Anchoring Effect of Abandoned Oil Wells in Coal, Oil, and Gas Co-Production Areas and Its Influence on Overburden Stability

Abstract

This study investigates the influence of oil well anchoring on overburden stability in coal, oil, and gas co-mining areas, combining mechanical theory and numerical simulations to systematically analyze the mechanical characteristics. First, a mechanical model of oil well anchoring was developed by considering the coupled interaction between the wellbore cement sheath and the surrounding rock, and the relationship between oil well anchoring and changes in the friction angle, cohesion, compressive strength, and Young’s modulus of the surrounding rock. Subsequently, a three-dimensional numerical simulation using FLAC3D 7.0 was conducted to analyze stress redistribution, displacement field evolution, and plastic zone distribution around the oil wells under different burial depths. The results indicate that as the burial depth increases, the peak stress around the oil wells rises from 0.37 MPa to 2.24 MPa, the displacement influence range expands from 18 m to 43 m, and the plastic zone remains confined between 0.9 m and 1.6 m. No significant stress coupling effects are observed between the well groups. These findings demonstrate that the anchoring effect of oil wells effectively regulates the stratigraphic stress field, mitigates overburden deformation, and enhances wellbore stability in coal, oil, and gas co-mining areas, providing a crucial theoretical basis and engineering reference for enhancing overburden stability in coal–oil co-mining areas.

1. Introduction

Coal, oil, and gas resources are found in overlapping regions within the Tarim, Jungar, Qaidam, and Ordos basins in China. The rational extraction of these resources, when coexisting, mutually influences each other [1,2,3]. The deeper burial of oil, which causes oil wells to intersect coal strata, results in oil and gas wellbores acting as channels that connect the surface with deep reservoirs. These wellbores are directly influenced by the mechanical properties of the overburden and the changes in the stress field surrounding them. Meng et al. [4] observed that variations in annular pressure can induce changes in the structural stress of the casing-cement ring-strata combination. In extreme cases, these variations can lead to the failure of the cement ring seal, resulting in casing damage. Nabipour et al. [5,6,7] investigated the variation in the distribution of stress intensity and its key influencing factors within a large wellbore stress combination system using numerical simulation methods. Deng et al. [8] conducted a systematic investigation into the effects of physical and geometrical parameters of the formation, the contact state between the cement ring and casing, the cement ring boundary, and the non-uniformity of ground stress on casing stresses.

Casing in oil wells typically has a large diameter (greater than 250 mm) and traverses coal-bearing formations. These casings are anchored by steel tubing in the form of cement to the well wall or external steel tubing, thereby creating an anchoring effect [9,10]. The anchoring of oil well casings within the formation, which interferes with the original strata, may have a limited scope of influence. However, it can affect the stability of the overlying rock layers, alter the original mechanical state, and consequently jeopardize the safety of the oil wells [11,12,13]. Several scholars [14,15,16] suggest that the anchoring effect of abandoned oil wells can effectively alter the stress distribution in the formation and influence the stability of coal seams, oil and gas reservoirs, and surrounding strata. Additionally, the anchoring effect plays a critical role in stabilizing the wellbore and supporting the overburden formation. Through a comparison of physical similarity simulation experiments, both with and without casing, Fan Siwei et al. [17] concluded that the subsidence of the overlying rock layer is reduced to varying degrees in different layers with casing, and the damage to the overlying rock layer is also minimized. Liang Shun [18,19] and colleagues conducted an in-depth study of the stability of shale gas wells that vertically intersect coal seams. They not only focused on the stability of these wells but also integrated the effects of topographic changes and coal seam depth on the integrity of oil and gas wellbore integrity, comprehensively evaluating the potential impact of these factors on well stability. This anchoring action is analogous to that of a large anchor rod, which stabilizes the coal pillar and its surrounding rock strata, thereby altering the mechanical properties of the strata surrounding the oil wells. Yang S. et al.; Ma J. et al; Shukla A. et al; Yang J. [20,21,22,23] investigated the mechanism of anchor anchoring, revealing the dynamic relationship between anchor force and ground deformation. They categorized this process into three stages: strengthening anchoring, stabilizing surrounding rock, and reducing deformation, which could provide insights for the research in this paper.

