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Modeling Clathrate Hydrate Formation dwhg C a h n Dioxide Injection into the Ocean G E R A L D D. HOLDER,’ ANTHONY V . C U G I N I , A N D ROBERT P . W A R Z I N S K I * US.Department of Energy, Pittsburgh Energy Technology Center, Pittsburgh, Pennsylvania 15236
Because of carbon dioxide’spotential role in global warming, there is considerable interest in methods of long-term sequestering of anthropogenic emissions of COz outside of the atmosphere. Such long-term storage of large quantities of COz has been proposed, but the feasibility of large land and ocean disposal options remains to be established (1). For ocean disposal, the effectiveness of C 0 2 sequestration depends on the relative amount released into the ocean, the depth of injection, and the chemical and physical behavior of COz in this environment. Predicting the actual fate of liquid COZinjected into the ocean at depths greater than 500 m is complicated by uncertainties associated with the physical behavior of COz under these conditions, primarily the formation of the icelike COz clathrate hydrate. Most attempts to model the injection process assume that rising COz droplets simply dissolve and do not take into account hydrate formation (2-4).
Pure COz hydrate is more dense than seawater and should sink if it forms upon injection of liquid Con. Apart from any adverse ecological effects, this would be viewed as a benefit since it could result in very long COz residence times in the ocean. However, rather than rapidly converting to pure hydrates, liquid COz droplets may form a thin, diffusion-limiting hydrate surface layer shortly after injection. Such phenomena have been experimentally observed for methane (5)and trichlorofluoromethane ( R l l ) in flowing seawater (6),for liquid COz in still water (7), and for COzrich globules collected at a natural ocean hydrothermal vent (8). The work reported here predicts the effect of hydrate formation on the fate of COZ droplets discharged into the ocean under hydrate-forming conditions. New information on hydrate growth rates recently determined by one of the authors is incorporated into the model.
Predicting the Fate of Hydrate-Forming Droplets One of the main uncertainties associated with hydrate formation under deep-ocean conditions is how fast the hydrates grow after nucleation. One of the authors (9)has recently measured the rate of growth for methane hydrate as it formed from a thin layer of melting ice in contact with flowing methane gas. The maximum linear growth rate observed was 0.02 cm of hydrate per hour of growth; Le., in 1 h the hydrate would get 0.02 cm thicker. In similar work (unpublished), the growth rate of C02 hydrate was * E-mail address:
[email protected].
Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261. +
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also measured and found to be slightlyfaster than methane hydrate. Under the conditions expected below 500 m in the ocean, the growth rate would likely be faster in a water/ liquid COZ system owing to more intimate contact provided by liquid rather than gaseous COZ. Here we use a growth rate of 0.04 cm/h. A rising, hydrate-coated particle would likely crack owing to expansion of the liquid COZ core as the pressure decreased. This has been observed for methane bubbles (5).We assume cracking of the shell would facilitate continued interaction of seawater and COz, thus permittingthe growth rate to be sustained at aconstant value. By this mechanism, the hydrate layer would expand, increasing the size of the particle. The buoyancy of a hydrate-forming COz droplet would depend upon the combined average density of the unconverted liquid COz and the hydrate film.For the liquid COz, density values as a function of pressure and temperature were obtained from the literature (10). The density of the COz hydrate depends upon its composition. If COz filled all of the available interstitial cages in the hydrate structure, the hydrate number (mol/mol of COz)would be 5.75, and its theoretical density would be 1.121 g/cm3. However, hydrates are not stoichiometric compounds, and hydrate numbers between 6 and 8 have been reported (2). Reported densities calculated by different methods range from 1.11to 1.13g/cm3(11). Forourpurposes,the hydrate number is taken as 7 , and the density of the hydrate is assumed to be 1.12 g/cm3. It is interesting to note that separate experimental accounts report that COz hydrate floated on the surface of water or seawater (12,13). We have observed the formation of COz hydrates in water in a high-pressure, variable-volume view cell (unpublished). The hydrates initially appeared snow-like and tended to float on the water surface. After several cycles of decomposition and formation and an equilibration period of 16 h, the hydrates changed to a transparent, ice-like appearance and tended to sink. Trapped, unconverted COZ may have caused the bulk density of the initially formed hydrates to be less than that of water. With time, this trapped COZ could be converted to hydrate, causing the density to increase and the appearance to change. Further experimental work is needed to quantify the change in bulk density of COz hydrates due to the effects of temperature, pressure, and time. The combined density of the hydrate-forming liquid COz particle is a weighted average of the densities of the liquid COZ and the solid hydrate. The equation which gives ep, the particle density is
where ec and @h are the liquid COz and hydrate densities, respectively, n is the hydrate number, and xh is the mass fraction of carbon dioxide converted to hydrate. The density of the particle is independent of particle shape or size. The particle will still sink if its density is greater than that of seawater, even if the hydrates grow in irregular form. To estimate the rise velocity of the hydrate-forming COO droplet, we used the model proposed by Herzog et al. for
0013-936X/95/0929-0276$09.00/0
@ 1994 American Chemical Society
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1500
1000
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0 400
0.0
FIGURE 1. Fate of hydrate-forming COZ droplets injected at various depths. Initial droplet diameters of 0.25, 0.50, 1.00, and 1.50 cm correspondto symbol size. Shallowest depth correspondsto minimum depth required to cause particle to sink at 500 m depth.
