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Studies of the hydrate cores have shown that natural fractures can be frequently observed in hydrate reservoirs, resulting in a fracturefilled hydrate. Therefore, it is highly necessary for industries to predict the gas well productivity of fracturefilled hydrate reservoirs. In this work, an embedded discrete fracture model is applied to characterize the natural fractures of fracturefilled gashydrate reservoirs. The nonlinear mass and energy conservation equations which are discretized with the finitedifference method are solved by the fully implicit approach, and the proposed model is justified by a commercial simulator. On the basis of the proposed model, we investigate the influences of natural fractures, fracture conductivity, and hydrate dissociation rate on the gas well productivity and the distributions of pressure, temperature, and hydrate saturation. The simulation results show that hydraulic and natural fractures exert significant impacts on the gas well productivity of the fracturefilled hydrate reservoirs, and the cumulative gas production is increased by 45.6% due to the existence of the connected natural fractures. The connected natural fractures can impose a more important influence on the gas well productivity than the unconnected natural fractures. The cumulative gas production is increased by 6.48% as
Natural gas hydrate (NGH) is formed from gas and water under particular pressure and temperature (
Developing gas hydrate is complicated which involves multiphase flow (gaswater) and hydrate phase transition. Moreover, thermal convection and hydrate decomposition occur during the development of gashydrate which can significantly affect temperature distribution and gas well productivity. Therefore, a comprehensive insight into the effect of hydrate phase transition on multiphase mass and heat transfer of gashydrate reservoirs is one of the key issues for optimizing hydrate development. The kinetic model proposed by
In all the aforementioned studies, the gashydrate reservoirs are assumed as a monoporous media where the gas hydrate can only be observed in the pore space. However, the most recent studies show that natural fractures commonly exist in gashydrate reservoirs (
As one of the most applicable and economical method, numerical simulation has been widely used for evaluating the effect of the complex natural fracture network on gas well productivity. However, in terms of capturing the geometries of natural fractures, the traditional numerical simulator requires applying the local grid refinement (LGR) technique or unstructured grids, which can be inconvenient. In order to overcome the deficiencies of the traditional numerical methods, the embedded discrete fracture model (EDFM) method has been introduced to describe complex fractures (
Although the EDFM was used widely to characterize the natural fracture in conventional oil/gas reservoirs, it has not been hitherto applied in gashydrate reservoirs to predict the gas well performance (
This study considers a fractured vertical well in a twodimension (2D) naturally fractured gas hydrate reservoir. In order to consider heat transfer and to characterize the complex fractures, we make the following assumptions to simulate gaswater flow in hydrate reservoirs.
(1) hydrate is treated as an immobile solid phase;
(2) the compressibility of rock and fluids are considered to characterize porosity change;
(3) the reservoir is homogeneous and the flow of water and gas conforms to Darcy’s law;
(4) the capillary pressure is neglected in the model;
(5) the effects of hydrate saturation changes, hydrate occurrence state, and pore structure on the relative permeability of gas and water are neglected;
(6) only thermal conduction and thermal convection in the reservoir are considered, and the influence of thermal radiation is neglected.
For the matrix system, the mass conservation equation of the gas and water can be expressed as (
For the intersecting fracture system, the mass conservation equation of the gas and water can be expressed as:
For hydrate, the mass conservation equations of the matrix and fracture systems are (
For the EDFM method, unrefined and structured grids are generally used to characterize complex natural fractures, and the finite difference method can be used as the numerical method to discretize mass conservation equations (
The discrete form of fluid flow between matrix grids in Eq.
Likewise, the discrete form of fluid flow between fracture grids in Eq.
The discrete form of mass transfer between matrix grid and fracture grid in Eqs
The discrete form of mass transfer between intersecting fracture grids in Eq.
The discrete form of mass transfer between the wellbore and fracture grid in Eq.
In Eq.
In Eqs
Schematic of the EDFM model for fractured hydrate reservoirs.
For type #1 NNC, the matrixfracture transmissibility factor can be expressed as (
In Eq.
In Eq.
In Eq.
The residual mass conservation equations in terms of the finite difference method can be expressed as (
For the hydrate, we can have:
For the matrix system, the energy conservation equation can be expressed as (
In addition, the energy conservation equation for the fracture system is:
The effective thermal conductivity
The internal energy
In Eq.
Energy exchange
In Eq.
