New Method to Analyse the Cement Sheath Integrity During the Volume Fracturing of Shale Gas
Abstract
:1. Introduction
2. The FEM Model of the Casing-Cement Sheath-Formation in Shale Formation
2.1. Anisotropic Elastic Constitutive Model of Bedding Shale
2.2. The Traditional Model of CCFS
- (1)
- The casing, cement sheath and formation are all homogeneous isotropic materials;
- (2)
- The casing, cement sheath and formation are completely cemented;
- (3)
- No initial stress exists in the cement sheath;
2.3. The Staged FEM Method
- As a first step, apply far-field stress and pore pressure to the formation, then the stress field is balanced.
- As a second step, drilling is simulated, and drilling fluid column pressure is imposed on the borehole wall to simulate the wellbore deformation and stress state during the drilling process.
- As a third step, cement sheath and casing are added simultaneously to the model, then the outer cement sheath boundary matches exactly with the deformed borehole.
- As a fourth step, pressure load is applied on the interior wall of the casing to simulate the downhole condition changes during the subsequent operations. The interface of cement sheath is simulated with the interface elements-based on the Coulomb friction model.
2.4. Failure Criterion of Cement Sheath
2.5. Model Verification
- (1)
- Calculation of formation radius:
- (2)
- Stress distribution and displacement change of assembly after cementing
- (3)
- Stress distribution of CCFS during hydraulic fracturing
- (1)
- The casing, cement sheath and formation are all homogeneous isotropic materials;
- (2)
- The casing, cement sheath and formation are completely cemented;
3. Case Study
3.1. Effect of Temperature Variation
3.2. Effect of Internal Pressure Variation
3.3. Effect of In-Situ Stress on the Stress of Perforated Casing
3.4. Effect of Pore Pressure
3.5. Effect of Formation Properties
3.6. Effects of Cement Properties
4. Conclusions
- (1)
- The internal casing pressure is rather high during fracturing, and the inner wall of cement sheath is subjected to tensile stress. Volume fracturing will greatly change the temperature of casing and cement sheath. The increase of fracturing fluid temperature and control of flow rate in the fracturing process can reduce the downhole temperature difference, which is conducive to reducing the temperature stress effect on the hoop stress of cement sheaths for shale gas wells.
- (2)
- Substantial formation of fractures and fracturing fluid infiltration into the formation during the multi-stage fracturing process will lead to changes in the geostress, pore pressure and formation property around the wellbore. The risk of cement sheath tensile failure is increased in the stress deficit zones and the pore pressure build-up zones. With the decreasing mechanical properties of formation in the fracturing process, the risk of cement sheath tensile failure is reduced to some extent.
- (3)
- The elastic modulus of cement sheath has a great effect on its structure. In the site construction, an appropriate reduction of cement sheath elastic modulus and optimization of cementing quality can markedly reduce the risk of cement sheath tensile failure.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
D−1 | Elastic flexibility matrix |
Ec | Elastic modulus of the cement, GPa |
Ef | Elastic modulus of formation, GPa |
Es | Elastic modulus of casing, GPa |
p | Horizontal stress, MPa |
pci | Initial stress of cement sheath, MPa |
pmi | Internal casing pressure, MPa |
pi | Hydrostatic pressure during cementing, MPa |
q | Vertical stress, MPa |
rf | Outer radius of formation, m |
rs1 | Original inner radius of casing, m |
rs2 | Original outer radius of casing, m |
rs2’ | Outer radius of deformation casing, m |
rw0 | Inner radius of wellbore after inner rock excavated, m |
rw1 | Inner radius of wellbore after cementing, m |
rwc | Radius of wellbore during drilling, m |
ucl | Inner radius of cement sheath, m |
uc2 | Outer radius of cement sheath, m |
ur | Radius of wellbore during drilling, m |
us | Outer radius variation of casing, m |
us2 | Outer radius of casing, m |
uw1 | Radius of wellbore, m |
vc | Poisson’s ratio of the cement |
vf | Poisson’s ratio of formation |
vs | Poisson’s ratio of casing |
Greek symbols | |
σ’ | Stress tensor |
σh | Minimum horizontal principal stress, MPa |
σv | Overburden pressure, MPa |
ε’ | Solid strain tensor |
α | constant term |
β | constant term |
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Medium | OD/ | ID/ | Young’s Modulus/ | Poisson’s Ratio | Internal Friction Angle/° | Cohesion/ |
---|---|---|---|---|---|---|
Casing | 139.7 | 131.98 | 210 | 0.3 | - | - |
Cement sheath | 215.9 | 139.7 | 9 | 0.15 | 17.1 | 21.6 |
Formation | 1270 | - | : 20 : 17 | : 0.20 : 0.18 | 30 | 59.3 |
Medium | Density/(kg·m−3) | Expansion Coefficient/°C−1 | Specific Heat Capacity/ | Thermal Conductivity Coefficient/ |
---|---|---|---|---|
Casing | 7800 | 1.22 × 10−5 | 460 | 45 |
Cement sheath | 1800 | 1.05 × 10−5 | 865 | 0.9 |
Formation | 2300 | 1.03 × 10−5 | 896 | 2.2 |
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Fan, M.; Li, J.; Liu, G. New Method to Analyse the Cement Sheath Integrity During the Volume Fracturing of Shale Gas. Energies 2018, 11, 750. https://doi.org/10.3390/en11040750
Fan M, Li J, Liu G. New Method to Analyse the Cement Sheath Integrity During the Volume Fracturing of Shale Gas. Energies. 2018; 11(4):750. https://doi.org/10.3390/en11040750
Chicago/Turabian StyleFan, Mingtao, Jun Li, and Gonghui Liu. 2018. "New Method to Analyse the Cement Sheath Integrity During the Volume Fracturing of Shale Gas" Energies 11, no. 4: 750. https://doi.org/10.3390/en11040750