Figure 1.
Shale gas production: (a) gas transport, (b) multiscale features.
Figure 1.
Shale gas production: (a) gas transport, (b) multiscale features.
Figure 2.
Natural gas
Z-factor for methane estimated by Peng–Robinson Equation-Of-State (PR-EOS) [
32] and empirical equation [
34];
T = 352 K,
= 191 K,
= 4.64 MPa,
R = 8.314 JK
mol
.
Figure 2.
Natural gas
Z-factor for methane estimated by Peng–Robinson Equation-Of-State (PR-EOS) [
32] and empirical equation [
34];
T = 352 K,
= 191 K,
= 4.64 MPa,
R = 8.314 JK
mol
.
Figure 3.
Methane viscosity
(in cp, 1 cp = 1 mPa·s) estimated by the Lee–Gonzalez–Eakin empirical correlation [
35] with
M = 16.04 g/mol and
T = 633.6 R.
Figure 3.
Methane viscosity
(in cp, 1 cp = 1 mPa·s) estimated by the Lee–Gonzalez–Eakin empirical correlation [
35] with
M = 16.04 g/mol and
T = 633.6 R.
Figure 4.
Langmuir and BET isotherms for = 0.0031 m/kg, = 7.89 MPa, T = 327.59 K, = 53.45 MPa, = 0.0015 m/kg, C = 24.56, and n = 4.46.
Figure 4.
Langmuir and BET isotherms for = 0.0031 m/kg, = 7.89 MPa, T = 327.59 K, = 53.45 MPa, = 0.0015 m/kg, C = 24.56, and n = 4.46.
Figure 5.
Permeability correction factor plotted against the Knudesen number for methane (T = 191 K, = m, = 0.1) with flow fields.
Figure 5.
Permeability correction factor plotted against the Knudesen number for methane (T = 191 K, = m, = 0.1) with flow fields.
Figure 6.
Permeability correction factor versus gas pressure with m = 0.5, = 0.5, = 180 MPa, = 38 MPa, and = 0.5.
Figure 6.
Permeability correction factor versus gas pressure with m = 0.5, = 0.5, = 180 MPa, = 38 MPa, and = 0.5.
Figure 7.
Normalized fracture conductivity plotted against the effective normal stress on a fracture for (a) propped fractures and (b) unpropped fractures.
Figure 7.
Normalized fracture conductivity plotted against the effective normal stress on a fracture for (a) propped fractures and (b) unpropped fractures.
Figure 8.
Permeability correction factor for hydraulic fractures and natural fractures with pressure = 34.5 MPa, = 29 MPa, and = 34 MPa.
Figure 8.
Permeability correction factor for hydraulic fractures and natural fractures with pressure = 34.5 MPa, = 29 MPa, and = 34 MPa.
Figure 9.
Nodes in an EDFM for the matrix, a hydraulic fracture, and a natural fracture.
Figure 9.
Nodes in an EDFM for the matrix, a hydraulic fracture, and a natural fracture.
Figure 10.
Scheme for the comparison with the CMG (Computer Modelling Group Ltd.) simulator (simulations VE1A, VE1B).
Figure 10.
Scheme for the comparison with the CMG (Computer Modelling Group Ltd.) simulator (simulations VE1A, VE1B).
Figure 11.
Results of the VE1A simulation: (a) gas flow rate and (b) cumulative gas production versus time t for fracture conductivity equal to 5 (green lines), 50 (blue lines) and 10,000 (red lines) mD-ft. Solid lines—ShOpen/EDFM; dashed lines—ShOpen/EFM; circles—CMG.
Figure 11.
Results of the VE1A simulation: (a) gas flow rate and (b) cumulative gas production versus time t for fracture conductivity equal to 5 (green lines), 50 (blue lines) and 10,000 (red lines) mD-ft. Solid lines—ShOpen/EDFM; dashed lines—ShOpen/EFM; circles—CMG.
Figure 12.
Grids for VE1B sensitivity analysis simulations: (a) Local Grid Refinement (LGR), (b) EDFM, (c) LGR+EDFM; the fracture cell is magnified 10 times.
Figure 12.
