An Investigation of the Influence of the Main Wellbore on the Wellbore Stability of Sidetracked Wellbore of the Deep Earth TK-1

Abstract

Deep Earth TK-1, China’s first 10,000 m scientific exploration well, encountered severe wellbore instability during sidetracking at a depth of approximately 9500 m under ultra-deep, high-stress conditions (maximum horizontal stress ${\sigma }_H$ = 230 MPa, minimum horizontal stress ${\sigma }_h$ = 200 MPa). To clarify how the original wellbore affects the stability of the sidetracked wellbore, single- and dual-well numerical models were established in COMSOL Multiphysics using the solid mechanics module and finite element method. The stress redistribution around the wellbore was analyzed before and after the collapse of the main wellbore, and the influences of well spacing and breakout geometry were quantified. The results show that a stress-relief “safe zone” forms along the direction of maximum horizontal stress before collapse and expands after collapse, allowing safer sidetracking within this range. In the dual-well model, the maximum stress difference around the sidetracked wellbore increases with well spacing and eventually approaches that of a single circular wellbore. The safe zone boundary was quantified for well spacings between 2.0 m and 3.5 m, depending on the major-axis enlargement ratio of the collapsed main wellbore. A larger major-axis enlargement ratio reduces far-field stress interference and expands the safe zone, whereas changes in the minor-axis enlargement ratio have little effect. These findings provide theoretical support for optimizing sidetracking design in ultra-deep wells.

1. Introduction

With the vigorous development of the petroleum industry, oil exploration and development have advanced into the ultra-deep strata. Compared to traditional shallow and medium-depth wells, ultra-deep wells encounter numerous complex challenges during the drilling process, such as a narrow safe density window for drilling fluids and poor wellbore stability [1,2].

The Deep Earth TK-1 well is located in Shaya County, within the hinterland of the Taklamakan Desert in the Xinjiang Uygur Autonomous Region. It is China’s first 10,000 m scientific exploration well, marking a major new breakthrough in the country’s series of deep earth exploration technologies and heralding the dawn of the “10,000 m era” for drilling capabilities.

Studies have shown that multiple deep wells have encountered wellbore instability problems under different complex geological conditions. For instance, in the SG3 well, formations below 8000 m are predominantly composed of biotite-gneiss with well-developed fractures, resulting in extremely complex geological conditions and frequent occurrences of instability [3]. Similarly, as shown in Figure 1, in the KTB well, sections at 6850–7300 m, 7490 m, and 7523 m exhibited abundant altered amphibolite and chlorite, leading to numerous weak planes in the formation that easily triggered breakouts. This well was ultimately drilled to a total depth of 9101 m [4,5]. Additionally, when the Jida-4 well penetrated the Sumsar Formation and the Hanabad-Rishton Formation, it encountered fragmented and fractured strata, causing severe breakouts and instability, with a final drilling depth of 6596 m [6,7]. Likewise, the Kuff well, while drilling through the Fiqa, Halul, and Thamama formations, encountered vuggy and fractured carbonate rocks, which also led to serious wellbore collapse and breakouts. The well was finally drilled to a depth of 6408 m [8,9].

To summarize, wellbore instability is a common issue in ultra-deep wells. When facing severe and complex instability, sidetracking often serves as a solution. Recent international research offers new insights: Marc Willerth et al. [10] quantified the economic costs of unplanned sidetracking, revealing that equipment loss and geological issues are primary triggers, emphasizing the importance of prevention for cost savings; Elshan Ismayilov’s [11] research indicates that engineering optimizations like dual-casing sidetracking, wellbore calibration, and ECD control can reduce non-productive time in slim-hole sidetracking; John Campbell et al. [12] improved the reliability of open-hole sidetracking through tool enhancements and innovative application of anchored cement systems; Marsel Akhmetov et al. [13] successfully executed sidetracking in eight wells by adopting rotary steerable systems (RSSs) and performance drilling motors (PDM) to optimize sidetracking initiation techniques, significantly boosting production and reducing non-productive time. These achievements provide valuable technical references for the sidetracking operations in the Deep Earth TK-1 well.

