Numerical simulation of depressurization exploitation of ...

Scientific Journal of Intelligent Systems Research Volume 3 Issue 3, 2021

ISSN: 2664-9640

192

Numerical simulation of depressurization exploitation of seabed surface gas hydrate based on Submarine natural gas hydrate

capping type pressure-reducing exploitation device

Chenxu Shu 1,2,3, Wei Li 1,2,3 , a *

1School of Mechanical and Electrical Engineering, Southwest Petroleum University, Chendu 610500, China

2Energy Equipment Research Institute, Southwest Petroleum University, Chengdu 6105003, China

3Key Laboratory of Oil and Gas Equipment Ministry of Education, Southwest Petroleum University, Chendu 610500, China

[email protected]

Abstract

We established a mathematical model for the gas hydrate decomposition by depressurization based on Submarine natural gas hydrate capping type pressure-reducing exploitation device, taking factors such as heat convection, gas–liquid two-phase flow, and hydrate decomposition kinetics into consideration. The basic law of depressurization exploitation of natural gas hydrate and the effects of the production pressure, absolute permeability of the reservoir, production temperature and initial hydrate saturation, on the decomposition results were analyzed using numerical simulation. The results showed that the lower the production pressure, the faster the hydrate decomposition, and the faster the reservoir temperature will drop. When the reservoir permeability is low, the production efficiency will be lower. The higher production temperature, the shorter production cycle and the higher production efficiency. The lower the hydrate saturation, the higher the initial gas production rate.

Keywords

Seafloor surface gas hydrate; The cap-top depressurizing exploitation device; Numerical Simulation; Temperature Field.

1. Introduction

Natural gas hydrate is a new type of energy with high energy density and has high resource value. The reserves of hydrate in China are huge, and the reserves of hydrate in sea area are about 80 billion tons of oil equivalent[1]. At present, the development of natural gas hydrate mainly adopts thermal stimulation method and pressure reduction method, which is through changing the environmental conditions of gas hydrate reservoir temperature and pressure. It promote that decomposition of natural gas hydrate to collect natural gas [2].

In July 2017, China first exploited marine gas hydrate in the South China Sea, which provided reliable data support for subsequent experimental research. However, the research of marine natural gas hydrate has been carried out in China for a short period of time, and it is still in the exploration stage, and no sustainable and efficient mining method has been formed yet.

Gas hydrate production by depressurization method refers to reducing the pressure of hydrate reservoir by pumping, making it unstable and decomposing, and then producing gas and water. Because depressurization mining does not require additional equipment input, nor does it require expensive continuous excitation, it has great advantages in technology and economy,


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so depressurization method is considered the most economical and effective production method in the current natural gas hydrate reservoir mining technology.

In this paper, a coupled numerical model of gas hydrate chemical decomposition and gas-water two-phase flow is established based on the cap-top depressurizing exploitation device[3] , considering the kinetics of hydrate decomposition, multi-phase flow and fluid heat transfer, and the finite element method[4] is used to solve the problem. The effects of different collection pressures on gas hydrate dissociation process in porous media are studied. At the same time, because the capping method is different from the traditional method, it has a unique boundary condition, that is, the upper edge of hydrate reservoir is covered by liquid phase.

Fig 1. Seabed gas hydrate cap - top depressurizing exploitation device

2. Gas hydrate mining mechanism

The decomposition and exploitation of natural gas hydrates involve a variety of physical and chemical processes, including phase equilibrium, decomposition kinetics, mass conservation, energy conservation, multiphase flow and permeability variation of porous media [5]. On the basis of this theory, the mathematical model of hydrate depressurization decomposition is established.

The numerical simulation proces herein is based on that following assumption:

Hydrate is a mono-component methane hydrate, and that formation or decomposition process of hydrate satisfies the phase equilibrium reaction;

Neglecting the dissolution of the gas phase produced by decomposition in water;

Considering that the reservoir is uniform porous medium, hydrate and solid sediments can not flow, gas-liquid flow in porous medium follows Darcy's law;

Recurrence of hydrate is not considered;

Viscosity dissipation is not considered.

