A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase...A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.展开更多
In order to investigate detonation propagation characteristics of different charge patterns,the detonation velocities of superposition strip shaped charges made up of a detonating cord and explosives were measured by...In order to investigate detonation propagation characteristics of different charge patterns,the detonation velocities of superposition strip shaped charges made up of a detonating cord and explosives were measured by a detonation velocity measuring instrument under conditions of different ignition.The experimental results and theoretical analysis show that the maximum detonation propagation velocity depends on the explosive materials with the maximum velocity among all the explosive materials.Using detonating cord in a superposition charge can shorten detonation propagation time and improve the efficiency of explosive energy.The measurement method of detonation propagation velocity and experimental results are presented and investigated.展开更多
Outcrop coal samples from the Shizhuang South Block of the Qinshui Basin,Shanxi Province,China,were subjected to true triaxial hydraulic fracturing experiments to simulate fracture propagation.Combined with CT scannin...Outcrop coal samples from the Shizhuang South Block of the Qinshui Basin,Shanxi Province,China,were subjected to true triaxial hydraulic fracturing experiments to simulate fracture propagation.Combined with CT scanning and three-dimensional fracture reconstruction,the study examined fracture propagation patterns and bedding activation behaviors under variable pumping-rate fracturing in coal reservoirs.Results indicate that the variable pumping-rate fracturing technique effectively overcomes the strong trapping effect of coal bedding.Micro-fractures are initiated at multiple weak points along bedding planes,leading to multi-point fracture initiation and competitive propagation of fractures toward the far field,thereby generating a more complex three-dimensional fracture network.The geometry and aperture of the induced fracture network are primarily controlled by the ramp-up rate of injection flowrate.A gradual ramp-up favors the development of a more complex fracture network,though at the expense of lower breakdown pressure,insufficient initiation,and narrower apertures.In contrast,a rapid ramp-up produces wider fractures and larger propped lengths,but results in more pronounced aperture fluctuations.For coal reservoirs with relatively high rock strength,a moderately higher ramp-up rate is recommended to avoid excessively narrow fractures and potential proppant bridging.Different coal lithotypes necessitate tailored ramp-up strategies to optimize fracture morphology and stimulation effectiveness.展开更多
The interaction process among hydraulic fractures and natural fractures,bedding planes,and other discontinuities during shale fracturing determines the complexity of the fracture network that is formed.However,the cur...The interaction process among hydraulic fractures and natural fractures,bedding planes,and other discontinuities during shale fracturing determines the complexity of the fracture network that is formed.However,the current conclusions and understanding of the mechanisms underlying the interaction between hydraulic and natural fractures,as well as their primary controlling factors,fail to meet the requirements of hydraulic fracturing operations,thereby restricting the efficient development of shale gas resources.Therefore,in this study,a coupled thermal-hydraulic-mechanical finite element numerical model that is based on the maximum tensile stress and the Mohr-Coulomb criterion is established,thereby considering rock deformation,fluid flow,and heat transfer.The reliability of this model is validated on the basis of previous research.This model is subsequently employed to simulate the propagation behavior of hydraulic fractures in shale with well-developed bedding.The results indicate that when hydraulic fractures propagate to the bedding,five propagation modes may occur:arrest,diversion,diversion and crossing,crossing and diversion,and direct crossing.These modes are controlled by factors such as the mechanical properties of the shale matrix and bedding,geostress,bedding dip angle,temperature,and fracturing fluid injection rate.During fracture propagation,increases in the elastic modulus ratio between the rock matrix and the bedding,the bedding dip angle,and the temperature are favorable for hydraulic fractures turning along the bedding,whereas increases in the difference in vertical stress and the injection rate are favorable for hydraulic fractures directly crossing the bedding.Second,on the basis of four influencing factors,namely,the shale matrix and bedding elastic modulus ratio,bedding dip angle,difference in vertical stress,and temperature,propagation criteria for hydraulic fractures along the bedding under various combinations of influencing factors are established.The results provide theoretical reference data for the design and optimization of fracturing in shale with well-developed bedding.展开更多
The long-term time series analysis of the SST (sea surface temperature) in the Eastern Equatorial Pacific Ocean and the monthly MSL (mean sea level) in the tropical Pacific Ocean is conducted. Their quasiperiodic and ...The long-term time series analysis of the SST (sea surface temperature) in the Eastern Equatorial Pacific Ocean and the monthly MSL (mean sea level) in the tropical Pacific Ocean is conducted. Their quasiperiodic and low-frequency oscillation features are revealed. The significant periods of low-frequency fluctuations for monthly MSL in the area of 20°N-20° S are between 43. 5 months and 50. 0 months, approximating closely to 47. 6 months which is the significant period of SST in the Eastern Equatorial Pacific Ocean. From the results of space-spectral analysis, the low-frequency fluctations of monthly MSL in the tropical Pacific Ocean appear to have a anticlockwise circularly-propagating pattern, which is, the Eastern Pacific Ocean (off-shore of Mexico) →the area of NEC (North Equatorial Current) →the Western Equatorial Pacific Ocean→the area of NECC (North Equatorial Counter-Current)→the Eastern Equatorial Pacific Ocean. The phases of the pattern correspond to those of El Nino cycle. On the basis of the above results,a basic model is established with stepwise-regression method, which can forecast El Nino events by the variations of monthly MSL at a few stations in the tropical Pacific Ocean 4 months ahead. The correlation coefficient between the forecasted series and the observed one is 0. 89.展开更多
基金financially supported by the National Natural Science Foundation of China (Grant No. 50879090)Key Research Program of Hydrodynamics of China (Grant No. 9140A14030712JB11044)
文摘A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.
