The dependence of groundwater quality on borehole depth is usually debatable in groundwater studies, especially in complex geological formations where aquifer characteristics vary spatially with depth. This study ther...The dependence of groundwater quality on borehole depth is usually debatable in groundwater studies, especially in complex geological formations where aquifer characteristics vary spatially with depth. This study therefore seeks to investigate the relationship between borehole depth and groundwater quality across the granitoid aquifers within the Birimian Supergroup in the Ashanti Region. Physicochemical analysis records of groundwater quality data were collected from 23 boreholes of public and private institutions in the Ashanti Region of Ghana, and the parametric values of iron, fluoride, total hardness, pH, nitrate, and nitrite were used to study the groundwater quality-depth relationship. The results showed that the depth-to-groundwater quality indicated a marginal increase in water quality in the range of 30 to 50 m, which is mathematically represented by the low-value correlation coefficient (r<sup>2</sup> = 0.026). A relatively significant increase occurs in the depth range of 50 to 80 m, which is given by a correlation coefficient of r<sup>2</sup> = 0.298. The mean percent parameter compatibility was 74%, 82%, 89%, and 97% at 50, 60, 70, and 80 m depths, respectively. The variations in groundwater quality per depth ratio ranged from 1.48, 1.37, 1.27, and 1.21 for 50, 60, 70, and 80 m depth, respectively. The recommended minimum borehole depth for excellent groundwater quality is suggested with a compatibility per meter depth ratio of 1.37. This results in a range between 50 and 70 m as the most desirable drilling depth for excellent groundwater quality within the granitoids of the Birimian Supergroup of the Ashanti Region in Ghana.展开更多
Imaging the wave velocity field surrounding a borehole while drilling is a promising and urgently needed approach for extending the exploration range of the borehole point.This paper develops a drilling process detect...Imaging the wave velocity field surrounding a borehole while drilling is a promising and urgently needed approach for extending the exploration range of the borehole point.This paper develops a drilling process detection(DPD)system consisting of a multifunctional sensor and a pilot geophone installed at the top of the drilling rod,geophones at the tunnel face,a laser rangefinder,and an onsite computer.A weighted adjoint-state first arrival travel time tomography method is used to invert the P-wave velocity field of rock mass while borehole drilling.A field experiment in the ongoing construction of a deep buried tunnel in southwestern China demonstrated the DPD system and the tomography method.Time-frequency analysis of typical borehole drilling detection data shows that the impact drilling source is a pulse-like seismic exploration wavelet.A velocity field of the rock mass in a triangular area defined by the borehole trajectory and geophone receiving line can be obtained.Both the borehole core and optical image validate the inverted P-wave velocity field.A numerical simulation of a checkerboard benchmark model is used to test the tomography method.The rapid convergence of the misfits and consistent agreement between the inverted and observed travel times validate the P-wave velocity imaging.展开更多
Radial borehole fracturing that combines radial boreholes with hydraulic fracturing is anticipated to improve the output of tight oil and gas reservoirs.This paper aims to investigate fracture propagation and pressure...Radial borehole fracturing that combines radial boreholes with hydraulic fracturing is anticipated to improve the output of tight oil and gas reservoirs.This paper aims to investigate fracture propagation and pressure characteristics of radial borehole fracturing in multiple layers.A series of laboratory experiments with artificial rock samples(395 mm×395 mm×395 mm)was conducted using a true triaxial fracturing device.Three crucial factors corresponding to the vertical distance of adjacent radial borehole layers(vertical distance),the azimuth and diameter of the radial borehole are examined.Experimental results show that radial borehole fracturing in multiple layers generates diverse fracture geometries.Four types of fractures are identified based on the connectivity between hydraulic fractures and radial boreholes.The vertical distance significantly influences fracture propagation perpendicular to the radial borehole axis.An increase in the vertical distance impedes fracture connection across multiple radial borehole layers and reduces the fracture propagation distance along the radial borehole axis.The azimuth also influences fracture propagation along the radial borehole axis.Increasing the azimuth reduces the guiding ability of radial boreholes,which makes the fracture quickly curve to the maximum horizontal stress direction.The breakdown pressure correlates with diverse fracture geometries observed.When the fractures connect multi-layer radial boreholes,increasing the vertical distance decreases the breakdown pressure.Decreasing the azimuth and increasing the diameter also decrease the breakdown pressure.The extrusion force exists between the adjacent fractures generated in radial boreholes in multiple rows,which plays a crucial role in enhancing the guiding ability of radial boreholes and results in higher breakdown pressure.The research provides valuable theoretical insights for the field application of radial borehole fracturing technology in tight oil and gas reservoirs.展开更多
In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated por...In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.展开更多
This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume i...This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume in horizontal well fracturing.A numerical model is established to investigate the production rate,reservoir pressure field,and CO_(2)saturation distribution corresponding to changing time of CO_(2)flooding with radial borehole fracturing.A sensitivity analysis on the influence of CO_(2)injection location,layer spacing,pressure difference,borehole number,and hydraulic fractures on oil production and CO_(2)storage is conducted.The CO_(2)flooding process is divided into four stages.Reductions in layer spacing will significantly improve oil production rate and gas storage capacity.However,serious gas channeling can occur when the spacing is lower than 20 m.Increasing the pressure difference between the producer and injector,the borehole number,the hydraulic fracture height,and the fracture width can also increase the oil production rate and gas storage rate.Sensitivity analysis shows that layer spacing and fracture height greatly influence gas storage and oil production.Research outcomes are expected to provide a theoretical basis for the efficient development of shale oil reservoirs in the vertical direction.展开更多
Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P...Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.展开更多
Meeting the climate change mitigation targets will require a substantial shift from fossil to clean fuels in the heating sector.Heat pumps with deep borehole exchangers are a promising solution to reduce emissions.Her...Meeting the climate change mitigation targets will require a substantial shift from fossil to clean fuels in the heating sector.Heat pumps with deep borehole exchangers are a promising solution to reduce emissions.Here the thermal behavior of deep borehole exchangers(DBHEs)ranging from 1 to 2 km was analyzed for various heat flow profiles.A strong correlation between thermal energy extraction and power output from DBHEs was found,also influenced by the heating profile employed.Longer operating time over the year typically resulted in higher energy production,while shorter one yielded higher average thermal power output,highlighting the importance of the choice of heating strategy and system design for optimal performance of DBHEs.Short breaks in operation for regenerating the borehole,for example,with waste heat,proved to be favorable for the performance yielding an overall heat output close to the same as with continuous extraction of heat.The results demonstrate the usefulness of deep boreholes for dense urban areas with less available space.As the heat production from a single DBHE in Finnish conditions ranges from half up to even a few GWh a year,the technology is best suitable for larger heat loads.展开更多
This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collec...This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.展开更多
This study proposes a framework to evaluate the performance of borehole arrangements for the design of rectangular shallow foundation systems under spatially variable soil conditions. Performance measures are introduc...This study proposes a framework to evaluate the performance of borehole arrangements for the design of rectangular shallow foundation systems under spatially variable soil conditions. Performance measures are introduced to quantify, for a fixed foundation layout and given soil sounding locations, the variability level of the foundation system bearing capacities in terms of their mean values and standard deviations. To estimate these measures, the recently proposed random failure mechanism method (RFMM) has been adopted and extended to consider any arrangement of rectangular foundations and boreholes. Hence, three-dimensional bearing capacity estimation under spatially variable soil can be efficiently performed. Several numerical examples are presented to illustrate the applicability of the proposed framework, including diverse foundation arrangements and different soil correlation structures. Overall, the proposed framework represents a potentially useful tool to support the design of geotechnical site investigation programs, especially in situations where very limited prior knowledge about the soil properties is available.展开更多
The knowledge of in situ stress is critical in safe and optimised extraction of minerals and energy resources.In situ stresses are either measured directly(e.g.overcoring)or estimated indirectly(e.g.borehole breakouts...The knowledge of in situ stress is critical in safe and optimised extraction of minerals and energy resources.In situ stresses are either measured directly(e.g.overcoring)or estimated indirectly(e.g.borehole breakouts).Borehole breakout analysis for in situ stress estimation is considered a relatively simple and cost-efficient technique.This technique,however,poses certain limitations such as complexities with progressive formation of breakouts and it requires inputs such as rock failure parameters that are not often available.As a result,significant effort has been made to develop new indirect methods for in situ stress estimation.Borehole deformation analysis using four-arm caliper has been recently proposed for in situ stress estimation and has shown promising results.In this study,we demonstrate a new methodology that analyses the borehole televiewer data with the technique of borehole deformation analysis to estimate the in situ stresses through a field case study.The advantages and challenges of using borehole televiewer data for stress estimation based on borehole deformation analysis are discussed and the best practice to obtain the reliable results is explained.The limitations of using fourarm caliper and borehole deformation analysis for in situ stress estimation are also discussed and it is shown how televiewer data can overcome such limitations.Finally,the in situ stress results obtained from televiewer data and borehole deformation analysis are compared with independent in situ stress measurements to show the robustness and reliability of the proposed methodology.展开更多
According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method(FEM) based fluid-solid coupling, an integrated geological-engineering method...According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method(FEM) based fluid-solid coupling, an integrated geological-engineering method of volume fracturing for fan-shaped well pattern is proposed considering the geomechanical modeling, induced stress calculation, hydraulic fracturing simulation, and post-frac productivity evaluation. Besides, we propose the differential fracturing design for the conventional productivity-area and the potential production area for fan-shaped horizontal wells. After the fracturing of the conventional production area for H1 fan-shaped well platform, the research shows that the maximum reduction of the horizontal principal stress difference in the potential productivity-area is 0.2 MPa, which cannot cause the stress reversal, but this reduction is still conducive to the lateral propagation of hydraulic fractures. According to the optimized fracturing design, in zone-Ⅰ of the potential production area, only Well 2 is fractured, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage;in zone-Ⅱ, Well 2 is fractured before Well 3, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage. The swept area of the pore pressure drop in the potential production area is small, showing that the reservoir is not well developed. The hydraulic fracturing in the toe area can be improved by, for example, properly densifying the fractures and adjusting the fracture distribution, in order to enhance the swept volume and increase the reservoir utilization.展开更多
