ARMA 16-246
Well Integrity Analysis: 3D Numerical Modeling of Cement Interface Debonding Feng, Y., Podnos, E. and Gray, K.E. The University of Texas at Austin, Austin, Texas, USA
Copyright 2016 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 50th US Rock Mechanics / Geomechanics Symposium held in Houston, Texas, USA, 26-29 June 2016. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.
ABSTRACT: With ongoing environmental concerns and increasingly stringent regulations, the traditional topic of wellbore integrity is more important than ever before. A great deal of importance is attached to the cement sheath because it is necessary to provide zonal isolation and well integrity during the life of a well. Debonding at the casing/cement or cement/formation interfaces, which may result in substantial flow channels and fluid leakage, is often responsible for the loss of wellbore integrity. A three-dimensional finite-element model is developed in this paper to simulate debonding fracture propagation at cement interfaces. Debonding is driven by pressure build-up at the casing shoe due to fluid leakage. The model can be used to quantify the length, width, and circumferential coverage of the debonding fracture. The simulation results show dependence of debonding fracture width and circumferential coverage on in-situ stress conditions, initial cracks around the casing shoe, and cement and formation properties. For example, with initial cracks in the cement interface, debonding fractures tend to develop vertically along the axis of a vertical well, rather than circumferentially around it. The method proposed herein presents a useful step towards prediction of well integrity and provides improved guidance for cement selection and completion optimization.
1. INTRODUCTION Well integrity, always of importance, is becoming more so because of increasing environmental concerns and regulatory activities. Moreover, increasingly hostile environments such as HTHP fields, ultra-deep-water fields, and geothermal fields, along with more complicated development operations, such as those encountered in gas producing wells, gas storage wells, water injectors, and cuttings/waste injectors, all present new challenges for well integrity. Failure of well integrity can lead to costly remedial operations or total loss of the well, severe environment contamination, and even fatal accidents to operating personnel. The cement sheath is the heart of well integrity. It is expected to ensure well integrity by providing zonal isolation and support for the casing throughout the life of a well, from well construction, hydrocarbon production, to post-abandonment (Gray, et al., 2009; Feng, 2016). A successful cementing job is expected to result in complete zonal isolation, without leaving any leakage pathway in the annulus between casing and formation. Unfortunately, this goal is not always achieved, and failure of cement
sheath commonly occurs during the life of a well (Fourmaintraux et al., 2005). Failure modes of the cement sheath may include: (1) tensile cracking in the cement, (2) plastic deformation in the cement, and (3) debonding at the cement/casing and/or cement/formation interfaces. These modes are thought to result from high stress/pressure levels encountered in the cement sheath during a well’s life. Cement sheath failure may also be induced by improper cement placement because of high well inclination, poor hole calibration, poor centralization, poor selection of chemical agents, or poor mud removal (Bois et al., 2011). For this study, attention is focused mainly on debonding at the cement interfaces. Several authors have developed models to simulate cement interface debonding, based on simplifications such as assumptions of linear elasticity for casing, cement and rock and initially intact cement sheath (Bosma et al., 1999; Fleckenstein et al., 2001; Fourmaintraux et al., 2005; Gray et al., 2009; Pattillo and Kristiansen, 2002; Ravi et al., 2002; Shahri et al., 2005). However, laboratory tests performed on a Class-G cement system show that rather than a one-phase linear elastic medium, the cement is better characterized as a porous media (Bois et al., 2012, 2011; Ghabezloo et al., 2008).