The overburden serves as the surrounding structure of the wellbore, and its stability not only determines whether the wellbore can remain safely operational over time but also influences the formation pressure balance, reservoir integrity, and the long-term sustainability of the regional geological environment [24,25,26]. During drilling, issues such as formation collapse, fracture expansion, and fluid intrusion may trigger wellbore destabilization, potentially leading to catastrophic consequences such as blowouts and formation slides. During the production phase, a decline in reservoir pressure may cause the formation to settle or compact, generating additional stresses on the overburden, thereby further threatening the stability of the wellbore [27,28]. Therefore, studying the effect of oil well anchoring on the stability of the overburden formation holds significant theoretical and practical value. This paper analyzes whether anchoring technology can effectively control the stress distribution in the formation around the wellbore and prevent the occurrence of formation slippage and fracture extension. This study focuses on the synergistic effects of cementing, casing anchoring, and mechanical equipment, and evaluates the impact of abandoning the anchoring effect of oil wells on the stability of the overburden formation. This research provides an important theoretical foundation and engineering guidance for enhancing the stability of overburden formations in coal and oil co-mining areas.

2. Project Overview

Using the 3106 working face of Well No. 1 at Checun Coal Mine in Yan’an City as the engineering background, which primarily extracts the 3-2 coal seam and has an average thickness of 1.14 m and a dip of less than 1°. The coal seam is located at depths ranging from 367 m to 437 m, with an average depth of 402 m. The immediate roof of the 3106 working face consists of muddy siltstone, while the main roof is composed of fine-grained sandstone. The immediate floor is muddy siltstone, and the main floor consists of medium-grained sandstone. Figure 1 illustrates the spatial relationship between the oil well cluster, the working face, and the geological borehole log.

Within the 3106 working face, Well Cluster 3261 consists of five producing oil wells arranged in a linear pattern. Security coal pillars have been established for Well Cluster 3261, each extending 200 m along the strike and inclination of the coal seam from the center of the oil wells, resulting in an overall coal pillar width ranging from 400 m to 420 m. Based on the trajectory data of five single wells with inclined boreholes within Well Cluster 3261, the complete well trajectory, from the opening hole through the inclined section, stable inclined section, and descending inclined section, was plotted. According to borehole completion data provided by the mine, a positioning analysis of the depth profiles of the five oil wells in Well Cluster 3261 indicates that the sloping point of the oil well pipelines is approximately at a formation depth of 400 m; however, geological data indicate that the average depth of the coal beds is 357 m, suggesting that the oil wells and their casings vertically penetrate the coal beds. Figure 2 presents the oil well profile and structure.

3. Theoretical Analysis of the Anchoring Action of Oil Wells on the Movement of Overburden Rock

3.1. Mechanisms Affecting Anchoring in Oil Wells

Oil well anchoring technology establishes a stable support system between the wellbore and the surrounding overburden through cementing, mechanical anchoring, and casing support. Anchoring technology creates a mechanically stable structure around the wellbore through the combined action of casing and cementing, regulating stress distribution within the formation (Figure 3) and enhancing wellbore stability. During drilling, the original formation stresses are disturbed, leading to high-stress concentration zones, and anchoring techniques redistributing stress and mitigating localized stress concentrations. Cementing creates an annular sealing structure between the wellbore wall and the formation, dispersing formation stress and preserving wellbore integrity. This reduces the risk of wellbore collapse in loose sand formations or high-pressure, low-permeability reservoirs, while also improving long-term wellbore stability and mitigating wellbore damage caused by stress fluctuations during oil and gas production.

The elastic mechanics model is applicable for analyzing the stress distribution along the wellbore wall, particularly in deep formations. Using the theory of thick-walled cylinders and accounting for the stress conditions on the wellbore wall due to internal and external pressures [29], the normal stress distribution in a cylindrical wellbore can be determined using the following equation:

$${\sigma }_n={\displaystyle \frac{P_{\mathit{out}}{r}_2^2-P_{\mathit{in}}{r}_1^2}{r_2^2-r_1^2}}$$

(1)

In the formula, $r_1$ and $r_2$ represent the inner and outer diameters of the wellbore, taken as 0.1 m and 0.2 m, respectively. $P_{\mathit{out}}$ and $P_{\mathit{in}}$ denote the external and internal pressures of the wellbore, respectively. In the Yan’an Zichang region, the internal wellbore fluid pressure is 25 MPa, while the external formation pressure is 12.5 MPa. Substituting these values into the equation, the normal stress is found to be positive, indicating that the wellbore wall is subjected to compressive stress.