Estimation of in situ stresses based on back-analysis of measured stress changes and displacements has become an alternative to the direct stress measurement methods.In order to help users conduct own measurement and ...Estimation of in situ stresses based on back-analysis of measured stress changes and displacements has become an alternative to the direct stress measurement methods.In order to help users conduct own measurement and analysis,this paper presents in detail a field stress back-analysis approach directly from borehole strain changes measured during nearby underground excavation.Essential formulations in major steps and the procedure for the entire analysis process are provided to allow users to follow.The instrument for borehole strain change measurement can be the CSIR or CSIRO stress cells and other borehole strain cells that can measure strains on borehole walls.Strain changes corresponding to the stress changes at a borehole location are calculated in borehole environment.The stress changes due to nearby excavation can be calculated by an analytical model for a single circular opening and simulated by a numerical model for non-circular and multiple openings.These models are based on isotropic,homogeneous and linear elastic assumptions.The analysis of borehole strain changes is accomplished by multiple linear regression based on error minimization and an integrated process provides the best-fit solution directly to the in situ stresses.A statistical technique is adopted for screening outliers in the measurement data,checking measurement compatibility and evaluating the reliability of analysis results.An application example is included to demonstrate the practical application and the analysis procedure.展开更多
Reef-bank reservoirs are an important target for petroleum exploration in marine carbonates and also an essential supplemental area for oil and gas production in China. Due to the diversity of reservoirs and the extre...Reef-bank reservoirs are an important target for petroleum exploration in marine carbonates and also an essential supplemental area for oil and gas production in China. Due to the diversity of reservoirs and the extreme heterogeneity of reef-banks, it is very difficult to discriminate the sedimentary facies and lithologies in reef-bank reservoirs using conventional well logs. The borehole image log provides clear identification of sedimentary structures and textures and is an ideal tool for discriminating sedimentary facies and lithologies. After examining a large number of borehole images and cores, we propose nine typical patterns for borehole image interpretation and a method that uses these patterns to discriminate sedimentary facies and lithologies in reeI^bank reservoirs automatically. We also develop software with user-friendly interface. The results of applications in reef-bank reservoirs in the middle Tarim Basin and northeast Sichuan have proved that the proposed method and the corresponding software are quite effective.展开更多
To minimize negative effects of geostress distribution on mining safety near the fault areas, the UPM40 triaxial geostress testing system was introduced to conduct in-situ geostress measurements at three sites and nin...To minimize negative effects of geostress distribution on mining safety near the fault areas, the UPM40 triaxial geostress testing system was introduced to conduct in-situ geostress measurements at three sites and nine points by the borehole stress-relief method. The results of strain?confining pressure curves show that rock masses at the three measuring sites exhibit comprehensive linear elasticity in spite of various fissures or cracks within rocks. Horizontal and vertical stress components distribute discrepantly near the fault areas, and the maximum lateral pressure coefficient is as high as 6.15. The maximum principle stress ranges from 8.01 to 14.93 MPa, and stress directions are in the range of N78.07°W?N17.55°W. Geostresses near fault areas are dominated by the horizontal tectonic stresses, while the lower values, compared to those under similar geological conditions are due to stress release by the fault. Additionally, the fault and shear stress nearby are partially responsible for asymmetric elongation and southwesterly migration of orebodies.展开更多
Transducers that are widely applied in cement bond evaluation tools, such as cement bond logs and variable density logs, cannot radiate acoustic energy directionally because of the characteristics of monopole sources....Transducers that are widely applied in cement bond evaluation tools, such as cement bond logs and variable density logs, cannot radiate acoustic energy directionally because of the characteristics of monopole sources. A phased arc array transmitter, which is a novel transducer that differs from monopole and dipole transducers, is presented in this study. To simulate the acoustic field generated by a phased arc array in a fluid-filled cased borehole with different channelings, a 3D finite-difference time-domain method is adopted. The acoustic field generated by a traditional monopole source is also simulated and compared with the field generated by the phased arc array transmitter. Numerical simulation results show that the phased arc array radiates energy directionally in a narrow angular range in the borehole, thereby compressing the acoustic energy into a narrow range in the casing pipe, the cement, and the formation. We present the analyses of first-arrival waveforms and the amplitudes of casing waves at different azimuthal angles for the two different sources. The results indicate that employing a directional source facilitates azimuthal identification and analysis of possible channeling behind the casing pipe.展开更多
To solve the problem of water seepage of vertical feeding borehole for solid materials,we established the fluid-solid coupling dynamic model of groundwater flowing in rock mass adjacent to the vertical feeding borehol...To solve the problem of water seepage of vertical feeding borehole for solid materials,we established the fluid-solid coupling dynamic model of groundwater flowing in rock mass adjacent to the vertical feeding borehole.Combining with the engineering geological conditions,we built a numeral model to study the influence rule of the aquifer hydraulic pressure and seepage location of feeding borehole on the amount of seepage with fnite element numerical method.The results show that the nonlinear relationship is presented among the amount of seepage,the seepage location and aquifer hydraulic pressure.The higher the aquifer hydraulic pressure is,the closer the distance between seepage location and aquifer is,and the faster the harmful levels of aquifer will grow.In practice,we calculated the allowable seepage of feeding borehole by the optimum moisture content and natural moisture content of backflling materials,and then determined the protection zone of feeding borehole,so the moisture content of backflling materials can be controlled within the scope of optimum moisture content.展开更多