Grids for VE1B sensitivity analysis simulations: (a) Local Grid Refinement (LGR), (b) EDFM, (c) LGR+EDFM; the fracture cell is magnified 10 times.
Figure 13.
Comparison of the results provided by ShOpen and CMG in terms of (a) gas flow rate and (b) cumulative production, for VE1B with 10,000 mD-ft.
Figure 13.
Comparison of the results provided by ShOpen and CMG in terms of (a) gas flow rate and (b) cumulative production, for VE1B with 10,000 mD-ft.
Figure 14.
Comparison of the results provided by ShOpen and CMG in terms of (a) gas flow rate and (b) cumulative production, for VE1B with 5 mD-ft.
Figure 14.
Comparison of the results provided by ShOpen and CMG in terms of (a) gas flow rate and (b) cumulative production, for VE1B with 5 mD-ft.
Figure 15.
Grids for VE1C simulation: (a) LGR, (b) EDFM, (c) LGR+EDFM.
Figure 15.
Grids for VE1C simulation: (a) LGR, (b) EDFM, (c) LGR+EDFM.
Figure 16.
Comparison of the results provided by using the different grids in terms of (a) gas flow rate and (b) normalized cumulative gas production, for VE1C.
Figure 16.
Comparison of the results provided by using the different grids in terms of (a) gas flow rate and (b) normalized cumulative gas production, for VE1C.
Figure 17.
Scheme for the comparison with the in-house simulator (simulation VE2).
Figure 17.
Scheme for the comparison with the in-house simulator (simulation VE2).
Figure 18.
Gas flow rate (
a) of VE2 and cumulative gas production (
b) for adsorption and slippage/diffusion, adsorption only, slippage/diffusion only, and no mechanisms; comparison between ShOpen and the in-house simulator [
59].
Figure 18.
Gas flow rate (
a) of VE2 and cumulative gas production (
b) for adsorption and slippage/diffusion, adsorption only, slippage/diffusion only, and no mechanisms; comparison between ShOpen and the in-house simulator [
59].
Figure 19.
AE1 simulation scheme (top) and relative EDFM grid with 28 linear HFs (bottom).
Figure 19.
AE1 simulation scheme (top) and relative EDFM grid with 28 linear HFs (bottom).
Figure 20.
Pressure contours after 1600 days for the Barnett shale reservoir (simulation AE1).
Figure 20.
Pressure contours after 1600 days for the Barnett shale reservoir (simulation AE1).
Figure 21.
History matching (a) and prediction (b) of the gas production rate in the Barnett shale reservoir (simulation AE1).
Figure 21.
History matching (a) and prediction (b) of the gas production rate in the Barnett shale reservoir (simulation AE1).
Figure 22.
Scheme of simulation AE2 showing the 28 HFs and the 248 NFs.
Figure 22.
Scheme of simulation AE2 showing the 28 HFs and the 248 NFs.
Figure 23.
Pressure contours at 3.75 years for the Barnett shale reservoir (simulation AE2) for the scenario with curvilinear HFs (top) and for the scenario with the DFN added (bottom).
Figure 23.
Pressure contours at 3.75 years for the Barnett shale reservoir (simulation AE2) for the scenario with curvilinear HFs (top) and for the scenario with the DFN added (bottom).
Figure 24.
Comparison of gas flow rate (a) and cumulative production (b) between the scenario with linear HFs and the scenario with curvilinear HFs and DFN and, in addition, consideration of HMC (simulation AE2).
Figure 24.
Comparison of gas flow rate (a) and cumulative production (b) between the scenario with linear HFs and the scenario with curvilinear HFs and DFN and, in addition, consideration of HMC (simulation AE2).
Table 1.
Comparison of methods for the prediction of gas transport in unconventional reservoirs; : nonlinear gas transport and storage, multiphase and multicomponent flow. DFN—Discrete Fracture Networks, EDFM—Embedded Discrete Fracture Model.
Table 1.
