Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strai...Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strain assumption may have large uncertainties when the fracture height is small. To solve this problem, a 3-D finite element method(FEM) is used to model wellbore strengthening and calculate the fracture width. Comparisons show that the 2-D plane strain solution is the asymptote of the 3-D FEM solution. Therefore, the 2-D solution may overestimate the fracture width. This indicates that the2-D solution may not be applicable in 3-D conditions. Based on the FEM modeling, a new 3-D semi-analytical solution for determining the fracture width is proposed, which accounts for the e ects of 3-D fracture dimensions, stress anisotropy and borehole inclination. Compared to the 2-D solution, this new 3-D semi-analytical solution predicts a smaller fracture width.This implies that the 2-D-based old design for wellbore strengthening may overestimate the fracture width, which can be reduced using the proposed 3-D solution. It also allows an easy way to calculate the fracture width in complex geometrical and geological conditions. This solution has been verified against 3-D finite element calculations for field applications.展开更多
Fracture is a common underground structure phenomenon,which can provide space and passage for the storage and migration of oil and gas.Borehole radar is a fast and high-resolution geophysical detection method,which ha...Fracture is a common underground structure phenomenon,which can provide space and passage for the storage and migration of oil and gas.Borehole radar is a fast and high-resolution geophysical detection method,which has been widely used in engineering,exploration and other fields.This paper mainly uses theoretical analysis and numerical simulation to study the variation law of the characteristics of the received borehole radar signal with the variation of fracture width.The Ricker wavelet is used as the pulse signal of the borehole radar.The results show that the amplitude of the signal received by the borehole radar first increases,then decreases,and finally tends to be a stable value with the increase of fracture width.The results have guiding significance for the detection of underground fractures and the estimation of fracture width by borehole radar.展开更多
By means of reasonable assumption and mathematical derivation, a theoretic expression of flow rate for a single fracture with linearly varying width was obtained. The mathematical derivation was based on the cubic law...By means of reasonable assumption and mathematical derivation, a theoretic expression of flow rate for a single fracture with linearly varying width was obtained. The mathematical derivation was based on the cubic law and the new theoretic expression was an extention of traditional parallel plate model. This study may help to analyze seepage in fractured rock mass.展开更多
The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By usin...The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.展开更多
Fractures in oil and gas reservoirs have been the topic of many studies and have attracted reservoir research all over the world. Because of the complexities of the fractures, it is difficult to use fractured reservoi...Fractures in oil and gas reservoirs have been the topic of many studies and have attracted reservoir research all over the world. Because of the complexities of the fractures, it is difficult to use fractured reservoir core samples to investigate true underground conditions. Due to the diversity of the fracture parameters, the simulation and evaluation of fractured rock in the laboratory setting is also difficult. Previous researchers have typically used a single material, such as resin, to simulate fractures. There has been a great deal of simplifying of the materials and conditions, which has led to disappointing results in application. In the present study, sandstone core samples were selected and sectioned to simulate fractures, and the changes of the compressional and shear waves were measured with the gradual increasing of the fracture width. The effects of the simulated fracture width on the acoustic wave velocity and amplitude were analyzed. Two variables were defined： H represents the amplitude attenuation ratio of the compressional and shear wave, and x represents the transit time difference value of the shear wave and compressional wave divided by the transit time of the compressional wave. The effect of fracture width on these two physical quantities was then analyzed. Finally, the methods of quantitative evaluation for fracture width with H and x were obtained. The experimental results showed that the rock fractures linearly reduced the velocity of the shear and compressional waves. The effect of twin fractures on thecompressional velocity was almost equal to that of a single fracture which had the same fracture width as the sum of the twin fractures. At the same time, the existence of fractures led to acoustic wave amplitude attenuations, and the compressional wave attenuation was two times greater than that of the shear wave. In this paper, a method was proposed to calculate the fracture width with x and H, then this was applied to the array acoustic imaging logging data.The application examples showed that the calculated fracture width could be compared with fractures on the electric imaging logs. These rules were applied in the well logs to effectively evaluate the fractures, under the case of no image logs, which had significance to prospecting and development of oil and gas in fractured reservoirs.展开更多
Present support theories contain a number of shortcomings in the designation of fractured roof bolt parameters of rectangular or trapezoidal coal roadways.Roof fall accidents occur easily in this kind of roadway.Based...Present support theories contain a number of shortcomings in the designation of fractured roof bolt parameters of rectangular or trapezoidal coal roadways.Roof fall accidents occur easily in this kind of roadway.Based on the Bossinesq equations and the Mohr strength theory,we propose a theory of an anchored cluster structure for fractured roofs and have investigated the formation of such an anchored cluster structure,its self stability mechanism and mechanical properties.The results show that an anchor and the surrounding fractured rock can form a string-like supporting structure,referred to as the structure of an anchored cluster for rational bolt parameters.Not only can the structure maintain its own stability,but as well undertake the load of the overlying strata.The designated support parameters,based on anchored cluster theory can overcome the shortcomings of other support theories applied to a fractured roof of rectangular roadways or could not be calculated.Our anchored cluster theory can provide a theoretical basis for the design of support for rectangular fractured roofs.Furthermore,the theory will help to reduce the probability of roof fall accidents caused by local fractured rock blocks,which can destroy a supporting structure.展开更多
Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results direc...Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results directly from the random width characterized by the artificial fractures. To solve this problem, a series of simulated fractured core samples made of stainless steel with a given width of fracture were prepared. The relative error for the width of artificial fracture decreased to 1%. The width of natural and artificial fractures in carbonate reservoirs can be estimated by image log data. A series of tests for formation damage were conducted by using the stainless steel simulated core samples flushed with different drilling fluids, such as the sulfonate/polymer drill-in fluid and the solids-flee drill-in fluid with or without ideal packing bridging materials. Based on the experimental results using this kind of simulated cores, a novel approach to the damage control of fractured carbonate reservoirs was presented. The effective temporary plugging ring on the end face of the simulated core sample can be observed clearly. The experimental results also show that the stainless steel simulated cores made it possible to visualize the solids and filtrate invasion.展开更多
To quantitatively determine the effect of different factors such as fracture width,dip angle,extension and filling material on Stoneley wave amplitude decreasing,the shock tube experiment method was changed from fixin...To quantitatively determine the effect of different factors such as fracture width,dip angle,extension and filling material on Stoneley wave amplitude decreasing,the shock tube experiment method was changed from fixing the sample and vertically moving the sensor in the borehole to fixing the sensors along the shock tube wall and vertically moving the sample without drilling the borehole in it.The measurement accuracy and the signal-to-noise ratio of the first Stoneley wave were improved by the time corrections and amplitude corrections of Stoneley wave signals.At the same time,21 sets of core models with different fracture parameters were processed for this measurement method by using full-diameter carbonate core,and relative amplitudes were defined to characterize Stoneley wave amplitude decreasing.The experimental results show that the relative amplitude of Stoneley wave exponentially decreases with increasing fracture width.The relative amplitude of Stoneley wave linearly decreases with increasing fracture dip angle.The relative amplitude of Stoneley wave exponentially decreases with increasing fracture extension.The relative amplitude of Stoneley wave decreases with increasing the permeability of filling material in the fracture.Under the above four conditions,the fracture width has the greatest effect on the decreasing of Stoneley wave amplitude,followed by the fracture extension and the permeability of filling material,and finally the fracture dip angle.展开更多
The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect.There are two shortcomings of current r...The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect.There are two shortcomings of current research on proppant equilibrium heights,one of which is that the effect of fracture widths is neglected when calculating the settling velocity and another of which is that the settling bed height is a constant when building the settling bed height growth rate model.To fill those two shortcomings,this work provides a novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments.A comparison between the results obtained from the novel model and the published model and experimental results indicates that the proposed model is verified.From the sensitivity analysis,it is concluded that the proppant equilibrium height increases with an increasing proppant density.The proppant equilibrium height decreases with an increase in the slickwater injection rate and increases with an increase in the proppant injection rate.The increase in proppant diameter results in an increasing the friction factor,which makes proppant equilibrium heights decrease.Meanwhile,the increase in proppant sizes results in an increase in proppant settling rates,which makes the proppant equilibrium height increase.When the effect of the proppant diameter on settling rates is more significant than that on friction factors,the equilibrium height increases with an increasing proppant size.This work provides a research basis of proppant distributions during the hydraulic fracture.展开更多
Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is...Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.展开更多
基金partially supported by National Key R&D Program of China (2017YFC0804108) during the 13th Five-Year Plan PeriodNational Science Foundation of China (51774136)+1 种基金Natural Science Foundation of Hebei Province of China (D2017508099)the Program for Innovative Research Team in the University sponsored by Ministry of Education of China (IRT-17R37)
文摘Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strain assumption may have large uncertainties when the fracture height is small. To solve this problem, a 3-D finite element method(FEM) is used to model wellbore strengthening and calculate the fracture width. Comparisons show that the 2-D plane strain solution is the asymptote of the 3-D FEM solution. Therefore, the 2-D solution may overestimate the fracture width. This indicates that the2-D solution may not be applicable in 3-D conditions. Based on the FEM modeling, a new 3-D semi-analytical solution for determining the fracture width is proposed, which accounts for the e ects of 3-D fracture dimensions, stress anisotropy and borehole inclination. Compared to the 2-D solution, this new 3-D semi-analytical solution predicts a smaller fracture width.This implies that the 2-D-based old design for wellbore strengthening may overestimate the fracture width, which can be reduced using the proposed 3-D solution. It also allows an easy way to calculate the fracture width in complex geometrical and geological conditions. This solution has been verified against 3-D finite element calculations for field applications.