During mining of lower protective coal seam, a surface borehole can efficiently extract not only the pressure-relieved gas from the protected layer, but also the gas from the mining layer gob. If the distance between ...During mining of lower protective coal seam, a surface borehole can efficiently extract not only the pressure-relieved gas from the protected layer, but also the gas from the mining layer gob. If the distance between the borehole and gob is too large, the quantity of gas drained from the protected layer decreases substantially. To solve this problem, a mathematical model for extracting pressure-relieved gas from a protected coal seam using a surface borehole was established, based on the radial gas flow theory and law of conservation of energy. The key factors influencing the quantity of gas and the drainage flow network using a surface borehole were presented. The results show that the quantity of pressure-relieved gas drained from the protected layer can be significantly increased by increasing the flow resistance of the borehole bottom. Application of this method in the Wulan Coal Mine of the Shenhua Group significantly increased the flow of pure gas and the gas concentration (by factors of 1.8 and 2.0, respectively), thus demonstrating the remarkable effects of this method.展开更多
Several days before the MsT. 0 Lushan earthquake, the YRY-4 borehole Strainmeter at Guza Station recorded prominent abnormal changes. The strain anomalies are very striking on the smooth background of several years' ...Several days before the MsT. 0 Lushan earthquake, the YRY-4 borehole Strainmeter at Guza Station recorded prominent abnormal changes. The strain anomalies are very striking on the smooth background of several years' recording after the Wenchuan earthquake. However, because construction in the town of Guza has been undergoing rapid development in recent years, many factors have interfered with observations at the station. Whether or not the observed strain changes before the Lushan earthquake were affected by any of the sources of interference becomes a question that must be answered. Among the likely sources of interference, apartment construction, sportsground reconstruction, and tunnel cutting can be excluded by analyzing the morphological characteristic of the anomalies. The two remaining most possible sources are road construction in front of the station and the water level change of the nearby Dadu River caused by water filling into and discharging from an upstream reservoir. Through field investigation, comparison of the correlation between the strain and the seismographic recordings, comparison of the correlation between the strain and the Dadu River flow recordings, and analysis of the strain anomaly characteristics, we conclude that the abnormal changes observed at Guza Station cannot be attributed to either of these two sources but should be related to the Lushan earthquake.展开更多
Based on the plane of weakness theory, a model for predicting borehole stability in fractured reservoirs under different stress states was estiblisted and the equations for solving borehole stability were developed. T...Based on the plane of weakness theory, a model for predicting borehole stability in fractured reservoirs under different stress states was estiblisted and the equations for solving borehole stability were developed. The minimum downhole pressures required to maintain borehole stability under different natural fracture occurrences were calculated by using the data from a well in the Tazhong (central Tarim) area, Tarim Basin, west China. Several conclusions were drawn for naturally fractured reservoirs with a dip angle from less than 10° to greater than 30°. Application in three wells in the Tazhong area indicates that this model is practically useful.展开更多
Estimation of horizontal stress magnitudes from borehole breakouts has been an attractive topic in the petroleum and mining industries,although there are critical research gaps that remain unfilled.In this paper,numer...Estimation of horizontal stress magnitudes from borehole breakouts has been an attractive topic in the petroleum and mining industries,although there are critical research gaps that remain unfilled.In this paper,numerical simulation is conducted on Gosford sandstone to investigate the borehole breakout and its associated borehole size effect,including temperature influence.The discrete element method(DEM)model shows that the borehole breakout angular span is constant after the initial formation,whereas its depth propagates along the minimum horizontal stress direction.This indicates that the breakout angular span is a reliable parameter for horizontal stress estimation.The borehole size effect simulations illustrated the importance of borehole size on breakout geometries in which smaller borehole size leads to higher breakout initiation stress as well as the stress re-distribution from borehole wall outwards through micro-cracking.This implies that the stress may be averaged over a distance around the borehole and breakout initiation occurs at the borehole wall rather than some distance into the rock.In addition,the numerical simulation incorporated the thermal effect which is widely encountered in deep geothermal wells.Based on the results,the higher temperature led to lower breakout initiation stress with same borehole size,and more proportion of shear cracks was generated under higher temperature.This indicates that the temperature might contribute to the micro-fracturing mode and hence influences the horizontal stress estimation results from borehole breakout geometries.Numerical simulation showed that breakout shape and dimensions changed considerably under high stress and high temperature conditions,suggesting that the temperature may need to be considered for breakout stress analysis in deep locations.展开更多
文摘The dependence of groundwater quality on borehole depth is usually debatable in groundwater studies, especially in complex geological formations where aquifer characteristics vary spatially with depth. This study therefore seeks to investigate the relationship between borehole depth and groundwater quality across the granitoid aquifers within the Birimian Supergroup in the Ashanti Region. Physicochemical analysis records of groundwater quality data were collected from 23 boreholes of public and private institutions in the Ashanti Region of Ghana, and the parametric values of iron, fluoride, total hardness, pH, nitrate, and nitrite were used to study the groundwater quality-depth relationship. The results showed that the depth-to-groundwater quality indicated a marginal increase in water quality in the range of 30 to 50 m, which is mathematically represented by the low-value correlation coefficient (r<sup>2</sup> = 0.026). A relatively significant increase occurs in the depth range of 50 to 80 m, which is given by a correlation coefficient of r<sup>2</sup> = 0.298. The mean percent parameter compatibility was 74%, 82%, 89%, and 97% at 50, 60, 70, and 80 m depths, respectively. The variations in groundwater quality per depth ratio ranged from 1.48, 1.37, 1.27, and 1.21 for 50, 60, 70, and 80 m depth, respectively. The recommended minimum borehole depth for excellent groundwater quality is suggested with a compatibility per meter depth ratio of 1.37. This results in a range between 50 and 70 m as the most desirable drilling depth for excellent groundwater quality within the granitoids of the Birimian Supergroup of the Ashanti Region in Ghana.