In addition to the engineering-oriented studies mentioned above, substantial progress has been made in numerical modeling of wellbore stability. The evolution of numerical models can be broadly categorized into four types based on their constitutive formulations and physical process coverage. The elastic model is the most fundamental approach. Assuming linear elastic behavior of rock, it solves the stress distribution around a circular hole subject to far-field in situ stresses [14,15]. Elastic models provide a computationally efficient first-order approximation for evaluating stress concentration and are widely adopted as the baseline for wellbore stability analysis. However, elastic models cannot capture plastic yielding and post-failure behavior near the wellbore. To address this limitation, elastoplastic models have been developed by incorporating failure criteria (e.g., Mohr–Coulomb, Drucker–Prager) and plastic flow rules, allowing for the simulation of plastic zone evolution and breakout growth [16]. The transition from elastic to elastoplastic formulations represents a major advancement in reproducing realistic wellbore failure geometries.

Recognizing that wellbore stability in deep and ultra-deep formations is influenced by multiple physical fields, thermo–hydro–mechanical (THM) coupled models have been proposed. These models integrate pore pressure diffusion, thermal stress induced by temperature gradients between drilling fluid and formation, and mechanical deformation. Fully coupled THM formulations, as well as thermo–poroelastic–plastic approaches, have been successfully applied to predict time-dependent wellbore behavior in high-temperature and high-pressure environments [17]. More recently, multi-field coupling has been extended to include chemical effects (THMC models), particularly for chemically active shale formations [18,19]. These advanced models offer high predictive accuracy but require extensive input parameters and significant computational resources.

Another emerging direction is the investigation of multi-well interference. While wellbore stability analysis has traditionally focused on isolated single wellbores, field operations increasingly involve adjacent wells in densely drilled fields, sidetracking from existing wellbore, and infill drilling. Previous studies on multi-well stress interaction have mainly addressed fracture propagation between parent and child wells in unconventional reservoirs [20]. However, systematic numerical investigations of stress interference between a collapsed original wellbore and a sidetracked wellbore—particularly the quantification of the “safe zone” along the maximum horizontal principal stress direction and its dependence on well spacing and breakout geometry—remain limited in the existing literature.

The present study fills this gap by establishing single- and dual-well numerical models using the finite element method. Targeting the specific ultra-deep, high-stress carbonate formation of the TK-1 well (fourth drilling section), this work quantifies the stress redistribution before and after the main wellbore collapse, identifies the “safe zone” for sidetracking along the maximum horizontal principal stress direction, and systematically analyzes the effects of well spacing and major-/minor-axis enlargement ratios of the collapsed wellbore on the stability of the sidetracked wellbore. Compared with advanced THM or elastoplastic formulations, the present elastic model offers a computationally efficient and physically transparent first-order approximation, which is particularly suitable for guiding field sidetracking designs where rapid parametric analysis is required. The findings provide direct theoretical support for optimizing sidetracking direction, controlling well spacing within the safe zone, and leveraging beneficial stress relief from the main wellbore collapse in ultra-deep well-drilling operations.

This study focuses on the wellbore instability encountered in the fourth drilling section of the TK-1 well. By integrating field operational parameters and employing finite element simulation, it analyzes the variations in stress field distribution before and after the instability of the main wellbore, as well as the stress interference effects on the sidetracked wellbore. The collapse mechanisms of both the main and sidetracked wellbores are elucidated, thereby providing a scientific theoretical basis for optimizing the drilling program.

2. Deep Earth TK-1 Well Multi-Bore Quadruple Drilling Operations

2.1. Geological Characteristics and Wellbore Trajectory

The drilling operations in the ultra-deep well TK-1 face extreme and harsh wellbore conditions characterized by ultra-deep depth, ultra-high temperature, ultra-high pressure, and high sulfur content—often summarized as the “three ultras and one high” [21,22,23]. This makes the well prone to complex downhole situations such as wellbore instability.

During the fourth drilling phase, the main borehole experienced severe instability, producing abundant cavings and leading to drill string failure. A sidetrack was initiated at ~9230 m from the main borehole wall, drilled along the maximum horizontal principal stress direction with inclination < 4.5° (Figure 2). The final center-to-center distance between the two boreholes reached 32.9 m (Figure 3).

2.2. Comparison of Drilling Parameters and Cuttings Characteristics

The original borehole used water-based mud (average ROP 2.05 m/h). The sidetracked borehole used water-based mud to 9416 m then switched to oil-based mud. Drilling efficiency deteriorated significantly after the switch (mechanical ROP fell from 2.54 to 0.65 m/h; Figure 4). Cuttings from the original borehole were mostly fragmented (<5% cleavage surfaces), whereas sidetrack cuttings exhibited cleavage features in >60% of samples (Figure 5).

