Horizontal well and multistage fracturing are the two key techniques for shale gas development, by creating complex fracture networks within tight formations [1
]. Due to the fact that tens of thousands of cubic meters of fracturing fluid are pumped into the downholes of shale gas wells and injected into the matrix of shale reservoirs, geostatic stress can be changed due to the elastic response of the rock mass to hydraulic fracturing. Pore pressure can also be changed due to fluid diffusion along a permeable fault zone [6
]. As a result of this, the casing string is exposed to a complex mechanical environment in the downhole, and therefore the risk of casing deformation increases dramatically [7
]. Previous studies have shown that casing deformations were observed during multistage fracturing in the United States and China, where the commercial development of shale gas is underway and investment is on the rise [10
]. Casing deformation has created a lot of problems for shale gas well completion and development, for example, bridge plugs could not be run to the projected depth, and normal stimulation operations were unable to be carried out. As a result of this, some fracturing sections either needed to be repaired, which increased the cost of well completion, or could only be abandoned, which decreased the productivity of the shale gas wells. In addition, based on previous studies about casing deformation in conventional oil and gas wells, it is known that casing deformation always intensifies over time, which could lead to security issues for the public or the shut-in of the well. Therefore, there is an urgent need to analyze the mechanisms and propose effective solutions for casing deformation.
Multi-finger calipers (MFC) and lead molds are two effective tools for monitoring the deformation features of the deformed part of a casing [12
]. Based on investigations into casing deformation by using both tools in China, there were four different types of casing deformations that were delineated, including extrusion deformation, shear deformation, bending deformation, and buckling. Casing shear deformation represented the largest portion of all of the deformed points. Statistic data showed that: (a) up to March 2016, a total of 90 horizontal wells were successfully fractured in Weiyuan-Changning block, Sichuan basin, casing deformation occurred in 32 wells, and 47 deformed points were found [14
]. 61.7% of all the casing deformed points were examplse of shear deformation [16
], and (b) by the end of May 2018, six horizontal wells were successfully fractured in Weirong block, where casing deformation occurred in five wells and 17 deformed points were found. Most of the deformed points were due to shear deformation. Serious casing deformation has occurred during multistage fracturing in shale gas wells in Simonette, Canada, although there is no previous public data. MFC surveys were conducted in five pads, including 28 wells in this study, and the statistical data showed that 52.2% of all the deformed points were due to shear deformation. From the above data, it can be seen that the study of the mechanisms of casing shear deformation appears to be particularly important to the research on casing deformation during multistage fracturing in shale gas wells.
Many related studies have been carried out, but most of them emphasized the inducement of casing shear deformation [17
]. Based on the previous research work, faults were easily reactivated when fracturing fluid flew into the cracks in the formation, and were more likely to slip along the unstable bedding planes or natural fractures under the action of their own gravity or external forces [18
]. Then, the casing strings which passed through the faults were sheared. Qian et al. [20
] pointed out that formation stress changed, due to opened and propped hydraulic fractures, and caused natural fractures to open or slip, which increased the risk of casing shear deformation. According to the microseismic data, Zoback and Snee [21
] believed that the high pore pressure generated during hydraulic fracturing operations induced slip on preexisting fractures and faults with a wide range of orientations. Meyer et al. [11
] analyzed the seismic data and multi-finger caliper data, and suggested that shear failure of pre-existing faults was likely the main cause of casing deformation. Some scholars have proposed a similar viewpoint and complimented the study, pointing out that when the borehole trajectory was inclined upward along the formation, after fracturing fluid flowed into the shale beddings, the fault could slip because of the effect of gravity [15
]. The mechanisms of fault slippage during or after multistage fracturing were discussed in most of the current research, but few have calculated the variation of the casing’s inner diameter, which was the determining factor of whether the bridge plug could pass through the deformed part of the casing, and therefore should be the evaluation basis for effective solutions to address the problem of casing shear deformation.
