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A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

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Petroleum Science 2024年第1期21卷 327-342页

作者： Qian Zhang Wen-Dong Wang Yu-Liang Su Wei Chen Zheng-Dong Lei Lei Li Yong-Mao Hao Key Laboratory of Unconventional Oil&Gas Development(China University of Petroleum(East China)) Ministry of EducationQingdao266580ShandongChina School of Petroleum Engineering China University of Petroleum(East China)Qingdao266580ShandongChina Shale Oil Development Branch Changqing Oilfield CompanyPetroChinaQingyang745708GansuChina PetroChina Research Institute of Petroleum Exploration&Development Beijing100083China

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

关键词： Multi-scale coupled flow Stress sensitivity Shale oil Micro-scale effect fractal theory

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Dynamic development model for long gap discharge streamer-leader system based on fractal theory

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Plasma Science and Technology 2022年第9期24卷 68-76页

作者：耿江海王权圣刘晓敏王平律方成丁玉剑 Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense North China Electric Power UniversityBaoding 071003People’s Republic of China China Electric Power Research Institute Beijing 100192People’s Republic of China

Establishing a long air gap discharge model considering the streamer-leader transition and randomness of the discharge path is of great signiflcance to improve the accuracy of discharge characteristic prediction and optimize external insulation design.Based on fractal theory and thermal ionization theory of streamer-leader transition,this work establishes a dynamic development model for the long air gap discharge streamer-leader system,which includes streamer inception,streamer development,leader inception,development of streamer-leader system and flnal jump.The positive discharge process of a 3 m rod plate is simulated to obtain the fractal distribution of the discharge path and the law of leader development for comparison with the discharge test results.The results show that the simulation model is similar to test results in the development characteristics of leader path distribution,each stage time and leader velocity.Finally,a simulation calculation of a 50%breakdown voltage of the rod-plate gap and ball-plate gap is carried out,with results fairly consistent with test data,proving the effectiveness and practicality of the model.

关键词： long air gap fractal theory thermal ionization streamer-leader system simulation model

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Contact Model of Revolute Joint with Clearance Based on fractal theory

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Chinese Journal of Mechanical Engineering 2018年第6期31卷 34-44页

作者： Shi-Hua Li Xue-Yan Han Jun-Qi Wang Jing Sun Fu-Juan Li Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan University

The contact sti ness of a mechanical bonding surface is an important parameter in determining the normal and radial contact force. To improve the calculation accuracy of the contact force model, the surface roughness of the bonding surface and the energy loss that necessarily occurs during the impact process should be considered com?prehensively. To study the normal contact force of a revolute joint with clearance more accurately in the case of dry friction, a nonlinear sti ness coe cient model considering the surface roughness was established based on fractal theory, which considers the elastic, elastic?plastic, and plastic deformations of the asperities of the contact surface during the contact process. On this basis, a modified nonlinear spring damping model was established based on the Lankarani–Nikravesh contact force model. The laws influencing the surface roughness, recovery coe cient, initial velocity, and clearance size on the impact force were revealed, and were compared with the Lankarani–Nikravesh model and a hybrid model using MATLAB. The maximum impact force was obtained using a modified contact force model under di erent initial velocities, di erent clearances, and di erent degrees of surface roughness, and the calculated results were then compared with the experiment results. This study indicates that the modified model can be used more widely than other models, and is suitable for both large and small clearances. In particular, the modified model is more accurate when calculating the contact force of a revolute joint with a small clearance.

关键词： fractal theory Modified contact model Surface roughness Lankarani–Nikravesh model

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MULTI-SCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON fractal theory

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Acta Mechanica Solida Sinica 2013年第4期26卷 344-352页

作者： Qiang Xu Jianyun Chen Jing Li Mingming Wang School of Civil and Hydraulic Eng. Dalian University of Technology State Key Lab. of Coastal and Ofshore Eng. Dalian University of Technology

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.

关键词： fractal theory concrete material fractal box dimension damage multi-scale constitutive relation

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Application Study of fractal theory in Mechanical Transmission

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Chinese Journal of Mechanical Engineering 2016年第5期29卷 871-879页

作者： ZHAO Han WU Qilin School of Mechanical and Automobile Engineering Hefei University of Technology

Mechanical transmissions are applied widely in various electrical and mechanical products, but some qualities of some high-end products can＇t meet people＇s demand, and need to be improved with some new methods or theories. The fractal theory is a new mathematic tool, which provides a new approach for the further study in the area of the mechanical transmission, and helps to solve some problems. The basic contents of the fractal theory are introduced firstly, especially the two important concepts, the self-similar fractal and the fractal dimension. Then, the deferent application of the fractal theory in this area are given to display how to further the study and improve some important characteristics of the mechanical transmission, such as contact surfaces, manufacturing precise, friction and wear, stiffness, strength, dynamics, fault diagnosis, etc. Finally, the problems of the fractal theory and its application are discussed, and some weaknesses, such as the calculation capacity of the fractal theory is not strong, are pointed out. Some new solutions are suggested, such as combining the fractal theory with the fuzzy theory, the chaos theory and so on. The new application fields of the fractal theory in the area of the mechanical transmission are proposed.