Additionally, non-linear stress-strain behavior of the rock formation is important (Morita and Gray, 1980). When either the cement sheath or the rock formation in the vicinity of the wellbore exhibit non-elastic or plastic behavior, appropriate constitutive laws for correct description of cement and formation behavior are essential for cement sheath modeling (Bois et al., 2011; Gray, et. al., 2009). Most previous studies simulating interface debonding by applying stress/pressure boundary conditions do not consider initially existing defects at the cement interfaces due to poor mud removal, cement shrinkage during hydration, or other operational factors (Bosma et al., 1999; Fleckenstein et al., 2001; Fourmaintraux et al., 2005; Gray et al., 2009; Ravi et al., 2002; Shahri et al., 2005). Additionally, most researchers have modeled interface debonding as a tensile or shear failure due to high local stress induced by the combined effects of farfield in-situ stress, fluid pressure in the wellbore (likely subjected to large changes during the life of a well), temperature changes, and differences in mechanical properties of the casing, cement and formation. However, when an initial crack due to poor mud removal or cement shrinkage, or an induced crack resulting from excessive shear/tensile stress, exists at the cement interface, then liquids and/or gas may invade into the crack, leading to pressure buildup and, ultimately to fracture propagation along the interface. Consequences of the debonding fracture propagation, such as leakage of formation fluids to the surface and/or uncontrolled inter-zonal flow, can result in severe operational troubles and/or substantial environmental pollution. Circumstances in which fluid-driven debonding fracture may occur include:
Changing mud while drilling
Pressure testing/cycling completion, and production
Perforation operations
Hydraulic fracturing
Fluid injection, such as gas injection, produced water re-injection, drilling cutting re-injection, steam injection, and flooding operations.
during
drilling,
Gray et al., (2009) developed numerical models to investigate cement debonding by modeling the casing/cement interface as a contact condition, which may allow zero or some amount of tension transmission across the interface, corresponding to the cases with no bonding strength and finite bonding strength respectively. Other researchers modeled the cement interface as a layer of interface elements based on a Coulomb friction model (Bosma et al., 1999; Ravi et al., 2002). While such models may be satisfactory for analyzing interface debonding when there is no fluid invasion into the annular cracks after debonding, they cannot simulate the propagation of
fluid-driven cracks along the interface, which requires fully-coupled modeling of the mechanical behavior of the casing/cement/formation system and fluid flow into and along the cracks. Great progress has been made in fully-coupled modeling of fluid-driven fracture in porous media in the past decade, such as the development of coupled pore pressure cohesive zone method and coupled pore pressure extended finite element method (Feng, 2016; Kostov et al., 2015; Searles et al., 2016; Wang, 2015; Yao et al., 2010). These modeling techniques can successfully account for several key phenomena of fluid-driven fractures in porous media, including fluid flow within the fracture, pore fluid flow in the porous media, deformation of porous medium, and fracture propagation (Zielonka et al., 2014). However, these techniques have not been applied to the study of cement sheath integrity until recently. To authors’ knowledge, Wang and Taleghani (2014) were the first to apply the coupled pore pressure cohesive zone method to this problem. They successfully modeled fluid-driven fracture propagation along the cement interfaces, which improved the understanding of cement bond failure due to excessive fluid pressure buildup at the interface. The work presented here is another implementation of the newest finite element methodology to cement integrity modeling. The numerical approach, i.e., cohesive zone theory and finite-element analysis, is similar to that used by Wang and Taleghani, but the model assumptions, interpretation methods, and specific focus employed in this paper are substantially different. Whereas Wang and Taleghani investigated the effects of bonding interface properties on propagation of a debonding fracture, the current study simulates non-uniform debonding fractures for various in-situ stress conditions and pre-existing cracks at the cement interfaces. This work is the first reported modeling of dynamic cement debonding from pre-existing cement interface cracks of different shapes/sizes due to hydraulically driven pressure. Chronology of these cracks, their propagation/extension, and accompanying fluid and pressure transmission, i.e., the loss of pressure integrity, cement channeling behind the pipe, are of considerable operational and regulatory consequences. How material behaviors are characterized is another important consideration. This paper utilizes plasticity material models for cement and formation and investigates their plastic deformation. Wang and Taleghani, on the other hand, model the cement and formation as linear-elastic materials. While the assumption of linear elasticity is quite convenient since it considerably simplifies the solution process, the elevated and complex stress states, temperature distributions, drilling mud and fluid mechanics, cement formulations, and rock formations collectively involved in casing,
cement, and formation interactions for subsurface environments may not support that assumption. The assumption of linearly elastic behavior allows superposition principles, but neither time dependency nor hysteresis can be considered. On the other hand, nonlinear and plasticity models can provide time dependent and history matching quantifications, with superposition processes being much more difficult.
criterion assumes that when the ratio of energy dissipated due to shear deformations to the total energy dissipated in the damage process reaches a critical value determined by the critical fracture energies of the material, the fracture will propagate. This criterion is more appropriate for situations where the critical fracture energies purely along the first and second shear direction are similar (Wang, 2015; Yao et al., 2010).
2. COUPLED PORE PRESSURE COHESIVE ZONE METHOD In this study, fracture propagation and fluid flow in the fluid-driven fracture along the cement interface are modeled using coupled pore pressure cohesive zone method. A traction-separation constitutive law and a fluid flow constitutive law are incorporated into the cohesive zone model to describe these two phenomena respectively. Fracture opening and propagation are modeled as the damage evolution between two initially bonded interfaces with zero interfacial thickness. The traction-separation constitutive law consists of three components: initial (before damage) loading behavior, damage initiation, and damage evolution of the cohesive elements. Fig.1 shows the traction-separation constitutive law used in this study. The initial loading process is assumed to follow linear elastic behavior. Damage begins when the stress/traction applied on the interface satisfies damage initiation criteria. A maximum nominal stress criterion is used as the damage initiation criterion, which assumes that damage begins when the traction on the interface reaches the tensile or shear strength (𝑇𝑜 ) of the interface. Beyond damage initiation, the stiffness of the interface begins to decrease and damage evolution occurs. Damage evolution describes the rate at which the stiffness is degraded once damage is initiated. In the study here, the damage evolution model is based on the Benzeggagh-Kenane fracture energy criterion (Benzeggagh and Kenane, 1996): 𝐺𝑛𝐶
+
(𝐺𝑠𝐶
𝐺 𝛽 − 𝐺𝑛𝐶 ) (𝐺𝑆 ) 𝑇
=𝐺
𝐶
(1)
where, 𝐺𝑛 , 𝐺𝑠 and 𝐺𝑡 are the energies dissipated due to deformations in the normal, the first shear, and the second shear directions, respectively; 𝐺𝑛𝐶 , 𝐺𝑠𝐶 and 𝐺𝑡𝐶 are the critical energies required to cause failure in the normal, the first shear, and the second shear directions, respectively; 𝐺𝑆 = 𝐺𝑠 + 𝐺𝑡 is the total energy dissipated due to deformations in the first and second shear directions; 𝐺𝑇 = 𝐺𝑛 + 𝐺𝑠 + 𝐺𝑡 is the total energy dissipated due to deformations in the normal, the first shear and the second shear directions; 𝐺 𝐶 = 𝐺𝑛𝐶 + 𝐺𝑠𝐶 + 𝐺𝑡𝐶 is the total critical fracture energy in the normal, the first shear and the second shear directions. This fracture
Fig.1. A typical traction-separation law
Upon opening of an interface fracture, fluid will flow into it. Fluid flow in the fracture includes two components, which are longitudinal flow along the fracture and normal fluid flow (leak-off) from fracture faces to the surrounding porous medium, and can be described by a set of equations (Zielonka et al., 2014):
Continuity equation (mass conservation) which assumes that the flow obeys Reynold’s lubrication theory: 𝜕𝑤 𝜕𝑡
+
𝜕𝑞𝑓 𝜕𝑠
+ 𝑣𝑡 + 𝑣𝑏 = 0
Tangential flow which assumes incompressible Newtonian fluid flow between narrow parallel plates (fracture surfaces) 𝑤 3 𝜕𝑝𝑓
𝑞𝑓 = − 12𝜇
(2)
𝑓
𝜕𝑠
(3)
Fluid leak-off (normal flow) equation 𝑣𝑡 = 𝑐𝑡 (𝑝𝑓 − 𝑝𝑡 )
(4)
𝑣𝑏 = 𝑐𝑏 (𝑝𝑓 − 𝑝𝑏 )
(5)
where 𝑤 is the fracture aperture; 𝑞𝑓 is the longitudinal fluid flow rate in the fracture; 𝑣𝑡 and 𝑣𝑏 are the normal flow velocities through the top and bottom faces of the fracture, which can be interpreted as fluid leak-off rate from the fracture into the surrounding porous medium; 𝜇𝑓 is the fluid viscosity; 𝑝𝑓 is the fluid pressure inside the fracture; 𝑝𝑡 and 𝑝𝑏 are the pore fluid pressure in the porous medium adjacent to the top and bottom faces of
the fracture; 𝑐𝑡 and 𝑐𝑏 are parameters that control fluid flow across the top and bottom fracture faces, usually referred as “leak-off coefficients”. The utilized normal flow model can be interpreted as a thin layer of filter cake on the fracture faces, which increases or reduces effective permeability of the fracture faces (Yao et al., 2010). It is obvious that for the debonding fracture along the casingcement interface, leak-off will occur only on the cement side, but not into the impermeable casing.
