Numerical Modeling of Variable Fluid Injection-Rate Modes on Fracturing Network Evolution in Naturally Fractured Formations
Abstract
:1. Introduction
2. Brief Description of Numerical Model
- (1)
- the RFPA-Flow code can simulate non-linear deformation of a quasi-brittle behavior by introducing heterogeneity of rock properties into the model, with an ideal brittle constitutive law for the local material;
- (2)
- by introducing a deterioration of element parameters after its failure, the RFPA code can simulate strain-softening and discontinuous mechanics problems in a continuum mechanics mode. For heterogeneity, the material properties (failure-strength σc and elastic modulus Ec) for elements are randomly distributed throughout the model by following a Weibull distribution:
3. Numerical Model Setup
3.1. Discrete Fracture Network Realization
- (1)
- Beacher DFN model. The Beacher model [33] is a flexible algorithm that can generate complicate joint networks. In this model, the joints are assumed to have finite trace length, which follow some statistical distributions. The centers of the joints are located in space according to a Poisson point process. The orientation of the joints in a Beacher discrete fracture network can either be constant or vary according to an orientation distribution. The number of the joints generated in a Baecher network is controlled by a joint intensity. So as to avoid boundary effects in a specified model region, the Baecher algorithm first increases the region before generating joints. After generating the joints according to the required joint intensity, the algorithm then clips the network with the original bounding region. Joints of the Baecher discrete network fracture generally terminate in intact rock. The main parameters for Baecher DFN model include the joint Orientation, Dip/Dip Direction, Joint Length and Joint Intensity. The Baecher DFN model can be re-generated, using a new sampling of the random variables (e.g., joint orientation, joint length).
- (2)
- Parallel Deterministic DFN model. The Parallel Deterministic DFN model allows us to define a network of parallel joints with fixed spacing and orientation. In this case, deterministic indicates that the length, spacing, and persistence of the joints are assumed to be constant (i.e., exactly known with no statistical variation). However, the Parallel Deterministic DFN model does allow randomness of the joint location.
3.2. RFPA-Flow Model Setup
3.3. Numerical Experiment Design
- Case 1
- Fluid injection rate decreases, then increases, and decreases again: 1.2 mL/s → 0.15 mL/s → 0.6 mL/s → 0.3 mL/s;
- Case 2
- Fluid injection rate decreases, then increases, and decreases again: 0.6 mL/s → 0.3 mL/s →1.2 mL/s → 0.15 mL/s;
- Case 3
- Fluid injection rate monotonicallydecreases: 1.2 mL/s → 0.6 mL/s → 0.3 mL/s → 0.15 mL/s;
- Case 4
- Fluid injection rate monotonicallyincreases: 0.15 mL/s → 0.3 mL/s → 0.6 mL/s → 1.2 mL/s.
- (a)
- Injection pressure, defined as the fluid pressure at the injection point;
- (b)
- Injection rate, defined as the fluid injection rate at different stages;
- (c)
- Stimulated total interaction area, defined as the interaction area of HF and DFN that has experienced a fluid pressure increase due to injection; and
- (d)
- Leak off ratio, defined as the total volume of fluid leaked into the DFN model and used in hydraulic fracture generation divided by the total volume of fluid injection.
4. Numerically Simulated Results and Discussion
4.1. General Observations
4.2. Microseismic Response
4.3. Hydraulic Fracture and Discrete Fracture Network Interaction
4.4. Hydraulic Fracturing Effectiveness Evaluation
4.5. Mechanism of Variable Injection-Rate Technology
4.6. Comparison with Constant Injection Rate Technology
5. Conclusions
- (1)
- The fluid injection rate is critical to the overall response of the formation in hydraulic fracturing. This work suggests that variable injection-rate plays a crucial role in hydraulic fracturing effectiveness for unconventional tight gas developments, and variable injection-rate will play a significant role in optimizing treating pressures, the created microseismicity and corresponding SRV, and well production.
- (2)
- The hydraulic fracturing effectiveness with variable flow rate technology is generally better than those of constant injection rate technology. Of the four studied cases, the effectiveness of the injection rate increasing at each stage is the best.
- (3)
- The mechanism of the variable injection-rate technology is the initiation of numerous under-fracturing points at different injection stages, branching and accumulation of micro-fractures, and the formation of a fracturing network. At the initial stage, many damaged elements (under-fracturing points) appear around the wellbore with the increase of pore pressure. Furthermore, the sudden increase of injection rate drives the dynamic propagation of hydraulic fractures along many branching fracturing points.
- (4)
- More natural fractures can be shearing stimulated by variable injection-rate technology, which is helpful in developing a complex fracturing network. Selecting the reasonable variable injection-rate occasion and injection-rate range is the key to this technology. However, these two problems can be solved by simulation tests.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Index | Rock Matrix | DFN-1 | DFN-2 | DFN-3 | Unit |
---|---|---|---|---|---|
Homogeneity index (m) | 2 | 3 | 3 | 3 | - |
Elastic modulus (E0) | 34 | 23 | 30 | 30 | GPa |
Poisson’s ratio (v) | 0.22 | 0.33 | 0.32 | 0.31 | - |
Internal friction angle (φ) | 53 | 30 | 32 | 35 | ° |
Compressive strength (σc) | 320 | 150 | 220 | 240 | MPa |
Tensile strength (σt) | 32 | 15 | 22 | 24 | MPa |
Coefficient of residual strength | 0.1 | 0.1 | 0.1 | 0.1 | - |
Permeability coefficient (k0) | 0.07 | 0.12 | 0.12 | 0.13 | mD |
Porosity | 0.07 | 0.17 | 0.13 | 0.11 | - |
Coupling coefficient (β) | 0.01 | 0.01 | 0.01 | 0.01 | - |
Coefficient of pore-water pressure (α) | 0.6 | 0.6 | 0.6 | 0.6 | - |
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Wang, Y.; Li, X.; Zhang, B. Numerical Modeling of Variable Fluid Injection-Rate Modes on Fracturing Network Evolution in Naturally Fractured Formations. Energies 2016, 9, 414. https://doi.org/10.3390/en9060414
Wang Y, Li X, Zhang B. Numerical Modeling of Variable Fluid Injection-Rate Modes on Fracturing Network Evolution in Naturally Fractured Formations. Energies. 2016; 9(6):414. https://doi.org/10.3390/en9060414
Chicago/Turabian StyleWang, Yu, Xiao Li, and Bo Zhang. 2016. "Numerical Modeling of Variable Fluid Injection-Rate Modes on Fracturing Network Evolution in Naturally Fractured Formations" Energies 9, no. 6: 414. https://doi.org/10.3390/en9060414