Computation of the filtration laws through porous media for a non-Newtonian fluid obeying the power law

We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach.     

Implication of surface modified NZVI particle retention in the porous media: Assessment with the help of 1-D transport model

Retention of surface-modified nanoscale zero-valent iron (NZVI) particles in the porous media near the point of injection has been reported in the recent studies. Retention of excess particles in porous media can alter the media properties. The main objectives of this study are, therefore, to evaluate the effect of particle retention on the porous media properties and its implication on further NZVI particle transport under different flow conditions. To achieve the objectives, a one-dimensional transport model is developed by considering particle deposition, detachment, and straining mechanisms along with the effect of changes in porosity resulting from retention of NZVI particles. Two different flow conditions are considered for simulations. The first is a constant Darcy’s flow rate condition, which assumes a change in porosity, causes a change in pore water velocity and the second, is a constant head condition, which assumes the change in porosity, influence the permeability and hydraulic conductivity (thus Darcy’s flow rate). Overall a rapid decrease in porosity was observed as a result of high particle retention near the injection points resulting in a spatial distribution of deposition rate coefficient. In the case of constant head condition, the spatial distribution of Darcy’s velocities is predicted due to variation in porosity and hydraulic conductivity. The simulation results are compared with the data reported from the field studies; which suggests straining is likely to happen in the real field condition.     

Particle transport within water-saturated porous media: Effect of pore size on retention kinetics and size selection

The transport and filtration behaviour of fine particles (silt) in columns packed with sand was investigated under saturated conditions by using step-input injections. Three samples of different particle size distributions (coarse medium, fine medium and a mixture of both) were used in order to highlight the influence of the pore size distribution on particle retention and size selection of recovered particles. The main parameters of particle transport and deposition were derived from the adjustment of the experimental breakthrough curves by an analytical model. The higher particle retention occurs in the mixture medium, owing to its large pore size distribution, and the filtration coefficient decreases with increasing flow velocity. Particle size distribution of recovered particles shows a thorough size selection: (i) the first recovered particles are the coarser ones; (ii) the size of the recovered particles increases with increasing flow velocity and enlarger pore distribution of the medium.     

Modeling heat and mass transfer during ground freezing subjected to high seepage velocities

Natural or induced groundwater flow may negatively influence the performance of artificial ground freezing: high water flow velocities can prevent frozen conditions from developing. Reliable models that take into consideration hydraulic mechanisms are then needed to predict the ground freezing development. For forty years, numerous thermo-hydraulic coupled numerical models have been developed. Some of these models have been validated against experimental data but only one has been tested under high water flow velocity conditions. This paper describes a coupled thermo-hydraulic numerical model completely thermodynamically consistent and designed to simulate artificial ground freezing of a saturated and non-deformable porous medium under seepage flow conditions. On some points, less restrictive assumptions than the ones usually used in the literature are considered. As for the constant-porosity assumption, its validity is verified. The model appears to be well validated against analytical solutions and a three-dimensional ground freezing experiment under high seepage flow velocity conditions. It is used to highlight key thermo-hydraulic mechanisms associated with phase change in a porous medium.     

Modelling of cement suspension flow in granular porous media

A theoretical model of cement suspensions flow in granular porous media considering particle filtration is presented in this paper. Two phenomenological laws have been retained for the filtration rate and the intrinsic permeability evolution. A linear evolution with respect to the volume fraction of cement in the grout has been retained for the filtration rate. The intrinsic permeability of the porous medium is looked for in the form of a hyperbolic function of the porosity change. The model depends on two phenomenological parameters only. The equations of this model are solved analytically in the one‐dimensional case. Besides, a numerical resolution based on the finite element method is also presented. It could be implemented easily in situations where no analytical solution is available. Finally, the predictions of the model are compared to the results of a grout injection test on a long column of sand. Copyright © 2005 John Wiley & Sons, Ltd.     

Transport and deposition of suspended particles in saturated porous media: hydrodynamic effect

A laboratory study was undertaken to determine the transport and deposition rate of suspended particles in columns of saturated porous media (gravel and glass beads), where the porous media were subjected to steady-state flow. Silt particles with a mode of 14 μm diameter (used as the suspended particles) and fluorescein (as the conservative tracer) were injected into the columns in short pulses. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with a first-order deposition rate. The experiments were performed using different flow rates. The suspended particle size distribution, the porous media, and the flow rates themselves were the main factors retained in this study to investigate the mechanisms governing the transport and deposition kinetics in detail. The results showed the existence of a flow rate, beyond which suspended particles travel faster than the conservative tracer. A decrease of the deposition rate of suspended particles beyond a critical flow velocity was also observed. Such behaviour led to consideration of the couple hydrodynamic-gravity forces at high flow rates. As the hydrodynamic force increases, particle deposition rates are reduced due to the effect of hydrodynamic forces inhibiting the deposition.     

复杂水力路径下非饱和流动的数值分析

多孔介质中的流动问题,与孔隙介质的特性,含水量状态以及含水量的变化历史密切相关。基于毛细循环滞回理论模型,考虑含水量变化历史对土水特征关系的影响,在开发的U-DYSAC2有限元程序中进行了相应的数值实施。在试验给定的初边值条件下进行了非饱和渗流模拟分析,并将模拟结果与实测数据比较,表明在压力边界条件反复变化下,考虑滞回效应能获得更接近实测的结果,证实该模型在模拟各种循环变化条件下非饱和土渗流初边值问题的适用性与必要性。对入渗重分布反复变化条件下非饱和土柱流动的数值模拟表明,考虑滞回与不考虑滞回条件下,含水量、孔隙水压力和湿峰的迁移的预测在入渗后的重分布过程差异较大。考虑滞回效应时,土柱上部的脱湿速率、下部的吸湿速率比不考虑滞回时要低。从而证实了非饱和多孔介质中的土水状态依赖于含水量变化,而且强烈依赖于土体的水力路径变化。因此,循环边界条件变化下,毛细滞回效应在非饱和渗流模拟中的影响显著,必须加以考虑。     

孔隙结构和水动力对饱和多孔介质中颗粒迁移和沉积特性的耦合影响

为了研究孔隙结构和水动力对悬浮颗粒在饱和多孔介质中沉积和迁移特性的影响,对天然硅粉（悬浮颗粒）和荧光素钠（示踪剂）在饱和多孔介质中的渗流迁移特性进行土柱试验,分别得到了5种不同渗流速度（0.033、0.066、0.132、0.199、0.265 cm/s）、两种不同多孔介质（石英砂和玻璃球）的悬浮颗粒和示踪剂全组合下的20条穿透曲线。根据试验结果,研究孔隙结构、渗流速度对饱和多孔介质中颗粒迁移和沉积过程中水动力作用机制、弥散效应、加速效应的影响。研究表明,悬浮颗粒的穿透曲线可以用一阶沉积动力学对流弥散方程的解析解来描述。随着渗流速度的增大,水动力学作用对颗粒出流浓度的影响越来越大,而孔隙结构的影响则相对减弱。同时,存在一个临界渗流速度值。当渗流速度超出该值时,悬浮颗粒迁移要快于示踪剂,而且临界渗流速度对于玻璃球和石英砂两种多孔介质是不同的;其次,在两种介质中,随渗流速度增大,弥散度增加,回收率和回收悬浮颗粒粒径增大,沉积系数先增大后减小。此外,在孔隙比相近的情况下,悬浮颗粒在玻璃球介质中的回收率要大于其在石英砂中的。可见,孔隙结构和渗流速度是影响饱和多孔介质中颗粒输运的重要因素,渗流速度越大,孔隙结构的作用越明显。     

悬浮颗粒的浓度对其在饱和多孔介质中迁移和沉积特性的影响

多孔介质中悬浮颗粒迁移和沉积特性的研究对地下污染物净化、石油开采、核废料处置、水土保持等有很重要的意义。对4种不同浓度的悬浮颗粒在3种不同的渗流速度下进行室内试验,研究悬浮颗粒的浓度对其迁移和沉积特性的影响。结果表明,在一定的悬浮颗粒浓度下,随着渗流速度的增加,穿透曲线中的悬浮颗粒的相对浓度也增大。同时,渗流速度一定时,悬浮颗粒的浓度存在一个临界值,小于该临界值,穿透曲线中的相对浓度随悬浮颗粒的浓度增大而增大;大于该临界值时,相对浓度随悬浮颗粒的浓度增大而减小。另外,悬浮颗粒的临界浓度是与渗流速度相关的,随着渗流速度增加,悬浮颗粒的临界浓度也逐渐增大     

高水力梯度条件下颗粒堆积型多孔介质渗流规律试验研究

煤矿开采面临的水文地质条件越来越复杂,尤其是遭遇承压含水层的水压力越来越大,突水灾害发生时必然会带来高水力梯度引起的破碎岩体突水通道内高速非线性渗流问题。据此,研制高水力梯度（最大600）条件下堆积型多孔介质中高速非线性渗流试验装置,采用堆积型钢球模拟破碎岩体,对粒径为1、2、3、4、5、6 mm共6种光滑钢球分别开展了一维均质圆柱渗流试验。试验结果表明：对于由1～6 mm钢球堆积而成的孔隙率为0.44～0.45的多孔介质,当水力梯度大于145时,通过分析水力梯度-平均流速（J-v）曲线和水力梯度-雷诺数（J-Re）关系曲线,将流动状态划分为3个模式：线性层流、非线性层流、紊流,并获得了从线性层流过渡到非线性层流的临界流速为0.23～0.78 cm/s、临界水力梯度为3～8;从层流到紊流转捩的临界流速为1.6～4.8 cm/s、临界水力梯度为90～145。从小粒径多孔介质到大粒径多孔介质的渗流过程中,临界流速越来越大,而临界水力梯度逐渐减小。 渗透率与粒径的平方、非达西流影响系数与粒径的倒数均呈线性正相关,非达西流影响系数随着渗透率的增加呈指数减小。该研究对多孔介质非线性渗流的理论研究以及实际工程中高承压含水层突涌水问题有重要借鉴意义。     

泥沙影响流速分布规律的试验研究

挟沙水流中泥沙颗粒的存在将影响水流的紊动结构,并进一步影响水流流速分布。采用超声流速仪MicroADV测量挟沙水流的时均流速沿垂线分布,分析了在不同水力条件、不同泥沙条件(包括泥沙浓度及颗粒粒径)下泥沙与水流相互作用对流速沿垂线分布的影响,在此基础上,考虑到现有流速分布公式在实际河道水流流速沿垂线分布中的应用,提出新的指数型流速分布公式形式;并根据实验资料,初步检验了该公式的精度,同时分析了指数型流速公式中系数k和指数m随泥沙浓度s、粒径d以及水力条件的变化规律。结果表明:系数k随泥沙浓度的增加而增大,同时水力条件以及泥沙颗粒粒径同样也影响着k的变化;而指数m随粒径d的增大而减小,随泥沙浓度s的增加而增大。     

