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Applied Energy xxx (2017) xxx-xxx

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Applied Energy

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Numerical study of gas production from methane hydrate deposits by depressurization at 274 K Minghao Yua⁠ , Weizhong Lia⁠ , Lanlan Jianga⁠ ,⁠ b⁠ ,⁠ ⁎⁠ , Xin Wanga⁠ , Mingjun Yanga⁠ , Yongchen Songa⁠ a b

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, China Research Institute of Innovative Technology for the Earth, Kizugawa City, Kyoto 619-0292, Japan

ABSTRACT

Keywords: Methane hydrate Decomposition Self-preservation effect Ice generation Depressurization

As a potential new source of energy, gas hydrate has been the focus of research around the world. In this study, based on a summary of existing models, a one-dimensional mathematical model containing four phases (water, gas, hydrate, and ice phases) and three constituents (water, gas, hydrate) based on the finite difference method (FDM) was established for analysing methane hydrate decomposition at a relatively low temperature condition (approximately 274 K) by depressurization in porous media. This model can be used to investigate gas hydrate exploitation under a wider range of temperatures (e.g., deep seabed or permafrost conditions). When the initial temperature of the hydrate reservoir is approximately 274 K, ice generation occurs during exploitation. This investigation focused on the characteristics of hydrate decomposition, ice generation and ice distribution by changing the parameters of relevant settings. The analysis addressed the effects of ice generation on pressure, temperature, permeability, and cumulative gas production; the influence of other relevant parameters on each other; the influential factors and features of cumulative gas production and the instantaneous gas generation rate. The results showed that ice generation gradually increases during the hydrate decomposition process and occurs early and near the production well due to a large pressure gradient. As an unfavourable factor, ice generation causes the absolute permeability, instantaneous gas generation rate and local pressure to decline. The production well pressure is the determinant of ice generation. Moreover, the final cumulative gas production is determined by the hydrate characteristics, which include the hydrate saturation, reservoir porosity and permeability. Ice generation reduces the gas generation rate, but this does not affect the final cumulative gas production.

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ARTICLE INFO

1. Introduction

Gas hydrate is a compound of gas molecules that are wrapped by the hydrogen bonds of water molecules onto a cage structure, and hydrate plays an important role in flow assurance, safety issues, energy recovery and climate change [1,2]. As a type of energy sources with great potential, gas hydrate has received considerable research attention in recent decades. The formation and decomposition of gas hydrate depend on the pressure, temperature, gas composition, salinity of the water, characteristics of the porous media and other factors. Hydrates remains stable at certain pressures and temperatures and achieves a balanced state [3]. Several methods are used for gas production (decomposition) from gas hydrate in the field, including depressurization, by decreasing the

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pressure of the system [4–6]; thermal stimulation, which involves hot water injection and increasing the temperature [7]; and a combination of depressurization and thermal stimulation [8,9]. In general, depressurization is considered the simplest and most promising method because of its effectiveness and the fast response of hydrate to pressure waves [10]. Several laboratory experiments used depressurization to recover gas hydrate, and showed that it is an effective gas production method. Several field tests, such as those at the Mallik site [11], North Slope of Alaska [12], Nankai Through along the Pacific coast of Japan [13], and in South China [14,15] have revealed that depressurization is the least energy intensive and most promising gas production method from the perspectives of energy efficiency and productivity. Three periods were defined during the depressurization process: free gas, mixed gas and gas production from hydrate decomposition [16]. Three major

Corresponding author at: Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, China. Email address: [email protected] (L. Jiang)

https://doi.org/10.1016/j.apenergy.2017.10.013 Received 19 January 2017; Received in revised form 3 October 2017; Accepted 5 October 2017 Available online xxx 0306-2619/ © 2017.