During the cementing process, the cement slurry fills the annular space between the wellbore and the formation, forming a high-strength cement sheath that effectively seals fractures around the wellbore. Once cured, the cement withstands the stresses associated with formation fracture propagation, preventing further fracture propagation near the wellbore, preventing reservoir fractures from intersecting the wellbore, reducing interformational fluid migration, and mitigating formation instability induced by reservoir pressure fluctuations, particularly in high-pressure gas reservoirs and multi-fractured zones.

The casing and cementing system collectively support the overburden, mitigating its settlement by uniformly transmitting formation pressure to deeper, stable strata. Casing support distributes overburden pressure and reduces formation stress around the wellbore. During resource extraction, deformation equilibrium of the formation around the wellbore is maintained through the compressive strength of the cement sheath, which improves the uniformity of formation pressure transmission, mitigates overburden damage due to localized overloading, and provides structural reinforcement for complex multi-layer formations, such as salt formations and coal-bed methane reservoirs.

The anchoring system maintains a strong bond between the wellbore and the surrounding formation during long-term operation, preventing casing and cement dislodgement caused by thermal expansion, contraction, or geological deformation. Optimizing the anchoring design enhances the system’s adaptability to long-term mechanical loads, improving the mechanical stability of the wellbore and overburden under prolonged high-temperature, high-pressure conditions, and mitigating the risk of equipment failure or geological hazards associated with wellbore deformation and formation subsidence. Oil well anchoring plays a critical role in maintaining overburden stability by regulating stress distribution and providing structural support.

3.2. Mechanics of Oil Wells in the Formation

Oil-bearing strata are typically situated beneath coal seams, necessitating the passage of oil wells and their casings through these seams. Their physical function resembles that of an anchor embedded within the strata, and their interaction with each stratum must be analyzed in relation to mechanical parameter variations in the cemented sheath surrounding the casing [17].

3.2.1. The Influence of Oil Wells on the Angle of Internal Friction of Surrounding Rock Formations

The internal friction angle of the pipe-anchored solid is governed by the internal friction angle of the casing, the internal friction angle of the surrounding rock prior to anchoring, and the interfacial stress between the casing and the surrounding rock. When the casing and surrounding rock are subjected to identical stress conditions, the internal friction coefficient corresponds to the internal friction angle of the pipe-anchored solid and is expressed as follows:

$$f=f_r\left(1-ns\right)+f_{b}nS$$

(2)

Difference between the internal friction angle of the anchored body in oil well casing and the surrounding rock is expressed as follows:

$$\Delta f=f-f_r=\left(f_b-f_r\right)nS$$

(3)

In the formula, $f$—coefficient of friction within the casing anchorage, $f_r$—coefficient of friction within the surrounding rock, $f_b$—coefficient of friction of the casing and the cement ring, $n$—density of the cement, and $S$—cross-sectional area of the casing and the cement ring.

In most cases, the coefficient of internal friction of the anchored solid around the casing is slightly lower than that of the surrounding rock mass, i.e., $f_b$<$f_r$. However, in the actual study, since the total area of the casing anchor solid is much smaller than the area of the formation in which it is anchored, the calculated value of the angle of internal friction of the anchor solid is equal to the angle of internal friction of the surrounding rock before anchoring. Considering that the oil wells are deeper, the number of formations anchored by the casing is relatively large, and the internal friction angle of siltstone is the largest among different rock formations, and considering the maximum effect of the oil well casing on the internal friction coefficient of the formation, the internal friction angle of muddy siltstone was used in this study to calculate the internal friction angle of the casing anchored solid, with an internal friction angle of 37° and internal friction coefficient of 0.75.

