幂律流体在多孔介质中径向渗流的分形模型

基于分形理论及毛细管模型,本文研究了非牛顿幂律流体在各向同性多孔介质中径向流动问题,推导了幂律流体径向有效渗透率的分形解析表达式．研究结果表明,幂律流体径向有效无量纲渗透率模型和Chang and Yortsos’s模型吻合很好;同时还得出幂律流体径向有效渗透率随孔隙率、幂指数的增加而增加,随迂曲度分形维数的增加而减少．     

渗流气体滑脱现象与渗透率变化的关系

气体在致密多孔介质中低速渗流时存在着因气体分子碰撞岩壁而引起的滑脱现象，它由介质的孔隙结构和气体分子的平均自由程共同决定。该现象使气测渗透率大于孔隙介质的绝对渗透率。介质中气体的低速渗流为黏滞流与滑脱流组成，各自所占比例与气体分子按自由程的分布有关。理论计算得到了低速气体渗流的气测渗透率Kg与绝对渗透率K0比值的关系式，实验结果与理论分析吻合。     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

多孔介质非线性渗流问题的摄动解

考虑变形多孔介质渗透参数(渗透率和孔隙度)与孔隙压力呈负指数变化的特点，建立了多孔介质渗流问题的数学模型，采用积分变换方法求出了一维非线性渗流问题的摄动解，并对常数渗透参数和指数渗透参数的渗流问题进行对比分析，计算结果表明：两者之间的差别较大，且渗透参数的变化对于流体渗流中后期过程有着重要的影响，但对渗流早期影响不大，这对于定量研究工程中非线性渗流问题模型参数的相对重要性提供了可靠的理论依据。     

基于孔与裂隙网络模型的平行微裂隙对驱油的影响规律研究

认识双重多孔介质中油水两相微观渗流机制是回答形成什么类型的裂隙网络可提高油藏采收率的关键. 微裂隙的分布可以提高多孔介质的绝对渗透率,但对于基质孔隙中的流体介质,微裂隙的存在会引起多孔介质中局部流体压力和流场的变化,导致局部流动以微裂隙流动为主,甚至出现窜流现象,降低驱油效率. 本文基于孔与裂隙双重网络模型,在网络进口设定两条平行等长且具有一定间隔的微裂隙,分析微裂隙的相对间隔(微裂隙之间距离/喉道长度)和微裂隙相对长度(微裂隙长度/喉道长度)对于微观渗流特征的影响. 结果表明:随微裂隙相对长度的增加,出现驱油效率逐渐降低,相对渗透率曲线中的油水共渗区水饱和度和等渗点增加,油水两相的共渗范围减小等现象;随着微裂隙之间相对间隔增大,周围越来越多的基质孔穴间的压力差减小,在毛管压力的限制下,驱替相绕过这些区域,而导致水窜现象.      

基于孔与裂隙网络模型的平行微裂隙对驱油的影响规律研究

认识双重多孔介质中油水两相微观渗流机制是回答形成什么类型的裂隙网络可提高油藏采收率的关键.微裂隙的分布可以提高多孔介质的绝对渗透率,但对于基质孔隙中的流体介质,微裂隙的存在会引起多孔介质中局部流体压力和流场的变化,导致局部流动以微裂隙流动为主,甚至出现窜流现象,降低驱油效率.本文基于孔与裂隙双重网络模型,在网络进口设定两条平行等长且具有一定间隔的微裂隙,分析微裂隙的相对间隔(微裂隙之间距离/喉道长度)和微裂隙相对长度(微裂隙长度/喉道长度)对于微观渗流特征的影响.结果表明:随微裂隙相对长度的增加,出现驱油效率逐渐降低,相对渗透率曲线中的油水共渗区水饱和度和等渗点增加,油水两相的共渗范围减小等现象;随着微裂隙之间相对间隔增大,周围越来越多的基质孔穴间的压力差减小,在毛管压力的限制下,驱替相绕过这些区域,而导致水窜现象.     

基于渗透率连续变化的低渗透多孔介质非线性渗流模型

基于低渗透多孔介质渗透率的渐变理论,确定了能精确描述低渗透多孔介质渗流特征的非线性运动方程,并通过实验数据拟合．验证了非线性运动方程的有效性。非线性渗流速度关于压力梯度具有连续-阶导数,方便于工程计算;由此建立了低渗透多孔介质的单相非线性径向渗流数学模型,并巧妙采用高效的Douglas-Jones预估一校正有限差分方法求得了其数值解。数值结果分析表明：非线性渗流模型为介于拟线性渗流模型和达西渗流模型之间的一种中间模型或理想模型,非线性渗流模型和拟线性渗流模型均存在动边界;拟线性渗流高估了启动压力梯度的影响,使得动边界的移动速度比实际情况慢得多;非线性越强,地层压力下降的范围越小,地层压力梯度越陡峭,影响地层压力的敏感性减弱,而影响地层压力梯度的敏感性增强。     

