# Stability Analysis of Near-Wellbore Reservoirs Considering the Damage of Hydrate-Bearing Sediments

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## Abstract

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## 1. Introduction

## 2. Theoretical Formulations

#### 2.1. Damage Statistical Constitutive Model for Hydrate-Bearing Sediments

_{0}, and γ are Weibull distribution parameters, and F is the hydrate-bearing sediment micro-intensity random distribution variable.

_{f}is the number of broken micro-elements, and N is the total number of micro-elements.

_{0}is the material parameter, which is related to the internal friction angle φ; I

_{1}is the first invariant of the stress tensor; and J

_{2}is the second invariant of the deviator stress tensor.

_{d}, ε

_{1d}). It is assumed that the sediment damage variable D is equal to 0 at the damage threshold point, which can be obtained by F − γ = 0 as follows:

#### 2.2. Multi-Field Coupling Model Considering Damage of Hydrate-Bearing Sediments

#### 2.2.1. Mechanical Field Control Equations

_{ij}′ is the effective stress tensor, ε

_{ij}is the strain tensor, λ and G are Lame constants, K′ is the drainage bulk modulus for porous media, α

_{T}is the volumetric thermal expansion coefficient, and T is temperature.

_{i}and u

_{i}are the components of the volume force and displacement in the i direction, and Ẽ and E are the elastic modulus after the damage and before the damage, respectively.

_{c}is the capillary pressure [21] and P

_{ce}is the nominal capillary pressure.

#### 2.2.2. Hydraulic Field Control Equations

_{l}is the gas and water saturation, ṁ

_{l}is the gas and water production rate, and the gas production rate ṁ

_{g}during hydrate dissociation can be obtained from the Kim–Bishnoi hydrate dissociation kinetic model [22]. P

_{l}is the pore gas pressure and pore water pressure, ε

_{v}is the volume strain, μ

_{l}is the dynamic viscosity coefficient of gas and water, φ

_{e}is the effective porosity, φ

_{e}= φ

_{0}(1 − S

_{h}), φ

_{0}is the porosity of porous media without hydrate, k

_{T}

_{l}is the diffusion rate of fluid under a temperature gradient, K is the absolute permeability of the porous media, K = K

_{0}(1 − S

_{h})

^{n}[23], K

_{0}is the absolute permeability of porous media without hydrate, n is the permeability decline index, and K

_{rl}is the relative permeability of the gas and water phase, described by the modified Corey model [24].

_{k}is the influence coefficient of the damage on the permeability.

#### 2.2.3. Energy Conservation Equation

_{α}is the specific heat, λ

_{α}is the heat transfer coefficient, q

_{h}is the latent heat of hydrate phase change, and q

_{in}is the external heat supply.

_{i}are the heat conductivity coefficients of the damaged and undamaged sediment skeleton, respectively; and α

_{λi}is the damage influence parameter on the heat conductivity coefficient.

## 3. Model Verification

#### 3.1. Verification of the Damage Statistical Constitutive Model of Hydrate-Bearing Sediments

_{0}, γ, and δ in the constitutive model. By handling the experimental data from Masui et al., E can be obtained as shown in Table 1, v = 0.219, and φ = 30°. The Weibull distribution parameters m and F

_{0}can be calculated according to the characteristic points of the stress–strain curve [12] and γ is determined according to Equation (8); these values are also shown in Table 1. The residual strength correction coefficient δ can be determined from the experimental results using the inversion trial method. The confining pressure values σ

_{3}in the experiments were 1.0 MPa, 2.0 MPa, and 3.0 MPa.