Energy exchange
In general, the discrete form for the energy conservation equation of matrix and fracture grids can be expressed as (
For Eqs
In order to examine the accuracy of the proposed model, we validate the proposed model against a commercial simulator CMG STARS. As the pressure is decreased in the reservoirs, the gas and water can be gradually released from the hydrate. To illustrate the fluid flow of different phases, we utilize the BrooksCorey equation (
Benchmark values of the parameters used for validation.
Parameter  Value  Unit  Parameter  Value  Unit 

Matrix permeability  1  mD  Matrix porosity  0.3  frac 
Hydrate saturation  0.3  frac  Gas saturation  0.1  frac 
Initial pressure  9.26  MPa  Initial temperature  12  °C 
Hydrate decay rate  1.07 × 10^{13}  mole/(day·KPa·m^{2})  Specific area  3.7 × 10^{5}  m^{2}/m^{3} 
Activity energy  81,084.2  J/mole  Reaction enthalpy  51,858  J/mole 
Rock thermal cond  1.5 × 10^{5}  J/(m·day·°C)  water thermal cond  6 × 10^{4}  J/(m·day·°C) 
Gas thermal cond  2.93 × 10^{3}  J/(m·day·°C)  Hydrate thermal cond  3.93 × 10^{4}  J/(m·day·°C) 
Rock heat capacity  840  J/(kg·°C)  Water heat capacity  4,200  J/(kg·°C) 
Gas heat capacity  2,400  J/(kg·°C)  Hydrate heat capacity  1.54 × 10^{3}  J/(kg·°C) 
Parameter A in Eq. (A3)  38.98  KPa  Parameter B in Eq. (A3)  −8,533.8  K 
In this case, we established a 155×155×30 m^{3} hydrate reservoir with a single fracture to conduct the validation.
Top view of the grid system used in CMG STARS.
Validation of the single fracture model:
In addition to the single fracture case, the validation was conducted on a complex fracture network model (see
Schematic diagram of complex fracture network model used for validation.
Validation of complex fracture model:
Based on the results shown in
With the aid of the proposed EDFM model, the authors studied the effects of natural fractures and heat transfer on the production of gashydrate reservoirs. The dimension of the reservoir is 310 × 310 × 30 m^{3} which is discretized into 31 × 31 × 1 grids. The values of the other reservoir and fluid parameters are the same as those in
In order to explore the effect of fracture networks on the performance of gashydrate production well, three scenarios were investigated: Scenario #1 which considers 30 natural fractures and 1 hydraulic fracture; Scenario #2 which only considers 1 hydraulic fracture; and Scenario #3 which contains no fracture.
Schematics of the different scenarios to investigate the effect of fracture networks:
Simulation outputs of different scenarios:
In this section, different numbers of natural fractures (
Schematics of the different scenarios to investigate the effect of the number of natural fractures:
Comparison of cumulative gas production of different scenarios with different values of
Group  Scenario number 


Cumulative gas production, 10^{4}m^{3}  Increment, % 

Group A  1  2  2  613.05  — 
2  10  2  621.18  1.33  
3  30  2  638.71  4.19  
4  50  2  652.78  6.48  
Group B  5  30  0  457.22  — 
6  30  1  552.98  20.94  
7  30  2  638.71  39.69  
8  30  4  655.55  43.38 
A comparison of pressure, temperature, and hydrate saturation after 1800 days of production with different values of
Pressure, temperature, and hydrate saturation field maps of different scenarios at the 1800th production day:
In this section, the authors discussed the impacts of dimensionless hydraulic fracture conductivity (
In Eq.
Simulation outputs of different scenarios with different values of hydraulic fracture conductivity:
Moreover, the authors varied the conductivity of natural fractures together with the conductivity of the hydraulic fracture to compare their effects on well productivity.
Comparison of cumulative gas production of a vertical well with different values of hydraulic fracture and natural fracture conductivity.
Cumulative gas production, 104m3  

Chf  Cnf=25 mD∙m  Cnf =125 mD∙m  Cnf =250 mD∙m 
25 mD∙m  364.92  368.08  368.43 
125 mD∙m  480.39  533.09  543.73 
250 mD∙m  506.07  568.35  582.69 
Hydrate dissociation rate also imposes a significant influence on the mass and heat transfer in developing gas hydrate. The kinetic model of Kim
The decomposition rate constant
Simulation outputs of different scenarios with different values of
In this work, we developed an embedded discrete fracture model to study the gas well productivity in fracturefilled gas hydrate reservoirs. By using a finitedifference scheme and a fully implicit method to solve the nonlinear equations, we validated the proposed model against a commercial simulator. In addition, we investigated the influences of natural fractures, fracture conductivity, and hydrate dissociation rate on mass and heat transfer of fracturefilled gas hydrate reservoir. The calculated results lead us to draw the following conclusions.