关键词： mechanical transmission fractal theory self-similar fractals fractal dimension

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Elastoplastic Contact Mechanics Model of Rough Surface Based on fractal theory

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Chinese Journal of Mechanical Engineering 2017年第1期30卷 207-215页

作者： YUAN Yuan GAN Li LIU Kai YANG Xiaohui School of Mechanical and Precision Instrument Engineering Xi'an University of Technology School of Mechanical Engineering Xi'an Jiaotong University

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

关键词： rough surfaces asperities fractal theory contact model

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Use of digital image analysis combined with fractal theory to determine particle morphology and surface texture of quartz sands

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Journal of Rock Mechanics and Geotechnical Engineering 2017年第6期9卷 1131-1139页

作者： Georgia S.Araujo Kátia V.Bicalho Fernando A.Tristao Federal Institute of Education Science and Technology of the State of Espírito SantoBrazil Department of Civil Engineering Federal University of Espírito SantoBrazil

The particle morphology and surface texture play a major role in influencing mechanical and hydraulic behaviors of sandy soils. This paper presents the use of digital image analysis combined with fractal theory as a tool to quantify the particle morphology and surface texture of two types of quartz sands widely used in the region of Vitória, Espírito Santo, southeast of Brazil. The two investigated sands are sampled from different locations. The purpose of this paper is to present a simple, straightforward,reliable and reproducible methodology that can identify representative sandy soil texture parameters.The test results of the soil samples of the two sands separated by sieving into six size fractions are presented and discussed. The main advantages of the adopted methodology are its simplicity, reliability of the results, and relatively low cost. The results show that sands from the coastal spit(BS) have a greater degree of roundness and a smoother surface texture than river sands(RS). The values obtained in the test are statistically analyzed, and again it is confirmed that the BS sand has a slightly greater degree of sphericity than that of the RS sand. Moreover, the RS sand with rough surface texture has larger specific surface area values than the similar BS sand, which agree with the obtained roughness fractal dimensions. The consistent experimental results demonstrate that image analysis combined with fractal theory is an accurate and efficient method to quantify the differences in particle morphology and surface texture of quartz sands.

关键词： Quartz sands Particle morphology and surface texture Image analysis fractal theory

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Application of fractal theory in Simulation of Ferromagnetic Elements' Hysteresis Loop in Transformer

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Journal of Beijing Institute of Technology 2003年第2期12卷 113-118页

作者：毕军付梦印张宇河 Department of Automatic Control

The simulation of the transformer transient is one of the indispensable qualifications for improving the performance of transformer protection, the key technique of the transformer's transient simulation is the treatment of ferromagnetic elements' loop. Thus the shapes of the primary hysteresis loop and each internal secondary hysteresis loop in the identical magnetism conducting are analyzed, and then it is proposed that there are some fractal characteristics in the relation between them. The fractal phenomenon of the ferromagnetic elements' hysteresis loop in the transformer's transient simulation is first brought forward, the mutuality between the ferromagnetic elements' primary hysteresis loop and its secondary hysteresis loops is revealed in mechanism by using the fractal theory. According to the iterated function system of fractal theory, the secondary hysteresis loops can be generated by the iterative calculation of the primary loop. The simulation results show the validity of this idea.

关键词： fractal theory hysteresis loop transformer simulation

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Novel welding image processing method based on fractal theory

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China Welding 2002年第2期11卷 95-99页

作者：陈强孙振国肖勇路井荣 TsinghuaUniversity

Computer vision has come into used in the fields of welding process control and automation. In order to improve precision and rapidity of welding image processing, a novel method based on fractal theory has been put forward in this paper. Compared with traditional methods, the image is preliminarily processed in the macroscopic regions then thoroughly analyzed in the microscopic regions in the new method. With which, an image is divided up to some regions according to the different fractal characters of image edge, and the fuzzy regions including image edges are detected out, then image edges are identified with Sobel operator and curved by LSM (Lease Square Method). Since the data to be processed have been decreased and the noise of image has been reduced, it has been testified through experiments that edges of weld seam or weld pool could be recognized correctly and quickly.

关键词： fractal theory welding image processing,edge detection

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Application of the fractal theory for evaluating effects of coal comminution by waterjet

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International Journal of Coal Science & Technology 2014年第4期1卷 450-455页

作者： Yaqing Li Greg Galecki Gul Akar Sezai Sen Yutao Zhang Key Lab of Mining and Disaster Prevention and Control in Western Mine Ministry of EducationXi’an710054China School of Energy Science and Engineering Xi’an University of Science and TechnologyXi’an 710054China Department of Mining and Nuclear Engineering Missouri University of Science and TechnologyRollaMO 65401USA Department of Mining Engineering Dokuz Eylul UniversityIzmirTurkey

Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribution(PSD)of ground coal is a key parameter in the preparation of slurries as it determines the settling behavior of the particles and viscosity of the coal-water mixture.There are several methods available for representation and evaluation of particle size analysis data.However,fractal theory provides a means by which the entire PSD of comminuted materials can be quantified by using of a specific and exact value.In this paper,a volume-based fractal model was deduced to characterize the PSD of the coal which is ground in a specially designed comminution cell.During the size reduction process,the inlet pressures up to 276 MPa were used.

关键词： Coal comminution fractal theory Particle size distribution Waterjet

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