2.3. Torque and Cavings Situation

Torque fluctuations in the original borehole were frequent and sustained (Figure 6a). In the sidetracked borehole, torque was largely stable at shallower depths but became fluctuating beyond ~9686 m (Figure 6b).

Analysis of field-cuttings returns revealed that the original wellbore predominantly yielded fragmented cuttings. Except for isolated depth intervals exhibiting minimal cavings, blocky and flaky cavings constituted 10–40% of the total cuttings volume as shown in Figure 7a. In contrast, the sidetracked wellbore primarily produced cleavage-featured cuttings, demonstrating the superior representative nature of the formations (Figure 7b). Throughout this interval, excluding reaming sections and sporadic zones, cavings remained minimal overall, with detailed data compiled in

Table 1. Overall development of rock debris falling from new wellbore.

Depth Interval/m	Cavings Condition	Primary Morphology
9416~9493	Sporadically observed 5–10% cavings content	Flaky
9493~9511	20–40% cavings content	Fragmented, Flaky
9511~9555	5~10% sporadically observed, 5–10% cavings content	Flaky
9555~9661	Cavings content increases to 15–20%	Flaky
9661~9685	Cavings content decreases below 5%	Flaky
9685~9723	Sporadically observed, 10–15% cavings content	Flaky, Fragmented
9723~9734	Cavings content decreases below 5%	Flaky
9734~9770	Cavings content increases to 10–15%; sporadic intervals with <5% content	Flaky, Blocky

.

2.4. Analysis of Logging Results from Sidetracked Wellbore

Caliper logs show five intervals: (1) 7856–9000 m: stable; (2) 9000–9230 m: small enlargement; (3) 9230–9416 m (water-based sidetrack): much lower enlargement than original borehole, confirming stress relief; (4) 9416–9700 m (oil-based): enlargement larger but still below original; (5) 9700–9889 m: good stability. Overall, sidetracking initially progressed smoothly, but as the well spacing increased, instability events (stuck pipe, hanging, top drive stalling) and cavings returns grew. Figure 8 shows the trend: complex conditions remain low at small spacings but rise markedly beyond a certain distance. Furthermore, during the sidetracking process, each drilling run exhibited a typical characteristic in torque fluctuation. When a new drill bit is first run in the hole, the drilling torque is relatively stable; after a certain period, torque fluctuation increases, which is analyzed as being an overall, namely, the sidetracked wellbore maintained stability and smooth drilling initially. However, as operations progressed, the distance between the new and original wellbores gradually exceeded the stress influence range. Subsequently, wellbore instability issues emerged, including stuck pipe, hanging, and top drive stalling, accompanied by a significant amount of cuttings returns. Figure 8, based on statistics of complex conditions in field sidetracked wellbores, reveals this trend. Therefore, numerical simulation is essential to investigate the influence of the mechanism of the main wellbore on the stability of the sidetracked wellbore, providing support for optimizing drilling design.

Due to minor bit damage leading to the loss of mechanical balance, drill string instability was induced, thus causing significant torque fluctuations.

3. Wellbore Stability Analysis in Single-Well Model

3.1. Single-Well Modeling and Solution

In this study, the fourth drilling section of the TK-1 well consists mainly of tight carbonate rocks with high brittleness. Under the short-term drilling conditions considered in this study, time-dependent effects are negligible, and prior to failure the rock primarily deforms elastically. So, the rock is treated as a homogeneous, isotropic, and linearly elastic material. Given the exclusion of time-dependent effects, the analysis is confined to static elasticity theory. Consequently, the solid mechanics module in COMSOL Multiphysics^® v. 6.4 is employed to numerically solve the problem via the finite element method, which proves suitable for addressing this linear problem [24,25,26].

1.

Initial and Boundary Conditions

The model’s initial state is assumed null, meaning that at the simulation onset, all variables remain static or in equilibrium states.

Within the scope of this study, the outer boundaries are defined as formation boundaries and remain constant throughout the investigation period. Along the X-axis direction, the model is subjected to the maximum horizontal in situ stress, while the minimum horizontal in situ stress acts along the Y-axis direction.

2.

Meshing

The model employs a free triangular mesh for discretization. To accurately capture the stress field distribution around the wellbore, mesh refinement is implemented in the near-wellbore region, as illustrated in Figure 9.

3.

