Casing wear and casing corrosion are serious problems affecting casing integrity failure in deep and ultra-deep wells.This paper aims to predict the casing burst strength with considerations of both wear and corrosion...Casing wear and casing corrosion are serious problems affecting casing integrity failure in deep and ultra-deep wells.This paper aims to predict the casing burst strength with considerations of both wear and corrosion.Firstly,the crescent wear shape is simplified into three categories according to common mathematical models.Then,based on the mechano-electrochemical(M-E)interaction,the prediction model of corrosion depth is built with worn depth as the initial condition,and the prediction models of burst strength of the worn casing and corroded casing are obtained.Secondly,the accuracy of different prediction models is validated by numerical simulation,and the main influence factors on casing strength are obtained.At last,the theoretical models are applied to an ultra-deep well in Northwest China,and the dangerous well sections caused by wear and corrosion are predicted,and the corrosion rate threshold to ensure the safety of casing is obtained.The results show that the existence of wear defects results in a stress concentration and enhanced M-E interaction on corrosion depth growth.The accuracy of different mathematical models is different:the slot ring model is most accurate for predicting corrosion depth,and the eccentric model is most accurate for predicting the burst strength of corroded casing.The burst strength of the casing will be overestimated by more than one-third if the M-E interaction is neglected,so the coupling effect of wear and corrosion should be sufficiently considered in casing integrity evaluation.展开更多
The casing deformation prevention technology based on the optimization of cement slurry is proposed to reduce the casing deformation of shale oil and gas wells during hydraulic fracturing. In this paper, the fracture ...The casing deformation prevention technology based on the optimization of cement slurry is proposed to reduce the casing deformation of shale oil and gas wells during hydraulic fracturing. In this paper, the fracture mechanism of hollow particles in cement sheath was firstly analyzed by discrete element method, and the effect of hollow particles in cement on casing deformation was investigated by laboratory experiment method. Finally, field test was carried out to verify the improvement effect of the casing deformation based on cement slurry modification. The results show that the formation displacement can be absorbed effectively by hollow particles inside the cement transferring the excessive deformation away from casing. The particles in the uncemented state provide deformation space during formation slipping. The casing with diameter of 139.7 mm could be passed through by bridge plug with the diameter of 99 mm when the mass ratio of particle/cement reaches 1:4. According to the field test feedback, the method based on optimization of cement slurry can effectively reduce the risk of casing deformation, and the recommended range of hollow microbeads content in the cement slurry is between 15% and 25%.展开更多
To address the challenges associated with difficult casing running,limited annular space,and poor cementing quality in the completion of ultra-deep wells,the extreme line casing offers an effective solution over conve...To address the challenges associated with difficult casing running,limited annular space,and poor cementing quality in the completion of ultra-deep wells,the extreme line casing offers an effective solution over conventional casings.However,due to its smaller size,the joint strength of extreme line casing is reduced,which may cause failure when running in the hole.To address this issue,this study focuses on the CST-ZTΦ139.7 mm×7.72 mm extreme line casing and employs the elastic-plastic mechanics to establish a comprehensive analysis of the casing joint,taking into account the influence of geometric and material nonlinearities.A finite element model is developed to analyze the forces and deformations of the extreme line casing joint under axial tension and external collapse load.The model investigates the stress distribution of each thread tooth subjected to various tensile forces and external pressures.Additionally,the tensile strength and crushing strength of the extreme line casing joint are determined through both analytical and experimental approaches.The findings reveal that,under axial tensile load,the bearing surface of each thread tooth experiences uneven stress,with relatively high equivalent stress at the root of each thread tooth.The end thread teeth are valuable spots for failure.It is observed that the critical fracture axial load of thread decreases linearly with the increase of thread tooth sequence.Under external pressure,the circumferential stress is highest at the small end of the external thread,leading to yield deformation.The tensile strength of the joint obtained from the finite element model exhibits a relative error of less than 7%compared to the analytical and experimental values,proving the reliability of the finite element model.The tensile strength of the joint is 3091.9 k N.Moreover,in terms of anti-collapse capability,the joints demonstrate higher resistance to collapse compared to the casing body,which is consistent with the test results where the pipe body experiences collapse and failure while the joints remain intact during the experiment.The failure load of the casing body under external collapse pressure is 87.4 MPa.The present study provides a basic understanding of the mechanical strengths of extreme line casing joint.展开更多
The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine...The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine the maximum fragment velocity.The current work builds on the published formula to further develop a formula for calculating the axial distribution characteristics of the fragment velocity.For this type of warhead,the simulation of the dispersion characteristics of the detonation products at different positions shows that the detonation products at the ends have a much larger axial velocity than those in the middle,and the detonation products have a greater axial dispersion velocity when they are closer to the central axis.The loading process and the fragment velocity vary with the axial position for both casing layers,and the total velocity of the fragments is the vector sum of the radial velocity and the axial velocity.At the same axial position,the acceleration time of the inner casing is greater than that of the outer casing.For the same casing,the fragments generated at the ends have a longer acceleration time than the fragments from the middle.The proposed formula is validated with the X-ray radiography results of the four warheads previously tested experimentally and the 3D smoothedparticle hydrodynamics numerical simulation results of several series of new warheads with different configurations.The formula can accurately and reliably calculate the fragment velocity when the lengthto-diameter ratio of the charge is greater than 1.5 and the thickness of the casing is less than 20%its inner radius.This work thus provides a key reference for the theoretical analysis and the design of warheads with multiple casings.展开更多
The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects...The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.展开更多