Comparison of methods for the prediction of gas transport in unconventional reservoirs; : nonlinear gas transport and storage, multiphase and multicomponent flow. DFN—Discrete Fracture Networks, EDFM—Embedded Discrete Fracture Model.
| Analytical | Semianalytical | Structured Grid | Unstructured Grid | EDFM |
---|
accuracy | ++ | ++ | +++ | +++ | ++ |
handling nonlinear mechanisms | + | + | +++ | +++ | +++ |
handling rock heterogeneity | + | + | +++ | +++ | +++ |
quality of DFN mesh | +++ | +++ | + | + | +++ |
preprocessing efficiency | +++ | +++ | +++ | +++ | ++ |
computational efficiency | +++ | +++ | + | ++ | ++ |
Table 2.
Adsorption and transport, corresponding models and domain for the gas flow; A—adsorption, T—transport.
Table 2.
Adsorption and transport, corresponding models and domain for the gas flow; A—adsorption, T—transport.
Mechanism | Model | Type | Domain |
---|
adsorption | Langmuir, BET | A | matrix |
slip flow/diffusion | Klinkenberg [36], Florence et al. [37], Javadpour et al. [38], Civan [39] | T | matrix |
non-Darcy flow | Darcy–Forchheimer | T | fracture |
Table 3.
Input data of the simulations for the comparison with CMG. BHP—bottom-hole pressure.
Table 3.
Input data of the simulations for the comparison with CMG. BHP—bottom-hole pressure.
Property | Unit | Value |
---|
domain dimensions | m | 606.6 × 606.6 |
formation thickness | m | 45.72 |
initial reservoir pressure | MPa | 34.47 |
reservoir temperature T | K | 327.60 |
Langmuir pressure | MPa | 8.96 |
Langmuir volume | m/kg | 0.0041 |
matrix porosity | - | 0.07 |
matrix compressibility | 1/Pa | 1.45 × 10 |
matrix permeability | nD | 500 |
fracture permeability | mD | 0.5–1000 |
fracture width w | m | 0.003 |
fracture half-length ½ | m | 106.68 |
fracture conductivity | mD-ft | 5–10,000 |
well BHP | MPa | 3.45 |
Table 4.
Key reservoir and simulation parameters of VE2.
Table 4.
Key reservoir and simulation parameters of VE2.
Property | Unit | Value |
---|
domain dimensions | m | 200,140 |
formation thickness | m | 10 |
initial reservoir pressure | MPa | 16 |
reservoir temperature T | K | 343.15 |
Langmuir pressure | MPa | 4 |
Langmuir volume | m/kg | 0.018 |
matrix porosity | - | 0.1 |
matrix compressibility | 1/Pa | 1.0 × |
matrix permeability | nD | 100 |
fracture porosity | - | 1.0 |
fracture permeability | D | 1 |
fracture width w | m | 1× |
well BHP | MPa | 4 |
wellbore skin factor s | - | 43 |
Table 5.
Input data for Barnett shale reservoir simulation AE1 [
60]; other input in
Table 2.
Table 5.
Input data for Barnett shale reservoir simulation AE1 [
60]; other input in
Table 2.
Property | Unit | Value |
---|
domain dimensions | m | 1200,300 |
formation thickness | m | 90 |
initial reservoir pressure | MPa | 20.34 |
reservoir temperature T | K | 352 |
rock density | kg/m | 2500 |
Langmuir pressure | MPa | 4.47 |
Langmuir volume | m/kg | 0.00272 |
matrix porosity | - | 0.1 |
matrix compressibility | 1/Pa | 1.0 × |
matrix permeability | nD | 200 |
fracture porosity | - | 0.03 |
fracture permeability | D | 1.0 × |
fracture width w | m | 0.003 |
fracture half-length ½ | m | 47.2 |
fracture conductivity | mD-ft | 1 |
well bottom-hole pressure BHP | MPa | 3.69 |
wellbore skin factor s | - | 19 |
Table 6.
Geomechanical parameters of Barnett shale for simulation AE2; the other input data are shown in
Table 2 and
Table 5.
Table 6.
Geomechanical parameters of Barnett shale for simulation AE2; the other input data are shown in
Table 2 and
Table 5.
Property | Unit | Value |
---|
Biot coefficient | - | 0.5 |
overburden stress | MPa | 38 |
maximum horizontal stress | MPa | 34 |
minimum horizontal stress | MPa | 29 |
effective modulus of the asperities | MPa | 180 |
Gangi exponential constant m | - | 0.5 |
N fracture permeability | mD | 10 |