粗糙裂隙水、气两相流相对渗透系数模型与数值分析

粗糙裂隙水、气两相流相对渗透系数是岩体工程多相渗流以及水力耦合分析的重要参数。从粗糙裂隙的细观结构出发，基于毛细吸持理论和立方定理，提出了粗糙裂隙水、气两相流相对渗透系数模型。通过与具有不同空间分布的粗糙裂隙水、气两相流试验数据对比分析，验证了模型的准确性。为进一步验证理论模型对不同粗糙程度裂隙的适用性，基于SRAM与Invasion Percolation模型，提出了粗糙裂隙的开度分布生成以及水、气两相流数值分析方法，计算结果表明理论模型与数值数据基本吻合一致，且优于X模型、V-C模型以及Corey模型。     

A pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures

This paper aims at developing a pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures. A simple general relationship between the local hydraulic conductivity and the flow velocity is proposed. A new governing equation for non-Darcy fluid flow through rough-walled fractures is then derived by introducing this relationship into the Reynolds equation. Based on the non-linear finite element method, a self-developed code is used to simulate the non-Darcy fluid flow through fractures. It is found that the macroscopic results obtained by the numerical simulation agree well with the experimental results. Furthermore, some interesting experimental observations can be reproduced.     

粗糙岩石裂隙低速非线性渗流模型及试验验证

岩体粗糙裂隙非线性渗透特性是岩体渗流研究的重要课题。针对Javadi所提T模型中亚裂隙中速度恒定这一假设的不足,将其修正为速度与开度成正比的经验关系,考虑黏性压降和局部压降,提出了新的低速下粗糙裂隙非线性渗流模型（MT模型）。为了验证MT模型的正确性,对5种不同粗糙裂隙进行了低流量的饱和渗流试验,将现有模型及MT模型的预测值与试验结果进行对比,分析表明MT模型与试验结果更为吻合,且模型适用于粗糙性系数JRC≤10的低粗糙度裂隙,雷诺数小于1 000的低流速情况。对MT模型进行分析,初步揭露了粗糙裂隙的非线性渗流机制,即小雷诺数下的Darcy流和大雷诺数下的Forchheimer流,并用临界雷诺数区分两种流动行为。分析了裂隙的粗糙度和开度对非线性渗流特性的影响,表明裂隙越粗糙或开度越小,则临界雷诺数越小,非线性作用将越强。提出了临界雷诺数与水力开度和绝对粗糙度的经验关系式,同时指出该关系式适用于JRC≤10的低粗糙度裂隙。     

Micro- and macro-behaviour of fluid flow through rock fractures: an experimental study

Microscopic and macroscopic behaviour of fluid flow through rough-walled rock fractures was experimentally investigated. Advanced microfluidic technology was introduced to examine the microscopic viscous and inertial effects of water flow through rock fractures in the vicinity of voids under different flow velocities, while the macroscopic behaviour of fracture flow was investigated by carrying out triaxial flow tests through fractured sandstone under confining stresses ranging from 0.5 to 3.0 MPa. The flow tests show that the microscopic inertial forces increase with the flow velocity with significant effects on the local flow pattern near the voids. With the increase in flow velocity, the deviation of the flow trajectories is reduced but small eddies appear inside the cavities. The results of the macroscopic flow tests show that the linear Darcy flow occurs for mated rock fractures due to small aperture, while a nonlinear deviation of the flow occurs at relatively high Reynolds numbers in non-mated rock fracture (Re?>?32). The microscopic experiments suggest that the pressure loss consumed by the eddies inside cavities could contribute to the nonlinear fluid flow behaviour through rock joints. It is found that such nonlinear flow behaviour is best matched with the quadratic-termed Forchheimer equation.     

Effect of roughness on water flow through a synthetic single rough fracture

A single fracture is usually idealized theoretically as smooth parallel plates, but the real fractures are rough-walled with points of contact. Though relative roughness is considered in quantifying the flow through a single rough fracture (SRF) previously, additional factors such as the distribution of rough elements and bending degree of streamlines should be considered in order to obtain more accurate results. Semiempirical friction factor (f) and discharge per unit width (q) equations are first deduced taking relative roughness, roughness elements distribution and streamline reattachment length into consideration. A horizontal SRF model was then set up and a series of experiments and simulations were performed. Main conclusions are drawn: Recirculation of streamlines arises in the rough element and the intensity of the recirculation increases with the angle from which the streamlines enter into the rough elements and Reynolds number (Re); streamlines are discontinuously distributed when asperity height is large and nonlinear flow occurs; the nonlinearity of the flow increases with the increasing the asperity height and Re; the critical value of related roughness used to judge whether the influence of roughness on water flow through a SRF can be ignored or not should be much lower than 0.033; the revised f and q equations under laminar flow through a SRF are proved to be better when calculating the f and q values.     

Numerical modeling of stress-permeability coupling in rough fractures

A numerical model is described for coupled flow and mechanical deformation in fractured rock. The mechanical response of rock joints to changes in hydraulic pressure is strongly influenced by the geometric characteristics of the joint surfaces. The concept of this work is to combine straightforward finite element solutions with complex and realistic fracture surface geometry in order to reproduce the non-linear stress-deformation-permeability coupling that is commonly observed in fractures. Building on the numerous studies that have expanded the understanding of the key parameters needed to describe natural rough-walled fractures, new methods have been developed to generate a finite element mesh representing discrete fractures with realistic rough surface geometries embedded in a rock matrix. The finite element code GeoSys/Rockflow was then used to simulate the coupled effects of hydraulic stress, mechanical stress, and surface geometry on the evolving permeability of a single discrete fracture. The modeling concept was experimentally verified against examples from the literature. Modeling results were also compared to a simple interpenetration model.     

三维交叉裂隙渗流传质特性数值模拟

对交叉裂隙渗流传质特性的定量描述是研究整个裂隙网络渗透传质特性的基础。为真实模拟水流及溶质在三维交叉裂隙中的运移过程,首先通过三维轮廓仪获取天然岩石裂隙表面的形貌数据,再应用三维重构技术生成相应的三维交叉裂隙模型,随后求解Navier-Stokes方程,假定溶质运移满足Fick定律,模拟水流和溶质在三维交叉裂隙中的运移过程。通过对比粗糙裂隙模型与平行平板模型的模拟结果发现：粗糙度对流体的分布及流动状态存在显著的影响;不同进、出口工况下的流体流动及溶质运移状态亦表明：裂隙交叉的几何形貌会显著地影响溶质混合行为。这些结果表明,目前被广泛采用的平行平板模型在评估岩体内特别是交叉口的物质运移特性时将导致较大的偏差,在将来的研究中有必要针对裂隙交叉口的几何特征建立修正的模型以提高评估的准确性。     

Simulation of fluid percolation in a rough-walled rock fracture

A comparison of experimental and numerical results is presented addressing two-phase immiscible displacement in rough fractures. Quasi-static, capillary displacement in a rough fracture is modeled using the modified invasion percolation approach proposed by Glass et al (1998), and the results are compared against experimental observations obtained from two-phase flow through a rock fracture using x-ray computed-tomography scanning. The model is based on an algorithm seeking the least resistant pathway for the advancement of the invading fluid using the Young-Laplace equation and accounting for local in-plane curvature of the advancing fluid front. The saturation distribution map generated by the model yields good agreement with the experimental phase distribution and presents more realistic phase structures than those obtained from the conventional invasion percolation approach. The improvement in the results obtained with the modified invasion percolation approach is attributed to the contribution of the in-plane curvature term, which captures the effect of regionalized apertures, rather than single-point apertures, on the shape of the invading front. Glass RJ, Nicholl MJ, Yarrington L (1998) A modified invasion percolation model for low-capillary number immiscible displacements in horizontal rough-walled fractures: influence of local in-plane curvature. Water Resour Res 34:3215–3234     

Friction Factor of Water Flow Through Rough Rock Fractures

Fluid flow through rock joints occurs in many rock engineering applications. As the fluid flows through rough-walled rock fractures, pressure head loss occurs due to friction drag of the wall and local aperture changes. In this study, the friction factor was experimentally investigated by performing flow tests through sandstone fractures with joint roughness coefficient ranging from 5.5 to 15.4 under changing normal stress from 0.5 to 3.5 MPa. According to the experimental results, the friction factor was formulated as a function of two-independent variables—Reynolds number and relative roughness. Relative roughness is defined as the ratio of maximum asperity height to equivalent hydraulic aperture. The experimental results show that the proposed predictor of the friction factor fits the data with a coefficient of determination R ² > 0.93. Sensitivity analyses indicate that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2. For Reynolds numbers greater than unity, the difference of friction factor induced by relative roughness is smaller. Inclusion of joint roughness in calculating the friction resistance to fluid flow in rough rock joints and the influence of normal stress to the joints is a major step towards more accurate predictions for fluid flow in underground joint networks. This study provides a significant improvement in fundamental understanding of fluid flow in the jointed strata.     

坡面流层流区动力学特性

为完善坡面水流的基础理论研究,基于定床水槽试验,以甘油溶液为试验流体,采用超声波测量技术,进行了4种粗糙度、5种坡度和13种单宽流量条件下的组合试验,研究了坡面流层流区的动力学特性及滚波特征。研究结果表明:在雷诺数为8~160的范围内,流态指数在理论值0.33附近波动,且随粗糙度的增大呈现先增大后减小的变化趋势,在粗糙度为0.10 mm附近达到峰值;阻力系数受坡度和粗糙度影响显著,可较好地由坡度、粗糙度和雷诺数的关系式表示;随着雷诺数的增大,滚波波速和波峰均呈幂函数形式递增,滚波周期大小无明显变化;坡度的增大会使层流失稳临界单宽流量减小,粗糙度的增大会使临界弗劳德数的均值减小。     

连续弯道水流模拟中二次流修正效果评价

为了选择适用于复杂连续弯道的二次流修正方法,选取了线性方法中两种典型的计算模式,通过在正交曲线坐标系二维浅水动量方程中增加扩散应力项开发了考虑二次流影响的平面二维水流模型。基于不同复杂度的4个连续弯道试验的水位和流速分布资料,通过理论分析和数值试验对比定量评估了传统二维模型和两种二次流修正方法在连续弯道水流模拟中的效果。测试结果表明,Delft3D模型的二次流修正方法自由度较高,适用于不同复杂度的连续弯道水流模拟,而Lien模型二次流修正方法适用于微弯或中弯,应用于中弯时需要慎重选用,不适用于急弯连续弯道模拟。两种方法比较,建议连续弯道水流模拟中优选Delft3D模型的二次流修正方法。     

用模式分类方法区分高、低含沙水流

在介绍模式分类方法的基础上,通过分析BP神经网络训练结果发现:高、低含沙水流挟沙力的变化规律有相似之处,说明挟沙规律不宜作为区别高、低含沙水流的标准,与前人的分析比较吻合;当多沙流体宾汉剪应力大于或小于某一数值组次的资料占总数的绝大多数时,这些组次训练结果与实测值符合较好,而另外组次训练结果与实测值有较大差别,这说明低含沙流体随着含沙量的增加流变方程由牛顿体向宾汉体模型转化时对应的宾汉剪应力有一个临界值。因此可将多沙流体的宾汉剪应力是否达到相应的临界值,作为区分高、低含沙水流的标准。对电木粉高含量的流体,该临界值约为3.2×10-1Pa。     

A segregated flow scheme to control numerical dispersion for multi-component flow simulations

One of the challenges for reservoir simulation is numerical dispersion. For waterflooding applications the effect is controlled due to the self-sharpening nature of a Buckley–Leverett shock. However, for multi-component flow simulations, incorrect wavespeeds can develop leading to the excessive smearing of fronts because of the coupling of compositional dispersion with the fractional flow. Rather than implementing a higher-order discretization method, we propose a simple scheme based on segregation-in-flow within a gridblock to control numerical dispersion. We extend the method originally proposed for polymer flooding to augmented waterflooding simulations in general as well as simulations of miscible or near miscible gas injection. For compositional simulations of gas injection, this is done through a coupled limited-flash/upstream-exclusion assumption. To test the scheme, an in-house streamline simulator has been modified and validated for modeling low-salinity floods as well as ternary two-phase displacements. Simulation results presented with and without segregation demonstrate the potential of the approach as a heuristic method to control numerical dispersion in multi-component flow simulations.     

双重介质模型在岩溶地下水流动系统模拟中的应用

文章采用不稳定层状裂隙水流模型,应用有限元-卷积结合法,模拟了岩溶地下水流动系统。相对于等效多孔介质模型,双重介质模型模拟的水位下降速度更小,达到稳定的时间更长。距抽水井较近的观测孔处,双重介质模型模拟的水位变化过程阶段性较明显,水位变化过程类似于承压含水层-弱透水层的释水过程,裂隙和孔隙基质分别相当于承压含水层和弱透水层。然后讨论了影响裂隙和孔隙基质间水流交换项的因素,分析了孔组抽水后的渗流场特征。     

水流分配策略随下坡坡度变化的多流向算法

提出了一种新的多流向算法方法(MFD-fg),其基本思想是水流分配策略应在空间上随着与下坡坡度相关的地形参数而变,从而地形对水流分配的影响可以得到合理、有效的建模。比较分析表明,MFD-fg采用以最大下坡坡度的线性函数对水流分配进行加权,是较好的水流分配策略。应用实验表明,与目前具代表性的单流向算法与多流向算法相比,MFD-fg方法的结果可获得更合理的汇流面积。     

泥石流的二维数学模型

泥石流是在重力作用下,由砂粒石块和水等组成的固液混合物,是一种发生于山区的复杂的地质灾害现象。泥石流主要是由暴雨诱发引起的,它沿着复杂的三维地形高速流动,具有流体流动的特性。为了模拟泥石流的运动规律,预测降雨诱发的泥石流的到达距离和泛滥范围,减少和避免泥石流引起的灾害,把泥石和雨水组成的固液混合物假定为遵循均匀、连续、不可压缩的、非定常的牛顿流体运动规律。基于质量守恒方程和Naiver-stokes方程,采用深度积分方法,推导出了一个模拟泥石流运动的二维数学模型。所有方程式可用有限差分法来求解。结合GIS,该模型可用于预测泥石流的流动距离和泛滥范围,以及泛滥范围内的危险房屋和路段,也可以用于泥石流灾害的风险性分析。     

Measurement of flow properties of expansive clays

The paper deals with the determination of the flow properties of expansive and unsaturated clays under different conditions of stress. By choosing the moisture content as the dependent variable, the well known non-linear diffusin equation is derived. Numerical solutions using a finite element program are presented, assuming a linear relationship between the moisture diffusivity and the concentration (the relative moisture content). These solutions are interpreted and a procedure is proposed to derive the flow properties of the clay from the sorption curves. Results of tests are presented and used to illustrate the procedure. It is found that the lower the stress applied, the smaller the initial moisture diffusivity and the stronger the dependence of the moisture diffusivity upon the concentration.     

Laboratory simulation of geogas microbubble flow

Preliminary laboratory tests provided first data on the behavior of gas microbubbles through porous media in the framework of the geogas theory. Under experimented conditions with laboratory equipment arranged for pressure controlled gas-tracer injection and sampling, gas microbubbles moved up to ten times faster than singlephase flow in dry media under the same injection pressure. Microbubbles were determined to be very sensitive to changes in injection pressure and their terminal velocity seems to be described with good approximation by the Stokes formula. The capability of microbubbles to pick up and transport upward for short distances solid ultra-small particles (metallic and radionuclide compounds) has been proved. Results are consistent with a time-dependent process linked to the transport properties of microbubbles (e.g., flotation), such as that reported by some authors.     

Initiation of motion in overland flow

This article reports the results of an experimental study concerning the initial movement of sediment in overland flow. Experiments were carried out in a small flume using water and quartz materials of various grain sizes. The comparison of our experimental results with classic criteria showed that the Shields-curve and the criterion of Yang can also be used for turbulent overland flow. Generally, higher shear stresses are necessary to provoke bed-instability under laminar flow conditions, especially at higher shear-velocity particle Reynolds numbers. A relative roughness effect also exists in laminar flow. Contrary to the observations by Savat on fixed beds, laminar flow does not show an ‘uncommon selectivity’, when loose, homogeneous beds are considered.     

Microbially induced calcite precipitation along a circular flow channel under a constant flow condition

Biogrouting is a new ground improvement method that has been studied in recent years. This method involves mainly the use of a microbially induced calcite precipitation process to bind soil particles to increase the strength or to fill in the pores of soil or joints of rock for seepage control. There are two major challenges in the use of biogrout for seepage control through rock joints. The first is how to inject the biogrout solutions, and the second is to understand the mechanisms for the formation of calcite under seepage flow. In this paper, a study on the injection of biogrout solution and the formation of precipitates along a circular 1D flow channel is presented. To minimize the influence of flow, a new one-phase injection method to inject bacterial solution and cementation agents simultaneously was adopted in this study. Factors affecting the formation and distribution of precipitates along the flow channel such as flow velocity, flow rate, and aperture of flow channel were investigated. The experimental results indicated that less calcite was precipitated at locations further away from the injection point due to depletion of the reactants’ concentrations along the flow path. Using the one-phase injection method, the bacterial activity had a major effect on the accumulation of the calcite on the inner surface of the flow channel. The total calcite precipitated on the surface of the flow channel increased slightly with increasing bacterial activity or flow rate. An equation to predict the distance travelled by the biosolution has been derived based on the testing results.