Physicochemical and Vibration Analysis of Christmas Tree Four-Way Flange Failure under Fracturing Process

School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China PetroChina Southwest Oil and Gasfield Company, Chengdu 610500, China HSE Quality Surveillance & Inspection Research Institute, CNPC Chuanqing Drilling Engineering Company Limited, Guanghan 613800, China Drilling and Production Engineering Technology Institute of CNPC Chuanqing Drilling Engineering Co. Ltd., Guanghan 613800, China


Introduction
Wellhead gas tree cross is an important wellhead equipment. It consists of main gate, cross flange, tubing gate, needle valve, pressure measuring gate, and casing gate. It is used to open and close the well and adjust the pressure. e main devices for operations such as gas volume, circulating well killing, down-pressure gauge pressure measurement, and wellhead pressure measurement are key safety pressure-bearing components that have failed repeatedly. e site urgently needs to obtain the failure mechanism and propose countermeasures. Krishna et al. [1] established a finite element model for bolted flange joints. e loading and unloading characteristics of the gaskets were obtained through experiments. e analysis showed that the distributed contact stress has a greater impact on the sealing performance than the flange specified by ASME rotation limit. Zhang et al. [2] studied the fracture of the four-way flange of the gas production tree at the KQ 65 wellhead through mechanical property testing and metallographic analysis and concluded that the fracture failure of the KQ65 wellhead production tree was caused by coupling effect of brittle microstructure and local stress concentration. Navas [3] and others used physical and chemical analysis, SEM-EDX analysis, and other analytical methods to study the erosion failure occurred in the wellhead choke. Circumferential channel creates a leak. Chen et al. [4] used SEM, EDS, tensile test, and fracture mechanics methods to carry out a case study on the failure of steam pipeline assembly equipment in a chemical plant, revealing and discussing the causes of failure, fracture mechanism, and failure mode. e fatigue life of mounting flange bolts was predicted. Tafreshi and Dover [5] used the finite element method to analyze the stress of drill string threaded connection and studied the full three-dimensional model of the connector under bending and torsional loads. ere is a slight change in thread geometry, but it can increase the fatigue life of the thread. Based on the strength and sealing requirements, Wang et al. [6] analyzed the integrity and tightness of the bolt flange connection with the help of Waters formula and finite element calculation and classified and evaluated the flange strength classification and sealing. ese can provide reference for practical application. Feng et al. [7] used chemical analysis and metallographic analysis to analyze the failure of the pipeline by a combination of spectroscopic, potential analysis, and X-ray diffraction. It is concluded that, before service, due to the presence of residual water after the hydrostatic test, it is easy to cause pipeline corrosion. After service, with the lower flow rate and prolonged shutdown, water settles to the bottom of the pipeline, which may also cause corrosion, and the presence of inclusions or small holes in the pipe body also accelerates the penetration rate of the pipeline. Wang et al. [8] others analyzed the causes of flange fractures by observing the appearance of cracks and fractures, metallographic analysis, and material composition detection. e author believes that the cracking mode of the flange is the stress corrosion caused by the noncompliance of the material grade and design requirements of the flange. Han et al. [9] established a finite element model of the connection consisting of flanges, gaskets, and bolts and studied the effects of bolt pretightening force and medium pressure on flange stress, strain, and sealing performance. It is concluded that the maximum von Mises stress value of the integral flange structure after pretightening and work occurs at the side of the bolt hole near the axis and at the connection of the flange neck and flange. e greater the pretightening force of the bolt, the greater the von Mises stress, contact stress, and deformation of the flange. Li [10] established the finite element model of flange, cross and octagonal steel ring based on the actual fracture of the flange, and studied the effects of different loads on the mechanical strength and sealing performance of the three components. e authors believe that as the external load increases, the stress and displacement of the flange and the cross section are continuously increasing. e maximum stress of the flange is greater than that of the cross and octagonal steel ring, which is a direct load. Abedi et al. [11] studied the cracking failure of an oil pipeline by means of microstructure analysis, corrosion product analysis, optical metallographic analysis of corrosion cross sections, fracture analysis, and energy spectrum analysis. e authors believe that carbonate-bicarbonate-induced stress corrosion cracking is the main cause of rupture and leakage of buried pipelines. Long et al. [12] others used a direct-reading spectrometer, Rockwell hardness tester, optical microscope analyzer, scanning electron microscope, energy dispersion spectrometer, electrochemical method, and finite element method to analyze the failure of a tubing pump. e authors believe that higher concentrations of down hole media CO 2 and Cl − are the environmental factors of damage, and the alternating stress caused by the cyclic movement of the pump is the main stress factor of the damage, and the high stress concentration of the threaded joint further causes cracking. Zhang et al. [13] analyzed the macroscopic morphology and microstructure of the cracks in the flanges of the holes, combined with metallographic analysis, mechanical properties testing, chemical composition analysis of flange materials, and energy spectrum analysis. e main reason for cracking is liquefaction. Cracking and sensitization of the flange material make the failure even more serious. Hu et al. [14] others performed optical microscopy on the failed copper alloy flange and analyzed the corrosion products by XPS. e reason for the failure is that, due to the limited deformation of the polytetrafluoroethylene, the polytetrafluoroethylene on the Monel gasket cannot enter the hole formed by dezincification and corrosion in the copper alloy, and then water passes through the continuous channel, causing the flange to leak. Zhu et al. [15] used scanning electron microscope and optical microscope to analyze the macro-and microstructure of the broken bolt, studied the properties of the material through chemical composition and metallographic structure, and established a finite element analysis of the connection system to maximize the stress e criterion evaluates the overall stress distribution. e authors believe that the cause of the fracture is high-cycle fatigue, and the initial location of the crack is consistent with the high stress concentration at the location of sudden change in curvature. Yi et al. [16] performed valve failure analysis by means of visual inspection, stereo microscope, optical microscope, scanning electron microscope, and computational fluid dynamics (CFD). e morphological analysis shows that the craters on the valve plug and the cage, especially the craters at the end of the valve plug, are mainly caused by cavitation, and the damage of the groove is corrosive caused by the impact of high-speed water. In a certain oilfield, the gas pressure of the wellhead gas tree was tested to 70 Mpa. When the Schlumberger fracturing process was performed, the maximum construction pressure was 65 MPa, and when the blowout operation was carried out after the cumulative fracturing was completed in the 22 layers of the 12 th stage, the wellhead big tree suddenly leaked. Seven failures of the four-way flange caused by the wellhead blowout operation have occurred so far, but no failure mechanism has been found.
is article combines physical and chemical analysis, structural calculation and analysis of flange connection with detection equipment, and numerical simulation analysis methods in conjunction with the failure condition of the flange in the field, in order to find the cause of the failure of the four-way flange.

Physicochemical Analysis
When the gas production tree of an oil field company was injecting gas from the bottom to top, a puncture occurred at the connection between the wellhead big cross and No. 3 valve. Figure 1 Table 1 below.

Chemical Composition Analysis
e material selected for the four-way flange is KQ52-35 steel, and KQ52-35 is an alloy steel containing alloy elements Mn, Cr, and Mo. e chemical composition of the four-way flange and the connecting valve was measured using a mobile direct-reading spectrometer. e specific chemical composition is shown in Table 2. e results show that the chemical composition of the four-way flange and the connecting valve meets the requirements of the standard.

Hardness Test
e Rockwell hardness tester is used to measure the hardness of the failed valve and the cross. In order to accurately reflect the true hardness of the failed valve and cross, according to the international standard GB/T 230.1-2018, 5 points were selected on the valve and cross to measure. ere are 5 test points on the valve: one at the horizontal symmetry of the flange at the nonspilled end of the failed valve, one at the horizontal symmetry of the flange at the pierced end of the failed valve, and the valve body of the failed valve. A total of 5 test points on the four-way body are, respectively, taken at the four-way body, the four-way upper flange symmetry point, and the four-way lower flange symmetry point. e Rockwell hardness test results are shown in Table 3. e test results show that the failed valves and crosses have higher hardness and meet the standard requirements.

Physical Model Establishment
After a series of physical and chemical analysis, the results show that the chemical composition, hardness, and tensile properties meet the standard requirements, not the failure caused by the material of the workpiece itself. Because the three-phase fluid in the pipeline will cause high-frequency vibration when the gas extraction tree is performing the discharge operation, a finite element structural dynamic analysis is performed on the four-way connection structure. Due to the symmetrical structure of the gas production tree at the wellhead, during the fracturing process, No. 2 gate valve and No. 1 large-diameter flat valve are closed, and the three-phase flow is discharged from the large cross through No. 3 valve and No. 6 valve. According to the installation method and drawing size, the structure analysis of No. 6 valve, No. 3 valve and the four-way connection is mainly focused on, ignoring other models of the structure, and the solid model established is shown in Figure 4, which is convenient for subsequent finite element calculation. According to the established solid finite element model, the mesh is divided, and the mesh quality meets the requirements. In order to simulate the failure process, a boundary condition was applied to the model. During the discharge process, a static pressure load of 22 MPa was applied to the pressure-bearing part of the inner hole, and a fixed constraint was imposed on the upper and lower parts of the cross. e bolt model is M22, and the preload force is loaded during installation. e preload force is calculated according to the standard recommended formula, Fv � (0.5∼0.7)σAs, where Fv is the preload force, s is the yield strength of the bolt, and the size is 960 MPa, As is the

Structural Vibration Analysis
Analyze the structural analysis of the flange connection during the discharge process and carry out the force analysis of the four-way flange connection subjected to vibration load, including modal analysis and harmonious response analysis.

Modal Analysis
Perform modal analysis of the structure, analyze the characteristics of the main modes of each order in the frequency range, where the flange connection structure is affected by the modal analysis method, and predict the structure generated by external or internal vibration sources in this frequency band. For finite element analysis, in general, the calculation of the natural frequencies of the first 6 orders can basically meet the general requirements. e calculation of the natural frequencies of the first 10 orders in this paper can meet the engineering calculation accuracy. Observing the mode shapes of ten orders, it can be found that the natural frequency gradually increases, and the number of deformation increases and decreases. From the analysis of the overall mode shape, the trend of the mode shapes of each order is obtained. e two valves are mostly deformed up and down in the horizontal direction, and the amount of deformation varies between 2.47 mm and 5.89 mm. is amount of deformation will accelerate the failure of the bolt connection stability, especially from the fourth, eighth, and tenth mode shapes found that the vibration characteristics are at the flange connection, which easily leads to deformation of the flange connection. e frequency and formation of each order are shown in Table 5 below. It can be found from the frequency values of each order in Table 5 that the modal frequency of the structure vibration is in the range of 40-1200 Hz. From the continuous equation, momentum equation, and the wave equation, we can get the relationship between the inlet and outlet pressure and speed of the straight pipe: where ρ 0 is the average density, unit: kg m −3 ; a is the sound velocity of the medium, unit: m s −1 ; a is the circular frequency of the pulsation, unit: rad s −1 ; unit: m. Set the boundary condition to one end as the closed end and the other end as the open end. Set the boundary condition between the gas tree and the open end to set the pressure to 0, and set the pressure to 0 if the pressure is not zero. 0; the right end is p 2 � 0 and u 2 � 1. Substituting these conditions into the above formula, we obtain cos ω a l � 0.
(2) e iterative method is used to find the natural frequencies of the three-phase currents in the order of 1 to n for each value of ω, from small to large. e calculated frequency of fluid vibration is in the range of 0-1200 Hz. When the vibration frequency of the structure and the fluid are the same, the two will cause resonance increased vibration.    Shock and Vibration

Harmonic Response Analysis
Harmonic response analysis is a technique for analyzing the steady-state response of a structure under a load that changes in a regular manner. Harmonic loads are applied and solved. All applied loads change simply and harmonically at a specified frequency (or frequency range). e deformation is restricted to zero, and the force of the valve body is 10 kN in the vertically upward direction (calculated based on the contact area of the fluid pressure with the hole in the valve body). Figure 5 is the stress cloud diagram of the bolt at different frequencies. When the frequency of the three-phase flow is 40 Hz, 240 Hz, 552 Hz, 688 Hz, and 1104 Hz, the threephase flow in the bolt and the valve body will resonate. As can be seen from the figure, the three-phase fluid and structure did not resonate at a frequency of 1200 Hz, and the stress of the bolt was 20.948 MPa. When the resonance occurred, the stress of the bolt was gradually increased. When the frequency was 1104 Hz, the bolt was subjected to the maximum stress. It reaches 2302.2 MPa, far exceeding its yield limit. Figure 6 shows the stress spectrum response curves of No. 1-8 bolts. ese parts will produce different magnitudes of stress in the frequency range of 0-1200 Hz. No. 1 bolt is the most stressed, followed by No. 5 and No.6 bolts. As shown in Figure 7, the spectral response curves of the deformation amount of No.       bolts have a small deformation and deformation e volume is about 0.03 mm. e amount of bolt deformation is connected to the cross, and the failure situation at the place coincides. At the same time, there are five peaks in the entire spectral response curve of the deformation. When the frequency of the three-phase flow in the valve is 40 Hz, 240 Hz, 552 Hz, 688 Hz, and 1104 Hz, the three-phase flow and fourway valve will resonate and cause the vibration to increase. e four-way valve structure is stimulated by the regular vibration, and No. 1, No. 2, No. 5, and No. 6 nuts are most excited by vibration and have the largest amount of deformation. At the same time, the three-phase flow in the valve and the valve body will cause resonance to cause vibration. Because this part is easy to relax, the nut will be reversed due to vibration, eventually the bolt will loosen and fall off, and the wellhead cross and No. 3 valve will have erosion failure.

Conclusion
After physical and chemical analysis, modal analysis, and harmonious response analysis of the failed four-way flange on the gas production tree, the following conclusions were reached: (1) Chemical composition analysis, hardness testing, and bolt tensile performance test results show that the chemical composition of the four-way flange and connecting valve meets the requirements of the standard; the failure of the valve and the four-way hardness is higher and meets the standard requirements. e bolts meet the requirements for tensile properties. (2) From the modal analysis and mode change, it is found that the valve body connection is equivalent to a cantilever beam. e end of No. 6 valve body is not fastened, which will cause No. 6 valve body to have a larger vibration amplitude, affecting No. 3 valve body and tighten the connection. Because the fluid in the blowout prevention pipeline is in a three-phase state, the vibration frequency is increased due to gas-liquid-solid. In addition, different bolt sizes will cause uneven distribution of different vibration deformations of the bolt, which may easily cause loosening accidents. (3) According to the harmonic response curves of Figures 6 and 7 above, it is found that the bolt will be subjected to different magnitudes of stress in the frequency range of 0-1200 Hz to produce different degrees of vibration. e maximum stress on the bolt is close to 110 MPa, and the vibration of the bolt. e maximum deformation reaches 0.1 mm.   Shock and Vibration (4) When the gas extraction tree is performing the spraying operation, the three-phase fluid will generate high-frequency vibration in the pipeline, which will cause the valve body to vibrate up and down. Due to the size of the bolt at the junction of the wellhead cross and No. 3 valve, the length is different, the load on the bolt is in an unbalanced state, and the nut is buckled, which causes leakage at the flange connection. Eventually, the wellhead cross and No. 3 valve have erosion failure. (5) It is recommended to regularly use an electronic torque wrench to detect the pretightening force of each bolt to prevent vibration and failure due to inconsistent pretightening force of the bolts.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.