce global warming on the order of 2-5 K over the next century (1), carbon dioxide is believed to have the potential to play an important role in greenhouse effects. As a result of this potential, the build up of carbon dioxide in the atmosphere due to anthropogenic emissions has become of great scientific and popular interest. These concerns have led various researchers to suggest the sequestration of carbon dioxide to remove it from the atmosphere. One set of potential sequestration scenarios involves the injection of carbon dioxide into the earth’s oceans. A potential drawback to these scenarios results from the solubility of carbon dioxide in water. Under normal conditions the level of carbon dioxide dissolved in seawater is well below its saturation point. Therefore, any carbon dioxide injected into the ocean (or some other aquifer) would dissolve in the water over time, with unknown ecological effects. This potential dissolution of carbon dioxide could be reduced or at least made to take place over a longer time frame if the carbon dioxide were injected into porous media where the fluid flow was restricted. The dissolution might be further retarded if the carbon dioxide was injected into the porous media under conditions such that carbon dioxide hydrates were stable. * Corresponding author phone: (304)293-2011 ext 2344; e-mail:
[email protected]. Permanent address: Department of Mathematics, P.O. Box 6310, West Virginia University, Morgantown, WV 26506-6310. † U.S. Department of Energy. ‡ West Virginia University. § Parsons Infrastructure and Technology Group. 5192
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Gas hydrates are crystalline structures belonging to a group of solids known as clathrates. Their structures involve a lattice made up of hydrogen-bonded water molecules containing cavities that can be occupied by gas molecules. These cavities are larger than those in crystalline ice, and it is only the occupation of a significant fraction of these cavities that prevents the structure from collapsing due to its own attractive forces. To achieve the necessary fractional occupancy of these cavities, the formation of gas hydrates requires low temperature-high-pressure conditions and can occur both above and below the freezing point of water. Salts present in seawater shift the formation conditions to either higher pressures or lower temperatures compared to its formation in pure water. In seawater, carbon dioxide hydrates form at pressures higher than 4.5 Mpa and temperatures lower than 283.4 K (2). As a result, carbon dioxide hydrates can form in the ocean at depths of 400 m or more (3). Even under these high pressure/low temperature conditions, carbon dioxide hydrates are only stable when in equilibrium with water that is either saturated or supersaturated with dissolved carbon dioxide (4). Since bulk seawater does not contain a sufficient concentration of dissolved carbon dioxide to stabilize the hydrate (4), hydrates involving carbon dioxide will not remain indefinitely and will dissociate into free carbon dioxide and water. The time scale over which this takes place will depend on the ambient conditions as well as the relative magnitude of the fluid flow in the vicinity of the hydrate. In sediments below the ocean floor (where the fluid flow is restricted), it has been suggested (5) that the dissociation of a portion of the hydrate present in the porous media might be able to raise the local concentration of carbon dioxide to a level capable of stabilizing the remaining hydrate. This scenario depends on the fluid flow though the region where the hydrate is sequestered being slow enough to be considered essentially zero. In such a region, where groundwater flows extremely slowly, carbon dioxide hydrates might act as plugs in the gaps and pores in the surrounding rock and/or sediment (5). This could result in the surrounding water being almost saturated with carbon dioxide, thereby stabilizing the hydrate and retarding its dissolution even more. Answers to questions of this type are potentially important for understanding the formation of subseafloor natural hydrates as well as potential engineering applications in which carbon dioxide containing gases would be injected to enhance the production of hydrocarbon gases and/or sequestration of carbon dioxide. While a large amount of experimental data are available concerning hydrate formation under bulk conditions, only a very few studies have addressed hydrate formation in porous media. Handa and Stupin (6) report equilibrium pressuretemperature data for both methane and propane hydrates in 7.5 nm nominal radius silica gel pores. Henry et al. (7) and Clarke et al. (8) separately presented calculations based on earlier statistical thermodynamic models. These two studies were aimed at explaining the observed differences between the equilibrium pressures observed in the bulk and those in the porous media used by Handa and Stupin (6). Both studies were unable to accurately reproduce the observed equilibrium pressures in the porous media. Experimental data for propane (9) and methane (10) hydrates in pores with 3, 5, and 7.5 nm nominal radii silica gel pores have recently been presented. In other work (10-12) the present authors addressed the discrepancy between the observed and predicted equilibrium pressures for these hydrates in silica gel pores by accounting for the effects of the pore size distribution. In these works the predicted equilibrium 10.1021/es015862u CCC: $22.00
