Study on sealing integrity of cement sheath in ultra deep well reservoir reconstruction

This article mainly studies the influence of high temperature, high pressure, and ultra‐deep well reservoir renovation construction on wellbore barriers, and explores the impact of reservoir renovation on cement sheath under high temperature and high‐pressure conditions. Combining the coupling effect of casing, cement, and formation rock, a three‐dimensional numerical model is established to analyze the stress changes and distribution of the cement sheath during the volume fracturing process. By establishing a numerical model for the analysis of the integrity of the wellbore during the fracturing process of the ultra‐deep well vertical section, the stress changes and distribution of the cement sheath during the fracturing process are analyzed. A numerical calculation model for crack propagation during perforation and cement sheath reservoir renovation is constructed, and the model results are verified through laboratory experiments and computed tomography scans. The shear failure of the cement sheath interface under different conditions such as different casing pressure, cement sheath thickness, elastic modulus, and Poisson's ratio is analyzed during the fracturing process. The research results can provide technical support for the integrity of the wellbore and the design of the well structure in similar ultra‐deep well development processes.


| INTRODUCTION
Cementing is a process of filling the annular space between the casing and the formation with cement to achieve a sealed wellbore. [1][2][3] It also provides support to the formation. After cementing, the integrity of the cement sheath is essential for the success of the well production. Therefore, studying the mechanical behavior of the cement sheath is crucial for the smooth completion of cementing and reservoir improvement projects. [4][5][6] Some researchers have conducted simulation studies on the effects of temperature and pressure changes on the cement sheath using corresponding simulation devices. The research method is to inject cement into the annular space between two layers of iron pipes and then apply hydraulic pressure or adjust the temperature inside the wellbore to change the stress state of the casing and the cement sheath. Finally, the changes in the bonding effect of the first and second interface of the cement sheath and the overall integrity of the cement sheath are studied. [7][8][9] Using experimental devices, more in-depth research has been conducted on the impact of changes in downhole construction conditions on the integrity of the cement sheath. They believe that the cement sheath should meet the short-term and long-term production tasks of the well and ensure its necessary strength requirements. [10][11][12][13][14] The convergence constraint method is applied to model the casing, cement sheath, and formation rocks as independent parts. The integrity of the cement sheath is determined by the intersection of the load-bearing characteristic curves of each part, avoiding the complicated problem of directly calculating the failure of the first and second interfaces. 15 Heathman found that changes in wellbore pressure can cause the cement sheath to fail. 16 Subsequently, they developed a personalized design method for cement slurry systems to address this issue and applied it to cementing a hightemperature and high-pressure gas well in East Texas. 17 Z. Shen and Beck developed a 3D finite element model considering five layers of strata to simulate the mechanical response of casing and cement sheath in nonuniform layers with interlayers. The radial stress of the composite is greatly affected by the elastic parameters of different layers, with maximum stress concentration appearing in sandstone. 18 The durability of cement sheath is described in relation to its mechanical properties to maintain system integrity during cyclic loading and to describe cement sheath damage during shale gas drilling, fracturing, and production processes. [19][20][21] Two cement slurry systems were used to cement a large number of shale gas wells, and relevant experiments were conducted in the laboratory. 22 A three-dimensional (3D) porous elastic model was established to simulate the lateral and vertical expansion of hydraulic fractures, focusing on the interface micro-annulus that may form during hydraulic fracturing construction. Field hydraulic fracturing construction data, rock physics logging, and radioactive tracer logging data were used to simulate most of the hydraulic fracturing engineering. 23,24 In response to the issue of the impact of bending stress caused by large inclination and irregular wellbore trajectory on casing strength, Paslay and Cernocky 25 found that bending stress has a significant impact on casing strength under conditions of high dogleg angle and long horizontal sections with irregular wellbore trajectory during on-site construction operations, and should be considered in casing strength design. 26 Wang pointed out that local bending, squeezing, and shear failure are the main forms of casing failure. 