The prodelta environment of a fjord: suspended particle dynamics

The dynamics of suspended particles within a fjord's estuarine circulation are investigated and the results compared with larger non-enclosed prodelta environments. In the upper prodelta, the seaward-flowing river plume flows over the ambient marine water depositing much of the initial riverine suspended load. Sedimentation is dominated by coarse silt and fine-grained sand particles with coarseness determined by the tidal and fluvial stage. Particles less than 10 μn have similar settling velocities regardless of size because they settle in flocs: the settling velocity at a water depth of 5 m is 30 m day^-1 and increases with depth so that at 30 m the particles settle at 100 m day^-1. For larger particles, the downward settling velocity enhancement due to flocculation decreases with increasing grain size. Hydraulic sorting allows the preferential settling of feldspar and quartz over mica. Particle dynamics in the lower prodelta are dependent on the character of the freshwater wedge that thins seaward of the upper prodelta. The vertical flux of particles is controlled by biogeochemical interactions such as pelletization of fine particles and flocculation (which occurs within rather than below the surface layer in contrast to the upper prodelta). The pellets are produced by indiscriminate filter feeding zooplankton. Across the lower prodelta the suspensate character, recognized in the composition of both flocs and pellets, changes from a dominance of mineral grains to that of autochthonous organic matter. The interaction of bacteria with the suspended particles increases with depth and seaward distance. At depth, the mucoid filaments form stable interconnecting webs. Particle concentration in the surface layer decreases at a rate proportional to the negative one-half and three-halves power of the distance seaward over the upper and lower prodelta, respectively. This relationship is hypothesized as being universal for large marine deltas dominated by buoyancy flow dynamics, regardless of the levels of initial riverine particle concentration or their composition.     

Transport and mobilization of multiwall carbon nanotubes in quartz sand under varying saturation

In this study, a series of sand packed columns were used to investigate the mobility of multiwall carbon nanotubes (MWCNTs) in unsaturated porous media under unfavorable conditions for deposition. The flow through column experiments were designed to assess water content, flow rate, and grain size effect on the mobility of MWCNTs. It was found that variation in water content had no significant effect on retention of MWCNTs until it was lowered to 16 % effective saturation. Thick water films, high flow rate, and repulsive forces between MWCNTs and porous media made MWCNTs highly mobile. Different porous media grain sizes (D ₅₀ = 150–300 μm) were used in this study. The mobility of MWCNTs slightly decreased in finer grain sands, which was deemed to be an effect of increase in surface area and the number of depositional sites, in combination with low-pore water velocity. However, physical straining was not observed in selected fine-grain sands and aspect ratio of MWCNTs had low impact on mobility. Variations in pore-water velocity were produced by both changes in water saturation and in flow rate. At high pore-water velocities, the MWCNTs were generally mobile. However, for the combination of low-pore water velocity with either low water saturation or small grain size, some retention of MWCNTs was observed. Hence, low velocity in combination with flow through smaller pores increased MWCNT deposition.     

西部典型矿区风积沙含水层突水溃沙的起动条件与运移特征

突水溃沙是西部矿井地质灾害的主要类型之一,为研究突水溃沙灾害的临界判据与水沙运移特征,以榆横矿区含水层风积沙为例,采用自主研发的水沙两相高速渗流试验设备,对4种不同粒径范围的风积沙进行了沙粒起动试验和溃沙试验,对混合风积沙进行了水沙两相高速渗流试验。得到了影响突水溃沙的2个临界速度条件：第一临界速度即沙粒起动速度,为0.38～1.26 mm/s;第二临界速度即溃沙临界速度,为2.48～3.54 mm/s。试验结果表明：体积膨胀是沙粒群起动的必要条件,突水溃沙灾害是起动的风积沙由量变逐步积累到质变的物理过程,分为3个阶段：（1）水携沙流动,（2）水沙混合流动,（3）沙携水流动。沙粒起动是水动能转变为沙动能的过程,溃沙时水沙混合流体运动表现为颗粒群浓度波传播的特征,沙粒间通过碰撞的形式传递能量。溃沙速率随初始水力梯度的增大呈指数增长,单位时间内溃沙量随水力梯度的增大而呈线性增加。     

An empirical model for the development and equilibrium morphology of current ripples in fine sand