2.1. Continuity equation

In that proces of decomposing and producing gas of natural gas hydrate, there are usually three phase[6] (gas phase, water phase, solid phase) and the continuity equation of each phase is as follows:

Hydrate continuity equation: 𝜕(𝜙𝜌ℎ𝑆ℎ)

𝜕(𝑡)= 𝑚ℎ (1)

Gas continuity equation: 𝜕(𝜙𝜌𝑔𝑆𝑔)

𝜕(𝑡)− ∇(

ρg𝐾krg

μg∇Pg) = 𝑚𝑔 (2)

Water continuity equation:


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𝜕(𝜙𝜌𝑤𝑆𝑤)

𝜕(𝑡)− ∇(

𝜌𝑤𝐾𝑘𝑟𝑤𝜇𝑤

∇𝑃𝑤) = 𝑚𝑤 (3)

In where,K is the absolute permeability of porous media𝜌𝑖 (i=w,g,h) is that density of each phase,𝑆𝑖(i=w,g,h) is the saturation of each phase,𝑃𝑖(i=w,g) is the pressure of water and gas phase,𝑘𝑟𝑖(i=w,g) is the permeability of water and gas phase,𝜇𝑖(i=w,g) is the kinematic viscosity of water and gas phase,𝑚𝑖(i=g,h,w) is the rate of production or consumption of each phase,𝜙 is the porosity of porous medium, and its value changes with the decomposition of hydrate:𝜙 =𝜙0(1 − 𝑆ℎ).

2.2. Energy equation

The energy equation follow that law of conservation of energy:

Energy increment = input energy - output energy

Specifically, in the numerical simulation of hydrate decomposition, it includes convection heat transfer of fluid, heat transfer of porous material[7], external injection heat and heat absorbed by hydrate decomposition. The specific equation is as follows:

𝜕(𝐶𝑡𝑇)

𝜕(𝑡)= ∇ [(𝜌𝑤𝐶𝑤

𝐾𝑘𝑟𝑤𝜇𝑤

∇𝑃𝑤 + 𝜌𝑔𝐶𝑔𝐾𝑘𝑟𝑔

𝜇𝑔∇𝑃𝑔)𝑇] + ∇(𝐾𝑡∇𝑇) − 𝑚ℎΔ𝐻 (4)

In where,T is temperature,𝐾𝑡is comprehensive heat transfer coefficient,𝐶𝑤 , 𝐶𝑔are water and gas

specific heat,Δ𝐻 is enthalpy change during hydrate decomposition[8],Ct is comprehensive specific heat capacity of the entire reservoir, the calculation method is as follows:

𝐶𝑡 = 𝜙(𝜌𝑤𝑆𝑤𝐶𝑤 + 𝜌𝑔𝑆𝑔𝐶𝑔) + 𝜌𝑟𝐶𝑟(1 − 𝜙) (5)

𝐾𝑡 = 𝜙(𝑆𝑤𝐾𝑤 + 𝑆𝑔𝐾𝑔 + 𝑆ℎ𝐾ℎ) + (1 − 𝜙)𝐾𝑟 (6)

In where,𝐾𝑖(i=w,g,h,r) is the heat transfer coefficient of water, gas, hydrate and porous media skeleton,𝐶𝑖(i=w,g,r)is the specific heat of water, gas and porous media, and 𝜌𝑟 is the density of porous media.

2.3. Infiltration equation

Relative permeability is the ratio of the effective permeability of the fluid at any saturation to the permeability at 100% saturation, and the relative permeability of the fluid under porous conditions is always less than 1.

The relative permeability model used in this problem is derived from Stone[9]and Aziz[10] studies:

𝑘𝑟𝑔 = (𝑆𝑔∗)

𝑛, 𝑆𝑔

∗ =(𝑆𝑔 − 𝑆𝑖𝑟𝑔)

(1 − 𝑆𝑖𝑟𝑤)(7)

𝑘𝑟𝑤 = (𝑆𝑤∗ )𝑛, 𝑆𝑤

∗ =(𝑆𝑤 − 𝑆𝑖𝑟𝑤)

(1 − 𝑆𝑖𝑟𝑤)(8)

In where,𝑘𝑟𝑤is that relative permeability of the wat phase, 𝑘𝑟𝑔is the relative permeability of the

gas phase, 𝑆𝑖𝑟𝑔, 𝑆𝑖𝑟𝑤is the content of bound gas and bound water in the porous medium, 𝑆𝑖𝑟𝑔 =

0.02, 𝑆𝑖𝑟𝑙 = 0.12, 𝑛 = 3.0.

