Figure 1.
Configuration of the laboratory and simulated “single completion” model. (
a) Configuration of the “single completion” laboratory test [
65], (
b) conceptual graph for the laboratory model, (
c) a cross-section at
y = 0.2 m of the numerical model built in RFPA, (
d) cutaway view of the numerical model built in RFPA.
Figure 1.
Configuration of the laboratory and simulated “single completion” model. (
a) Configuration of the “single completion” laboratory test [
65], (
b) conceptual graph for the laboratory model, (
c) a cross-section at
y = 0.2 m of the numerical model built in RFPA, (
d) cutaway view of the numerical model built in RFPA.
Figure 2.
Injection pressure response and rate variations during fracturing (the laboratory pressure and injection rate curves are redrawn from [
65]).
Figure 2.
Injection pressure response and rate variations during fracturing (the laboratory pressure and injection rate curves are redrawn from [
65]).
Figure 3.
Fracture propagation paths obtained from “single completion” laboratory test [
65] and RFPA-Petrol analysis.
Figure 3.
Fracture propagation paths obtained from “single completion” laboratory test [
65] and RFPA-Petrol analysis.
Figure 4.
Configurations of multilayered laboratory-scale models: (a) Configuration of the 3D model; (b) cross-section of the 3D model; (c) slices at x = 0.181 m, y = 0.2 m, and z = 0.132 m of simulated model Multi-E1.
Figure 4.
Configurations of multilayered laboratory-scale models: (a) Configuration of the 3D model; (b) cross-section of the 3D model; (c) slices at x = 0.181 m, y = 0.2 m, and z = 0.132 m of simulated model Multi-E1.
Figure 5.
The hydraulic aperture (m) of the control model Multi-00: (a) The 3D view; (b) the slice at y = 0.2 m.
Figure 5.
The hydraulic aperture (m) of the control model Multi-00: (a) The 3D view; (b) the slice at y = 0.2 m.
Figure 6.
The minimum compressive principal effective stress (MPa) of models with different interlayer Young’s modulus and strength at t = 2000 s: (a) Multi-E1, E1/E0 = 0.3; (b) Multi-E2, E2/E0 = 0.6; (c) Multi-00, E0/E0 = 1.0; (d) Multi-E3, E3/E0 = 1.4; (e) Multi-E4, E4/E0 = 1.7; (f) Multi-E5, E5/E0 = 2.0.
Figure 6.
The minimum compressive principal effective stress (MPa) of models with different interlayer Young’s modulus and strength at t = 2000 s: (a) Multi-E1, E1/E0 = 0.3; (b) Multi-E2, E2/E0 = 0.6; (c) Multi-00, E0/E0 = 1.0; (d) Multi-E3, E3/E0 = 1.4; (e) Multi-E4, E4/E0 = 1.7; (f) Multi-E5, E5/E0 = 2.0.
Figure 7.
The fracture radius of models with different interlayer Young’s modulus and strength at
t = 2000 s (the primary fracture curves are redrawn from [
67]).
Figure 7.
The fracture radius of models with different interlayer Young’s modulus and strength at
t = 2000 s (the primary fracture curves are redrawn from [
67]).
Figure 8.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer Young’s modulus and strength.
Figure 8.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer Young’s modulus and strength.
Figure 9.
The minimum compressive principal effective stress (MPa) of models with different interlayer Poisson’s ratio at t = 2000 s: (a) Multi-Po1, v1/v0 = 0.5; (b) Multi-Po2, v2/v0 = 0.75; (c) Multi-00, v0/v0 = 1.0; (d) Multi-Po3, v3/v0 = 1.25; (e) Multi-Po4, v4/v0 = 1.5; (f) Multi-Po5, v5/v0 = 2.0.
Figure 9.
