An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks

In this paper, an analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks is presented. A dual-domain model is applied to simulate the heterogeneous porous media embedded with a constructal tree network based on the fractal distribution of pore space and tortuosity nature of flow paths. The analytical expressions for seepage velocity, pressure drop, local and global permeability of the network and binary system are derived, and the transport properties for the optimal branching structure are discussed. Notable is that the global permeability (K_n) of the network and the volume fraction (f_n) occupied by the network exhibit linear scaling law with the fractal dimension (D_p) of channel diameter bylogK_n∼0.46D_p and logf_n∼1.03D_p, respectively. Our analytical results are in good agreement with the available numerical results for steady-state soil vapor extraction and indicate that the fractal dimension for pore space has significant effect on the permeable properties of the media. The proposed dual-domain model may capture the characteristics of heterogeneous porous media and help understanding the transport mechanisms of the radial flow in the media.     

多孔介质热导率的数值计算

通过数值模拟得出面积分形维数和孔隙率相同,而孔隙结构不同的分形多孔介质的导热特性是不相同的.说明仅仅依靠孔隙率和分形维数两个参数无法有效确定多孔介质的热物理性质,寻找新的表征孔隙结构的参数是必要的.同时也说明了前人所得出的关于多孔介质的热物性的解析表达式具有一定的局限性和不确定性.     

随机多孔介质的蒙特卡罗重构与渗流特性模拟

根据多孔介质微观结构的分形尺度标度特征,采用蒙特卡罗方法分别重构随机多孔介质的微观颗粒和孔隙结构,并基于分形毛管束模型研究多尺度多孔介质的气体渗流特性,建立多孔介质微观结构和宏观渗流特性的定量关系。结果表明：分形蒙特卡罗重构的多孔介质微细结构接近真实介质结构,气体渗流特性的计算结果与格子玻尔兹曼模拟数据较为吻合; 多孔介质气体渗透率随着克努森数的增加而增大,孔隙分形维数对于气体渗流的微尺度效应具有显著影响,而迂曲度分形维数对于表观渗透率和固有渗透率的比值影响可以忽略。提出的分形蒙特卡罗方法具有收敛速度快且计算误差与维数无关的优点,有利于深入理解多尺度多孔介质的渗流机理。     

基于分形理论的多孔介质导热系数研究

本文根据分形理论,对多孔介质几何结构进行了描述,计算出了不同孔隙率多孔介质简化模型的剖面面积分布分形维数d,并利用分形维数结合土壤导热模型推出了土壤的有效导热系数表达式,计算结果表明,该方法是符合客观实际的．     

超声波作用下污泥水分扩散过程的数值模拟

建立了超声波作用下污泥内部水分扩散模型,利用分形理论对超声波(20 kHz)作用下污泥内部孔隙结构进行描述,探讨了超声波声能密度对污泥孔隙表面分形维数df及孔隙通道曲折度分形维数dw的影响,在此基础上建立了超声波作用下多孔介质中液体有效扩散系数的分形模型,对不同声能密度超声波辐照下污泥水分扩散过程进行了数值模拟.研究发...     

Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids

The 3D profile surface parameter H _q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H _q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H _q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.     

Transport properties of saturated and unsaturated porous fractal materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with phi is found to follow a power law of the form alpha approximately phi (-E) for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity alpha with filling fraction phi is presented and is given by alpha approximately phi(D_{w}-2/D_{f}-d_{E}), where D_{f} is the fractal dimension, D_{w} is the random walk dimension, and d_{E} is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.     

Longitudinal dispersion of solutes in porous media solely by advection

The purpose of this work is to predict the transport of non-sorbing solutes through water flow in the subsurface. We derive what we consider to be the first reliable calculations of the entire distribution of arrival times, W(t), for non-sorbing solutes in advective flow in strongly disordered porous media. Solutes treated can be contaminant plumes from any source or radioactive tracers, both experimentally and naturally generated. Our approach is microscopic and based on effects of disorder. It generates longitudinal dispersion (in the direction of flow) in the absence of diffusion. Effects on dispersion from a single capillary tube velocity distribution, known to produce long-tailed arrival time distributions, are also neglected. On the other hand, our calculations are based on effects generated from real porous media, such as wide pore-size distributions and complex connectivity. In particular, the calculation of the distribution of arrival times is based on a distribution of conserved fluxes and the known tortuosity of the associated geometrical paths. The results are found to be predictive when compared with simulations of two-dimensional flow on percolation structures, and appear to have relevance for experiments as well.     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media

We consider the application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media. It is found that answers to interesting physics questions can be expressed in terms of several new fractal dimensions (in addition to the fractal dimensiond _f ): (1)d _f ^BB , the fractal dimension of the backbone, arises in connection with electric current flow, (2)d _red, the fractal dimension of the singly connected bonds in the backbone, arises in connection with its equivalence to the thermal scaling power, (3)d _E, the fractal dimension of the of the elastic backbone, (4)d _u, the fractal dimension of the unscreened perimeter, arises in connection with the viscosity singularity at the gelation threshold, (5)d _min the fractal dimension of the minimum path (or chemical distance) between two sites, arises in co-nnection with the Aharony-Stauffer conjecture, (6)dw, the fractal dimension of a random walk, (7)d _G, the fractal dimension of growth sites that arise as a random walk creates a cluster. Relations among these fractal dimensions are discussed, some of which can be proved and others of which are conjectures whose validity has been established only in certain limiting cases.Supported in part at the Center for Polymer Studies by grants from ONR and NSF.     