Analysts can more precisely identify the deformation situation of a casing’s deformed parts by using an MFC tool. Some scholars have expounded upon the application of an MFC tool in conventional oil and gas wells, which indicated that MFC data could accurately reflect the actual deformation of the casing string in the well [12
]. Despite the clear benefits of MFC surveys, this kind of technique remains challenging to implement in extensive regional oil and gas fields, due to the significant cost of a full system. As a result, there has been little research providing the evidence of MFC data, and only some conducted prospective studies. Marc [22
] collected MFC measurement results from 30 wells from 2003 to 2013, showing that the shear deformation features were localized over a relatively short length (several feet), and resulted from a relative displacement of the upper part of the well compared to the lower part. According to the measurement results of the MFC tool, some mathematical and numerical models were established to simulate the progress of fault slipping, so as to calculate the degree of casing shear deformation. Gao et al. [23
] analyzed the characteristics of casing shear deformation, established a 3D finite element model to simulate the stress-strain status and the deformation process, and pointed out that no cementing near the position of slipping was beneficial to the mitigation of casing shear deformation. Chen et al. [16
] presented a mathematical model for establishing the relationship between microseismic moment magnitude and degree of casing sheared deformation. Guo et al. [24
] developed a numerical model and calculated the influences of slip distance, slip angle, and the mechanical parameters of cement sheath on casing stress. But few of the above studies analyzed the difference between measurement results and actual deformation, and have not put forward solutions to casing shear deformation and showed their validity in engineering in practice. Therefore, it is still a great challenge to solve the problem of casing shear deformation.
In this study, MFC surveys on casing deformation in Canada were implemented, and the mechanisms of casing shear deformation that occurred at the interface between different layers were studied. A new 3D numerical model was developed to simulate the progress of fault slipping, the variation of a casing’s inner diameter along the axis was calculated based on the analysis of MFC surveys. The numerical simulation results were verified through the measured data. Six influential factors, including the slip distance, casing inner pressure, thickness of production casing and intermediate casing, and mechanical parameters of cement sheath were analyzed. Furthermore, proposals for mitigation or avoidance of casing shear deformation were suggested, and some of them were applied to the engineering in practice and were proven to be effective.
4. Numerical Simulation
In order to calculate the variation of the casing’s inner diameter, a numerical model was developed and the influential factors were taken into account. Simulations were carried out by using the commercial software Abaqus (6.14-1), which can be used to perform and post-process simulations of various cases, and for statistical sensitivity analysis. The measurement results of the MFC tool are used to confirm the validity of the proposed Finite Element Model (FEM).
4.1. Model Geometry and Discretization
Physical model. The assembly, which contains a production casing-cement sheath-intermediate casing -cement sheath formation, located above the intermediate casing shoe, was selected as the research object. It was assumed that the casings were centered and the cement sheaths were integral. The formation includes two blocks, the upper block which represented the Nisku formation was the fixed part, and the lower block which represented Ireton formation was the slip part, as shown in Figure 8
Numerical model. A three-dimensional (3D) nonlinear FEM was established to simulate the slip progress of the fault and the mechanical behaviors of the casing shear deformation, as shown in Figure 8
b. As assumed above, the casings were centered, and the cement sheaths showed complete integrity. The outer diameter of the model was 3 m × 3 m × 8 m, which was ten times greater than the size of the borehole, thus allowing the influence of the boundary to avoid the effects on the stress.
Discretization. During the simulation, the materials in the model were chosen assuming that the casing followed the elastically-perfect plastic constitutive relationship with the Von Mises yield criterion, and the cement sheath and formation followed the elastic-plastic constitutive relationship with the Mohr-Coulomb criterion. In order to reflect the casing deformation accurately, the solid element (3D stress, C3D8R) is used to analyze the cement sheath-intermediate casing-cement sheath formation, and the shell element (shell, S4R) is used to study production casing. During the progress of discretizing the finite element model, in order to increase the computational accuracy, the structured grid and variable density meshing method is applied to the model.
4.2. Boundary Conditions and Simulation Steps
Boundary Conditions. In terms of load and constraint sets, the composite boundary of the upper part was fixed by imposing displacement constraints, and the slip displacement of the Ireton part is imposed on the corresponding formation’s surface. Through finite element predefined field function, far-field stress was applied, and the hydraulic pressure was added to the inner wall of the casing. The stress field of the research object, which was part of the inclination segment, could be obtained by three-time rotations from the original coordinate system, and this was then applied to the numerical software (Appendix A
). The pressure of fracturing fluid was applied to the casing’s inner pressure.
In order to reflect the actual conditions of the casing, the transient temperature change of the model was taken into account. The initial temperature of assembly was equal to formation temperature, and the outside surface of the model was one of the temperature boundaries and was set as a stable thermal source. The casing’s inner wall was another temperature boundary, and its temperature was equal to that of the fracturing fluid, which should be calculated by a wellbore temperature field model during fracturing (Appendix B
). The variation of time-dependent temperature was the input for the numerical model as a dynamic boundary.
Simulation Steps. At the first step, the temperature variations of the well are calculated when imposing the dynamic boundary at the inner wall of the production casing. Subsequently, the calculated temperature distribution, geo-stress, and the internal pressure are applied to the assembly, and the initial state of equilibrium is reached. Lastly, the lower block slipped and casing deformation occurred, then the displacement of casing’s inner wall was calculated. During the third step, for sensitivity purposes, the slip distance, casing inner pressure, the production and intimate casing thickness, and mechanical parameters of cement sheath will be changed in order to find the optimal parameters during simulation.