定量开采条件下径向渗流的液固耦合问题

考虑到多孔介质渗透率随孔隙度变化的特点，建立了力学模型，研究定量抽放问题；对于广义平面应力状态下的非线性渗流耦合问题，提出了解的构造方法和解耦方法；求出了耦合条件下的孔隙压力，多孔介质总应力、总应变和总位移的解析解；进行了实例计算，并与Biot理论进行了对比，结果表明两种理论的差别很大。因此在渗透系数有较明显变化的场舍下不能采用Biot理论进行分析。     

关节软骨两相多孔介质非线性模型的有限元方法

基于混合物理论的两相多孔介质模型可以准确描述关节软骨的力学行为，关节软骨的渗透率与固体相体积应变相关。本文研究这一模型的非线性有限元法。具体采用伽辽金加权残值法得到有限元平衡方程，编制了有限元程序，进而对关节软骨围限压缩蠕变和应力松弛行为进行了数值模拟。与视渗透率为常数的线性模型的计算结果比较表明，在变形较大时，渗透率随固体相体积应变变化这一非线性效应不容忽视。     

变开度岩体裂隙多相渗流实验与有效渗透率模型

岩体裂隙的有效渗透率是描述岩体非饱和或多相渗流的关键参数,而裂隙开度是影响有效渗透率的重要因素.通过自主研发的粗糙裂隙多相渗流可视化实验平台,针对天然岩体裂隙复制而成的裂隙模型开展变开度条件下的多相渗流可视化实验,研究开度变化对多相渗流流动结构以及有效渗透率的影响.研究表明:非湿润相流体运动通道,在低流量比条件下呈现出气泡流流动结构,而在高流量比条件下呈现较为稳定的通道流流动结构.随着开度的增加,非湿润相流动通道的分支变少、等效宽度增加,两相流体的有效渗透率均增大,流动结构趋于稳定.可视化结果还阐明了柱塞流流动结构下,两相流体交替占据裂隙空间的竞争机制:当非湿润相流体通道由连续转变为不连续时,裂隙进出口压差显著增加;反之,当该通道由不连续转变为连续时,压差显著减小.最后,基于分形理论以及渗透率统计建模方法,建立了考虑开度效应的岩体裂隙多相渗流有效渗透率理论模型,并通过实验测定的有效渗透率数据验证了该模型的正确性与有效性.     

Study of the effect of capillary pressure on the permeability of porous media embedded with a fractal-like tree network

In this paper, the analytical expressions for permeability of (both saturated and unsaturated) porous media embedded with a fractal-like tree network are presented based on fractal theory and technique when the capillary pressure is taken into account. Both the dimensionless effective permeability and the relative permeability of the composites, which are defined as porous media embedded with a fractal-like tree network in this work, are derived and found to be a function of saturation, the capillary pressure and microstructural parameters of the networks. The relative permeabilities predicted by the present fractal model are compared with the available experimental data and a fair agreement between them is found.     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

Network model evaluation of permeability and spatial correlation in a real random sphere packing

In principle, network models can replicate exactly the microstructure of porous media. In practice, however, network models have been constructed using various assumptions concerning pore structure. This paper presents a network model of a real, disordered porous medium that invokes no assumptions regarding pore structure. The calculated permeability of the model agrees well with measured permeabilities, providing a new and more rigorous confirmation of the validity of the network approach. Several assumptions commonly used in constructing network models are found to be invalid for a random packing of equal spheres. In addition, the model permits quantification of the effect of pore-scale correlation (departure from randomness) upon permeability. The effect is comparable to reported discrepancies between measured permeabilities and predictions of other network models. The implications of this finding are twofold. First, a key assumption of several theories of transport in porous media, namely that pore dimensions are randomly distributed upon a network, may be invalid for real porous systems. Second, efforts both to model and to measure pore-scale correlations could yield more accurate predictions of permeability.     

A Fractal Model for Oil Transport in Tight Porous Media

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.     

A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media

The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.     

Effective permeability of cracked unsaturated porous materials

This study focuses on a theoretical estimation of the effective permeability of unsaturated cracked porous media. The closed-form flow solution around and in a superconductive crack, embedded in an infinite porous matrix under a far-field condition, is recalled first. Then the solution of flow around a completely unsaturated (empty) crack that is considered as an obstruction against the flow is determined. The flow solution for partially saturated crack in special configurations is obtained by superposition of the two basic solutions for superconductive and empty cracks. The contribution of an unsaturated crack, with a given saturation degree, to the effective permeability is estimated by using dilute upscaling scheme. Numerical results obtained by Finite Elements Method, are in good agreement with the theoretical results for weak crack densities but show the additional effect of cracks interaction for higher densities.     

Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcys equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.     

On the Permeability of Fractal Tube Bundles

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability?Cporosity relationships represented by the Kozeny?CCarman equations and Archie??s law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability?Cporosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability?Cporosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature.