Uniqueness of the equilibrium relationship among temperature, pressure and liquid water content in hydrate-bearing soils

Highlights

• Unydrated water content is uniquely related to temperature shift for the HBS for a given amount of salt.

• A theoretical model is developed to describe the equilibrium relationship among P-T-w.

• An analytical procedure is proposed to calculate the dissociation curves.

Abstract

The dissociation curves of pore hydrate, conventionally depicted on the P-T plane, depend generally upon the adopted experimental conditions. In this paper, the experimental results are presented on the phase equilibrium conditions for the hydrate-bearing soils (HBS) at different initial water contents, amounts of the dissolvable salt and initial vessel pressures. It is shown that a unique relationship exists between the unhydrated liquid water content and the temperature shift induced by capillary and osmotic effects, if the total amount of the dissolvable salt in the pore water is given. A theoretical model is developed, which can describe a general relationship among pressure, temperature and unhydrated water content for the hydrate-bearing soils in equilibrium. It is shown that the experimental results obtained under different experimental conditions can be very well described by the proposed model. In particular, the new model predicts that, independent of pressure and temperature, the liquid water content can be one-to-one related to the temperature shift to the extent that the total amount of the dissolvable salt is specified. Based on this, a new procedure is proposed to predict the dissociate curves associated with hydrate dissociation under different experimental conditions.

Introduction

The phase equilibrium condition of gas hydrate, which describes the relationship between pressure and temperature of the hydrate in equilibrium, is one of the key components in the evaluation of the natural gas hydrate reserves and the design of cost-effective production systems of gas hydrate (Sloan, 1998; Kvenvolden et al., 1995; Chong et al., 2015; Xu et al., 2016; Merey, 2016; Li et al., 2018; Hussein et al., 2020). Earlier research efforts were mainly focused on the thermodynamic behavior of gas hydrates in solution-gas binary systems (Hammerschmidt 1934; Duan et al., 1992). Numerous experiments were performed to obtain the equilibrium boundaries of gas hydrates formed in aqueous solutions. Nakano et al. (1999) suggested that the published experimental data on the equilibrium condition for methane-bulk water-hydrate system were quite consistent with those by Marshall et al. (1964) and Kobayashi et al. (1949). Cha et al. (2016) studied the effect of salts on the equilibrium condition of methane hydrate, and showed that their experimental results agreed well with previously published data (Maekawa et al., 1995; Mohammadi et al., 2008). Although various experimental conditions characterized by the volume of vessel, the amount of solution, initial pressure and temperature had been adopted in the experiments, the measured phase boundaries on the pressure (P)-temperature (T) plane were unique if both the guest gas and salt components were the same. Similar conclusions have also been founded in other reports (Shahnazar et al., 2014; Hu et al., 2017; Lv et al., 2018; Nakane et al., 2019; Piramoon et al., 2019).

In porous media, the phase equilibrium of gas hydrate becomes much more complicated. Earlier researches in this respect were concerned only with the porous media with uniform pore sizes or a narrow pore-size distribution. Handa and Stupin (1992) first demonstrated that the equilibrium pressures of the methane and propane hydrates in 7.5 nm radius silica-gel were higher than those in bulk water. Østergaard et al. (2002) measured the equilibrium data of methane hydrates in the silica glass pores of 30.6, 15.8, and 9.2 nm diameters, respectively, and indicated that the equilibrium boundaries in the similar diameter pores matched well with the previous study (e.g., Uchida et al. (2002)). Anderson et al. (2003a) measured the phase boundaries of CH₄ and CO₂ hydrates in the porous medium with a pore size similar to that adopted by Uchida et al. (2002), and their results indicated that the tested equilibrium data were unique on the P-T plane, although various experimental conditions were adopted. Thus, based on the experimental results of gas-solution binary systems, the uniqueness relationship of phase boundary depended only on the pore size, provided that the components of gas and pores solution are given. Similar results were also experimentally observed by numerous other studies (Cornelius et al., 2017, Liu et al., 2018, Tejaswi et al., 2014).

The gas hydrate-bearing sediments in nature generally possess a broad pore-size distribution. In such environments, the phase equilibrium of pore hydrate is no longer unique (Park et al., 2018). Uchida et al. (2004) had shown that the equilibrium boundary of pore hydrate gradually approached to that of the bulk hydrate in the natural silica sand and sandstone, which essentially reflected the influence of cumulative volume distribution of natural sediments. Smith et al. (2002a, 2002b) and Wilder et al. (2001) experimentally demonstrated that the observed equilibrium pressure in porous media with widely distributed pore sizes was dependent on the ratio of headspace volume (the volume of vessel subtracted by the volume occupied by the soil particles) to the volume of the porous medium. This implied that the measured P-T phase boundaries were influenced by the experimental conditions including the procedure adopted, the volume fraction of headspace, the volume of vessel, the size of sample, the initial water content, and so on.

To resolve the above apparent difficulty, Smith et al. (2002a, 2002b) and Wilder et al. (2001) introduced an additional degree of freedom, i.e., pore radius, into van der Waals and Platteeuw (1959)'s model (i.e., the vdWP model), and cast the phase equilibrium boundary into the pressure (P)-temperature (T)-pore radius (r) space. They showed that the uniqueness of the phase boundary could be recovered if the cumulative pore size distribution curve was provided. In this model, the capillary effect is taken into account by introducing the Young-Laplace equation, and the effect of salt is also considered by introducing the activity of water in the pore solution. Although this model can address well the experimental results of phase equilibrium, it requires as input the pore-size distribution data, which may not be readily obtained. In addition, this model had not been verified by the experimental data of salty porous media, which commonly occur in natural sediments.

Recently, Zhou et al. (2019) developed a phase equilibrium model for pore hydrate using the chemical potential formulation of the empty H₂O lattice, proposed by van der Waals and Platteeuw (1959), based on statistic mechanics, and the chemical potential of unhydrate water, proposed by Wei (2014), based on a chemo-mechanical theory of porous media. Zhou et al. (2019) showed that a unique relationship generally existed among unhydrated water content (w), pressure (P) and Temperature (T) for the hydrate-bearing sediments in equilibrium. In contrast to the generalized vdWP model (e.g., Smith et al., 2002a; 2002b; Wilder et al., 2001), however, Zhou et al. (2019)'s model requires the soil water retention curve as input, instead of the cumulative pore-size distribution data. This feature is desirable, since the matric suction isotherm is a macroscopic property, which can be readily determined in the laboratory. Although Zhou et al. (2019)'s model predicts that an equilibrium relationship among P, T and w is unique to the extent that the amount of salt is specified in the tested sample, more experiments need to be performed to explore the effect of salt concentration on the equilibrium condition of pore hydrate.

The objective of the paper is two-folded, i.e., to present the experimental results on the equilibrium condition of pores hydrates in mixed sand-clay sediments obtained under various experimental conditions, and to develop a theoretical approach to predicting the dissociation curves. We shall show, experimentally and theoretically, that there exists a unique relationship between temperature shifts and unhydrated water content (w) in the hydrate-bearing soils in equilibrium, which is dependent only upon the total amount of dissolvable salts in the pore water, and independent of the initial water content, sample volume, headspace volume, and other conditions adopted in the experiments.