Based on structural distribution and fault characteristics of the Luzhou block,southern Sichuan Basin,as well as microseismic,well logging and in-situ stress data,the casing deformation behaviors of deep shale gas wel...Based on structural distribution and fault characteristics of the Luzhou block,southern Sichuan Basin,as well as microseismic,well logging and in-situ stress data,the casing deformation behaviors of deep shale gas wells are summarized,and the casing deformation mechanism and influencing factors are identified.Then,the risk assessment chart of casing deformation is plotted,and the measures for preventing and controlling casing deformation are proposed.Fracturing-activated fault slip is a main factor causing the casing deformation in deep shale gas wells in the Luzhou block.In the working area,the approximate fracture angle is primarily 10°-50°,accounting for 65.34%,and the critical pore pressure increment for fault-activation is 6.05-9.71 MPa.The casing deformation caused by geological factors can be prevented/controlled by avoiding the faults at risk and deploying wells in areas with low value of stress factor.The casing deformation caused by engineering factors can be prevented/controlled by:(1)keeping wells avoid faults with risks of activation and slippage,or deploying wells in areas far from the faulting center if such avoidance is impossible;(2)optimizing the wellbore parameters,for example,adjusting the wellbore orientation to reduce the shear force on casing to a certain extent and thus mitigate the casing deformation;(3)optimizing the casing program to ensure that the curvature radius of the curved section of horizontal well is greater than 200 m while the drilling rate of high-quality reservoirs is not impaired;(4)optimizing the fracturing parameters,for example,increasing the evasive distance,lowering the single-operation pressure,and increasing the stage length,which can help effectively reduce the risk of casing deformation.展开更多
Large-scale sand fracturing is a necessary means in the efficient exploitation of shale gas/oil.However,in the process of fracturing operation,the sand carrying fluid and proppant easily causes scouring and wear to pr...Large-scale sand fracturing is a necessary means in the efficient exploitation of shale gas/oil.However,in the process of fracturing operation,the sand carrying fluid and proppant easily causes scouring and wear to production strings,especially the casing perforation system,which damage the wellbore integrity and deformation to affect the subsequent fracturing.For this problem,taking the actual construction conditions and perforation technology of an oilfield in western China as an example,the structural parameters of the downhole string were measured and the wall thickness reduction model of casing perforation suitable for large-displacement sand fracturing in horizontal well section was established.With software ANSYS-FLUENT,the casing perforation erosion under the conditions of different displacements,sand content and perforation sand-passing quantity in the process of sand fracturing was simulated and calculated.The influences of three parameters on perforation erosion and expansion were analyzed and the prediction chart of the influences of three main control factors on perforation erosion and expansion was established.The perforation erosion images after fracturing construction were obtained with the downhole eagle perforation logging technology.The logging chart results were compared with the downhole eagle perforation data.The error between the established numerical simulation calculation charts and the real logging data was about 5%,indicating that the simulation charts were the valuable reference.展开更多
An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non...An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.展开更多
A three-dimensional model for the numerical simulation of casing-cement behavior is used to investigate residual strength in the perforated casing of ultra deep wells.The influence of the hole diameter,hole density an...A three-dimensional model for the numerical simulation of casing-cement behavior is used to investigate residual strength in the perforated casing of ultra deep wells.The influence of the hole diameter,hole density and phase angle on the residual strength of the casing under non-uniform stress and fracturing conditions is revealed through the consideration of different perforation parameters.It is shown that the residual strength of the casing increases with the hole diameter and periodically changes with the hole density;the phase angle is the main factor that affects the residual strength of the perforated casing,and the perforation should be avoided in the direction of the minimum principal stress to reduce stress concentration at the perforation hole.Moreover,as shown by a companion orthogonal experiment,the descending order of influence of the different influential parameters is:phase angle,hole diameter,hole density and the thickness of casing.展开更多
Down-the-hole(DTH)hammer with casing while drilling(CWD)is a technology that has been proven to be able to alleviate many of the problems faced by complex formations.However,the drill bit is suffered from rapid wear,l...Down-the-hole(DTH)hammer with casing while drilling(CWD)is a technology that has been proven to be able to alleviate many of the problems faced by complex formations.However,the drill bit is suffered from rapid wear,low drilling efficiency,and high energy consumption due to the unreasonable tooth arrangement and impact energy selection in drilling process,which affect the application effect of this technology.ABAQUS software was used for numerical simulation of rock breaking behavior under impact load with the single,three,and five teeth arrangement drill bit respectively,to improve the application effect and solve the aforementioned technical problems.Based on the calculated parameters of tooth arrangement,we designed a novel drill bit for hard rocks and provided a theoretical basis for the tooth arrangement of largediameter drill bits.展开更多
This work focus on the stress distribution of the casing-cement-formation(CCF)multilayer composite system,which is a borehole system with multiple casings and cement sheathes.Mostof the previous relevant studies are b...This work focus on the stress distribution of the casing-cement-formation(CCF)multilayer composite system,which is a borehole system with multiple casings and cement sheathes.Mostof the previous relevant studies are based on the traditional CCF system with the single casing and cement sheath,but these results are not adaptive to the CCF system multiple composite system.In this paper,the FEM numerical model of CCF multilayer composite system was constructed.Numerical simulations were calculated and compared with the system which consists of the single casing and cement sheath.Results show that the multilayer composite system possesses better performance.On this basis,the sensitivity analysis of main influence mechanical parameters such as in-situ stress,the elastic of cement sheathes and the elastic of formation are conducted.The cement sheath on the inside,namely cement sheath-1,is sensitive to its elastic modulus;meanwhile,the cement sheath on the outside,namely cement sheath-2,is not so sensitive to the elastic modulus of cement sheath-1.Cement sheath-1 and cement sheath-2 are all sensitive to the elastic modulus of cement sheath-2,and the mises stress of them has opposite trend to the elastic modulus of cement sheath-2.The proper values of elastic modulus of cement sheath-1 and cement sheath-2 are 5GPa and 5GPa to 30GPa,respectively.Under the in-situ stress ratio σh/σH=0.7,the maximum mises stress of cementsheath-1 and cement sheath-2 increase as the increase of σh,and they are nearly equal when σh=15GPa.This research can be helpful for the design and analysis of CCF multilayer composite system.展开更多