27 Yan et al. 2 pointed out that during the high-volume fracturing process, the temperature in the wellbore drops rapidly, causing the volume of the confined liquid in the cement sheath voids to shrink, resulting in a decrease in pressure in the cement sheath voids. Due to the extremely low permeability of tight shale reservoirs, the reservoir cannot replenish pressure in a short period of time, resulting in the casing being subjected to local nonuniform loads. During the fracturing process, the combined action of internal high pressure and local external loads may cause deformation of the downhole casing. Second, Jandhyala, Chiney, and others studied the effect of the increase in confined water flow pressure (APB 28 ) in the sealed casing cement sheath voids on the wellbore and believed that under extreme conditions, the APB effect might cause serious damage to the cement sheath and casing. 29,30 Dusseault et al., 31 Daneshy, 32 and others believe that during the fracturing operation, injection of fracturing fluid will cause cracks to appear between the casing and formation, resulting in a pseudo-openhole environment around the wellbore. The appearance of cracks will cause a decrease in the strength of the formation. 33 Jackson and Murphey conducted similar experimental tests but focused on the changes in the internal pressure of the casing. 34 Albawi 35 tested the bonding changes of the cement ring under cyclic temperature loads and found that the bonding failure of the cement ring mainly occurred during the initial temperature change. Boukhelifa et al. 36 studied the effects of temperature and pressure loads on the cement ring bonding and found that the bonding strength of the cement ring was most severely damaged when the temperature change range reached 56°C. Shadravan 37 found that the cement ring would reach its yield limit and fail after several cycles of loading. Philippacopoulos and Berndt, 38 Gray et al., 39 Bosma, 40 Takase, 41 and others established thermal-elastic models of the cement ring using finite element software and believed that temperature decrease would cause the interface of the cement ring to stretch and debond, while temperature increase would cause the shear failure of the cement ring. The wellbore is a combination of the casing cement ring (the first interface) and the cemented wellbore (the second interface). During the fracturing process of ultra-deep wells, cyclic pressure is prone to causing micro-annuli at the first interface, which in turn leads to pressure on the annular space. Currently, some studies use physical modeling methods to analyze the impact of cyclic pressure on the bonding surface of the cement ring and conclude that the cement ring at the first interface produces micro-annuli due to plastic deformation. However, physical modeling methods cannot fully simulate the actual downhole mechanical environment, and measuring on a micrometer scale is challenging. Therefore, it is necessary to establish corresponding numerical models and analyze the impact of reservoir transformation on the cement ring and its integrity under high-temperature and high-pressure conditions in ultra-deep wells during the fracturing process. This is of great significance.

| Geometric model
During the perforation completion operation, the perforation bullet is installed in the perforation gun body, and the shaped charge perforation bullet forms a shaped charge jet under the propulsion of the explosive after the perforation bullet is detonated, which penetrates the wellbore. This paper studies the effect of reservoir transformation on the cement after perforation, and the specific information about the cement perforation is as follows: the model of the perforation bullet is SDP41PYX25, the diameter of the shaped charge perforation bullet is 41 mm, the cone angle of the shaped charge casing is 46°, and the charge amount is 25 g, as shown in Figure 1.
In this paper, the 3D numerical model consists of casing, cement, and formation rock. The numerical model aims to analyze the stress changes and distribution of the cement sheath during the process of volume fracturing. First, the coupled calculation of the perforation section fracturing fluid flow field and temperature field is carried out using ANSYSFluent software to obtain the dynamic changes of the wellbore temperature field of the perforation section. Then, the thermomechanical coupling simulation calculation under fracturing conditions is performed using the commercial finite element software ABAQUS. The model adopts transient analysis and considers the comprehensive effect of temperature load and mechanical load, with the initial temperature of the model being the reservoir temperature. The outer surface of the formation is set as a stable heat source, and another temperature boundary is that the inner wall temperature of the casing is equal to the initial temperature of the fracturing fluid during the fracturing process. At the same time, the dynamic boundary of the fracturing fluid temperature changing with time is input into the numerical model. To simplify the calculation, the numerical model makes the following assumptions: 1. Assume that the casing is centered and the integrity of the cement sheath is good before fracturing. 2. The perforation channel is regarded as a hollow cylinder, and the variation of the pore diameter in the formation is ignored. 3. The casing steel, cement, and formation rock are all considered to be isotropic elastic materials. The Mohr-Coulomb criterion is used to judge the failure of the cement sheath, which can greatly reduce the calculation cost caused by considering plastic deformation. 4. The seepage process of the fracturing fluid along the borehole wall is ignored.