3.2.2. The Effect of Oil Wells on the Cohesion of the Rock Formations Surrounding Them

As the casing itself has a certain bending capacity, it will provide some restraint to the horizontal misalignment between the rock layers. From the perspective of the surrounding rock casing increases the shear strength of the rock mass. From the analysis of the tangential force of the casing, the tangential anchoring force of the casing originates from the binding force of the casing on the horizontal displacement of the surrounding rock, and the maximum value of the horizontal displacement binding force is the shear strength of the casing. The casing-enclosed rock bond exhibits specific cohesive properties, and the casing anchorage cohesion $c$ is:

Since the casing possesses a certain bending capacity, it provides restraint against horizontal misalignment between rock layers. From the perspective of the surrounding rock, the presence of the casing enhances the shear strength of the rock mass. Analyzing the tangential force of the casing, the tangential anchoring force originates from the constraint imposed by the casing on the horizontal displacement of the surrounding rock. The maximum horizontal displacement constraint force corresponds to the shear strength of the casing.

The casing-enclosed rock bond exhibits cohesive properties, and the casing anchorage cohesion $c$ is expressed as follows:

$$c=c_r+nS\left(c_b-c_r\right)$$

(4)

The increment produced by the casing of an oil well on the cohesive force of the formation surrounding is expressed as follows:

$$\Delta c=c-c_r=nS\left(c_b-c_r\right)+{\sigma }_b\mathit{tan}\phi$$

(5)

In the formula, $c_r$—rock cohesion, $c_b$—cementing cement cohesion, ${\sigma }_b$—casing axial stress acting on the geotechnical body, and $\phi$—rock internal friction angle.

Based on the geological data, it can be determined that the muddy siltstone on the 3-2 coal seam has a maximum internal friction angle of 37°. Considering the maximum effect of the oil well casing on this cohesion, the cohesion of the rock body is calculated using the cohesion of the muddy siltstone, which is 14.14 MPa. The axial stress of the oil well casing and cement ring on the surrounding rock body is similar to that generated by the casing’s self-weight, and based on the calculations in Equations (4) and (5), the cohesive force of the anchoring solids for a single casing in the 3-2 coal seam is 19.65 MPa, and the increase in the cohesive force is 5.51 MPa.

3.2.3. Effect of Oil Well Casing on the Compressive Strength of the Rock Formation Surrounding It

Analyzing along the axial direction of the casing, the casing borehole undergoes a transition from a bi-directional force system to a tri-directional force system. This transition occurs due to the potential deformation of the casing, which induces axial stress on the surrounding rock, thereby enhancing its compressive strength in the horizontal direction.

According to the Mohr–Coulomb strength criterion, the compressive strength of the casing-anchored solid in the horizontal direction is given as follows:

$${\sigma }_s={\displaystyle \frac{2c \mathit{cos}\phi }{1-\mathit{sin}\phi }}$$

(6)

The uniaxial compressive strength of the anchored surrounding rock mass of the oil well is expressed as follows:

$${\sigma }_c={\displaystyle \frac{2c_r \mathit{cos}\phi }{1-\mathit{sin}\phi }}$$

(7)

The increment of uniaxial strength of the surrounding rock after casing insertion is expressed as follows:

$$\Delta \sigma ={\sigma }_x-{\sigma }_c=2nS\left(c_b-c_r\right){\displaystyle \frac{\mathit{cos}\phi }{1-\mathit{sin}\phi }}+2{\sigma }_b \mathit{tan}\phi$$

(8)

In the formula, $c$—cohesion of surrounding rock after casing insertion, and $c_r$—cohesion of surrounding rock before casing insertion.

Based on the calculations from Equations (6) and (7), the uniaxial compressive strength of the casing-anchored solid in oil wells in the horizontal direction reaches 37.2 MPa after the casing is embedded into the rock formation. Simultaneously, the increment in uniaxial compressive strength due to casing anchorage is determined to be 13.06 MPa. These results indicate that the insertion of the oil well casing significantly enhances the mechanical properties of the surrounding formation, effectively upgrading its original strength parameters.

