Analysis of Cement Sheath–Rock Damage Mechanism—A Case Study on Water Injection Wells

Abstract

In the field of water injection wells within oilfields, comprehending the intricate mechanics of water channeling and the resulting rock damage on the external cemented surface holds paramount significance for the efficient management of reservoirs. This paper presents a comprehensive study aimed at illuminating the complex nature of rock damage on the external cemented surface of casings and deciphering the underlying mechanisms that underpin water channeling occurrences. To this end, a robust constitutive model is established and refined to capture the multifaceted interactions inherent in rock damage on the cemented surface. This model introduces a modified bonding force approach to enhance shear stress precision and thoughtfully accounts for the profound effects of elastic–plastic behavior, cracking damage, and elastic-cracking coupling damage on damage progression. Subsequently, the refined model is employed to investigate rock damage on the external cemented surface of water injection wells, encompassing variations in confining pressure, rock width on the cemented surface, and the ratio of Young’s modulus between the cement sheath and the rock. The research findings emphasize the interplay between cracking and elastic damage as the catalyst for rock damage on the cemented surface. Impressively, the accuracy of the refined constitutive model for the cemented surface has advanced by over 5% compared to prior studies. The manipulation of confining pressure and the Young’s modulus ratio enhances peak fracture water pressure, signifying substantive strides in comprehending damage propagation mechanics. Furthermore, the study discerns the negligible influence of rock width on the cemented surface regarding damage patterns. These findings have important implications for the effective management of water injection wells, providing insights for the restoration of water channeling wells and proactive measures against water channeling phenomena. They also contribute to the refinement of well cementing practices and the proficient management of water channeling and water flooding in oilfields. The research findings have profound implications for the domain of water injection wells, offering novel insights into the restoration of water channeling wells and the implementation of preemptive measures against water channeling phenomena. These findings hold the potential to guide the refinement of well cementing practices and the adept management of water channeling and water flooding wells within the studied oilfield.

1. Introduction

In the field of water injection in oilfield development, water breakthrough and casing failure are common challenges. These issues have various consequences, including reduced water injection efficiency and potential contamination of surface water due to suboptimal cementing quality. The aforementioned issue presents inherent safety and environmental hazards within oilfields. It is noteworthy that a substantial proportion (approximately 20%) of well shutdowns and incidents in the Y oilfield are attributed to water breakthroughs, impeding the advancement of water injection development. Academic research on water–oil well communication has reached a consensus that the primary factor contributing to water intrusion is composite rock damage involving the casing cement sheath and the surrounding rock [1]. Contemporary research on water breakthrough beyond the casing of water injection wells primarily concentrates on two fundamental factors: the occurrence of cracking damage on the bonded surface of the rock–cement sheath composite material and the impairment to the cement sheath itself.

Research on the damage of cement–rock interfaces encompasses a wide range of aspects, from the development of techniques [2,3] to the impacts of hydration reactions [4]. It emphasizes the role they play in reducing the strength of composite rock bonding surfaces. Subsequently, stress-induced cracking occurs. Although cracking damage can lead to water infiltration, the causes of such damage are complex. In fact, the damage incurred on composite rocks outside the casing of water injection wells is not limited to cracking; it also includes elastic damage. This elastic damage disrupts the integrity of the composite rock, especially when subjected to axial stresses induced by water pressure.

Studies on cement–rock interface damage have focused on investigating the influence of factors such as compressive strength [5], Young’s modulus [6], friction angle, and cohesion [7,8] on the instability and damage of cement sheaths. Some researchers have also noted the impact of filter cake on shear strength [9,10], leading to further research on the primary causes of cement–rock interface cracking under tension [11]. Andjelkovic et al. [12] have drawn attention to the influence of adhesion forces between rock and cement sheaths, while Kronis et al. [13] studied the debonding behavior of concrete–rock samples. These studies have contributed to understanding the characteristics of damage development in cement sheaths and the interaction between rock and cement sheaths. However, there is still a need for comprehensive research and analysis, specifically focusing on the characteristics of cement–rock interface damage in water injection wells.

Research on the mechanisms of water breakthrough in water injection wells can be categorized into two main aspects: mechanisms related to the injected water and mechanisms occurring outside the casing. While scholars such as Wei et al. [14] and You et al. [15] have conducted extensive studies on the water flooding mechanism, particularly during the injection process, their focus has mainly revolved around the formation of water channels between oil and water zones. It is important to note that research on the mechanisms occurring outside the casing is multifaceted, with a primary emphasis on two key areas.

One aspect involves analyzing the damage to the cement sheath. Bu et al. [16] have proposed that cement with a high elastic modulus can generate significant tensile stress at the cement–casing interface, leading to integrity damage outside the casing. In contrast, Liu et al. [17] attribute the damage to the cement sheath outside the gas well casing to the differential effect of the elastic modulus between the cement sheath and the formation rock on radial stress. They believe that an increase in the elastic modulus of the cement sheath will significantly elevate the radial stress at the interface.

