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Correlation of Hydrate-Film Growth Rate at the Guest/Liquid-Water Interface to Mass Transfer Resistance Kota Saito,*,† Amadeu K. Sum,‡ and Ryo Ohmura† Department of Mechanical Engineering, Keio UniVersity, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan, and Center for Hydrate Research, Chemical Engineering Department, Colorado School of Mines, Golden, Colorado 80401
The correlation of hydrate-film growth rate at the guest/liquid-water interface to mass transfer limitations is considered. Most of the hydrate-film growth rate data from the literature are compiled based on the system subcooling (∆T), suggesting predominant heat transfer limitations. In this communication, we investigate how existing data on hydrate-film growth is better correlated to solubility differences of the guest species in equilibrium with bulk fluid and hydrate. Investigations of the limiting factors on the formation and growth of clathrate hydrates have long been of scientific and industrial interest. Modeling of the formation and growth of hydrates in a highly agitated system such as stirred reactor and bubble column has been improved1-6 in the past three decades, whereas much discussion still exists in the literature7-12 on the limiting factors affecting the hydrate-film growth along the guest/ liquid-water interface. Some studies7-9 suggest the hydrate-film growth are significantly affected by heat transfer, that is, the hydrate-film growth is dependent on the subcooling (∆T) of the system. The subcooling (∆T) is the difference between the equilibrium water-hydrate-gas formation temperature (Teq) and the experimental system temperature (Tex), ∆T ≡ Teq - Tex. Figure 1 shows a compilation of data from the literature for the hydrate-film growth rate based on the reported subcooling (∆T) in the system. As seen in the figure, there is a wide range of growth rates, in particular the growth rate of CO2 hydrates which is higher by 1-2 orders of magnitude than those of methane and propane hydrates. If heat transfer limitations, defined by ∆T, were the dominant controlling process for hydrate-film growth, one would expect to observe a better correlation of the data to ∆T, as opposed to the large scatter for any given value of ∆T. As such, we examined whether the hydrate-film growth can, instead, be correlated to mass transfer effects at the guest/liquidwater interface. For mass transfer processes, the concentration difference (∆X) is often used as the driving force. Figure 2 illustrates the hydrate-film growth at the guest/liquid-water interface. Here, we assume that three-phase equilibrium locally exists at the front of the hydrate-film growing at the guest/liquidwater interface. The driving force, ∆X, is the difference between the solubility of the guest (Xeq,int) in liquid-water at the guest/ liquid-water interface at the system temperature (Tex) and the solubility of the guest (Xeq,hyd) in liquid/water at the hydrate equilibrium temperature (Teq) at the hydrate-film front, ∆X ≡ Xeq,int - Xeq,hyd. Figure 3 shows a schematic of the solubility for the guest in liquid-water as a function of the temperature. The solid line corresponds to the two-phase equilibrium conditions with the solubility of the guest in bulk liquid-water, and the dashed line is the equilibrium solubility of the guest in liquid-water in * To whom correspondence should be addressed. E-mail: msksaito@ z8.keio.jp. † Keio University. ‡ Colorado School of Mines.
equilibrium with the hydrate.The intersection of the lines indicates the liquid-water-hydrate-guest phase equilibrium condition at the equilibrium temperature Teq under the experimental pressure. The solubility Xeq,int corresponds to the experimental system temperature Tex. Figure 4 replots the data for the systems in Figure 1 with ∆X as a measure of the driving force for hydrate-film growth. In addition, the plot also includes data for CO2 hydrate growth at the interface of liquid-water-liquid-CO2 systems.9 The solubility values (Xeq,int) and (Xeq,hyd) were calculated with HWHydrateGUI.13 The deviations of the predictions with HWHydrate from the existing experimental data14-17 are calculated to be mostly within (5%, at worst within (15% over the pressure-temperature conditions that corresponds to the hydrate-film growth experiments, specifically pressures from 3.5 to 10.5 MPa, temperatures from 274 to 283 K for methane, 0.3 to 0.5 MPa, 273 to 277 K for propane, and 3 to 5 MPa, 274
Figure 1. Dependence of hydrate-film growth rate on the subcooling ∆T for several reported studies: (O) methane at 5.60 MPa;7 (4) methane at 8.15 MPa;7 (0) methane at 10.56 MPa;7 (×) propane 0.31 at MPa;7 (+) propane 0.41 at MPa;7 (/) propane at 0.51 MPa;7 ()) methane;8 (b) CO2(V) at 3 MPa.9
Figure 2. Illustration of hydrate-film growth at the guest/liquid-water interface.
10.1021/ie1000696 2010 American Chemical Society Published on Web 06/28/2010
Ind. Eng. Chem. Res., Vol. 49, No. 15, 2010
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Acknowledgment The author would like to thank Mr. Masatoshi Kishimoto for his assistance in the data process. This study was supported by a Grant-in-Aid for Science Research from the Japan Society for the Promotion of Science (Grant 19760137) and by a Grantin-Aid for the Global Center of Excellent Program for “Center for Education and Research of Symbiotic, Safe and Secure System Design” from the Ministry of Education, Culture, Sport, and Technology in Japan. A.K.S. acknowledges the support of DuPont for a DuPont Young Professor Award. Literature Cited Figure 3. Schematic of solubility curves of guest species in liquid-water.
Figure 4. Dependence of hydrate-film growth rate on the concentration difference ∆X for the systems in Figure 1 with the addition of the data by Uchida et al.:3 (O) methane at 5.60 MPa;7 (4) methane at 8.15 MPa;7 (0) methane at 10.56 MPa;7 (×) propane at 0.31 MPa;7 (+) propane at 0.41 MPa;7 (/) propane at 0.51 MPa;7 ()) methane;8 (b) CO2(V) at 3 MPa;9 (9) CO2(L) at 5 MPa.9 Dotted-dashed, dashed, and solid lines indicate the fit to the curves with the structure I hydrate data (methane and CO2), structure II hydrate data (propane), and all of the data, respectively.
to 280 K for CO2. Because it is likely that the difference in the crystallographic structure has significant effect on the hydratefilm growth, the three different fitting curves are shown in Figure 4 corresponding to the correlation for (1) structure I hydrate data (CH4 and CO2); (2) structure II hydrate data (propane); and (3) all of the data. As seen from the data in Figure 4, the hydrate-film growth rate increases with increasing ∆X and can be well correlated by a power-law function. Comparison of Figures 1 and 4 suggests that the hydratefilm growth rate data are better correlated with ∆X than with ∆T, i.e., the mass transfer of the guest species may have significant effect on the hydrate-film growth at the guest/liquidwater interface, as opposed to heat transfer limitations alone. The implication of this analysis is that hydrate growth studies must carefully account for both heat and mass transfer limitations and not only heat or mass transfer in the design and analysis of experimental measurements.
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ReceiVed for reView January 12, 2010 ReVised manuscript receiVed March 25, 2010 Accepted June 16, 2010 IE1000696
