A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing
Abstract
:1. Introduction
2. Governing Equation for the THGM Coupling Process
2.1. Shale Reservoir Deformation Considering Gas Adsorption and Thermal Expansion
2.2. Permeability Evolution for Thermal Fracturing Process
2.3. Two-Phase Flow, including Adsorption and Dissolution
2.4. Heat Conduction of Two-Phase Flow Considering Thermal Convection
2.5. Multiple Physical Field Coupling Model
3. Modelling Results and Discussions
3.1. Permeability Test of Shale after 50 °C Temperature Treatment
3.2. Establishment of the Numerical Model
3.3. Evolution of Temperature Field
3.4. Capillary Pressure and Water Saturation of Shale
3.5. Permeability of Shale and Shale Gas Saturation Change
4. Production Capacity Analysis of Heat Injection in Enhanced Shale Gas Recovery
4.1. Numerical Model of Heating-Enhanced Shale Gas Recovery
4.2. Analysis of Shale Gas Production Efficiency by Thermal Injection
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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NO. | Hight (mm) | Diameter (mm) | Quality (g) | Pore Volume after 50 °C (cm3) | |||
---|---|---|---|---|---|---|---|
Before | After | Before | After | Before | After | ||
6#-1 | 51.14 | 51.08 | 25.5 | 25.10 | 66.81 | 67.08 | -- |
6#-2 | 51.34 | 51.18 | 25.28 | 25.08 | 66.89 | 67.34 | 1.179 |
6#-3 | 51.24 | 51.18 | 25.32 | 25.04 | 66.95 | 67.39 | 1.168 |
Temperature (°C) | Confining Pressure (psi) | Test Pressure (psi) | Permeability (mD) |
---|---|---|---|
20 | 2900 | 800 | 0.000931 |
50 | 2900 | 800 | 0.001126 |
Parameters | Unit | Value | Physical Meaning |
---|---|---|---|
1625 | Gas specific heat capacity | ||
0.2 | Water thermal conductivity | ||
0.6 | Gas thermal conductivity | ||
Water viscosity | |||
Gas viscosity | |||
0.01 | Porosity | ||
Es | MPa | 2713 | Young’s modulus of shale |
VL | 0.0467 | Langmuir adsorption volume constant | |
PL | 0.0467 | Langmuir adsorption pressure constant | |
1/K | Shale thermal expansion coefficient | ||
K | 293.15 | Initial temperature | |
MPa | 3 | Initial mean pressure | |
1250 | Specific heat capacity of shale | ||
m2 | Initial permeability | ||
Rsw | 1.3 | Gas solubility | |
0.2 | Residual water saturation | ||
0.15 | Residual gas saturation | ||
1/MPa | 0.07 | Pressure correction coefficient for gas adsorption | |
1/K | 0.02 | Temperature correction coefficient for gas adsorption | |
Dc | m2/s | Capillary diffusion coefficient |
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Shang, X.; Zhang, Z.; Yang, W.; Wang, J.G.; Zhai, C. A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing. Mathematics 2022, 10, 3473. https://doi.org/10.3390/math10193473
Shang X, Zhang Z, Yang W, Wang JG, Zhai C. A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing. Mathematics. 2022; 10(19):3473. https://doi.org/10.3390/math10193473
Chicago/Turabian StyleShang, Xiaoji, Zhizhen Zhang, Weihao Yang, J.G. Wang, and Cheng Zhai. 2022. "A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing" Mathematics 10, no. 19: 3473. https://doi.org/10.3390/math10193473
APA StyleShang, X., Zhang, Z., Yang, W., Wang, J. G., & Zhai, C. (2022). A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing. Mathematics, 10(19), 3473. https://doi.org/10.3390/math10193473