Regarding damage to the cement–rock interface, notable scholars such as Mouzannar et al. [18], Tian et al. [19], and others have designed concrete–rock models to analyze shear-induced interface damage through controlled laboratory experiments, thus revealing the framework of damage models. Despite extensive research on water injection, water breakthrough, casing damage, and concrete–rock models, there are still limitations in directly applying these findings to understand water breakthrough outside the casing of water injection wells.

Cheng et al. [20] and Wu et al. [21] have explored the mechanisms of cement sheath damage by examining the parameters relating to cement slurry performance. In the field of numerical simulation, Khodami et al. [22] implemented a three-dimensional finite element model to analyze well integrity, investigating the plastic deformation of wellbore cement and the utilization of the von Mises yield criterion under different stress scenarios. The study also examined the mechanical properties of the formation. Zhou and Bi [23] (2018) developed a hydro-mechanical coupling dynamic model (PD) to derive the mechanical behavior of rock damage under coupled effects. Gu et al. [24] utilized the ABAQUS software to perform three-dimensional simulation analysis, incorporating geological mechanics modeling data and taking into account the wells’ environmental conditions, while examining the effect of casing spacing on cement integrity through sensitivity analysis and parameter testing.

To comprehend the current production status of water injection wells in area Y, a geometric model of the cement sheath–rock bonding surface is established. An improved bonding force formula is utilized to enhance the accuracy of the shear stress model, thereby revealing the damage characteristics supporting these interfaces. The damage process of the rock at the bonding surface encompasses shear cracking damage and elastoplastic damage, where the elastoplastic damage model adopts a statistical damage model, and the elemental strength adheres to the Mohr–Coulomb criterion [17]. Drawing upon this foundation, a coupled damage model has been devised to accurately characterize the attributes of the rock outside the casing in water injection wells. The evolution process of damage in the cemented rock under fluid–solid coupling is studied through numerical simulation. This study provides a theoretical roadmap to enhance understanding and develop prevention strategies for water breakthrough in water injection wells in area Y.

2. Cement–Rock Bond Interface Damage Model

2.1. Stress Analysis of the Bond Interface Rocks

The cement–rock bond interface can be effectively represented as a transitional layer between the rock and cement sheath. To explore the damage mechanism of the bonded interface rocks, a simplified model was utilized. In this model, the rock, cement sheath, and bond interface rock portion were considered as homogeneous media with uniform properties, as depicted in Figure 1. Additionally, it is assumed that each medium satisfies the Mohr–Coulomb strength criterion and is not influenced by the surface shape of the bond interface rocks.

When the stress on the interface between the cement and rock shifts, it not only affects the interface strength but also causes modifications to the bonding strength between the cement–rock interface and the cement sheath. The stress and strain formulas for the cement–rock interface can be represented as (1) and (2):

$$\left\{\mathsf{\sigma }\right\}={\left[{\mathsf{\sigma }}_{\mathrm{x}},{\mathsf{\sigma }}_{\mathrm{y}},\mathsf{\tau }\right]}^{\mathrm{T}}$$

(1)

$$\left\{\epsilon \right\}={\left[{\epsilon }_x,{\epsilon }_y,\gamma \right]}^{\mathrm{T}}$$

(2)

where σ_x and σ_y represent the stress components in the x and y directions, respectively, while τ denotes the shear stress component. The variables ε_x and ε_y denote the strain components in the x and y directions, respectively, and γ represents the shear strain component.

When damage occurs along the cement–rock interface, the total shear stress on the interface can be expressed as the sum of the shear stress and bond strength, as indicated by Equation (3):

$$\mathsf{\tau }={\mathsf{\tau }}_{\mathrm{c}}+{\mathsf{\tau }}_{\mathrm{f}}$$

(3)

$${\mathsf{\tau }}_{\mathrm{c}}={\mathsf{\sigma }}_{\mathrm{n}}\tan \mathsf{\theta }+{\mathrm{C}}_{\mathrm{j}}$$

(4)

where ${\mathsf{\tau }}_{\mathrm{c}}$ represents the shear stress on the bond interface rocks,${\mathsf{\tau }}_{\mathrm{f}}$ represents the bonding force on the bond interface rocks, ${\mathsf{\sigma }}_{\mathrm{n}}$ represents the normal stress on the bond interface, $\mathsf{\theta }$ represents the internal friction angle of the bond interface rocks, and ${\mathrm{C}}_{\mathrm{j}}$ represents the cohesion of the bond interface rocks.

Equation (5), proposed in previous studies, establishes a relationship between shear strength and microhardness based on strain gradient plasticity [25]. However, this formula does not take into account the bonding quality between concrete and rock or the adhesive forces present at the interface.

$${\mathsf{\tau }}_{\mathrm{f}}=\frac{\sqrt{3}{\displaystyle \iint }\mathrm{hvds}}{9\mathrm{A}}$$

(5)

where hv represents the failure strength of the bonding points, A represents the projected surface area covered by the rock–cement sheath combination on the plane, and s represents the contact area between the rock and cement.