基金the support of the National Natural Science Foundation of China(Nos.42207211,42202320 and 42172296)Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education,Tongji University(No.KLE-TJGE-G2304).
文摘Imaging the wave velocity field surrounding a borehole while drilling is a promising and urgently needed approach for extending the exploration range of the borehole point.This paper develops a drilling process detection(DPD)system consisting of a multifunctional sensor and a pilot geophone installed at the top of the drilling rod,geophones at the tunnel face,a laser rangefinder,and an onsite computer.A weighted adjoint-state first arrival travel time tomography method is used to invert the P-wave velocity field of rock mass while borehole drilling.A field experiment in the ongoing construction of a deep buried tunnel in southwestern China demonstrated the DPD system and the tomography method.Time-frequency analysis of typical borehole drilling detection data shows that the impact drilling source is a pulse-like seismic exploration wavelet.A velocity field of the rock mass in a triangular area defined by the borehole trajectory and geophone receiving line can be obtained.Both the borehole core and optical image validate the inverted P-wave velocity field.A numerical simulation of a checkerboard benchmark model is used to test the tomography method.The rapid convergence of the misfits and consistent agreement between the inverted and observed travel times validate the P-wave velocity imaging.
基金The authors gratefully acknowledge the financial support received from the Strategic Cooperation Technology Projects of CNPC and CUPB(No.ZLZX2020-01)the National Key Scientific Research Instrument Research Project of NSFC(No.51827804).
文摘Radial borehole fracturing that combines radial boreholes with hydraulic fracturing is anticipated to improve the output of tight oil and gas reservoirs.This paper aims to investigate fracture propagation and pressure characteristics of radial borehole fracturing in multiple layers.A series of laboratory experiments with artificial rock samples(395 mm×395 mm×395 mm)was conducted using a true triaxial fracturing device.Three crucial factors corresponding to the vertical distance of adjacent radial borehole layers(vertical distance),the azimuth and diameter of the radial borehole are examined.Experimental results show that radial borehole fracturing in multiple layers generates diverse fracture geometries.Four types of fractures are identified based on the connectivity between hydraulic fractures and radial boreholes.The vertical distance significantly influences fracture propagation perpendicular to the radial borehole axis.An increase in the vertical distance impedes fracture connection across multiple radial borehole layers and reduces the fracture propagation distance along the radial borehole axis.The azimuth also influences fracture propagation along the radial borehole axis.Increasing the azimuth reduces the guiding ability of radial boreholes,which makes the fracture quickly curve to the maximum horizontal stress direction.The breakdown pressure correlates with diverse fracture geometries observed.When the fractures connect multi-layer radial boreholes,increasing the vertical distance decreases the breakdown pressure.Decreasing the azimuth and increasing the diameter also decrease the breakdown pressure.The extrusion force exists between the adjacent fractures generated in radial boreholes in multiple rows,which plays a crucial role in enhancing the guiding ability of radial boreholes and results in higher breakdown pressure.The research provides valuable theoretical insights for the field application of radial borehole fracturing technology in tight oil and gas reservoirs.
基金Project supported by the National Natural Science Foundation of China (Grant No.42074139)the Natural Science Foundation of Jilin Province,China (Grant No.20210101140JC)。
文摘In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.
基金This study has been funded by the National Science Fund for Distinguished Young Scholars(No.52204063)Science Foundation of China University of Petroleum,Beijing(No.2462023BJRC025).Moreover,we would like to express our heartfelt appreciation to the Computational Geosciences group in the Department of Mathematics and Cybernetics at SINTEF Digital for developing and providing the free open-source MATLAB Reservoir Simulation Toolbox(MRST)used in this research.