Applicability and limitations of the 2D plane-strain elastic model.

The sidetracked wellbore in the TK-1 well has an inclination angle below 4.5° (see Section 2.1), making it nearly vertical. For vertical or near-vertical wellbores subjected to horizontal principal stresses, the stress distribution around the wellbore is essentially independent of the vertical coordinate, and the plane-strain condition is a standard and well-validated approximation in wellbore mechanics. Therefore, a 2D cross-section perpendicular to the wellbore axis suffices to capture the primary stress concentration and relief mechanisms. Previous work [27] shows that the 2D solution is the asymptote of the 3D solution, further validating the applicability of the 2D model for stress analysis away from discontinuities.

The linear elastic assumption, as justified above, is appropriate for the tight, brittle carbonate rocks of the fourth drilling section under short-term drilling conditions prior to failure. Time-dependent effects and thermal transients are negligible in this low-permeability formation. Due to the extremely low permeability, pore pressure diffusion is negligible over the short drilling exposure time; consequently, poroelastic effects on the stress field are not considered.

However, the following limitations should be recognized: (1) the model does not account for formation heterogeneity or well deviation beyond 5°; (2) thermo–hydro–mechanical (THM) coupling effects, which may become significant in highly permeable, ductile, or high-temperature formations, are omitted; (3) the elastic model cannot capture plastic-yielding or post-failure deformation. For the specific conditions of the TK-1 well, these simplifications are acceptable and provide a first-order quantitative understanding of stress redistribution. For highly deviated wells or long-term exposure, a full 3D or THM analysis would be required. Based on field data from the TK-1 primary wellbore and field geomechanical parameters (as shown in

Table 2. Geomechanical parameters of single-well model.

Parameter	Value/Unit
Wellbore Radius	0.12/m
Target Formation Depth	9530/m
Maximum Horizontal In Situ Stress	230/MPa
Minimum Horizontal In Situ Stress	200/MPa
Elastic Modulus	75/GPa
Poisson’s Ratio	0.2
Equivalent Circulating Density (ECD)	$1.46/\mathrm{g}\text{·}$cm−3
Gravitational Acceleration	$10/\mathrm{m}\text{·}$s−2

), a single-well model was constructed.

4.

Basic Parameters.

3.2. Pre-Failure Wellbore Stress Distribution

Contour maps of maximum principal stress, minimum principal stress, and principal stress difference distribution around the wellbore are plotted in Figure 10. The results indicate stress concentration along the direction of the minimum horizontal in situ stress (Y-axis), whereas stress relief occurs along the maximum horizontal in situ stress direction (X-axis). The peak stress difference around the wellbore reaches 256.27 MPa.

In response to the aforementioned phenomena, in-depth analysis is conducted on the stress components along both principal directions around the wellbore.

As shown in Figure 11, due to the formation of the main wellbore, stress release occurs along the direction of the maximum horizontal in situ stress in the formation—manifested as a stress level lower than the original in situ stress in the X-direction (as shown in Figure 11a)—while stress concentration occurs in the Y-direction, where the stress exceeds the original in situ stress (as shown in Figure 11b). Due to the stress release in the direction of maximum in situ stress and the stress concentration in the direction of minimum in situ stress, an area with a differential stress lower than the original stress difference forms around the wellbore (as shown in Figure 11c), which is referred to as the “safe zone,” as illustrated in Figure 11d.

Conversely, along the direction of the minimum horizontal in situ stress in the formation, stress concentration occurs in the X-direction (with stress higher than the original in situ stress) (as shown in Figure 12a), while stress release occurs in the Y-direction (with stress lower than the original in situ stress) (as shown in Figure 12b). Due to the stress release in the direction of the minimum in situ stress and the stress concentration in the direction of the maximum in situ stress, the differential stress around the wellbore is generally greater than the original stress difference (as shown in Figure 12c). Directional drilling along the orientation of the minimum in situ stress is more hazardous, as shown in Figure 12d.

3.3. Post-Failure Wellbore Stress Distribution

Following the wellbore collapse, the primary wellbore deforms from a circular to an elliptical shape, specifically exhibiting an increase in the wellbore radius along the minimum principal stress orientation. Contour maps of the maximum principal stress, minimum principal stress, and principal stress difference distribution around the wellbore are illustrated in Figure 13.

As shown in Figure 14, along the direction of the maximum horizontal in situ stress in the formation, after collapse, the maximum in situ stress is further released, manifested as a decrease in the principal stress along the short axis X-direction ( as shown in Figure 14a), while the minimum in situ stress becomes more concentrated, manifested as an increase in the principal stress along the short-axis Y-direction within a certain area ( as shown in Figure 14b). Therefore, the range of the “safe zone” increases (as shown in Figure 14c).

Simulation results demonstrate that a “safe zone” forms along the maximum horizontal in situ stress direction before and after wellbore collapse of the primary wellbore. Within this zone, sidetracking operations can be safely executed. However, as operations progress, the increasing inter-well distance eventually exceeds the safe zone boundaries. This leads to elevated differential stresses, triggering secondary wellbore instability—a phenomenon validated by field observations.

The single-well analysis above reveals that a “safe zone” exists along the maximum horizontal principal stress direction. However, in the field, the sidetracked wellbore is not isolated—it interacts with the pre-existing, collapsed main wellbore. To quantify this interaction and its dependence on well spacing and breakout geometry, a dual-well model is established in the following section.

4. Dual-Well Wellbore Stability Analysis

4.1. Dual-Well Modeling

Building upon the single-well model with unchanged geological parameters, boundary conditions, and fundamental assumptions, the primary wellbore is artificially deformed from circular to elliptical [28,29]. This elliptical approximation is based on caliper log observations from the collapsed TK-1 main wellbore, which show an approximately elliptical enlargement after failure, with the major axis aligned with the minimum horizontal principal stress direction.

The dual-well model employs a domain size that varies with the well spacing to maintain sufficient distance from the outer boundaries (typically >50 times the wellbore radius) and avoid boundary effects on the stress field. The left boundary is loaded with the maximum horizontal principal stress, and the lower boundary with the minimum horizontal principal stress. The upper and right boundaries are set as roller supports (zero normal displacement). Both the minor axis of the main wellbore and the radius of the sidetracked circular wellbore are 0.12 m. The main wellbore is artificially deformed into an elliptical shape according to specified major-axis and minor-axis enlargement ratios (see Section 4.2 and Section 4.3).

For meshing, a free triangular mesh is used. The near-wellbore regions are locally refined through COMSOL’s automatic adaptive mesh refinement to resolve high stress gradients, while the element size gradually increases toward the outer boundaries, as illustrated in Figure 15. This approach balances computational efficiency and numerical accuracy without requiring manually prescribed element sizes.

4.2. Post-Enlargement Wellbore Stress Distribution Along Major Axis

Under identical geological conditions, simulations are performed for wellbore stress distributions at major-axis enlargement rates of 50%, 80%, and 100% in the primary wellbore, while calculating the maximum stress difference around the sidetracked wellbore.

When the major-axis enlargement rate is 50% with a well-to-well distance of 2 m, the maximum stress difference around the sidetracked wellbore resembles that of the circular single-well model and subsequently stabilizes, as shown in Figure 16.

When the major-axis enlargement rate reaches 80% with a well-to-well distance of 3 m, the maximum stress difference around the sidetracked wellbore approximates that of the circular single-well model and subsequently stabilizes, as shown in Figure 17.

When the major-axis enlargement rate is 100% with a well-to-well distance of 3.5 m, the maximum stress difference around the sidetracked wellbore closely matches that of the circular single-well model and subsequently stabilizes, as shown in Figure 18.

Under varying major-axis enlargement rates, correlation curves between the maximum stress difference around the sidetracked wellbore and well-to-well distance were constructed for different spacing configurations, as shown in Figure 19.

As shown in Figure 19, under varying major-axis enlargement rates of the primary wellbore, the stress difference around the sidetracked wellbore initially increases then stabilizes with increasing well-to-well distance, ultimately approaching the stress difference of the circular single-well model. Critically, higher enlargement rates reduce stress differences in the sidetracked wellbore at identical well spacings, thereby delaying wellbore instability. Concurrently, larger enlargement rates diminish the far-field stress influence radius, enabling a shorter well-to-well distance to achieve the baseline circular single-well stress difference. This phenomenon expands the extent of the “safe zone”, validating that increased enlargement rates enhance drilling safety margins.

4.3. Post-Enlargement Wellbore Stress Distribution Along Minor Axis

Under identical geological conditions, simulations were conducted for wellbore stress distributions with the primary wellbore’s major-axis enlargement rate fixed at 100% and minor-axis enlargement rates at 50%, 70%, and 90% while calculating the maximum stress difference around the sidetracked wellbore.