3.2.4. The Effect of Oil Well Casing on the Modulus of Elasticity of the Rock Formation Surrounding It

The casing reduces the amount of deformation of the surrounding rock, but in the case of the surrounding rock is subjected to the same upper load, when the amount of deformation is reduced, it can be regarded as the deformation modulus of the whole composed of casing anchorage and surrounding rock becomes larger. The change in mechanical parameters of the surrounding rock by casing has the following relationship:

$$E={\displaystyle \frac{E_r}{1-\lambda {\mu }_r}}$$

(9)

$$\mu ={\displaystyle \frac{{\mu }_r-\lambda }{1-\lambda {\mu }_r}}$$

(10)

$$\lambda ={\displaystyle \frac{\frac{{\mu }_r-\lambda }{1-\lambda {\mu }_r}}{{\frac{1}{E}}_r+\frac{1}{nS{E}_b}}}$$

(11)

In the formula, $E$—original modulus of elasticity, $E_b$—post-change modulus of elasticity, $E_r$—modulus of elasticity of the enclosing rock mass, ${\mu }_r$—original Poisson’s ratio of the enclosing rock mass and $\mu$—post-change Poisson’s ratio of the enclosing rock side.

3.3. Stability Analysis of Overlying Rocks Under Anchorage

3.3.1. Borehole Plasticity Zone Range

According to the rupture of the plastic zone within the stress field of an oil borehole into a logarithmic spiral as mentioned in “Petroleum well construction drilling & well completion”, its diameter slopes upwards by $\delta$ degrees [30], as shown in Figure 4.

After applying the theoretical analysis of Mohr–Coulomb theory to this, the radius $r_p$ of the plastic zone of the stress field in the oil borehole is expressed as follows:

$$r_p={\left[{\displaystyle \frac{2{\sigma }^{\prime }-C_o+\left(1+\frac{1+sin\phi }{1-sin\phi }\right)C_{j}ctg\phi }{\left(1+\frac{1+sin\phi }{1-sin\phi }\right)\left(p_w-p_r\right)+C_{j}ctg{\phi }_j}}\right]}^{{\displaystyle \frac{1}{Q}}}$$

(12)

In the formula, $C_o$—cohesion of primary rock, $r_p$—size of oil well casing, $C_j$—cohesion of jointed rock, $\phi$—angle of internal friction, $p_w$—bottomhole pressure, and $p_r$—reservoir pressure.

According to Equation (12), considering the plastic range that causes cracks around the borehole, and substituting the data of 3-2 coal seam, it can be calculated that 3-2 coal seam $r_p=2.13r_w$, i.e., the radius of the plastic zone is 2.13 times that of the diameter of the borehole, and it is further calculated that the theoretical plastic zone of the stress field of the oil well is 1.43 m.

In the design and construction of oil wells, the stability of the overburden is one of the key factors affecting the stability of the well wall and ensuring safe extraction.

3.3.2. Overburden Stress Analysis

For static ground stress field conditions, the radial stress, tangential stress expressions are as follows:

$${\sigma }_r={\displaystyle \frac{P_e}{1-{\nu }^2}}\left({\displaystyle \frac{R_2^2}{R_1^2}}\right)$$

(13)

In the formula, $P_e$ is the external pressure, Yan’an Checun coal mine No. 1 well ground stress is 10.5 MPa, and the inner and outer radius of the well wall is 0.1 m and 0.2 m, respectively. $\upsilon$ for the Poisson’s ratio of the material, take 0.3. Substituting the data can be obtained as ${\sigma }_r=46.15$ MPa.

$${\sigma }_{\theta }={\displaystyle \frac{P_e}{2}}\left({\displaystyle \frac{R_2^2}{R_1^2}}+1\right)$$

(14)

In the formula, $P_e$ is the external pressure, the same as 10.5 MPa, the inner and outer radius of the well wall is 0.1 m and 0.2 m, respectively, and the substitution of data can be obtained as ${\sigma }_{\theta }=26.25$ MPa.

3.3.3. Stability Analysis of Overburden

(1)

Stability analysis of layered rocks

Since coal seams in northern Shaanxi usually show a near-horizontal bedding structure, all bedded rocks are assumed to be near-horizontal beds in this study, and stability analyses were conducted accordingly. Stability analyses of overburden rocks typically predict instability risk using the classical shear-slip theory. The stability of the well wall is primarily assessed based on shear force when anchorage effects are considered.

