Natural rock joint permeability deviates from the classic fluid flow governing equations due to the inher-ent fracture surface roughness(i.e.,contact points,spatial correlation,matching,varying aperture,iso-lated void...Natural rock joint permeability deviates from the classic fluid flow governing equations due to the inher-ent fracture surface roughness(i.e.,contact points,spatial correlation,matching,varying aperture,iso-lated voids,infilling material,tortuosity and channellings)and engineering disturbance such as excavations.To improve the accuracy of fracture permeability evaluation,many efforts have been made in analytical,experimental,and numerical methods.This study reviews the modified mathematical gov-erning equations of fluid flow and classifies them based on different influencing factors,such as friction factor,aperture,tortuosity,inertia,and various in situ stress effects.Various experimental and simulation techniques for the coupled normal-and shear-stress flow problems were assessed,and their advantages and disadvantages were also analysed.Furthermore,different surface roughness descriptions and their impacts on mechanical and hydraulic behaviours were discussed,followed by the potential research directions for fracture flow problems.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
Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on ...Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.展开更多
The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has...The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.展开更多
Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of t...Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of the evolution of the flow pattern at places far from the outlet. The relationship between the hydraulic gradient and the flow velocity at different points, and the proportion evolution of the linear and nonlinear portions in the Forchheimer formula are then discussed. Three major conclusions are obtained. First, the non-Darcian flow exists in a single fracture in different laboratory tests. Better fitting accuracy is obtained by using the Forchheimer formula than by using the Darcy law. Second, the proportion of the Darcy flow increases with the increase of the observation scale. In places far enough, the Darcy flow prevails, and the critical velocity between the non-Darcian flow and the Darcy flow decreases as the fracture aperture increases. Third, when the fracture aperture increases, the critical Reynolds number between the non-Darcian flow and the Darcy flow decreases.展开更多
The formulae for average velocity of groundw-ater flow in a single fracturewere derived based on the characteristics of fracture properties and hydraulic methods. The resultsshow that the average velocity is proportio...The formulae for average velocity of groundw-ater flow in a single fracturewere derived based on the characteristics of fracture properties and hydraulic methods. The resultsshow that the average velocity is proportional to the square root of the hydraulic gradient. Inorder to verify the results, a laboratory model was established, and the experimental data wereanalyzed. Experimental results indicate that the relation between the average velocity and hydraulicgradient is nonlinear, and can he filled with power functions. And for both the unconfined andconfined flows, the value of the exponent of power functions are close to 0. 5. Thus the experimental results agree well with those from the theoretical analysis. By comparing the calculated andmeasured values of the average velocity under the same conditions, the formulae presented herein aremore effective than the traditional formula based on Darcy' s Law. These results provide theevidences of non-Dar-cy's flow in single fracture.展开更多
To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures,a set of single fracture physical models were produced using the WeierstrasseMandelbrot f...To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures,a set of single fracture physical models were produced using the WeierstrasseMandelbrot functions to test the seepage flow performance.Six single fractures,with various surface roughnesses characterized by fractal dimensions,were built using COMSOL multiphysics software.The fluid flow behavior through the rough fractures and the influences of the rough surfaces on the fluid flow behavior was then monitored.The numerical simulation indicates that there is a linear relationship between the average flow velocity over the entire flow path and the fractal dimension of the rough surface.It is shown that there is good agreement between the numerical results and the experimental data in terms of the properties a of the fluid flowing through the rough single rock fractures.展开更多
The validity of Local Cubic Law （LCL） is an important issue to study groundwater flow and transport in fractured media. According to laboratory simulaion tests, the average velocity with a lower gradient in a single...The validity of Local Cubic Law （LCL） is an important issue to study groundwater flow and transport in fractured media. According to laboratory simulaion tests, the average velocity with a lower gradient in a single fracture is calculated by the LCL, which is compared with the measured average velocity. Then dye tracer test is designed and completed. The evidence for non-LCL, is drawn from the results of the simulation tests and the dye tracer tests. Then the Reynolds number of groundwater is calculated, the critical value of Re for laminar flow is discussed in a single fracture under different conditions. The motion types for groundwater flow have been discussed.展开更多
