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Chuangbing Zhou - One of the best experts on this subject based on the ideXlab platform.
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Effects of non-darcy flow on heat-flow coupling process in complex fractured rock masses
Journal of Natural Gas Science and Engineering, 2020Co-Authors: Chi Yao, Qinghui Jiang, Yulong Shao, Jianhua Yang, Fan Huang, Chuangbing ZhouAbstract:Abstract This paper presented a heat-flow coupling model for simulation of heat transfer process in complex fractured rock masses considering non-Darcy flow. Firstly, the Forchheimer Equation and the Reynolds Equation were coupled to obtain the governing Equation to describe the non-Darcy flow behaviors. Then, combined with the heat transfer Equation and considered the heat exchange process between fractures and rock matrix, the heat-flow coupling model was established. The model was solved by the finite element method. The calculation results of the non-Darcy flow model were compared with the fluid flow test results of crossed fracture and complex fracture network models and a good agreement was observed. The numerical simulation results of non-Darcy flow and heat transfer model were compared with analytical solution of flow-heat coupling in a single fracture, and the numerical solution and the analytical solution agreed well. Finally, a two-dimensional complex fracture network was generated for numerical experiments, and effects of equivalent hydraulic aperture df and hydraulic gradient J on the flow behaviors and the heat-transfer process in complex fractured rock masses were systematically discussed. Results showed that the proposed model can well describe the non-Darcy flow characteristics as well as the heat-flow coupling process in complex fracture networks. Considering the non-Darcy flow behaviors, the average temperature of the outlet dropped slower under non-Darcy than which under Darcy flow. It was also found that effects of non-Darcy flow on the heat transfer process will be more significant as the hydraulic gradient or the equivalent hydraulic aperture increases.
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a Forchheimer Equation based flow model for fluid flow through rock fracture during shear
Rock Mechanics and Rock Engineering, 2018Co-Authors: Guan Rong, Chuangbing Zhou, Jie Yang, Long Cheng, Jie Tan, Jun PengAbstract:Shear deformation-induced hydraulic conductivity change in fracture has been studied for decades. However, the existing models to link shear deformation and hydraulic behaviors are less accurate due to complex flow in rock fractures. This study presents an improved flow model for calculating nonlinear flow behaviors in rock fractures during shear. In this model, the linear and nonlinear coefficients in the Forchheimer Equation were determined using mechanical aperture and fracture roughness coefficients. The mechanical aperture was equal to the initial aperture plus the change of the aperture due to shear-induced dilation. The dilation curve was divided into three stages and analytical expressions for modeling the dilation curve were established by incorporating the joint roughness coefficient (JRC) and the mobilized roughness coefficient (JRCmob). In addition, shear-flow tests were conducted on marble and granite fractures with normal stress between 0.5 and 3.0 MPa. The experimental data were used to verify the proposed model. The results show that the proposed model predicts flow in rock fractures well.
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the friction factor in the Forchheimer Equation for rock fractures
Rock Mechanics and Rock Engineering, 2016Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Min WangAbstract:The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer Equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers.
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nonlinear flow behavior at low reynolds numbers through rough walled fractures subjected to normal compressive loading
International Journal of Rock Mechanics and Mining Sciences, 2015Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Shu FangAbstract:Abstract This study experimentally investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0–30.0 MPa). Both mated granite and unmated sandstone fractures were adopted for water flow tests and the experimental results were well fitted with the Forchheimer Equation. The coefficients of viscous and inertial pressure drops experience an enlargement of 2–5 orders of magnitude with the increasing confining pressure. The critical Reynolds number Re c was successfully estimated based on the Forchheimer Equation by taking α percentage (usually 10%) of the nonlinear effect as the critical point between the linear and nonlinear flow. The obtained Re c versus confining pressure curves generally display a nonlinear weakening stage (I) in the early stage of confining pressure loading, which is followed by a nonlinear enhancement stage (II) as the confining pressure further increases. A zoning map of fluid flow regimes based on Re c in the full range of the confining pressures (1.0–30.0 MPa) was presented. For the first time, an empirical relationship between the nonlinear coefficient B and the hydraulic aperture e h in rock fractures under varying confining pressure was developed based on the laboratory observations. A critical Reynolds number Equation was then proposed to quantify the onset of nonlinear flow through rough-walled fractures with varying e h .