4.3. Geological and Mechanical Parameters
As a horizontal shale gas well in Simonette, 12-10 wells were drilled to the maximum vertical depth of 3920 m, with a horizontal segment length of 2450 m. The measured and true vertical depths of the interface between the Nisku and Ireton formations were 3786 m and 3742 m, respectively. The horizontal minimum in-situ stress and vertical in-situ stress gradients were 2.3 MPa/100 m, 2.0 MPa/100 m, and 2.5 MPa/100 m, respectively. The hole inclination angle is 24°, and the well azimuth angle is 78°. The pumping pressure of fracturing was 77 MPa, and the fracturing fluid friction is approximately 10 MPa. The fracturing fluid density was 1.28 g/cm3
, then the casing’s inner pressure in the interface was about 115 MPa. The discharge of fracturing fluid is 12 m3
/min, and the fracturing time is 4 h. Other geological and mechanics parameters are shown in Table 1
and Table 2
6. Results Comparison and Mitigation Method
The method in this study presented a way to evaluate the reduction of casing’s inner diameter. Using to the microseismic measurements, microseismic moment magnitude can be obtained. And based on the study of Chen et al. [14
], slip distance can be calculated. Then, by using the model proposed in this study, the diameter of a casing’s inner wall after fault slipping can be computed. The computed results and the measurement results by using MFC tools were compared, as shown in Figure 24
. It can be seen that the numerical method in this study has an accuracy of up to 90.17%, and it can be used to select the soluble bridge plug after casing shear deformation, achieving the purpose of overcoming the problem that MFC measurement is costly, as mentioned above.
According to the above analysis, it could be seen that decreasing the slip distance was the best way to protect the casing. In order to mitigate or eliminate fault slipping, the interface between the Nisku and Ireton formations should avoid being opened during the operation of well cementation. As a consequence, the well structure was optimized. The depth of the intermediate casing shoe was reduced to approximately 3600 m, and the depth was more than 100 m above the interface between the Nisku and Ireton formations. The method was applied to nine wells, eight wells did not occur casing shear deformation, which was proved to be the most efficient and economical way. And the engineering practice supported the correctness of the analysis in this study.
Casing shear deformation occurring during multistage fracturing was monitored by using MFC tools, and the cause of the shear deformed points located at the interface between the Nisku and Ireton formations was analyzed. A new investigation based on the MFC measurement results was carried out, and the impact of influential factors on the reduction of a casing’s inner diameter was studied. The following conclusions were drawn:
(1) MFC surveys were carried out to monitor the casing deformation occurring during multistage fracturing in Simonette, Canada. Statistical data showed that shear deformation was the main type of casing deformation, and the shear deformed points can be classified as two types according to the positions of occurrence: shear deformed points located at the position of the interface between the Nisku and Ireton formations (75%), and in the horizontal segment (25%).
(2) The cause of casing shear deformation occurring at the interface between the Nisku and Ireton formations was analyzed. When the interface between the different layers was opened during the operation of well cementation, the friction coefficient between the layers decreases dramatically. During multistage fracturing, the fault was activated and slipped along the interface, which was verified by the microseismic data.
(3) A numerical model has been developed to analyze the reduction of the casing’s inner diameter. The simulation results showed that: (a) fault slipping caused the reduction of casing inner diameter, and the maximum change appeared at the position of the interface of the two formations; (b) the cross-section of the casing calculated by the numerical model was similar to the shape reflected by MFC data in that particular position.
(4) A sensitivity analysis was carried out and the influence of slip distance, the casing’s inner pressure, the mechanical parameters of the cement sheath, and the intermediate and production casing thickness on the reduction of the casing’s inner diameter were analyzed. According to the numerical analysis results, decreasing the slip distance, maintaining high pressure, decreasing the Poisson ratio of the cement sheath, and increasing the casing thickness were beneficial for protecting the integrity of casing. Furthermore, the effectiveness of increasing the intermediate casing thickness is greater than increasing that of the production casing.
(5) Measurement results were compared with computed results to verify the method proposed in this study. The numerical method in this study has an accuracy of up to 90.17%, which can be used as basis for choosing soluble bridge plugs. In addition, the well structure was optimized, and the depth of the intermediate casing shoe was reduced to approximately 3600 m, which was more than 100 m above the interface between the Nisku and Ireton formations. The effectiveness of this method was verified by engineering in practice, as eight of nine wells did not incur casing deformation after implementation of the method.