# Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}over 30 years.

## 1. Introduction

## 2. Thermal Interaction of a Well with Permafrost: Physical Problem Formulation

_{2–4}), with relict methane hydrates possibly occurring in the 60–120 m interval; average moisture content 32%; freezing point is around −1 °C.

_{1}); 22% moisture content; freezing point is −2 °C.

_{1}-mK

_{2}); 23% average moisture content; freezing point is −2 °C.

^{2}(lower boundary condition), was around 210 m, and the temperature-depth profile fitted the pattern of a well from the Bovanenkovo field (Figure 3).

^{3}, and its pressure was ~10 MPa.

^{3}density) were 840 J/(kg·K) and 1 W/(m·K).

_{r}with regard to phase changes, in the axisymmetric case, was

- ${\rho}_{s},{C}_{s},{\lambda}_{s}$—density, specific heat, and thermal conductivity of solid particles, respectively. Thermal conductivity was calculated as a function of temperature, tabulated, or polynomial;
- ${\rho}_{f},{C}_{f},{\lambda}_{f}$—density, specific heat, and thermal conductivity of fluid, respectively.
- $n,{\theta}_{i}(t),L,{T}_{liq},{T}_{sol}$—porosity, phase composition (ice saturation, possibly depending on temperature according to the unfrozen water curve), specific heat of phase transitions, and the temperature at the beginning and end of phase transitions, respectively;
- Properties of the fluid depending on its state (with possible regard for salinity), found via water and ice properties [63,64] as:$${\rho}_{f}={\rho}_{i}{\theta}_{i}+{\rho}_{w}(1-{\theta}_{i}),{C}_{f}=\frac{{\rho}_{i}{\theta}_{i}{C}_{i}+{\rho}_{w}(1-{\theta}_{i}){C}_{w}}{{\rho}_{f}},{\lambda}_{f}={\lambda}_{i}^{{\theta}_{i}}{\lambda}_{w}^{1-{\theta}_{}}$$
- $\rho ,\widehat{C},\lambda $- density, effective heat capacity, and thermal conductivity of permafrost, respectively, found as:$$\rho ={\rho}_{f}n+{\rho}_{s}(1-n),\widehat{C}=n{\rho}_{f}{C}_{eff,uw}+(1-n){\rho}_{s}{C}_{s},\lambda ={\lambda}_{f}^{n}{\lambda}_{s}^{1-n}$$

_{r}is a rectangle (in cylindrical coordinates) bounded by the lifting pipe/air interface on the left and by the ground surface on the top, with its vertical and horizontal (radial) sizes of 550 m and 50 m, respectively.

^{2}, at the base of the modeling domain and zero along the side boundaries, provided that the thermal effect of the well remained within the <50 m radius for 30 years of operation.

## 3. Results and Discussion

^{2}≥ 0.99 for all fluid types). This is an illustration of quasiparabolic self-similar asymptotic thaw behavior after short initial heating till the end of the 30 yr well lifespan.

^{3}after 30 years of gas production, corresponding to a daily emission of 50 m

^{3}(Figure 12).

## 4. Conclusions

^{3}in the absence of heat insulation. Meanwhile, the well design with insulated tubing can prevent thawing and the emission of methane, which can cause a twenty-five times greater greenhouse effect than CO

_{2}.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Temperature–depth profile from a site within the Bovanenkovo gas-condensate field: well log (1) [52] and initial value used in calculations (2).

**Figure 6.**Permafrost temperature variations around a producing gas well (along the radius off the well center) after 1, 10, 20, and 30 years of operation (left to right). Permafrost contains gas hydrates within the depth interval of 60–120 m, with hydrate saturation ${S}_{h}$ = 20%; ice saturation ${S}_{i}$ = 80%.

**Figure 7.**Permafrost temperature variations around a producing gas well (along the radius off the well center) after 1, 10, 20, and 30 years of operation (left to right). Permafrost contained gas hydrates within the depth interval of 60–120 m, with hydrate saturation ${S}_{h}$ = 20%; hydrate and ice saturation ${S}_{h}+{S}_{i}$ = 70%.