(1) This proposed numerical model is reliable for evaluating the gas well productivity of fracturefilled hydrate reservoirs considering the effect of natural fractures and heat transfer, and the research results are of great significance to guide the efficient development of fracturefilled hydrate reservoirs.
(2) Both hydraulic fractures and natural fractures can increase gas well productivity. Moreover, the connected natural fractures can exert a more important influence on the well productivity than the unconnected natural fractures. The cumulative gas production is increased by 6.48% as
(3) The gas well production rate is increased by increasing fracture conductivity, and the conductivity of hydraulic fracture exerts a more significant influence on the gas well productivity than that of natural fracture. The relative cumulative gas production increment is 15.14% and 58.15% as
(4) The well productivity is increased as the hydrate dissociation rate is increased. Besides, a higher hydrate dissociation rate can lead to a lower temperature along fractures due to a larger reduction of solid hydrate. The minimum temperature along natural fractures is around 6.3°C with the value of
The original contributions presented in the study are included in the article/
YC: methodology, conceptualization, writing original draft, review, and editing. BT: conceptualization, reviewing, and editing. WL: conceptualization, reviewing, and editing. CL: investigation, reviewing. YZ: reviewing.
The authors are grateful to the National Natural Science Foundation of China (51991365), China Geological Survey Project (No. DD20211350), and Guangdong Major Project of Basic and Applied Basic Research (No. 2020B0301030003).
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
The Supplementary Material for this article can be found online at:
Contact area, m^{2}
Hydrate decomposition surface area, m^{2}/m^{3}
Specific area, m^{2}/m^{3}
Contact area of matrix and fracture segments, m^{2}
Rock compossibility coefficient, MP^{1}
Gas and water compossibility coefficient, MP^{1}
Heat capacities of gas, water and hydrate, J/(kg·°C)
Average normal distance between matrix and fracture grid, m
Average normal distance from the fracture to the intersection, m
Reaction activation energy, J/mole
Enthalpy of the water and gas, J
Reaction enthalpy, J
Matrix and fracture permeability, mD
Matrix and fracture permeability, mD
Relative permeability
Hydrate decomposition rate constant, mole/(m^{3}·KPa·day)
Intrinsic reaction rate constant, mole/(m^{3}·KPa·day)
Mass of hydrate dissociation, kg
Mass accumulation due to hydrate dissociation, kg
Molecular weight of water, gas, and hydrate, kg/gmole
Hydrate number
Pressure, MPa
Equilibrium pressure of hydrate, KPa
Well bottomhole pressure, MPa
Volumetric flow rates between intersecting fractures, m^{3}/day
Volumetric flow rates between matrix and fracture, m^{3}/day
Volumetric flow rates between fracture and well, m^{3}/day
Gas constant, J/moleK
Equivalent wellbore radius, m
Wellbore radius, m
Water, gas, and hydrate saturation
Temperature, °C
Equilibrium temperature of hydrate, °C
Reference temperature, °C
Transmissibility between fracture segments in same fracture
Fracturefracture transmissibility
Matrixmatrix transmissibility
Matrixfracture transmissibility
Reference temperature, °C
Internal energy, J
Internal energy of matrix system, J
Internal energy of fracture system, J
Internal energy of gas and water, J
Hydrate internal energy, J
Rock internal energy, J
Heat absorbed by hydrate decomposition
Energy exchange between different fracture, J
Energy exchange between fracture and well, J
Energy exchange between matrix and fracture system, J
Volumetric flow rates, m^{3}/day
Rock volume, m^{3}
Void pore volume, m^{3}
Thermal conductivity, J/(m·day·°C)
Effective thermal conductivity, J/(m·day·°C)
Water, gas, and hydrate thermal conductivity, J/(m·day·°C)
Average thermal conductivity between fractures, J/(m·day·°C)
Gas and water viscosity, mPa·s
Hydrate density, kg/m^{3}
Fluid density, kg/m^{3}
Porosity
Void porosity
Length, width, and thickness of fracture grids
Length, width, and thickness of matrix grids
Matrix
Fracture
Gas and water
Solid hydrate