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1.
Todd H. Skaggs 《Advances in water resources》2011,34(10):1335-1342
Critical path analysis (CPA) is a method for estimating macroscopic transport coefficients of heterogeneous materials that are highly disordered at the micro-scale. Developed originally to model conduction in semiconductors, numerous researchers have noted that CPA might also have relevance to flow and transport processes in porous media. However, the results of several numerical investigations of critical path analysis on pore network models raise questions about the applicability of CPA to porous media. Among other things, these studies found that (i) in well-connected 3D networks, CPA predictions were inaccurate and became worse when heterogeneity was increased; and (ii) CPA could not fully explain the transport properties of 2D networks. To better understand the applicability of CPA to porous media, we made numerical computations of permeability and electrical conductivity on 2D and 3D networks with differing pore-size distributions and geometries. A new CPA model for the relationship between the permeability and electrical conductivity was found to be in good agreement with numerical data, and to be a significant improvement over a classical CPA model. In sufficiently disordered 3D networks, the new CPA prediction was within ±20% of the true value, and was nearly optimal in terms of minimizing the squared prediction errors across differing network configurations. The agreement of CPA predictions with 2D network computations was similarly good, although 2D networks are in general not well-suited for evaluating CPA. Numerical transport coefficients derived for regular 3D networks of slit-shaped pores were found to be in better agreement with experimental data from rock samples than were coefficients derived for networks of cylindrical pores. 相似文献
2.
The effect of temperature on the seepage transport of suspended particles in a porous medium 
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下载免费PDF全文 The main purpose of this study is to experimentally investigate the effect of temperature on the seepage transport of suspended particles (SP) with a median diameter of 10–47 μm in a porous medium for various seepage velocities. The results show that the rise of temperature accelerates the irregular movements of SPs in the porous medium and reduces their migration velocity. As a result, the pore volume corresponding to the peak value of the breakthrough curves is apparently delayed, and the peak value in the effluent is decreased. The migration velocity of SPs decreases with increasing particle size, regardless of the Darcy velocity and temperature. The longitudinal dispersivity of SPs decreases slightly with increasing temperature and then remains almost unchanged. Larger particles experience more irregular movements induced by the limit of pore size, which leads to a larger dispersivity. The deposition coefficient increases with increasing temperature, especially in the case of a high seepage velocity, and then tends to be stable. The deposition coefficient for large‐sized particles is higher than that for small‐sized particles, which can be attributed to the restriction of large‐sized particles by the narrow pores in the porous medium. The recovery rate decreases slightly with the increase of temperature until a critical value is reached, beyond which it remains almost unchanged. In summary, temperature is a significant factor affecting the transport and deposition of SPs in the porous medium, and the transport parameters such as particle velocity, dispersivity, and deposition coefficient. 相似文献
3.
孔隙纵横比是描述多孔岩石微观孔隙结构特征的重要参数,目前用于获取岩石完整孔隙纵横比分布的经典模型为David-Zimmerman(D-Z)孔隙结构模型,该模型假设岩石由固体矿物基质、一组纵横比相等的硬孔隙以及多组纵横比不等的微裂隙构成,并认为固体矿物基质和硬孔隙均不受压力影响,在此基础上,利用超声纵横波速度的压力依赖性反演岩石硬孔隙和各组微裂隙的孔隙纵横比及孔隙度.该方法的关键点在于以累积裂隙密度为桥梁,借助等效介质理论建立了岩石弹性模量和孔隙纵横比之间的内在联系.但在D-Z模型中,多重孔隙岩石累积裂隙密度的计算直接由单重孔隙裂隙密度公式实现,这种近似导致该模型在许多情况下难以获得良好的反演精度.为了完善经典D-Z模型,本文提出了一种基于虚拟降压的孔隙纵横比分布反演策略,通过多个假想降压过程实现累积裂隙密度的准确计算,并将基于DEM和MT的经典D-Z模型推广到KT和SCA中,结合四种等效介质理论建立了一套完整的反演流程.采用一系列砂岩和碳酸盐岩样品,测试了反演流程在实际岩芯孔隙纵横比提取中的应用效果,研究结果表明:与D-Z模型相比,本文方法的模拟结果与实际数据吻合更好,并同时适用于砂岩和碳酸盐岩;此外,通过分析四种等效介质理论的模拟结果发现,本文方法并不十分依赖于等效介质理论的选择,这些理论获得的孔隙结构参数随压力的变化趋势基本一致,数值上仅存在略微差异,且这种差异随着压力的增大逐渐消失.本文方法是经典D-Z孔隙结构模型的重要补充,对岩石孔隙结构表征、流体饱和岩石速度预测以及孔间喷射流效应的模拟具有十分重要的意义. 相似文献
4.