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essary to analyse the effects of ice formation on gas hydrate decomposition. The effects of ice formation are related to the decomposition kinetics of gas hydrate. The kinetic model (Kim-Bishnoi model) of hydrate decomposition was first proposed by Kim et al. [35]. The results revealed that the decomposition rate was proportional to the particle surface area and the difference in the fugacity of methane at the equilibrium pressure and decomposition pressure. In the kinetic model, the system is composed of heat and three mass components. Musuda et al. [17] developed a three-dimensional form of the hydrate decomposition kinetic model and used the model to simulate gas hydrate exploitation at the field scale. The potential gas flux generated by the kinetics of hydrate decomposition, gas flow and heat transfer was calculated, and gas production at the lab scale was mainly limited by heat transfer [23]. By considering the particle surface area during ice formation, the kinetic model has the ability to predict ice formation during gas hydrate decomposition. Some limited studies of hydrate depressurization were conducted using the kinetic model [26]. However, studies of gas hydrate decomposition kinetics during ice formation are rare. Although significant progress has been made in the numerical simulation of natural gas hydrate decomposition characteristics, most models have overlooked the ice phase. Notably, knowledge of the effect of ice generation on some important parameters (including pressure, temperature, and permeability) remains insufficient. Additionally, the effect of ice generation on the gas production rate is unclear. The changes in these parameters, which must be considered in the process of gas hydrate exploitation, must be investigated. In this study, we develop a comprehensive mathematical model based on the kinetic model. The proposed model includes water, gas, hydrate, and ice phases and three components. After validating the mathematical models, the dynamic process of gas production from a hydrate reservoir at 274 K is analysed. Specifically, the effect of ice formation on hydrate decomposition is investigated. Additionally, the effects of the initial hydrate saturation, initial pore structure including porosity and initial absolute permeability, and ice generation on gas production from hydrates were analysed.

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factors determine the depressurization-induced gas production rate: the kinetics of methane hydrate decomposition, gas flow through the reservoir, and heat transfer to the dissociating zone [17]. Several decomposition experiments have been conducted to investigate the influences of the temperature, pressure [18], concentration [19], salt level and injection rate [20]. However, several mechanisms of gas hydrate preservation may affect depressurization. These mechanisms include the methane hydrate self-preservation effect and reformation during the production of gas from hydrate deposits during depressurization. The self-preservation effect was observed and described in early 1986. A surprisingly slow decomposition was observed during gas hydrate production in the Gulf of Mexico at an ambient pressure and −20 °C [21]. Later, Yakushev and Istomin reported decomposition rates that were several orders of magnitude lower than the expected decomposition values, especially at low temperatures below the freezing point and at atmospheric pressure [22]. The low decomposition rates were attributed to the self-preservation effect. Generally, the self-preservation effect results in the extremely slow decomposition of gas when the external pressure decreases the three-phase equilibrium pressure of the gas-ice-hydrate system at subzero temperatures as a result of thin ice film emergence on the gas hydrate surface [23,24]. The self-preservation effect is critical for the feasibility of hydrate-based gas storage technology. However, the mechanisms of the self-preservation effect remain poorly understood due to insufficient information describing the precise composition of the original hydrate, the common presence of large fractions of ice as a secondary phase, the unknown extent of decomposition and the alteration experienced during transport [25]. The self-preservation effect is enhanced by increasing pressure and decreasing temperature [23]. Recently, many studies related to hydrate decomposition have mainly focused on the dependence of self-preservation on ice formation at a temperature below 273 K and an ambient or moderate pressure [26–28]. At ambient pressure, unstable gas hydrates decompose rapidly to free gas and ice. The ice film exhibits fractal features and increases mass transfer resistance during the diffusion of methane from the hydrate region [23]. The ice film creates unexpected stability under non-equilibrium conditions and slows decomposition [29]. In contrast, experimental data collected using electron-micros-copy revealed self-preserved (partly dissociated) methane hydrate particles that no evidence was found for ice-rind development around individual hydrate grains [30]. Additionally, the gas production rate was obviously enhanced around the freezing point [31]. Although the detailed mechanism remains unclear, ice formation plays an important role in hydrate decomposition. Hence, the energy efficiency remains questionable if gas hydrated decomposes at freezing point. Considering the temporal and spatial limitations of monitoring during ice formation, numerical simulation has the advantage of being low cost and allowing for easy adjustment of the space and temporal scales. A single-phase model was proposed based on a conventional, adjacent, hidden, and step-down decomposition process; however, dynamic water flow conditions could not be simulated with this model [32]. A two-phase, three-dimensional variable composition model was developed to simulate decomposition and formation processes (involving water and any mixture of methane, ethane, or propane) and address fundamental questions regarding the feasibility of gas production schemes and the utilization of gas hydrate, an unconventional energy resource [33]. Then, a three-phase, multicomponent model that treats decomposition as a condition of methanol injection was developed [34]. An analytical model was presented to analyse the main factors that affect hydrate decomposition in porous media. Researchers found that the most important reservoir variable was the permeability of the ice region that formed during hydrate decomposition. Moreover, models that couple multiphase and multicomponent factors are nec

