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nonlinear flow Properties of Newtonian Fluids through Rough Crossed Fractures

Computer Modeling in Engineering & Sciences 2023年第8期136卷 1427-1440页

作者： Zhenguo Liu Shuchen Li Richeng Liu Changzhou Zheng Geotechnical and Structural Engineering Research Center Shandong UniversityJinan250061China Sinohydro Foundation Engineering Co. Ltd.Tianjin301700China State Key Laboratory for Geomechanics andDeepUnderground Engineering China University of Mining and TechnologyXuzhou221116China

The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length,aperture,and surface roughness of fractures.A total of 252 computational runs are performed by creating 36 computational domains,in which the Navier-Stokes equations are *** results show that the nonlinear relationship between flow rate and hydraulic gradient follows Forchheimer’s law–based *** the hydraulic gradient is small(i.e.,10^(−6)),the streamlines are parallel to the fracture walls,indicating a linear streamline *** the hydraulic gradient is large(i.e.,10^(0)),the streamlines are disturbed by a certain number of eddies,indicating a nonlinear streamline *** patterns of eddy distributions depend on the length,aperture,and surface roughness of *** the increment of hydraulic gradient from 10^(−6) to 10^(0),the ratio of flow rate to hydraulic gradient holds constants and then decreases slightly and finally decreases *** fluid flow experiences a linear flow regime,a weakly nonlinear regime,and a strongly nonlinear regime,*** critical hydraulic gradient ranges from 3.27×10^(−5) to 5.82×10^(−2) when fracture length=20–100mmandmechanical aperture=1–*** joint roughness coefficient plays a negligible role in the variations in critical hydraulic gradient compared with fracture length and/or mechanical *** critical hydraulic gradient decreases with increasing mechanical aperture,following power-law *** parameters in the functions are associated with fracture length.

关键词： Crossed fractures surface roughness aperture nonlinear flow critical hydraulic gradient

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nonlinear flow numerical simulation of low-permeability reservoir

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Journal of Central South University 2012年第7期19卷 1980-1987页

作者：于荣泽卞亚南周舒王楷军吕琦陈朝辉 PetroChina Research Institute of Petroleum Exploration&Development-Langfang Special Oil Development Company of Liaohe Oilfield Company Down-hole Service Company of Xinjiang Oilfield Company Geological Scientific Research Institute of Shengli Oilfield Company CNOOC Energy Technology&Service-Oilfield Engineering Research Institute

A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability *** well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear *** nonlinear flow numerical simulation program was compiled based on black-oil model.A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability *** comprehensive comparison and analysis of the simulation results of Darcy flow,quasi-linear flow and nonlinear flow were *** dimensionless permeability coefficient distribution was gained to describe the nonlinear flow *** result shows that compared with the results of Darcy flow,when considering nonlinear flow,the oil production is low,and production decline is *** fluid flow in reservoir consumes more driving energy,which reduces the water flooding *** flow model overstates the reservoir flow capability,and quasi-linear flow model overstates the reservoir flow *** flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is *** nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability *** water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture,and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.

关键词： low-permeability reservoir nonlinear flow mathematical model numerical simulation

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Effect of shear-induced contact area and aperture variations on nonlinear flow behaviors in fractal rock fractures

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Journal of Rock Mechanics and Geotechnical Engineering 2023年第2期15卷 309-322页

作者： Changsheng Wang Richeng Liu Yujing Jiang Gang Wang Hengjie Luan Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation Shandong University of Science and TechnologyQingdao266590China State Key Laboratory of Mining Disaster Prevention and Control Co-founded By Shandong Province and the Ministry of Science and Technology Shandong University of Science and TechnologyQingdao266590China State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou221116China School of Engineering Nagasaki UniversityNagasaki852-8521Japan

This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 *** granite fractures with different roughnesses are selected and quantified using variogram fractal *** obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture *** flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact *** the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts *** on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.

关键词： Fracture Shear displacement Fractal dimension nonlinear flow Contact area flow visualization

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MATHEMATICAL MODEL OF TWO-PHASE FLUID nonlinear flow IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

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Applied Mathematics and Mechanics(English Edition) 2003年第10期24卷 1184-1193页

作者：邓英尔刘慈群 State Key Laboratory of Oil-Gas Reservoir Geology and Development Engineering Department of Energy Chengdu University of Technology Chengdu 610059 P.R.China Institute of Porous flow and Fluid Mechanics Chinese Academy of Sciences Langfang

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

关键词： low permeability porous media two-phase fluid nonlinear flow finite difference method extrapolation method

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nonlinear fluid flow through three-dimensional rough fracture networks:Insights from 3D-printing,CT-scanning,and high-resolution numerical simulations

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Journal of Rock Mechanics and Geotechnical Engineering 2021年第5期13卷 1020-1032页

作者： Bo Li Jiafei Wang Richeng Liu Yujing Jiang Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province Shaoxing UniversityShaoxing312000China State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou221116China School of Engineering Nagasaki UniversityNagasaki852-8521Japan

nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically *** physical models of DFNs were 3D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of *** validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models.A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer’s law and geometrical *** results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks,numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital *** in DFNs become increasingly tortuous as the fracture number and roughness increase,resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations,which can be well characterized by the Forchheimer’s *** critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture,fracture number and roughness,following a power *** increases in fracture aperture and number provide more paths for fluid flow,increasing both the viscous and inertial *** value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability,following a power function with an exponent a of 3,and a proportional coefficient b mathematically correlated with the geometrical parameters.

关键词： nonlinear flow 3D-printing CT-scanning Fracture network Permeability Fluid flow test

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EXACT SOLUTIONS FOR nonlinear TRANSIENT flow MODEL INCLUDING A QUADRATIC GRADIENT TERM

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Applied Mathematics and Mechanics(English Edition) 2004年第1期25卷 102-109页

作者：曹绪龙同登科王瑞和 Institute of Chemical Physics Department of Applied Mathematics

The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.

关键词： nonlinear flow integral transform analytical solution well test analysis

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Assessments of the effects of various fracture surface morphology on single fracture flow: A review

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International Journal of Mining Science and Technology 2023年第1期33卷 1-29页

作者： Min Gao Chengguo Zhang Joung Oh School of Minerals and Energy Resources Engineering University of New South WalesSydney NSW 2052Australia

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 *** improve the accuracy of fracture permeability evaluation,many efforts have been made in analytical,experimental,and numerical *** 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 *** experimental and simulation techniques for the coupled normal-and shear-stress flow problems were assessed,and their advantages and disadvantages were also ***,different surface roughness descriptions and their impacts on mechanical and hydraulic behaviours were discussed,followed by the potential research directions for fracture flow problems.

关键词： Surface roughness Single fracture nonlinear flow Coupled hydromechanical(HM)behaviours

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Analysis of nonlinear Seepage Characteristics of High Water Cut Preferential Channel

Analysis of Nonlinear Seepage Characteristics of High Water ...

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作者： Feng-jun HAO Li-bing FU Lun ZHAO Jun LAN Research Institute of Petroleum Exploration and Development PetroChina

After long-term water injection,some preferential seepage channels would form which are several times or even hundreds of times larger than the original channels in the *** inefficient and ineffective circulating water injection caused by the preferential channel restricts the efficient development of the *** this paper,based on the seepage law of the preferential channel,the seepage model for the preferential channel is *** pressure gradient,seepage velocity and average formation pressure under the nonlinear seepage flow are *** nonlinear seepage characteristics in the preferential channel are *** comparing with the Darcy linear flow,it is considered that the existence of the preferential channel has a great influence on the production,and the influence of the nonlinear flow in the preferential channel should be considered in the calculation of the development index.

关键词： Preferential channel nonlinear flow Forchheimer equation Pressure gradient

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