When the shear stress in the overburden rock exceeds its shear strength, slippage, and destabilization occur. In cases of rock instability, well wall failure generally occurs at a critical stress threshold. The expression for critical shear stress is given as follows:

$${\tau }_{cr}=C+{\sigma }_n·\mathit{tan}\left(\phi \right)$$

(15)

In the formula, $c$ is the cohesion of geotechnical materials, 0.83 MPa is taken for the 3-2 coal seam, ${\sigma }_n$ is the normal stress, 29.17 MPa, and $\phi$ is the friction angle (internal friction angle). The value of 37° is taken for substituting the data to obtain ${\tau }_{cr}=23.04$ MPa.

(2)

Factor of Safety for overburden instability analysis

In order to quantify the risk of overburden destabilization, a Factor of Safety (FS) is often used to evaluate the stability of the well wall as follows:

$$FS={\displaystyle \frac{\sigma }{\tau }}$$

(16)

If the safety factor $FS<1$, then the risk of well wall instability is high.

4. Numerical Simulation Study of the Effect of Anchoring on Overburden Rock in Oil Wells

4.1. Modeling and Scenarios

The FLAC3D 7.0 numerical simulation software was employed to model and calculate the geomechanical behavior of the system. The overall model dimensions were set as L × W × H = 150 m × 150 m × 105 m based on the actual geological conditions of Well No. 1 at Checun Coal Mine. To accommodate the petroleum well casing and its surrounding structures, cylindrical voids with a diameter of 0.93 m were excavated within the stratum.

After achieving excavation equilibrium, each cylindrical void was filled with cement sheaths represented by annular rings with an outer diameter of 0.50 m and a thickness of 0.25 m, simulating the cementing cement. The cementing material used was Portland cement (API Grade G), a calcium carbonate–silica mixture with minor amounts of iron ore and gypsum, as per industry standards.

To ensure model accuracy and minimize computational errors, the grid resolution was refined within 50 m of the well complex perimeter. The top boundary of the model was set as a free boundary, while loads were applied based on stratigraphic relationships. Displacement constraints were imposed on all other boundaries. Additionally, to simulate realistic geological conditions, a coal boundary pillar with a width of 50 m was maintained at the x- and y-direction edges of the model, as illustrated in Figure 5.

The physical–mechanical parameters of the coal rock body listed in

Table 1. Physical and mechanical parameters of coal rock bodies.

Lithologic Characters	Density (kg/m3)	Bulk Modulus/GPa	Shear Modulus/GPa	Friction Angle/(°)	Force of Cohesion/MPa	Tensile Strength/MPa
Siltstone mud	2490	2.4	1.63	35	1.56	1.92
Fine grained sandstone	2490	3.7	2.20	35	2.12	2.43
Muddy Siltstone	2530	3.0	1.67	37	1.36	2.17
Medium grained sandstone	2500	2.3	1.25	34	2.12	3.12
3# Coal seam	1400	2.2	1.30	33.5	0.9	1.63

were obtained from actual field tests and laboratory tests. In the course of the study, the field test data were obtained from the geological exploration and rock mechanics tests conducted on the No. 1 shaft of Checun coal mine in Yan’an City, Shaanxi Province. The laboratory tests, on the other hand, obtained the specific physical–mechanical parameters by conducting a series of mechanical property tests on the collected rock samples, including compression strength, friction angle, shear strength, and so on.

In the numerical simulation of oil well borehole excavation, the wellbore is first excavated at the surface coordinates of the designated oil well, which serves as the reference point. Subsequently, the borehole is backfilled with a cementing ring of the predetermined dimensions as established in the initial model setup. The simulation process involves excavating the entire oil well borehole, followed by filling it with cementing material once excavation equilibrium is achieved. The detailed procedural workflow is illustrated in Figure 6.

4.2. Analysis of Oil Wells Within a Cluster of Wells with Different Burial Depth Pairs

(1)

Stress changes in oil wells at different burial depths

Through numerical simulation, the maximum principal stress distribution around the oil well was extracted at various burial depths, and its variation trend is illustrated in Figure 7. The results indicate the following:

• The peak stress increases with increasing burial depth.
• At a burial depth of 10 m, the peak stress around the oil well is only 0.37 MPa, with a stress concentration range of less than 1.2 m.
• At a burial depth of 105 m, the peak stress rises to 2.24 MPa, while the stress concentration range expands to 4 m, and the stress concentration zone contracts toward the well wall.

