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101.
G.?ChristakosEmail author 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(5):276-290
We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126). 相似文献
102.
103.
104.
We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with
large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to
a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface
between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many
small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles,
slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method
for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry,
as long as it aligns with the grid. We prove optimal global first-order L
2 convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify
these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower
dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface
in transition to the Stokes elements. 相似文献
105.
106.
Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media 总被引:1,自引:0,他引:1
A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradpc in combination with a chord-slope technique must be utilized. 相似文献
107.
General absorbing boundary conditions based on Biot's two-phase mixture theory and paraxial approximation is presented for the dynamic analysis of fluid-saturated porous media with isotropic, transverse isotropic, and anisotropic properties. For the last two cases, the equivalent Lame's constants, under conditions of uniqueness, are introduced to facilitate the analytical solutions. The numerical results show that the proposed absorbing boundary can greatly suppress spuriously reflected waves and efficiently model the far field of the system with sufficient accuracy. 相似文献
108.
This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool. 相似文献
109.
Elastic wave velocities and the ratiov
P/v
S were studied for dry and initially saturated samples of carbonate and crystalline rocks at pressures to 2 kbar. In initially saturated samplesv
P increases in crystalline rock, whereas in sedimentary rock it may either increase or decrease with increasing pressure. Under the same conditionsv
S remains approximately constant in crystalline rocks and decreases in sedimentary samples. The ratiov
P/v
S as a function of pressure increases in dry rocks and decreases in saturated ones. Saturated samples always have higherv
P/v
S ratios than dry ones. It appears that the geometry of the pore space influences the acoustic properties of saturated crystalline rocks. 相似文献
110.
应用混合变量弹性动力学方程和线性常微分方程组的矩阵指数解法,将层状介质中广泛应用的弹性波传播矩阵解法推广至横向非均匀介质,给出了一种可计算复杂地质体中弹性波传播的广义传播矩阵数值解法。该方法可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。 相似文献