2. Model

2.1. Physical model

A schematic diagram of gas hydrate decomposition by depressurization is shown in Fig. 1. The initial parameters of the reservoir are as follows: pressure P0 = 3 MPa, temperature T0 = 274 K, absolute permeability K0 = 1000 mD, ice initial saturation Si0 = 0, water initial saturation Sw0 = 0.2, gas hydrate initial saturation Sh0 = 0.45, gas initial saturation Sg0 = 0.35, and the porosity of the reservoir ? = 0.2. The reservoir is assumed to have a homogenous porosity and permeability varies with time during gas hydrate decomposition. The low production well pressure P1 leads to the reservoir pressure being lower than the hydrate phase equilibrium pressure at temperature T0. The hydrate in the reservoir is decomposed into water and methane gas. Under a pressure difference, these components can be extracted via production wells. Combined with existing models and the described physical model, a one-dimensional mathematical model of hydrate decomposition due to depressurization that considers the ice phase is developed. The basic assumptions of the model are as follows: (1) The model considers four phases (water, gas, hydrate, and ice phases) and three components (water, gas and hydrate); (2) The hypothesis for hydrate, ice and the solid skeleton is stillness, and the gas and liquid two-phase flow conforms to Darcy’s law; (3) The secondary hydrate-generation processes are disregarded;

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Fig. 1. A schematic diagram of the gas hydrate decomposition by depressurization (P0 is the initial reservoir pressure, T0⁠ is initial temperature, K0⁠ absolute permeability, and Si0, Sw0, Sh0 , and Sg0 are the saturation levels of ice, water, gas hydrate and gas, respectively).

(4) The gas and liquid seepage and leakage through the cover layer, dissolution of gases in water and slippage effect are disregarded; (5) There is no external heat source; (6) It is assumed that each parameter in the reservoir is isotropic; and (7) Gravity is disregarded.

Ice generation should be considered not only in mass and energy transfer but also in the process of hydrate decomposition. The equation of decomposition dynamics proposed by Kim et al. [35] is shown in Eq. (3), and it describes the relationships between hydrate decomposition and the pressure, temperature, and particle surface area. Many classical mathematical models were later incorporated into this model.

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2.2. Mathematical model

The mathematical model is based on the mass conservation equation and energy conservation equation [27,36].The relationship between velocity and pressure is described by Darcy’s law, and the model includes this relationship in the mass conservation equation. Moreover, a dynamic decomposition dynamics equation including ice was included in the model.

where mg is the mass of methane gas production in a unit volume per unit time; k0 is the hydrate decomposition kinetic constant, which depends on the hydrate particle geometry, and in this study the value of k0 is 1.25 × 105⁠ mol/m2⁠ Pa s [39]; ΔEα (in this study the value is 81084.19722 J/mol [39]) is the activation energy; R is a gas constant; T is temperature; Mg is the molar mass of methane; Pe is the balance pressure that depends on temperature; Pg is the pressure of gas; and As is the decomposition surface area. In this study, we calculated Pe based on the methane hydrate phase equilibrium equation proposed by Selim et al. [40] as shown in Eq. (4). In the model, Pe changes with temperature.

(1) Mass conservation equation

The mass conservation equation for ice, gas, water, and hydrate can be described as follows. (1)

where ρw and ρg are the water and methane gas densities, respectively; and

are the water and methane seepage velocities, respec-

(2) Energy conservation equation

(2)

constant pressure; and the subscripts

(5)

here, to calculate the absolute permeability considering the effect of ice, we modified the absolute permeability model proposed by Masuda et al. [39] as shown in Eq. (6). Specifically, we added ice saturation to the Masuda model.