To accurately describe the influence of bond strength, the cement–rock interface is divided into Ni individual cells with N bonding points. The bond strength between these locations signifies the strength at which the cement–rock interface fails. When the cement–rock interface undergoes shear and experiences cracking, the bond strength is influenced by the diffusion and solidification processes occurring on the surfaces of both the rock and the cement sheath. Hence, the formula for bond strength can be expressed as Equation (6).

$${\mathsf{\tau }}_{\mathrm{f}}=\frac{\mathrm{N}{{\displaystyle \int }}_0^{\mathrm{n}}(\mathrm{hv}+{\mathsf{\tau }}_{\mathrm{cf}})\mathrm{ds}}{{\mathrm{N}}_{\mathrm{i}}\mathrm{B}}\left(1+\mathrm{k}1/\mathrm{k}2\right)$$

(6)

where k1 and k2 are the normal permeabilities of the rock and the cement–rock interface, and B is an experimental coefficient. ${\mathsf{\tau }}_{\mathrm{cf}}$ represents the adhesive force on the rock surface, as represented by Equation (7):

$${\mathsf{\tau }}_{\mathrm{cf}}=\mathrm{E}\Delta \mathsf{\epsilon }+{\mathsf{\mu }\mathsf{\sigma }}_3+{\mathsf{\mu }\mathsf{\sigma }}_2$$

(7)

where $\Delta \mathsf{\epsilon }$ represents the disparity in strain between the rock and cement sheath, $\mathsf{\mu }$ is the Poisson’s ratio, and ${\mathsf{\sigma }}_2$ and ${\mathsf{\sigma }}_3$ are the second and third principal stresses.

The two-dimensional constitutive equation for the bonded rock at the bond interface, as represented by Equation (8):

$$\left\{\begin{array}{c}{\mathsf{\epsilon }}_{\mathrm{x}}\\ {\mathsf{\epsilon }}_{\mathrm{y}}\\ \mathsf{\gamma }\end{array}\right\}=\frac{1}{\mathrm{E}}\left[\begin{array}{ccc}1& -\mathsf{\mu }& 0\\ -\mathsf{\mu }& 1& 0\\ 0& 0& 1/\mathrm{G}\end{array}\right]\left\{\begin{array}{c}{\mathsf{\sigma }}_{\mathrm{x}}\\ {\mathsf{\sigma }}_{\mathrm{y}}\\ \mathsf{\tau }\end{array}\right\}$$

(8)

Assuming that the equivalent thickness of rock and concrete in the interfacial rock is the same, G can be expressed as Equation (9) [26]:

$$\mathrm{G}=\frac{1}{2\left(2+\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{s}}\right)}$$

(9)

where E represents the Young’s modulus of the rock being bonded at the interface, μ denotes the Poisson’s ratio of the rock being bonded at the interface, and μ_s stands for the Poisson’s ratio of the rock itself.

2.2. Constitutive Model Considering Damage Parameters for Bonded Rock at the Bond Interface

During the actual oilfield development process, when the rock material on the bonding surface undergoes damage, the trajectory of damage evolution gradually expands along the interface. This progressive process ultimately leads to the occurrence of the cement sheath’s failure, triggering a chain reaction that results in casing damage, water channeling, and other well-related failures. It is important to note that throughout the entire damage process, the bonded surface rock is subjected to both tensile and shear stress-induced damage. In the bonded surface rock and reservoir rock, when the bonded surface rock encounters peak shear or tensile stress, the damage initiation occurs.

The damage to the bonded surface rock can be categorized into two distinct aspects. Firstly, the damage caused by normal stress primarily relates to the tensile strength of the adhered rock at the bonding interface. Secondly, another small plane emerges along the tangential direction of the bonding surface. This component encompasses the collective impact of cleavage damage caused by the bonded surface, interwoven with the combined effect of shear stress.

Taking into account the damage effect during the deformation of the bond interface, the stress–strain equation with damage parameters can be expressed as Equation (10):

$${{\mathsf{\sigma }}_{\mathrm{ij}}}^{\prime }=\left(1-\mathrm{D}\right){\mathsf{\sigma }}_{\mathrm{ij}}={\mathrm{C}}_{\mathrm{ij}}:{\mathsf{\epsilon }}_{\mathrm{ij}}$$

(10)

The degradation constitutive relationship matrix of bonded rock at the bond interface, considering damage parameters can be expressed as Equation (11) [27]:

$${\mathrm{C}}_{\mathrm{i}}{}_{\mathrm{j}}=\frac{1}{\mathrm{E}}\left[\begin{array}{ccc}{\mathrm{d}}_1& -{\mathrm{d}}_2\mathsf{\mu }& 0\\ -{\mathrm{d}}_2\mathsf{\mu }& {\mathrm{d}}_1& 0\\ 0& 0& {\mathrm{d}}_2/\mathrm{G}\end{array}\right]$$

(11)

where d₁ = (1 − D1) and d₂ = (1 − D2). D1 represents the damage value in the normal direction, while D2 represents the damage value in the tangential direction on the bonded rock at the bond interface. The shear cracking damage D21 of the bond interface can be expressed as Equation (12):

$$\mathrm{D}21=1-\left(\frac{{\mathsf{\delta }}_{\mathrm{f}}}{\mathsf{\delta }}\right)\left[1-\frac{1-\exp \left(-\mathsf{\alpha }1\left(\frac{\mathsf{\delta }-{\mathsf{\delta }}_{\mathrm{f}}}{{\mathsf{\delta }}_{\mathrm{c}}-{\mathsf{\delta }}_{\mathrm{f}}}\right)\right)}{1-\exp \left(-\mathsf{\alpha }1\right)}\right]$$