#### 3.2. Verification of the Multi-Field Coupling Model

## 4. Numerical Solution of the Multi-Field Coupling Model Considering Hydrate-Bearing Sediment Damage

#### 4.1. Multi-Field Coupling Model Numerical Calculation Conditions

_{H}and the minimum horizontal in situ stress σ

_{h}were applied to the sides of BC and CD, respectively. The vertical displacement and horizontal displacement were respectively restricted on the sides of AB and DE. Hydraulic field boundary conditions were set as follows: the initial pore pressure boundary on the sides of BC and CD, impermeable boundaries at AB and DE, a depressurization boundary at AE, and a constant pressure P = 2.84 MPa at the bottom hole were set in the simulation. Thermal field boundary conditions were set as follows: the boundaries of BC and CD were constant-temperature boundaries and the boundaries of AB and DE were adiabatic boundaries. The main model parameters were selected from Masui et al. [27] and Liu et al. [29]. The physical and mechanical parameters of the hydrate-bearing sediments are shown in Table 2, and the thermodynamic parameters are shown in Table 3.

#### 4.2. Numerical Results and Analysis

#### 4.2.1. The Evolution of Hydrate Saturation in the Reservoir

#### 4.2.2. The Evolution of Pore Pressure in the Reservoir

#### 4.2.3. The Evolution of the Damage Area in the Reservoir

#### 4.2.4. Stability Analysis of the Near-Wellbore Reservoir

_{b}was defined [30]. When F

_{b}≤ 1, the reservoir is unstable, and the smaller F

_{b}is, the worse the reservoir stability is. When F

_{b}> 1, the reservoir is in a stable state.

_{y}= −0.0011 m (the negative value indicates compression deformation) without considering the influence of sediment damage but u

_{y}= −0.0016 m with considering the influence of sediment damage. The vertical deformation is increased by approximately 45.5% compared to the case where the influence of sediment damage is not considered. This indicates that when the influence of sediment damage is taken into account, greater deformation of the near-wellbore reservoir is predicted.

## 5. Conclusions

- (1)
- With continuous hydrate dissociation, the cementation of the sediment gradually decreases, and the structural damage gradually increases; this will lead to the partial softening and stress release of the stratum and will result in the decline of the bearing capacity of the reservoir. Therefore, damage of hydrate-bearing sediments has an adverse impact on the stability of the near-wellbore reservoir.
- (2)
- Under the effect of non-uniform horizontal in situ stress, the stress in the direction of minimum horizontal in situ stress is the most concentrated. Coupled with the reservoir strength reduction caused by hydrate dissociation and structural damage of sediments, the reservoir instability zone in this direction which is the priority position of mechanical instability, further expands.
- (3)
- Affected by the wellbore effect and hydrate dissociation, reservoirs near the wellbore are more susceptible to instability when compared with reservoirs farther from the wellbore.
- (4)
- With continuous hydrate dissociation, the cementation structure of sediments is gradually damaged, and the capacity of the reservoir for resisting deformation also declines. In practical engineering, the hydrate dissociation caused by gas hydrate exploitation may lead to obvious seabed deformation.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Comparisons of stress–strain theoretical curves and test curves of hydrate-bearing sediments under different hydrate saturations. (

**a**) S

_{h}= 0%; (

**b**) S

_{h}= 25.7%; (

**c**) S

_{h}= 40.7%; (

**d**) S

_{h}= 55.1%.

**Figure 3.**Comparison of stress–strain theoretical curves and test curves of hydrate-bearing sediments under different confining pressures.

**Figure 6.**Comparisons of experimental and numerical results of the temperature at the three different positions A, B, and C of the sandstone core.

**Figure 8.**Spatial evolution of hydrate saturation of strata at different times. (

**a**) Hydrate saturation in the reservoir at t = 0 h; (

**b**) Hydrate saturation in the reservoir at t = 24 h; (

**c**) Hydrate saturation in the reservoir at t= 48 h; (

**d**) Hydrate saturation in the reservoir at t = 72 h.

**Figure 10.**Spatial evolution of the average pore pressure of strata at different times. (

**a**) Average pore pressure in the reservoir at t = 0 h; (

**b**) Average pore pressure in the reservoir at t = 24 h; (

**c**) Average pore pressure in the reservoir at t = 48 h; (

**d**) Average pore pressure in the reservoir at t = 72 h.

**Figure 12.**Spatial evolution of the damage area of strata at different times. (

**a**) Damage area at t = 0 h; (

**b**) Damage area at t = 24 h; (

**c**) Damage area at t = 48 h; (

**d**) Damage area at t = 72 h.

**Figure 15.**Curves of the effective stress of Point F with and without considering damage of hydrate-bearing sediments.

