Evaluating the Effects of Proppant Flowback on Fracture Conductivity in Tight Reservoirs: A Combined Analytical Modeling and Simulation Study
Abstract
:1. Introduction
2. Methodology
2.1. Analytical Models
2.1.1. Critical Velocity
Physical Model and Assumptions
Equivalent Capillary Force
Critical Velocity of Proppant Flowback
- (1)
- Before fracture closure
- (2)
- After fracture closure
2.1.2. Fracture Conductivity
- (1)
- Before fracture closure
- (2)
- After fracture closure
2.2. Finite-Element Simulation
2.2.1. Assumptions
2.2.2. Mesh Geometry and Conditions
3. Application and Results
3.1. Field and Well Information
3.2. Results of Base Case
3.3. The Effects of Water Saturation in Fractures
3.3.1. Critical Velocity
3.3.2. Proppant Flowback Volume and Fracture Conductivity
3.4. The Effects of Net Pressure in Fractures
3.4.1. Critical Velocity
3.4.2. Proppant Flowback Volume and Fracture Conductivity
4. Summary and Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Capillary pressure, in Pa. | |
R | Radius of proppant, in m. |
Radius of curved interface between wetting and non-wetting phases, in m. | |
Radius related to , in m. | |
Interfacial tension, in mN/m. | |
Contact angle, in °. | |
Angle for the interface between two phase fluid and proppant, in °. | |
Volume of wetting phase saturation, dimensionless. | |
Volume of pore space, in m3. | |
Volume of wetting phase, in m3. | |
Cylinder volume, in m3. | |
Volume at the upper and lower cylinder, in m3. | |
Volume at the side of cylinder, in m3. | |
Equivalent capillary force, in N. | |
G | Net gravity, in N. |
Viscous dragging force, in N. | |
Proppant density, in g/cm3. | |
Fracturing fluid density, in g/cm3. | |
v | Flowback velocity, in m/s. |
Resistance coefficient, dimensionless. | |
Re | Reynolds number, dimensionless. |
Viscosity of fracturing fluid, in mPa·s. | |
Resistance moment, in m. | |
Driving force moment, in m. | |
Bonding force, in N. | |
Friction force, in N. | |
Down force of liquid, in N. | |
Net pressure in fractures, in Pa. | |
Friction coefficient, dimensionless. | |
Film parameter, in cm. | |
Coefficient of bonding force, in dyn/cm. | |
Fracture conductivity, in m3. | |
Permeability of propped fracture, in m2. | |
Width of propped fracture, in m. | |
Fracture porosity, dimensionless. | |
r | Radius of pore throat, in m. |
Tortuosity, dimensionless. | |
without any proppant embedment or deformation, in m. | |
m | Total number of proppant layer, dimensionless. |
N | Total number of proppant, dimensionless. |
Fracture half length, in m. | |
Fracture height, in m. | |
Loss in fracture width, in m. | |
Proppant deformation, in m. | |
Proppant embedment, in m. | |
Poisson ratio of proppant, dimensionless. | |
Elastic modulus of proppant, in Pa. | |
Poisson ratio of formation, dimensionless. | |
Formation elastic modulus, in Pa. |
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Parameters | Value |
---|---|
Half-length of the fracture, (m) | 118.95 |
Fracture height, (m) | 42 |
Volume of pumped proppant, (m3) | 40 |
Proppant radius, R (m) | 350 |
Proppant density, (g/cm3) | 3.16 |
Volume density of proppant, (g/cm3) | 1.74 |
Fracturing fluid density, (g/cm3) | 1.03 |
Fracturing fluid viscosity for gel breaking, (mPa·s) | 3.5 |
Friction coefficient of quartz, | 0.75 |
Film parameter of quartz, (cm) | 0.0000213 |
Bonding force coefficient of quartz, (dyne/cm) | 2.56 |
Surface tension of gel breaking fracturing fluid, (mN/m) | 24.4 |
Wetting angle, (°) | 2 |
Net pressure in fractures, (Pa) | 1 |
Wetting-phase saturation in the fracture, (%) | 14.7 |
Poisson’s ratio of proppant, | 0.25 |
Elastic modulus of proppant, ( Pa) | 100 |
Poisson’s ratio of formation, | 0.19 |
Elastic modulus of formation, ( Pa) | 34 |
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Cheng, Y.; Li, Z.; Fu, Y.; Xu, L. Evaluating the Effects of Proppant Flowback on Fracture Conductivity in Tight Reservoirs: A Combined Analytical Modeling and Simulation Study. Energies 2024, 17, 4250. https://doi.org/10.3390/en17174250
Cheng Y, Li Z, Fu Y, Xu L. Evaluating the Effects of Proppant Flowback on Fracture Conductivity in Tight Reservoirs: A Combined Analytical Modeling and Simulation Study. Energies. 2024; 17(17):4250. https://doi.org/10.3390/en17174250
Chicago/Turabian StyleCheng, Yishan, Zhiping Li, Yingkun Fu, and Longfei Xu. 2024. "Evaluating the Effects of Proppant Flowback on Fracture Conductivity in Tight Reservoirs: A Combined Analytical Modeling and Simulation Study" Energies 17, no. 17: 4250. https://doi.org/10.3390/en17174250
APA StyleCheng, Y., Li, Z., Fu, Y., & Xu, L. (2024). Evaluating the Effects of Proppant Flowback on Fracture Conductivity in Tight Reservoirs: A Combined Analytical Modeling and Simulation Study. Energies, 17(17), 4250. https://doi.org/10.3390/en17174250