基金Supported by National Natural Science Foundation of China (Nos. 41874136 and 42074146)。
文摘Fracture is a common underground structure phenomenon,which can provide space and passage for the storage and migration of oil and gas.Borehole radar is a fast and high-resolution geophysical detection method,which has been widely used in engineering,exploration and other fields.This paper mainly uses theoretical analysis and numerical simulation to study the variation law of the characteristics of the received borehole radar signal with the variation of fracture width.The Ricker wavelet is used as the pulse signal of the borehole radar.The results show that the amplitude of the signal received by the borehole radar first increases,then decreases,and finally tends to be a stable value with the increase of fracture width.The results have guiding significance for the detection of underground fractures and the estimation of fracture width by borehole radar.
基金supported by the National Basic Research Program of China(2009CB219605)the National Natural Science Foundation of China(41074040)
文摘By means of reasonable assumption and mathematical derivation, a theoretic expression of flow rate for a single fracture with linearly varying width was obtained. The mathematical derivation was based on the cubic law and the new theoretic expression was an extention of traditional parallel plate model. This study may help to analyze seepage in fractured rock mass.
基金Project supported by the National Natural Science Foundation of China (No.90305023)
文摘The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.
基金supported in part by the National Natural Science Foundation of China (Grant No. 41174096)the Graduate Innovation Fund of Jilin University (Project No. 2016103)
文摘Fractures in oil and gas reservoirs have been the topic of many studies and have attracted reservoir research all over the world. Because of the complexities of the fractures, it is difficult to use fractured reservoir core samples to investigate true underground conditions. Due to the diversity of the fracture parameters, the simulation and evaluation of fractured rock in the laboratory setting is also difficult. Previous researchers have typically used a single material, such as resin, to simulate fractures. There has been a great deal of simplifying of the materials and conditions, which has led to disappointing results in application. In the present study, sandstone core samples were selected and sectioned to simulate fractures, and the changes of the compressional and shear waves were measured with the gradual increasing of the fracture width. The effects of the simulated fracture width on the acoustic wave velocity and amplitude were analyzed. Two variables were defined： H represents the amplitude attenuation ratio of the compressional and shear wave, and x represents the transit time difference value of the shear wave and compressional wave divided by the transit time of the compressional wave. The effect of fracture width on these two physical quantities was then analyzed. Finally, the methods of quantitative evaluation for fracture width with H and x were obtained. The experimental results showed that the rock fractures linearly reduced the velocity of the shear and compressional waves. The effect of twin fractures on thecompressional velocity was almost equal to that of a single fracture which had the same fracture width as the sum of the twin fractures. At the same time, the existence of fractures led to acoustic wave amplitude attenuations, and the compressional wave attenuation was two times greater than that of the shear wave. In this paper, a method was proposed to calculate the fracture width with x and H, then this was applied to the array acoustic imaging logging data.The application examples showed that the calculated fracture width could be compared with fractures on the electric imaging logs. These rules were applied in the well logs to effectively evaluate the fractures, under the case of no image logs, which had significance to prospecting and development of oil and gas in fractured reservoirs.
