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

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.

Non-Darcy Flow in Molding Sands

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%.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices.Several key aspects of fundamental mechanisms,numerical modeling and engineering applications of flow in fractured rocks are discussed.First,the microscopic mechanisms of fluid flow in fractured rocks,especially under the complex conditions of non-Darcian flow,multiphase flow,rock dissolution,and particle transport,have been revealed through a com-bined effort of visualized experiments and theoretical analysis.Then,laboratory and field methods of characterizing hydraulic properties(e.g.intrinsic permeability,inertial permeability,and unsaturated flow parameters)of fractured rocks in different flow regimes have been proposed.Subsequently,high-performance numerical simulation approaches for large-scale modeling of groundwater flow in frac-tured rocks and aquifers have been developed.Numerical procedures for optimization design of seepage control systems in various settings have also been proposed.Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed.Finally,three case studies are presented to illustrate the applications of the improved theoretical understanding,characterization methods,modeling approaches,and seepage and deformation control strategies to geotechnical engi-neering projects.

Impact of seepage flow on sediment resuspension by internal solitary waves:parameterization and mechanism

Sediment incipient motion is the first step in sediment resuspension.Previous studies ignored the effect of seepage flow on the mobility of sediment particles and simplified the seabed surface as a rigid boundary.A flume experiment was designed to innovatively divide the seabed into two parts to control the dynamic response of the seabed and control the seepage conditions.In the experiment,the seabed sediments and the amplitude of internal solitary waves(ISWs)were changed to compare and analyze the impact of seepage flow on the sediment resuspension by shoaling ISWs.Moreover,parametric research and verification were carried out.Results indicate that seepage flow can greatly influence fine sand,promote sediment resuspension,and increase the amount of suspension by two times on average.However,seepage flow had a little effect on the suspension of clayey silt and sandy silt.Besides,seepage force was added to the traditional gravity,drag force,and uplift force,and the parameterization of threshold starting shear stress of coarse-grained sediments was developed.The results of this parameterization were verified,and seepage force was critical to parameterization.The threshold starting shear stress was reduced by 54.6%after increasing the seepage force.The physical mechanism of this process corresponded to the vertical reciprocating transient seepage in and out the seabed interface caused by the wave-induced transient excess pore water pressure.This quantitative study on seepage flow for shear stress of coarse-grained sediments induced by ISWs is critical to geohazard assessment.

Experimental Study of Seepage Properties of Non-Darcy Flow in Granular Coal Gangues

By using the steady-state seepage method, a patent seepage device together with the MTS815.02 Rock Me- chanics Test System is used to test the seepage properties of non-Darcy flow in a granular gangue with five different grain sizes during the compaction. The experimental results show that the seepage properties are not only related to the stress or displacement level, but also to the grain size, the pore structure of the granular gangue, and the current porosity. The permeability and the non-Darcy flow coefficient can be fitted respectively by the cubic polynomials and the power functions of the porosity. Formally, the flow in granular gangue satisfies the Forchheimer’s binomial flow, but under the great axial and confining pressure and owing to the grain’s crushing, the flow in granular gangues is different from that in rock-fills which are naturally piled up. As a result, the non-Darcy flow coefficient may be negative.

Vertical Migration of Fine-Grained Sediments from Interior to Surface of Seabed Driven by Seepage Flows–‘Sub-Bottom Sediment Pump Action'

A scientific hypothesis is proposed and preliminarily verified in this paper: under the driving of seepage flows, there might be a vertical migration of fine-grained soil particles from interior to surface of seabed, which is defined as ‘sub-bottom sediment pump action' in this paper. Field experiments were performed twice on the intertidal flat of the Yellow River delta to study this process via both trapping the pumped materials and recording the pore pressures in the substrate. Experimental results are quite interesting as we did observe yellow slurry which is mainly composed of fine-grained soil particles appearing on the seabed surface; seepage gradients were also detected in the intertidal flat, under the action of tides and small wind waves. Preliminary conclusions are that ‘sediment pump' occurs when seepage force exceeds a certain threshold: firstly, it is big enough to disconnect the soil particles from the soil skeleton; secondly, the degree of seabed fluidization or bioturbation is big enough to provide preferred paths for the detached materials to migrate upwards. Then they would be firstly pumped from interior to the surface of seabed and then easily re-suspended into overlying water column. Influential factors of ‘sediment pump' are determined as hydrodynamics(wave energy), degree of consolidation, index of bioturbation(permeability) and content of fine-grained materials(sedimentary age). This new perspective of ‘sediment pump' may provide some implications for the mechanism interpretation of several unclear geological phenomena in the Yellow River delta area.