In this article,the Non-Aqueous Phase Liquid（NAPL）transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method（LBM）with special consideration of wettab...In this article,the Non-Aqueous Phase Liquid（NAPL）transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method（LBM）with special consideration of wettability effects.With the help of the model,the contact angle of the non-wetting phase and wetting phase interface at a solid wall could be adjusted.By considering a set of appropriate boundary conditions,the fractured conductivity was investigated in condition that the NAPL blocks the channels in the single filled fracture.In order to study the wettability effects on the NAPL transport,a constant driving force was introduced in the Shan-Chen multi-component multiphase LBM.Flow regimes with different wettabilities were discussed.Simulated results show that the LBM is a very instrumental method for simulating and studying the immiscible multiphase flow problems in single filled fracture.展开更多
Ground penetrating radar（GPR） can be used to image fractures and monitor fluid flow in the subsurface. Conventional GPR imaging uses single-polarization, co-polarized acquisition. We examine the use of cross-polariz...Ground penetrating radar（GPR） can be used to image fractures and monitor fluid flow in the subsurface. Conventional GPR imaging uses single-polarization, co-polarized acquisition. We examine the use of cross-polarized GPR signals for imaging flow channeling in a discrete horizontal fracture. Numerical modeling（FDTD） demonstrates that when the fracture channel is oriented at an oblique angle to the survey line, depolarization of the GPR signal results in scattered energy along the cross-polarized components. When the channel is oriented parallel or orthogonal to the survey line, all scattered energy is captured by the co-polarized components and no signal is present in the cross-polarized orientation. Multipolarization, time-lapse 3D GPR field data were acquired at the Altona Flat Rock test site in New York State. The GPR surveys were conducted during background fresh fracture water conditions and during a natural gradient saline tracer test which was used to highlight flow channels along a sub-horizontal fracture. Amplitude analysis of the cross-polarized data reveals flow channeling that is in agreement with the co-polarized GPR images and with independent hydraulic tests. This investigation demonstrates that cross-polarized components of GPR signals can be used to enhance imaging of flow channels in fractured media.展开更多
文摘Natural rock joint permeability deviates from the classic fluid flow governing equations due to the inher-ent fracture surface roughness(i.e.,contact points,spatial correlation,matching,varying aperture,iso-lated voids,infilling material,tortuosity and channellings)and engineering disturbance such as excavations.To improve the accuracy of fracture permeability evaluation,many efforts have been made in analytical,experimental,and numerical methods.This study reviews the modified mathematical gov-erning equations of fluid flow and classifies them based on different influencing factors,such as friction factor,aperture,tortuosity,inertia,and various in situ stress effects.Various experimental and simulation techniques for the coupled normal-and shear-stress flow problems were assessed,and their advantages and disadvantages were also analysed.Furthermore,different surface roughness descriptions and their impacts on mechanical and hydraulic behaviours were discussed,followed by the potential research directions for fracture flow problems.
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.
文摘Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.
基金supported by the National Science Funds for Distinguished Young Scholar of China (Grant No. 51125017)the National Basic Research Program of China (Grant Nos. 2010CB226804,2011CB201201)+2 种基金the National Natural Science Foundation of China (Grant No. 50974125)the International Cooperation Project of Ministry of Science & Technology of China (Grant No. 2012DFA60760-2)NSFC International Cooperation and Exchange Program (Grant No. 51120145001)
文摘The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.41272251,41372245)
文摘Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of the evolution of the flow pattern at places far from the outlet. The relationship between the hydraulic gradient and the flow velocity at different points, and the proportion evolution of the linear and nonlinear portions in the Forchheimer formula are then discussed. Three major conclusions are obtained. First, the non-Darcian flow exists in a single fracture in different laboratory tests. Better fitting accuracy is obtained by using the Forchheimer formula than by using the Darcy law. Second, the proportion of the Darcy flow increases with the increase of the observation scale. In places far enough, the Darcy flow prevails, and the critical velocity between the non-Darcian flow and the Darcy flow decreases as the fracture aperture increases. Third, when the fracture aperture increases, the critical Reynolds number between the non-Darcian flow and the Darcy flow decreases.
基金Project supported by the National Natural Science Foundation of China.(Grant No:40202027)
文摘The formulae for average velocity of groundw-ater flow in a single fracturewere derived based on the characteristics of fracture properties and hydraulic methods. The resultsshow that the average velocity is proportional to the square root of the hydraulic gradient. Inorder to verify the results, a laboratory model was established, and the experimental data wereanalyzed. Experimental results indicate that the relation between the average velocity and hydraulicgradient is nonlinear, and can he filled with power functions. And for both the unconfined andconfined flows, the value of the exponent of power functions are close to 0. 5. Thus the experimental results agree well with those from the theoretical analysis. By comparing the calculated andmeasured values of the average velocity under the same conditions, the formulae presented herein aremore effective than the traditional formula based on Darcy' s Law. These results provide theevidences of non-Dar-cy's flow in single fracture.