3. MODEL FORMULATION AND IMPLEMNTATION 3.1. Modeling Goals The first goal of this study was to develop a general finiteelement framework for simulating cement sheath debonding in a vertical well due to fluid-driven fracture propagation along the cylindrical interfaces of cement sheath with casing and formation. Debonding fractures are modeled with the coupled pore pressure cohesive zone approach. The framework should also take into account other crucial aspects of the casing/cement/formation system, including nonlinearity of the constitutive equations, interaction between different materials, poromechanical nature of cement response, plastic deformation of cement and formation, three dimensionality of in-situ stresses. The framework should have the flexibility to be readily modified for a nonvertical well, casing eccentricity, and more complex material models. The second objective of the paper was to apply this finiteelement framework to investigate the propagation of debonding fracture from a casing shoe, for various initial micro-annular-fractures around the shoe, different in-situ stress states, and different material properties. Also, the development of plastic deformation in the cement during debonding fracture growth should be followed. To achieve these goals, a general-purpose nonlinear finite element code Abaqus/Standard was selected (SIMULIA, 2016). The recently developed capabilities of Abaqus to model fully-coupled, fluid-driven fracture in porous medium, are particularly useful for studies of hydraulic fracturing related problems in the petroleum industry (Kostov et al., 2015; Searles et al., 2016; Wang, 2015; Yao et al., 2010).
3.2. Model Geometry and Discretization Geometry. Since a debonding fracture may develop both circumferentially and vertically at the cement interface with a non-uniform pattern, the traditional 2D model, assuming plane stress/strain conditions, cannot correctly predict fracture growth (Wang and Taleghani, 2014). In addition, accurate modeling of nonlinear effects, such as interface discontinuity and material plasticity, depends highly on the ability to model 3D stress state (Gray et al., 2009). Therefore, a 3D model was developed in this study
for the cement sheath integrity problem, as shown in Fig.2a. A vertical well is modeled with its axial direction coinciding with the Z-axis of the Cartesian coordinate system, as depicted in Fig.2a. The X-axis and Y-axis are oriented along the direction of the maximum and minimum horizontal stresses, respectively. The components of the model including casing, cement and formation are shown in the plane view of Fig.2b, and the interface between casing and cement is shown in Fig.2c. For the present study, only debonding at the casing/cement interface is considered, while the outer interface at the cement/formation is assumed to be functionally bonded. However, debonding at the outer interface can be easily included with minor model modification. Because of the symmetry of the problem, only one quarter of the system is modeled. The casing inner radius is 8.41 cm, and outer radius is 9.69 cm, i.e. the casing thickness is 1.28 cm. The drilling hole size is 12.07 cm, hence the thickness of the cement sheath between casing and formation is 2.38 cm. The casing/cement interface is modeled using a layer of cohesive elements with zero thickness. The total size of the quarter model is 10×10×40 m. The casing shoe, where leakage occurs and pressure builds up, is at the bottom of the wellbore, as illustrated on Fig. 2a. Discretization. The casing is discretized using 3D linear full-integration solid stress elements without degree of freedom of pore pressure. Cement and formation are discretized using 3D linear full-integration poroelastic elements. The casing/cement interface is discretized with a layer of coupled pore pressure and deformation cohesive elements which allow for propagation of the debonding fracture and fluid flow in the fracture, as described in Section 2. Fig.2 shows the overall mesh of the model, with 1500, 2000, 20500, and 500 elements being used to mesh casing, cement, formation, and cohesive interface, respectively. Since interface failure, large plastic deformation, and high stress levels are expected close to the wellbore, especially near the casing shoe, the mesh in this region is refined, while coarser elements located farther away from the casing shoe, both in lateral and vertical directions.
