On-machine measurement(OMM)stands out as a pivotal technology in complex curved surface adaptive machining.However,the complex structure inherent in workpieces poses a significant challenge as the stylus orientation f...On-machine measurement(OMM)stands out as a pivotal technology in complex curved surface adaptive machining.However,the complex structure inherent in workpieces poses a significant challenge as the stylus orientation frequently shifts during the measurement process.Consequently,a substantial amount of time is allocated to calibrating pre-travel error and probe movement.Furthermore,the frequent movement of machine tools also increases the influence of machine errors.To enhance both accuracy and efficiency,an optimization strategy for the OMM process is proposed.Based on the kinematic chain of the machine tools,the relationship between the angle combination of rotary axes,the stylus orientation,and the calibration position of pre-travel error is disclosed.Additionally,an OMM efficiency optimization model for complex curved surfaces is developed.This model is solved to produce the optimal efficiency angle combinations for each to-be-measured point.Within each angle combination,the effects of positioning errors on measurement results are addressed by coordinate system offset and measurement result compensation method.Finally,the experiments on an impeller are used to demonstrate the practical utility of the proposed method.展开更多
Large,3D curved electronics are a trend of the microelectronic industry due to their unique ability to conformally coexist with complex surfaces while retaining the electronic functions of 2D planar integrated circuit...Large,3D curved electronics are a trend of the microelectronic industry due to their unique ability to conformally coexist with complex surfaces while retaining the electronic functions of 2D planar integrated circuit technologies.However,these curved electronics present great challenges to the fabrication processes.Here,we propose a reconfigurable,mask-free,conformal fabrication strategy with a robot-like system,called robotized‘transfer-and-jet’printing,to assemble diverse electronic devices on complex surfaces.This novel method is a ground-breaking advance with the unique capability to integrate rigid chips,flexible electronics,and conformal circuits on complex surfaces.Critically,each process,including transfer printing,inkjet printing,and plasma treating,are mask-free,digitalized,and programmable.The robotization techniques,including measurement,surface reconstruction and localization,and path programming,break through the fundamental constraints of 2D planar microfabrication in the context of geometric shape and size.The transfer printing begins with the laser lift-off of rigid chips or flexible electronics from donor substrates,which are then transferred onto a curved surface via a dexterous robotic palm.Then the robotic electrohydrodynamic printing directly writes submicrometer structures on the curved surface.Their permutation and combination allow versatile conformal microfabrication.Finally,robotized hybrid printing is utilized to successfully fabricate a conformal heater and antenna on a spherical surface and a flexible smart sensing skin on a winged model,where the curved circuit,flexible capacitive and piezoelectric sensor arrays,and rigid digital–analog conversion chips are assembled.Robotized hybrid printing is an innovative printing technology,enabling additive,noncontact and digital microfabrication for 3D curved electronics.展开更多
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol ...In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.展开更多
In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 ...In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.展开更多
The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this arti...The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.展开更多
This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and...This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.展开更多
This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applic...This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.展开更多
A homological analogue of curve complex of a closed connected orientable surface is developed and studied. The dis-tance in this complex is shown to be quite computable and an algorithm given (Theorem 3.5). As an appl...A homological analogue of curve complex of a closed connected orientable surface is developed and studied. The dis-tance in this complex is shown to be quite computable and an algorithm given (Theorem 3.5). As an application of this complex it is shown that for a closed orientable 3-manifold, and any of its Heegaard splittings, one can give an algorithm to decide whether the manifold contains a 2-sided, non-separating, closed incompressible surface (Theorem 1.1).展开更多
With the continuous development and advancement of science and technology,the work of tool path planning has received extensive attention.Among them,curved surface generation and data processing are the focus of manag...With the continuous development and advancement of science and technology,the work of tool path planning has received extensive attention.Among them,curved surface generation and data processing are the focus of management and design,which necessitate the full application of reverse design of complex curved surface components to complete numerical control processing,effective optimization and upgrading,integration the tasks of point cloud data collection,and point cloud data processing to ensure that the corresponding computer numerical control machining model can exert its actual value.This paper briefly analyzes the basic principles of curved surface reconstruction as well as discusses the reverse design of complex curved components and the experimental processes and results that involved computer numerical control machining,which serves the purpose as reference only.展开更多
An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve...An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can＇t solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps： （1） decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron; （2） reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces; （3） combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.展开更多
Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate...Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.展开更多
We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