The minimum compressive principal effective stress (MPa) of models with different interlayer Poisson’s ratio at t = 2000 s: (a) Multi-Po1, v1/v0 = 0.5; (b) Multi-Po2, v2/v0 = 0.75; (c) Multi-00, v0/v0 = 1.0; (d) Multi-Po3, v3/v0 = 1.25; (e) Multi-Po4, v4/v0 = 1.5; (f) Multi-Po5, v5/v0 = 2.0.
Figure 10.
The fracture radius of models with different interlayer Poisson’s ratio at t = 2000 s.
Figure 10.
The fracture radius of models with different interlayer Poisson’s ratio at t = 2000 s.
Figure 11.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer Poisson’s ratio.
Figure 11.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer Poisson’s ratio.
Figure 12.
The seepage fields (MPa) of models with different interlayer permeability at t = 2000 s: (a) Multi-k1, k1/k0 = 10−3; (b) Multi-k2, k2/k0 = 10−2; (c) Multi-k3, k3/k0 = 10−1; (d) Multi-00, k0/k0 = 100; (e) Multi-k4, k4/k0 = 101; (f) Multi-k5, k5/k0 = 102.
Figure 12.
The seepage fields (MPa) of models with different interlayer permeability at t = 2000 s: (a) Multi-k1, k1/k0 = 10−3; (b) Multi-k2, k2/k0 = 10−2; (c) Multi-k3, k3/k0 = 10−1; (d) Multi-00, k0/k0 = 100; (e) Multi-k4, k4/k0 = 101; (f) Multi-k5, k5/k0 = 102.
Figure 13.
The fracture radius of models with different interlayer permeability at
t = 2000 s (the primary fracture curves are redrawn from [
67]).
Figure 13.
The fracture radius of models with different interlayer permeability at
t = 2000 s (the primary fracture curves are redrawn from [
67]).
Figure 14.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer permeability.
Figure 14.
The breakdown pressure/time and reopening pressure/time of fractures in models with different interlayer permeability.
Figure 15.
The configuration of the multilayered numerical models for investigation the sensitivity of fluid properties: the slices at x = 0.181 m, y = 0.2 m, and z = 0.132 m of the model.
Figure 15.
The configuration of the multilayered numerical models for investigation the sensitivity of fluid properties: the slices at x = 0.181 m, y = 0.2 m, and z = 0.132 m of the model.
Figure 16.
The seepage fields (MPa) of models with different inlet flux when the primary fracture reaches the boundary: (a) Multi-Q1, t = 3120 s, Q1/Q0 = 0.5; (b) Multi-Q2, t = 2480 s, Q2/Q0 = 0.7; (c) Multi-01, t = 2120 s, Qo/Q0 = 1.0; (d) Multi-Q3, t = 1920 s, Q3/Q0 = 1.25; (e) Multi-Q4, t = 1640 s, Q4/Q0 = 1.75; (f) Multi-Q5, t = 1560 s, Q5/Q0 = 2.0.
Figure 16.
The seepage fields (MPa) of models with different inlet flux when the primary fracture reaches the boundary: (a) Multi-Q1, t = 3120 s, Q1/Q0 = 0.5; (b) Multi-Q2, t = 2480 s, Q2/Q0 = 0.7; (c) Multi-01, t = 2120 s, Qo/Q0 = 1.0; (d) Multi-Q3, t = 1920 s, Q3/Q0 = 1.25; (e) Multi-Q4, t = 1640 s, Q4/Q0 = 1.75; (f) Multi-Q5, t = 1560 s, Q5/Q0 = 2.0.
Figure 17.
The fracture radius of models with different inlet flux when the primary fractures reach the boundary.
Figure 17.
The fracture radius of models with different inlet flux when the primary fractures reach the boundary.
Figure 18.
The breakdown pressure/time and reopening pressure/time of fractures in models with different inlet flux.
Figure 18.
The breakdown pressure/time and reopening pressure/time of fractures in models with different inlet flux.
Figure 19.