The energy conservation equation is given as follows

is the thermal conductivity;

(4)

Ignoring the effect of ice generation, As is related to the porosity (? ), absolute permeability (K) and hydrate saturation (Sh) as shown in Eq. (5) [41].

tively; mw, mg, and mh are the masses of water and gas from hydrate decomposition per unit volume per unit time and hydrate consumption mass, respectively; Sj (j = w,g,h,i) the saturation of each phase; and ? is the porosity.

where

(3)

is the specific heat at a

represent the solid matrix,

(6)

where K0 is the initial absolute permeability, Si is ice saturation, and N is the permeability decline index, which is set to N = 4 in this study. According to a previous study [42], ice prefers to adhere to the surface of the hydrate as ice is generated. The schematic diagram of this process is shown in Fig. 2a. In the figure, parts of the hydrate (the blue area) are covered by generated ice (the white area). Thus, the reactive specific surface area of the hydrate is reduced. This area is an im

water, methane gas, hydrate and ice, respectively. ΔHh is the heat absorption capacity per unit mass of hydrate decomposition, and ΔHi is the latent heat per unit mass of frozen water. In this study, the constant values of ΔHh and ΔHi are 453,500 [37] and 334000 J/kg [38] respectively. (3) Equation of decomposition dynamics including ice

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Fig. 2. A schematic diagram (a) of ice generation on the hydrate surface during hydrate decomposition and an idealized schematic diagram (b) of area covered by ice.

portant factor that can influence the rate of hydrate decomposition. Therefore, this study proposes a method of calculating the area covered by ice based on the per unit volume of ice generation. This relationship can be described by the coefficient

Table 1 Values of basic reservoir parameters in the hydrate depressurization model. Parameter

, where A is the ice coverage

area and Vi is the ice generating volume, which can be described by the ice saturation Si. We propose an idealized hypothesis that ice generation occurs in a rectangular or cylindrical shape (as Fig.2b shows). Thus, coefficient Y can be expressed as follows: (7) whereh is the thickness of the ice. h can be calculated according to the classic Stefan solution [43,44]:

Value

Parameter

Value

Reservoir length, L (m)

30

44.3

Initial permeability, K0⁠ (md) Porosity, Φ (%)

97.98

Initial reservoir pressure, PW ⁠ (MPa)

3.75

Initial hydrate saturation, Sh⁠ (%) Initial water saturation, Sw⁠ (%) Initial gas saturation, Sg⁠ (%) Permeability reduction index, N

18.2

20.6 35.1 4

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portions of the simulation code involving ice. Instead, the influence of ice generation during methane hydrate decomposition was generated through changing other parameters. Thus, if the results of the basic program compare favourably to the experimental data, the model including ice generation can be used. We calculated the cumulative gas production over 500 h and compared the results with the experimental data. A comparison of the cumulative gas production results is shown in Fig. 3. Notably, the numerical simulation results exhibit good agreement with the experimental data, and the final gas production estimates are highly consistent. In addition, the variations in the curve of the model results coincide with those in the experimental curve. Although some minor deviations can be observed, they are likely associated with the heterogeneity of the initial hydrate distribution and accuracy of the temperature and pressure measurements in the experiment. This result indicates that the mathematical model is capable of simulating the process of methane gas hydrate decomposition by depressurization.

(8)

where λi is the heat conductivity coefficient of ice, ρi is the density of ice, ΔHi is the latent heat of freezing, Ti is the freezing temperature, T is the actual temperature, and t is time. Therefore, Eq. (5) can be transformed into Eq. (9). (9)

The finite difference method (FDM) was used to discretize the mass conservation equation and energy conservation equation. This study focuses on natural gas hydrate production by depressurization, so the temperature and pressure of the production well at the boundary are set to constants (the temperature is 274 K and pressure is 0.8 MPa). Two other pressure boundaries were established, including a fully developed boundary and an impermeable boundary. The calculation results differed according to the boundary conditions. The fully developed boundary is similar to reservoir conditions at the field scale, and the impermeable boundary is suitable for laboratory-scale analyses. The results of this study must be comparable with experimental results, therefore, an impermeable boundary is adopted. The boundary pressure (except the production well pressure) was set to 3.5 MPa (the initial pressure of the reservoir). 3. Results and analysis

The mathematical model, which included the four phases of gas, water, hydrate and ice, was used to calculate changes in relevant parameters and conduct an in-depth analysis. 3.1. Comparison of numerical simulations and experimental data

This study used experimental data from Masuda et al. [41] to verify the mathematical model. For the model verification, we set the parameter values based on experimental results, as presented in Table 1. Because the experiment did not consider ice generation, we excluded

Fig. 3. Comparison of cumulative gas production estimated using the proposed model and from the experiments of Musuda et al. [41]

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3.2. Ice generation

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During the process of heat absorption, the temperature decreases from the initial temperature (274 K). when the temperature decreases to the freezing point, ice forms quickly. The saturation of the ice phase as a function of time was calculated, as shown in Fig. 4. Notably, ice is generated on the near wall at 1 min. Moreover, ice forms rapidly within 60 min but is limited to a small region, and the ice saturation increases from 0.18% to 0.55%. Through 600 min, the maximum saturation of ice increases by 1.5% at the near well and 0.35%in the region far from the well. Additionally, a saturation gradient exists because of the large pressure gradient. A larger pressure gradient corresponds to a fast decomposition rate, which leads to a temperature drop around the region near the well. As shown in Fig. 4, the ice saturation is limited during the overall depressurization process, while the hydrate saturation generally reaches 40%. Ice generation, however, strongly influences the decomposition process. The saturation of ice is orders of magnitude less than the saturation of hydrate. Moreover, it is difficult to distinguish between the hydrate, ice, water, and gas in lab experiments, emphasizing the importance of numerical studies of ice generation.

Fig. 5. Pressure distribution for conditions including and excluding ice at 3000 min (Pw is the water pressure, and L is the distance from the well).

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3.3. The effect of ice generation on pressure and permeability

With ice generation, the pressure and permeability in the reservoir differ from the case without ice generation. For example, at 3000 min, as shown in Fig. 5, the pressure declines sharply near the production well and a pressure gradient exists. With ice generation, the pressure increases. Ice generation suppresses the gas flow, causing the pressure of the reservoir to increase. Thus, to some extent, the influence of the low pressure of the production well on the internal reservoir is reduced. The maximum pressure difference between the two cases (with ice generation and without ice generation) is so small (less than 0.1 MPa) that the influence of ice generation on pressure can be disregarded. In addition, the absolute permeability is reduced by ice generation. Permeability declines significantly near the borehole (Fig. 6), because ice is generated and forms a solid phase. This solid phase occupies the pores of the reservoir, resulting in a sharp reduction in the pore space.

Fig. 6. The absolute permeability in the models with ice and without ice (K is the absolute permeability, and L is the distance from the well).

However, in the region far from the production well, ice rarely generates; therefore, the absolute permeability is similar to the case without ice generation. Moreover, ice generation has a protective effect on the gas hydrate [42], and the content of the solid phase barely fluctuates. 3.4. The effect of the initial hydrate saturation on the pressure, permeability and temperature By using the mathematical model, the effect of the initial hydrate saturation on the pressure, temperature and absolute permeability was analysed. For hydrate saturations of 0.25 and 0.45, the related parameters were simulated at 300 and 600 min (Fig. 7). Because of the boundary condition, the pressure near the production well (the first node in Fig. 7a) is independent of the initial saturation. However, the pressure for Sh0 = 0.45 is obviously higher than that for Sh0 = 0.25 because the gas hydrate blocks part of the pore and

Fig. 4. The saturation of ice varies with time in the reservoir (Si is the ice saturation, and L is the distance from the well).

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Fig. 7. Pressure (a), absolute permeability (b) and temperature (c) in the reservoir under different initial hydrate saturations of 0.25 and 0.45 at 300 min and 600 min (Pw is the water pressure; K is the absolute permeability; T is the temperature; and L is the distance from the well).

suppresses the flow. Thus, the pressure is slowly transmitted from the boundary to the reservoir. In this case, the amount of hydrate is higher and the pressure in the reservoir is higher for the same production time. As the production time increases, the boundary pressure is gradually transmitted to the internal nodes and the pressure in the reservoir declines. Fig. 7b shows that the absolute permeability varies with hydrate saturation and production time, and the absolute permeability gradually decreases. The average permeability is high at small hydrate saturation levels and long production times. However, the permeability also depends on the blocking action of the solid hydrate. Notably, the permeability decreases to approximately 0.35 D when the gas hydrate saturation increases from 0.25 to 0.45. For the same hydrate saturation, when the production time changes from 300 to 600 min, the permeability slightly increases by approximately 0.05 D. This change indicates that the influence of hydrate saturation on the absolute permeability is greater than that associated with the production time. Moreover, at the same production time, the permeability of the reservoir at Sh0 = 0.25 and Sh0 = 0.45 decreases to approximately 0.06 D and 0.04 D, respectively. This result indicates that the production efficiency is higher when the initial saturation of the hydrate is low.

In contrast to other parameters, the temperature in the reservoir changes with the production time. This can be proven by calculating the temperature distribution at 300, 3000, and 30000 min. The associated simulation results are shown in Fig. 8. At 300 min, the temperature 10 m from the production well remains at the initial value. As the production process continues, the temperature changes with hydrate decomposition, and the reservoir temperature decreases as a whole. Before 3000 min, the temperature increases gradually, especially in areas near the production well. This change occurs because at that moment, a larger pressure gradient in this region leads to drastic hydrate decomposition and high heat absorption, which causes the temperature to decline significantly. This study defines this phenomenon as pressure gradient preponderance. As production continues, the pressure gradient decreases gradually, and the influence of hydrate decomposition on temperature weakens. At 30,000 min, due to the influence of the boundary condition, the temperature near the production well decreases initially and then increases. This phenomenon is defined as boundary temperature preponderance. At 300 and 600 min, the temperature increases constantly (Fig. 8c), and both times are within the scope of the “pressure gradient preponderance”. Here, the exploitation time is long, considerable heat is absorbed, and the temperature is low. Fig. 8c shows that there is an inter

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low hydrate saturation is beneficial to pressure transfer at the boundary; therefore, the pressure declines. 3.5. Gas production

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Gas production is one of the most important processes that affects hydrate exploitation. During depressurization, cumulative gas production increases dramatically at the beginning of production and then stabilizes. At an early stage, a high pressure gradient drives gas generated from hydrate decomposition to the production well. Later, less gas is generated, and gas flow to the production well decreases. Moreover, other parameters can influence gas production. The effects of the initial hydrate saturation (Sh0), initial pore structure including porosity (?) and initial absolute permeability (K0⁠ ) and ice generation on gas produced from hydrate were estimated. The analysis method consisted of setting a series of values for these parameters (Sh0 = 0.45, ? = 0.2, K0⁠ = 1000 mD). Then, only one parameter was changed to analyse the associated effect. Fig. 10 shows the dependence of gas production on the initial hydrate saturation. The results indicate that gas production is lower at a lower initial hydrate saturation (Sh0 = 0.25), and the instantaneous gas rate is low at an early stage (approximately 150 h). When the existing hydrate saturation per unit volume is high, the gas deliverability of the reservoir is high. Moreover, the reaction surface area increases with increased hydrate saturation, and the gas production rate also increases. At the end of the gas production stage, gas production stabilizes. The cumulative gas production at a high initial hydrate saturation was larger (nearly 440 Nm3⁠ ) than that at a low hydrate saturation (370 Nm3⁠ ). Cumulative gas production in the reservoir at different porosities and permeabilities is shown in Fig. 11. Fig. 11a shows that at an early stage, gas production increases sharply, and the effect of the porosity can be ignored until approximately 100 h. As gas is continuously produced, the cumulative gas production in the porous medium with a high porosity ( ? = 0.4) increases more than at a porosity of (? = 0.2) because at the same saturation level, a high porosity results in more hydrate decomposition. At the beginning of the decomposition process, the actual flow conduit and pressure gradient are almost the same; therefore, the gas production rates are extremely similar. By contrast, when the permeability decreases by a factor of ten, the rate of gas production dramatically improves, as shown in Fig. 11b. The cumulative gas production continues to increase until 1500 h.

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Fig. 8. Temperature distribution at different times (300, 3000, and 30,000 min) (T is the temperature, and L is the distance from the well).

section point in the temperature curves at the same production time and different hydrate saturations. This occurs because a large pressure gradient exists near the production well, therefore, a high level of hydrate saturation in the reservoir leads to high hydrate decomposition and heat absorption. In the reservoir far from the production well, the pressure is high when the hydrate saturation level is high; thus, hydrate decomposition is limited and the temperature is high. To investigate the effect of the initial hydrate saturation on pressure and temperature dynamics, the pressure was varied with time at a position of 1 m (node 1), as shown in Fig. 9. At the initial hydrate saturation of 0.45, the pressure initially decreases quickly and becomes stable after 200 min. At a saturation level of 0.25, the pressure gradually reduces. Moreover, at 0.45, the pressure is higher than that at 0.25 before 450 min. After this point, the saturation declines, causing a large pressure drop. Specifically, a hydrate saturation gradient forms and results in a rapid pressure decrease. However, as noted previously,

Fig. 10. Cumulative gas production for different initial hydrates saturation.

Fig. 9. The pressure at node 1 under different initial hydrate saturations (0.25 and 0.45) from 0 to 600 min (Pw is the water pressure). 7


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Fig. 11. Cumulative gas production in the reservoir at different porosities (a) and permeabilities (b).

without ice generation are similar to the experimental data, reflecting the independence of ice generation at this stage. With continued gas production at a constant boundary temperature, the effect of ice generation can be disregarded. Overall, the final gas production estimates from experiments and the numerical results of the models with and without ice generation Are similar. According to the comparison and analysis above, the proposed model is suitable for simulating and investigating methane hydrate exploitation under depressurization. The improved model can simulate the changes in some important parameters during methane hydrate exploitation under a wide range of temperatures, including those below the freezing point. Thus, the calculation results reflect the hydrate self-preservation caused by ice formation. This factor cannot be ignored during the process of gas hydrate exploitation at low-temperature conditions, such as those in deep seabed or permafrost regions. Notably, the results of this study suggest that the gas production rate will decrease if ice is generated during hydrate exploitation. This phenomenon has been reported during practical production, such as in the Gulf of Mexico. In addition, the results of this study indicate that the gas production rate decreases significantly in the middle of the production process (in this paper, from approximately 200 min to 300 min). In addition, the position of the lowest temperature in the reservoir moves away from the production well over time. Moreover, ice generation is concentrated in the region near the well. All these findings can be used to determine where and when a heat source should be added to improve the efficiency of gas production. Additionally, the results provide a fundamental basis for methods that combine depressurization and thermal stimulation. However, in actual production, the relationships between gas production and influential factors must be accurately quantified. Therefore, in the further, this model can support important assessments of hydrate exploitation in the field.

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However, at the end of production, the gas production at a low permeability (K0⁠ = 100 mD) stabilizes at a high value. At high porosity and permeability levels, flow paths form, and the gas flows through the preferential flow paths. Thus, gas production is enhanced by these flow paths. In addition, low porosity and permeability suppress the flow of gas, resulting in a slow rate of hydrate decomposition. Notably, the final gas production is the same under different porosity and permeability conditions for the same amount of hydrate decomposition. To investigate the effect of ice generation on gas production, the cumulative gas production was compared based on models with and without ice generation and experimental data [41]. As shown in Fig. 12, the numerical results of the model with ice generation are similar to those of the experimental data for gas production at an early stage. Moreover, the cumulative values of the model without ice generation are initially larger than those of the other model because ice generation reduces the surface area available for hydrate decomposition. Ice also occupies the pore space and suppresses the flow of gas. Therefore, ice generation strongly influences gas production in the early stage. However, in the late stage, the numerical results calculated from the model

4. Conclusion

An improved mathematical and numerical model was proposed for methane hydrate decomposition by depressurization at a relatively low temperature (274 K) in porous media. The model can be used to investigate the potential of ice generation. In the process of hydrate exploration, the amount of ice generation increases gradually over time. Ice saturation declines from the area near the production well to the internal reservoir. The ice generation influences relevant parameters during hydrate production by depressurization. Moreover, the absolute permeability of the reservoir decreases with ice generation, but the in

Fig. 12. Comparison of cumulative gas production based on experiments [41] and simulations with and without ice generation. 8

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fluence of the pressure can be disregarded. The change in temperature as production progresses is complex. Initially, the temperature increases from the area near the production well to the internal reservoir. Later, the temperature in the reservoir near the production well decreases initially and then increases. Hydrate saturation in the reservoir is the determinant of the final gas production. Other factors, which include permeability and ice generation, only influence the gas production rate. In addition, different initial hydrate saturations can affect other parameters, including pressure, temperature and permeability. High initial hydrate saturations can result in high average pressures and low reservoir permeability at the same time during production. However, compared with the temperature at low hydrate saturations, the temperature at high saturations is lower near the production well and higher farther from the production well. Ice formation not only interferes with the decomposition of methane hydrate but also decreases the permeability. Therefore, the gas production rate declines if ice formation occurs during the process of hydrate exploitation.

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Acknowledgements

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This study was supported by the Major Program of National Natural Science Foundation of China (51436003) and the Natural Science Foundation of China (grant nos. 51276030 and 51506024).

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