At shallow burial depths (10–30 m), the stress concentration zones are more dispersed. However, at greater depths (80–105 m), stress localizes around the wellbore, leading to higher localized stress.

As burial depth increases, interactions between adjacent well groups intensify:

• At shallow depths (10–60 m), no significant stress overlap is observed between wells.
• At greater depths (90–105 m), neighboring well stress fields exhibit superposition effects, leading to an expansion of the stress concentration zones.

(2)

Displacement changes in oil wells at different burial depths

The displacement variation in the rock formation surrounding the oil well exhibits the following characteristics as burial depth increases:

• At a burial depth of 30 m, the displacement influence range is 18 m.
• At a burial depth of 105 m, the displacement influence range expands to 41 m, indicating a larger affected zone and an enhanced constraining effect of the oil well.

When the oil wells are shallowly buried (10–60 m), formation subsidence is more pronounced, and the restraining effect of the oil wells on the deformation of the surrounding rock is relatively weak. However, at greater burial depths (80–105 m), the overall formation subsidence decreases, suggesting that oil wells exert a significant inhibiting effect on formation settlement, as shown in Figure 8.

(3)

Changes in plastic zone of oil wells under different burial depths

The plastic zone surrounding oil wells is a critical parameter for assessing rock formation damage. Simulation results indicate the following, as shown in Figure 9:

• The plastic zone remains limited in extent under all burial depth conditions, ranging between 0.9 m and 1.6 m.
• At a burial depth of 105 m, the plastic zone reaches its maximum extent of 1.6 m but does not exhibit significant penetration-induced damage.
• The plastic zone is primarily localized around the wellbore, with no overlap between plastic zones of adjacent wells, suggesting the absence of stress coupling effects between neighboring wells.

Based on the simulation results, the anchoring effect of oil wells intensifies with increasing burial depth, primarily reflected in the expansion of the stress concentration area and the increase in the displacement influence range. For deeply buried oil wells (>80 m), the constraint on stratum subsidence is significantly enhanced, with an influence range extending to 41 m. However, displacement variations in the rock strata immediately surrounding the oil wells are smaller compared to displacement changes at greater distances from the wells. The plastic zone remains stable within a range of 0.9 to 1.6 m, without forming penetrative damage.

Based on numerical simulation results, the overburden subsidence in the vicinity of the wellbore is significantly lower than that observed at greater distances. Specifically, strata near the wells exhibit 31–48% less subsidence compared to distal regions. This phenomenon is attributed to the mechanical support provided by the casing-anchored system, which effectively redistributes stress and constrains vertical displacement in the immediate vicinity of the wellbore.

In contrast, overburden at greater distances experiences more pronounced deformation due to the absence of direct structural reinforcement, leading to an increased magnitude of subsidence. These findings underscore the critical role of the wellbore and its anchoring system in stabilizing the surrounding formation and mitigating excessive surface deformation.

The presence of oil wells and cementing cement exert a restraining effect on formation subsidence displacement, functioning similarly to anchors embedded within the geological strata. This anchoring mechanism effectively enhances the stability of the overlying rock mass, mitigating excessive deformation and ensuring structural integrity.

5. Conclusions

• The stress field distribution characteristics of a single oil well in the formation were theoretically calculated, revealing that the plastic zone radius extends to 1.43 m. A mechanical analysis of the casing and cementing cement demonstrated that their primary function is to enhance the cohesion of the rock mass and increase the internal friction angle. After casing anchorage, the cohesion of the surrounding rock increased by 5.51 MPa, while the increment in the internal friction angle was negligible. The casing anchorage mechanism improves the compressive and shear strength of the rock mass and modifies its elastic modulus and Poisson’s ratio. Within the plastic zone, the uniaxial compressive strength of the casing-anchored solid increased by 23.06 MPa, the elastic modulus reached 13.245 GPa, and Poisson’s ratio was 0.257. These findings indicate a significant reinforcement effect of casing anchorage on the surrounding rock mass, contributing to enhanced stability and mechanical performance.
• Based on the FLAC3D 7.0 numerical model, the stress peak around the oil wells gradually increases with burial depth, rising from 0.37 MPa to 2.24 MPa. Simultaneously, the displacement influence range of the oil well cluster in each monitored stratum also exhibits a progressive expansion, extending from 18 m to 43 m. Furthermore, the subsidence displacement of the rock strata in proximity to the oil wells is significantly smaller compared to that of more distant formations, indicating that oil wells exert a restraining effect on stratum subsidence. These findings underscore the mechanical stabilization role of oil wells in mitigating excessive deformation within the surrounding strata.
• Oil well anchoring technology ensures well wall stability by regulating stress distribution, supporting the overburden, and enhancing the compressive and shear strength of the well structure. Through the synergistic effect of cementing and casing support, the anchoring system effectively mitigates the risk of well wall instability. The oil well casing functions analogous to an embedded anchor within the formation, thereby enhancing the structural integrity and damage resistance of the surrounding rock mass.

6. Discussion

The study presented herein offers valuable insights into the anchoring effect of abandoned oil wells on the stability of overburden within coal, oil, and gas co-production zones. The integration of mechanical modeling with numerical simulations forms a robust framework for understanding the influence of wellbore infrastructure on the stability of surrounding rock. Consequently, the findings significantly enhance our understanding of both the mechanical interactions between oil well casings and surrounding rock formations, as well as the broader implications for geotechnical stability in multi-resource extraction zones.

• The anchoring effect induced by oil well casings plays a crucial role in stabilizing the overburden above oil and gas reservoirs [31]. The results of this study demonstrate that oil well casings, particularly those penetrating coal seams, substantially alter the stress distribution within the surrounding strata. As the burial depth of oil wells increases, the mechanical benefits of casing anchorage become more pronounced. Mechanical parameters such as cohesion, internal friction angle, and compressive strength are all enhanced by the anchoring effect, thereby reinforcing the integrity of the overburden and mitigating the risk of subsidence and fracture propagation. The results of numerical modeling clearly illustrate how oil well anchoring reduces subsidence in the near-wellbore region, offering vital protection against overburden damage. Notably, the depth-dependent expansion of stress concentration zones and the displacement influence range provide key insights into how anchoring can regulate stress distribution in the subsurface. These findings emphasize the importance of wellbore design, particularly in deeper burial zones where stress concentration becomes more localized and the potential for wellbore destabilization increases.
• One of the most important findings of this study is the significant role that anchoring plays in redistributing subsurface stresses. The mechanical model of the study effectively illustrates how casing systems, through their interaction with surrounding rock, prevent excessive deformation in the overburden, particularly in high-stress environments. By creating a stable support structure within the geological strata, anchoring mechanisms reduce the likelihood of rock slippage and wellbore collapse—risks commonly associated with complex multi-layer formations, such as coal seams and high-pressure gas reservoirs [32]. The results of this study complement earlier works by expanding the focus to include oil and gas co-production zones, which are increasingly prevalent in global resource extraction strategies. The integration of casing and cementing systems in this study enhances rock cohesion and shear strength, providing a detailed quantitative basis for understanding how wellbore infrastructure can modulate the stress and strain fields in the surrounding strata.
• The theoretical analysis of casing and cementing systems, coupled with the results of numerical simulations, provides critical practical implications for the design of oil and gas extraction operations in coal, oil, and gas co-production zones. The ability to predict and manage overburden stability using anchoring technology will allow engineers to devise more effective strategies for wellbore construction, maintenance, and abandonment. Particularly in regions where resources are located at considerable depths, such as the Yan’an coal mines in China, the anchoring effect offers a viable method for enhancing wellbore stability and preventing catastrophic failures during both drilling and production. Furthermore, the reduction in formation subsidence observed in the study underscores the potential for anchoring systems to mitigate the environmental impact of resource extraction. By minimizing ground deformation and maintaining geological stability, oil well anchoring technologies can contribute to more sustainable extraction practices, reducing the environmental risks associated with traditional mining and drilling methods.
• While this study makes significant contributions to understanding the anchoring effect on overburden stability, several aspects require further investigation. First, the model used in this study primarily considers the mechanical interaction between oil well casings and surrounding rock but does not fully account for the complexities introduced by fluid dynamics within the wellbore. Future studies could expand the model to incorporate the effects of pressure variations resulting from fluid injection or extraction, which may further influence the stability of surrounding strata.