The seepage fields (MPa) of models with different hydraulic fluid viscosity when the primary fractures reach the boundary: (a) Multi-vis1, t = 1160 s, μ1/μ0 = 0.2; (b) Multi-vis2, t = 1650 s, μ2/μ0 = 0.5; (c) Multi-01, t = 2120 s, μ0/μ0 = 1.0; (d) Multi-vis3, t = 2322 s, μ3/μ0 = 2.0; (e) Multi-vis4, t = 2491 s, μ4/μ0 = 4.0; (f) Multi-vis5, t = 2750 s, μ5/μ0 = 6.0.
Figure 19.
The seepage fields (MPa) of models with different hydraulic fluid viscosity when the primary fractures reach the boundary: (a) Multi-vis1, t = 1160 s, μ1/μ0 = 0.2; (b) Multi-vis2, t = 1650 s, μ2/μ0 = 0.5; (c) Multi-01, t = 2120 s, μ0/μ0 = 1.0; (d) Multi-vis3, t = 2322 s, μ3/μ0 = 2.0; (e) Multi-vis4, t = 2491 s, μ4/μ0 = 4.0; (f) Multi-vis5, t = 2750 s, μ5/μ0 = 6.0.
Figure 20.
The fracture radius of models with different hydraulic fluid viscosity when the primary fractures reach the boundary.
Figure 20.
The fracture radius of models with different hydraulic fluid viscosity when the primary fractures reach the boundary.
Figure 21.
The breakdown pressure/time and reopening pressure/time of fractures in models with different viscosity to summarize, the RFPA-Petrol was used to investigate the influence of the hydraulic fracturing fluid properties on the propagation of dual hydraulic fractures in a multilayered laboratory-scale model. It is found that fracturing fluid properties play a key role in whether dual fractures can cross the barrier. When the low viscosity fluid is used, or the injection flux is small, the dual fractures cannot cross the barrier and the secondary fracture may merge into the primary fracture. If high viscosity fluid is used or injection flux is large, the primary fracture penetrates the barrier and branches off above the barrier. The secondary fracture is influenced by both the fluid properties and the primary fracture, so the injection should control properly to make sure that both of the dual fractures penetrate the barrier.
Figure 21.
The breakdown pressure/time and reopening pressure/time of fractures in models with different viscosity to summarize, the RFPA-Petrol was used to investigate the influence of the hydraulic fracturing fluid properties on the propagation of dual hydraulic fractures in a multilayered laboratory-scale model. It is found that fracturing fluid properties play a key role in whether dual fractures can cross the barrier. When the low viscosity fluid is used, or the injection flux is small, the dual fractures cannot cross the barrier and the secondary fracture may merge into the primary fracture. If high viscosity fluid is used or injection flux is large, the primary fracture penetrates the barrier and branches off above the barrier. The secondary fracture is influenced by both the fluid properties and the primary fracture, so the injection should control properly to make sure that both of the dual fractures penetrate the barrier.
Table 1.
Material parameters and boundary conditions of the simulated “single completion” model in RFPA-Petrol.
Table 1.
Material parameters and boundary conditions of the simulated “single completion” model in RFPA-Petrol.
Parameter | Symbol | Value 1 | Unit |
---|
Young’s modulus | Em | 7000 | MPa |
Uniaxial compressive strength | pm | 35 | MPa |
Homogeneity index | m | 4 | - |
Permeability | κ | 8 × 10−20 | m2 |
Poisson’s ratio | ν | 0.20 | - |
Specific storage | Ss | 1.38 × 10−6 | m−1 |
Flux | Q | 2.40 × 10−8 | m3/s |
Fracture fluid density | ρ | 1000 | kg/m3 |
Fracture fluid viscosity | μ | 0.005 | Pa·s |
Maximum horizontal stress | σx, σH | 6 | MPa |
Vertical stress | σy, σv | 7 | MPa |
Minimum horizontal stress | σz, σh | 5 | MPa |
Table 2.
Material parameters of oil-bearing layers of the multilayered numerical model in RFPA-Petrol.
Table 2.
