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COMMENTS Comments on “Anomalous Preservation of Pure Methane Hydrate at 1 atm” Joseph W. Wilder*,†,‡ and Duane H. Smith†,‡ National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia 26507-0880, and Departments of Mathematics and Physics, West Virginia UniVersity, Morgantown, West Virginia 26506. ReceiVed: April 18, 2001 In a recent paper,1 Stern et al. reported the observation of a temperature range over which methane hydrates decomposed at rates that were several orders of magnitude smaller than those observed at temperatures either above or below this range. These authors suggested that the hydrate in this region behaved as if it were a different material or in a different geochemical state.1 The results of Stern et al.1 are of considerable interest for the very difficult problem of the recovery of naturally occurring samples. Moreover, they have led us to consider how studies of the kinetics of hydrate decomposition [see chapter 3 of ref 2 and references therein] might take advantage of the work by Langmuir3-5 and others6-9 who have studied the theory of endothermic decomposition reactions. For experiments carried out at a constant (nonzero) pressure such as those of Stern et al.,1 the decomposition kinetics are strongly dependent on pressure. For such cases, the SmithTopley effect10-12 results in a variation of the reaction rate with pressure characterized by the presence of both a maximum and a minimum.10,11 This effect is often caused by large thermal gradients in the gas layer close to the interface due to the endothermic nature of the reaction.12 Work on the SmithTopley effect may be of direct relevance to the work of Stern et al., in which the large temperature differences1 (up to 30 K) between the sample and surroundings would certainly have resulted in steep thermal gradients in the gas near the hydrate sample. The work of Langmuir3-5 established an experimental method to remove the effects of factors such as those described above during the study of the endothermic dissociation of a solid compound to a solid and a gaseous product (e.g., decomposition of a clathrate hydrate to ice and free gas). The essential features of this method are that the experiments need to be carried out in a vacuum and that the sample temperature must be maintained at a constant system temperature. In this way, neither heat transfer nor gas-phase diffusion limits the reaction rate, and the maximum amount of information about the chemical step of the dissociation can be obtained. For these conditions, maximum possible rates can be predicted using equilibrium pressure data and the kinetic theory of gases.3,13,14 The validity of these predictions has been established6 by measurement of the * To whom correspondence should be addressed. E-mail: wilder@ math.wvu.edu. Permanent Address: Department of Mathematics, PO Box 6310, West Virginia University, Morgantown, West Virginia 26506-6310. † U.S. Department of Energy. ‡ West Virginia University.
decomposition rates of samples exposed to vacuum. These predictions were originally made by Langmuir3 as part of the first explicit formulation of the principle of microscopic reversibility. The Hertz-Knudsen-Langmuir (HKL) equation,3,7 which gives the rate (Jmax) of unretarded decomposition in a vacuum in moles per unit time per unit area, can be used to predict the maximum possible rate at which the dissociation can take place; this rate depends only on the temperature (T), the equilibrium gas pressure (Peq) at that temperature, and the molecular weight (M) of the gas and is given by Jmax(T) ) Peq(T)/x2πMRT. This maximum rate can only be achieved if the experimental conditions are such that the pressure of the gas has no effect on the decomposition rate (i.e., under vacuum) and if the formation of the solid product does not impede future decomposition. Beruto and Searcy concluded that the comparison of measured dissociation rates into vacuum with those predicted by the HKL equation gave information about the kinetics of the “chemical step” of the dissociation;7 another conclusion was that the ratio of these two rates was a useful parameter for correlating and predicting decomposition rates.7 The experiments suggested by Searcy and Beruto6 for the endothermic dissociation of calcite (CaCO3), if used to study hydrate dissociation, might give insight into the nature of the rate-limiting step in the dissociation of gas hydrates. In