Monitoring models for base flow effect and daily variation of dam seepage elements considering time lag effect

Affected by external environmental factors and evolution of dam performance, dam seepage behavior shows nonlinear time-varying characteristics. In this study, to predict and evaluate the long-term development trend and short-term fluctuation of the dam seepage behavior, two monitoring models were developed, one for the base flow effect and one for daily variation of dam seepage elements. In the first model, to avoid the influence of the time lag effect on the evaluation of seepage variation with the time effect component of seepage elements, the base values of the seepage element and the reservoir water level were extracted using the wavelet multi-resolution analysis method, and the time effect component was separated by the established base flow effect monitoring model. For the development of the daily variation monitoring model for dam seepage elements, all the previous factors, of which the measured time series prior to the dam seepage element monitoring time may have certain influence on the monitored results, were considered. Those factors that were positively correlated with the analyzed seepage element were initially considered to be the support vector machine(SVM) model input factors, and then the SVM kernel function-based sensitivity analysis was performed to optimize the input factor set and establish the optimized daily variation SVM model. The efficiency and rationality of the two models were verified by case studies of the water level of two piezometric tubes buried under the slope of a concrete gravity dam.Sensitivity analysis of the optimized SVM model shows that the influences of the daily variation of the upstream reservoir water level and rainfall on the daily variation of piezometric tube water level are processes subject to normal distribution.

Influence of underground water seepage flow on surrounding rock deformation of multi-arch tunnel

Based on a typical multi-arch tunnel in a freeway, the fast Lagrangian analysis of continua in 3 dimensions(FLAC3D) was used to calculate the surrounding rock deformation of the tunnel under which the effect of underground water seepage flow was taken into account or not. The distribution of displacement field around the multi-arch tunnel, which is influenced by the seepage field, was gained. The result indicates that the settlement values of the vault derived from coupling analysis are bigger when considering the seepage flow effect than that not considering. Through the contrast of arch subsidence quantities calculated by two kinds of computation situations, and the comparison between the calculated and measured value of tunnel vault settlement, it is found that the calculated value(5.7-6.0 mm) derived from considering the seepage effect is more close to the measured value(5.8-6.8 mm). Therefore, it is quite necessary to consider the seepage flow effect of the underground water in aquiferous stratum for multi-arch tunnel design.

Effect of Downward Seepage on Turbulent Flow Characteristics and Bed Morphology around Bridge Piers

在这个工作，试验性的调查被追求了分析影响向下在在在冲积隧道的圆形的桥码头附近的旋涡结构的流动和相应变化的狂暴的特征上的渗出物。实验为没有渗出物， 10% 渗出物和 20% 渗出物盒子与不同尺寸的圆形的墩在沙床隧道被进行。象速度和雷纳兹压力那样的狂暴的流动统计的测量被发现在 scour 洞在以内否定墩在上游而申请向下，渗出物延迟在速度和雷纳兹引起减少的流动的颠倒强调。更高级的雷纳兹砍因为生产，应力在下游的方面占优势弄醒旋涡。到彻底的雷纳兹的所有爆炸事件的贡献砍压力生产被观察了增加与向下渗出物。不可分的规模的分析建议旋涡的那种尺寸与渗出物增加，它为粒子活动性的增加负责。开始搜索评价是消退逐渐地象与一样与膨胀预定的更多增加了向下渗出物。存在向下，渗出物向墩的下游的方面减少旋涡和移动的深度和长度。

Numerical simulation of seepage flow field in groundwater source heat pump system and its influence on temperature field

Energy utilization in the aquifers is a new technology closely related to development of heat pump technique. It is significant for the flow distribution to be predicted in the aquifer surrounding the Groundwater Source Heat Pump System (GSHPS). The authors presented a new concept of "flow transfixion" by analyzing general features of aquifers, and then discussed interaction of the flow transfixion with the heat transfixion, which has practical significance to projects. A numerical model of groundwater flow was established based on the basic tenets of water-heat transferring in the aquifer. On this basis the flow field and the temperature field of GSHPS for a site in Shenyang City were numerically simulated. The basis of the flow transfixion was obtained; it was discussed for the influence of the flow transfixion on the heat transfixion. To a certain extent, the study offers some reference for the projects' design of GSHP in the studied area.

RULE OF TRANSIENT PHREATIC FLOW SUBJECTED TO VERTICAL AND HORIZONTAL SEEPAGE

In a semi-infinite aquifer bounded by a channel, a transient flow model is constructed for phreatic water subjected to vertical and horizontal seepage. Based on the first linearized Boussinesq equation, the analytical solution of the model is obtained by Laplace transform. Having proven the transformation between the analytical solution and some relevant classic formulas, suitable condition for each of these formulas is demonstrated. On the base of the solution, the variation of transient flow process caused by the variables, such as vertical infiltration intensity, fluctuation range of river stage, aquifer parameters such as transmissivity and specific yield, and the distance from calculating point to channel boundary, are analyzed quantitatively one by one. Lagging effect will happen to the time, when phreatic water gets its maximum fluctuation velocity, response to the varying of the variables stated above. The condition for some variables to form equivalent lagging effect is demonstrated. Corresponding to the mathematical charac teristics of the analytical solution, the physical implication and the fluctuation rule of groundwater level are discussed.

A well test analysis model of generalized tube flow and seepage coupling

"Generalized mobility"is used to realize the unification of tube flow and seepage in form and the unification of commonly used linear and nonlinear flow laws in form,which makes it possible to use the same form of motion equations to construct unified governing equations for reservoirs of different scales in different regions.Firstly,by defining the generalized mobility under different flow conditions,the basic equation governing fluid flow in reservoir coupling generalized tube flow and seepage is established.Secondly,two typical well test analysis models for coupling tube flow and seepage flow are given,namely,pipe-shaped composite reservoir model and partially open cylindrical reservoir model.The log-log pressure draw-down type-curve of composite pipe-shaped reservoir model can show characteristics of two sets of linear flow.The log-log pressure drawdown plot of partially opened cylindrical reservoir model can show the characteristics of spherical flow and linear flow,as well as spherical flow and radial flow.The pressure build-up derivative curves of the two models basically coincide with their respective pressure drawdown derivative curves in the early stage,pulling down features in the late stage,and the shorter the production time is,the earlier the pulling down feature appears.Finally,the practicability and reliability of the models presented in this paper are verified by three application examples.

THE ANALYTIC RESOLUTIONS AND APPLICATIONS OF THE NON－LINEAR SEEPAGE FLOW EQUATIONS OF COAL INFUSION

hi this paper. the author uses the theory of fluid mechanics. dynamics of fluids in Porous media. gas seepage flow in coal seams and combines the tests in the laboratory with the actual coal infusion to have an investigating and study from the theory to the mechanism of coal infusion to wet coal seams. through the analysis to the process of coal infusion the author builds up the mathematical models and has a detailed discussion to the boundary conditions of coal infusion. Because the equation sets to describe coal infusion are non-linear. we have made a simplification to them to use the dimension analysis theory by leading into the non-dimensions of water pressure of coal infusion, seepage flow rate. increment of coal seam moisture and so on Besides the analytic and approximate solutions have also been discussed. At last. we use the scientific research item of the actual coal infusion to illustrate the effects and importance of the theory to direct actual coal infusion and its designs.

A new classification of seepage control mechanisms in geotechnical engineering

Seepage flow through soils,rocks and geotechnical structures has a great influence on their stabilities and performances,and seepage control is a critical technological issue in engineering practices.The physical mechanisms associated with various engineering measures for seepage control are investigated from a new perspective within the framework of continuum mechanics;and an equation-based classification of seepage control mechanisms is proposed according to their roles in the mathematical models for seepage flow,including control mechanisms by coupled processes,initial states,boundary conditions and hydraulic properties.The effects of each mechanism on seepage control are illustrated with examples in hydroelectric engineering and radioactive waste disposal,and hence the reasonability of classification is demonstrated.Advice on performance assessment and optimization design of the seepage control systems in geotechnical engineering is provided,and the suggested procedure would serve as a useful guidance for cost-effective control of seepage flow in various engineering practices.

Characteristics of non-Darcy flow in low-permeability reservoirs

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.

Seepage simulation of high concrete-faced rockfill dams based on generalized equivalent continuum model

This research focused on the three-dimensional(3 D) seepage field simulation of a high concrete-faced rockfill dam(CFRD) under complex hydraulic conditions. A generalized equivalent continuum model of fractured rock mass was used for equivalent continuous seepage field analysis based on the improved node virtual flow method. Using a high CFRD as an example, the generalized equivalent continuum range was determined, and a finite element model was established based on the terrain and geological conditions, as well as structural face characteristics of the dam area. The equivalent seepage coefficients of different material zones or positions in the dam foundation were calculated with the Snow model or inverse analysis. Then, the 3 D seepage field in the dam area was calculated under the normal water storage conditions, and the corresponding water head distribution, seepage flow, seepage gradient, and seepage characteristics in the dam area were analyzed. The results show that the generalized equivalent continuum model can effectively simulate overall seepage patterns of the CFRD under complex hydraulic conditions and provide a reference for seepage analysis of similar CFRDs.

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

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.

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

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.

A state‑of‑the‑art review on rock seepage mechanism of water inrush disaster in coal mines

Water inrush is one of the most dangerous disasters in coal mining.Due to the large-scale mining and complicated hydrogeological conditions,thousands of deaths and huge economic losses have been caused by water inrush disasters in China.There are two main factors determining the occurrence of water inrush:water source and water-conducting pathway.Research on the formation mechanism of the water-conducting pathway is the main direction to prevent and control the water inrush,and the seepage mechanism of rock mass during the formation of the water-conducting pathway is the key for the research on the water inrush mechanism.This paper provides a state-of-the-art review of seepage mechanisms during water inrush from three aspects,i.e.,mechanisms of stress-seepage coupling,fow regime transformation and rock erosion.Through numerical methods and experimental analysis,the evolution law of stress and seepage felds in the process of water inrush is fully studied;the fuid movement characteristics under diferent fow regimes are clearly summarized;the law of particle initiation and migration in the process of water inrush is explored,and the efect of rock erosion on hydraulic and mechanical properties of the rock media is also studied.Finally,some limitations of current research are analyzed,and the suggestions for future research on water inrush are proposed in this review.

Non-Darcy flows in layered porous media(LPMs)with contrasting pore space structures

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.