The geometric model of the perforation segment of the wellbore is established as shown in Figure 2, with an outer diameter of 139.7 mm and a thickness of 7 mm for the casing, and a thickness of 38 mm for the cement sheath. Due to considerations of grid size and computation time, the size of the formation is set as a cylinder with a diameter of Φ2 × 0.4 m. Since the geometric shape of the model is somewhat complex, tetrahedral grids are used, and the mesh is refined around the borehole. The material parameters for the fracturing fluid, casing, cement, and formation rock are listed in Table 1 and formation are obtained from the literature. Based on the established logging data, the formation confining pressure is set to 146.5 MPa.
As we focus on the failure of the cement sheath during the fracturing process in this paper, it is crucial to select an appropriate failure criterion for the cement sheath. Numerous studies have shown that the failure of the cement sheath is mainly due to tensile failure caused by circumferential stress exceeding the tensile strength and shear failure caused by cement sheath yielding. Therefore, we adopt the Mohr-Coulomb failure criterion and the maximum tensile stress criterion as the failure criteria for the downhole cement sheath. To describe the shear failure of the cement sheath conveniently, we define the shear failure coefficient η with its expression given in Equation (2-1). When η > 1, it is considered that the cement sheath will undergo shear failure. According to the experimental results of Teodoriu, the cohesion τ 0 and internal friction angle ψ of the cement stone are 18.5 MPa and 23.6°, respectively.
(tan + 1) + tan 2 . (1) The equation shows that τ 0 is the cohesive strength of the cement stone in MPa, ψ is the internal friction angle in degrees, and σ 1 and σ 3 are the maximum and minimum principal stresses of the cement stone, respectively.
Hydraulic fracturing is a construction process involving the coupling of multiple fields, such as temperature, seepage, and stress fields. When the fracturing fluid reaches the perforated section of the wellbore, it enters the formation cracks through the perforation holes. At the same time, the heat exchange between the formation rock and fluid and the wellbore continues. To solve the transient stress field in the cement sheath, the heat transfer process between the wellbore and formation rock is calculated using the ANSYSFLUENT18.1 F I G U R E 2 Geometric model of perforated wellbore. Thermal expansion coefficient (10 −6°C−1 ) 13 11 10.5 -software to obtain the temperature field changes inside the wellbore and formation during the process. Then, the temperature field data is imported into ABAQUS2018, and the transient temperature field is used as the boundary condition of the model to calculate the transient stress changes inside the cement sheath during the process. The calculation process of the model is shown in Figure 3.
Using the field deep well test fracturing curve shown in Figure 4, the pressure change curve inside the casing is used as the pressure boundary condition of the casing wall. As the flow rate of the fracturing fluid is transient, the inlet temperature of the fracturing fluid in the perforated section of the wellbore needs to be calculated separately and used as the inlet temperature of the fracturing fluid in the perforated section of the wellbore. In addition, the end faces of the casing, cement sheath, and formation rock and the outer wall surface of the formation rock are all fixed displacement constraints. Furthermore, the outer wall surface of the formation rock is considered a stable heat source, and the wall temperature of 128°C is used as one of the boundary conditions for heat transfer. The temperature of the inner wall of the casing and the pore wall obtained from the coupled calculation is used as another boundary condition for heat transfer.

| Equation of control
During the fracturing process, the Reynolds number of the fracturing fluid flowing inside the wellbore is greater than 8 × 10 4 , indicating that the fluid is in a turbulent state. In this study, the RNG k-ε turbulence model was chosen to simulate the flow of the fracturing fluid. The RNG k-ε turbulence model is an improved version of the standard k-ε model that can solve for flows with high strain rates. Additionally, the RNG theory employs analytical formulas to calculate effective viscosity, enabling the RNG k-ε turbulence model to accurately simulate high Reynolds number flows.
The continuity equation, momentum equation, and energy equation for the flow of the fracturing fluid inside the wellbore are as follows: F I G U R E 3 Calculating procedure of the numerical model.
F I G U R E 4 Dynamic input parameter variation in the numerical model.
The energy equation of heat transfer in solids is In this equation, ρ is the fluid density in kg m −3 , u i and u j are the fluid velocities in m s −1 , t is the flow time in s, μ is the fluid viscosity in Pa s, Pr is the Prandtl number, dimensionless, ST is the dissipation energy due to viscous action in J, and k is the thermal conductivity of the solid in W (m°C) −1 .