Its relation is shown in fig.2:


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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rela

tive

per

meab

ilit

y

Water saturation

krg

krw

Fig2. Relative permeability curve of water and gas

2.4. Kinetic equation of hydrate decomposition

Hydrate decomposition is base on that Kim-Bishnoi kinetic model[11]:

𝑚𝑔 = 𝑘𝑑𝑀𝑔𝐴𝑠(𝑓𝑒 − 𝑓𝑔) (9)

In where,𝑘𝑑 is that rate constant of hydrate decomposition, 𝐴𝑠is the specific surface area of the decomposition reaction, 𝑓𝑒, 𝑓𝑔are the reaction equilibrium fugacity and the local gas fugacity, in

the actual process, they are substituted by the critical pressure and the gas pressures 𝑃𝑒 , 𝑃𝑔

respectively[12].

The hydrate decomposition rate constant kd is calculate by that following equation[6]:

kd = 𝑘0exp(−Δ𝐸

𝑅𝑇)

In where,k0 = 1.25× 105, ΔE is chemical reaction activation energy, and ΔE/𝑅 = 9752.73K,T is temperature.

The equilibrium pressure is a function of temperature and its equation is as follows [13]:

𝑃𝑒 = 1.15 exp (𝑒1 −𝑒2𝑇) (10)

In where, e1, 𝑒2 are regression functions,e1 = 49.3185, e2 = 9459.

2.5. Other equation

The unknown quantities 𝑆𝑔,𝑆𝑤,𝑆ℎ,P,T needed to be solved in this mathematical model.

According to the equilibrium relationship of hydrate reaction, the following relationship can be obtained:

−mh =𝑁𝑀𝑤 +𝑀𝑔

𝑀𝑔𝑚𝑔 (11)

mw =𝑀𝑤

𝑀𝑔

𝑚𝑔 (12)

In where, Mw,Mg are that relative atomic mass of water and natural gas respectively, N is the

wat combination number, generally take N=6.

Since that porous medium contain only water, gas and hydrate, the saturation relationship can be obtained:

𝑆𝑔 + 𝑆𝑤 + 𝑆ℎ = 1 (13)

𝐴𝑠 is the specific surface area of the reaction. As the reaction time advances, the proportion of water phase and gas phase changes continuously, that is, the flow space changes with time, so the specific surface area of the reaction also changes with time[14]:


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𝐴𝑠 = √𝜙𝑤𝑔3

2𝐾,𝜙𝑤𝑔 = 𝜙0(1 − 𝑆ℎ) (14)

In where, K is absolute permeability, ϕ𝑤𝑔 is that sum of space occupied by water and gas

phase,𝑆ℎis hydrate saturation, is a function related to time, and 𝜙0 is the initial porosity rate of porous medium.

The capillary force is as follow[15]:

𝑃𝑐 = 𝑃𝑤 − 𝑃𝑔 (15)

And capillary force is a function only related to liquid saturation[16]:

𝑃c = 𝑃𝑐𝑜 [(𝑆𝑤∗ )−

1𝜆 − 1]

𝜆

(16)

In where, λ is constant coefficient, λ = 0.45；𝑃𝑐𝑜 is inlet capillary pressure,𝑃𝑐𝑜 = 1kPa.

The simultaneous equations (1), (2), (3) and (4) can obtain the control equations for the decomposition of water, gas, solid three-phase and temperature change in the porous medium.

By means of finite difference method, the simultaneous equations are discretized into linear algebraic equations, and the algebraic equations with the center difference discrete in space and the first order backward difference discrete in time are obtained. Then the Newton iterative method is used for coupling solution, and the values of pressure, temperature and saturation are obtained by using the implicit numerical method.

