# A Study on the Production Simulation of Coal–Shale Interbedded Coal Measure Superimposed Gas Reservoirs under Different Drainage Methods

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## Abstract

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## 1. Introduction

_{4}in coal and shale and the dynamic change characteristics of coal and shale permeability, a fluid–solid coupling mathematical model of coal measure superimposed gas reservoirs was developed. Numerical simulations of coal measure gas output are carried out, and the gas production effect of coal measure gas wells under different drainage modes is discussed, which provides a scientific basis for the development of coal measure gas in the Dahebian block.

## 2. Coal Measure Superimposed Gas Reservoir Drainage Mathematical Model

#### 2.1. Basic Assumptions

_{4}and water in different reservoirs follows Darcy’s law, and water and CH

_{4}are saturated in the fractures of coal and shale reservoirs. (3) The adsorption and desorption of CH

_{4}mainly occur in the pores of the coal and shale matrix, and the diffusion process of CH

_{4}in the matrix follows Fick’s first diffusion law. (4) The deformation of rock mass conforms to the assumption of small deformation, while the adsorption, desorption, and effective stress of CH

_{4}will change the volume of the coal and shale matrix. (5) The reservoir temperature change is not considered in the process of coal measure gas drainage.

#### 2.2. Governing Equations of Mechanical Field

_{i}(i = x,y,z) is the displacement in the i direction; v is the Poisson’s ratio; K is the bulk modulus (Pa); F

_{i}is the force in the i direction; α

_{m}and α

_{f}are Biot effective pressure coefficients; K

_{n}is the stiffness of fracture (Pa); P

_{f}and P

_{m}are the fluid pressure in the fracture and the gas pressure in the matrix (Pa); ε

_{a}is the matrix desorption shrinkage strain; V

_{sg}is the adsorbed gas content (m

^{3}/kg); and a

_{sg}is the adsorption strain coefficient (kg/m

^{3}).

_{f}) in the fracture can be expressed as follows [25,26,27]:

_{fw}and P

_{fg}are the water pressure and gas pressure in the fracture (Pa), respectively, while S

_{w}and S

_{g}are water saturation and gas saturation, respectively.

_{L}is the Langmuir volume constant (m

^{3}/kg), and P

_{L}is the Langmuir pressure constant (Pa).

#### 2.3. Governing Equation of Hydraulic Field

_{4}in the superimposed reservoir is in a dynamic equilibrium state, and the CH

_{4}pressure in the matrix is equal to the CH

_{4}pressure in the fracture. After the beginning of drainage, CH

_{4}in the matrix begins to desorb. According to the Fick‘s diffusion law and the mass conservation equation of CH

_{4}in the coal and shale matrix, the CH

_{4}migration equation in the coal and shale reservoir matrix can be expressed as follows [29]:

_{m}is the methane content in the matrix (kg/m

^{3}); τ is the methane desorption time (s); and M

_{g}is the CH

_{4}molar mass (kg/mol).

_{s}is the coal skeleton density (kg/m

^{3}), and ϕ

_{m}is the porosity in the matrix system.

_{4}to the fracture. The coal and shale matrix can be considered the mass source of CH

_{4}in the fracture. The mass conservation equation of CH

_{4}in the fracture of coal and shale can be expressed as follows [27,28]:

_{f}is the porosity in the fracture; u

_{g}and u

_{w}are the velocities of gas and water (Pa·s); Q

_{g}and Q

_{w}are gas and water sources or sinks, respectively; and k

_{rg}and k

_{rw}are the relative permeabilities of gas and water, respectively, which are given as follows [9,30,31]:

_{wr}is the irreducible water saturation, and S

_{gr}is the residual gas saturation.

_{z}is the velocity of interlayer flow, which can be expressed as follows [32]:

_{c}is interlayer permeability, and div(P

_{z}) is the pressure gradient.

#### 2.4. Porosity and Permeability Equations in Reservoirs

_{0}is the initial value of the variable, ε

_{a}is the deformation of the coal and shale matrix caused by gas adsorption, ε

_{v}is the volumetric strain, and K

_{s}is the bulk modulus (Pa).

_{0}is the initial absolute permeability (m

^{2}).