-This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tid...-This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tide protection, anti-wave, land development, traffic and tourism. The new kind of breakwater optimized by wave model test has been utilized in the seawall in the coast regulation project in Zhanjiang City, and good results have been achieved.展开更多
Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper...Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.展开更多
A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natu...A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.展开更多
In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of...In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.展开更多
Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable app...Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.展开更多
This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angle...This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.展开更多
Affected by reservoir heterogeneity,developed natural fractures,and bedding fractures,the fracturing pressure curves in fracturing of shale gas horizontal wells present complex shapes.A large amount of information con...Affected by reservoir heterogeneity,developed natural fractures,and bedding fractures,the fracturing pressure curves in fracturing of shale gas horizontal wells present complex shapes.A large amount of information contained in the fracturing curves is still not fully excavated.Based on the theory of shale gas fracture network fracturing,the calculation model of bottom hole net pressure is established by integrating the real-time data such as casing pressure,pump rate,and proppant concentration.Net pressure slope and net pressure index are constructed as key parameters,and the net pressure curve is divided dynamically to describe the mechanical conditions corresponding to the fracture propagation behavior during the fracturing process.Six fracture propagation modes were identified,including fracture network propagation,fracture propagation blockage,normal fracture propagation,fracture propagation long bedding,fracture height growth,and rapidfluidfiltration,and then the operation pressure curve diagnosis and identification method were formed for shale gas fracture network fracturing in horizontal wells.The shortcomings of conventional operation curve diagnosis and identification methods are abandoned and the fracture network complexity index is presented.The higher index indicates more time of fracture network propagation and fracture propagation along bedding and the better reservoir stimulation effect.The model is applied to shale gas wells in the southeastern margin of Sichuan Basin,and the average fracture network complexity index of a single well is 0.3,which is in good agreement with the microseismic monitoring results.This proves the good reliability of the method developed.The method is helpful to improve the potential and level of fracturing stimulation of shale reservoirs and is of great significance for improving the post-fracturing evaluation technology of fracture network and guiding the real-time dynamic adjustment offield fracturing operations.展开更多
基金Projects(51775445,52175435)supported by the National Natural Science Foundation of ChinaProject(CX2023051)supported by the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China。
文摘On-machine measurement(OMM)stands out as a pivotal technology in complex curved surface adaptive machining.However,the complex structure inherent in workpieces poses a significant challenge as the stylus orientation frequently shifts during the measurement process.Consequently,a substantial amount of time is allocated to calibrating pre-travel error and probe movement.Furthermore,the frequent movement of machine tools also increases the influence of machine errors.To enhance both accuracy and efficiency,an optimization strategy for the OMM process is proposed.Based on the kinematic chain of the machine tools,the relationship between the angle combination of rotary axes,the stylus orientation,and the calibration position of pre-travel error is disclosed.Additionally,an OMM efficiency optimization model for complex curved surfaces is developed.This model is solved to produce the optimal efficiency angle combinations for each to-be-measured point.Within each angle combination,the effects of positioning errors on measurement results are addressed by coordinate system offset and measurement result compensation method.Finally,the experiments on an impeller are used to demonstrate the practical utility of the proposed method.
基金The authors acknowledge support from the National Nat-ural Science Foundation of China(51635007,51925503,51705179)Natural Science Foundation of Hubei Province of China(2020CFA028).
文摘Large,3D curved electronics are a trend of the microelectronic industry due to their unique ability to conformally coexist with complex surfaces while retaining the electronic functions of 2D planar integrated circuit technologies.However,these curved electronics present great challenges to the fabrication processes.Here,we propose a reconfigurable,mask-free,conformal fabrication strategy with a robot-like system,called robotized‘transfer-and-jet’printing,to assemble diverse electronic devices on complex surfaces.This novel method is a ground-breaking advance with the unique capability to integrate rigid chips,flexible electronics,and conformal circuits on complex surfaces.Critically,each process,including transfer printing,inkjet printing,and plasma treating,are mask-free,digitalized,and programmable.The robotization techniques,including measurement,surface reconstruction and localization,and path programming,break through the fundamental constraints of 2D planar microfabrication in the context of geometric shape and size.The transfer printing begins with the laser lift-off of rigid chips or flexible electronics from donor substrates,which are then transferred onto a curved surface via a dexterous robotic palm.Then the robotic electrohydrodynamic printing directly writes submicrometer structures on the curved surface.Their permutation and combination allow versatile conformal microfabrication.Finally,robotized hybrid printing is utilized to successfully fabricate a conformal heater and antenna on a spherical surface and a flexible smart sensing skin on a winged model,where the curved circuit,flexible capacitive and piezoelectric sensor arrays,and rigid digital–analog conversion chips are assembled.Robotized hybrid printing is an innovative printing technology,enabling additive,noncontact and digital microfabrication for 3D curved electronics.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project (Grant No. S30504)
文摘In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.