Intermediate casings in the build sections are subject to severe wear in extended-reach drilling. This paper presents a new method for predicting the depth of a wear groove on the intermediate casing. According to ene...Intermediate casings in the build sections are subject to severe wear in extended-reach drilling. This paper presents a new method for predicting the depth of a wear groove on the intermediate casing. According to energy principle and dynamic accumulation of casing wear by tool joints, a model is established to calculate the wear area on the inner wall of the casing. The relationship functions between the wear groove depth and area are obtained based on the geometry relationship between the drillstring and the wear section and the assumption that the casing wear groove is crescent-shaped. The change of casing wear groove depth versus drilling footage under different-sized drillstrings is also discussed. A mechanical model is proposed for predicting casing wear location, which is based on the well trajectory and drillstring movement. The casing wear groove depth of a planned well is predicted with inversion of the casing wear factor from the drilled well and necessarily revised to improve the prediction accuracy for differences between the drilled well and the planned well. The method for predicting casing wear in extended-reach drilling is verified through actual case study. The effect of drillstring size on casing wear should be taken into account in casing wear prediction.展开更多
To study the casing deformation(CD)in shale gas well fracturing caused by natural fracture slip,a fracture face stress model is built based on stress analysis,and a CD prediction model is established based on complex ...To study the casing deformation(CD)in shale gas well fracturing caused by natural fracture slip,a fracture face stress model is built based on stress analysis,and a CD prediction model is established based on complex function to analyze factors affecting wellbore shear stress and CD.(1)The fracture and wellbore approach angles have significant impacts on the wellbore shear stress.In Weiyuan shale gas field,Sichuan Basin,under the common wellbore approach angle of nearly 90°,the wellbore is subjected to large shear stress and high risk of CD at the fracture approach angle range of 20° to 55° or its supplementary angle range.(2)When the fracture is partially opened,the wellbore shear stress is positively correlated with the fluid pressure,and negatively correlated with the fracture friction coefficient;when the fracture is fully opened,the wellbore shear stress is positively correlated with the natural fracture area.(3)The lower the elastic modulus and the longer the fracture length,the more serious the CD will be,and the Poisson’s ratio has a weak influence on the CD.The deformation first increases and then decreases with the increase of fracture approach angle,and reaches the maximum when the fracture approach angle is 45°.(4)At a given fracture approach angle,appropriately adjusting the wellbore approach angle can avoid high shear stress acting on wellbore,and reasonable control of the fluid pressure in the fracture can reduce the CD risk.The shear stress acting on casing is usually much greater than the shear strength of casing,so increasing casing strength or cementing quality have limited effect on reducing the risk of CD.Caliper logging data has verified that the CD prediction model is reliable,so the model can be used to establish risk analysis chart and calculate deformation value,to provide a reference for quick CD risk prediction in fracturing design.展开更多
There has been lack of work efforts on how to optimize cementing and completing parameters in order to prevent casing failure induced by formation slippage in pertroleum industry scope.Once the weak plane fails,the fo...There has been lack of work efforts on how to optimize cementing and completing parameters in order to prevent casing failure induced by formation slippage in pertroleum industry scope.Once the weak plane fails,the formation will become easily undertaken slippage across a large area along its interface.The plenty of horizontal planes of weakness in reservoir formations,as reported for a number of oilfields,can easily undertaken slippage once it fails.To address the problem,three-dimensional finite element models were established by taking into considerations the elastoplastic mechanical characteristics of both the casing and the near-wellbore rock.Two types of casing impairment scenarios were considered:Casing collapse(that causes tubing stuck in the well)and complete casing shear-off.In this study,the critical slip displacement of casing shear damage under both cemented and un-cemented conditions was calculated,and the critical displacement of casing with various wall thicknesses and steel grades was compared.A new cementing practice for the Daqing oilfield was then proposed by optimizing casing parameters according to API standards,and a new research method was also put forward by proposing new casing materials to effectively mitigate casing failure caused by formation slippage for the future.Modeling results indicate that the stress and deformation associated with casing in the un-cemented condition is more diffused and the critical slippage displacement is larger than that in the cemented condition.Therefore,the un-cemented condition is more effective in preventing casing shear failure and easier for casing repair,for the case of casing damage caused by formation shear slippage.Casing elongation is the key parameter of casing shear failure in the un-cemented condition.Lower grade casing exhibits a larger critical slippage displacement because of its higher elongation capacity under stress.Casing with lower grade and smaller thickness provides more advantages in preventing casing damage in formations abundant with horizontal weak layers.If the elongation of casing can be largely improved,the critical displacement value can be increased by 21.40%.Higher grade and thicker casing is adapted for mitigate casing failure caused by formation slippage.展开更多
In the enhanced geothermal systems wells, casing temperature variation produces casing thermal stresses, resulting in casing uplift or bucking. When the induced thermal stresses exceed casing material's yield stre...In the enhanced geothermal systems wells, casing temperature variation produces casing thermal stresses, resulting in casing uplift or bucking. When the induced thermal stresses exceed casing material's yield strength, the casing deforms and collapses. The traditional casing design standard only considers the influence of temperature variation on casing material's yield strength. Actually, for commonly used grades of steel pipe, casing's material properties-such as yield strength, coefficient of thermal expansion, and modulus of elasticity change with temperature variation. In this paper, the modified thermal stress equation is given. Examples show that the allowable temperature of the material grade N80's casing is only 164 ℃, which is much lower than that of the traditional design standard. The effective method to improve the casing pipe's allowable temperature is pre-stressed cementing technology. Pre-stressed cementing includes pre-tension stress cementing and pre-pressure stress cementing. This paper focuses on the design method of full casing pre-tension stress cementing and the ground anchor full casing string pre-tension cementing construction process.展开更多
Considering the elastic supports,the finite element model of rotor-bladed disk-casing system is established using commercial software ANSYS/LS-DYNA.Assuming that broken blade is released from the disk,the complicate r...Considering the elastic supports,the finite element model of rotor-bladed disk-casing system is established using commercial software ANSYS/LS-DYNA.Assuming that broken blade is released from the disk,the complicate rubbing responses of unbalanced rotor-bladed disk-casing system are studied under different operational speeds.In addition,influences of both plastic deformation of blade and casing failure are analyzed.The results show that there exist some multiple even fractional frequencies in the transient and steady vibration responses of unbalanced rotor.Besides,one nodal diameter vibration of bladed disk coupling with the lateral vibration of the shaft as well as the first order bending vibration of blade can be excited under low operational speed,while the first order bending vibration of blade coupling with the lateral vibration of disk-shaft is easily excited under high operational speed.During rubbing process,three distinct contact states can be observed:broken blade-casing contact,broken blade-blade component-casing contact and broken blade-casing contact/blade component-casing contact/blade selfcontact.It is worth noting that the third contact state is related to the operational speed.With the increase of operational speed,self-contact in the blade may occur.展开更多