**Figure 17.**The distributions of polar coordinates of the reservoir stability coefficient with and without considering damage of hydrate-bearing sediments at different positions.

**Figure 18.**Curves of the vertical deformation of Point F with and without considering damage of hydrate-bearing sediments.

S_{h}/% | σ_{3}/MPa | E/MPa | m | F_{0}/MPa | γ/MPa |
---|---|---|---|---|---|

0 | 1 | 216.34 | 0.767 | 6.581 | 1.437 |

25.7 | 1 | 532.97 | 0.691 | 7.041 | 3.034 |

40.7 | 1 | 578.67 | 0.678 | 8.340 | 3.467 |

55.1 | 1 | 717.11 | 0.662 | 8.809 | 4.710 |

34.3 | 1 | 533.96 | 0.687 | 8.257 | 3.236 |

34.3 | 2 | 542.35 | 0.710 | 12.789 | 4.559 |

34.3 | 3 | 626.24 | 0.718 | 14.330 | 6.519 |

Parameters | Physical Meaning | Values |
---|---|---|

ρ_{s} (kg/m^{3}) | Soil skeleton density | 2150 |

ρ_{h} (kg/m^{3}) | Hydrate density | 917 |

ρ_{w} (kg/m^{3}) | Water density | 1000 |

μ_{w} (Pa·s) | Hydrodynamic viscosity coefficient | 1 × 10^{−3} |

μ_{g} (Pa·s) | Gas dynamic viscosity coefficient | 1.25 × 10^{−5} |

E (MPa) | Elastic Modulus | 204.8 + 875.5 S_{h} |

K_{0} (m^{2}) | Absolute permeability | 0.5 × 10^{−14} |

σ_{H} (MPa) | Maximum horizontal in situ stress | 1.5 |

σ_{h} (MPa) | Minimum horizontal in situ stress | 1 |

Parameters | Physical Meaning | Values |
---|---|---|

λ_{g} (W·m^{−1}·K^{−1}) | Gas heat conductivity coefficient | 0.056 |

λ_{w} (W·m^{−1}·K^{−1}) | Water heat conductivity coefficient | 0.5 |

λ_{h} (W·m^{−1}·K^{−1}) | Hydrate heat conductivity coefficient | 0.46 |

λ_{s} (W·m^{−}^{1}·K^{−}^{1}) | Soil skeleton heat conductivity coefficient | 2.9 |

C_{g} (J·kg^{−}^{1}·K^{−}^{1}) | Gas specific heat | 2180 |

C_{w} (J·kg^{−}^{1}·K^{−}^{1}) | Water specific heat | 4200 |

C_{h} (J·kg^{−}^{1}·K^{−}^{1}) | Hydrate specific heat | 2220 |

C_{s} (J·kg^{−}^{1}·K^{−}^{1}) | Soil skeleton specific heat | 750 |

α_{T} (°C^{−1}) | Volumetric thermal expansion coefficient | 1 × 10^{−8} |

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**MDPI and ACS Style**

Zhang, X.; Xia, F.; Xu, C.; Han, Y.
Stability Analysis of Near-Wellbore Reservoirs Considering the Damage of Hydrate-Bearing Sediments. *J. Mar. Sci. Eng.* **2019**, *7*, 102.
https://doi.org/10.3390/jmse7040102

**AMA Style**

Zhang X, Xia F, Xu C, Han Y.
Stability Analysis of Near-Wellbore Reservoirs Considering the Damage of Hydrate-Bearing Sediments. *Journal of Marine Science and Engineering*. 2019; 7(4):102.
https://doi.org/10.3390/jmse7040102

**Chicago/Turabian Style**

Zhang, Xiaoling, Fei Xia, Chengshun Xu, and Yan Han.
2019. "Stability Analysis of Near-Wellbore Reservoirs Considering the Damage of Hydrate-Bearing Sediments" *Journal of Marine Science and Engineering* 7, no. 4: 102.
https://doi.org/10.3390/jmse7040102