基金The authors are grateful to the National Natural Science Funds for Distinguished Young Scholars of China(Grant No 51125017)the National Natural Science Foundation of China(Grant No 51374213)+3 种基金the Creative Research Group Program of Jiangsu Province(Grant No 2014-27)the Priority Academic Program Development of Jiangsu Higher Education Institutions(Grant No PAPD-2014-12)the Open Research Project of State Key Laboratory for Geomechanics and Underground Engineering(Grant No SKLGDUEK1318)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No 51421003)for their financial supports.
文摘To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures,a set of single fracture physical models were produced using the WeierstrasseMandelbrot functions to test the seepage flow performance.Six single fractures,with various surface roughnesses characterized by fractal dimensions,were built using COMSOL multiphysics software.The fluid flow behavior through the rough fractures and the influences of the rough surfaces on the fluid flow behavior was then monitored.The numerical simulation indicates that there is a linear relationship between the average flow velocity over the entire flow path and the fractal dimension of the rough surface.It is shown that there is good agreement between the numerical results and the experimental data in terms of the properties a of the fluid flowing through the rough single rock fractures.
基金Project supported by the National Natural Science Foundation of China (Grant No :40202027) and Fok Ying Tung Ed-ucation Foundation (Grant No :91079)
文摘The validity of Local Cubic Law （LCL） is an important issue to study groundwater flow and transport in fractured media. According to laboratory simulaion tests, the average velocity with a lower gradient in a single fracture is calculated by the LCL, which is compared with the measured average velocity. Then dye tracer test is designed and completed. The evidence for non-LCL, is drawn from the results of the simulation tests and the dye tracer tests. Then the Reynolds number of groundwater is calculated, the critical value of Re for laminar flow is discussed in a single fracture under different conditions. The motion types for groundwater flow have been discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.51079043,41172204)the Program for Non-profit Industry Financial Program of Ministry of Water Resources(Grant Nos.200901064,201001020)the Research Innovation Program for College Graduates of Jiangsu Province(Grant No.CXZZ11_0450)
文摘In this article,the Non-Aqueous Phase Liquid（NAPL）transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method（LBM）with special consideration of wettability effects.With the help of the model,the contact angle of the non-wetting phase and wetting phase interface at a solid wall could be adjusted.By considering a set of appropriate boundary conditions,the fractured conductivity was investigated in condition that the NAPL blocks the channels in the single filled fracture.In order to study the wettability effects on the NAPL transport,a constant driving force was introduced in the Shan-Chen multi-component multiphase LBM.Flow regimes with different wettabilities were discussed.Simulated results show that the LBM is a very instrumental method for simulating and studying the immiscible multiphase flow problems in single filled fracture.
基金supported by the US Department of Energy Environmental Remediation Sciences Program (No. 07-358509)the US Department of Energy Geothermal Technologies Program (No. DE-EE0002767)GPR instrumentation was funded by the National Science Foundation (No. EAR/IF-0345445)
文摘Ground penetrating radar（GPR） can be used to image fractures and monitor fluid flow in the subsurface. Conventional GPR imaging uses single-polarization, co-polarized acquisition. We examine the use of cross-polarized GPR signals for imaging flow channeling in a discrete horizontal fracture. Numerical modeling（FDTD） demonstrates that when the fracture channel is oriented at an oblique angle to the survey line, depolarization of the GPR signal results in scattered energy along the cross-polarized components. When the channel is oriented parallel or orthogonal to the survey line, all scattered energy is captured by the co-polarized components and no signal is present in the cross-polarized orientation. Multipolarization, time-lapse 3D GPR field data were acquired at the Altona Flat Rock test site in New York State. The GPR surveys were conducted during background fresh fracture water conditions and during a natural gradient saline tracer test which was used to highlight flow channels along a sub-horizontal fracture. Amplitude analysis of the cross-polarized data reveals flow channeling that is in agreement with the co-polarized GPR images and with independent hydraulic tests. This investigation demonstrates that cross-polarized components of GPR signals can be used to enhance imaging of flow channels in fractured media.
