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Effects of fracture evolution and non-darcy flow on the thermal performance of enhanced geothermal system in 3D complex fractured rock

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International Journal of Mining Science and Technology 2024年第4期34卷 443-459页

作者： Yachen Xie Jianxing Liao Pengfei Zhao Kaiwen Xia Cunbao Li Department of Civil and Mineral Engineering University of TorontoToronto M5S1A4Canada College of Water Resources and Hydropower Sichuan UniversityChengdu 610225China State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsWuhan 430071China College of Civil Engineering Guizhou UniversityGuiyang 550025China Institute of Geosafety School of Engineering and TechnologyChina University of GeosciencesBeijing 100083China State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering Shenzhen UniversityShenzhen 518060China

In fractured geothermal reservoirs,the fracture networks and internal fluid flow behaviors can significantly impact the thermal performance.In this study,we proposed a non-darcy rough discrete fracture network(NR-DFN)model that can simultaneously consider the fracture evolution and non-darcy flow dynamics in studying the thermo-hydro-mechanical(THM)coupling processes for heat extraction in geothermal reservoir.We further employed the model on the Habanero enhanced geothermal systems(EGS)project located in Australia.First,our findings illustrate a clear spatial-temporal variation in the thermal stress and pressure perturbations,as well as uneven spatial distribution of shear failure in 3D fracture networks.Activated shear failure is mainly concentrated in the first fracture cluster.Secondly,channeling flow have also been observed in DFNs during heat extraction and are further intensified by the expansion of fractures driven by thermal stresses.Moreover,the combined effect of non-darcy flow and fracture evolution triggers a rapid decline in the resulting heat rate and temperature.The NR-DFN model framework and the Habanero EGS's results illustrate the importance of both fracture evolution and non-darcy flow on the efficiency of EGS production and have the potential to promote the development of more sustainable and efficient EGS operations for stakeholders.

关键词： Coupled THM model non-darcy flow Deformable DFN Enhanced geothermal systems

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non-darcy flow in Molding Sands

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Open Journal of Applied Sciences 2024年第4期14卷 976-982页

作者： Miguel A. Barron-Meza Joan Reyes-Miranda Daniel Flores-Sanchez Departamento de Materiales Universidad Autonoma Metropolitana Azcapotzalco Ciudad de Mexico Mexico

darcy’s law is widely used to describe the flow in porous media in which there is a linear relationship between fluid velocity and pressure gradient. However, it has been found that for high numbers of Reynolds this law ceases to be valid. In this work, the Ergun equation is employed to consider the non-linearity of air velocity with the pressure gradient in casting sands. The contribution of non-linearity to the total flow in terms of a variable defined as a non-darcy flow fraction is numerically quantified. In addition, the influence of the shape factor of the sand grains on the non-linear flow fraction is analyzed. It is found that for values of the Reynolds number less or equal than 1, the contribution of non-linearity for spherical particles is around 1.15%.

关键词： darcy’s Law Molding Sands non-darcy flow Reynolds Number Shape Factor

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A fractal approach to low velocity non-darcy flow in a low permeability porous medium

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Chinese Physics B 2014年第4期23卷 385-389页

作者：蔡建超 Institute of Geophysics and Geomatics Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education China University of Geosciences

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.

关键词： fractal porous media non-darcy flow threshold pressure gradient scaling law

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One-dimensional non-darcy flow in a semi-infinite porous media:a multiphase implicit Stefan problem with phases divided by hydraulic gradients

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Acta Mechanica Sinica 2017年第5期33卷 855-867页

作者： G.Q.Zhou Y.Zhou X.Y.Shi State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and Technology School of Mechanics and Civil Engineering China University of Mining and Technology JiangSu Collaborative Innovation Center for Building Energy Saving and Construct Technology

One-dimensional non-darcy flow in a semi-infinite porous media is investigated. We indicate that the non-darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.

关键词： Moving boundary problem Stefan problem Analytical solution non-darcy flow Soil consolidation

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Efect of double dispersion on non-darcy mixed convective flow over vertical surface embedded in porous medium

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Applied Mathematics and Mechanics(English Edition) 2013年第10期34卷 1247-1262页

作者： A. A. AFIFY N. S. ELGAZERY Department of Mathematics Faculty of Science Helwan UniversityCairo 11795 Egypt Department of Mathematics Faculty of Education Ain Shams UniversityCairo 11234 Egypt

A numerical study of a non-darcy mixed convective heat and mass transfer flow over a vertical surface embedded in a dispersion, melting, and thermal radiation is porous medium under the effects of double investigated. The set of governing boundary layer equations and the boundary conditions is transformed into a set of coupled nonlinear ordinary differential equations with the relevant boundary conditions. The transformed equations are solved numerically by using the Chebyshev pseudospectral method. Comparisons of the present results with the existing results in the literature are made, and good agreement is found. Numerical results for the velocity, temperature, concentration profiles, and local Nusselt and Sherwood numbers are discussed for various values of physical parameters.

关键词： mixed convection non-darcy flow porous medium double dispersion melting thermal radiation Chebyshev pseudospectral method

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Characteristics of non-darcy flow in low-permeability reservoirs

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Petroleum Science 2011年第1期8卷 55-62页

作者： Yao Yuedong Ge Jiali Key Laboratory of Petroleum Engineering of the Ministry of Education China University of PetroleumBeijing 102249 China

Well testing is recognized as an effective means of accurately obtaining the formation parameters of low-permeability reservoirs and effectively analyzing the deliverability.Well test models must comply with the particular characteristics of flow in low-permeability reservoirs in order to obtain reasonable well test interpretation.At present,non-darcy flow in low-permeability reservoirs is attracting much attention.In this study,displacement tests were conducted on typical cores taken from low-permeability reservoirs.Two dimensionless variables were introduced to analyze the collected experimental data.The results of the dimensionless analysis show whether non-darcy flow happens or not depends on the properties of fluid and porous media and the pressure differential.The combination of the above three parameters was named as dimensionless criteria coefficient（DCC）.When the value of the DCC was lower than a critical Reynolds number（CRN）,the flow could not be well described by darcy＇s law（so-called non-darcy flow）,when the DCC was higher than CRN,the flow obeyed darcy＇s law.Finally,this paper establishes a transient mathematical model considering darcy flow and non-darcy flow in low-permeability reservoirs,and proposes a methodology to solve the model.The solution technique,which is based on the Boltzmann transformation,is well suited for solving the flow model of low-permeability reservoirs.Based on the typical curves analysis,it was found that the pressure and its derivative curves were determined by such parameters as non-darcy flow index and the flow characteristics.The results can be used for well test analysis of low-permeability reservoirs.

关键词： Low-permeability non-darcy flow dimensionless analysis transient flow well testing

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non-darcy flow in oil accumulation (oil displacing water) and relative permeability and oil saturation characteristics of low-permeability sandstones

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Petroleum Science 2010年第1期7卷 20-30页

作者： Zeng Jianhui Cheng Shiwei Kong Xu Guo Kai Wang Hongyu State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum Beijing 102249 China School of Natural Resources and Information Technology China University of Petroleum Beijing 102249 China CNPC Greatwall Drilling Company Beijing 100101 China

Hydrocarbon resources in low-permeability sandstones are very abundant and are extensively distributed. Low-permeability reservoirs show several unique characteristics, including lack of a definite trap boundary or caprock, limited buoyancy effect, complex oil-gas-water distribution, without obvious oil-gas-water interfaces, and relatively low oil （gas） saturation. Based on the simulation experiments of oil accumulation in low-permeability sandstone （oil displacing water）, we study the migration and accumulation characteristics of non-darcy oil flow, and discuss the values and influencing factors of relative permeability which is a key parameter characterizing oil migration and accumulation in low-permeability sandstone. The results indicate that： 1） Oil migration （oil displacing water） in low- permeability sandstone shows non-darcy percolation characteristics, and there is a threshold pressure gradient during oil migration and accumulation, which has a good negative correlation with permeability and apparent fluidity; 2） With decrease of permeability and apparent fluidity and increase of fluid viscosity, the percolation curve is closer to the pressure gradient axis and the threshold pressure gradient increases. When the apparent fluidity is more than 1.0, the percolation curve shows modified darcy flow characteristics, while when the apparent fluidity up＂ non-darcy percolation curve; 3） Oil-water is less than 1.0, the percolation curve is a ＂concave- two-phase relative permeability is affected by core permeability, fluid viscosity, apparent fluidity, and injection drive force; 4） The oil saturation of low- permeability sandstone reservoirs is mostly within 35%-60%, and the oil saturation also has a good positive correlation with the permeability and apparent fluidity.

关键词： non-darcy flow relative permeability oil saturation low-permeability sandstone

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Research advances in non-darcy flow in low permeability media

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Journal of Groundwater Science and Engineering 2021年第1期9卷 83-92页

作者： HAO Hong-bo LV Jie CHEN Yan-mei WANG Chuan-zi HUANG Xiao-rui College of Resources and Environment Yantze UniversityWuhan 430100China Wuhan Zhong Di Huanke Hydrological EngineeringEnvironmental Science and Technology Consulting Co.LtdWuhan 430075China State Key Laboratory of Groundwater Protection and Utilization of Coal Mining Beijing 102200China

More and more experimental results show that darcy’s law is not fully applicable in low permeability media,and non-darcy flow has been identified.In this paper we reviewed the research of non-darcy flow experiments in low-permeability media in recent decades,discuss the existence of non-darcy flow,and summarize its constitutive equations.The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-darcy flow.On this basis,the future development of non-darcy flow experiments in the rock and clay media were discussed,in order to provide a certain reference for subsequent research on seepage laws in low permeability media.

关键词： Low permeability media non-darcy flow Constitutive equation Critical point criterion

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non-darcy flows in layered porous media(LPMs)with contrasting pore space structures

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Petroleum Science 2022年第5期19卷 2004-2013页

作者： Xue-Yi Zhang Zhi Dou Jin-Guo Wang Zhi-Fang Zhou Chao Zhuang School of Earth Sciences and Engineering Hohai UniversityNanjing 210098JiangsuChina

Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,darcy and non-darcy)were observed.The influence of the interface of layers on non-darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the non-darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For non-darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.

关键词： non-darcy flow Layered porous media Heterogeneity Forchheimer equation Simulations

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Numerical Simulation of a Two-Phase flow with Low Permeability anda Start-Up Pressure Gradient

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Fluid Dynamics & Materials Processing 2023年第1期19卷 175-185页

作者： Xuanyu Dong Jingyao Yang School of Geosciences Yangtze UniversityWuhan430100China Gas Production Plant 5 Changqing Oilfield Company of PetroChinaXi’an710000China

A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.

关键词： Low-permeability reservoirs two-phase flow water cut start-up pressure gradient non-darcy flow

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