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Evaluation of Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures
Journal of Hydrology, 2015Co-Authors: Yifeng Chen, Jia-qing Zhou, Chuangbing ZhouAbstract:Summary This study focuses on experimental evaluation of the Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0 MPa to 30.0 MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid–water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer Equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical Equations were proposed for parametric expression of the Forchheimer’s nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy’s law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer’s law incorporated with the single-parameter Equation to that predicted by the Darcy’s law. A sensitivity analysis was performed using the double-parameter Equation for examining the dependence of the Forchheimer’s nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers.
Yifeng Chen - One of the best experts on this subject based on the ideXlab platform.
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a Forchheimer s law based analytical model for constant rate tests with linear flow pattern
Advances in Water Resources, 2019Co-Authors: Yifeng Chen, Mingming Liu, Zhibing YangAbstract:Abstract Aquifers with quasi-linear flow pattern are frequently envisaged in fractured zones, in oil, gas or enhanced geothermal reservoirs, or in civil engineering where cut-off walls are constructed. The water flow towards a well in this linear aquifer system has been long investigated under Darcian flow condition, but remains an open issue for non-Darcian flow. In this study, a general linearization approximation strategy is suggested for the Forchheimer Equation, and an analytical solution is proposed by using Laplace transform for non-Darcian flow towards a well in aquifers laterally bounded by no-flow barriers. Numerical simulations using the finite volume method prove that the linearization approximation performs best when it takes the mean of two commonly-used strategies, and the analytical model is sufficiently accurate at late times for observation wells located moderately far from the source. The proposed model was applied to data interpretation of the pumping tests at the Changheba dam foundation bounded by two cut-off walls in Southwest China, where the drawdown curves can be divided into 1D flow, transitional flow and 2D flow stages as a result of lateral flow through weathered bedrocks at late times. The proposed model provides a valuable tool for characterizing the hydraulic properties of aquifers and reservoirs with a linear flow pattern and for assessing the possible leakage through the lateral barriers by type curve matching.
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the friction factor in the Forchheimer Equation for rock fractures
Rock Mechanics and Rock Engineering, 2016Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Min WangAbstract:The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer Equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers.
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nonlinear flow behavior at low reynolds numbers through rough walled fractures subjected to normal compressive loading
International Journal of Rock Mechanics and Mining Sciences, 2015Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Shu FangAbstract:Abstract This study experimentally investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0–30.0 MPa). Both mated granite and unmated sandstone fractures were adopted for water flow tests and the experimental results were well fitted with the Forchheimer Equation. The coefficients of viscous and inertial pressure drops experience an enlargement of 2–5 orders of magnitude with the increasing confining pressure. The critical Reynolds number Re c was successfully estimated based on the Forchheimer Equation by taking α percentage (usually 10%) of the nonlinear effect as the critical point between the linear and nonlinear flow. The obtained Re c versus confining pressure curves generally display a nonlinear weakening stage (I) in the early stage of confining pressure loading, which is followed by a nonlinear enhancement stage (II) as the confining pressure further increases. A zoning map of fluid flow regimes based on Re c in the full range of the confining pressures (1.0–30.0 MPa) was presented. For the first time, an empirical relationship between the nonlinear coefficient B and the hydraulic aperture e h in rock fractures under varying confining pressure was developed based on the laboratory observations. A critical Reynolds number Equation was then proposed to quantify the onset of nonlinear flow through rough-walled fractures with varying e h .
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Evaluation of Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures
Journal of Hydrology, 2015Co-Authors: Yifeng Chen, Jia-qing Zhou, Chuangbing ZhouAbstract:Summary This study focuses on experimental evaluation of the Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0 MPa to 30.0 MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid–water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer Equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical Equations were proposed for parametric expression of the Forchheimer’s nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy’s law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer’s law incorporated with the single-parameter Equation to that predicted by the Darcy’s law. A sensitivity analysis was performed using the double-parameter Equation for examining the dependence of the Forchheimer’s nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers.
Vassilios A Tsihrintzis - One of the best experts on this subject based on the ideXlab platform.
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determination of Forchheimer Equation coefficients a and b
Hydrological Processes, 2007Co-Authors: Melina G Sidiropoulou, Konstadinos N Moutsopoulos, Vassilios A TsihrintzisAbstract:This study focuses on the determination of the Forchheimer Equation coefficients a and b for non-Darcian flow in porous media. Original theoretical Equations are evaluated and empirical relations are proposed based on an investigation of available data in the literature. The validity of these Equations is checked using existing experimental data, and their accuracy versus existing approaches is studied. On the basis of this analysis, some insight into the physical background of the phenomenon is also provided. The dependence of the coefficients a and b on the Reynolds number is also detected, and potential future research areas, e.g. investigation of inertial effects for consolidated porous media, are pointed out. Copyright © 2006 John Wiley & Sons, Ltd.