3. Numerical simulation model

The physical model is shown in Fig.3:

Fig3. Physical model

In this paper, the physical model is that in the top cover collection device, the longitudinal hydrate is decomposing and changing in pressure reduction, in which the distribution of gas phase and liquid phase in the device plays the role of regulating the pressure in the device. The specific principle is not within the scope of this research, take one section of the reservoir for dispersion, namely the hydrate reservoir area shown in Figure 3, and make corresponding numerical simulation.

Reservoir parameters in numerical simulation are shown in Table 1[17].


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Table 1 Reservoir parameters

Name Parameter Value

Reservoir temperature Ti 6℃

Reservoir pressure Pi 8MPa

hydrate saturation Sh 0.5

Upper boundary liquid saturation Swg 1

Initial porosity 𝜙0 0.3

Reservoir permeability K 300mD

4. Numerical simulation of depressurization mining mechanism

Taking 2MPa,3MPa,4MPa and 4.5MPa as production pressure respectively, the production condition of natural gas hydrate in depressurization environment was analyzed.

Fig.4 shows the variation of gas phase saturation in depth under different production pressures. It can be seen that the smaller the collection pressure, the greater the rate of hydrate decomposition and the faster the rate of natural gas generation. This is because the pressure is the main driving force of hydrate decomposition during depressurization production, and the greater the pressure difference, the greater the decomposition power.

It can also be seen that although the higher the collection pressure, the slower the gas production rate, the lower the residual gas saturation in the reservoir one year later.

This is because the dissociation process is accompanied by a large amount of water production, and the rapid dissociation speed will cause the water saturation to rise rapidly, thereby reducing the relative permeability of the gas phase, so that part of the gas backlog in the reservoir.

0.0 0.5 1.0 1.50.00

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Gas

satu

rati

on

Depth(m)

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30d

1year

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Gas

satu

rati

on

Depth(m)

5min

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720min

2880min

4320min

30d

1year

B

Gas

satu

rati

on

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

C

Gas

satu

rati

on

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

D

A) 2MPa B)3MPa C)4MPa D)4.5MPa

Fig4. The distribution of gas saturation with depth at different pressures and different times

Fig.5 shows the variation of hydrate saturation along the depth direction. Obviously, there is a sharp decomposition front in the evolution of the initial dissociation stage. At this stage, dissociation takes place in a narrower region and the surrounding medium can provide sufficient heat to hydrate. As the dissociation continues, the hydrate dissociates in a wide area, which requires a large amount of heat, and the surrounding medium can not provide the


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required heat immediately. Therefore, the hydrate can not dissociate and form a wide dissociation zone in a short time, and can only advance backward in a narrow decomposition zone. Under different collection pressure, the advancing speed of the decomposition front is inversely proportional to the collection pressure.

0.0 0.5 1.0 1.5

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Hydr

ate

satu

rati

on

Depth(m)

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30d

1year

A

Hydr

ate

satu

rati

on

Depth(m)

5min

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30d

1year

BHy

drat

e sa

tura

tion

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

C

Hydr

ate

satu

rati

on

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

D

A)2MPa B)3MPa C)4MPa D)4.5Mpa

Fig5. Distribution of hydrate saturation with depth under different pressures and different times

Fig.6 shows changes in temperature in the formation of the hydrate. With the continuous generation of natural gas hydrate, the temperature in the region decreases due to dissociation and endothermic. Therefore, under the driving force of temperature difference, heat flows from the surrounding environment to the hydrate dissociation zone. At the same time, it can be seen that the smaller the collection pressure, the more intense the decomposition process of the decomposition front, which leads to the rapid temperature drop, so that the entire reservoir will be in the lower temperature environment, and the lower reservoir temperature will hinder the backward advancement of the decomposition front. It can be seen that the heating equipment has a positive effect on the exploitation of hydrate.