(12)

In the equation, The shear displacement corresponding to the peak shear stress can be denoted as ${\mathsf{\delta }}_{\mathrm{f}}$, the displacement at the point of residual shear stress can be represented as ${\mathsf{\delta }}_{\mathrm{c}}$, and a1 represents a material property, which is determined to be 5 based on the experimental study in reference [19]. The damage caused by the bonding force can be expressed using statistical damage parameters as Equation (13):

$$\mathrm{D}22=1-\exp \left[-{\left(\frac{\mathrm{F}}{\mathrm{F}0}\right)}^{\mathrm{m}}\right]$$

(13)

where m and F0, respectively, represent the influence of the Weibull distribution function on the shape and size of rock microelements, and F represents the distribution variable of microelement strength. By coupling Equations (12) and (13), we can obtain Equation (14):

D2 = D21 + D22 − D21 × D22

(14)

According to porous media theory, the constitutive relationship of rock at the bonded interface follows the generalized Hooke’s law. Taking into account the displacement conditions under loading, the coupled fluid–solid Navier equation can be expressed as Equation (15):

$${\mathrm{Gu}}_{\mathrm{i},\mathrm{j}}+\frac{\mathrm{G}}{1-2\mathsf{\mu }}{\mathrm{u}}_{\mathrm{j},\mathrm{i}}-\mathsf{\alpha }\mathrm{P}+{\mathrm{F}}_{\mathrm{i}}=0$$

(15)

where ${\mathrm{u}}_{\mathrm{i},\mathrm{j}}$ denotes the partial derivative of the velocity component u_i with respect to the spatial coordinate x_j, ${\mathrm{u}}_{\mathrm{j},\mathrm{i}}$ denotes the partial derivative of the velocity component u_j with respect to the spatial coordinate x_i, μ represents the Poisson’s ratio, ${\mathrm{F}}_{\mathrm{i}}$ denotes the volume force per unit volume in the i direction (where i is x, y, or z), P represents the fluid pressure, and $\mathsf{\alpha }$ denotes the Biot coefficient.

2.3. Darcy’s Seepage Equation

The Darcy velocity represents the relative velocity between the fluid and the rock skeleton particles. In the casing water channeling problem, only single-phase fluid is considered. According to Darcy’s law, its expression can be derived as Equation (16):

$$\mathrm{v}=\frac{-\mathrm{K}}{\mathsf{\varphi }\mathsf{\vartheta }}\left(\nabla {\mathrm{P}}_{\mathrm{w}}+{\mathsf{\rho }}_{\mathrm{w}}\mathrm{g}\right)$$

(16)

where the permeability of the porous medium is denoted as K, the porosity is represented by $\mathsf{\varphi }$, the viscosity of the fluid is ϑ, the fluid pressure is P_w, and the fluid density is ρ_w.

The continuity equation for single-phase fluid is used to describe the water channeling phenomenon outside the casing in wells and can be expressed as Equation (17):

$$\frac{\partial \left({\mathsf{\rho }}_{\mathrm{w}}\mathsf{\Phi }\right)}{\partial \mathrm{t}}+\nabla \left(-\frac{{\mathsf{\rho }}_{\mathrm{w}}}{{\vartheta }_{\mathrm{w}}}\nabla \mathrm{p}\right)+{\mathsf{\rho }}_{\mathrm{w}}\mathsf{\alpha }\frac{\partial {\mathsf{\epsilon }}_{\mathrm{v}}}{\partial \mathrm{t}}={\mathrm{Q}}_{\mathrm{m}}$$

(17)

$$\frac{\partial \left({\mathsf{\rho }}_{\mathrm{w}}\mathsf{\Phi }\right)}{\partial \mathrm{t}}={\mathsf{\rho }}_{\mathrm{w}}\mathrm{S}\frac{\partial {\mathrm{P}}_{\mathrm{w}}}{\partial \mathrm{t}}$$

(18)

where ε_v is the volumetric strain, the variable t represents time, u represents fluid velocity, Q_m represents the mass source term, and S represents the storage coefficient.

The relationship between the evolution of porosity in rock bonding interfaces and damage progression during stress–strain changes [28].

$$\mathsf{\varphi }=\left({\mathsf{\varphi }}_0-{\mathsf{\varphi }}_{\mathrm{R}}\right)\exp \left({\mathsf{\alpha }}_{\mathrm{t}}{\mathsf{\sigma }}_{\mathrm{m}}\right)+{\mathsf{\varphi }}_{\mathrm{R}}$$

(19)

In the equation, initial porosity is denoted as ${\mathsf{\varphi }}_0$, porosity after damage is represented by ${\mathsf{\varphi }}_{\mathrm{R}}$, the stress sensitivity coefficient is denoted as α_t with a value of 5.0 × 10^−8/Pa, and σ_m is the effective mean stress.

$${\mathsf{\sigma }}_{\mathrm{m}}=\frac{{\sigma }_1+{\sigma }_2+{\sigma }_3}{3}$$

(20)