Simulation results reveal that with the major-axis enlargement rate held constant, the maximum stress difference around the sidetracked wellbore converges to that of the circular single-well model at a well-to-well distance of 2.5 m across all tested minor-axis enlargement rates, subsequently stabilizing, as shown in Figure 20.

Under varying minor-axis enlargement rates, correlation curves between the maximum stress difference around the sidetracked wellbore and well-to-well distance were constructed for different spacing configurations, as shown in Figure 21.

As shown in Figure 21, under varying minor-axis enlargement rates of the primary wellbore, the stress difference around the sidetracked wellbore initially increases then stabilizes with increasing well-to-well distance, ultimately approaching the stress difference of the circular single-well model. However, unlike the effect of major-axis enlargement rates, variations in the minor-axis enlargement rate do not alter the influence radius on the far-field stress distribution.

4.4. Engineering Implications and Model Validation

The dual-well numerical results provide direct theoretical support for optimizing sidetracking design in ultra-deep wells, and their validity is verified by field observations from the TK-1 well.

First, the optimal sidetracking direction is clearly identified as the maximum horizontal principal stress direction, where a stress-relief “safe zone” exists with lower principal stress difference. Drilling along the minimum horizontal principal stress direction will lead to severe stress concentration and significantly increase wellbore instability risk.

Second, moderate collapse of the main wellbore has a beneficial effect on subsequent sidetracking. A larger major-axis enlargement ratio of the collapsed main wellbore reduces the far-field stress influence radius and expands the safe zone. In contrast, changes in the minor-axis enlargement ratio have a negligible effect on the stress distribution around the sidetracked wellbore.

Third, the quantitative safe zone criterion is established. The safe zone is defined as the region where the maximum principal stress difference around the sidetracked wellbore ($\Delta \sigma$) is less than that of a single isolated wellbore ($\Delta {\sigma }_{single}$). The critical well spacing $d_{crit}$ (distance at which $\Delta \sigma$ = $\Delta {\sigma }_{single}$) varies with the major-axis enlargement ratio: ~2.0 m for 50% enlargement, ~3.0 m for 80% enlargement, and ~3.5 m for 100% enlargement. Field observations (Figure 8) show that complex conditions became pronounced at approximately 4 m, which is slightly larger than the simulated values. This discrepancy is expected due to model simplifications, but the overall trend of “stability at small spacings and instability beyond a threshold” is fully consistent, validating the safe zone concept at a semi-quantitative level.

5. Conclusions

1. A stress-relief “safe zone” develops along the maximum horizontal principal stress direction. After the main wellbore collapse (enlargement along the minimum stress direction), this zone expands, providing a more favorable stress environment for sidetracking ($\Delta \sigma$ < $\Delta {\sigma }_{single}$).

2. Significant stress interference exists between the main wellbore and the sidetracked wellbore. The maximum stress difference around the sidetracked wellbore increases with well spacing and eventually approaches that of a single isolated wellbore. Larger major-axis enlargement ratios reduce the far-field stress influence radius, allowing safe sidetracking at closer distances.

3. The following engineering guidelines are proposed for ultra-deep well sidetracking operations: (1) sidetrack along the maximum horizontal principal stress direction to utilize the stress-relief effect; (2) keep the well spacing within the safe zone to retain the beneficial stress interference from the main wellbore; (3) a moderately collapsed main wellbore is advantageous as it enlarges the safe zone, while changes in the minor-axis enlargement ratio can be neglected.

4. The 2D plane-strain elastic model adopted in this study is suitable for near-vertical, tight, brittle carbonate formations under short-term drilling conditions. However, several limitations should be noted: (1) the model does not account for thermos–hydro–mechanical-chemical (THMC) coupling effects, which may explain the discrepancy between the predicted expanded safe zone and the observed drop in ROP after switching to oil-based mud; (2) the 2D approximation is reasonable for the safe-zone range (2–4 m) but cannot fully capture the 3D geometry near the sidetrack window; (3) the study uses a relative definition of the safe zone based on the collapsed single wellbore, without incorporating a failure criterion to provide quantitative factors of safety. Future work will extend parametric analysis to include in situ stress ratio, elastic modulus, wellbore diameter and formation anisotropy, and incorporate a suitable failure criterion with measured strength parameters to generalize the quantitative criteria to a wider range of ultra-deep well conditions.