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

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6.00

6.05

Temperature(℃)

Depth(m)

5min

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2880min

4320min

30d

1year

A

Temperature(℃)

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

B

Temperature(℃)

Depth(m)

5min

20min

60min

2880min

4320min

30d

1year

C

Temperature(℃)

Depth(m)

5min

20min

60min

720min

2880min

4320min

30d

1year

D

A)2MPa B)3MPa C)4MPa D)4.5Mpa

Fig6. Temperature distribution with depth at different pressures and different times


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Fig.7 and Fig.8 show the production rate and accumulated gas production under the production pressure of 2MPa,3MPa,4MPa and 4.5MPa respectively. It can be seen that the peak value of gas production rate decreases with the increase of production pressure, and the arrival time of the peak value also shifts with the increase of production pressure. As mentioned above, the main driving force of depressurization production is pressure difference, and the lower the production pressure, the higher the rate of hydrate decomposition, the higher the rate of gas production, and the higher the peak value of gas production. However, too low pressure will lead to rapid cooling, which will inhibit the decomposition of residual gas hydrate, increase the probability of hydrate re-generation, and also lead to a rapid increase in water yield, so that part of the gas phase due to the reduction of relative permeability and backlog in the reservoir, resulting in a decline in gas production.

0 1x105 2x105 3x105 4x105 5x105 6x105

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Gas

rate

(m^3

/day

)

Time(min)

Gas rate(m^3/day)

Time(min)

2MPa

3MPa

4MPa

4.5MPa

Fig7 Gas production rate under different production pressures

0 1x105 2x105 3x105 4x105 5x105 6x105

-1

0

1

2

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6

Cumu

lati

ve g

as p

rodu

ctio

n(m^

3)

Time(min)

2MPa

3MPa

4MPa

4.5MPa

Fig8 Cumulative gas production under different production pressures

5. Analysis of influencing factors

5.1. Effect of absolute permeability of reservoir

Fig.9 shows the variation trend of gas production rate under the conditions of reservoir permeability of 100mD,150mD and 200mD respectively, and Fig.10 shows corresponding accumulated gas production.

It can be seen from fig.9 that gas production rate rises to a maximum in a short time, then falls rapidly to a certain value, and steady production continues to decrease for a period of time until zero. At the same time, it can be seen that regardless of the permeability, the time when the gas production rate reaches the peak value is basically the same, and the larger the permeability is, the larger the rate peak value is. In terms of total gas production, the higher the reservoir permeability, the higher the production.


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0 1x105 2x105 3x105 4x105 5x105 6x105

0.0

0.1

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0.0

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0.3

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0.5

0.6

Gas

rate

(m^3

/day

)

Time(min)

Gas rate(m^3/day)

Time(min)

100mD

150mD

200mD

Fig9 Gas production rate under different permeability

0 1x105 2x105 3x105 4x105 5x105 6x105

0

1

2

3

4

Cumu

lati

ve g

as p

rodu

ctio

n(m^

3)

Time(min)

100mD

150mD

200mD

Fig10 Cumulative gas production under different permeability

It can be seen from Fig.11 that low permeability will cause water and gas flow to be blocked, which will cause part of natural gas to be retained in the reservoir. It can be seen that for the reservoir with low permeability, the production efficiency of simple depressurization production is low, so it should be considered to cooperate with other methods.

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.600.020

0.025

0.030

0.035

0.040

0.045

Gas saturation

Depth(m)

100mD

150mD

200mD

Fig.11 Variation of gas saturation under different reservoir permeability one year later

5.2. Effect of mining temperature

Fig.12 shows the relationship between the production temperature and gas production rate when the production temperature is 10°C,15°C,20°C and 25°C respectively, and Fig.13 shows the relevant cumulative gas production.

It can be seen from fig.12 that that relationship between permeability and gas production rate is similar, the gas production rises rapidly to the peak first, then drops rapidly, and the higher the temperature, the higher the rate peak. This is because the gas hydrate decomposition reaction is an endothermic reaction, the higher the production temperature will provide more heat, so that the reservoir temperature will not fall too fast, suppress the decomposition of


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residual hydrate. From the point of view of cumulative gas production, the temperature change has little effect on the total gas production. The main effect is the total time required for mining. Therefore, under the same mining pressure, heating can shorten the mining cycle and improve the mining efficiency.