Casing treatment is a widely employed technique to increase the stall margins of turbomachineries. In the last several decades, many researches on casing treatment have been carded out. However, the mechanism of its e...Casing treatment is a widely employed technique to increase the stall margins of turbomachineries. In the last several decades, many researches on casing treatment have been carded out. However, the mechanism of its expanding stall margins is still not very clear. Till now, most casing teatment schemes are designed for axial compressors, while the investigations on casing treatments in centrifugal compressors are rarely reported. Moreover, current investigation methods mainly focus on experiments, and perfect theoretic al analysis is not yet feasible. In order to study the effectiveness and further the mechanism of casing treatments in centrifugal compressors, in this paper, a computationally based investigation of the impact of the self-recireulating casing treatment on the performance of a radial compressor is carried out. The results indicate that, by casing bleed and injection, the casing treatment with inclined blades in the cavity expands the stall margin most. At low mass flows, the reversed flow through the cavity with inclined blades develops the counter swirl flow in front of the impeller inlet, which is considered to benefit increasing the pressure rise from the injection port to the bleed port and thereby augment the recirculating flow. At 120% design speed, the stall margin is larger than that at the design speed. However, the cost of extending the stall margin is the reduction of isentropic efficiency. A mended casing treatment by shifting the bleed port upstream is also studied. It is demonstrated that, relative to the original casing treatment, this mend can improve the efficiency evidently notwithstanding a little narrowing of the flow range.展开更多
Casing collapse is one of the costly incidents in the oil industry. In the oil fields of southwest Iran, most casing collapses have occurred in Gachsaran formation, and the halite rock salt layer in this formation may...Casing collapse is one of the costly incidents in the oil industry. In the oil fields of southwest Iran, most casing collapses have occurred in Gachsaran formation, and the halite rock salt layer in this formation may be the main cause for these incidents because of its peculiar creep behavior. In this research, triaxial creep experiments have been conducted on Gachsaran salt samples under various temperatures and differential stresses. The main purpose was to determine the creep characteristics of Gachsaran rock salt,and to examine the role of creep in several casing collapses that occurred in this formation. Results indicated that the halite rock salt of Gachsaran formation basically obeys the power law;however, its creep parameters are quite different from other halite rocks elsewhere. The time-dependent creep of Gachsaran rock salt exhibits strong sensitivity to temperature change;however, its sensitivity to variation of differential stress is rather low. The numerical simulation of the rock salt creep in a real oil well demonstrated the importance of creep and reservoir conditions on the safety factor of the tubing related to casing collapse.展开更多
Sustained casing pressure (SCP) in gas wells brings a serious threat to worker safety and environmental protection. According to geological conditions, wellbore structure and cement data of gas wells in the Sichuan-...Sustained casing pressure (SCP) in gas wells brings a serious threat to worker safety and environmental protection. According to geological conditions, wellbore structure and cement data of gas wells in the Sichuan-Chongqing region, China, the position, time, environmental condition and the value of SCP have been analyzed. On this basis, the shape of the pressure bleed-down plot and pressure buildup plot were diagnosed and the mechanism of SCP has been clarified. Based on generalized annular Darcy percolation theory and gas-liquid two-phase fluid dynamics theory, a coupled mathematical model of gas migration in a cemented annulus with a mud column above the cement has been developed. The volume of gas migrated in the annulus and the value of SCP changing with time in a gas well in Sichuan have been calculated by this model. Calculation results coincided well with the actual field data, which provide some reference for the following security evaluation and solution measures of SCP.展开更多
This paper presents a theoretical method and a finite element method to describe wellhead movement and uncemented casing strength in offshore oil and gas wells.Parameters considered in the theoretical method include o...This paper presents a theoretical method and a finite element method to describe wellhead movement and uncemented casing strength in offshore oil and gas wells.Parameters considered in the theoretical method include operating load during drilling and completion and the temperature field,pressure field and the end effect of pressure during gas production.The finite element method for multistring analysis is developed to simulate random contact between casings.The relevant finite element analysis scheme is also presented according to the actual procedures of drilling,completion and gas production.Finally,field cases are presented and analyzed using the proposed methods.These are four offshore wells in the South China Sea.The calculated wellhead growths during gas production are compared with measured values.The results show that the wellhead subsides during drilling and completion and grows up during gas production.The theoretical and finite element solutions for wellhead growth are in good agreement with measured values and the deviations of calculation are within 10%.The maximum von Mises stress on the uncemented intermediate casing occurs during the running of the oil tube.The maximum von Mises stress on the uncemented production casing,calculated with the theoretical method occurs at removing the blow-out-preventer (BOP) while that calculated with the finite element method occurs at gas production.Finite element solutions for von Mises stress are recommended and the uncemented casings of four wells satisfy strength requirements.展开更多
文摘Casing wear and casing corrosion are serious problems affecting casing integrity failure in deep and ultra-deep wells.This paper aims to predict the casing burst strength with considerations of both wear and corrosion.Firstly,the crescent wear shape is simplified into three categories according to common mathematical models.Then,based on the mechano-electrochemical(M-E)interaction,the prediction model of corrosion depth is built with worn depth as the initial condition,and the prediction models of burst strength of the worn casing and corroded casing are obtained.Secondly,the accuracy of different prediction models is validated by numerical simulation,and the main influence factors on casing strength are obtained.At last,the theoretical models are applied to an ultra-deep well in Northwest China,and the dangerous well sections caused by wear and corrosion are predicted,and the corrosion rate threshold to ensure the safety of casing is obtained.The results show that the existence of wear defects results in a stress concentration and enhanced M-E interaction on corrosion depth growth.The accuracy of different mathematical models is different:the slot ring model is most accurate for predicting corrosion depth,and the eccentric model is most accurate for predicting the burst strength of corroded casing.The burst strength of the casing will be overestimated by more than one-third if the M-E interaction is neglected,so the coupling effect of wear and corrosion should be sufficiently considered in casing integrity evaluation.
基金the supports of project funded by China Postdoctoral Science Foundation(2023M743886)Project of Shale Gas Evaluation and Exploitation Key Laboratory of Sichuan Province(YSK2023004)youth project funded by Shaanxi Province Natural Science Basic Research Program(2024JC-YBQN-0522)。
文摘The casing deformation prevention technology based on the optimization of cement slurry is proposed to reduce the casing deformation of shale oil and gas wells during hydraulic fracturing. In this paper, the fracture mechanism of hollow particles in cement sheath was firstly analyzed by discrete element method, and the effect of hollow particles in cement on casing deformation was investigated by laboratory experiment method. Finally, field test was carried out to verify the improvement effect of the casing deformation based on cement slurry modification. The results show that the formation displacement can be absorbed effectively by hollow particles inside the cement transferring the excessive deformation away from casing. The particles in the uncemented state provide deformation space during formation slipping. The casing with diameter of 139.7 mm could be passed through by bridge plug with the diameter of 99 mm when the mass ratio of particle/cement reaches 1:4. According to the field test feedback, the method based on optimization of cement slurry can effectively reduce the risk of casing deformation, and the recommended range of hollow microbeads content in the cement slurry is between 15% and 25%.
基金financially supported by National Natural Science foundation of China(Grant No.52104006)Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance(Grant No.2020CX040202)。
文摘To address the challenges associated with difficult casing running,limited annular space,and poor cementing quality in the completion of ultra-deep wells,the extreme line casing offers an effective solution over conventional casings.However,due to its smaller size,the joint strength of extreme line casing is reduced,which may cause failure when running in the hole.To address this issue,this study focuses on the CST-ZTΦ139.7 mm×7.72 mm extreme line casing and employs the elastic-plastic mechanics to establish a comprehensive analysis of the casing joint,taking into account the influence of geometric and material nonlinearities.A finite element model is developed to analyze the forces and deformations of the extreme line casing joint under axial tension and external collapse load.The model investigates the stress distribution of each thread tooth subjected to various tensile forces and external pressures.Additionally,the tensile strength and crushing strength of the extreme line casing joint are determined through both analytical and experimental approaches.The findings reveal that,under axial tensile load,the bearing surface of each thread tooth experiences uneven stress,with relatively high equivalent stress at the root of each thread tooth.The end thread teeth are valuable spots for failure.It is observed that the critical fracture axial load of thread decreases linearly with the increase of thread tooth sequence.Under external pressure,the circumferential stress is highest at the small end of the external thread,leading to yield deformation.The tensile strength of the joint obtained from the finite element model exhibits a relative error of less than 7%compared to the analytical and experimental values,proving the reliability of the finite element model.The tensile strength of the joint is 3091.9 k N.Moreover,in terms of anti-collapse capability,the joints demonstrate higher resistance to collapse compared to the casing body,which is consistent with the test results where the pipe body experiences collapse and failure while the joints remain intact during the experiment.The failure load of the casing body under external collapse pressure is 87.4 MPa.The present study provides a basic understanding of the mechanical strengths of extreme line casing joint.
基金supported by the National Natural Science Foundation of China(Grant No.11872121)。
文摘The double casing warhead with sandwiched charge is a novel fragmentation warhead that can produce two groups of fragments with different velocity,and the previous work has presented a calculation formula to determine the maximum fragment velocity.The current work builds on the published formula to further develop a formula for calculating the axial distribution characteristics of the fragment velocity.For this type of warhead,the simulation of the dispersion characteristics of the detonation products at different positions shows that the detonation products at the ends have a much larger axial velocity than those in the middle,and the detonation products have a greater axial dispersion velocity when they are closer to the central axis.The loading process and the fragment velocity vary with the axial position for both casing layers,and the total velocity of the fragments is the vector sum of the radial velocity and the axial velocity.At the same axial position,the acceleration time of the inner casing is greater than that of the outer casing.For the same casing,the fragments generated at the ends have a longer acceleration time than the fragments from the middle.The proposed formula is validated with the X-ray radiography results of the four warheads previously tested experimentally and the 3D smoothedparticle hydrodynamics numerical simulation results of several series of new warheads with different configurations.The formula can accurately and reliably calculate the fragment velocity when the lengthto-diameter ratio of the charge is greater than 1.5 and the thickness of the casing is less than 20%its inner radius.This work thus provides a key reference for the theoretical analysis and the design of warheads with multiple casings.
基金financially supported by the National Natural Science Foundation of China(No.52175352)the Xing Liao Ying Cai Project of Liaoning Province(No.XLYC2008036)the Shenyang Youth Innovation Talent Support Program(No.RC220429)。
文摘The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.