**Figure 8.**Permafrost temperature variations around a producing gas well (along the radius off the well center) after 30 years with different hydrate saturations of 0%, 20%, and 40% (${S}_{h}+{S}_{i}$ = 100%), and incomplete pore filling with hydrate ${S}_{h}$ = 20%; ice ${S}_{i}$ = 50% (left to right) in depth interval of 60–120 m.

**Figure 9.**Mean annual permafrost temperature variations around a producing gas well at depths 1, 10, 20, 30, and 40 m, after 30 years of operation. Permafrost contained gas hydrates in the depth interval of 60–120 m, with hydrate saturation ${S}_{h}$ = 20%; hydrate+ice saturation ${S}_{h}+{S}_{i}$ = 70%.

**Figure 10.**Time-dependent thawing radius variations in the 60–120 m depth interval at different hydrate saturations. ${S}_{h}$, ${S}_{i}$, and ${S}_{g}$ refer to hydrate, ice, and gas saturation, respectively.

**Figure 11.**Time-dependent thaw variations in the 60–120 m depth interval at different hydrate saturation values. ${S}_{h}$, ${S}_{i}$, and ${S}_{g}$ refer to hydrate, ice, and gas (methane) saturation, respectively.

**Figure 12.**Potential methane emission from gas hydrate-bearing permafrost (60–120 m depth interval) associated with well–permafrost interaction at different hydrate saturation values. ${S}_{h}$, ${S}_{i}$, and ${S}_{g}$ refer to hydrate, ice, and gas (methane) saturation, respectively.

Layer | Depth Interval, m | Moisture Content W, wt. % | Porosity, Volume Fraction | Density of Solid Particles, kg/m^{3} | Heat Capacity of Solid Particles, J/kg×K | Thermal Conductivity of Solid Particles, W/mK |
---|---|---|---|---|---|---|

1 | 0–150 | 32 | 0.45 | 2600 | 758 | 2.4 |

2 | 150–250 | 22 | 0.36 | 2550 | 700 | 2.4 |

3 | 250–550 | 23 | 0.37 | 2550 | 710 | 1.9 |

No | Casing | Outer Diameter, mm | Inner Diameter, mm | Cement Outer Diameter, mm | Depth, m |
---|---|---|---|---|---|

1 | Conductor pipe | 426 | 404 | 490 | 120 |

2 | Surface casing | 324 | 304 | 394 | 450 |

3 | Intermediate casing | 245 | 224 | 295 | 774 |

168 | 150 | 216 | 774 m to reservoir | ||

4 | Lifting pipe with insulation | 168 | 100 | --- | 55 |

5 | Lifting pipe | 114 | 100 | --- | 55 m to reservoir |

**Table 3.**Thermal properties of lean clay (depth interval 60–120 m) free from gas hydrates, with regard to the phase state of pore moisture and temperature.

Temperature, °C | Relative Content of Unfrozen Water, % | $\mathbf{Fluid}\mathbf{Density}\left({\mathit{\rho}}_{\mathit{f}}\right),\mathbf{kg}/{\mathbf{m}}^{3}$ | $\mathbf{Effective}\mathbf{Heat}\mathbf{Capacity}\left({\mathit{C}}_{\mathit{e}\mathit{f}\mathit{f},\mathit{u}\mathit{w}}\right),\mathbf{J}/\mathbf{kg}\xb7\mathbf{K}$ |
---|---|---|---|

5 | 100 | 1000.0 | 4186 |

0 | 100 | 1000.0 | 4186 |

−0.9 | 100 | 1000.0 | 4186 |

−1 | 20 | 933.6 | 32,001 |

−2 | 11 | 926.1 | 8918 |

−4 | 7 | 922.8 | 7193 |

−6 | 4 | 920.3 | 3814 |

−8 | 3 | 919.5 | 3793 |

−10 | 2 | 918.7 | 3438 |

**Table 4.**Thermal properties of lean clay containing 20% of pore gas hydrates (depth interval 60–120 m), with regard to the phase state of pore moisture and temperature.