基金Supported by the National Natural Science Foundation of China (10531090)Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)
文摘In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.
基金Supported by NSF of Henan Province of China(20001110001)
文摘The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.
基金Supported by the National Natural Science Foundation of China (10971224)
文摘This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.
文摘This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.
文摘A homological analogue of curve complex of a closed connected orientable surface is developed and studied. The dis-tance in this complex is shown to be quite computable and an algorithm given (Theorem 3.5). As an application of this complex it is shown that for a closed orientable 3-manifold, and any of its Heegaard splittings, one can give an algorithm to decide whether the manifold contains a 2-sided, non-separating, closed incompressible surface (Theorem 1.1).
文摘With the continuous development and advancement of science and technology,the work of tool path planning has received extensive attention.Among them,curved surface generation and data processing are the focus of management and design,which necessitate the full application of reverse design of complex curved surface components to complete numerical control processing,effective optimization and upgrading,integration the tasks of point cloud data collection,and point cloud data processing to ensure that the corresponding computer numerical control machining model can exert its actual value.This paper briefly analyzes the basic principles of curved surface reconstruction as well as discusses the reverse design of complex curved components and the experimental processes and results that involved computer numerical control machining,which serves the purpose as reference only.
文摘An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can＇t solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps： （1） decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron; （2） reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces; （3） combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.
基金Ministry of Science,Technology and Innovation(MOSTI),Malaysia for the Science Fund,Vot No.5450657
文摘Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
文摘-This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tide protection, anti-wave, land development, traffic and tourism. The new kind of breakwater optimized by wave model test has been utilized in the seawall in the coast regulation project in Zhanjiang City, and good results have been achieved.
基金The NSF(11601209)of ChinaResearch Foundation(201601239)for Doctor of Liaoning Province+1 种基金Scientific Research Fund(L201683660)of Liaoning Provincial Education DepartmentYouth Foundation(LS2015L002)of Liaoning Normal University
文摘Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.
基金supported by the National Natural Science Foundation of China(Nos.10932001,11072015, and 10761005)the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20101102110016)the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)
文摘A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.
基金The second author was supported by the National Natural Science Foundation of China(11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)The third author was supported by the Foundation of Guangzhou Civil Aviation College(18X0428).
文摘In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.
文摘Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.
基金Supported by Shandong Province Higher Educational Science and Technology Program(No.J12LN34)Shandong Ji'nan College and Institute Independent Innovation Project(No.201303011,No.201303021,No.201303016)
文摘This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.
基金National Natural Science Foundation of China Basic The ory of Efficient Development of Shale Oil and Gas(No.51490653)Theory and Method of Efficient Construction of Fracture Network in Deep and Ultra-Deep Shale Gas Horizontal Wells(No.U19A2043)Theory and Method of Long-term Propping for Deep Shale Gas Hydraulic Fractures based on DEM-LBM Hydro-Mechanical Coupling(No.52104039).
文摘Affected by reservoir heterogeneity,developed natural fractures,and bedding fractures,the fracturing pressure curves in fracturing of shale gas horizontal wells present complex shapes.A large amount of information contained in the fracturing curves is still not fully excavated.Based on the theory of shale gas fracture network fracturing,the calculation model of bottom hole net pressure is established by integrating the real-time data such as casing pressure,pump rate,and proppant concentration.Net pressure slope and net pressure index are constructed as key parameters,and the net pressure curve is divided dynamically to describe the mechanical conditions corresponding to the fracture propagation behavior during the fracturing process.Six fracture propagation modes were identified,including fracture network propagation,fracture propagation blockage,normal fracture propagation,fracture propagation long bedding,fracture height growth,and rapidfluidfiltration,and then the operation pressure curve diagnosis and identification method were formed for shale gas fracture network fracturing in horizontal wells.The shortcomings of conventional operation curve diagnosis and identification methods are abandoned and the fracture network complexity index is presented.The higher index indicates more time of fracture network propagation and fracture propagation along bedding and the better reservoir stimulation effect.The model is applied to shale gas wells in the southeastern margin of Sichuan Basin,and the average fracture network complexity index of a single well is 0.3,which is in good agreement with the microseismic monitoring results.This proves the good reliability of the method developed.The method is helpful to improve the potential and level of fracturing stimulation of shale reservoirs and is of great significance for improving the post-fracturing evaluation technology of fracture network and guiding the real-time dynamic adjustment offield fracturing operations.