2002 American Chemical Society Published on Web 10/26/2002
pressures were exactly matched to the experimental pressures by treating the effective pore radius as a fitting parameter. The interpretations of these experimental data were based on a new conceptual model of hydrate dissociation in porous media and were used to reconstruct pore-volume distributions in the porous media. Comparison of pore-size distributions based on hydrate equilibrium data and those obtained from nitrogen desorption studies suggested that the model can be used to interpret hydrate equilibrium data obtained for porous media with radii in the nanometer scale, which may be relevant to hydrate formation in certain sediments. The pore sizes for certain clays under sedimentary conditions are on the order of several nanometers (13). In addition, the work of Clennell et al. (14) reports that the analysis of hydrate containing sediment samples from Leg 164 of the Blake Outer Ridge contained pore diameters that ranged from a few nanometers to a few microns. The purpose of our work is to address the effects of pore size on carbon dioxide hydrate equilibrium conditions. By performing experiments in the pore size range where this effect can be seen, we hope to be able to form a basis for deciding if pore size needs to be addressed in carbon dioxide sequestration scenarios. It has been suggested that pore-size effects could be responsible for the observed shifts in bottom simulation reflectors observed in some naturally occurring hydrate deposits. The results we present represent a first step toward data for carbon dioxide that address the importance of pore size on the equilibrium of this hydrate. In this paper we present both experimental results and theoretical calculations for carbon dioxide hydrate formation in silica gel pores with nominal 3, 5, or 7.5 nm radii. The presented data are for a range of pore sizes, all of which involve capillary effects that strongly affect the equilibrium pressure. As discussed above, these data should help to delineate the effects of pore size on carbon dioxide hydrate dissociation and aid in the assessment of the role of their effects on the potential sequestration of carbon dioxide below the ocean floor or in other deep aquifers.
Experimental Methods Carbon dioxide with minimum purity of 99.9 mol % was obtained from Matheson. The pore size distribution and pore volume of each of the silica gel samples used in the experiments have been reported on previously (9, 10). A high-pressure cell about 30 mL in volume constructed using stainless steel tubing of 1 in. o.d. (0.091 in. wall thickness) and 1 in. to 0.25 in. Swagelock reducers was used. One of the reducers was fitted with 0.125 in. tubing and a Swagelock fitting to connect a transducer to the cell. The silica gel samples, without any further treatment, were placed in a desiccator containing degassed, distilled water for a period of 4-6 days to prepare silica gel with sorbed water. In all of the experiments reported here, the uptake of water per gram of silica gel corresponded to the total pore volume reported by the manufacturer. The cell was loaded with about 140 5-mm-diameter glass beads, and a slurry consisting of liquid nitrogen and silica gel containing pore water was poured over the glass beads, coating them with the silica gel. The sealed cell was then connected to a vacuum manifold and cooled in liquid nitrogen. The cell was evacuated to about 50 milliTorr and held at that pressure for 30 min to remove air from the cell. The cell was transferred to a temperaturecontrolled chiller (Neslab Model RTE 140) and then connected to the carbon dioxide cylinder and the transducer. The bath temperature was read with a Hart Scientific model 1006 MicroTherm thermometer with a sensitivity of 0.001 K. The bath temperature was stable to within 0.05 K. The pressure measurements were made with a 20.78 MPa full scale transducer (Setra Model 204) which was calibrated by the dead weight method. The accuracy of the transducer was
TABLE 1. Experimentally Measured Equilibrium Pressures for Carbon Dioxide Hydrate in Nominal 3.0, 5.0, or 7.5 nm Silica Gel Poresa 3.0 nm T (K)
P(MPa)
reff (nm)
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276
0.599 0.628 0.675 0.705 0.724 0.749 0.788 0.836 0.892 0.934 0.990 1.101 1.201 1.291 1.388 1.495 1.618
2.08 2.17 2.23 2.34 2.49 2.65 2.79 2.93 3.06 3.26 3.46 3.48 3.59 3.77 3.96 4.18 4.39
5.0 nm P(MPa)
reff (nm)
0.707 0.765 0.804 0.877 0.943 1.004 1.086 1.177 1.292 1.401 1.536 1.666 1.837 2.028 2.229 2.455 2.685
3.52 3.66 3.94 4.06 4.28 4.59 4.83 5.08 5.26 5.57 5.82 6.22 6.48 6.78 7.20 7.67 8.38
7.5 nm P(MPa)
reff (nm)
0.708 0.778 0.851 0.885 0.94 0.997 1.069 1.138 1.278 1.375 1.499 1.609 1.739
6.99 7.68 8.40 8.74 9.28 9.84 10.55 11.24 12.62 13.58 14.80 15.88 17.16
a Also given are the corresponding effective radii (r ) calculated eff using eq 1.