Cement and Formation. The cement and formation rock are modeled as elastic/perfectly plastic porous materials. The Mohr-Coulomb plasticity model is used. The elastic material properties consist of Young’s modulus, 𝐸, and Poisson’s ratio, 𝑣 ; the Mohr-Coulomb plasticity properties consist of internal friction angle, φ, and cohesive strength, 𝑐; and the porous properties are defined by porosity, ∅ , and permeability, 𝑘 . The properties of cement and formation used in this paper are reported in Table 1 and Table 2, respectively, with each of them consisting of a base case and several supplementary cases for sensitivity study purposes.
Fig.2. Cement sheath model. (a) one-quarter geometry; (b) top view of the casing/cement/formation system; (c) interface between casing and cement
Interface Bond. As stated above, the interface between casing and cement is modeled using a layer of zero thickness coupled pore pressure and deformation cohesive elements, which incorporates a tractionseparation law to describe fracture propagation behavior and a flow rule for fluid flow in the fracture. A major challenge in using a cohesive model is the determination of cohesive properties of the casing/cement interface. Very little data are available in the literature. Here the cohesive properties used for the casing/cement interface, including tensile strength, shear strength, cohesive stiffness, and critical energy, are based on data reported by Wang and Taleghani (2014), where they estimated cohesive properties of the cement interface through numerically simulating and matching the pipe (casing) push-out tests by Carter and Evans (1964). The leakage fluid is assumed to be water, and a very small leak-off coefficient is used for the fracture surface on the cement side due to low permeability of the cement. The parameters utilized for the cohesive interface bond are summarized in Table 3.
3.3. Material Models Casing. The steel casing is assumed to be linearly elastic in this study, with Young’s modulus, 𝐸, and Poisson’s ratio, 𝑣, equal to 2.0×108 kPa and 0.27, respectively.
Table 1. Cement properties Young’s Modulus, 𝐸
Poisson’s Ratio, 𝑣
Friction Angle, 𝜑
Cohesive strength, 𝑐
Permeability, 𝑘
(o)
kPa
mD
Porosity, ∅
Type
kPa
C1
2.00E+07
0.26
27
8.00E+03
0.05
0.2
C2*
3.00E+07
0.26
27
1.00E+04
0.05
0.2
C3
8.00E+07
0.26
27
1.50E+04
0.05
0.2
* C2 is the base case.
Table 2. Formation properties Young’s Modulus, 𝐸
Poisson’s Ratio, 𝑣
Friction Angle, 𝜑
Cohesive strength, 𝑐
Permeability, 𝑘
(o)
kPa
mD
Porosity, ∅
Type
kPa
F1*
3.30E+06
0.26
30
5.00E+03
1.0
0.2
F2
5.00E+06
0.26
30
7.00E+03
1.0
0.2
F3
4.00E+07
0.26
30
1.20E+04
1.0
0.2
* F1 is the base case.