文摘This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume in horizontal well fracturing.A numerical model is established to investigate the production rate,reservoir pressure field,and CO_(2)saturation distribution corresponding to changing time of CO_(2)flooding with radial borehole fracturing.A sensitivity analysis on the influence of CO_(2)injection location,layer spacing,pressure difference,borehole number,and hydraulic fractures on oil production and CO_(2)storage is conducted.The CO_(2)flooding process is divided into four stages.Reductions in layer spacing will significantly improve oil production rate and gas storage capacity.However,serious gas channeling can occur when the spacing is lower than 20 m.Increasing the pressure difference between the producer and injector,the borehole number,the hydraulic fracture height,and the fracture width can also increase the oil production rate and gas storage rate.Sensitivity analysis shows that layer spacing and fracture height greatly influence gas storage and oil production.Research outcomes are expected to provide a theoretical basis for the efficient development of shale oil reservoirs in the vertical direction.
基金financially supported by National Natural Science Foundation of China(Grant Nos.52074312 and 52211530097)CNPC Science and Technology Innovation Foundation(Grant No.2021DQ02-0505).
文摘Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.
文摘Meeting the climate change mitigation targets will require a substantial shift from fossil to clean fuels in the heating sector.Heat pumps with deep borehole exchangers are a promising solution to reduce emissions.Here the thermal behavior of deep borehole exchangers(DBHEs)ranging from 1 to 2 km was analyzed for various heat flow profiles.A strong correlation between thermal energy extraction and power output from DBHEs was found,also influenced by the heating profile employed.Longer operating time over the year typically resulted in higher energy production,while shorter one yielded higher average thermal power output,highlighting the importance of the choice of heating strategy and system design for optimal performance of DBHEs.Short breaks in operation for regenerating the borehole,for example,with waste heat,proved to be favorable for the performance yielding an overall heat output close to the same as with continuous extraction of heat.The results demonstrate the usefulness of deep boreholes for dense urban areas with less available space.As the heat production from a single DBHE in Finnish conditions ranges from half up to even a few GWh a year,the technology is best suitable for larger heat loads.
基金funded by the Australian Coal Industry’s Research Program(ACARP,Grant No.C26063).
文摘This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.
基金support of the Polish National Agency for Academic Exchange under the Bekker NAWA Programme(Grant No.BPN/BEK/2021/1/00068)which founded the postdoctoral fellowship at the Institute of Risk and Reliability at Leibniz University Hannover.The first author would also like to thank to Prof.Wengang Zhang and Chongzhi Wu(School of Civil Engineering,Chongqing University)for inspiring discussions initi-ated by High-end Foreign Expert Introduction program(Grant No.DL2021165001L)by the Ministry of Science and Technology(MOST),ChinaThe second author would like to thank the support from ANID(National Agency for Research and Development,Chile)and DAAD(German Academic Exchange Service,Germany)under CONICYT-PFCHA/Doctorado Acuerdo Bilateral DAAD Becas Chile/2018-62180007.The third author gratefully acknowledges the support by ANID under its program FONDECYT(Grant No.1200087).
文摘This study proposes a framework to evaluate the performance of borehole arrangements for the design of rectangular shallow foundation systems under spatially variable soil conditions. Performance measures are introduced to quantify, for a fixed foundation layout and given soil sounding locations, the variability level of the foundation system bearing capacities in terms of their mean values and standard deviations. To estimate these measures, the recently proposed random failure mechanism method (RFMM) has been adopted and extended to consider any arrangement of rectangular foundations and boreholes. Hence, three-dimensional bearing capacity estimation under spatially variable soil can be efficiently performed. Several numerical examples are presented to illustrate the applicability of the proposed framework, including diverse foundation arrangements and different soil correlation structures. Overall, the proposed framework represents a potentially useful tool to support the design of geotechnical site investigation programs, especially in situations where very limited prior knowledge about the soil properties is available.
文摘The knowledge of in situ stress is critical in safe and optimised extraction of minerals and energy resources.In situ stresses are either measured directly(e.g.overcoring)or estimated indirectly(e.g.borehole breakouts).Borehole breakout analysis for in situ stress estimation is considered a relatively simple and cost-efficient technique.This technique,however,poses certain limitations such as complexities with progressive formation of breakouts and it requires inputs such as rock failure parameters that are not often available.As a result,significant effort has been made to develop new indirect methods for in situ stress estimation.Borehole deformation analysis using four-arm caliper has been recently proposed for in situ stress estimation and has shown promising results.In this study,we demonstrate a new methodology that analyses the borehole televiewer data with the technique of borehole deformation analysis to estimate the in situ stresses through a field case study.The advantages and challenges of using borehole televiewer data for stress estimation based on borehole deformation analysis are discussed and the best practice to obtain the reliable results is explained.The limitations of using fourarm caliper and borehole deformation analysis for in situ stress estimation are also discussed and it is shown how televiewer data can overcome such limitations.Finally,the in situ stress results obtained from televiewer data and borehole deformation analysis are compared with independent in situ stress measurements to show the robustness and reliability of the proposed methodology.