The RNG k-ε turbulence model is based on the Reynolds-averaged Navier-Stokes equations and energy equation. The Reynolds-averaged momentum equation and the energy equation in the fluid domain can be respectively expressed as where the turbulent stress ρu u − ′ ′ i j and turbulent heat flux To calculate the turbulent kinetic energy k and the turbulent kinetic energy dissipation rate ε, the transport equation is solved. The transport equation for the RNGk-ε model is modified based on the standard k-ε model.
where S k is the user-defined turbulence dynamics source term energy, G k is the additional term of turbulent kinetic energy caused by the average velocity gradient, whose expression as The expressions of transient turbulent viscosity and effective viscosity are respectively In addition, C* ε 2 is a constant coefficient C ε 2 revised, the expression as where η = S k /ε is the ratio of user-defined turbulent flow energy term to turbulent kinetic energy dissipation rate, dimensionless. In this chapter, the values of constant coefficients in the RNGk-ε model are as follows: C μ = 0.085, C 1ε = 0.085, C 2ε = 1.68, η 0 = 4.38, β = 0.012, α k = α ε = 1.393. In addition, the near-wall flow is processed using the standard wall function provided by ANSYSFLUENT. The standard wall function uses the semi-empirical method to calculate the viscous influence region between the wall and the fully developed turbulent region. y* is an important dimensionless near-wall distance parameter, which is defined as where k P is the turbulent kinetic energy at point P near the wall, J; y P is the distance between the near wall point P and the wall surface, m; μ is the dynamic viscosity of the fluid, Pa s. Another dimensionless near-wall parameter T* is used to calculate the temperature in the near-wall region, and its expression is where κ was von Karman's constant, κ = 0.4187; E is the empirical constant, E = 9.793; Pr is the molecular Prandtl number; Pr t is the turbulent Prandt number. The linear relationship between formation temperature and depth is as follows: where T z is the formation temperature at a certain depth,°C ; T b is land surface temperature,°C; α is the geothermal gradient,°C m −1 ; z represents reservoir depth, m; b is the base depth, m.
The formation is composed of multi-layer casing, cement sheath, and formation. Its heat transfer model can be seen as the heat transfer of multiple cylinder walls in the radial and axial directions. Its mathematical model is where T fk is the temperature of casing/cement sheath/ rock,°C; ρ fk is the density of casing/cement sheath/ rock, kg m −3 ; c fk is the specific heat capacity of casing/cement sheath/rock, J (kg°C) −1 ; λ fk is the thermal conductivity of casing/cement sheath/rock, W (m°C) −1 ; k Depending on the size of casing layer, generally 4 ≤ k ≤ 11.

| APPLICATION AND CASE STUDY
By using the 3D numerical model and control equations established earlier, the stress changes and distribution patterns of the cement ring during the volume fracturing process were analyzed. A numerical calculation model for crack propagation was constructed during the perforated cement ring reservoir transformation process, and the model results were validated using laboratory experiments and computed tomography (CT) scans. The shear failure of the cementing interface under different conditions, such as casing pressure, cement ring thickness, elastic modulus, and Poisson's ratio, was analyzed during the fracturing process.