Saeid Jamshidi Ramin Bozorgmehry Boozarjomehry Mahmoud Reza Pishvaie 《Advances in water resources》2009
In pore network modeling, the void space of a rock sample is represented at the microscopic scale by a network of pores connected by throats. Construction of a reasonable representation of the geometry and topology of the pore space will lead to a reliable prediction of the properties of porous media. Recently, the theory of multi-cellular growth (or L-systems) has been used as a flexible tool for generation of pore network models which do not require any special information such as 2D SEM or 3D pore space images. In general, the networks generated by this method are irregular pore network models which are inherently closer to the complicated nature of the porous media rather than regular lattice networks. In this approach, the construction process is controlled only by the production rules that govern the development process of the network. In this study, genetic algorithm has been used to obtain the optimum values of the uncertain parameters of these production rules to build an appropriate irregular lattice network capable of the prediction of both static and hydraulic information of the target porous medium. 相似文献
5.
We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology. 相似文献
6.
R.C. Acharya M.I.J. van Dijke K.S. Sorbie S.E.A.T.M. Van der Zee A. Leijnse 《Advances in water resources》2007
We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented. Within the bonds, two different velocity profiles are used. At the network scale the longitudinal dispersion of the particles is quantified through the coefficient DL, for which we evaluate a number of methods already known in the literature. Additionally, we introduce a new method for derivation of DL based on the first-arrival times distribution (FTD). To validate our particle tracking method, we simulate Taylor’s classical experiments in a single tube. Subsequently, we carry out network simulations for a wide range of the characteristic Péclet number Pe? to assess the various methods for obtaining DL. Using the new method, additional simulations have been carried out to evaluate the choice of nodal jump conditions and velocity profile, in combination with varying network heterogeneity. In general, we conclude that the presented network model with particle tracking is a robust tool to obtain the macroscopic longitudinal dispersion coefficient. The new method to determine DL from the FTD statistics works for the full range of Pe?, provided that for large Pe? a sufficiently large number of particles is used. Nodal jump conditions should include molecular diffusion and allow jumps in the upstream direction, and a parabolic velocity profile in the tubes must be implemented. Then, good agreement with experimental evidence is found for the full range of Pe?, including increased DL for increased porous medium heterogeneity. 相似文献
7.
Sizeable amounts of connected microporosity with various origins can have a profound effect on important petrophysical properties of a porous medium such as (absolute/relative) permeability and capillary pressure relationships. We construct pore-throat networks that incorporate both intergranular porosity and microporosity. The latter originates from two separate mechanisms: partial dissolution of grains and pore fillings (e.g. clay). We then use the reconstructed network models to estimate the medium flow properties. In this work, we develop unique network construction algorithms and simulate capillary pressure–saturation and relative permeability–saturation curves for cases with inhomogeneous distributions of pores and micropores. Furthermore, we provide a modeling framework for variable amounts of cement and connectivity of the intergranular porosity and quantifying the conditions under which microporosity dominates transport properties. In the extreme case of a disconnected inter-granular network due to cementation a range of saturations within which neither fluid phase is capable of flowing emerges. To our knowledge, this is the first flexible pore scale model, from first principles, to successfully approach this behavior observed in tight reservoirs. 相似文献
8.