基于分形多孔介质三维网络模型的非混溶两相流驱替数值模拟

提出了一个描述多孔介质孔隙尺寸分布的三维分形网络模型,利用该模型对多孔介质中的非混溶两相流驱替进行了数值模拟,研究了孔隙尺寸分布分维D_f和两相流黏滞比M对驱替前沿指进型的影响,结果表明指进型容量维数D_h随着孔隙尺寸分布分维D_f以及黏滞比M的增大而减少,并通过曲线拟合得到了它们之间的定量关系. 关键词： 多孔介质 三维网络 黏滞指进 非混溶两相流     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

A new empirical model for the acoustic properties of loose granular media

This paper examines physical parameters of loose granular mixes and their empirical relations to the acoustic performance of these mixes. In this work a new classification of granular media has been proposed which is related to the characteristic particle dimension and the specific density of the grain base. It has been shown that this classification is a useful characteristic for rapid evaluation of the acoustic performance of loose granular mixes. The characteristic impedance and propagation constant have been measured for a representative selection of grain mixes and used to develop a new empirical model. This model relates the above acoustic characteristics to the characteristic particle dimension, porosity, tortuosity and specific density of the grain base, which are routinely measurable parameters. A very good agreement with the experimental data is illustrated in the frequency range of 250-4000 Hz for materials with the grain base of 0.4-3.5 mm and specific densities between 200 and 1200 kg/m³. Unlike many theoretical models for the prediction of the acoustic properties of porous media, the proposed expressions do not involve any special functions of complex argument, empirical shape factors or sophisticated characteristics of porous structure. These are practical enough to be of interest to acoustic and noise control engineers and material manufacturers.     

An universal relation between fractal and Euclidean (topological) dimensions of random systems

It is shown that a dimension-invariant form for fractal dimension D of random systems (where d is Euclidean dimension of the embedding space) is in good agreement with results of numerical simulations performed by different authors for critical (p=p _c ) and subcritical (p<p _c ) percolation, for lattice animals, and for different aggregation processes. Received: 9 July 1998 / Revised and Accepted: 12 July 1998     

裂缝-孔隙型双重介质油藏渗吸机理的分形分析

低渗透油藏常常伴随裂缝发育,形成裂缝-基质双重介质.自发渗吸是低渗裂缝性水驱油藏的重要采油机理,有顺向和逆向两种渗吸方式.基于基质孔隙结构的分形特征,引入分形几何对裂缝性双重介质渗吸机理的判据进行了改进,建立了渗吸机理的分形判据模型,并进一步推导了结构常数的解析表达式.结果表明,渗吸机理的判别参数是基质孔隙度、高度、孔隙分形维数、流动迂曲度、最大孔隙直径、界面张力、油水密度差以及接触角的函数.改进后的判据模型与现有结果一致.最后绘制了判别渗吸机理的图版,为利用表面活性剂提高低渗透油藏采收率提供理论依据.     

Simulation of the relationship between porosity and tortuosity in porous media with cubic particles

Tortuosity is an important parameter used in areas such as vascular medicine,neurobiology,and the field of soil permeability and diffusion to express the mass transport in porous media.It is a function of the porosity and the shape and distribution of particles.In this paper,the tortuosity of cubic particles is calculated.With the assumption that the porous medium is homogeneous,the problem is converted to the micro-level over a unit cell,and geometry models of flow paths are proposed.In three-dimensional(3D) cells,the flow paths are too complicated to define.Hence,the 3D models are converted to two-dimensional(2D) models to simplify the calculation process.It is noticed that the path in the 2D model is shorter than that in the 3D model.As a result,triangular particles and the interaction are also taken into consideration to account for the longer distance respectively.We have proposed quadrate particle and interaction(QI) and quadrate and triangular particle(QT) models with cubic particles.Both models have shown good agreement with the experimental data.It is also found that they can predict the toruosities of some kinds of porous media,like freshwater sediment and Negev chalk.     

FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET

Viscous fingering (VF) in random Sierpinski carpet is investigated by means of successive over-relaxation technique and under the assumption that bond radii are of Rayleigh distribution. In the random Sierpinski network, the VF pattern of porous media in the limit M→∞ (M is the viscosity ratio and equals to η₂/η₁ where η₁ and η₂ are the viscosities of the injected and displaced fluids, respectively) is found to be similar to the diffusion-limited aggregation (DLA) pattern. The interior of the cluster of the displacing fluid is compact on long length scales when M=1, and the pores in the interior of the cluster have been completely swept by the displacing fluid. For finite values of M such as M≥10, the pores in the interior of the cluster have been only partly swept by the displacing fluid on short length scales. But for values of M in 1f(α) sites have velocites scaling as L^-α; and the scaling function f(α) is measured and its variation with M is found.     

A Particle Resistance Model for Flow through Porous Media

A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere. The proposed model is expressed as a function of porosity, fluid property, particle size, fluid velocity （or Reynolds number） and fractal characters D f of particles in porous media. The model predictions are in good agreement with the experimental data. The validity of the proposed model is thus verified.     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

A difference-fractal model for the permeability of fibrous porous media

In this Letter, a difference-fractal model for the permeability of viscous flow through fibrous porous media is proposed. Since fractal objects have well-defined geometric properties, and are discrete and discontinuous, we apply the difference approach to developing the fractal model. The model of non-dimensional permeability is expressed as a function of porosity and fractal dimension. To verify the validity of the proposed model, the predicted permeability values are compared with those of experimental measurements. A good agreement between the prediction of the fractal model and the existing experimental data from the literature is found.