A flume study on the development and equilibrium morphology of current ripples in fine sand (D₅₀ = 0·238 mm) was performed to extend an empirical model for current ripple stability in 0·095 mm sand to larger grain sizes. The results of the flume experiments agree with the very fine sand model that current ripple development from a flat bed is largely independent of flow velocity. At all flow velocities, ripples evolve from incipient, through straight, sinuous and non-equilibrium linguoid, to equilibrium linguoid plan morphology. The time needed to achieve an equilibrium linguoid plan form is related to an inverse power of flow velocity and ranges from several minutes to more than hundreds of hours. Average equilibrium height and length are 17·0 mm and 141·1 mm respectively. These values are about 20% larger than in very fine sand. Equilibrium ripple height and length are proportional to flow velocity near the stability field of dunes. In the same velocity range, a characteristic grouping of ripples with smaller ripples migrating on the upstream face of larger ripples was observed. Bed-form development shows a conspicuous two-phase behaviour at flow velocities < 0·49 m s^?1. In the first phase of development, ripple height and length increase along an exponential path, similar to that at higher flow velocities, thus reaching intermediate equilibrium values of 14·8 mm and 124·5 mm respectively. After some time, however, a second phase commences, that involves a rapid increase in bed-form size to the typical equilibrium values for 0·238 mm sand. A comparison with literature data shows that the results obtained for 0·238 mm sand agree reasonably well with other flume studies at similar grain size. Yet considerable variability in the relationships between ripple dimensions and flow strength ensues from, among others, underestimation of equilibrium time, shallow flow depths and differences in sediment texture.     

Effets de la vitesse d'écoulement sur le transport et la cinétique de dépôt de particules en suspension en milieu poreux saturé

We study in this paper the transport and deposition of suspended particles in saturated porous media. Some chromatographic short-pulse tests were performed in a laboratory column with a tracer and two types of suspended particles. A mathematical model was used to determine the hydrodispersive parameters and deposition rates from the breakthrough curves. The results show that the fitted parameters obtained vary with the flow rate and the characteristics of the suspended particles. We also observe, at high flow rates, that particles have a migration velocity higher than that of the conservative tracer. To cite this article: A. Benamar et al., C. R. Geoscience 337 (2005).     

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

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软流层部分熔融岩浆竖向迁移模型分析

针对地幔蠕动过程中，软流层部分熔融岩浆上升这一地质背景，从力学的基本原理出发，将软流层岩石抽象为一类充满液体的多孔介质，并假定其以均匀速度上升，对岩石中部分熔融岩浆的迁移机理进行了分析，得到了一组简化的公式，并进行了计算。结果表明在此简化模型下，可以得到一个临界速度值的表达式。当岩石上升的速度低于该临界数值时，部分熔融岩浆将在一定的界面上形成；若大于这个临界数值，部分熔融岩浆的形成将滞后到一段竖向区域内完成。同时简单的计算结果也说明部分熔融岩浆的迁移运动是实现热量及成矿物质元素向上迁移的重要原因。其结果和某些岩浆过程的地质分析是一致的，这对进一步研究地幔蠕动及其成矿动力学具有重要的意义。     

堰槽组合设施测流机制试验研究

山区季节性溪流流量变化大,已有灌溉渠道量水设施难以在较大流量范围内均达到测流精度要求,本文以克伦普堰和排淤量水槽组合而成的堰槽组合量水设施为试验对象,通过试验探究其测流机制。根据流量在5~79 L/s范围内的概化水槽水力性能试验,分析不同流量下的水面线、弗劳德数、垂线纵向时均流速、薄水层特征长度和特征宽度的变化,建立不同流量阈值范围内的测流公式。结果表明:①随流量的增大,堰槽组合设施流动形态从槽内流变为堰流,流量阈值对应的阈值相对水深为0.885,拟合得到组合设施槽内流和堰流的测流公式,与实测流量对比,相对误差小于3%。②组合设施槽内流和堰流水力特性不同,槽内流时槽内各测点纵向时均流速、薄水层的特征长度和特征宽度以及综合流量系数均随着流量增大而增大;堰流时,排淤量水槽槽内前段各测点纵向时均流速随着流量增大而减小,后段各测点纵向时均流速随着流量增大而增大,槽内收缩扭面段中部附近断面平均流速大小一致。③堰槽组合流量系数随着流量增大而减小。④堰槽设施下游薄水层的特征长度和特征宽度随着流量增大有下降趋势,最大值均出现在流量阈值情况下。本研究有效解决了流量变幅较大的明渠测流设施匮乏问题,可为山区季节性溪流测流设施应用提供参考。