This paper presents application of a series of algorithms used to extract pore network structure from high-resolution three-dimensional synchrotron microtomography images of unconsolidated porous media systems. These algorithms are based on the three-dimensional skeletonization that simplifies the pore space to networks in the form of nodes connected to paths. Dilation algorithms were developed to generate inscribed spheres on the nodes and paths of the medial axis to represent pore-bodies and pore-throats of the network, respectively. The end result is a physically representative pore network structure, i.e. three-dimensional spatial distribution (i.e. x-, y-, and z-coordinates) of pore-bodies and pore-throats, pore-body size distribution, pore-throat size distribution, and the connectivity. Systems analyzed in this study include different glass bead systems and natural marine sand. The media ranged in size from 0.123 to 1.0 mm, while the image volumes ranged between 7.7 and 108.9 mm3. In addition to extracting the pore network structure, the porosity, specific surface area, and representative elementary volume analysis on the porosity were calculated. Spatial correlation between pore-body sizes in the network was investigated using semivariograms and integral scale concepts. The impact of resolution on the calculated property was also investigated.
In this work, we show that microtomography is an effective tool to non-destructively extract the structure of many systems. The quality of the datasets depends on photon energy, photon flux, size of the sample, type of the sample, and size of the sample ‘features’. Results show that the developed method of extracting pore network structure is applicable to ideal and natural porous media systems. The impact of resolution on the quantification of the network structure properties varies in its significance based on feature size of the system and the properties being calculated. Therefore, a thorough resolution sensitivity analysis should be carried out to determine the degree of error associated with a system imaged at a given resolution. 相似文献
9.
This paper reports experimental measurements performed to test the ability of electrical resistivity tomography (ERT) imaging to provide quantitative information about transport parameters in porous media such as the dispersivity α, the mixing front velocity u, and the retardation factor R(f) associated with the sorption or trapping of the tracers in the pore structure. The flow experiments are performed in a homogeneous porous column placed between two vertical set of electrodes. Ionic and dyed tracers are injected from the bottom of the porous media over its full width. Under such condition, the mixing front is homogeneous in the transverse direction and shows an S-shape variation in the flow direction. The transport parameters are inferred from the variation of the concentration curves and are compared with data obtained from video analysis of the dyed tracer front. The variations of the transport parameters obtained from an inversion performed by the Gauss-Newton method applied on smoothness-constrained least-squares are studied in detail. While u and R(f) show a relatively small dependence on the inversion procedure, α is strongly dependent on the choice of the inversion parameters. Comparison with the video observations allows for the optimization of the parameters; these parameters are found to be robust with respect to changes in the flow condition and conductivity contrast. 相似文献
10.
It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
11.
A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images 总被引：1，自引：0，他引：1
Alireza HajizadehAliakbar Safekordi Farhad A. Farhadpour 《Advances in water resources》2011,34(10):1256-1267
Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image. 相似文献
12.
A.R. Mazaheri B. Zerai G. Ahmadi J.R. Kadambi B.Z. Saylor M. Oliver G.S. Bromhal D.H. Smith 《Advances in water resources》2005,28(12):1267-1279
For single-phase flow through a network model of a porous medium, we report (1) solutions of the Navier–Stokes equation for the flow, (2) micro-particle imaging velocimetry (PIV) measurements of local flow velocity vectors in the “pores throats” and “pore bodies,” and (3) comparisons of the computed and measured velocity vectors. A “two-dimensional” network of cylindrical pores and parallelepiped connecting throats was constructed and used for the measurements. All pore bodies had the same dimensions, but three-different (square cross-section) pore-throat sizes were randomly distributed throughout the network. An unstructured computational grid for flow through an identical network was developed and used to compute the local pressure gradients and flow vectors for several different (macroscopic) flow rates. Numerical solution results were compared with the experimental data, and good agreement was found. Cross-over from Darcy flow to inertial flow was observed in the computational results, and the permeability and inertia coefficients of the network were estimated. The development of inertial flow was seen as a “two-step” process: (1) recirculation zones appeared in more and more pore bodies as the flow rate was increased, and (2) the strengths of individual recirculation zones increased with flow rate. Because each pore-throat and pore-body dimension is known, in this approach an experimental (and/or computed) local Reynolds number is known for every location in the porous medium at which the velocity has been measured (and/or computed). 相似文献
13.
Michael C. Brooks William R. Wise Michael D. Annable 《Ground Water Monitoring & Remediation》1999,19(2):105-113
Two types of gas-phase flow patterns have been discussed and observed in the in situ air sparging (ISAS) literature: bubble flow and air channels. A critical factor affecting the flow pattern at a given location is the grain size of the porous medium. Visualization experiments reported in the literature indicate that a change in the flow pattern occurs around 1 to 2 mm grain diameters, with air channels occurring below the transition size and bubbles above. Analysis of capillary and buoyancy forces suggests that for a given gas-liquid-solid system, there is a critical size that dictates the dominant force, and the dominant force will in turn dictate the flow pattern. The dominant forces, and consequently the two-phase flow patterns, were characterized using a Bond number modified with the porous media aspect ratio (pore throat to pore body ratio). Laboratory experiments were conducted to observe flow patterns as a function of porous media size and air flow rate. The experimental results and the modified Bond number analysis support the relationship of flow patterns to grain size reported in the literature. 相似文献
14.
15.
Interphase mass transfer in porous media is commonly modeled using Sherwood number expressions that are developed in terms of fluid and porous medium properties averaged over some representative elementary volume (REV). In this work the influence of sub-grid scale properties on interphase mass transfer was investigated using a two-dimensional pore network model. The focus was on assessing the impact of (i) NAPL saturation, (ii) interfacial area (iii) NAPL spatial distribution at the pore scale, (iv) grain size heterogeneity, (v) REV or domain size and (vi) pore scale heterogeneity of the porous media on interphase mass transfer. Variability of both the mass transfer coefficient that explicitly accounts for the interfacial area and the mass transfer coefficient that lumps the interfacial area was examined. It was shown that pore scale NAPL distribution and its orientation relative to the flow direction have significant impact on flow bypassing and the interphase mass transfer coefficient. This results in a complex non-linear relationship between interfacial area and the REV-based interphase mass transfer rate. Hence, explicitly accounting for the interfacial area does not eliminate the uncertainty of the mass transfer coefficient. It was also shown that, even for explicitly defined flow patterns, changing the domain size over which the mass transfer process is defined influences the extent of NAPL bypassing and dilution and, consequently, the interphase mass transfer. It was also demonstrated that the spatial variability of pore scale parameters such as pore throat diameters may result in different rates of interphase mass transfer even for the same pore size distribution index. 相似文献
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含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微观裂缝流量表达式,通过网络模型和流量守恒条件,得到含有三维裂缝/软孔隙网络的多孔介质渗透率计算方法.数值算例表明,预测结果与实验数据分布范围吻合很好,能够给出不同类型岩心对应孔隙纵横比的分布图.三维裂缝/软孔隙网络模型建立了宏观可观测量与裂缝参数之间关系,能够定量分析岩石渗透率随裂缝体密度、纵横比、孔隙流体类型和围压等因素的变化规律,为复杂条件下储层渗透率预测提供了一种有效方法. 相似文献
18.
《Advances in water resources》2002,25(5):565-576
In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils. 相似文献
19.
介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性. 相似文献
20.
As is frequently cited, dispersivity increases with solute travel distance in the subsurface. This behaviour has been attributed to the inherent spatial variation of the pore water velocity in geological porous media. Analytically solving the advection–dispersion equation with distance-dependent dispersivity is extremely difficult because the governing equation coefficients are dependent upon the distance variable. This study presents an analytical technique to solve a two-dimensional (2D) advection–dispersion equation with linear distance-dependent longitudinal and transverse dispersivities for describing solute transport in a uniform flow field. The analytical approach is developed by applying the extended power series method coupled with the Laplace and finite Fourier cosine transforms. The developed solution is then compared to the corresponding numerical solution to assess its accuracy and robustness. The results demonstrate that the breakthrough curves at different spatial locations obtained from the power series solution show good agreement with those obtained from the numerical solution. However, owing to the limited numerical operation for large values of the power series functions, the developed analytical solution can only be numerically evaluated when the values of longitudinal dispersivity/distance ratio eL exceed 0·075. Moreover, breakthrough curves obtained from the distance-dependent solution are compared with those from the constant dispersivity solution to investigate the relationship between the transport parameters. Our numerical experiments demonstrate that a previously derived relationship is invalid for large eL values. The analytical power series solution derived in this study is efficient and can be a useful tool for future studies in the field of 2D and distance-dependent dispersive transport. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献