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Numerical Estimation of Casing Integrity under Injection Pressure for Fracturing of Shale Gas Formation Xinpu Shen 1 1
Senior Technical Advisor, Halliburton Consulting, 2107 City West Blvd, Houston, TX USA., E-mail:
[email protected]
ABSTRACT: Injection pressure is a key factor in the design of a successful formation stimulation treatment of shale gas—the higher the pressure, the larger the stimulated volume. However, if the pressure is too high, the risk of compromising casing integrity during the injection process is also high. This paper analyzes a practical case of casing integrity problem resulting from injection in a field in southwest China. The purpose is to investigate the relative importance of the factors that influence casing integrity in a horizontal well section, and to determine the upper bound of the safe injection pressure. Calculations were performed by using porous elastoplastic model with finite element method. Anisotropy caused by non-uniform distribution of natural fractures is also included. For the specific casing and formation environment, it was found that casing integrity mainly depends on these three parameters: injection pressure, casing strength, and cement quality. The maximum inward displacement of casing can reach 16 mm and results in serious ovalization under 90 MPa injection pressure, given non-uniform distribution of natural fractures and poor cementing quality. But plastic deformation disappears with 80 MPa injection pressure when all other factors remain unchanged. Consequently, the upper bound of safe injection pressure is set as 80MPa. INTRODUCTION Shale gas is a major type of unconventional oil and gas resource, and it is currently in full-scale development, both in the US and abroad. Compared with the scale and history of international development, especially in the North American region, shale gas development in China is still under developing (Shen, 2012; Chen, 2011). Chinese shale gas reserves are abundant in the southwest region, where many drilling exploration and development projects are ongoing. Because of the complex geological structure and relatively deep location, there are various problems associated with drilling exploration and mining projects. Here, only the issue of casing integrity as it relates to fracturing is discussed. Fracturing is required to exploit shale gas and oil resources where low permeability exists. Using higher fracturing pressure during the stimulation process ensures that a
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larger crack zone range results from the fracturing treatment, which, correspondingly, provides a greater oil and gas yield. However, when the fracturing pressure is too high, and there are other unfavorable conditions, the casing can become seriously deformed, and further construction, even the whole engineering outcome, can be affected. Therefore, the mechanical behavior of the casing under given conditions should be forecast with a numerical simulation to predict casing deformation in advance, achieve further integration with the actual control measures, and select a rational fracturing pressure, which will greatly influence the project’s progress. Based on the case of an actual project for Petro China, a simplified mechanical model for the fracturing of the horizontal well section reservoir stratum of a shale gas resource is discussed in this paper. The factors that can impact the casing integrity were studied and assessed one-by-one through numerical simulation; finally, the major factors were identified according to the results of the numerical simulation. MECHANICAL MODEL Based on the information of a real case of shale gas formation fracturing, the research adopts a plane strain model to simulate the horizontal well section as well as casing and its cement ring and shale formation. The corresponding finite element mesh is shown in Figs. 1 and 2. The model is 500-m high and 1000-m wide. The true vertical depth (TVD) of the top surface is 2100 m, and the surface load is also the corresponding gravitational load of 2100 m. The lower left part of the model is the naturally cracked zone, where a lower Young’s modulus will be assigned. Because of the possibly uneven distribution of the crack, two types of materials are used here to simulate the two regions of both formations. Fig. 2 is the zoomed view around the casing in Fig. 1. This figure shows that the innermost layer is the casing and that the external cement sheath is divided into two parts to simulate the uneven inner sheath property distribution caused by the potential well cementation mass difference.
Location of the wellbore
FIG. 1. Mesh: overall mesh, simplified plane strain model.
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Formation-2
Formation-1
Cem-2
injection pressure
Cem-1
FIG. 2. Mesh: zoomed view around casing of the mesh. The input data of the model include the following: 1) initial geostress field: sequence and direction of principal stress; 2) casing: geometric parameters, material parameters; 3) cement sheath: geometric parameters, material parameters; 4) mechanical properties of the rock formations; 5) injection pressure; and 6) initial pore pressure. The specific values of the parameters are provided in the following paragraphs. Initial Geostress Field: Sequence and Direction of Principal Stress, and initial pore pressure The TVD of the casing is 2600 m, the vertical stress is Sig_v=63 MPa, the minimum horizontal principal stress is Sh=66.2 MPa, and the maximum horizontal principal stress is SH=66.6 MPa. The direction of the maximum horizontal principal stress (SH) is parallel to the wellbore axis. The initial pore pressure is set as 30 MPa. In the process of determining values of geostress, density logging data shown in Fig. 3 is used. Reverse fault stress pattern was found in practice for geostress distribution in this region. Casing: Geometric Parameters, Material Parameters The inner diameter of the casing is 0.1214 m, the wall thickness is 0.0091494 m, the material density of the P110 steel of which the casing is made is 7922 kg/m3, and the intensity is 758 MPa. The modulus of elasticity is E=206 GPa, the modulus of shearing is G=79.38 GPa, and the Poisson’s ratio is 0.3. In the calculation, the ideal elastoplastic model is used to simulate plastic deformation (Dassault Systems, 2008) of the casing material. Cement Sheath: Geometric Parameters, Material Parameters The inner diameter of the cement sheath is 0.1397 m, the outer diameter is 0.2159 m, the material density is 1900 kg/m3, the modulus of elasticity of regular cementing material is E=27.2 GPa, and the Poisson’s ratio is 0.3. To simulate the unevenness of the cement sheath filling caused by poor well cementation quality, the dark (Cem-1) and light (Cem-2) parts of the cement sheath material in the figure are respectively given different modulus values of elasticity. In detail, Young’s modulus given to Cem-1 is the original regular value of E=27.2 GPa. And the value for Cem-2 which is the weaker one is E1=60% of E =16.32GPa.
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Mechanical Properties of the Rock Formations Logging data shown in track-1 and track-2 in Fig.3 has been used to derive the mechanical properties of this well. 1-D analysis has been done with DrillworksTM. Fig. 3 shows the Poison’s ratio (track-3), Young’s modulus (track-5), and overburden stress gradient (track-4).
FIG. 3. Illustration of logging data and mechanical properties derived with DrillworksTM. The rock density used in the model is 2650 kg/m3, the modulus of elasticity is E=40 GPa, and the Poisson’s ratio is 0.25. To simulate the unevenness of the natural fracture distribution, the blue and grey parts of the formation material in the figure are respectively given different modulus values of elasticity. Microseismic monitoring has been done for this project in this field. The monitored micro seismic data shown in Fig.4 appears significant asymmetry to the axial direction of the given horizontal wellbore. This asymmetry was interpreted as a result of asymmetric distribution of initial natural fracture.
FIG. 4. Illustration of non-uniform distribution of monitored micro-seismic activities.
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In order to take into account of the asymmetric distribution of natural fractural as well as induced fracture shown in Fig.4, non-uniform distribution of mechanical properties. This is modeled by using two different sets of values of material property parameters: formation-1 and formation-2 shown in Fig.2. Due to injection stimulation, formation of shale gas reservoir was fractured. Consequently, values of the Young’s modulus of this fractured formation will be degraded from its original value E0 to a smaller value E. Reference has been made two the works reported in (Xinpu Shen, 2012; Xinpu Shen, 2014). To simulate the crack phenomenon during fracturing, the elastic-plastic damage constitutive model (Lubliner et al., 1989; Lee and Fenves, 1998) was adopted as formation material. The continuum damage used there is a representation of degradation of Young’s modulus. In the work reported there, maximum value of Young’s modulus degradation within formation around the wellbore is 40%. Accordingly, values of Young’s modulus used in this model are: E0 for formation-1; and 65% of E0 is set for E of formation-2. Injection Pressure The bottom-hole injection pressure of the fracturing process is calculated from pumping pressure with the assumption of no friction drag. The peak value of fluid pressure applied on the inner surface of the casing is P=90 MPa. Boundary Conditions The boundary conditions of the model are set up as follows: normal zero displacement constraint on both lateral surfaces as well as the bottom surface, with the surface pressure load on top, which simulates the overburden gravity load. NUMERICAL RESULTS The Abaqus finite element software is used here in the calculation. Fig. 5 shows the casing deformation and stress distribution within the casing obtained from the numerical calculation, under the injection pressure P (P=90 MPa). For clear illustration, the figure only shows the casing and its deformation and conceals the formation and cement sheath. The color image in the figure is the casing position after deformation, and the monochromatic image is the casing position before deformation. The figure indicates significant horizontal deformation of the casing under the injection pressure. The maximum value of von Mises equivalent stress within the casing is up to 800 MPa, which exceeds the initial yield limit and results in significant plastic deformation. Figure 6 shows the horizontal displacement of the casing under an injection pressure of P=90 MPa. From this figure, it can be observed that the maximum value of displacement is 16.2 mm, and the maximum value of vertical deformation is less than 1 mm, which is very small. Therefore, the major deformation occurs in the horizontal direction. An interpretation of this displacement result is that: total value of overburden doesn’t change during the injection process; therefore, little
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deformation occurs in vertical direction. On the other hand, both value and direction of horizontal stress will change due to variation of pore pressure as well as fracture development, displacement in horizontal direction will be the major deformation component.