## 3. Model Validation

#### 3.1. Simulation Case

^{3}/t, and each coal seam in the well field is a methane-rich coal seam (Figure 2). The C409 coal and its roof and floor generally contain gas, and the gas content of the coal seam is much higher than that of other lithologic reservoirs. The peak values of gas logging are generally 5~20 times those of non-coal seams (Figure 1c).

#### 3.2. Numerical Parameters and Their Schemes

#### 3.3. Boundary Conditions

_{fg}

_{0}= 9.203 MPa; the actual bottom hole flow pressure of the gas well was set as the internal boundary condition, and the other boundaries were designated non-flow boundaries. For the physical model, the upper boundary was designated a vertical downward boundary load, the lower boundary was designated a fixed constraint, and the surrounding area was designated a slip boundary.

#### 3.4. History Fitting

_{4}in the production well with the numerical simulation results, it can be seen that the simulated daily gas production is in good agreement with the measured daily gas production, with an error of 10.7%. The applicability and accuracy of the mathematical model are verified, which provides a basis for estimating dynamic changes in reservoir parameters in subsequent research and development (Figure 4).

## 4. Results

## 5. Discussion

#### 5.1. Influencing Factors of Gas Production Effect of Coal Measure Gas Wells under Different Drainage Methods

#### 5.1.1. Influence of Pressure Conduction Mode on Gas Production Effect

#### 5.1.2. The Influence of Gas Content Change on Gas Production Effect

^{3}/t, the gas content of the shale roof decreases by 0.15 m

^{3}/t, and the gas content of the shale floor decreases by 0.25 m

^{3}/t (Figure 8a); at 14 m from the wellbore, the gas content of the coal reservoir decreases by 2.31 m

^{3}/t, the gas content of the shale roof decreases by 0.08 m

^{3}/t, and the gas content of the shale floor decreases by 0.09 m

^{3}/t. With the increase in distance, the drop in reservoir pressure decreases, and the desorption amount of the reservoir matrix decreases gradually (Figure 8b).

^{3}/t, the gas content of the shale roof is reduced by 0.28 m

^{3}/t, and the gas content of the shale floor is reduced by 0.30 m

^{3}/t (Figure 8a); at a distance of 14 m from the wellbore, the gas content of the coal reservoir is reduced by 2.39 m

^{3}/t, the gas content of the shale roof is reduced by 0.09 m

^{3}/t, and the gas content of the shale floor is reduced by 0.09 m

^{3}/t (Figure 8b). In addition, at a distance of 1.4 m from the wellbore, there is a significant difference in the reduction in gas content in the shale roof and floor under single-layer drainage. This is mainly due to the difference in reservoir pressure between the shale roof and floor reservoirs. The floor is thinner than the roof, and the reservoir pressure is more susceptible to the change in coal seam reservoir pressure. Under multi-layer drainage, the reservoir pressure conduction efficiency of the shale roof is improved, facilitating the desorption and diffusion of methane in the shale matrix. Compared with single-layer drainage, the reduction in gas content in each reservoir has increased, which is more conducive to the increase in production.

#### 5.1.3. The Influence of Permeability on Gas Production Effect

#### 5.2. Enlightenment of Coal Measure Gas Development Project

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Location and gas content of the study area: (

**a**) Guizhou Province in China, (

**b**) the Dahebian block, and (

**c**) gas content of the W1 well.

**Figure 3.**Geological model of coal measure gas drainage: (

**a**) geometric model, (

**b**) mesh partition, and (

**c**) wellbore and observation points.

**Figure 5.**Cumulative gas production (

**a**) under different drainage methods, (

**b**) from each layer under multi-layer drainage, and (

**c**) under different drainage methods (coal).

**Figure 6.**Direction of reservoir pressure conduction in the 30th day under different drainage modes: (

**a**) single-layer drainage and (

**b**) multi-layer drainage.

**Figure 7.**Dynamic distribution of reservoir pressure under different drainage methods: (

**a**) single-layer drainage and (

**b**) multi-layer drainage.

**Figure 8.**Change in matrix gas content under different drainage methods: (

**a**) observation points (A, B, C) and (

**b**) observation points (A′, B′, C′).

**Figure 9.**Permeability ratio changes under different drainage methods: (

**a**) observation points (A, B, C) and (

**b**) observation points (A′, B′, C′).

Parameter | Value | Parameter | Value |
---|---|---|---|

Fracture half-length (m) | 157.9/165.9 | Support crack half-length (m) | 147.3/160.4 |