Temperature, °C | Hydrate Saturation, % | $\mathbf{Fluid}\mathbf{Density}\left({\mathit{\rho}}_{\mathit{f}}\right),\mathbf{kg}/{\mathbf{m}}^{3}$ | Effective Heat Capacity, $\left({\mathit{C}}_{\mathit{e}\mathit{f}\mathit{f},\mathit{g}\mathit{h}}\right),\mathbf{J}/\mathbf{kg}\xb7\mathbf{K}$ |
---|---|---|---|

10 | 0 | 1000.0 | 4186 |

0 | 0 | 1000.0 | 4186 |

−0.9 | 0 | 1000.0 | 4186 |

−1 | 0 | 917.0 | 8634 |

−1.5 | 2 | 916.7 | 28,365 |

−2 | 10 | 915.3 | 28,404 |

−2.5 | 18 | 913.9 | 8656 |

−3 | 20 | 913.6 | 2060 |

−5 | 20 | 913.6 | 2060 |

**Table 5.**Thermal properties of lean clay containing 20% of pore gas hydrates and 30% air (depth interval 60–120 m), with regard to the phase state of pore moisture and temperature.

Temperature, °C | Hydrate Saturation, % | Fluid Density $\left({\mathit{\rho}}_{\mathit{f}}\right),\mathbf{kg}/{\mathbf{m}}^{3}$ | Effective Heat Capacity $\left({\mathit{C}}_{\mathit{e}\mathit{f}\mathit{f},\mathit{g}\mathit{h}}\right),\mathbf{J}/\mathbf{kg}\xb7\mathbf{K}$ |
---|---|---|---|

10 | 0 | 700.0 | 4186 |

0 | 0 | 670.0 | 4186 |

−0.9 | 0 | 700.0 | 4186 |

−1 | 0 | 641.9 | 11,451 |

−1.5 | 2 | 641.6 | 39,645 |

−2 | 10 | 640.2 | 39,724 |

−2.5 | 18 | 638.8 | 11,496 |

−3 | 20 | 638.5 | 2060 |

−5 | 20 | 638.5 | 2060 |

**Table 6.**Thermal properties of lean clay containing 40% of pore gas hydrates (depth interval 60–120 m), with regard to the phase state of pore moisture and temperature.

Temperature, °C | Hydrate Saturation, % | $\mathbf{Fluid}\mathbf{Density}\left({\mathit{\rho}}_{\mathit{f}}\right),\mathbf{kg}/{\mathbf{m}}^{3}$ | Effective Heat Capacity $\left({\mathit{C}}_{\mathit{e}\mathit{f}\mathit{f},\mathit{g}\mathit{h}}\right),\mathbf{J}/\mathbf{kg}\xb7\mathbf{K}$ |
---|---|---|---|

10 | 0 | 1000.0 | 4186 |

0 | 0 | 1000.0 | 4186 |

−0.9 | 0 | 1000.0 | 4186 |

−1 | 0 | 917.0 | 15,208 |

−1.5 | 4 | 916.3 | 54,690 |

−2 | 20 | 913.6 | 58,145 |

−2.5 | 37 | 910.7 | 11,989 |

−3 | 40 | 910.2 | 2060 |

−5 | 40 | 910.2 | 2060 |

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**MDPI and ACS Style**

Chuvilin, E.; Tipenko, G.; Bukhanov, B.; Istomin, V.; Pissarenko, D.
Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost. *Geosciences* **2022**, *12*, 115.
https://doi.org/10.3390/geosciences12030115

**AMA Style**

Chuvilin E, Tipenko G, Bukhanov B, Istomin V, Pissarenko D.
Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost. *Geosciences*. 2022; 12(3):115.
https://doi.org/10.3390/geosciences12030115

**Chicago/Turabian Style**

Chuvilin, Evgeny, Gennadiy Tipenko, Boris Bukhanov, Vladimir Istomin, and Dimitri Pissarenko.
2022. "Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost" *Geosciences* 12, no. 3: 115.
https://doi.org/10.3390/geosciences12030115