Material parameters of oil-bearing layers of the multilayered numerical model in RFPA-Petrol.
Parameter | Symbol | Value 1 | Unit |
---|
Homogeneity index | m | 4 | - |
Young’s modulus | Em | 7000 | MPa |
Uniaxial compressive strength | pm | 35 | MPa |
Poisson’s ratio | ν | 0.20 | - |
Permeability | κ | 8 × 10−20 | m2 |
Specific storage | Ss | 1.38 × 10−6 | m−1 |
Table 3.
The material parameters of the interlayer in multilayered laboratory-scale models.
Table 3.
The material parameters of the interlayer in multilayered laboratory-scale models.
Model Number | Young’s modulus 1 (MPa) | Uniaxial Compressive 1 Strength (MPa) | Poisson’s Ratio | Permeability 1 (m2) |
---|
Multi-00 | 7000 | 35 | 0.20 | 8×10−20 |
Multi-E1 | 2100 | 11 | 0.20 | 8 × 10−20 |
Multi-E2 | 4200 | 21 | 0.20 | 8 × 10−20 |
Multi-E3 | 9800 | 49 | 0.20 | 8 × 10−20 |
Multi-E4 | 11,900 | 60 | 0.20 | 8 × 10−20 |
Multi-E5 | 14,000 | 70 | 0.20 | 8 × 10−20 |
Multi-Po1 | 7000 | 35 | 0.10 | 8 × 10−20 |
Multi-Po2 | 7000 | 35 | 0.15 | 8 × 10−20 |
Multi-Po3 | 7000 | 35 | 0.25 | 8 × 10−20 |
Multi-Po4 | 7000 | 35 | 0.30 | 8 × 10−20 |
Multi-Po5 | 7000 | 35 | 0.40 | 8 × 10−20 |
Multi-k1 | 7000 | 35 | 0.20 | 8 × 10−23 |
Multi-k2 | 7000 | 35 | 0.20 | 8 × 10−22 |
Multi-k3 | 7000 | 35 | 0.20 | 8 × 10−21 |
Multi-k4 | 7000 | 35 | 0.20 | 8 × 10−19 |
Multi-k5 | 7000 | 35 | 0.20 | 8 × 10−18 |
Table 4.
Material parameters of the barrier and the oil-bearing layers in the multilayered numerical model in RFPA-Petrol.
Table 4.
Material parameters of the barrier and the oil-bearing layers in the multilayered numerical model in RFPA-Petrol.
Parameter | Symbol | Oil-Bearing Layer Value | Barrier Value | Unit |
---|
Macroscopic Young’s modulus | Em | 7000 | 14,000 | MPa |
Macroscopic strength | pm | 35 | 70 | MPa |
Poisson’s ratio | ν | 0.20 | 0.25 | - |
Permeability | κ | 8 × 10−20 | 4 × 10−21 | m2 |
Table 5.
The flux and viscosity of the fracturing fluid in multilayered laboratory-scale models.
Table 5.
The flux and viscosity of the fracturing fluid in multilayered laboratory-scale models.
Model Number | Flux (m3/s) | Viscosity (Pa·s) |
---|
Multi-01 | 1.13 × 10−10 | 0.005 |
Multi-Q1 | 5.60 × 10−11 | 0.005 |
Multi-Q2 | 8.40 × 10−11 | 0.005 |
Multi-Q3 | 1.40 × 10−10 | 0.005 |
Multi-Q4 | 1.96 × 10−10 | 0.005 |
Multi-Q5 | 2.25 × 10−10 | 0.005 |
Multi-vis1 | 1.13 × 10−10 | 0.001 |
Multi-vis2 | 1.13 × 10−10 | 0.0025 |
Multi-vis3 | 1.13 × 10−10 | 0.075 |
Multi-vis4 | 1.13 × 10−10 | 0.01 |
Multi-vis5 | 1.13 × 10−10 | 0.02 |
Table 6.
Possible scenarios upon the intersection between dual fractures and the interlayer.