文摘In order to investigate detonation propagation characteristics of different charge patterns,the detonation velocities of superposition strip shaped charges made up of a detonating cord and explosives were measured by a detonation velocity measuring instrument under conditions of different ignition.The experimental results and theoretical analysis show that the maximum detonation propagation velocity depends on the explosive materials with the maximum velocity among all the explosive materials.Using detonating cord in a superposition charge can shorten detonation propagation time and improve the efficiency of explosive energy.The measurement method of detonation propagation velocity and experimental results are presented and investigated.
基金Supported by China National Petroleum Corporation North China Oilfield Company Medium-to-Long-Term Research Project:“Key Technologies for Efficient Fracturing and Enhanced Production in Coalbed Methane”.
文摘Outcrop coal samples from the Shizhuang South Block of the Qinshui Basin,Shanxi Province,China,were subjected to true triaxial hydraulic fracturing experiments to simulate fracture propagation.Combined with CT scanning and three-dimensional fracture reconstruction,the study examined fracture propagation patterns and bedding activation behaviors under variable pumping-rate fracturing in coal reservoirs.Results indicate that the variable pumping-rate fracturing technique effectively overcomes the strong trapping effect of coal bedding.Micro-fractures are initiated at multiple weak points along bedding planes,leading to multi-point fracture initiation and competitive propagation of fractures toward the far field,thereby generating a more complex three-dimensional fracture network.The geometry and aperture of the induced fracture network are primarily controlled by the ramp-up rate of injection flowrate.A gradual ramp-up favors the development of a more complex fracture network,though at the expense of lower breakdown pressure,insufficient initiation,and narrower apertures.In contrast,a rapid ramp-up produces wider fractures and larger propped lengths,but results in more pronounced aperture fluctuations.For coal reservoirs with relatively high rock strength,a moderately higher ramp-up rate is recommended to avoid excessively narrow fractures and potential proppant bridging.Different coal lithotypes necessitate tailored ramp-up strategies to optimize fracture morphology and stimulation effectiveness.
基金supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(No.2025ZD1401403-04)the PetroChina’s Fundamental Prospective Project(Nos.2024DJ8705,2023ZZ08 and 2024DJ23)。
文摘The interaction process among hydraulic fractures and natural fractures,bedding planes,and other discontinuities during shale fracturing determines the complexity of the fracture network that is formed.However,the current conclusions and understanding of the mechanisms underlying the interaction between hydraulic and natural fractures,as well as their primary controlling factors,fail to meet the requirements of hydraulic fracturing operations,thereby restricting the efficient development of shale gas resources.Therefore,in this study,a coupled thermal-hydraulic-mechanical finite element numerical model that is based on the maximum tensile stress and the Mohr-Coulomb criterion is established,thereby considering rock deformation,fluid flow,and heat transfer.The reliability of this model is validated on the basis of previous research.This model is subsequently employed to simulate the propagation behavior of hydraulic fractures in shale with well-developed bedding.The results indicate that when hydraulic fractures propagate to the bedding,five propagation modes may occur:arrest,diversion,diversion and crossing,crossing and diversion,and direct crossing.These modes are controlled by factors such as the mechanical properties of the shale matrix and bedding,geostress,bedding dip angle,temperature,and fracturing fluid injection rate.During fracture propagation,increases in the elastic modulus ratio between the rock matrix and the bedding,the bedding dip angle,and the temperature are favorable for hydraulic fractures turning along the bedding,whereas increases in the difference in vertical stress and the injection rate are favorable for hydraulic fractures directly crossing the bedding.Second,on the basis of four influencing factors,namely,the shale matrix and bedding elastic modulus ratio,bedding dip angle,difference in vertical stress,and temperature,propagation criteria for hydraulic fractures along the bedding under various combinations of influencing factors are established.The results provide theoretical reference data for the design and optimization of fracturing in shale with well-developed bedding.
文摘The long-term time series analysis of the SST (sea surface temperature) in the Eastern Equatorial Pacific Ocean and the monthly MSL (mean sea level) in the tropical Pacific Ocean is conducted. Their quasiperiodic and low-frequency oscillation features are revealed. The significant periods of low-frequency fluctuations for monthly MSL in the area of 20°N-20° S are between 43. 5 months and 50. 0 months, approximating closely to 47. 6 months which is the significant period of SST in the Eastern Equatorial Pacific Ocean. From the results of space-spectral analysis, the low-frequency fluctations of monthly MSL in the tropical Pacific Ocean appear to have a anticlockwise circularly-propagating pattern, which is, the Eastern Pacific Ocean (off-shore of Mexico) →the area of NEC (North Equatorial Current) →the Western Equatorial Pacific Ocean→the area of NECC (North Equatorial Counter-Current)→the Eastern Equatorial Pacific Ocean. The phases of the pattern correspond to those of El Nino cycle. On the basis of the above results,a basic model is established with stepwise-regression method, which can forecast El Nino events by the variations of monthly MSL at a few stations in the tropical Pacific Ocean 4 months ahead. The correlation coefficient between the forecasted series and the observed one is 0. 89.