0.006 MPa. The hydrate was prepared by charging the cell with carbon dioxide gas at a pressure much higher than the expected equilibrium pressure in order to accelerate the rate of hydrate formation. As hydrate formed and the pressure in the cell dropped, additional gas was added to the cell. This process was repeated until no pressure change was observed over a period of 6-12 h. The details of the preparation of the hydrates and the subsequent determination of the equilibrium pressure-temperature profiles for their dissociation are reported elsewhere (9) and were similar to that used previously (9) by the present authors for silica gels with nominal 3.0, 5.0, or 7.5 nm pores. In this work we report equilibrium pressure-temperature data for the dissociation of carbon dioxide hydrates in silica gels with nominal pore radii of 3.0, 5.0, or 7.5 nm.
Results and Discussion Hydrate Equilibrium Data. Equilibrium pressures were obtained for the dissociation of carbon dioxide hydrate in silica gel with nominal 3, 5, or 7.5 nm radius pores at various temperatures. The equilibrium pressure-temperature data for the silica gel samples (corrected for the vapor pressure of water) are given in Table 1 and are shown graphically in Figure 1. Included in Figure 1 are the experimentally measured data for bulk carbon dioxide hydrate (taken from ref 2, pp 331-336). Figure 1 shows that the relative increase in the dissociation pressures reported in this work for pore hydrate as compared to that for bulk hydrate varied with the pore size. Correct interpretation of the experimental results for hydrate dissociation in porous media containing a broad distribution of pore sizes requires the use of statisticalthermodynamic calculations. As discussed in a recent work (12), the equilibrium pressure measured at a specific temperature in a porous medium as the result of a series of hydrate decomposition experiments depends on the sample size, the volume of the free space in the reaction cell, the temperature at which the experiments are started, and the amount of hydrate allowed to dissociate to establish equiVOL. 36, NO. 23, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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aqueous phase of the reference state, ηi is the number of cavities of type i in the hydrate lattice, and Yi denotes the probability of a cavity of type i being occupied by the guest molecule and is given in terms of the fugacity of the hydrate guest in the gaseous state (fi) and the Langmuir adsorption constant (Ci) by
Yi )
FIGURE 1. Experimentally measured equilibrium pressures for carbon dioxide hydrate in silica gels of nominal pore radii 3 (9), 5 (b), or 7.5 ([) nm. Also shown are results (2) for bulk hydrate formation (×).