The evolution equation of permeability can be obtained through the porosity solution formula [21]:

$$\mathrm{k}={\mathrm{k}}_0{\left({\mathsf{\varphi }}_0/{\mathsf{\varphi }}_{\mathrm{R}}\right)}^3\exp \left({\mathsf{\alpha }}_{\mathrm{t}}\mathrm{D}\right)$$

(21)

In the equation, k₀ is the initial permeability and D is the damage parameter of the rock bonding interface. The damage along the tangent direction of the bonding interface crack is denoted as D, according to the rock bonding interface damage law, and the permeability in the tangent and normal directions of the rock bonding interface is represented by parameters k₁ and k₂, respectively. Assuming the principal stress direction and the x-axis form an angle β, Equation (22) provides a mathematical expression for calculating the permeability k of the rock bonding interface [29]:

$$\mathrm{k}=\left[\begin{array}{ccc}{\mathrm{k}}_1{\cos }^2\mathsf{\beta }+{\mathrm{k}}_2{\sin }^2\mathsf{\beta }& \left({\mathrm{k}}_1-{\mathrm{k}}_2\right)\cos \mathsf{\beta }\sin \mathsf{\beta }& 0\\ \left({\mathrm{k}}_1-{\mathrm{k}}_2\right)\cos \mathsf{\beta }\sin \mathsf{\beta }& {\mathrm{k}}_1{\cos }^2\mathsf{\beta }+{\mathrm{k}}_2{\sin }^2\mathsf{\beta }& 0\\ 0& 0& {\mathrm{k}}_2\end{array}\right]$$

(22)

where: ${\mathrm{k}}_1={\mathrm{k}}_0{\left({\mathsf{\varphi }}_0/{\mathsf{\varphi }}_{\mathrm{R}}\right)}^3\exp \left({\mathsf{\alpha }}_{\mathrm{t}}{\mathrm{D}}_1\right),{\mathrm{k}}_2={\mathrm{k}}_0{\left({\mathsf{\varphi }}_0/{\mathsf{\varphi }}_{\mathrm{R}}\right)}^3\exp \left({\mathsf{\alpha }}_{\mathrm{t}}\mathrm{D}\right)$.

3. Validation of the Damage Model

The direct shear tests mentioned in the literature were conducted specifically on the RMT-150 system, which is a well-established and widely used apparatus in the field, as shown in Figure 2. The maximum normal force and shear force were 1000 kN and 500 kN, respectively. In compliance with the methodologies prescribed by the International Society for Rock Mechanics (ISRM), this machine possesses the capability to perform direct shear tests. It operates by applying shear stress at a controlled rate of 0.005 mm/s, facilitating a clear observation of the post-peak behavior exhibited by the cohesive interface.

COMSOL Multiphysics is a powerful finite element analysis software that can be used for the simulation and solving of various physical phenomena. It features high flexibility, user-friendliness, and high scalability, making it an important tool in scientific research and engineering design. In this study, COMSOL software was utilized, and a newly developed constitutive model was employed for numerical simulations. The introduced novel damage function D2 was utilized to investigate the damage evolution behavior of interface rock in the study.

To ascertain the efficacy of the damage model, a comprehensive evaluation was carried out by comparing the numerical simulation results with experimental findings. The size of the model was set at 150 mm × 150 mm, with the bottom fixed and the top boundary subjected to a pressure of 2 MPa. The model underwent a shearing displacement rate of 0.005 mm/s along the cement–rock interface, with a total of 2642 grid nodes. The dimensions, loading speed, and applied pressure in the numerical model were carefully matched with the laboratory test parameters to ensure precise validation results.

A damage model was formulated by utilizing the available experimental data as a foundation. The peak displacements were δ_f = 0.65 mm and δ_c = 0.91 mm. The fundamental parameters are presented in

Table 1. Basic parameters of the composite rock model [19].

Material	Material Elastic Modulus	Cohesion	Frictional Angle
	(GPa)	(MPa)	(°)
Rock	24	1.1	48
Concrete	33	1.5	52

.

To validate the effectiveness of the damage model, a comprehensive comparison was conducted between the numerical simulation results and the experimental findings. The occurrence of simultaneous complete rock damage and fracture along the interface is visually depicted in Figure 3. As shown in (a), the experimental observations demonstrate the appearance of interface cracks within the composite rock. In a corresponding manner, the numerical simulation outputs presented in (b) indicate that the rock damage along the interface primarily manifested at the junction between the rock and cement sheath. This manifestation occurred under the influence of shear stress, aligning with the observed experimental results.

Formula (5) is defined as the uncorrected bonding force, while Formula (6) represents the established model for the corrected bonding force. In Figure 4, when the normal pressure is 2 MPa, the curve of the corrected bonding force shows significantly improved accuracy compared to the uncorrected curve. It is worth noting that the adjusted curve exhibits a peak stress of 4.37 MPa. When compared to the experimental data, the error in peak stress is only 0.68%. In contrast, the uncorrected curve indicates a peak stress of 4.1 MPa, deviating from the measured experimental value by 6.82%. Therefore, once the bonding force is corrected, the numerical simulation results demonstrate a significant enhancement in accuracy, as shown in

Table 2. Statistical comparison of shear stress between experimental and numerical simulation results.