基金Supported by the PetroChina Scientific Research and Technology Development Project (2022KT1205)。
文摘Based on structural distribution and fault characteristics of the Luzhou block,southern Sichuan Basin,as well as microseismic,well logging and in-situ stress data,the casing deformation behaviors of deep shale gas wells are summarized,and the casing deformation mechanism and influencing factors are identified.Then,the risk assessment chart of casing deformation is plotted,and the measures for preventing and controlling casing deformation are proposed.Fracturing-activated fault slip is a main factor causing the casing deformation in deep shale gas wells in the Luzhou block.In the working area,the approximate fracture angle is primarily 10°-50°,accounting for 65.34%,and the critical pore pressure increment for fault-activation is 6.05-9.71 MPa.The casing deformation caused by geological factors can be prevented/controlled by avoiding the faults at risk and deploying wells in areas with low value of stress factor.The casing deformation caused by engineering factors can be prevented/controlled by:(1)keeping wells avoid faults with risks of activation and slippage,or deploying wells in areas far from the faulting center if such avoidance is impossible;(2)optimizing the wellbore parameters,for example,adjusting the wellbore orientation to reduce the shear force on casing to a certain extent and thus mitigate the casing deformation;(3)optimizing the casing program to ensure that the curvature radius of the curved section of horizontal well is greater than 200 m while the drilling rate of high-quality reservoirs is not impaired;(4)optimizing the fracturing parameters,for example,increasing the evasive distance,lowering the single-operation pressure,and increasing the stage length,which can help effectively reduce the risk of casing deformation.
基金support from Sichuan Science and Technology Program(21JCQN0066)supported by National Natural Science Foundation of China(No.51774249).
文摘Large-scale sand fracturing is a necessary means in the efficient exploitation of shale gas/oil.However,in the process of fracturing operation,the sand carrying fluid and proppant easily causes scouring and wear to production strings,especially the casing perforation system,which damage the wellbore integrity and deformation to affect the subsequent fracturing.For this problem,taking the actual construction conditions and perforation technology of an oilfield in western China as an example,the structural parameters of the downhole string were measured and the wall thickness reduction model of casing perforation suitable for large-displacement sand fracturing in horizontal well section was established.With software ANSYS-FLUENT,the casing perforation erosion under the conditions of different displacements,sand content and perforation sand-passing quantity in the process of sand fracturing was simulated and calculated.The influences of three parameters on perforation erosion and expansion were analyzed and the prediction chart of the influences of three main control factors on perforation erosion and expansion was established.The perforation erosion images after fracturing construction were obtained with the downhole eagle perforation logging technology.The logging chart results were compared with the downhole eagle perforation data.The error between the established numerical simulation calculation charts and the real logging data was about 5%,indicating that the simulation charts were the valuable reference.
基金supported by the National Natural Science Foundation of China[51804061,51974052,51774063]the Academician Led Special Project of Chongqing Science and Technology Commission[cstc2017zdcy-yszxX0009]+1 种基金the Chongqing Research Program of Basic Research and Frontier Technology[cstc2019jcyj-msxmX0199,cstc2018jcyjAX0417]the Chongqing Education Committee foundation[KJQN201901544,KJZD-K201801501].
文摘An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.
基金supported by the National Natural Science Foundation of China[52074326].
文摘A three-dimensional model for the numerical simulation of casing-cement behavior is used to investigate residual strength in the perforated casing of ultra deep wells.The influence of the hole diameter,hole density and phase angle on the residual strength of the casing under non-uniform stress and fracturing conditions is revealed through the consideration of different perforation parameters.It is shown that the residual strength of the casing increases with the hole diameter and periodically changes with the hole density;the phase angle is the main factor that affects the residual strength of the perforated casing,and the perforation should be avoided in the direction of the minimum principal stress to reduce stress concentration at the perforation hole.Moreover,as shown by a companion orthogonal experiment,the descending order of influence of the different influential parameters is:phase angle,hole diameter,hole density and the thickness of casing.
基金Project of National Key Research and Development of China(No.2018YFC1505303).
文摘Down-the-hole(DTH)hammer with casing while drilling(CWD)is a technology that has been proven to be able to alleviate many of the problems faced by complex formations.However,the drill bit is suffered from rapid wear,low drilling efficiency,and high energy consumption due to the unreasonable tooth arrangement and impact energy selection in drilling process,which affect the application effect of this technology.ABAQUS software was used for numerical simulation of rock breaking behavior under impact load with the single,three,and five teeth arrangement drill bit respectively,to improve the application effect and solve the aforementioned technical problems.Based on the calculated parameters of tooth arrangement,we designed a novel drill bit for hard rocks and provided a theoretical basis for the tooth arrangement of largediameter drill bits.
基金the Independent Innovation Research Program of China University of Petroleum(East China)(Grant No.27RA2215005)the National Key Research and Development Program of China(Grant No.2017YFC0307604).
文摘This work focus on the stress distribution of the casing-cement-formation(CCF)multilayer composite system,which is a borehole system with multiple casings and cement sheathes.Mostof the previous relevant studies are based on the traditional CCF system with the single casing and cement sheath,but these results are not adaptive to the CCF system multiple composite system.In this paper,the FEM numerical model of CCF multilayer composite system was constructed.Numerical simulations were calculated and compared with the system which consists of the single casing and cement sheath.Results show that the multilayer composite system possesses better performance.On this basis,the sensitivity analysis of main influence mechanical parameters such as in-situ stress,the elastic of cement sheathes and the elastic of formation are conducted.The cement sheath on the inside,namely cement sheath-1,is sensitive to its elastic modulus;meanwhile,the cement sheath on the outside,namely cement sheath-2,is not so sensitive to the elastic modulus of cement sheath-1.Cement sheath-1 and cement sheath-2 are all sensitive to the elastic modulus of cement sheath-2,and the mises stress of them has opposite trend to the elastic modulus of cement sheath-2.The proper values of elastic modulus of cement sheath-1 and cement sheath-2 are 5GPa and 5GPa to 30GPa,respectively.Under the in-situ stress ratio σh/σH=0.7,the maximum mises stress of cementsheath-1 and cement sheath-2 increase as the increase of σh,and they are nearly equal when σh=15GPa.This research can be helpful for the design and analysis of CCF multilayer composite system.