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approximate analytical solutions of the Forchheimer Equation
Journal of Hydrology, 2005Co-Authors: Konstadinos N Moutsopoulos, Vassilios A TsihrintzisAbstract:In this paper we derive approximate analytical solutions for non-steady-state, non-linear flows through porous media, described by the Forchheimer Equation. We demonstrate that one has to distinguish between two characteristic regimes. In early times, the hydraulic gradient is steep, and subsequently the inertial terms are dominant. One obtains the leading hydraulic behavior by neglecting linear terms describing the viscous dissipation mechanisms. In moderate times, as the disturbance introduced upstream propagates through the entire medium, the hydraulic gradient, and subsequently the inertial effects become less important: the leading behavior corresponds to the Darcy solution. The influence of the inertia mechanisms in this regime is taken into account by computing higher order correction terms, by means of perturbation analysis. The verification of the analytical solution is done by comparison with numerical results of a finite volume code. As application of the developed theory the water volume accumulated in an aquifer due to river flooding is presented. q 2004 Elsevier B.V. All rights reserved.
Mark Foley - One of the best experts on this subject based on the ideXlab platform.
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investigation of gas flow through soils and granular fill materials for the optimisation of radon soil depressurisation systems
Journal of Environmental Radioactivity, 2019Co-Authors: Marta Fuente, Eduardo Munoz, Isabel Sicilia, Jamie Goggins, Le Chi Hung, Borja Frutos, Mark FoleyAbstract:Abstract The purpose of this study is to investigate gas flow through different types of granular fill materials and soil by means of a series of experimental laboratory tests, in relation to soil depressurisation systems for radon reduction under buildings and the soil surrounding the foundation. Gas permeability characterisation of materials used as granular fill material beneath the slab in buildings is a key parameter for the optimum performance of soil depressurisation systems to mitigate radon. A test apparatus was developed, adapted from previous studies, to measure the gas permeability of the samples and Finite Element Method numerical simulations were validated to simulate the flow behaviour through them. Theoretical expressions for permeability were discussed based on the analysis of experimental results and numerical simulations, finding that Darcy-Forchheimer Equation provides the best match to the experimental results. Darcy's law also proved to be suitable for low gas velocities, whereas Ergun's Equation resulted in a poor fit of the experimental data. Benchmark analysis of the granular fill materials under study and other European standards (Spanish, Irish and British) is also presented.
Jia-qing Zhou - One of the best experts on this subject based on the ideXlab platform.
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the friction factor in the Forchheimer Equation for rock fractures
Rock Mechanics and Rock Engineering, 2016Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Min WangAbstract:The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer Equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers.
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nonlinear flow behavior at low reynolds numbers through rough walled fractures subjected to normal compressive loading
International Journal of Rock Mechanics and Mining Sciences, 2015Co-Authors: Jia-qing Zhou, Chuangbing Zhou, Yifeng Chen, Shu FangAbstract:Abstract This study experimentally investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0–30.0 MPa). Both mated granite and unmated sandstone fractures were adopted for water flow tests and the experimental results were well fitted with the Forchheimer Equation. The coefficients of viscous and inertial pressure drops experience an enlargement of 2–5 orders of magnitude with the increasing confining pressure. The critical Reynolds number Re c was successfully estimated based on the Forchheimer Equation by taking α percentage (usually 10%) of the nonlinear effect as the critical point between the linear and nonlinear flow. The obtained Re c versus confining pressure curves generally display a nonlinear weakening stage (I) in the early stage of confining pressure loading, which is followed by a nonlinear enhancement stage (II) as the confining pressure further increases. A zoning map of fluid flow regimes based on Re c in the full range of the confining pressures (1.0–30.0 MPa) was presented. For the first time, an empirical relationship between the nonlinear coefficient B and the hydraulic aperture e h in rock fractures under varying confining pressure was developed based on the laboratory observations. A critical Reynolds number Equation was then proposed to quantify the onset of nonlinear flow through rough-walled fractures with varying e h .
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Evaluation of Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures
Journal of Hydrology, 2015Co-Authors: Yifeng Chen, Jia-qing Zhou, Chuangbing ZhouAbstract:Summary This study focuses on experimental evaluation of the Forchheimer Equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0 MPa to 30.0 MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid–water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer Equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical Equations were proposed for parametric expression of the Forchheimer’s nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy’s law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer’s law incorporated with the single-parameter Equation to that predicted by the Darcy’s law. A sensitivity analysis was performed using the double-parameter Equation for examining the dependence of the Forchheimer’s nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers.