Coupled Thermo-Hydro-Mechanical-Chemical Modeling of Water Leak-Off Process during Hydraulic Fracturing in Shale Gas Reservoirs
Abstract
:1. Introduction
2. Chemical-Potential Equilibrium Formulation
2.1. Derivation of Non-Isothermal Chemical Potential Difference for Different Solutions
2.2. Non-Isothermal Chemical Potential Difference between the Slickwater and Formation Brine
3. Mean-Stress Geomechanical Formulation
4. Fluid and Heat Flow Formulation
- (1)
- Fluid Flow in the Hydraulic Fracture
- (2)
- Heat Flow in the Hydraulic Fracture
- (3)
- Fluid Flow in the Natural Fracture
- (4)
- Heat Flow in the Natural Fracture
- (5)
- Fluid Flow in the Matrix
- (6)
- Heat Flow in the Matrix
5. Coupling and Solution of Simulator Equations
6. Numerical Simulation Cases
6.1. Simulation Model Description
6.2. Basecase Simulation Results
6.3. Sensitivity Simulation and Analysis
7. Limitations of the Work
8. Conclusions
- (1)
- During the 1.5 h of fracturing-fluid pumping, water has been leaking from hydraulic fractures to the natural fractures and the matrix, and, during the well shut-in, the leak-off continues. The thermal-osmotic and chemical-osmotic pressures, which are positive driven forces besides the hydraulic pressure difference during the pumping and well shut-in, have aggravated the water leak-off. A multi-field coupled invasion region surrounding the hydraulic fractures in natural fractures and the matrix is created, respectively, during the slickwater injection due to the leak-off mechanism.
- (2)
- After 1.5 h of water injection, the total injection volume from the wellbore to hydraulic fractures is 17,089 m3, of which approximately 9209 m3 leaks into natural fractures and 5900 m3 leaks into the matrix. After the 24-h shut-in, the total leak-off ratio reaches 54.2% and approximately 46.2% of injected water leaks into the matrix.
- (3)
- The four dominating phenomena, i.e., hydraulic pressure, natural-fracture density, chemical osmosis and thermal osmosis, show various influences on fracturing-fluid leak-off. Among them, the hydraulic pressure has the greatest effect, followed by the temperature-difference-induced thermal osmosis and the salt-concentration-difference-induced chemical osmosis. The natural-fracture density is the weakest factor to the water leak-off under this simulation condition, however, its dilation during the hydraulic fracturing can lead to an extra large amount of injected water, which will be stored inside rather than leaked into the matrix.
- (4)
- Results from this study provide a better understanding of the fluid and heat transport mechanism of water-based fracturing-fluids in shale gas reservoirs. We can infer that a shale gas reservoir with low pressure, high temperature, high salinity and high natural-fracture density is highly absorbent, which leads to the high injection capacity and high leak-off volume.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Parameter, Symbol | Value | Parameter, Symbol | Value |
---|---|---|---|
Initial mean stress, σmi | 52 MPa | Initial porosity, φiF, φif , φim | 0.15, 0.015, 0.05 |
Initial reservoirpressure, pi | 25 MPa | Stress-dependent coefficient, ckF, ckf, ckm | 0.05, 0.12, 10−5 MPa−1 |
Reservoir temperature, T | 323 K | Initial water saturation, SwiF, Swif, Swim | 0.2, 0.2, 0.2 |
Poisson’s ratio, ν | 0.2 | Irreducible water saturation, Sw,irrF, Sw,irrf, Sw,irrm | 0.1, 0.2, 0.6 |
Water density, ρw | 1000 kg/m3 | Permeability, kF, kf, km | 100 md, 10,000 nd, 100 nd |
Water viscosity, ηw | 0.8 mPa∙s | Injected water salinity, Cinj | 1000 ppm |
Water compressibility, cw | 4 × 10−4 MPa−1 | Biot coefficient, βF, βf, βm | 0.76, 0.06, 0.18 |
Natural fracture density, nf | 5 | Initial salinity, CiF, Cif, Cim | 1000, 10,000, 280,000 ppm |
Membrane efficiency, λ | 0.06 | Volume proportion of source rock, Sk | 0.1 |
Langmuir’s pressure, pL | 5.8 MPa | Ideal gas constant, R | 8.314 J/(mol·K) |
Rock density, ρr | 2560 kg/m3 | Langmuir’s volume, VL | 3.32 × 10−3 m3/kg |
Gas compressibility, cg | 0.03 MPa−1 | Gas density at standard condition, ρgsc | 0.77 kg/m3 |
Gas viscosity, ηg | 0.058 mPa·s | Partial molar volume of water, Vw,m | 18.02 × 10−6 m3/mol |
Injected water temperature, Tf | 288 K | Partial molar entropy of water, Sw,m | 69.91 J/(mol·K) |
Heat capacity of rock, Cr | 774 J/(kg·K) | Heat capacity of fluid, Cw | 4200 J/(kg·K) |
Solid bulk modulus Kr | 11.44 GPa | Thermal diffusivity coefficient, De | 1.6 × 10−6 m2/s |
Basecase | Pi = 30 MPa | Pi = 36 MPa | Ti = 333 K | Ti = 343 K | Cim = 180,000 | Cim = 18,000 | nf = 1 | nf = 30 | |
---|---|---|---|---|---|---|---|---|---|
(m3) | 17,089 | 12,317 | 7627 | 17,713 | 18,145 | 17,086 | 17,078 | 16,054 | 20,122 |
(m3) | 9209 | 6380 | 3662 | 9561 | 9814 | 9206 | 9199 | 8649 | 10,965 |
(m3) | 5900 | 4086 | 2343 | 6194 | 6399 | 5878 | 5853 | 5542 | 6348 |
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Wang, F.; Li, B.; Zhang, Y.; Zhang, S. Coupled Thermo-Hydro-Mechanical-Chemical Modeling of Water Leak-Off Process during Hydraulic Fracturing in Shale Gas Reservoirs. Energies 2017, 10, 1960. https://doi.org/10.3390/en10121960
Wang F, Li B, Zhang Y, Zhang S. Coupled Thermo-Hydro-Mechanical-Chemical Modeling of Water Leak-Off Process during Hydraulic Fracturing in Shale Gas Reservoirs. Energies. 2017; 10(12):1960. https://doi.org/10.3390/en10121960
Chicago/Turabian StyleWang, Fei, Baoman Li, Yichi Zhang, and Shicheng Zhang. 2017. "Coupled Thermo-Hydro-Mechanical-Chemical Modeling of Water Leak-Off Process during Hydraulic Fracturing in Shale Gas Reservoirs" Energies 10, no. 12: 1960. https://doi.org/10.3390/en10121960