3.1 | Analysis of influencing factors of casing pressure Figure 5 shows the variation curves of the shear failure coefficients of the first and second interfaces of the cement ring under different casing pressures during the initial stage of fracturing. The calculation results indicate that when the peak casing pressure decreases from 90 MPa to 50 MPa, the shear failure coefficient of the first interface of the cement ring also decreases, but the numerical value is still greater than 1, indicating that reducing the casing pressure cannot avoid shear failure of the first interface of the cement ring. When the peak casing pressure decreases from 90 to 50 MPa, the shear failure coefficient of the second interface of the cement ring also decreases, and when the casing pressure drops to 70 MPa, the numerical value of the shear failure coefficient is less than 1, indicating that reducing the casing pressure can effectively avoid the shear failure of the second interface of the cement ring. However, since the pump pressure on-site often increases with the increase in displacement, the controllable range of casing pressure needs to consider the requirements of formation fracturing, and comprehensive consideration is required in the construction design.  Figure 6 shows the variation of the shear failure coefficient of the first and second interfaces of the cement ring under different cement elastic moduli. The calculation results show that as the cement elastic modulus decreases from 11 to 5 GPa, the shear failure coefficient of the first interface of the cement ring decreases rapidly, and the shear failure coefficient on the second interface also decreases. When the cement elastic modulus decreases to 7 GPa, the shear failure coefficient of the non-pore part of the second interface of the cement ring drops to below 1. It can be seen that reducing the elastic modulus of the cement stone in fracturing construction can to some extent reduce the risk of shear failure of the cement ring. Based on the above analysis, it is necessary to carry out research on optimizing the cement slurry formula on-site and select low-modulus cement for cementing operations. However, due to the strong discreteness of the Poisson's ratio of the cement, it is difficult to stably control it on-site. Therefore, it is recommended to adjust the cement Poisson's ratio in conjunction with the cement elastic modulus, which can be more easily controlled on-site. Figure 8 shows the change in the shear failure coefficient of cement sheath interface 1 and interface 2 under different cement sheath thicknesses. The calculation results show that as the cement sheath thickness increases, the shear failure coefficient of the cement sheath slightly decreases, but the decrease is small and not enough to prevent shear failure of the cement sheath. This indicates that the influence of the thickness of the cement sheath on the shear failure coefficient is far less than that of its own mechanical parameters. Therefore, regarding the necessity of perforation expansion for the current perforated interval, the results show that even after the perforation expansion, it is still difficult to avoid shear failure. Therefore, how to suppress the expansion of cement cracks in the later stage is a problem that needs to be considered for deep wells in the southern margin area.  Figure 9 shows the change in circumferential stress of the cement sheath under the temperature field at the time of 20 min after the start of fracturing. The calculation results show that the circumferential stress of the cement sheath is always in a compressive state during the fracturing process and forms a spindle-shaped compressive stress zone concentrated at the pore channel. To further illustrate the stress change process of the cement sheath during fracturing, the distribution curves of circumferential stress on interface 1 and interface 2 within the central cross-section of the pore were plotted as shown in Figure 10. As shown in Figure 10, both interface 1 and interface 2 of the cement sheath are under compressive stress at non-pore positions during the fracturing process when pump pressure is applied at the wellhead, and the compressive stress on interface 2 is higher than that on interface 1. Therefore, the cement sheath will not experience tensile failure at nonperforated positions. However, besides the tension that leads to tensile failure, the extrusion of the earth's stress and the pressure in the wellbore can also cause shear failure. To this end, the distribution curves of shear failure coefficients on interface 1 and interface 2 within the central cross-section of the pore were plotted as shown in Figure 12. As shown in Figure 12, during the fracturing process, shear failure will occur at the pore positions of both interface 1 and interface 2 of the cement sheath.

| THE VALIDITY OF THE MODEL
The shear failure coefficient is calculated based on the maximum/minimum principal stress in Figure 11. The variation of the shear failure coefficient at the measuring points of the first and second interfaces at 10°, 20°, and 40°p ositions is selected with the wellbore central axis as the center. It can be seen from Figure 12 that the cement sheath at the 10°position undergoes shear failure, while the cement sheath at the 20°and 40°positions remains sealed and intact during the fracturing process. To show the possible area of shear failure of the cement sheath, the distribution curve of the shear failure coefficient at different positions of the cement sheath in the circumferential direction is plotted at the beginning of fracturing (t = 20 min) in Figure 13. It can F I G U R E 9 Tangential stress of the perforated cement sheath at t = 20 min. be seen from Figure 13 that the shear failure coefficient on the first and second interfaces of the cement sheath is only greater than 1 near the orifice, indicating that the orifice of the cement sheath is a dangerous area for the wellbore to lose the seal. The shear failure coefficient at other positions is less than 1 and is safe during the fracturing process. fracturing process, while both tensile and shear failures exist at the wellbore. 2. Microcracks around the borehole will not propagate along the wellbore axis, but will rapidly turn and propagate radially along the cement sheath section to stop at the second interface. The radial crack propagation process of the cement sheath mainly occurs in the early stage of fracturing, and the pressure difference between the crack mouth and the crack tip gradually decreases with the progress of fracturing. 3. A numerical calculation model for crack propagation during the perforation-cement sheath reservoir transformation process has been constructed, and the model results have been validated by laboratory experiments and CT scans. 4. The shear failure at the first and second interfaces of the wellbore under different conditions such as casing internal pressure, cement sheath thickness, elastic modulus, and Poisson's ratio during the fracturing process has been studied through simulation results.