TABLE 2. System Parameters for Carbon Dioxide Hydrate Decomposition in Silica Gels Having the Indicated Nominal Pore Radii (g)a
sample size free space vol (cm3)
3.0 nm
5.0 nm
7.5 nm
7.3756 27.3
8.0714 23.5
6.8589 26.0
Cifi . ∆H W ) ∆H 0W + 1 + Cifi
librium at the initial temperature. In addition, the porevolume distribution of the porous medium (not the nominal pore radius) and the percent conversion of pore-water to hydrate also affect the measured equilibrium pressures (12). As a result, measured equilibrium pressures at a specific temperature for identical media can be significantly different, while those for different media may be superposed (12). These seeming inconsistencies can be resolved by applying a previously developed model (10, 11) to interpret the data. The sample sizes and the volumes of the free space in the reaction cell are given in Table 2 for the measurements reported in this work. The temperatures at which the experiments were started are given in Table 1. Only a negligible amount of hydrate was allowed to dissociate prior to the first equilibrium measurement, and the percent conversions of water to hydrate are discussed later in the text. The pore-volume distributions of the media used here are reported elsewhere (10). The Thermodynamic Model. The models used here have been developed in detail elsewhere (10, 11). A single equation involving Tf and Pf (the temperature and pressure under which the hydrate forms) can be given for hydrate formation in a porous medium in the following form (7, 8, 10, 11):
∆µ0W
-
∫
Tf
T0
RT0
∆H w dT + RT2
∑ i
∆Vw dP - ln(γwXw) + RTf 2cos(θ)σhw ) 0 (1) ηiln(1 - Yi) + VL r
∫
Pf
0
In eq 1, Tf and Pf are the temperature and pressure at which the hydrate forms, T0 is the temperature of the standard reference state (T ) 273.15 K, P ) 0), ∆µ0W is the chemical potential difference between the empty hydrate lattice and 5194
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T
T0
∆Cp(T′)dT′
where ∆H 0W is a reference enthalpy difference between the empty hydrate lattice and the aqueous phase at the reference temperature, ∆Cp(T′) ) ∆C0p + b(T′ - T0), where ∆C0p is the reference heat capacity difference, and b is an experimentally determined constant. ∆VW, the volume difference between the empty hydrate and solid or liquid water (at T0), is assumed constant (but different for the two phases), VL is the molar volume of water in the aqueous state, θ is the wetting angle between the pure water phase and the hydrate, σhw is the surface tension between the aqueous and hydrate phases, and r is the (actual) radius of the pore. The fourth term on the left-hand side of eq 1 is used to model the affect of the solubility of the hydrate former on the activity (γwXw) of water. The Soave-Redlich-Kwong equation of state (2) was used to calculate the fugacity (f) of the gas and along with the gas solubility can be used to calculate Xw, the mole fraction of water in the water-rich phase (2)
f
Xw ) 1 - Xg ) 1 -
hw exp
a
Mass of silca gel plus sorbed water (the porous media were completely saturated with water prior to hydrate formation).
∫
PV h RT
( )
(2)
where the Henry’s law constant hw is given by (2)
ln(hw) ) - (hw(0)/R + hw(1)/RT + hw(2)ln(T)/R + hw(3)T/R), (3) with the values for the parameters in eq 3 being taken from Table 5.3 of ref 2. The temperature dependence of the Langmuir constants may be modeled in several different manners, all of which are based on the use of bulk hydrate equilibrium data to determine the best fits for the model parameters for each hydrate. In this work the temperature dependence of the Langmuir constants is accounted for by using the form presented by Munck et al. (15), Ci ) Ai/T exp(Bi/T), where Ai and Bi are experimentally fit parameters and are dependent on which guest molecule is present. See ref 11 for the details of the application of this equation to finding the formation pressure given the formation temperature and pore size. The estimation of the parameters used to model the Langmuir adsorption constants as well as the enthalpy and chemical potential differences for the reference state are critical to the accurate prediction of hydrate equilibrium pressures. For a broad range of hydrate-forming gases (including hydrocarbons such as methane and propane), a single set of values of ∆H 0W and ∆µ0W allows for the determination of the parameters needed to calculate the Langmuir adsorption constants for the various hydrate guests. The hydrate equilibrium pressures predicted on the basis of these parameters are, in general, sufficiently accurate for most applications. In the case of carbon dioxide, however, use of this same set of ∆H 0W and ∆µ0W results in relatively high errors in the prediction of the equilibrium pressure at low temperatures. For example, Figure 2 shows experimental bulk carbon dioxide hydrate equilibrium pressures (open circles; from pp 331-336 of ref 2) as well as predictions (open triangles) obtained using the program CSMHYD that accompanies ref 2. As can be seen in Figure 2, the error in the
FIGURE 2. Comparison of predictions using the standard values of ∆H 0W and ∆µ0W(4), predictions (this work) using a modified set of parameters (b), and experimental data (2) for bulk carbon dioxide hydrate (O).
TABLE 3. Parameter Values for Carbon Dioxide Hydrate Formation property
unit
bulk value
∆µW0 (∆H 0W)ice (∆H 0W)liq ∆Cp0
J/mol J/mol J/mol J/mol‚K
∆Vw σhw b
m3/mol J/m2 J/mol‚K2
Ai
K/MPa
Bi
K
1380.8 130011 -471111 -34.58311 T>T0 3.31511 TT0 0.12111 T