FIG. 5. Casing deformation and stress distribution, with maximum injection pressure of P=90 MPa.
FIG. 6. Casing deformation and displacement (components distribution), with maximum injection pressure of P=90 MPa. Various combinations of values of injection pressure and natural fracture distribution, as well as non-uniform distribution of Young’s modulus within the concrete ring, are simulated in this calculation. Values of maximum von Mises equivalent stress within the casing that correspond to each set of a combination of parameter values are obtained (Table 1). Table 1 shows that, when the bottom-hole pressure (BHP) is BHP=80 MPa and if the uneven distribution of the cement sheath material is only the result of well cementation quality, the maximum equivalent stress within the casing is 608 MPa; meanwhile, if there is also an uneven distribution of the formation’s natural fracture, the stress can be up to 720 MPa with the same injection pressure of 80 MPa. When the internal casing pressure, corresponding to the injection pressure, is BHP=90 MPa and the formation has uneven material properties and poor well cementation sheath quality, the maximum equivalent stress within the casing is 800
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MPa, which exceeds the initial intensity and can result in serious deformation. Table 1. Maximum values of von Mises equivalent stress within the casing corresponding to each set of input data Maximum Injection value of von Pressure Mises Stress /MPa within Casing /MPa 90
800
90
688
90
791
90
726
80
608
80
720
Strength of P110 /MPa
Distribution of Asymmetric Properties Cement Natural Sheath Fractures Properties Asymmetric
Asymmetric
Asymmetric 758 Asymmetric
Asymmetric
Asymmetric
CONCLUSIONS The work reported here is based on a real case of shale gas stimulation in the southwest region of China. A simplified mechanical model was built for casing integrity assessment under fracturing pressure. In this calculation, the factors that can impact casing integrity were investigated and evaluated one-by-one through numerical simulation. According to the results of the numerical simulation, the major factors that impact casing integrity were identified as follows: • The significant ovalization of the casing’s cross-sectional is the result of the joint action of high injection pressure and non-uniform distribution of the natural fracture within the formation. • To ensure the casing integrity during the formation stimulation process, casing deformation should be strictly monitored during the process of injection. When an obvious casing deformation tendency is detected, injection pressure should be immediately reduced to avoid serious casing integrity problems. • Upper bound of injection pressure window is determined with given material properties of casing, cementing as well as formation. Degradation of Young’s modulus caused by injection fracturing is modeled with simplified method. It should be noticed that injection pressure window proposed here is an important concept for the design of stimulation work. This window actually defines a reasonable range of the value of injection pressure: its lower bound is the value below
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which the formation cannot be fractured, and its upper bound is the value above which the casing will lose its integrity. Here only the upper bound of the injection window is investigated. REFERENCES Chen, M. (2011). Scientific assessment of horizontal well reservoir transformation and control fracturing technology, In: Complex Structure Static Optimization Design and Drilling Completion Control Technology Gao, D. (Editor). China University of Petroleum Press, Dongying, Shandong Province, 118-169. Dassault Systems. (2008). Abaqus Analysis User’s Manual. Vol. 3: Materials, Version 6.8, Vélizy-Villacoublay, France: Dassault Systems, 19.3.1-17 – 19.3.214. Lee, J. and G.L. Fenves. (1998). Plastic-damage model for cyclic loading of concrete structures. ASCE J. Engng Mech. (124) 8: 892-900. Lubliner, J., J. Oliver, S. Oller, and E. Onate. (1989). A plastic damage model for concrete. Int. J. Solids & Struct. (25) 3: 299-326. Shen, X. (2012). Cohesive crack for quasi brittle fracture and numerical simulation of hydraulic fracture. In: Drilling and Completion in Petroleum EngineeringTheory and Numerical Application. Shen, X., Bai, M., and Standifird, W. (Editors). CRC Press Taylor & Francis, London, UK, 175-191. Xinpu Shen (2012). Modelling fractures with continuum damage and its numerical application to stimulation estimates. Paper No: ARMA 12-196. The 46th US Rock Mechanics / Geomechanics Symposium held in Chicago, IL, USA, 24-27 June 2012, 1-7. Xinpu Shen (2014). Numerical analysis on the interaction between two zipper frac wells using the continuum damage method. OTC -24975, presented at the Offshore Technology Conference Asia (OTC Asia), 25-28 March 2014, Malaysia, 1-11.
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