Sample	Peak Stresses	Residual Stresses	Error Analysis of Peak Value
	(MPa)	(MPa)	%
Test data	4.4	2.2	/
Uncorrected simulation data	4.10	2.35	6.82
Corrected simulation data	4.37	2.35	0.68

.

In Figure 5, the stress–displacement curve for the rock joint interface under shear stress at 4 MPa normal pressure is shown. The curve is compared between the bonding force calculated using Formula (5) from the literature, the modified model, and the experimental results from reference [19]. The trend of the modified model curve closely aligns with the experimental curve. The experimental peak shear stress is 4.3 MPa, while the simulated peak shear stresses for the modified model and the literature are 4.41 MPa and 3.89 MPa, respectively, with errors of 2.56% and 9.53%. Compared to the results from the literature, the modified model exhibits an improved accuracy of 6.97%, indicating a significant enhancement in computational precision.

Table 3. Comparison of shear stress test results and numerical simulation.

Test Sample	Normal Stresses	Peak shear Stress (MPa)			Corrected Error (%)	Uncorrected Error (%)
	(MPa)	Test Data	Revised Data	Unrevised Data
s2-1	2	4.50	4.41	4.21	2.00	6.44
s2-3	2	4.90	5.01	4.64	2.24	5.31
s2-4	2	4.40	4.37	4.10	3.37	6.82
s4-2	4	4.30	4.41	3.89	2.56	9.53
s4-3	4	5.40	5.48	5.03	1.48	6.85
s6-1	6	6.50	6.45	6.18	0.77	4.92

provides a comparison between the experimental data and the numerical simulation results. The comparison shows that the accuracy of the corrected data has increased by more than 5% compared to the uncorrected data. This suggests that the modified model is more reasonable and accurate than both the uncorrected model and the model described in the literature.

4. Numerical Simulation Analysis of Water Channeling outside Casing in Water Injection Wells

4.1. Bonded Interface Rock Model outside Casing in Water Injection

Water channeling in the casing of water injection wells is caused by the progressive advancement of injected water along the bonded surface rock. The primary cause of external water channeling in the casing is the damage to the bonded surface rock induced by fluid–solid coupling. COMSOL simulation software, a widely utilized and powerful tool for multi-physics field simulations, is capable of effectively handling coupled problems in multiple physical domains. Moreover, its numerical algorithms offer high precision, and the obtained numerical solutions have undergone extensive testing and verification. In this study, a model of the bonded surface rock outside the casing of a water injection well was established using COMSOL software to simulate the evolution of damage under the influence of fluid–solid coupling. The model comprises a square shape measuring 2 m × 2 m and features a central crack with a length of 1 m, as shown in Figure 6. The crack experiences a pressure loading rate of 0.5 MPa/s. The parameters utilized in the model can be found in

Table 4. Numerical simulation parameters of the bonding interface rock.

Material Parameters of Rock and Cement Ring	Numerical Value	Unit
Density of rock ρm	2600	kg/m3
Density of cement ring ρy	2000	kg/m3
Young’s modulus of rock E1	50	GPa
Young’s modulus of cement ring E2	10	GPa
Poisson’s ratio of rock μ1	2.012
Poisson’s ratio of cement ring μ2	2.341
Permeability of rock k1	1 × 10−16	m2
Permeability of cement ring k2	1 × 10−14	m2
Rock Material Parameters of the Bonding Surface	Numerical Value	Unit
Tensile strength ft	10	MPa
Compressive strength fc	60.1	MPa
Initial porosity Φ0	0.15
Residual porosity Φr	0.03
Biot’s coefficient α	0.5
Density ρw	930	kg/m3
Viscosity ϑw	1.2 × 10−4	Pa·s
Compressibility cw	4.1 × 10−10	Pa−1
Fracture energy per unit area Ψi	300	J/m2

.

The experimental setup includes a cylindrical specimen with dimensions of 50 mm (width) × 100 mm (height). The specimen’s material strength follows a Weibull distribution with a shape parameter (m) of 2.34 and a characteristic strength (F0) of 60.1 MPa. In the process of validating fluid–solid coupling, a constant water pressure of 3 MPa is exerted on the top surface of the specimen. The specimen is loaded uniformly with a loading rate of 0.5 mm/s to ensure a gradual loading progression.

4.2. Bonded Interface Rock Model outside Casing in Water Injection

Based on oilfield water injection development practices, the progression of water injection time and the advancement of adjacent formations in the injection zone contribute to the dynamic changes in reservoir pressure. The confining pressure on the bonded rock surfaces fluctuates with the dynamic changes during water injection well production. These fluctuations in confining pressure lead to different damage profiles on the bonded surfaces based on specific operational conditions.

In addition, the variation in wellbore diameter during the drilling of water injection wells leads to different widths of bonded rock surfaces, which consequently results in diverse damage patterns. The performance and quality of the cement slurry utilized during the cementing process contribute to discrepancies in the Young’s modulus of the cement sheath. These variations in Young’s modulus subsequently lead to fluctuations in shear strength. The crucial factors impacting water infiltration outside the casing encompass confining pressure, cemented rock width, and the ratio of Young’s modulus between the cement sheath and the rock. A meticulous study of these factors is imperative to comprehend their nuanced effects on the damage mechanisms of the cemented rock.