基金provided by the National Natural Science Foundation of China (No.50774077)the Ministry of Education for New Century Excellent Talent Support Program of China (No.NCET-06-0475)the Science Foundation for Youth Scholar of China University of Mining and Technology (Beijing) (No.2009QZ01)
文摘Present support theories contain a number of shortcomings in the designation of fractured roof bolt parameters of rectangular or trapezoidal coal roadways.Roof fall accidents occur easily in this kind of roadway.Based on the Bossinesq equations and the Mohr strength theory,we propose a theory of an anchored cluster structure for fractured roofs and have investigated the formation of such an anchored cluster structure,its self stability mechanism and mechanical properties.The results show that an anchor and the surrounding fractured rock can form a string-like supporting structure,referred to as the structure of an anchored cluster for rational bolt parameters.Not only can the structure maintain its own stability,but as well undertake the load of the overlying strata.The designated support parameters,based on anchored cluster theory can overcome the shortcomings of other support theories applied to a fractured roof of rectangular roadways or could not be calculated.Our anchored cluster theory can provide a theoretical basis for the design of support for rectangular fractured roofs.Furthermore,the theory will help to reduce the probability of roof fall accidents caused by local fractured rock blocks,which can destroy a supporting structure.
文摘Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results directly from the random width characterized by the artificial fractures. To solve this problem, a series of simulated fractured core samples made of stainless steel with a given width of fracture were prepared. The relative error for the width of artificial fracture decreased to 1%. The width of natural and artificial fractures in carbonate reservoirs can be estimated by image log data. A series of tests for formation damage were conducted by using the stainless steel simulated core samples flushed with different drilling fluids, such as the sulfonate/polymer drill-in fluid and the solids-flee drill-in fluid with or without ideal packing bridging materials. Based on the experimental results using this kind of simulated cores, a novel approach to the damage control of fractured carbonate reservoirs was presented. The effective temporary plugging ring on the end face of the simulated core sample can be observed clearly. The experimental results also show that the stainless steel simulated cores made it possible to visualize the solids and filtrate invasion.
基金Supported by the PetroChina’s Fundamental Research Project(2019A-3609)。
文摘To quantitatively determine the effect of different factors such as fracture width,dip angle,extension and filling material on Stoneley wave amplitude decreasing,the shock tube experiment method was changed from fixing the sample and vertically moving the sensor in the borehole to fixing the sensors along the shock tube wall and vertically moving the sample without drilling the borehole in it.The measurement accuracy and the signal-to-noise ratio of the first Stoneley wave were improved by the time corrections and amplitude corrections of Stoneley wave signals.At the same time,21 sets of core models with different fracture parameters were processed for this measurement method by using full-diameter carbonate core,and relative amplitudes were defined to characterize Stoneley wave amplitude decreasing.The experimental results show that the relative amplitude of Stoneley wave exponentially decreases with increasing fracture width.The relative amplitude of Stoneley wave linearly decreases with increasing fracture dip angle.The relative amplitude of Stoneley wave exponentially decreases with increasing fracture extension.The relative amplitude of Stoneley wave decreases with increasing the permeability of filling material in the fracture.Under the above four conditions,the fracture width has the greatest effect on the decreasing of Stoneley wave amplitude,followed by the fracture extension and the permeability of filling material,and finally the fracture dip angle.
基金the National Natural Science Foundation of China(No.51974343)Independent Innovation Scientific Research Project(science and engineering)of China University of Petroleum(East China)(No.20CX06089A)Qingdao Postdoctoral Applied Research Project(No.qdyy20200084)。
文摘The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect.There are two shortcomings of current research on proppant equilibrium heights,one of which is that the effect of fracture widths is neglected when calculating the settling velocity and another of which is that the settling bed height is a constant when building the settling bed height growth rate model.To fill those two shortcomings,this work provides a novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments.A comparison between the results obtained from the novel model and the published model and experimental results indicates that the proposed model is verified.From the sensitivity analysis,it is concluded that the proppant equilibrium height increases with an increasing proppant density.The proppant equilibrium height decreases with an increase in the slickwater injection rate and increases with an increase in the proppant injection rate.The increase in proppant diameter results in an increasing the friction factor,which makes proppant equilibrium heights decrease.Meanwhile,the increase in proppant sizes results in an increase in proppant settling rates,which makes the proppant equilibrium height increase.When the effect of the proppant diameter on settling rates is more significant than that on friction factors,the equilibrium height increases with an increasing proppant size.This work provides a research basis of proppant distributions during the hydraulic fracture.
文摘Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.
