Estimating the thickness of hydrate films from their lateral growth rates: application of a simplified heat transfer model
Introduction
Clathrate hydrates (abbreviated to “hydrates” hereafter) are crystalline compounds composed of hydrogen-bonded water molecules configured into cages, each enclosing at most one molecule of some apolar substance called “guest substance” or “hydrate former”. With a few exceptions, hydrate formers are immiscible with liquid water. Thus, hydrates generally form and grow at the interface between liquid water and a hydrate former in the state of a liquid or a gas, taking the form of thin, polycrystalline films. The thickness of such films is of substantial interest in relation to various aspects of energy and environmental technologies such as carbon dioxide (CO2) disposal into deep ocean and natural-gas pipeline plugging due to hydrate formation, in which CO2 and natural-gas species (methane, ethane and propane) serve as the hydrate former. As demonstrated by Ohmura et al. [1] very recently, the thickness of hydrate films may be measured by an optical interferometer (or some other instruments) integrated into a specially designed experimental setup. However, it is very difficult to apply such measurement technique to, for example, CO2– and methane–hydrate films formed under very high pressures (typically of the order of 10 MPa). In the case of field experiments, we can rarely use precise measuring instruments. It is likely that the results of field experiments are available only in the form of low-magnification records of hydrate film growth along water/hydrate-former interfaces [2]. Thus, it may be worth considering a means of estimating, even roughly, the thickness of hydrate films from their macroscopic observations easily available.
This paper presents a practical method of estimating the thickness of hydrate films, relying on the observed rates of their lateral growth. The method is based on a simple model of convective transfer of heat of hydrate formation from the edge of each film to the surrounding, i.e., the water and the hydrate-former phases. This method is used to estimate the thickness of CO2–hydrate films, processing the experimental data on the rate of lateral film growth reported by Uchida et al. [3] and Hirai et al. [4].
Section snippets
Heat transfer model of Uchida et al. [3] — a critical review
Uchida et al. [3] were probably the first to note the possible relation between the rate of lateral growth of a hydrate film and its thickness. In considering this relation, they clarified their physical view of the phenomenon of interest, i.e., the lateral growth of a hydrate film along an interface between water and hydrate-former phases is rate-controlled by the diffusive transfer of heat, which is generated at the front edge of the film where the three phases meet, into the bulk of each
CO2–hydrate films observed by Uchida et al. [3]
Uchida et al. [3] measured vf of hydrate films growing on the surface of liquid-water drops hung in liquid or gaseous CO2 under pressures 1.8–7.2 MPa. The vf data they obtained are plotted against ΔTtri in Fig. 2. The solid curves drawn in Fig. 2 represent the vf−ΔTtri relations obtained by arbitrarily assuming δ values to be invariable with ΔTtri and by substituting ΔTtri for ΔT in Eq. (7). (C is evaluated at pressure p=5 MPa and temperature T∞=5°C, using PROPATH [7] for computing the relevant
Discussion and concluding remarks
The heat transfer model described in Section 2.2 should be regarded as the first approximation of the mechanism controlling the lateral growth of hydrate films along water/hydrate-former interfaces. The model includes great simplification of the film-edge profile and the geometry of the three-phase contact. Presumably, the edge of each hydrate film in a real system is not symmetric about the water/hydrate-former interface but is mostly wetted by water because of the hydrophilic nature of the
Acknowledgements
The author thanks Dr. T. Uchida (Hokkaido Nat. Ind. Res. Inst.), Prof. S. Hirai (Tokyo Inst. Technol.) and Dr. Y. Tabe (TIT, currently with Ebara Corp.) for their kind responses to the author's inquiries about their experiments cited in this paper. Dr. T. Mochizuki (Tokyo Gakugei Univ.) kindly helped the author in evaluating the physical properties necessary in this study. The author also thanks T. Shigetomi (currently with Osaka Gas Co.), H. Sakaguchi, R. Kamakura and H. Migita, students in
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