Table 3. Interface bond properties Cohesive Stiffness
Shear Strength
Tensile Strength
Critical Energy
Leak-off Coefficient
Fluid Viscosity
kPa
kPa
kPa
J/m2
m/s/Pa
cp
8.50E+07
2,000
500
100
5.897E-12
1.0
3.4. Boundary Conditions and Simulation Steps Boundary Conditions. In order to reduce computation burden of the 3D model, only one-quarter of the domain is modeled as shown in Fig.2a. Symmetry boundary conditions are applied to the front and left surfaces of the model in Fig.2a. The vertical displacement at the bottom surface is constrained. An overburden pressure of 11,000 kPa is applied at the top surface of model. Maximum horizontal stress parallel to the X-axis and minimum horizontal stress parallel to the Y-axis are applied on the right surface and back surface of Fig.2a, respectively. Different horizontal stress ratios, as given in Table 4, are used to investigate the effect of stress anisotropy on cement interface debonding. The initial pore pressure is assumed equal to 6,000 kPa. A constant wellbore fluid pressure of 7,200 kPa is applied on the inner surface of the casing. Because height of the simulation domain is relatively small, no initial stress or pressure variation is considered in the vertical direction. Table 4 summarizes different types of loads assigned to model. Initially existing cracks, through which leakage occurs and a fracture growth initiates, are assigned at the casing/cement interface around the casing shoe. The width and height of all the initial cracks are constant and equal to 2 mm and 20 mm respectively. Various
circumferential crack extents are used, in an attempt to investigate interface debonding patterns with different initial crack shapes. The circumferential extent of the initial crack is quantified using an arc angle. A 0𝑜 arc angle indicates there is no initial crack, and a 90𝑜 angle means a crack extending throughout the circumference of the circular interface. Table 5 provides a detailed description of the initial crack shapes modeled in this study. Simulation Steps. Two steps were used in each simulation. At the first step, far-field horizontal stress, overburden pressure, and initial pore pressure are applied to the configuration and initial state of equilibrium is reached. No debonding occurs during this step except at the pre-assigned cracks around the casing shoe. The second step simulates leakage and pressure buildup at the casing shoe and their consequences, including debonding fracture propagation along the casing/cement interface and plastic deformation development in the cement at the same time. Pressure buildup around the casing shoe is achieved as a result of fluid charge (leakage) into the cement interface with a very small charge rate.
Table 4. In-situ stresses, pore pressure and wellbore pressure applied to the model Horizontal Stress Ratio** Type
Minimum Horizontal Stress
Maximum Horizontal Stress
Overburden Pressure
Initial Pore Pressure
Wellbore Pressure
kPa
kPa
kPa
kPa
kPa
SR0*
1
9,600
9,600
11,000
6,000
7,200
SR1
1
8,000
8,000
11,000
6,000
7,200
SR1.1
1.1
8,000
8,800
11,000
6,000
7,200
SR1.2
1.2
8,000
9,600
11,000
6,000
7,200
SR1.25
1.25
8,000
10,000
11,000
6,000
7,200
SR1.3
1.3
8,000
10,400
11,000
6,000
7,200
SR1.35
1.35
8,000
10,800
11,000
6,000
7,200
SR1.4
1.4
8,000
11,200
11,000
6,000
7,200
* SR0 is the base case; ** Horizontal stress ratio is the ratio of maximum horizontal stress to minimum horizontal stress.
Table 5. Geometry of the initial cracks at the casing shoe Q1
Q2
Q3
Q4*
Circumferential Extent, (o)
30
45
60
90
Thickness, mm
2
2
2
2
Height, mm
20
20
20
20
Type
Initial Crack Shape
* Q4 is the base case.
4. RESULTS Using the finite-element model described above, the cement interface debonding was investigated for various combinations of in-situ stresses, pre-exiting cracks around the casing shoe, and cement and formation properties. The following subsections summarize the simulation results.
4.1. Cement Interface Debonding with Anisotropic Horizontal Stress In-situ stresses are always compressive and resist debonding at cement interface unless the stress anisotropy is too large. However, when leakage is present, fluid pressure may build up in the interface, ultimately resulting in sufficient pressure to overcome effect of the in-situ compressive stress and initiation of a hydraulic fracture along the interface. To investigate the effects of
non-uniform (horizontal) in-situ stress on the development of the debonding fracture, several cases with different horizontal stress ratios as reported in Table 4 are simulated. For comparison purposes, only two cases, SR1 and SR1.2 with horizontal stress ratios equal to 1.0 (uniform) and 1.2 respectively, are selected for analysis. Fig.3 illustrates creation of the debonding fracture near the casing shoe for the two selected cases by the end of the second simulation step. A comparison between these cases shows that:
For the case (SR1) with uniform horizontal stress, the width of the debonding fracture is constant around the casing, as shown in Figs. 3 and 4.
For the case (SR1.2) with anisotropic horizontal stress, the debonding fracture is not uniform, with a smaller width in the direction of the maximum horizontal stress (X-axis) and a larger width in the
direction of the minimum horizontal stress (Yaxis), as shown in Figs.3 and 4. This is because the casing/cement interface is under a larger compressive stress in the direction of maximum horizontal stress, but under a smaller compression in the direction of minimum horizontal stress. This observation is consistent with the conclusion of hydraulic fracturing studies that a fracture should occur in the plane perpendicular to the least principal stress (Feng et al., 2015; Feng and Gray, 2016a, 2016b; Gray et al., 2009; Hubbert and Willis, 1957; Yew and Weng, 2014; Zoback, 2010).
Where fracture occurs, high pressure in the fracture and large plastic strain in the cement exist. The large plastic strain induced by fracture propagation may lead to material damage, such as creation of voids and microcracks in the cement (Gray et al., 2009), and consequently further damage of well integrity. Another observation is that the fluid-driven debonding fracture tends to develop vertically, rather than circumferentially around the casing. When an 90𝑜 initialcircumferential crack exists, for example, case Q4 in Table 5 and Fig.5, the fracture will propagate at the minimum horizontal stress (Y-axis) side because the resistance to fracture opening is the smallest. However, if the initial crack does not cover the full circumference of the interface, such as cases Q1, Q2, and Q3 in Table 5 and Fig.5, the fracture is more inclined to propagate in the vertical rather than in the circumferential direction, and results in a larger fracture length compared with case Q4. For cases Q1, Q2, and Q3, the fractures actually had some circumferential growth, but they did not extend all the way to the minimum horizontal stress (Y-axis).
Fig.3. Interface fracture shapes of two cases with uniform horizontal stress (SR1) and non-uniform horizontal stress (SR1.2). The pictures are top views of the cut sections of the casing/cement/interface system at 0.5 m above the casing shoe.
Fig.4. Interface fracture width around wellbore for the two cases in Fig.3. 0 degree and 90 degree correspond to the directions of the maximum and minimum horizontal stress, respectively.
4.2. Cement Interface Debonding for Different Initial Cracks Fig.5 shows the growth of the fracture, distribution of pressure in the fracture, and distribution of plastic strain in the cement by the end of the second step for the four cases with different initially existing cracks around the casing shoe as given in Table 5. The in-situ stress type is reported in Table 4 as SR1.2 and the material properties used are the base values defined in Section 3. The results show that the patterns of the developments of fracture, pressure, and plastic strain are related to each other.
Fig.5. Developments of fracture geometry, fracture pressure and cement plastic strain for different initial crack sizes. The pictures are front views of the one-quarter model from the angular bisector of the intersection angle of X- and Y-axis, with maximum horizontal stress in the X-axis direction and minimum horizontal stress in the Y-axis direction. The circumferential extents of the initial cracks for cases Q1 through Q4 are 30o, 45o, 60o and 90o, respectively. SDEG is a scalar stiffness degradation variable that indicates the state of damage in the cement interface from no damage (SDEG=0) to complete damage (SDEG=1.0). POR is fluid pressure in kPa in the debonding fracture. PEEQ is equivalent plastic strain in the cement.
4.3. Cement Interface Debonding with Different Cement and Formation Properties To investigate the influence of cement properties on the propagation of debonding fracture due to excessive pressure buildup around the casing shoe, three types of cement system with different stiffnesses, as given in Table 1, were considered. Type C3 corresponds to “stiffcement” with a high value of Young’s modulus and a high value of cohesive strength. To the contrary, type C1 is “compliant-cement” with lower values of Young’s modulus and cohesive strength. Properties of cement type C2 are in between those for stiff- and compliant-cements. The rest of the input variables are provided in Section 2.
input variables are based on the values of base cases provided in Section 2. Fig.7 illustrates the simulation results of the three cases. It shows a strong dependence of the development of fracture height on the stiffness of the formation rock. The higher stiffness (i.e. the higher the Young’s modulus and the higher the cohesive strength) of the formation, the larger the fracture length that will develop. This result can be explained with the same statement that was made above for the influence of cement stiffness on fracture growth.
Fig.6 shows the fracture growth and pressure distribution at the cement interface for the three different cement stiffnesses by the end of the second simulation step. The debonding fracture with stiff cement has a larger growth in height than the facture with soft cement. This is likely because stiffer cement restricts fracture opening in the radial direction of the wellbore. Thus, with the same volume of fluid leakage into the casing shoe, the stiffer cement shows a larger fracture length.
Fig.7. Development of fracture geometry and fracture pressure for different formation properties. The pictures are front views of the one-quarter model from the angular bisector of the intersection angle of X- and Y-axis, with maximum horizontal stress in the X-axis direction and minimum horizontal stress in the Y-axis direction. The properties for formation types F1 through F3 are given in Table 2.
5. CONCLUSIONS
Fig.6. Developments of fracture geometry and fracture pressure for different cement properties. The pictures are front views of the one-quarter model from the angular bisector of the intersection angle of X- and Y-axis, with maximum horizontal stress in the X-axis direction and minimum horizontal stress in the Y-axis direction. The properties for cement types C1 through C3 are given in Table 1.
Effects of formation properties on debonding fracture propagation were also investigated. Similar to the analysis of cement properties, three types of formation system with different stiffness as given in Table 2 were studied. Formation type F3 corresponds to “stiff-formation” with high values of Young’s modulus and cohesive strength, and formation type F1 is “compliant- formation” with lower Young’s modulus and cohesive strength. Properties of formation type F2 is in between of them. All the other
A 3D finite-element model was developed to simulate the cement debonding due to the propagation of a fluid-driven fracture along the cement-casing interface. The model successfully takes into account the main elements of well integrity analysis, such as interaction between different materials, poroelastic nature of the cement, plastic deformation of cement and formation, three dimensionality and anisotropy of in-situ stresses, propagation of debonding fracture, and flow of fracturing fluid. The model was used to quantify fracture geometry and fracture pressure distribution for different in-situ stresses, pre-exiting cracks at the casing shoe, and cement and formation properties. The results show that nonuniform debonding fractures occur under these conditions. With anisotropic horizontal stress, the resulting fracture has a smaller width in the direction of the maximum horizontal stress and a larger width in the direction of the minimum horizontal stress. With initial cracks in the cement interface, debonding fractures for a
vertical well tend to develop in axial direction, rather than circumferentially. The results also demonstrate that the debonding fracture propagation is highly influenced by the stiffness of cement and formation. The proposed model provides a useful tool for simulating the debonding at cement interface caused by leakage and pressure buildup around the casing shoe. In particular, it might be useful for evaluating the risk of cement sheath failure for pressure tests, perforation, hydraulic fracturing, and other types of fluid or gas injection operations during the production phase.
6. ONGOING AND FUTURE WORK The cement interface debonding model results reported herein are results from the project, “Cement Sheath and Casing Shoe Integrity”. Future work includes such subjects as debonding at the cement/formation interface; fracture and failure of cement; non-uniform cement properties; cement with gas or mud channels; thermal effects while cooling or heating the cement sheath; loading/unloading cycling during pressure tests and production operations; eccentric casing; and timedependent material models. Ongoing work in (Wider Windows JIP, 2016) is directed towards quantifying these casing/cement/formation interactions and the fluid leakage and pressure transmission integrity of them. Experimental results (cement slurry to full set) on several oilfield cements include shrinkage; mechanical behavior during loading and unloading processes; stress-strain paths; uniaxial, biaxial, and triaxial strengths; static and dynamic moduli available to the project from previous work (Life-Of-Well JIP, 2010).
ACKNOWLEDGMENT The authors wish to thank the Wider Windows Industrial Affiliate Program, the University of Texas at Austin, for financial and logistical support of this work. Project support and technical discussions with industrial colleagues from Wider Windows sponsors BHP Billiton, British Petroleum, Chevron, ConocoPhillips, Halliburton, Marathon, National Oilwell Varco, Occidental Oil and Gas, and Shell are gratefully acknowledged.
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