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1.0

Gas

rate

(m^3

/day

)Time(min)

Gas

rate

(m^3

/day

)

Time(min)

25℃ 35℃ 45℃

Fig12 Gas production rate at different temperatures

0 1x105 2x105 3x105 4x105 5x105 6x105

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Cumulative gas production(m^3)

Time(min)

25℃ 35℃ 45℃

Fig13 Cumulative gas production at different temperatures

Fig.14 shows the variation of gas saturation with reservoir depth after one year of production. It can be seen that the change of production temperature has little effect on the gas content of reservoir backlog after the completion of production.

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

0.020

0.022

0.024

0.026

0.028

0.030

0.032

0.034

0.036

0.038

Gas saturation

Depth(m)

25℃ 35℃ 45℃

Fig.14 Variation of gas saturation under different mining temperature one year later

5.3. Effect of hydrate saturation

Fig.15 shows the relationship between saturation and gas production rate when reservoir hydrate saturation is 0.2,0.3,0.4 and 0.5 respectively, and Fig.16 shows corresponding cumulative gas production.

As can be seen from Fig.15, similar trends are observed, and the lower the hydrate saturation, the higher the peak value of the gas production rate, which is caused by the special boundary


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conditions of the capping production device (i.e., the liquid saturation on the upper surface of the reservoir is 1), under the condition of constant porosity, the smaller the hydrate saturation means that the more liquid phase fills the pores, and the higher the liquid saturation, the higher the thermal conductivity of the porous medium, so that the heat is more easily transferred in the medium, so that the required heat is more easily obtained when the hydrate is decomposed.

From this, it can be seen that the cap mining unit has certain advantages for the low gas hydrate saturation area.

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0.2

0.3

0.4

0.5

Fig15 Gas production rate under different hydrate saturations

0 1x105 2x105 3x105 4x105 5x105 6x105

0

1

2

3

4

5

Cumu

lati

ve g

as p

rodu

ctio

n(m^

3)

Time(min)

0.2

0.3

0.4

0.5

Fig16 Cumulative gas production under different hydrate saturations

Fig.17 shows the gas saturation in the hydrate reservoir after one year of production. It can be seen from the figure that the saturation of hydrate in the reservoir does not affect the final production efficiency, but only the total amount of gas produced.

0.00 0.50 1.00 1.50

0.020

0.025

0.030

0.035

0.040

Gas

satu

rati

on

Depth(m)

0.2

0.3

0.4

0.5

Fig.17 Variation of gas saturation under different hydrate saturation one year later


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6. Conclusion

In this pap, a coupled numerical model for that chemical decomposition of natural gas hydrate and gas-water two-phase percolation problem is established, and the finite element method is used to solve the problem. on the basis of this, the numerical simulation of cap-type negative pressure mining is carried out, and the following conclusions are obtained:

(1)The gas production rate of depressurization decomposition of natural gas hydrate is divided into four stages:1. The gas production rate increases rapidly;2. The gas production rate decreases rapidly;3. The gas production rate develops steadily;4. The gas production rate decreases gradually to zero.

(2)In the process of hydrate depressurization collection, the hydrate is not decomposed evenly in the whole reservoir, but pushed backward gradually with a narrow front of decomposition, and the advancing speed of the front of decomposition is negatively related to the production pressure.

(3)The production pressure affects the production rate and the production peak, too low production pressure will cause the rapid increase of water yield, which will lead to the rapid rise of water saturation in the reservoir, leading to the rapid decline of relative permeability of gas phase, resulting in the accumulation of partially decomposed gas in the reservoir, which is not conducive to the development of production.

(4)The higher the reservoir permeability, the higher the gas production rate in the early stage; the smaller the reservoir permeability, the smaller the accumulated gas production, and the more residual gas remains in the reservoir. If the permeability of reservoir is too low, the production efficiency is relatively low by using depressurization method alone, and the combination of depressurization method and other methods can be considered.

(5)The higher the mining temperature, the higher the peak gas production rate and the stable gas production rate, but the final cumulative gas production has little effect. Increasing the mining temperature can shorten the mining period and improve the mining efficiency.

(6)The arrival time of peak gas production rate is only related to the production pressure; temperature, saturation and permeability only affect the peak gas production rate.

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