基金Supported by National Natural Science Foundation of China (52104029,U2139204)PetroChina Science and Technology Innovation Foundation (2021 DQ02-0501)。
文摘According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method(FEM) based fluid-solid coupling, an integrated geological-engineering method of volume fracturing for fan-shaped well pattern is proposed considering the geomechanical modeling, induced stress calculation, hydraulic fracturing simulation, and post-frac productivity evaluation. Besides, we propose the differential fracturing design for the conventional productivity-area and the potential production area for fan-shaped horizontal wells. After the fracturing of the conventional production area for H1 fan-shaped well platform, the research shows that the maximum reduction of the horizontal principal stress difference in the potential productivity-area is 0.2 MPa, which cannot cause the stress reversal, but this reduction is still conducive to the lateral propagation of hydraulic fractures. According to the optimized fracturing design, in zone-Ⅰ of the potential production area, only Well 2 is fractured, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage;in zone-Ⅱ, Well 2 is fractured before Well 3, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage. The swept area of the pore pressure drop in the potential production area is small, showing that the reservoir is not well developed. The hydraulic fracturing in the toe area can be improved by, for example, properly densifying the fractures and adjusting the fracture distribution, in order to enhance the swept volume and increase the reservoir utilization.
文摘Estimation of in situ stresses based on back-analysis of measured stress changes and displacements has become an alternative to the direct stress measurement methods.In order to help users conduct own measurement and analysis,this paper presents in detail a field stress back-analysis approach directly from borehole strain changes measured during nearby underground excavation.Essential formulations in major steps and the procedure for the entire analysis process are provided to allow users to follow.The instrument for borehole strain change measurement can be the CSIR or CSIRO stress cells and other borehole strain cells that can measure strains on borehole walls.Strain changes corresponding to the stress changes at a borehole location are calculated in borehole environment.The stress changes due to nearby excavation can be calculated by an analytical model for a single circular opening and simulated by a numerical model for non-circular and multiple openings.These models are based on isotropic,homogeneous and linear elastic assumptions.The analysis of borehole strain changes is accomplished by multiple linear regression based on error minimization and an integrated process provides the best-fit solution directly to the in situ stresses.A statistical technique is adopted for screening outliers in the measurement data,checking measurement compatibility and evaluating the reliability of analysis results.An application example is included to demonstrate the practical application and the analysis procedure.
基金sponsored by the National S&T Major Special Project(No.2008ZX05020-01)
文摘Reef-bank reservoirs are an important target for petroleum exploration in marine carbonates and also an essential supplemental area for oil and gas production in China. Due to the diversity of reservoirs and the extreme heterogeneity of reef-banks, it is very difficult to discriminate the sedimentary facies and lithologies in reef-bank reservoirs using conventional well logs. The borehole image log provides clear identification of sedimentary structures and textures and is an ideal tool for discriminating sedimentary facies and lithologies. After examining a large number of borehole images and cores, we propose nine typical patterns for borehole image interpretation and a method that uses these patterns to discriminate sedimentary facies and lithologies in reeI^bank reservoirs automatically. We also develop software with user-friendly interface. The results of applications in reef-bank reservoirs in the middle Tarim Basin and northeast Sichuan have proved that the proposed method and the corresponding software are quite effective.
基金Projects(50934002,51104011)supported by the National Natural Science Foundation of ChinaProject(2012BAB08B02)supported by the National Key Technologies R&D Program during the 12th Five-year Plan of China
文摘To minimize negative effects of geostress distribution on mining safety near the fault areas, the UPM40 triaxial geostress testing system was introduced to conduct in-situ geostress measurements at three sites and nine points by the borehole stress-relief method. The results of strain?confining pressure curves show that rock masses at the three measuring sites exhibit comprehensive linear elasticity in spite of various fissures or cracks within rocks. Horizontal and vertical stress components distribute discrepantly near the fault areas, and the maximum lateral pressure coefficient is as high as 6.15. The maximum principle stress ranges from 8.01 to 14.93 MPa, and stress directions are in the range of N78.07°W?N17.55°W. Geostresses near fault areas are dominated by the horizontal tectonic stresses, while the lower values, compared to those under similar geological conditions are due to stress release by the fault. Additionally, the fault and shear stress nearby are partially responsible for asymmetric elongation and southwesterly migration of orebodies.
基金supported by the National Natural ScienceFoundation of China (Grant Nos. 11204380, 11374371, 11134011 and 61102102)National Science and Technology Major Project (Grant No. 2011ZX05020-009)PetroChina Innovation Foundation (2013D-5006-0304)
文摘Transducers that are widely applied in cement bond evaluation tools, such as cement bond logs and variable density logs, cannot radiate acoustic energy directionally because of the characteristics of monopole sources. A phased arc array transmitter, which is a novel transducer that differs from monopole and dipole transducers, is presented in this study. To simulate the acoustic field generated by a phased arc array in a fluid-filled cased borehole with different channelings, a 3D finite-difference time-domain method is adopted. The acoustic field generated by a traditional monopole source is also simulated and compared with the field generated by the phased arc array transmitter. Numerical simulation results show that the phased arc array radiates energy directionally in a narrow angular range in the borehole, thereby compressing the acoustic energy into a narrow range in the casing pipe, the cement, and the formation. We present the analyses of first-arrival waveforms and the amplitudes of casing waves at different azimuthal angles for the two different sources. The results indicate that employing a directional source facilitates azimuthal identification and analysis of possible channeling behind the casing pipe.
