Application of the shrinking-core model to the kinetics of repeated formation of methane hydrates in a system of mixed dry-water and porous hydrogel particulates
Graphical abstract
A schematic illustration of methane concentration profiles in a dry-water droplet (left), a porous hydrogel particle (middle), and a free water droplet (right) in a hydrates forming cycle.
Introduction
Gas hydrates are solid, non-stoichiometric compounds of small gas and water molecules formed at a low temperature and high pressure (Englezos, 1993, Sloan, 2003). The gas molecules are trapped in cages of hydrogen-bonded water molecules, therefore they also are known as clathrate hydrates, in which water is the host molecule and the gas is the guest molecule. Natural gas hydrates form when the gas molecules are in contact with water at temperatures lower than 300 K and moderate pressures (more than 0.6 MPa) (Sloan, 2003). If all cavities are filled, one volume of solid hydrates can store up to 180 volumes (at standard conditions) of methane gases (Sloan, 2003). In addition to this, natural gas hydrates can be held in a metastable solid state at atmospheric pressure (Gudmundsson et al., 1994). These factors make gas hydrates technology an alternative option for the transport and storage of natural gas in stranded and marginal gas fields (Gudmundsson and Børrehaug, 1996). Gas hydrates also have been proposed as a means for separating and refining hydrocarbons, removing contaminants, desalination and treatment of water, and CO2 sequestration (Gudmundsson et al., 1998). The past decade has witnessed increasing research activities in the direction of utilizing gas hydrates technology for hydrogen storage (Lee et al., 2005, Struzhkin et al., 2007), CO2 capture (Klara and Srivastava, 2002, Yang et al., 2008), and purification of other gases (Eslamimanesh et al., 2012, Vorotyntsev et al., 1996). However, the industrial application of gas hydrate technology has been hindered by such problems as slow formation rate and low gas capacity, as well as the presence of interstitial water trapped between already formed hydrates particles, which in turn have a negative impact on the capability and economy of scaling up the process (Zhong and Rogers, 2000). It is generally accepted that these problems are associated with the slow mass, in particular, and heat transfer during the hydrates formation process (Mori and Mochizuki, 1997, Vysniauskas and Bishnoi, 1983). Continuous efforts have been made to increase the gas-water interfacial surface areas, and to promote gas hydrates formation through the use of chemical additives and hydrates promoters. By doing so, the mass and heat transfer can be enhanced, the hydration kinetics improved and the entrapment of water molecules reduced. Chemical promoters, including tetrahydrofuran (THF) and cyclopentane, have been used to reduce the induction time and the hydrates formation pressure (Lang et al., 2010). Surfactants (Okutani et al., 2008, Zhong and Rogers, 2000) also have been used as additives to increase both the methane hydrates storage capacity and the hydrates formation kinetics. The accelerating effects of surfactants on hydrates formation are remarkable (Rogers et al., 2007), however the rapid formation of hydrates in the presence of surfactants causes elevated temperature which suppresses the further formation of hydrates, therefore reducing the effectiveness of the surfactants (Yang et al., 2011). The hydrates promoters occupy some of the cavities, leading to reduced gas capacity (Carter et al., 2010). Various mechanical methods have been investigated for the enhancement of the mass transfer and hydrates formation rate. Such methods as spraying, stirring, bubbling, and spraying with stirring (Lang et al., 2010) have been widely reported to be able to achieve effective formation kinetics. However, the high energy consumption, together with increased equipment capital and maintenance costs, involved in these methods are drawbacks for large scale production.
It is known that the formation kinetics of gas hydrates is limited by the diffusion of gas molecules through the formed hydrate film or shell. More recent studies have been focused on the development of porous solid materials to support the methane clathration with enhanced mass and heat transfer through the increased ratio of surface area and volume (Lee et al., 2005). The most studied materials include active carbons (Perrin et al., 2003), aluminum foam (Fan et al., 2012, Yang et al., 2011), and commercialized ZIF-8 (Mu et al., 2012). Porous polymers, such as polystyrene-based polyHIPE (high internal phase emulsion) (Su et al., 2009), foamed polyurethane (Talyzin, 2008), and the slightly cross-linked poly (acrylic acid) sodium salts (Su et al., 2009) have been reported to produce a significant increase in the storage capacity of hydrogen in THF-stabilized clathrates. However, using the same materials as a support media for methane storage was less successful (Su et al., 2009, Wang et al., 2009). The low methane storage capacity was assumed to be due to the hydrophobicity of the polymer and its poor water wettability. When using dry-water, a much higher methane storage capacity (175 v/v) and a relatively rapid formation rate of methane hydrates was observed (Wang et al., 2008). However, reversible storage of methane gases using such a system was compromised, due to the limited stability of dry-water droplets during the freeze–thaw cycles. We have developed a mixed system combining dry-water (DW) droplets with porous hydrogel (HYD) microspheres for reversible methane storage. The results have demonstrated a high reversibility with promising hydration kinetics (Ding et al., 2013).
It is worth noting that most of the aforementioned work has been focused on the development of novel materials for the enhancement of the hydrates formation kinetics and gas capacity. Little has been investigated regarding the mechanism of gas hydrates formation in these porous media. An understanding of the formation mechanism is critical for the advancement of both the design and the development of novel materials, and for the ultimate application of hydrates technologies for gas storage, CO2 capture and sequestration, and the purification of other gases.
In the current study, a modified shrinking-core model (Shi et al., 2011) was used to simulate the repeated methane hydrates formation process in a system containing both DW droplets and porous HYD particles. The methane diffusivity, the adsorption rate constant, and the contribution of water from various sources, were quantitatively determined using this model. The objective of this work was to explore how hydrates were formed in the investigated systems, why there was a reduction of gas capacity in the mixed system when compared with the pure DW droplets system, and how HYD particles have enhanced the reversibility of methane storage in the hydrates.
Section snippets
Materials and experimental data
The materials used for repeated methane formation were porous HYD microspheres mixed with DW droplets. The experimental data, representing the change of pressure and temperature with time, in a 300 ml reactor, were provided by Ding et al. (2013) and are displayed in Fig. 1. The data were collected from four particulate systems including, DW, DW+PHEMA (<100 μm), DW+PHEMA-co-MAA (<100 μm) and DW+PHEMA-co-MAA (>100 μm). In the sample codes, PHEMA stands for poly (2-hydroxyethyl methacrylate) whilst
The pure DW system
Gas consumption in the pure DW system during the first cycle was simulated. The results are shown in Fig. 7. It can be seen that the proposed model fits the experimental data well. The absolute average deviation (AAD) was about 2% and the variance was lower than 8.4×10−6 (Table 1).
The extracted hydrates formation parameters in the pure DW droplets system are listed in Table 1. These include the initial methane diffusivity, the attenuation coefficient for methane diffusivity and the adsorption
Conclusions
In summary, a modified shrinking-core model was employed to quantitatively study the repeated methane formation in a system containing dry-water droplets and porous hydrogel particles. The model has been proved to be valid. The simulated results were in good agreement with the experimental data. Quantitative data were obtained, including the methane diffusivity and its attenuation coefficient, the methane adsorption rate constant, and the distribution and water conversion in relation to the
Nomenclature
- AAD
absolute average deviation within experimental period, %
- C
concentration of methane, mol/m3
- Df
methane diffusivity, m2/s
- K⁎
methane adsorption rate constant, mol/(m2 s MPa)
- M
molecular weight, g/mol
- ng,t
accumulated methane consumption at time t, mol
- p
pressure, MPa
- r
radius, m
- R
gas constant, J/(mol K)
- t
time, s
- T
temperature, K
- V
volume, m3
- Wd
total gas molecule diffusion rate, mol/s
- Wc
total gas consumption rate, mol/s
- WC
water cut in different parts, %
- z
the compressibility factor in real gas law
- β
hydration number
- ζ
Greek symbols
Acknowledgements
The authors wish to thank the Australia–China Natural Gas Technology Partnership Fund for financial assistance towards this work.
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Present address: Department of Petroleum Storage and Transportation Engineering, University of Petroleum-Beijing, Beijing 102249, China.