Dynamic Response Mechanism and Risk Assessment of Threaded Connections During Jarring Operations in Ultra-Deep Wells

Abstract

With the frequent occurrence of stuck pipe incidents during the ultra-deep well drilling operation, the hydraulic-while-drilling (HWD) jar has become a critical component of the bottom hole assembly (BHA). However, during jarring operations for stuck pipe release, the drill string experiences severe vibrations induced by the impact loads from the jar, which significantly alter the stress state and dynamic response of the threaded connections—the structurally weakest elements—under cyclic dynamic loading, often leading to fracture failures. here, a thread failure incident of a hydraulic jar in an ultra-deep well in the Tarim Basin, Xinjiang, is investigated. A drill string dynamic impact model incorporating the actual three-dimensional wellbore trajectory is established to capture the time-history characteristics of multi-axial loads at the threaded connection during up and down jarring. Meanwhile, a three-dimensional finite element model of a double-shouldered threaded connection with helix angle is developed, and the stress distribution of the joint thread is analyzed on the boundary condition acquired from the time-history characteristics of multi-axial loads. Numerical results indicate that the axial compression induces local bending of the drill string during down jarring, resulting in significantly greater bending moment fluctuations than in up jarring and a correspondingly higher amplitude of circumferential acceleration at the thread location. Among all thread positions, the first thread root at the pin end consistently experiences the highest average stress and stress variation, rendering it most susceptible to fatigue failure. This study provides theoretical and practical insights for optimizing drill string design and enhancing the reliability of threaded connections in deep and ultra-deep well drilling.

1. Introduction

As a critical tool that can be directly connected to the drill string, the while-drilling jar has become an essential component of drill string systems in deep and ultra-deep wells. This tool can effectively address complex situations such as a stuck pipe encountered during drilling by applying instantaneous impact loads upwards or downwards [1,2]. However, due to its unique impact excitation working mechanism, the wellbore drill string will experience intense vibration and be subjected to complex alternating loads under impact loading during jarring for stuck pipe freeing operations. At this time, the threaded connections, being the weakest link in the wellbore drill string, experience even more complex stress states. In particular, the connection threads between the drilling jar and the drill string are more prone to fatigue cracking or even fracture under sustained impact excitation and alternating loads, severely limiting the efficiency and reliability of drilling jarring for stuck pipe freeing and drilling operations [3,4]. Therefore, in-depth research on the force characteristics and failure mechanisms of connection threads during jarring for stuck pipe freeing is of significant engineering importance for improving the safety and operational efficiency of deep and ultra-deep well drilling operations.

To further investigate the vibration and impact behavior of the drill string in the wellbore during drilling, Luciano P. P. de Moraes et al. [5] developed a four-degree-of-freedom, non-smooth coupled vibration model. They systematically modeled the multi-modal response in the wellbore, revealing the influence of different vibration modes on the dynamic characteristics of the drill string. Xie et al. [6] based on the geometric characteristics of variable cross-section drill strings, established an acoustic wave parameter transfer matrix model applicable to cylindrical and conical section rods. This model characterized the spatial distribution of the drill string’s vibration response from a wave propagation perspective. Chen et al. [7] proposed a fatigue damage model coupling drill string vibration behavior with the sticking point release process, analyzing the dynamic response patterns of the drill string under different excitation load amplitudes and frequencies. Li et al. [8] developed a memory-type vibration monitoring device integrated with a triaxial accelerometer. They found that the impact vibration generated during drill string rotation and stick-slip is closely related to the working state of torsional impactors and while-drilling jars. Guo et al. [9], based on the working principle of torsional impactors, systematically analyzed the control effect of impact tools on the drill string’s vibration response. To address the difficulty in accurately obtaining impact forces due to high jarring frequencies and short load durations during stuck pipe freeing operations, Kenneth R. Newman et al. [10] proposed a finite element method-based impact force calculation model for while-drilling jars, significantly improving the prediction accuracy of impact force time-history characteristics. Bu et al. [11], based on one-dimensional wave theory, studied the propagation behavior of impact waves within the drill string excited by acoustic wave vibrators. They pointed out that stress peaks generated by excitation resonance are one of the key factors inducing fatigue damage in connection threads. Mou et al. [12] employed a combined experimental and finite element approach to design a drill string vibration load acquisition device, enabling thread fatigue life prediction analysis.

During deep and ultra-deep well drilling, connection threads are prone to failure due to severe impact and complex loads. Di et al. [13] found that unreasonable drill string assemblies can cause strong impacts between the drill string and the wellbore, resulting in significant bending moments at the thread connections, which become the main cause of thread damage. To mitigate thread back-off during stuck pipe freeing operations, Chaouki Boufama et al. [14] suggested placing the while-drilling jar between the drill collar and heavy-weight drill pipe, which can effectively reduce bending moment loads by approximately 40%. Lin et al. [15] established a two-dimensional axisymmetric finite element model of a double-shouldered thread joint under combined loads and developed software with elastoplastic analysis capabilities. Cao et al. [16] studied the dynamic response of threads under different excitation loads based on Timoshenko beam theory and the finite element method. Zhang et al. [17] improved the Hopkinson tensile bar technique based on the stress wave reflection method, achieving controllable cyclic loading under impact fatigue of thread fasteners. They found that the fatigue life is closely related to the loading stress amplitude. To clarify the mechanical properties of threads under impact loads, Wang et al. [18] proposed using double-shouldered thread joints instead of conventional API single-shoulder structures to suppress thread damage induced by impact torque, by establishing the relationship between equivalent impact torque and thread crest slippage. This approach was successfully applied in China’s first Ten-thousand-meter well, SDTK-1. Lin et al. [19] compared the fatigue life of double-shouldered threads and standard API threads under multiaxial alternating loads, finding that the former’s life can be up to 30 times that of the latter under the same loads. Yu et al. [20] proposed enhancing connection strength by reducing thread taper and increasing the contact area of the secondary shoulder, while Ben Amir et al. [21] pointed out that increasing tooth height and tooth number helps to mitigate local deformation caused by stress waves. Considering the influence of thread structure asymmetry and contact state, Yang [22] established a three-dimensional nonlinear finite element model including the meshing section and the retraction groove, revealing the significant effect of the transition fillet and structural discontinuities of the double-shoulder structure on shoulder stress and contact pressure distribution.

Despite extensive research conducted on the vibration response of drill strings and the mechanical properties of connection threads over the past decades, a thorough and systematic understanding of the mechanical evolution characteristics and failure mechanisms of connection threads under impact dynamic loads during jarring for stuck pipe freeing is still lacking. Prior to jarring operations, the driller typically induces an initial axial preload in the drill string through lifting or lowering operations [23]. During jarring for stuck pipe freeing, the drill string undergoes severe axial impacts within the wellbore, leading to intense vibration. Under the combined action of various dynamic alternating loads, the stress state and response characteristics of the connection threads change significantly. To address this challenge, we take a thread failure incident of a hydraulic jar in an ultra-deep well in the Tarim Basin as the engineering background. A transient finite element dynamic impact model of the drill string during the jarring process is established, incorporating the actual three-dimensional wellbore trajectory, to systematically analyze the force response characteristics of the drill string in the connection thread region. Then, based on the dynamic loads in this region during jarring used as boundary conditions, a three-dimensional dynamic analysis model of a double-shouldered threaded connection with a helix angle is developed to study its stress evolution mechanism under combined axial tension or compression impact and bending moment, and to predict potential failure locations and risk levels. The results of this study provide theoretical support and engineering references for the safety assessment of wellbore tubular structures and optimization of thread connections during deep and ultra-deep well drilling and workover operations.

2. Operating Principle of While-Drilling Jarring Tools

According to the jarring operation procedure and the structural characteristics of the while-drilling jar [24], the process can be divided into four stages: initial state, energy storage, pressure release, and instantaneous impact, as illustrated in Figure 1. When the axial load reaches the trigger threshold for up or down jarring, the while-drilling jar initiates the energy storage. During this process, hydraulic fluid in the cylinder can only flow from the upper chamber to the lower chamber through the throttling valve orifice in the piston, while the drill string above and below the jar begins to accumulate elastic potential energy. When the mandrel passes the top of the sealing ring, the high-pressure fluid in the large chamber rapidly discharges into the small chamber, instantly releasing the accumulated elastic potential energy in the drill string at both ends and converting it into kinetic energy of the piston. As the upper and lower pistons jar, a huge impact force will be generated at the collision position of the pistons. The hydraulic shell of the impact device and the lower drill string will acquire kinetic energy due to the impact behavior of the upper and lower pistons. This kinetic energy will be transmitted along the drill string to the stuck point, thereby achieving the effect of freeing.

3. Dynamic Model of Drill String in the Stuck Pipe Freeing Process

To investigate drill string vibration and impact loading during the jarring process, the following assumptions are made:

(1)

The drill string undergoes linear elastic deformation during both upward and downward jarring operations.

(2)

The drill string is initially aligned with the wellbore trajectory.

(3)

The specific internal configuration of the jar is disregarded, and it is simplified as a regular annular component.

(4)

With the jar as the central point, the drill string is divided into up and down sections.

(5)

Only longitudinal vibration of the drill string is considered.

(6)

The loss of energy, such as heat and sound energy, caused by the shock is not considered.

During stuck pipe freeing operations using a while-drilling jar, the drill string in the wellbore will experience significant vibration under impact loading. Figure 2 shows the forces acting on an arbitrary differential element of the drill string in the wellbore during jarring for stuck pipe freeing. As shown in the figure, the drill string in the wellbore (assuming wellhead and sticking point locations) will be subjected to external loads such as gravity, fluid pressure, elastic restoring force, and impact load [25]. Combining these forces with D’Alembert’s principle, the differential equation of drill string vibration can be expressed as:

$$\mathsf{\rho }Adx{\displaystyle \frac{{\partial }^{2}u}{\partial t^2}}=\left(\mathrm{E}A{\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial }{\partial x}}(\mathrm{E}A{\displaystyle \frac{\partial u}{\partial x}})dx\right)+\mathsf{\rho }\mathrm{g}Adx-Pdx-\mathrm{E}A{\displaystyle \frac{\partial u}{\partial x}}-\xi {\displaystyle \frac{\partial u}{\partial t}}dx$$

(1)

where $\rho$ is the density of the drill string material; A is the cross-sectional area of the drill string; u is the displacement; E is the elastic modulus; g is the acceleration due to gravity; $\xi$ is the viscous friction drag coefficient; P is the drilling fluid pressure.

During the drill string vibration process, energy dissipation and vibration attenuation occur due to factors such as wellbore fluid, geometric structure, and material properties. These effects lead to a gradual reduction in the amplitude and intensity of the drill string vibration over time. To comprehensively account for these damping effects, the drill string damping coefficient ξ can be considered as:

$$\xi ={\displaystyle \frac{2\mathsf{\pi }\mu \lambda }{{\rho }_{\mathrm{q}}{A}_{\mathrm{q}}\ln (D_{\mathrm{w}}/2R_{\mathrm{oq}})}}$$

(2)

Equation (1) can be simplified as

$$\mathsf{\rho }Adx{\displaystyle \frac{{\partial }^{2}u}{\partial t^2}}={\displaystyle \frac{\partial }{\partial x}}(\mathrm{E}A{\displaystyle \frac{\partial u}{\partial x}})dx+\mathsf{\rho }\mathrm{g}Adx-\xi {\displaystyle \frac{\partial u}{\partial t}}dx-Pdx$$

(3)

where μ is the dynamic viscosity of the drilling fluid; $\lambda$ is the damping increase coefficient due to drill string eccentricity; $D_{\mathrm{w}}$ is the borehole diameter; $R_{\mathrm{oq}}$ is the outer radius of the drill string;

Combining the damping coefficient ξ, the final longitudinal vibration equation of the drill string, as derived from Equation (3), can be written as:

$$\mathsf{\rho }Adx{\displaystyle \frac{{\partial }^{2}u}{\partial t^2}}={\displaystyle \frac{\partial }{\partial x}}(\mathrm{E}A{\displaystyle \frac{\partial u}{\partial x}})dx+\mathsf{\rho }\mathrm{g}Adx-{\displaystyle \frac{2\mathsf{\pi }\mu \lambda }{\mathsf{\rho }A\ln \left(D/2R\right)}}{\displaystyle \frac{\partial u}{\partial t}}dx-Pdx$$

(4)

The initial conditions can be established as

$$\left\{\begin{array}{l}\mu \left(x,0\right)=0\\ {\displaystyle \frac{\partial \mu \left(x,0\right)}{\partial t}}=0\end{array}\right.$$

(5)

The boundary conditions can be obtained as

$$\left\{\begin{array}{l}{\left.{\displaystyle \frac{\partial \mu \left(x,t\right)}{\partial x}}\right|}_{x=0}=0\\ {\left.{\displaystyle \frac{\partial \mu \left(x,t\right)}{\partial x}}\right|}_{x=L}=0\end{array}\right.$$

(6)

By Equations (5) and (6) into Equation (4), the impact force of the drilling jar can be calculated as.

$$F_D={\left.EA{\displaystyle \frac{\partial u}{\partial x}}dx\right|}_{x=L}$$

(7)

4. Dynamic Mechanical Model of Threaded Connections

4.1. Torque Strength of Threaded Connection

Since the connection threads of the drilling jar utilize double-shoulder biased trapezoidal special threads, their torsional strength is associated with material properties, connection dimensions and types, pitch, taper, as well as the friction coefficients of the mating surfaces, threads, and shoulders [26]. Based on the mathematical model for calculating torsional strength theory recommended by API standard RP7G, the formulas for calculating the torsional strength of the external shoulder and the internal shoulder are presented as follows, respectively:

$$T^{\prime }={\displaystyle \frac{Y_{\mathrm{m}}A}{12}}(R_{\mathrm{s}}f+{\displaystyle \frac{R_{\mathrm{t}}\mu }{\cos \theta }}+{\displaystyle \frac{p}{2\mathsf{\pi }}})$$

(8)

$$T^{″}={\displaystyle \frac{Y_{\mathrm{m}}{A}_{\mathrm{s}}}{12}}({\displaystyle \frac{P}{2\mathsf{\pi }}}+{\displaystyle \frac{R_{\mathrm{t}}\mu }{\cos \theta }}+{\displaystyle \frac{{R^{\prime }}_{\mathrm{s}}\mu }{\cos \alpha }})$$

(9)

where T’ is the make-up torque strength on the external shoulder, N mm; T” is the make-up torque strength on the inner shoulder, N mm; Y_m is the material yield strength, MPa; A is the minimum cross-sectional area at the root of the external and internal threads of the external shoulder, mm²; R_s is the average radius of the external shoulder, mm; μ is the coefficient of friction, dimensionless; R_t is the average radius at the mid-point of the thread, mm; θ is the half-angle of the thread profile, degrees; p is the thread pitch, mm; A_s is the cross-sectional area at the pin nose, mm²; R’_s is the average radius of the inner shoulder, mm.

And the total torque strength of the double-shoulder thread on the drill pipe is:

$$T=T^{\prime }+T^{″}$$

(10)

where T is the total make-up torque of the double-shoulder thread, N mm.

4.2. Mechanical Governing Equations and Finite Element Discretization

During stuck pipe freeing operations, the connection threads of the drilling jar will be subjected to transient impacts and complex alternating loads. Therefore, to more accurately reflect the dynamic behavior of the connection threads of the drilling jar, it is necessary to employ finite element control equations for solution and computation. The governing equations are as follows:

$${\displaystyle \underset{v}{\iiint }{\sigma }_{ij}}\delta {\epsilon }_{ij}\mathrm{d}v={\displaystyle \underset{s}{\iint }{x}_i}\delta u_i\mathrm{d}s$$

(11)

where ${\sigma }_{ij}$ is the Cauchy stress tensor; $\delta {\epsilon }_{ij}$ is the virtual strain tensor; $x_i$ is the load vector per unit surface; $\delta u_i$ is the virtual displacement; s is the surface area, m²; v is the volume, m³.

Based on finite element discretization, the virtual displacement $\delta u_i$ and virtual strain tensor $\delta {\epsilon }_{ij}$ in the above equation, can be expressed as:

$$\delta u_i={\displaystyle \sum _I{N}_I}\delta u_{Ii}$$

(12)

$$\delta {\epsilon }_{ij}={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{\partial \delta u_i}{\partial x_j}}+{\displaystyle \frac{\partial \delta u_j}{\partial x_i}}\right)$$

(13)

where $N_I$ is the shape function; $u_I$ is the nodal displacement.

Substituting the discretized equations above into the governing equation yields the dynamic equilibrium equation:

$$\mathrm{M}\ddot{u}+\mathrm{C}\dot{u}+\mathrm{K}u=\mathrm{F}$$

(14)

where $\ddot{u}$ is the nodal acceleration vector; $\dot{u}$ is the nodal velocity vector; M is the mass matrix; C is the damping matrix; K is the stiffness matrix; F is the nodal load vector.

Subsequently, the explicit dynamics formulation employs the central difference method to derive the recursive expressions for velocity and acceleration:

$${\ddot{u}}_n={\mathrm{M}}^{-1}\left({\mathrm{F}}_n-\mathrm{C}{\dot{u}}_{n-{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}-\mathrm{K}{u}_n\right)$$

(15)

$${\dot{u}}_{n+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}={\dot{u}}_{n-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+\Delta t_n{\ddot{u}}_n$$

(16)

5. Numerical Simulations

5.1. Simulation Model

Based on what was explained in previous sections, an analysis is conducted on the dynamic characteristics of connection threads during jarring operations in an ultra-deep well located in the Tarim Basin, China. According to the drilling report, a stuck pipe incident occurred when the drilling depth reached 8118 m, and the drill string was made of carbon steel with steel grade S135. Therefore, the driller adopted continuous jarring operations using a while-drilling hydraulic jar by Gaofeng Hydraulic Drilling Jar, Guizhou, China, to free the stuck tools. to free the stuck tools. However, during this process, the threaded connection at the lower end of the jar failed. It was observed that the external thread of the jar connection had fractured at the first engaged thread near the primary shoulder. The photograph of the threaded connection fracture is shown in Figure 3. Combined with the fractographic analysis of the fracture surface, it was revealed that the fracture exhibited distinct features of crack initiation and propagation, followed by a clearly defined plastic tearing zone in the later stage of failure. These characteristics collectively indicate that the threaded connection failed due to fatigue-induced damage.

Based on the finite element explicit integration algorithm, a dynamic impact model of the drill string, considering the actual three-dimensional wellbore trajectory, was established to capture the time-history characteristics of multiaxial loads acting on threaded connections during jarring operations, as shown in Figure 4. In the modeling process, axial displacement constraints were first applied to the upper and lower impact hammers of the jar, while axial loads F Top and F Bot were applied at the wellhead and sticking point, respectively, so that the axial forces at both ends of the jar gradually reached the trigger load. Under these conditions, the drill string in the wellbore deformed progressively and accumulated elastic strain energy, manifesting as tensile deformation during up-jarring and compressive deformation during down-jarring. Once the axial load at the jar reached the triggering threshold, the displacement constraints at the impact hammers and the axial loads at the wellhead and sticking point were immediately released, while the drill string at the wellhead and sticking point was kept fixed in position. Consequently, the stored elastic energy in the drill string was rapidly released, driving the relative motion of the upper and lower pistons of the jar and eventually producing an impact load through piston-to-piston contact. To further investigate the dynamic characteristics of the threaded connections, a three-dimensional finite element model of a double-shoulder threaded connection with a helical angle was developed. Boundary conditions were derived from the multiaxial load histories obtained in the jarring process, and the stress distribution within the connection threads was analyzed. In the modeling, a point-to-surface coupling method was used to connect the upper and lower surfaces of the pin and box threads to coupling points, with the lower coupling point fixed and a rated make-up torque applied to the upper coupling point through a smooth loading scheme. The time-varying axial force and bending moment of the drill string at the fracture location during jarring were then imposed on the coupling point to capture the dynamic response of the threads under variable loads.

To improve computational efficiency and model convergence, the drill string was modeled using Beam31 elements, while the jar was simplified as two solid cylinders discretized with C3D8R solid elements. In addition, random contact formulations were employed to account for both the stochastic interactions between the drill string and the wellbore wall during jarring and the dynamic contact along the thread engagement surfaces, thereby reproducing the realistic contact behavior during impact. The parameters of the finite element model are listed in

Table 1. The parameters of the finite element model.

Parameter	Yield Strength of Drill Pipe Body (MPa)	Friction Coefficient Between Drill String and Casing	Friction Coefficient Between Drill String and Wellbore
Value	931	0.25	0.35
Parameter	Yield strength of threaded section (MPa)	Make-up torque (kN·m)	Thread friction coefficient
Value	827.58	18	0.08

.

5.2. Simulation Result

5.2.1. Stress Analysis of Threaded Connections During Make-Up Process

Combining the make-up torque of the drilling jar connection threads and employing a smooth amplitude application method similar to the sine curve, the stress distribution contours under different make-up torques are obtained, as shown in Figure 5. It can be seen from the figure that, as the make-up torque gradually increases, the threaded structure exhibits a significant axial displacement. Furthermore, the external shoulder engagement surface of the threads makes initial contact and exhibits a pronounced stress concentration phenomenon. When the make-up torque is 10 kN·m, the maximum Mises stress in the threaded connection reaches 710.82 MPa. However, at this point, the internal shoulder of the thread has not yet made contact, and a significant gap remains. When the make-up torque reaches its rated make-up torque of 18.4 kN·m, a distinct high-stress region is generated in the stress relief groove of the box thread near the external shoulder. The maximum stress is 831.18 MPa, exceeding the material’s yield strength of 827.58 MPa, indicating that the region has locally entered a plastic state. However, compared to the overall structure, the plastic region is limited only to structural protrusions such as the tips of some thread crests, and the overall thread structure remains in a safe condition.

Figure 6 illustrates the Mises stress distribution contours of the drill string connection threads under the rated make-up torque. As shown in the figure, the stress distribution in the thread exhibits a distinct gradient under the applied make-up torque. The high-stress regions in the pin thread are primarily concentrated at the external shoulder corner and the first two thread turns near the larger end, with a maximum Mises stress of 726.36 MPa. In contrast, the high-stress regions in the box thread are primarily distributed within the stress relief groove adjacent to the external shoulder, and localized plastic damage has occurred in certain areas. In comparison, the thread flanks and engagement surfaces near the internal shoulder exhibit significantly lower stresses. This indicates that the external shoulders of the double-shoulder threads bear the primary sealing function under the applied make-up torque.

5.2.2. Dynamic Response of the Drill String During Jarring Operations

Based on the force state of the drill string and the location of the stuck point within the wellbore, drilling jarring operations during stuck pipe freeing operations can be categorized into up jarring and down jarring scenarios. To analyze the load behavior of the connection thread location under these two scenarios, Figure 7 shows the time-dependent variations in axial force and bending moment at the drill string’s coupling point coinciding with the connection thread location during the up and down jarring processes, respectively. As shown in Figure 7, approximately 63.8 ms after the instantaneous release of the jarring hydraulic pressure as the jar’s upper and lower pistons make impact contact, the axial force at the connection thread location rapidly increases, reaching a maximum value of 675.01 kN at approximately 115 ms. As the axial impact load propagates gradually along the drill string towards both ends, the axial load at the connection thread location gradually stabilizes. During this process, under the influence of the axial impact load, the wellbore drill string undergoes significant vibration, causing substantial fluctuations in the bending moment at the connection thread location. Specifically, when the axial impact load reaches its maximum value, the bending moment at this location in the drill string also reaches its maximum in the X-direction, with a magnitude of 9.21 kN·m. The bending moment in the Y-direction subsequently reaches its maximum value (−5.28 kN·m) at 143 ms. It is worth noting that because the drill string within the wellbore is under tension during the up-jarring operation, significant instability phenomena such as buckling do not occur. Instead, the wellbore drill string primarily undergoes bending deformation along the wellbore trajectory. This explains why the magnitude of the bending moment variations at the connection thread location is relatively small during up-jarring stuck pipe freeing operations.

Figure 8 illustrates the time-dependent curves of axial force and bending moment at the drill string’s connection thread location during down jarring for stuck pipe freeing operations. As shown in the figure, the upper and lower pistons of the drilling jar make impact contact 118 ms after hydraulic release, generating an axial compressive load of 475.67 kN. Concurrently, the bending moment at this drill string location reaches its maximum value of 8.15 kN·m in the Y-direction. As the axial impact load propagates gradually along the drill string towards both ends, the axial load at the connection thread location experiences significant oscillatory attenuation, and the bending moment in the drill string fluctuates substantially.

Compared to up-jarring operations, down-jarring typically requires the driller at the wellhead to lower the drill string to pre-compress the jar axially to meet the trigger conditions. Consequently, in addition to bending deformation along the wellbore trajectory, the drill string is highly susceptible to localized buckling and instability deformation under the axial compressive load. This results in a significantly increased amplitude of bending moment fluctuations at the connection thread location, leading to a more complex stress state in the structure. The bending moment variations are more pronounced in the Y-direction compared to the X-direction, indicating that the buckling phenomenon in the drill string due to the axial compressive load is more severe in the Y-direction.

5.2.3. Dynamic Evolution Characteristics of Connection Threads

Figure 9 shows the stress distribution contours of the connection threads at different time instances during up and down jarring for stuck pipe freeing operations. The X and Y directions in Figure 7 and Figure 8 correspond to the coordinate system in Figure 9, where the X direction represents the lateral direction. As shown in Figure 9, a distinct stress concentration phenomenon consistently exists near the external shoulder of the connection threads during the jarring process. However, because the axial load and bending moment continuously fluctuate over time, the stress response of the threads exhibits significant dynamic characteristics, particularly in the first two thread turns at the large end of the male thread, where the Mises stress varies more drastically with time. Specifically, at 115 ms after hydraulic release, the Mises stress on the thread crests at the left end (positive X-direction) of the connection thread is generally higher than that on the right end (negative X-direction). As the load changes, the stress distribution state in the threads reverses at 143 ms, at which point the thread crest stress on the negative X-direction is higher than that on the left end. Compared to up jarring operations, the stress difference between the two ends of the connection thread is more significant during down jarring, indicating that the thread connection experiences more severe alternating loads during down jarring operations as the drill string undergoes compressive bending and drastic changes in bending moment.

Figure 10 shows the time-dependent fluctuation curves of the circumferential acceleration at the pin thread coupling point during up and down jarring processes. As observed from the figure, following the instantaneous release of hydraulic pressure, which causes a sudden decrease in the external load on the drill string at the connection thread location, the force state of the threaded connection experiences a drastic change. This, in turn, leads to a significant increase and pronounced fluctuations in the circumferential acceleration at this location. Combining this with Figure 7 and Figure 8, it can be seen that during the jarring process, the drill string at the connection thread location undergoes severe axial impact loads and bending moment variations, causing the connection threads to exhibit complex dynamic response characteristics. Particularly in the down-jarring scenario, the wellbore drill string is more prone to compressive buckling and localized instability under the action of circumferential compressive loads. This results in a significantly higher amplitude of circumferential acceleration fluctuations at the thread coupling point compared to up-jarring operations. Furthermore, during up-jarring operations, the peak circumferential acceleration at this coupling point occurs at 115.1 ms after jarring release, with a value of 0.338 m/s². In contrast, during downward jarring operations, the peak occurs at 118.3 ms, with a value of 0.3 m/s², both of which are consistent with the time-dependent patterns of external load changes on the wellbore drill string

As the magnitude and direction of the resultant force on the connection threads fluctuate during jarring due to changes in the bending moment in the X and Y directions of the drill string at the connection location, the stress concentration regions on the threads vary constantly at different jarring time instances. Therefore, to investigate the force characteristics of the thread crests during jarring for stuck pipe freeing operations, with the X and Y directions as reference, the average Mises stress of each pin thread crest along the path in the positive and negative X and Y directions was extracted during up and down jarring, as shown in Figure 11. As observed from the figure, under the influence of the make-up torque, the Mises stress of the pin thread crests in different orientations exhibits a trend of being large at both ends and small in the middle during jarring. Compared to other thread crests, the Mises stress at the external shoulder and the first three thread crests of the pin thread in different orientations is significantly higher. This indicates that during jarring for stuck pipe freeing operations, the high-stress region of the pin thread is consistently located at the thread crests near the external shoulder; that is, this region represents a potential thread failure risk point.

6. Connection Thread Failure Risk Assessment and Discussion

Mises stress at the center nodes corresponding to the thread root and thread crest of the thread crests near the pin thread external shoulder were selected to conduct a comparative analysis of the connection thread risk locations during up and down jarring, as shown in Figure 12. As observed from the figure, compared to other locations, the innermost point corresponding to the first thread root of the pin thread exhibits the highest average stress and stress variation amplitude during both up and down jarring operations. Specifically, during up-jarring operations, the maximum Mises stress at this node is 709 MPa, the average stress is 606 MPa, and the stress variation amplitude is 347 MPa. During down jarring operations, the average stress is 557 MPa, and the stress variation amplitude is 220 MPa. This indicates that the first thread root of the pin thread is more susceptible to fatigue failure than other thread crests.

7. Conclusions

In this paper, a drill string dynamic impact model incorporating the actual three-dimensional wellbore trajectory is developed to investigate the time-history characteristics of multi-axial loads at the threaded connection during upward and downward jarring. Subsequently, a three-dimensional finite element model of a double-shouldered threaded connection with helix angle is constructed, and the stress distribution of the joint threads is analyzed using boundary conditions derived from the multi-axial load histories. Simulation results show that under impact loading, the drill string undergoes pronounced vibrations during up and down jarring operations, resulting in significant fluctuations in bending moments. Notably, during the down-jarring operation, the axial compressive loads induce local bending of the drill string, leading to substantially greater bending moment variations at the threaded connection compared to upward jarring. This, in turn, causes more pronounced stress differentials and circumferential acceleration fluctuations across the threaded ends during downward impacts.

Furthermore, under axial dynamic loading, high-stress regions consistently occur near the external thread shoulder and the adjacent thread roots. Among these, the first thread root at the pin end exhibits the highest average stress and the largest stress fluctuations, making it highly prone to crack initiation and fatigue failure during jarring operations. Therefore, after completing operations, non-destructive testing (NDT) of the threaded connections should be conducted promptly to identify any potential cracks, thereby preventing fractures during subsequent jarring operations.