Keywords

1 Introduction

Natural gas hydrate (NGH) is one of the most important sources of alternative energy, which draws the attention to the whole world [1, 2]. Generally, NGH widely exists in oceanic and permafrost regions under the condition of high pressure and low temperature [3]. Driven by the energy demand and technological advancement, natural gas hydrate production is conducted worldwide to extract natural gas from the reservoirs, such as the South China Sea and the Eastern Nankai Trough [4, 6].

Changes in physical fields and dissociation front are important for analyzing production performance during gas extraction from natural gas hydrate reservoirs [6]. Zheng et al. [7] studied the controlling mechanisms of hydrate dissociation front with the lab-scale and field-scale models. The results indicate that using optimized characteristic time is a key factor in estabilishing calculation models. Afterward, A pragmatic criterion was developed to illustrates the relations among controlling mechanisms, hydrate dissociation modes, and characteristics of dissociation front [8]. Besides, the investigation on advance of dissociation front is essential for optimizating gas production and preventing the risks [9]. However, the dissociations on characteristics of dissociation front and formation responses during hydrate production are insufficient.

In this paper, we investigate the dissociation performance of gas hydrate reservoirs by depressurization method. The responses of pore pressure and temperature of formation are discussed. Besides, the distribution of hydrate, water, and gas saturation as well as dissociation front of hydrate are studied. This work can provide a reference for the practical application and numerical simulation in natural gas hydrate development.

2 Numerical Model

2.1 Governing Equations

The continuity equation of hydrate, water, and gas are given as follows:

$$\frac{{\partial \left( {\varphi \rho_{h} S_{h} } \right)}}{\partial t} = - m_{h}$$
(1)
$$\frac{{\partial \left( {\varphi \rho_{w} S_{w} } \right)}}{\partial t} - \nabla \cdot \left[ {\frac{{K_{rw} K\rho_{w} }}{{\mu_{w} }}\left( {p_{w} + \rho_{w} g} \right)} \right] = m_{w}$$
(2)
$$\frac{{\partial \left( {\varphi \rho_{w} S_{w} } \right)}}{\partial t} - \nabla \cdot \left[ {\frac{{K_{rw} K\rho_{w} }}{{\mu_{w} }}\left( {p_{w} + \rho_{w} g} \right)} \right] = m_{w}$$
(3)

The dissociation process of hydrate in the reservoirs can be described by the Kim-Bishoni kinetic model.

$$m_{g} = k_{d0}^{{}} \exp \left( {\frac{{\Delta E_{a} }}{RT}} \right)M_{{CH_{4} }} A_{rs} \left( {p_{e} - p_{g} } \right)$$
(4)
$$A_{rs} = \varphi S_{h} \sqrt {\frac{{\varphi \left( {1 - S_{h} } \right)}}{2K}}$$
(5)
$$K = K_{0} \left( {1 - S_{h} } \right)^{n}$$
(6)

Correspondingly, the generation rate of water and dissociation rate of hydrate are showed as follows:

$$m_{w} = m_{g} N_{h} \frac{{M_{{H_{2} O}} }}{{M_{{CH_{4} }} }}$$
(7)
$$m_{h} = - m_{g} \frac{{M_{H} }}{{M_{{CH_{4} }} }}$$
(8)
$$P_{e} = \exp \left( {A_{0} + A_{1} T + A_{2} T^{2} + A_{3} T^{3} + A_{4} T^{4} + A_{5} T^{5} } \right)$$
(9)
$$p_{w} = p_{g} - p_{c}$$
(10)

The energy conservation is expressed as:

$$\begin{gathered} \frac{{\partial \left[ {\rho_{w} \varphi S_{w} C_{w} T + \rho_{g} \varphi S_{g} C_{g} T + \rho_{h} \varphi S_{h} C_{h} T + \rho_{s} \left( {1 - \varphi } \right)C_{s} T} \right]}}{\partial t} + \hfill \\ \nabla \cdot \left( {\rho_{w} \varphi S_{w} {{\varvec{\upnu}}}_{w,t} C_{w} T + \rho_{g} \varphi S_{g} {{\varvec{\upnu}}}_{g,t} C_{g} T} \right) = \nabla \cdot \lambda_{eff} \nabla T + Q_{h} \hfill \\ \end{gathered}$$
(11)
$$Q_{h} = \frac{{m_{h} }}{{M_{h} }}\left( {B_{1} + B_{2} T} \right)$$
(12)

The heat transfer coefficient of the HBS can be determined by the sediments, hydrate, water, and gas.

$$\lambda_{eff} = \left( {1 - \varphi } \right)\lambda_{s} + \varphi \left( {S_{g} \lambda_{g} + S_{w} \lambda_{w} + S_{h} \lambda_{h} } \right)$$
(13)