基金support from the national projects (Grant No.: 2009ZX05009-005 and 2010CB226703)
文摘Intermediate casings in the build sections are subject to severe wear in extended-reach drilling. This paper presents a new method for predicting the depth of a wear groove on the intermediate casing. According to energy principle and dynamic accumulation of casing wear by tool joints, a model is established to calculate the wear area on the inner wall of the casing. The relationship functions between the wear groove depth and area are obtained based on the geometry relationship between the drillstring and the wear section and the assumption that the casing wear groove is crescent-shaped. The change of casing wear groove depth versus drilling footage under different-sized drillstrings is also discussed. A mechanical model is proposed for predicting casing wear location, which is based on the well trajectory and drillstring movement. The casing wear groove depth of a planned well is predicted with inversion of the casing wear factor from the drilled well and necessarily revised to improve the prediction accuracy for differences between the drilled well and the planned well. The method for predicting casing wear in extended-reach drilling is verified through actual case study. The effect of drillstring size on casing wear should be taken into account in casing wear prediction.
基金Supported by National Natural Science Foundation of China(51904258,51874250)Project of Science and Technology of Shale Gas Exploration&Development of CCDC(2019-JS-941)National Major Project of Science and Technology(2016ZX05048-004-006)。
文摘To study the casing deformation(CD)in shale gas well fracturing caused by natural fracture slip,a fracture face stress model is built based on stress analysis,and a CD prediction model is established based on complex function to analyze factors affecting wellbore shear stress and CD.(1)The fracture and wellbore approach angles have significant impacts on the wellbore shear stress.In Weiyuan shale gas field,Sichuan Basin,under the common wellbore approach angle of nearly 90°,the wellbore is subjected to large shear stress and high risk of CD at the fracture approach angle range of 20° to 55° or its supplementary angle range.(2)When the fracture is partially opened,the wellbore shear stress is positively correlated with the fluid pressure,and negatively correlated with the fracture friction coefficient;when the fracture is fully opened,the wellbore shear stress is positively correlated with the natural fracture area.(3)The lower the elastic modulus and the longer the fracture length,the more serious the CD will be,and the Poisson’s ratio has a weak influence on the CD.The deformation first increases and then decreases with the increase of fracture approach angle,and reaches the maximum when the fracture approach angle is 45°.(4)At a given fracture approach angle,appropriately adjusting the wellbore approach angle can avoid high shear stress acting on wellbore,and reasonable control of the fluid pressure in the fracture can reduce the CD risk.The shear stress acting on casing is usually much greater than the shear strength of casing,so increasing casing strength or cementing quality have limited effect on reducing the risk of CD.Caliper logging data has verified that the CD prediction model is reliable,so the model can be used to establish risk analysis chart and calculate deformation value,to provide a reference for quick CD risk prediction in fracturing design.
基金This work was financially supported by the Science Foundation Project in Heilongjiang Province of China(No.QC2018047).
文摘There has been lack of work efforts on how to optimize cementing and completing parameters in order to prevent casing failure induced by formation slippage in pertroleum industry scope.Once the weak plane fails,the formation will become easily undertaken slippage across a large area along its interface.The plenty of horizontal planes of weakness in reservoir formations,as reported for a number of oilfields,can easily undertaken slippage once it fails.To address the problem,three-dimensional finite element models were established by taking into considerations the elastoplastic mechanical characteristics of both the casing and the near-wellbore rock.Two types of casing impairment scenarios were considered:Casing collapse(that causes tubing stuck in the well)and complete casing shear-off.In this study,the critical slip displacement of casing shear damage under both cemented and un-cemented conditions was calculated,and the critical displacement of casing with various wall thicknesses and steel grades was compared.A new cementing practice for the Daqing oilfield was then proposed by optimizing casing parameters according to API standards,and a new research method was also put forward by proposing new casing materials to effectively mitigate casing failure caused by formation slippage for the future.Modeling results indicate that the stress and deformation associated with casing in the un-cemented condition is more diffused and the critical slippage displacement is larger than that in the cemented condition.Therefore,the un-cemented condition is more effective in preventing casing shear failure and easier for casing repair,for the case of casing damage caused by formation shear slippage.Casing elongation is the key parameter of casing shear failure in the un-cemented condition.Lower grade casing exhibits a larger critical slippage displacement because of its higher elongation capacity under stress.Casing with lower grade and smaller thickness provides more advantages in preventing casing damage in formations abundant with horizontal weak layers.If the elongation of casing can be largely improved,the critical displacement value can be increased by 21.40%.Higher grade and thicker casing is adapted for mitigate casing failure caused by formation slippage.
基金supported by the Hydrogeology Survey And Comprehensive Evaluation of Large Basin and Deep Typical Southeast Coastal Region(No.12120114025101)
文摘In the enhanced geothermal systems wells, casing temperature variation produces casing thermal stresses, resulting in casing uplift or bucking. When the induced thermal stresses exceed casing material's yield strength, the casing deforms and collapses. The traditional casing design standard only considers the influence of temperature variation on casing material's yield strength. Actually, for commonly used grades of steel pipe, casing's material properties-such as yield strength, coefficient of thermal expansion, and modulus of elasticity change with temperature variation. In this paper, the modified thermal stress equation is given. Examples show that the allowable temperature of the material grade N80's casing is only 164 ℃, which is much lower than that of the traditional design standard. The effective method to improve the casing pipe's allowable temperature is pre-stressed cementing technology. Pre-stressed cementing includes pre-tension stress cementing and pre-pressure stress cementing. This paper focuses on the design method of full casing pre-tension stress cementing and the ground anchor full casing string pre-tension cementing construction process.
基金supported by the National Natural Science Foundation of China(No.11772089)the Fundamental Research Funds for the Central Universities (Nos. N160312001and N160313004)the Research Project of State Key Laboratory of Mechanical System and Vibration(No.MSV201707)
文摘Considering the elastic supports,the finite element model of rotor-bladed disk-casing system is established using commercial software ANSYS/LS-DYNA.Assuming that broken blade is released from the disk,the complicate rubbing responses of unbalanced rotor-bladed disk-casing system are studied under different operational speeds.In addition,influences of both plastic deformation of blade and casing failure are analyzed.The results show that there exist some multiple even fractional frequencies in the transient and steady vibration responses of unbalanced rotor.Besides,one nodal diameter vibration of bladed disk coupling with the lateral vibration of the shaft as well as the first order bending vibration of blade can be excited under low operational speed,while the first order bending vibration of blade coupling with the lateral vibration of disk-shaft is easily excited under high operational speed.During rubbing process,three distinct contact states can be observed:broken blade-casing contact,broken blade-blade component-casing contact and broken blade-casing contact/blade component-casing contact/blade selfcontact.It is worth noting that the third contact state is related to the operational speed.With the increase of operational speed,self-contact in the blade may occur.
基金supported by National Natural Science Foundation of China (Grant No. 50776056)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2006AA05Z250)
文摘Casing treatment is a widely employed technique to increase the stall margins of turbomachineries. In the last several decades, many researches on casing treatment have been carded out. However, the mechanism of its expanding stall margins is still not very clear. Till now, most casing teatment schemes are designed for axial compressors, while the investigations on casing treatments in centrifugal compressors are rarely reported. Moreover, current investigation methods mainly focus on experiments, and perfect theoretic al analysis is not yet feasible. In order to study the effectiveness and further the mechanism of casing treatments in centrifugal compressors, in this paper, a computationally based investigation of the impact of the self-recireulating casing treatment on the performance of a radial compressor is carried out. The results indicate that, by casing bleed and injection, the casing treatment with inclined blades in the cavity expands the stall margin most. At low mass flows, the reversed flow through the cavity with inclined blades develops the counter swirl flow in front of the impeller inlet, which is considered to benefit increasing the pressure rise from the injection port to the bleed port and thereby augment the recirculating flow. At 120% design speed, the stall margin is larger than that at the design speed. However, the cost of extending the stall margin is the reduction of isentropic efficiency. A mended casing treatment by shifting the bleed port upstream is also studied. It is demonstrated that, relative to the original casing treatment, this mend can improve the efficiency evidently notwithstanding a little narrowing of the flow range.
基金funded by Iran National Science Foundation (Grant No. 96001589 and contract No. 96002219)
文摘Casing collapse is one of the costly incidents in the oil industry. In the oil fields of southwest Iran, most casing collapses have occurred in Gachsaran formation, and the halite rock salt layer in this formation may be the main cause for these incidents because of its peculiar creep behavior. In this research, triaxial creep experiments have been conducted on Gachsaran salt samples under various temperatures and differential stresses. The main purpose was to determine the creep characteristics of Gachsaran rock salt,and to examine the role of creep in several casing collapses that occurred in this formation. Results indicated that the halite rock salt of Gachsaran formation basically obeys the power law;however, its creep parameters are quite different from other halite rocks elsewhere. The time-dependent creep of Gachsaran rock salt exhibits strong sensitivity to temperature change;however, its sensitivity to variation of differential stress is rather low. The numerical simulation of the rock salt creep in a real oil well demonstrated the importance of creep and reservoir conditions on the safety factor of the tubing related to casing collapse.
基金co-financed by the China National Natural Science Foundation and Shanghai Baosteel Group Corporation (No. 51074135)Program for New Century Excellent Talents in University (No. NCET-08-0907)Jilin Oilfield Company Project (No. JS10-W-14-JZ-32-51)
文摘Sustained casing pressure (SCP) in gas wells brings a serious threat to worker safety and environmental protection. According to geological conditions, wellbore structure and cement data of gas wells in the Sichuan-Chongqing region, China, the position, time, environmental condition and the value of SCP have been analyzed. On this basis, the shape of the pressure bleed-down plot and pressure buildup plot were diagnosed and the mechanism of SCP has been clarified. Based on generalized annular Darcy percolation theory and gas-liquid two-phase fluid dynamics theory, a coupled mathematical model of gas migration in a cemented annulus with a mud column above the cement has been developed. The volume of gas migrated in the annulus and the value of SCP changing with time in a gas well in Sichuan have been calculated by this model. Calculation results coincided well with the actual field data, which provide some reference for the following security evaluation and solution measures of SCP.
基金financial support from the National Key Sci-Tech Major Special Item(No.2011ZX05026-001)Program for Changjiang Scholars and Innovative Research Team in University(IRT1086)
文摘This paper presents a theoretical method and a finite element method to describe wellhead movement and uncemented casing strength in offshore oil and gas wells.Parameters considered in the theoretical method include operating load during drilling and completion and the temperature field,pressure field and the end effect of pressure during gas production.The finite element method for multistring analysis is developed to simulate random contact between casings.The relevant finite element analysis scheme is also presented according to the actual procedures of drilling,completion and gas production.Finally,field cases are presented and analyzed using the proposed methods.These are four offshore wells in the South China Sea.The calculated wellhead growths during gas production are compared with measured values.The results show that the wellhead subsides during drilling and completion and grows up during gas production.The theoretical and finite element solutions for wellhead growth are in good agreement with measured values and the deviations of calculation are within 10%.The maximum von Mises stress on the uncemented intermediate casing occurs during the running of the oil tube.The maximum von Mises stress on the uncemented production casing,calculated with the theoretical method occurs at removing the blow-out-preventer (BOP) while that calculated with the finite element method occurs at gas production.Finite element solutions for von Mises stress are recommended and the uncemented casings of four wells satisfy strength requirements.