In the operational stage of water injection wells, significant factors impacting water channeling outside the casing involve confining pressure, bonded rock width, and the relative Young’s modulus between the cement sheath and the rock. Conducting in-depth research on these factors is vital for comprehending their subtle influences on the damage mechanisms of bonded rock surfaces.

4.3. Effect of Confining Pressure on Bonded Interface Rock Damage

Damage occurs on the bonded rock surfaces of cemented formations with increasing confining pressures of 1 MPa, 3 MPa, 5 MPa, 8 MPa, and 10 MPa. Higher confining pressure correlates with an escalation in the injection pressure at which damage is observed. Based on Figure 7 and Figure 8, observation shows that at 326, the levels of confining pressure (5, 8, and 10 MPa) significantly affect the occurrence of damage on the bonded rock surfaces. The damage propagates along the bonded surfaces of the rock–cement interface while also extending to one side of the cement sheath at the model boundary. Injected water diffuses along both sides of the crack, and due to the damaged bonded surfaces, there is preferential flow along the rock–cement interface. Higher confining pressures result in higher water pressures within the preferential flow channels.

Numerical simulations were performed using COMSOL software to model the damage evolution in the bonded rock under fluid–solid coupling. The resulting numerical solutions were compared with analytical solutions derived from the damage model calculations. The evolution of shear stress on both sides of the crack demonstrates a similar pattern, as shown in Figure 9. With the increase in confining pressure, there is a corresponding rise in the peak stress during the damage process of the bonded rock surfaces. This suggests that inducing damage becomes more challenging as the confining pressure increases. Figure 10 illustrates the variation in peak stress during the damage process of the bonded rock surfaces under varying levels of confining pressure. The analytical solutions for the peak stress values at confining pressures of 1, 3, 5, 8, and 10 MPa are approximately 4.087, 5.021, 5.55, 6.66, and 7.22 MPa, respectively. The corresponding numerical solutions for peak stress are approximately 4.068, 4.952, 5.517, 6.592, and 7.096 MPa, respectively. The average error between the numerical and analytical solutions is 1.03%. Thus, the numerical simulation results accurately and scientifically describe the damage characteristics of the bonded rock surfaces under varying confining pressures.

4.4. Study on the Evolution of Damage for Bonded Interface Rock with Different Widths (w)

We conducted numerical simulations on models of bonded rock surfaces with varying width dimensions: 0.02 m, 0.05 m, 0.1 m, 0.15 m, and 0.2 m. The objective was to explore the influence of width variations on the progression of damage. The numerical simulation results were analyzed to evaluate the impact of width on rock damage under fluid–solid coupling and examine the patterns of damage evolution on bonded rock surfaces with varying widths. As shown in Figure 11 and Figure 12, it is evident that increasing the water injection pressure leads to the primary propagation of damage along the interface between the rock and the protective cement sheath. During the bonded rock surface damage, significant damage is observed on one side of the cement sheath at the interface position. Hydraulic pressure mainly propagates along the damaged zone and around the cracks.

Based on Figure 13 and Figure 14, it can be observed that as the width (w) of the cemented interface rock increases from 0.02 m to 0.2 m, the shear stress exhibits a relatively small change. The peak shear stress remains relatively stable with respect to the width of the cemented interface. The numerical solutions obtained from the model closely match the analytical solutions, with a maximum error of 5.44%.

These findings suggest that the damage evolution of the cemented interface rock is minimally affected by its width. The shear stress behavior shows little sensitivity to changes in width dimensions. Therefore, it can be concluded that the width of the cemented interface has a limited influence on the overall damage evolution process.

4.5. Investigating the Influence of Different Cement Sheath–Rock Modulus Ratios on Damage Behavior

The quality of cementing directly affects the integrity of the cement sheath during the cementing process. Furthermore, different types of cement slurries can also influence the durability of the cement sheath after cementing. To investigate the influence of cement slurry on the damage to bonded rock surfaces during cementing, numerical simulations were carried out using various shear modulus values for the cement sheath: 6 GPa, 10 GPa, 15 GPa, 18 GPa, and 20 GPa. We conducted numerical simulations, setting the ratio (represented as λ) of Young’s modulus between the cement sheath and the rock to different values of 0.12, 0.2, 0.3, 0.36, and 0.4.

Based on Figure 15 and Figure 16, it is observed that when the λ value ranges from 0.12 to 0.36, damage occurs on the bonded rock surfaces under the influence of water injection pressure. The damage propagates towards the vicinity of the interface, parallel to the cement sheath, while the fluid pressure is distributed along the bonded surface and cracks. When the value of λ is 0.4, the damage on the bonded rock surfaces initially expands along the interface between the cement sheath and the rock and subsequently propagates towards the wellbore. The fluid pressure is significantly controlled by the damaged zone, resulting in a shorter length of damage on the bonded rock surface and a smaller range of diffusion for the fluid pressure.