Total crack height (m) | 24.2/38.8 | Total height of support cracks (m) | 22.6/35.1 |

Vertical depth at the top of the crack (m) | 903.2/889.9 | Vertical depth of supporting crack top (m) | 904.6/893.4 |

The bottom of the crack is deep (m) | 927.4/928.7 | The bottom of the support crack is deep (m) | 927.2/928.5 |

Variable | Parameter | Value | Unit |
---|---|---|---|

ϕ_{m}_{10} | Initial porosity for coal matrix | 4.50 | % |

ϕ_{f}_{10} | Initial porosity for coal fracture | 2.30 | % |

ϕ_{m}_{20} | Initial porosity for shale matrix | 3.20 | % |

ϕ_{f}_{20} | Initial porosity for shale fracture | 1.12 | % |

k_{10} | Initial reservoir permeability (Coal) | 0.550 | 10^{−3} μm^{2} |

k_{20} | Initial reservoir permeability (Shale) | 0.197 | 10^{−3} μm^{2} |

K_{1} | Bulk modulus (Coal) | 3.0 | GPa |

K_{2} | Bulk modulus (Shale) | 6.550 | GPa |

υ_{1} | Poisson’s ratio of coal | 0.350 | - |

υ_{2} | Poisson’s ratio of shale | 0.280 | - |

K_{s} | Skeleton bulk modulus | 7.340 | GPa |

ρ_{s}_{1} | Density of coal skeleton | 1470 | kg m^{−3} |

ρ_{s}_{2} | Density of shale | 2660 | kg m^{−3} |

μ_{w} | Gas dynamic viscosity | 1 × 10^{−3} | Pa·s |

μ_{g} | Water dynamic viscosity | 1.84 × 10^{−5} | Pa·s |

P_{L}_{1} | Langmuir pressure constant (Coal) | 2.07 | MPa |

V_{L}_{1} | Langmuir volume constant (Coal) | 0.0256 | m^{3}·kg^{−1} |

P_{L}_{2} | Langmuir pressure constant (Shale) | 1.01 | MPa |

V_{L}_{2} | Langmuir volume constant (Shale) | 0.02 | m^{3}·kg^{−1} |

b_{1} | Klinkenberg factor | 0.76 | MPa |

R | Gas molar constant | 8.314 | J·mol^{−1}·K^{−1} |

P_{s} | Standard atmospheric pressure | 101 | kPa |

T_{s} | Standard temperature | 273.5 | K |

Schemes | Drainage Pressure/MPa | Simulation Duration/d |
---|---|---|

Production history fitting | Actual bottom hole flowing pressure | 500 |

Single-layer drainage (coal seam perforation) | 0.16 | 2000 |

Multi-layer drainage (full-stage perforation) | 0.16 | 2000 |

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**MDPI and ACS Style**

Wang, W.; Liu, S.; Sang, S.; Du, R.; Liu, Y.
A Study on the Production Simulation of Coal–Shale Interbedded Coal Measure Superimposed Gas Reservoirs under Different Drainage Methods. *Processes* **2023**, *11*, 3424.
https://doi.org/10.3390/pr11123424

**AMA Style**

Wang W, Liu S, Sang S, Du R, Liu Y.
A Study on the Production Simulation of Coal–Shale Interbedded Coal Measure Superimposed Gas Reservoirs under Different Drainage Methods. *Processes*. 2023; 11(12):3424.
https://doi.org/10.3390/pr11123424

**Chicago/Turabian Style**

Wang, Wenkai, Shiqi Liu, Shuxun Sang, Ruibin Du, and Yinghai Liu.
2023. "A Study on the Production Simulation of Coal–Shale Interbedded Coal Measure Superimposed Gas Reservoirs under Different Drainage Methods" *Processes* 11, no. 12: 3424.
https://doi.org/10.3390/pr11123424