基金funded by the State Key Development Program for Basic Research of China(No.2013CB227900)the National High Technology Joint Research Program of China(No.2012BAB13B00)
文摘To solve the problem of water seepage of vertical feeding borehole for solid materials,we established the fluid-solid coupling dynamic model of groundwater flowing in rock mass adjacent to the vertical feeding borehole.Combining with the engineering geological conditions,we built a numeral model to study the influence rule of the aquifer hydraulic pressure and seepage location of feeding borehole on the amount of seepage with fnite element numerical method.The results show that the nonlinear relationship is presented among the amount of seepage,the seepage location and aquifer hydraulic pressure.The higher the aquifer hydraulic pressure is,the closer the distance between seepage location and aquifer is,and the faster the harmful levels of aquifer will grow.In practice,we calculated the allowable seepage of feeding borehole by the optimum moisture content and natural moisture content of backflling materials,and then determined the protection zone of feeding borehole,so the moisture content of backflling materials can be controlled within the scope of optimum moisture content.
文摘During mining of lower protective coal seam, a surface borehole can efficiently extract not only the pressure-relieved gas from the protected layer, but also the gas from the mining layer gob. If the distance between the borehole and gob is too large, the quantity of gas drained from the protected layer decreases substantially. To solve this problem, a mathematical model for extracting pressure-relieved gas from a protected coal seam using a surface borehole was established, based on the radial gas flow theory and law of conservation of energy. The key factors influencing the quantity of gas and the drainage flow network using a surface borehole were presented. The results show that the quantity of pressure-relieved gas drained from the protected layer can be significantly increased by increasing the flow resistance of the borehole bottom. Application of this method in the Wulan Coal Mine of the Shenhua Group significantly increased the flow of pure gas and the gas concentration (by factors of 1.8 and 2.0, respectively), thus demonstrating the remarkable effects of this method.
基金supported by the Special Fund for Earthquake Research in the Public Interest(201108009)
文摘Several days before the MsT. 0 Lushan earthquake, the YRY-4 borehole Strainmeter at Guza Station recorded prominent abnormal changes. The strain anomalies are very striking on the smooth background of several years' recording after the Wenchuan earthquake. However, because construction in the town of Guza has been undergoing rapid development in recent years, many factors have interfered with observations at the station. Whether or not the observed strain changes before the Lushan earthquake were affected by any of the sources of interference becomes a question that must be answered. Among the likely sources of interference, apartment construction, sportsground reconstruction, and tunnel cutting can be excluded by analyzing the morphological characteristic of the anomalies. The two remaining most possible sources are road construction in front of the station and the water level change of the nearby Dadu River caused by water filling into and discharging from an upstream reservoir. Through field investigation, comparison of the correlation between the strain and the seismographic recordings, comparison of the correlation between the strain and the Dadu River flow recordings, and analysis of the strain anomaly characteristics, we conclude that the abnormal changes observed at Guza Station cannot be attributed to either of these two sources but should be related to the Lushan earthquake.
文摘Based on the plane of weakness theory, a model for predicting borehole stability in fractured reservoirs under different stress states was estiblisted and the equations for solving borehole stability were developed. The minimum downhole pressures required to maintain borehole stability under different natural fracture occurrences were calculated by using the data from a well in the Tazhong (central Tarim) area, Tarim Basin, west China. Several conclusions were drawn for naturally fractured reservoirs with a dip angle from less than 10° to greater than 30°. Application in three wells in the Tazhong area indicates that this model is practically useful.
基金The work reported here is funded by Australian Coal Industry’s Research Program(ACARP)grant no.C26063.
文摘Estimation of horizontal stress magnitudes from borehole breakouts has been an attractive topic in the petroleum and mining industries,although there are critical research gaps that remain unfilled.In this paper,numerical simulation is conducted on Gosford sandstone to investigate the borehole breakout and its associated borehole size effect,including temperature influence.The discrete element method(DEM)model shows that the borehole breakout angular span is constant after the initial formation,whereas its depth propagates along the minimum horizontal stress direction.This indicates that the breakout angular span is a reliable parameter for horizontal stress estimation.The borehole size effect simulations illustrated the importance of borehole size on breakout geometries in which smaller borehole size leads to higher breakout initiation stress as well as the stress re-distribution from borehole wall outwards through micro-cracking.This implies that the stress may be averaged over a distance around the borehole and breakout initiation occurs at the borehole wall rather than some distance into the rock.In addition,the numerical simulation incorporated the thermal effect which is widely encountered in deep geothermal wells.Based on the results,the higher temperature led to lower breakout initiation stress with same borehole size,and more proportion of shear cracks was generated under higher temperature.This indicates that the temperature might contribute to the micro-fracturing mode and hence influences the horizontal stress estimation results from borehole breakout geometries.Numerical simulation showed that breakout shape and dimensions changed considerably under high stress and high temperature conditions,suggesting that the temperature may need to be considered for breakout stress analysis in deep locations.