Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-pla...Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.展开更多
The Sinian Dengying Formation gas reservoir in the Anyue gas field of the Sichuan Basin is an ultra-deep ancient dolomite karst gas reservoir,whose development is of high difficulty,for the reservoir is thin and scatt...The Sinian Dengying Formation gas reservoir in the Anyue gas field of the Sichuan Basin is an ultra-deep ancient dolomite karst gas reservoir,whose development is of high difficulty,for the reservoir is thin and scattered with strong heterogeneity and is overall characterized by low porosity and low permeability.In order to provide support for the large-scale productivity construction of the gas reservoir of the fourth member of Dengying Formation(Deng 4 Member)in the marginal platform belt of the Anyue gas field,this paper carries out multi-discipline comprehensive researches on the technical bottlenecks based on the geological characteristics of the gas reservoir.In addition,the targeted key technologies for the efficient development of gas reservoirs were developed in the mode of“simultaneous research,application and improvement”.And the following research results are obtained.First,based on the modeling technology of fracturedevuggy dolomite karst reservoirs,accurate modeling of karst reservoirs is realized.Late actual drilling results show that the model's coincidence rate is increased from 63.0% to 90.7% and the“transparency”of gas reservoirs is achieved.Second,based on the reserve mobility evaluation technology of lowporosity and highly-heterogeneous karst reservoirs,the recovery factors of different reservoirs are determined.And consequently,the lower limit of well-controlled reserves and radius for the efficient development of different reservoirs are obtained and type Ⅰ and Ⅱ reservoirs are selected as the main development targets.Third,based on the development optimization design technology of highly-heterogeneous karst gas reservoirs,it is recommended to apply highly-deviated wells(the maximum deviation angle of 75°-84°)in the situations with multiple reservoirs crossed and superimposed.If type Ⅰ and Ⅱ reservoirs are developed intensively,it is recommended to adopt horizontal well drilling with a horizontal section of 800-1100 m.What's more,the reasonable well spacing in type Ⅰ and Ⅱ reservoirs shall be 1.6-3.3 km and 0.9-1.4 km,respectively.Fourth,based on the distinguished drilling technology of highly-deviated wells/horizontal wells in deep carbonate rocks,the fault complexity ratio is decreased from 20.7% to 4.9%,so safe and fast drilling and completion of highly-deviated wells/horizontal wells is realized and well control risks are diminished.What's more,the drilling rates of type Ⅰ and Ⅱ reservoirs are increased from 24.2% to 87.3%,indicating an effective improvement of reservoir drilling rates.Fifth,based on the open-hole segmented accurate acid fracturing technology of highly-deviated and horizontal wells,the difficulty in the highly-heterogeneous reservoir stimulation by horizontal well drilling is solved by conducting the differentiated acid fracturing process of“one segment,one strategy”.Based on the application of these innovative development technologies in the Deng 4 Member gas reservoir in the marginal platform belt of the Anyue gas field,the annual natural gas production capacity and cumulative natural gas production by the end of December 2020 are 60×10^(8) m^(3) and 103×10^(8) m^(3),respectively.In this way,the Sinian Dengying Formation gas reservoir of the Anyue gas field,the economic benefit of which is close to the marginal benefit,becomes the main force of conventional natural gas production increase.展开更多
基金supported by the National Natural Science Foundation of China(11072060)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.
基金Project supported by the National Science and Technology Major Project“Demonstration Project of Giant Carbonate Gas Field Development in Sichuan Basin”(No.2016ZX05052)the PetroChina Major Technology Special Project“Research and Application of Key Technology for Large-scale Efficient Development of the Fourth Member of Dengying Formation in Central Sichuan”(No.:2016E-0606).
文摘The Sinian Dengying Formation gas reservoir in the Anyue gas field of the Sichuan Basin is an ultra-deep ancient dolomite karst gas reservoir,whose development is of high difficulty,for the reservoir is thin and scattered with strong heterogeneity and is overall characterized by low porosity and low permeability.In order to provide support for the large-scale productivity construction of the gas reservoir of the fourth member of Dengying Formation(Deng 4 Member)in the marginal platform belt of the Anyue gas field,this paper carries out multi-discipline comprehensive researches on the technical bottlenecks based on the geological characteristics of the gas reservoir.In addition,the targeted key technologies for the efficient development of gas reservoirs were developed in the mode of“simultaneous research,application and improvement”.And the following research results are obtained.First,based on the modeling technology of fracturedevuggy dolomite karst reservoirs,accurate modeling of karst reservoirs is realized.Late actual drilling results show that the model's coincidence rate is increased from 63.0% to 90.7% and the“transparency”of gas reservoirs is achieved.Second,based on the reserve mobility evaluation technology of lowporosity and highly-heterogeneous karst reservoirs,the recovery factors of different reservoirs are determined.And consequently,the lower limit of well-controlled reserves and radius for the efficient development of different reservoirs are obtained and type Ⅰ and Ⅱ reservoirs are selected as the main development targets.Third,based on the development optimization design technology of highly-heterogeneous karst gas reservoirs,it is recommended to apply highly-deviated wells(the maximum deviation angle of 75°-84°)in the situations with multiple reservoirs crossed and superimposed.If type Ⅰ and Ⅱ reservoirs are developed intensively,it is recommended to adopt horizontal well drilling with a horizontal section of 800-1100 m.What's more,the reasonable well spacing in type Ⅰ and Ⅱ reservoirs shall be 1.6-3.3 km and 0.9-1.4 km,respectively.Fourth,based on the distinguished drilling technology of highly-deviated wells/horizontal wells in deep carbonate rocks,the fault complexity ratio is decreased from 20.7% to 4.9%,so safe and fast drilling and completion of highly-deviated wells/horizontal wells is realized and well control risks are diminished.What's more,the drilling rates of type Ⅰ and Ⅱ reservoirs are increased from 24.2% to 87.3%,indicating an effective improvement of reservoir drilling rates.Fifth,based on the open-hole segmented accurate acid fracturing technology of highly-deviated and horizontal wells,the difficulty in the highly-heterogeneous reservoir stimulation by horizontal well drilling is solved by conducting the differentiated acid fracturing process of“one segment,one strategy”.Based on the application of these innovative development technologies in the Deng 4 Member gas reservoir in the marginal platform belt of the Anyue gas field,the annual natural gas production capacity and cumulative natural gas production by the end of December 2020 are 60×10^(8) m^(3) and 103×10^(8) m^(3),respectively.In this way,the Sinian Dengying Formation gas reservoir of the Anyue gas field,the economic benefit of which is close to the marginal benefit,becomes the main force of conventional natural gas production increase.