particular, Searcy and Beruto discussed a set of experiments to determine whether the rate-limiting step is the desorption of excited molecules, the catalyzed dissociation of molecules from active sites or particles, or some surface reaction of the dissociation process.6 Searcy and Beruto9 later extended their results to the case when both the product gas pressure and the thickness of the barrier formed by the solid product influenced the reaction rate. The rate equations that they presented were functions only of the activities of the reaction components, of measured rates of dissociation in a vacuum when the barrier is negligible, and of measurable transmission properties of the barrier. Similar to the work that has been done on hydrate decomposition, the work prior to that of Beruto and Searcy on (solid) calcite decomposition to (solid) calcium oxide and (gaseous) carbon dioxide did not involve decomposition into vacuum, and many of the experiments involved granular samples. Beruto and Searcy7 ascribed the large variance in reported apparent reaction orders for the decomposition7 to factors related to the experimental conditions that controlled the kinetics. Some of the factors suggested for calcite decomposition may also be relevant for hydrates. For example, Hills15,16 suggested that for “large” samples the observed decomposition rates may be controlled not by a chemical step at the interface but by the transfer of heat to the reaction boundary or by the transfer of gas away from it. In granular samples, it has been proposed that the transport of the generated gas to the outer surface might be inhibited such that a higher pressure could be maintained in the interior (pore space) of the sample,7 allowing the establishment of a local region of near equilibrium in the interior. A related factor suggested by Davidson et al.17 for gas hydrates is that the diffusion of the gas might be inhibited by a sheath of ice formed during the decomposition. Within either type of
10.1021/jp011450w CCC: $22.00 © 2002 American Chemical Society Published on Web 11/21/2001
Comments interior pore space (where the gas pressure could be close to the equilibrium pressure), the overall decomposition rate would be roughly proportional to the difference between the equilibrium and local pressures.7 Near the outer portion of the sample, more efficient escape of the gas into the surrounding system would result in a lower partial pressure and the rate of dissociation might be controlled by a solid state or surface reaction.7 We believe that future kinetic studies of gas hydrate decomposition can be made more effective by consideration of the large body of literature available on the kinetics of nonhydrate, endothermic dissociation reactions, only a small part of which has been discussed here. Acknowledgment. This work was completed while J.W.W. was a Senior Research Associate of the National Research Council and was funded by the Office of Fossil Energy, U.S. Department of Energy. References and Notes (1) Stern, L. A.; Circone, S.; Kirby, S. H.; Durham, W. B. J. Phys. Chem B 2001, 105, 1756.
J. Phys. Chem. B, Vol. 106, No. 1, 2002 227 (2) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: New York, 1997. (3) Langmuir, I. Phys. ReV. 1916, 8, 149. (4) Langmuir, I. J. Am. Chem. Soc. 1913, 35, 931. (5) Langmuir, I. J. Am. Chem. Soc. 1916, 38, 2263. (6) Searcy, A. W.; Beruto, D. J. Phys. Chem. 1974, 13, 1298. (7) Beruto, D.; Searcy, A. W. J. Chem. Soc., Faraday Trans. 1 1974, 70, 2145. (8) Searcy, A. W.; Beruto, D. J. Phys. Chem. 1976, 80, 425. (9) Searcy, A. W.; Beruto, D. J. Phys Chem. 1978, 82, 163. (10) Bertrand, G.; Lallemant, M.; Watelle, G. J. Inorg. Nucl. Chem. 1974, 36, 1303. (11) Bertrand, G.; Lallemant, M.; Watelle, G. J. Inorg. Nucl. Chem. 1978, 40, 819. (12) Bertrand, G.; Lallemant, M.; Mokhisse, A.; Watelle, G. Phys. Chem. Liq. 1977, 6, 215. (13) Paule, R. C.; Margrave, J. L. In The Characterization of High Temperature Vapors; Margrave, J. L., Ed.; Wiley: New York, 1967; Chapter 6. (14) Searcy, A. W. In Chemical and Mechanical BehaVior of Inorganic Materials; Searcy, A. W., Ragone, D. V., Colombo, U., Eds.; Wiley: New York, 1970; Chapter 6. (15) Hills, A. W. D. Chem. Eng. Sci. 1968, 23, 297. (16) Hills, A. W. D. Heat and Mass Transfer in Process Metallurgy Institute of Mineralogy and Metallurgy: London, 1967. (17) Davidson, D.; Garg, S.; Gough, S.; Handa, Y.; Ratcliffe, C.; Ripmeester, J.; Tse, J. Geochim. Cosmochim. Acta 1986, 50, 619.
