共查询到20条相似文献，搜索用时 34 毫秒
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本文利用优化的25点频率-空间域有限差分算法对基于BISQ模型双相各向同性介质中的地震波进行了数值模拟.通过与经典的Biot模型理论模拟结果进行对比,分析了Biot流动（宏观流体流动）和Squirt流动（微观流体流动）耦合作用对地震波在孔隙介质中传播特性的影响.数值模拟在地震频段进行,结果显示：在理想相界和黏滞相界情况下,Squirt流动机制都比Biot流动机制产生了更大的速度频散和能量衰减.其中,在Biot流动和Squirt流动耦合作用下的快P波的速度和振幅小于仅考虑Biot流动影响下快P波速度和振幅,而且慢P波的衰减也更加强烈.本文还研究了地震波在双层双相各向同性介质分界面处的反射和透射特征,双相介质中波的反射与透射现象类似于单相介质的情况.模拟结果表明,利用优化25点频率-空间域有限差分法模拟双相孔隙介质中的地震波场是可行的,这为开展双相孔隙介质全波形反演问题的研究提供了可能. 相似文献
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Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion Dm of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated. 相似文献
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Jacob Bear 《Advances in water resources》1977,1(1):15-23
A general methodology is presented for describing transport phenomena in porous media at a macroscopic level. Then, these macroscopic balance equations are integrated (or averaged) along the vertical for confined, leaky and phreatic aquifers.The results are employed to derive (averaged) aquifer equations for the flow of water and of a solute (hydrodynamic dispersion). It is shown that in all cases, the resulting equation is identical to that derived on the basis of an assumption of horizontal flow (the Dupuit assumption).Macrodispersion, occurring at the aquifer level, is discussed and appropriate coefficients are proposed. 相似文献
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Kevin O'Neill 《Advances in water resources》1981,4(4):150-164
Governing equations can be derived for transient, three-dimensional transport of heat and mass in compressible, liquid saturated fractured porous media. Recently developed mathematical techniques can be used which relate local space averages of derivatives of medium properties to the derivatives of those averages. Using these techniques, well established thermomechanical transport equations which apply at microscopic points may be transformed into equations in macroscopic variables; i.e. in variables which pertain to the scale of observation. In the absence of chemical reactions, transfer between source entities and the medium may be taken care of in a consistent, physically realistic way, such that macroscopic source terms arise naturally in the course of the macroscopization procedures. 相似文献
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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
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Chaotic advection at the pore scale: Mechanisms,upscaling and implications for macroscopic transport
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection—involving exponential stretching and folding of fluid elements—the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture. 相似文献
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ABSTRACT Forward–backward solute dispersion with an intermediate point source in one-dimensional semi-infinite homogeneous porous media is studied in this paper. Solute transport under sorption conditions, first-order decay and zero-order production terms are included. The first type of boundary condition is taken as a constant point source at an intermediate point from where forward and backward solute dispersion is examined. The Laplace transform method is adopted to solve the governing equation analytically. All the analytical results are obtained in graphical form to investigate the forward–backward solute transport in porous media for various hydrological input data. The graphical nature of the analytical solution is compared with numerical data taken from existing literature and similar results are obtained. Also, numerical solution of the governing equation is obtained by the Crank-Nicolson finite difference scheme and validated with the analytical solution, which demonstrates good agreement between them. Accuracy of the solution is also observed by using RMSE. 相似文献
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Fractal generation of surface area of porous media 总被引：2，自引：0，他引：2
Hongbing Sun Manfred Koch 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(2):83-96
Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
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Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
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Sergei A. Fomin Vladimir A. ChugunovToshiyuki Hashida 《Advances in water resources》2011,34(2):205-214
The paper provides an introduction to fundamental concepts of mathematical modeling of mass transport in fractured porous heterogeneous rocks. Keeping aside many important factors that can affect mass transport in subsurface, our main concern is the multi-scale character of the rock formation, which is constituted by porous domains dissected by the network of fractures. Taking into account the well-documented fact that porous rocks can be considered as a fractal medium and assuming that sizes of pores vary significantly (i.e. have different characteristic scales), the fractional-order differential equations that model the anomalous diffusive mass transport in such type of domains are derived and justified analytically. Analytical solutions of some particular problems of anomalous diffusion in the fractal media of various geometries are obtained. Extending this approach to more complex situation when diffusion is accompanied by advection, solute transport in a fractured porous medium is modeled by the advection-dispersion equation with fractional time derivative. In the case of confined fractured porous aquifer, accounting for anomalous non-Fickian diffusion in the surrounding rock mass, the adopted approach leads to introduction of an additional fractional time derivative in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties can be readily modeled and analyzed. 相似文献
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J. Zhu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(6):447-461
A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving
scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or
volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of
fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated
and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport
in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the
water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal
dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against
the plume scale. 相似文献
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Reconstruction of porous media using multiple-point statistics with data conditioning 总被引：1，自引：0，他引：1
Ting Zhang Yi Du Tao Huang Xue Li 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):727-738
The reconstruction of porous media is of great importance in predicting fluid transport properties, which are widely used in various fields such as catalysis, oil recovery, medicine and aging of building materials. The real three-dimensional structural data of porous media are helpful to describe the irregular topologic structures of porous media. By using multiple-point statistics (MPS) to extract the characteristics of real porous media acquired from micro computed tomography (micro-CT) scanning, the probabilities of structural characteristics of pore spaces are obtained first, and then reproduced in the reconstructed regions. One solution to overcome the anisotropy of training images is to use real 3D volume data as a training image (TI). The CPU cost and memory burden brought up by 3D simulations can be reduced greatly by selecting the optimal multiple-grid template size that is determined by the entropy of a TI. Moreover, both soft data and hard data are integrated in MPS simulation to improve the accuracy of reconstructed images. The variograms and permeabilities, computed by lattice Boltzmann method, of the reconstructed images and the target image obtained from real volume data are compared, showing that the structural characteristics of reconstructed porous media using our method are similar to those of real volume data. 相似文献
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Elastic properties of fluid saturated porous media with aligned fractures can be studied using the model of fractures as linear-slip interfaces in an isotropic porous background. Such a medium represents a particular case of a transversely isotropic (TI) porous medium, and as such can be analyzed with equations of anisotropic poroelasticity. This analysis allows the derivation of explicit analytical expressions for the low-frequency elastic constants and anisotropy parameters of the fractured porous medium saturated with a given fluid. The five elastic constants of the resultant TI medium are derived as a function of the properties of the dry (isotropic) background porous matrix, fracture properties (normal and shear excess compliances), and fluid bulk modulus. For the particular case of penny-shaped cracks, the expression for anisotropy parameter ε has the form similar to that of Thomsen [Geophys. Prospect. 43 (1995) 805]. However, contrary to the existing view, the compliance matrix of a fluid-saturated porous-fractured medium is not equivalent to the compliance matrix of any equivalent solid medium with a single set of parallel fractures. This unexpected result is caused by the wave-induced flow of fluids between pores and fractures. 相似文献