Capillary pressure is given based on Van-Genuchten model.

$$p_{c} = p_{0} \left[ {\left( {\frac{{S_{w} - S_{wr} }}{{1 - S_{wr} }}} \right)^{{ - {1 \mathord{\left/ {\vphantom {1 \lambda }} \right. \kern-\nulldelimiterspace} \lambda }}} - 1} \right]^{1 - \lambda }$$
(14)

The relative permeability of water and gas endpoints of hydrate-free sediments are calculated by the following equations.

$$K_{rw} = K_{rwo} \left( {\frac{{S_{w} - S_{wr} }}{{1 - S_{wr} }}} \right)^{{n_{w} }}$$
(15)
$$K_{rg} = K_{rgo} \left( {\frac{{S_{g} - S_{gr} }}{{1 - S_{gr} }}} \right)^{{n_{g} }}$$
(16)

2.2 Model Descriptions

Figure 1 shows the cylindrical model of natural gas hydrate reservoir. The radius is 100 m and the height is set as 20 m. A well is designed in the centre of this model which is used for producing natural gas from this reservoir.

Fig.1.
figure 1

Model construction for the simulation.

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2.3 Initial and Boundary Conditions

The initial conditions in this model are determined by referring the previous studies [10]. The initial formation temperature and pore pressure are set as 288.15K and 14MPa, respectively. Besides, the initial water and hydrate saturation are 0.5 and 0.5, respectively.

The parameters are determined according to the previous studies and geological data in the South China Sea [11, 12], as shown in Table 1.

Table 1. Parameters used in this model.
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3 Results and Discussions

3.1 Description of Specimens

Figure 2 shows the distribution of pore pressure during gas hydrate production. The pore pressure increases from near-well region to far well formation. The depressurization and hydrate dissociation lead to the changes in the pore pressure field, which reflects the mass transfer process with the multi-phase flow.

Fig. 2.
figure 2

Variation of pore pressure versus production time

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Figure 3 illustrates the distribution of temperature in the natural gas hydrate formation. The temperature increases from well to formation, which is caused by the heat transfer and hydrate dissociation. The distribution of temperature varies during production process due to the heat and mass transfer.

Fig. 3.
figure 3

Variation of the temperature of formation versus production time

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3.2 Variation of Hydrate, Gas, and Water Saturation

Distribution of hydrate and water saturation during gas hydrate production are displayed in Figs. 4 and 5. The results indicate that the hydrate saturation decreases significantly with production time. Meanwhile, it is lower near well induced by the hydrate dissociation compared with that in the zone far from the well.

In addition, the water saturation increases due to the produced water from the hydrate dissociation. The water in the formation is also extracted to the ground. These factors affect the water distribution in the formation. The phase transition of hydrate occurs during production, which brings in variation of hydrate and water saturation.

Fig. 4.
figure 4

Distribution of hydrate saturation during hydrate production

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Fig. 5.
figure 5

Distribution of water saturation during hydrate production

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Similarly, the gas saturation increases in near well region, which is caused by the hydrate dissociation and gas extraction, as shown in Fig. 6. The gas produced through hydrate dissociation is extracted from the formation, which leads to the variation of gas saturation and changes in distribution characteristics.

Fig. 6.
figure 6

Distribution of gas saturation during hydrate production

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3.3 Hydrate Dissociation Front

Figure 7 demonstrates the variation of hydrate saturation during gas extraction. It can be observed that the hydrate saturation in near-well region is lower. The dissociation zone expands with production time, as shown in Fig. 7(b). The hydrate dissociation front moves toward the further bore zone due to the changes in the dissociation zone.

Fig. 7.
figure 7

Variation of hydrate saturation and dissocation front during production

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As mentioned above, the controlling mechanisms of hydrate dissociation and characteristics of dissociation front depend on the pressure and temperature conditions of the well and the properties of the formtation. The dissociation front reflects the production process of the natural gas hydrate.

4 Conclusion

Based on the results and discussions presented above, the conclusions are obtained as below:

  1. (1)

    Dissociation performance of natural gas hydrate in the formation is a complex process associated with heat and mass transfer as well as phase transition. Numerical simulation on hydrate production provides the references of dissociation characteristics and changes in physical fields for analyzing natural gas hydrate production.

  2. (2)

    Distribution of multi-physical fields varies during hydrate dissociation, which is determined by the gas extraction as well as the heat and mass transfer process. The hydrate saturation decreases in near-well formation, while the gas saturation increases.

  3. (3)

    The dissociation zone expands, and hydrate dissociation front moves to far well formation with production time. The multi-field responses of natural gas hydrate reservoirs are related to the hydrate dissociation performance during natural gas hydrate production.