solid particles (2). Assuming a drag coefficient of 1,the rise velocity, u,is given by
u = [8gr(e, - ep)/(3ep)1”2
(2)
where r is the radius of the particle, andgis the gravitational constant. Since the particle radius and density are constantly increasing as hydrates form, the rise velocity will change during the course of hydrate formation. Based upon the above assumptions, the fate of hydrateforming C02 droplets as a function of size and injection depth were calculated. Figure 1depicts the vertical distance such droplets rise before sufficient hydrate is formed to make the particle more dense than the surrounding seawater. The time it takes to traverse this distance for four different size particles released at depths from 500 to 2000 m is also shown. Liquid C02 is more compressible than seawater; thus, at the greater depths, the density of the injected liquid C02 approaches that of the surrounding seawater and the distance the hydrate-formingdroplet rises before beginning to sink is less than that for the same size droplet injected at shallower depths. As the injected droplet size increases, greater vertical distances are traversed owing to the dominating effect of the buoyancy of the liquid C02. Rise times on the order of several hours are predicted for the larger droplets. Only for the smaller droplet sizes can sufIicienthydrate form to limit the vertical rise of the particle and permit shallower injection depths to be utilized. For each size droplet in Figure 1,the shallowest injection depth shown is the depth from which the hydrate-forming droplet would just begin to sink at 500 m. We do not attempt to predict the behavior of the hydrate-coated C02 droplets above 500 m owing to the fact that near this depth the liquid C02 remaining in the droplet would vaporize, destroying the hydrate-coated particle. The hydrate itself would probably not be stable above this same depth. As noted above, the results in Figure 1 were calculated using a constant hydrate growth rate of 0.04 cmlh, twice that observed for hydrates forming from melting ice and methane or COz vapor. If actual growth rates are slower, even greater injection depths would be required. This is shown in Figure 2 along with data assuming that the COz dissolves into unsaturated seawater with no hydrate
0.5
1 .o
1.5
Initial Droplet Diameter, cm FIGURE 2. Injection depth required for hydrate-forming droplet to begin sinking at 500 m ocean depth at different hydrate growth rates. For comparison, the required injection depths for complete dissolution at 500 m in the absence of hydrate formation is also shown (2).
formation. The minimum injection depth for a rising hydrate-forming droplet to begin to sink at 500 m or for a nonhydrate-forming droplet to completely dissolve by the time it reaches this same depth is shown as a function of the initial droplet diameter. The need for much greater injection depths for droplets undergoing hydrate formation is apparent. For a droplet with an initial diameter of 1.0 cm, the added injection depth can be 900 m or more if a diffusion-limiting hydrate film forms that grows at the assumed rate. Shallower depths could be used if the actual rate of C02 hydrate growth is faster. At a growth rate of 0.80 cm/h, a hydrate-forming droplet will not rise more than a similar droplet undergoing simple dissolution.
Conclusion Disposal of anthropogenic emissions of C02 into the ocean may be required to mitigate rises in atmospheric levels of this greenhouse gas if other measures are ineffective and the worst global warming scenarios begin to occur. As one of the major unresolved technical issues involved with the deep-ocean disposal of CO2, hydrate formation warrants further experimental investigation. Clearly, hydrate film formation on COz droplets injected into the deep ocean will increase estimates of required injection depths and decrease the maximum allowable droplet size suitable for effective sequestration to occur. If not properly understood and controlled, hydrate formation can severely limit the dissolution process, permit COZ to rise to undesirable depths, and thus defeat the objectives of deep-ocean injection. Development of methods to either preclude this event or to rapidly form particles containing sufficient hydrate to sink in the ocean is necessary to establish the technical feasibility of deep-ocean disposal of COz.
Literature Cited (1) A Research Needs Assessment for the Capture, Utilization and
Disposal of Carbon Dioxide fromFossil Fuel-Fired Power Plants; DOE Report DOE/ER-30194;July 1993; available NTIS. (2) Herzog, H.; Golomb, D.; Zemba, S. Environ. Prog. 1991, 10, 64. (3) Liro, C. R.; Adams, E. E.; Herzog, H. G. Energy Convers. Manage. 1992, 33, 667.
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(4) Wilson, T. R. S. Energy Convers. Manage. 1992,33, 627. (5) Maini, B. B.; Bishnoi, P. R. Chem. Eng. Sci. 1981,36, 183. (6)Austvik, T.; Laken, K. P. Energy Convers. Manage. 1992,33,659. (7) Aya, I.; Yamane, K.; Yamada, N. Fundamentals ofphase Change: Freezing, Melting, and Sublimation;ASME: Fairtield, NJ, 1992; HTD Vol. 215,pp 17. (8) Sakai, H.;Gamo, T.; Kim, E.-% Tsutsumi, M.; Tanaka, T.; Ishibashi, J.; Wakita, H.; Yamano,M.; Oomori, T. Science 1990, 248,1093. (9)Holder, G. D.;Zele, S.; Enick, R.; LeBlond, C. Ann. N.Y. Acad. Sci. 1994,715,344. (10)Vargaftik,N. B. T a b b on the ThermophysicalProperties ofLiquids and Guses, 2nd ed.; Hemisphere Publishing, John Wiley & Sons: New York. 1975.
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(11)Wahakis, J. G.;Chen, H A ; Suwandi, M. S.; Barduhn, A. J. US. Department of Interior, Office of SalineWater Report INT-OSW72-830. U.S. Department of Interior, Washington, DC, available NTIS. (12)U n d , C. H.;Katz, D. L. Petroleum Transactions; AIME: N e w York, April 1949;p 83. (13)Masutani, S. M.;Kinoshita, C. M.; Nihous, G. C.; Ho, T.; Vega, L. A. Energy Convers. Manage. 1993,34,865.
Received for review August 4, 1994. Revised manuscript received October 19, 1994. Accepted October 27, 1994.
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