Based on Figure 17 and Figure 18, it is observed that as the λ value increases, the peak fluid pressure during the damage of bonded rock surfaces also increases. The peak shear stress values obtained from the analytical solutions for different ratios (λ) of Young’s modulus between the cement sheath and the rock are 2.34 MPa, 3.861 MPa, 5.65 MPa, 6.618 MPa, and 7.642 MPa. In contrast, the numerical solutions yield peak shear stress values of 2.13 MPa, 3.616 MPa, 5.516 MPa, 6.632 MPa, and 7.9 MPa. The maximum error between the two methods is 8.97%, with an average error of 2.82%. This indicates some deviation or discrepancy between the analytical and numerical results in predicting the peak shear stress. After linear regression of the numerical solutions for the peak shear stress under different λ values, the slope is 20.5 with an accuracy of 0.9915. Therefore, it can be concluded that the numerical simulation method produces small errors compared to the analytical solutions under different ratios of Young’s modulus, indicating the scientific validity of the numerical modeling approach. This model is suitable for studying water channeling phenomena in injection wells under various cementing quality conditions. A higher ratio of Young’s modulus implies greater difficulty in damaging the bonded rock surfaces, thus improving cementing quality becomes one of the methods to prevent water channeling outside the casing of the injection well.

5. Discussion

In this study, a comprehensive damage model was designed that incorporated the complex interaction between bonded rock surfaces and the dynamic coupling of fluid and solid. The robustness of this model was validated by using COMSOL software to compare it with test data of cemented rock specimens. Impressively, the stress–strain numerical curves exhibited significant consistency with the experimental data before reaching the peak values. These findings collectively verify that the primary source of damage takes place at the interface between the bonded rock surfaces and the cement sheath surrounding the injection well casing. The progressive deterioration along these interfaces contributes to the occurrence of water channeling phenomena within the casing.

The damage model considering the fluid–solid coupling effects on bonded rock surfaces was constructed in this study and numerically simulated using COMSOL software. The validation of the numerical results was performed by comparing the stress–strain numerical curves with experimental data of cemented rock specimens, showing a high level of agreement before reaching the peak values. The study findings indicate that the damage occurring outside the casing of injection wells primarily occurs at the cement–rock interface of bonded rock surfaces, and this progressive damage along the bonded rock surfaces results in water channeling inside the injection well casing.

In addition, this study verified cement sheath damage as one of the main causes of water channeling outside the casing of injection wells through numerical simulation. The damage primarily occurs at the bonded interface between rock and cement, and the conclusions obtained from the numerical simulations are similar to those of other researchers. However, previous studies did not consider the elastic–plastic damage occurring during the process of crack formation in the bonded rock surfaces, as well as the influence of fluid–solid coupling during the cracking process.

This study deviates from prior research by specifically investigating the impact of variations in bottomhole pressure on the progression of the complete damage path of the cement sheath in the surrounding rock formation. The analysis is based on the current developmental stage of the Y oilfield. By simulating the effects of parameter changes on the cement sheath damage, we aim to elucidate the impact of these changes on the overall rock damage. The existing constitutive model needs further improvement to achieve higher fidelity. It is important to emphasize that the damage to the cement sheath surface is intrinsically linked to both the integrity of the cement sheath and the overall quality of the cementing operation. Consequently, future endeavors should meticulously investigate the impact of cementing quality on rock damage occurring on the surface of the cement sheath. In summary, the description of the damage model established in our study reveals the complex mechanisms of water channeling in injection wells. The damage model developed in this study, which is scientifically elucidated, offers a theoretical foundation for addressing compromised wells as well as evaluating and managing water channeling and water flooding in wells affected by cement damage.

6. Conclusions

Based on the current developmental status in Field Y, this study investigates the damage mechanism of interfacial rock in water injection wells. By employing theoretical analysis and numerical simulations considering fluid–solid coupling, the evolution of interfacial rock damage is comprehensively explored. The research findings lead to the following conclusions:

The interfacial rock in the cemented zone undergoes damage under the effect of fluid–solid coupling. The numerical simulation results indicate that water breakthrough outside the casing is caused by the evolution of interfacial rock damage.

This study establishes a shear stress correction model for cement–rock interfaces, which improves the accuracy of numerical simulations by more than 5% compared to traditional models. The modified model enables a more scientifically reasonable calculation of the shear stresses at cement–rock interfaces.

Through comparing the variation patterns of peak stress under different conditions, the linear fitting slopes of peak stress with respect to different confining pressures, widths of interfacial rocks, and modulus ratios are 3.84, −1.51, and 19.99, respectively. A larger slope indicates a more pronounced influence of the parameter on the peak stress of interfacial rocks. Thus, it can be inferred that the damage to the interfacial rocks of the injection well is primarily related to the Young’s modulus ratio of cement to rock.

This study provides theoretical evidence for the mechanisms of water channeling at cement–rock interfaces in water injection wells, which contributes to the management and control of water influx outside the casing in oil fields. The shear force correction model for cement–rock interfaces enables oilfield engineers to accurately assess the damage at cement–rock interfaces. The related technological improvements provide guidance for the prevention and control of water channeling and water flooding in oilfield water injection operations, promoting advances in research on technologies related to water channeling and water flooding in oil fields.