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  • 1
    Electronic Resource
    Electronic Resource
    Concentration fluctuations and dilution in two-dimensionally periodic heterogeneous porous media (1996)
    Springer
    Transport in porous media 22 (1996), S. 91-119 
    Details
    ISSN: 1573-1634
    Keywords: concentration fluctuations ; peak concentration ; dilution ; heterogeneity ; local dispersion ; microscale ; fluctuation dissipation ; coefficient of variation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Dilution of solute in two-dimensionally periodic heterogeneous porous media is assessed by numerically simulating advection-dispersion. The concentration fluctuations, created by advective heterogeneity, are destroyed by local dispersion, over a characteristic variance residence time (VRT). For an impulse introduction of solute, initially, plumes become increasingly irregular with time—the coefficient of variation (CV) of concentration grows with time. A priori, the spatial second moment and mean concentrations are insufficient measures of dilution, because concentration fluctuations can be large. At large times (t 〉 VRT) the relative concentration fluctuations weaken—the concentration CV was observed to slowly decrease with time. At the center of mass the general trend of the decreasing CV follows VRT/t (predicted by Kapoor and Gelhar). The VRT is found to be an increasing function of the log hydraulic conductivity microscale. In employing effective dispersion coefficents to model the mean concentration, it needs to be recognized that excursions of concentrations around the mean are singularly determined by local dispersion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00974313
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  • 2
    Electronic Resource
    Electronic Resource
    On the modeling of miscible flow in multi-component porous media (1995)
    Springer
    Transport in porous media 21 (1995), S. 19-46 
    Details
    ISSN: 1573-1634
    Keywords: Miscible flow ; micropore convection ; micropore diffusion ; heterogeneity ; breakthrough curve
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An analytical model of miscible flow in multi-component porous media is presented to demonstrate the influence of pore capacitance in extending diffusive tailing. Solute attenuation is represented naturally by accommodating diffusive and convective flux components in macropores amd micropores as elicited by the local solute concentration and velocity fields. A set of twin, coupled differential equations result from the Laplace transform and are solved simultaneously using a differential operator for one-dimensional flow geometry. The solutions in real space are achieved using numeric inversion. In addition, to represent more faithfully the dominant physical processes, this approach enables efficient and stable semi-analytical solution procedure of the coupled system that is significantly more complex than current capacitance type models. Parametric studies are completed to illustrate the ability of the model to represent sharp breakthrough and lengthy tailing, as well as investigating the form of the nested heterogeneity as a result of solute exchange between macropores and micropores. Data from a laboratory column experiment is examined using the present model and satisfactory agreement results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00615333
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  • 3
    Electronic Resource
    Electronic Resource
    Flow behaviour in the presence of wettability heterogeneities (1996)
    Springer
    Transport in porous media 25 (1996), S. 217-233 
    Details
    ISSN: 1573-1634
    Keywords: heterogeneity ; wettability ; displacement ; flow in porous media ; capillary pressure ; drainage ; imbibition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The physical processes occurring during fluid flow and displacement within porous media having wettability heterogeneities have been investigated in specially designed heterogeneous visual models. The models were packed with glass beads, areas of which were treated with a water repellent to create wettability variations. Immiscible displacement experiments show visually the effect of wettability heterogeneities on the formation of residual oil and recovery due to capillary trapping. This work demonstrates by experiment the importance of incorporating reservoir heterogeneity into pore displacement analysis, essential for the correct interpretation of core data and for directing the route for scale-up of the processes to reservoir scale.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00135857
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  • 4
    Electronic Resource
    Electronic Resource
    Non-Newtonian Flow in a Variable Aperture Fracture (1998)
    Springer
    Transport in porous media 30 (1998), S. 75-86 
    Details
    ISSN: 1573-1634
    Keywords: fracture ; aperture ; heterogeneity ; non-Newtonian ; power-law fluid ; groundwater ; transmissivity ; nonlinear seepage
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n=1 all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006512822518
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  • 5
    Electronic Resource
    Electronic Resource
    Comparison of fast algorithms for estimating large-scale permeabilities of heterogeneous media (1995)
    Springer
    Transport in porous media 19 (1995), S. 123-137 
    Details
    ISSN: 1573-1634
    Keywords: Effective permeability ; heterogeneity ; renormalisation group method ; random walks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The problem of upscaling permeability data from the core to the reservoir grid block scale for input into flow simulators is addressed. Two fast, approximate algorithms which have been suggested for this purpose—one based on random walks and the other on real-space renormalisation group methods—are compared using the results of numerical tests performed on 30 different heterogeneous permeability realisations in 3-D. The results show that random walks outperform renormalisation for this problem, being computationally more efficient and demonstrating significantly better accuracy for particular cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00626662
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  • 6
    Electronic Resource
    Electronic Resource
    On the spatial-temporal averaging method for modeling transport in porous media (1996)
    Springer
    Transport in porous media 22 (1996), S. 1-51 
    Details
    ISSN: 1573-1634
    Keywords: averaging theorem ; heterogeneity ; macroscopic equation ; microscopic equation ; probabilistic average ; REV ; spatial average ; spatial-temporal average ; temporal average ; transport equation ; volume average
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The spatial-temporal averaging procedure is considered with a nonhomogeneous distribution of elementary domains in the spatial-temporal space and the probabilistic interpretation of the ST-averaging is also given. Several averaging theorems and corollaries about the averages of spatial and temporal derivatives are presented and rigorously proved which allow elementary domain to vary in space and time. The macroscopic transport equation in the most general condition and the simplified macroscopic equation under the special form of distributions are developed which may be reduced to the classical macroscopic transport equation as the spatial-temporal average degenerates into the volume average.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00974310
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  • 7
    Electronic Resource
    Electronic Resource
    Vorticity in Three-Dimensionally Random Porous Media (1997)
    Springer
    Transport in porous media 26 (1997), S. 109-119 
    Details
    ISSN: 1573-1634
    Keywords: vorticity ; random porous media ; microscales ; spectral method ; heterogeneity ; random field ; stochastic.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The flow gradient tensor controls the rate of dissipation of concentration fluctuations due to local dispersion, and therefore determines the rate of dilution of solute in a spatially random flow field. Off-diagonal terms of the flow gradient tensor quantify the rotational characteristics of the flow. A leading order description of the vorticity $$(\omega = (\omega _1 ,\omega _2 ,\omega _3 ))$$ , of flow in a three-dimensionally random spatially correlated hydraulic conductivity field $$(K({\text{x}}))$$ is made by relating the vorticity spectrum to the spectrum of ln $$K({\text{x}})$$ . Distinct components of the vorticity are found to be linearly uncorrelated $$(\overline {\omega _i \omega _j } = 0,i \ne j)$$ . The characteristic vorticity component in the bulk flow direction is zero $$(\sigma _{\omega _1 } = 0)$$ , and the characteristic vorticity in the transverse directions $$(\sigma _{\omega _2 } ,\sigma _{\omega _3 } )$$ are inversely proportional to the hydraulic conductivity microscales in the other transverse direction, as exhibited in a numerical calculation of the vorticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006593712793
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  • 8
    Electronic Resource
    Electronic Resource
    Effective hydraulic conductivities in unsaturated heterogeneous media by Monte Carlo simulation (1995)
    Springer
    Transport in porous media 18 (1995), S. 203-216 
    Details
    ISSN: 1573-1634
    Keywords: heterogeneity ; effective properties ; hydraulic conductivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract When modeling flow and transport through unsaturated heterogeneous geological deposits, it may be neither computationally nor technically feasible to account for the actual heterogeneity in the simulations. One would fall short in terms of technical feasibility because there is simply no way that the entire spatial domain could be characterized (e.g., you cannot measure hydraulic conductivity at every location at a site). With respect to computational feasibility, the non-linear nature of the Richards equation (which is used to model the flow process) makes simulation of most sites extremely computationally intensive. The computational roadblock is being dismantled as computer hardware advances, but our inability to precisely characterize geological heterogeneity is expected to remain with us for a very long time. To address this problem, the analyst typically uses average or ‘effective’ properties to model flow and transport behavior through heterogeneous media. In this paper, a variety of approaches for developing effective unsaturated flow properties are assessed. Computational results have been obtained which give the hydraulic conductivity ratios (K parallel/K nomal) for highly nonisotropic layered materials. These results are compared with analytical models. Good agreement was obtained for all soil saturation levels except for extremely dry conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00616931
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  • 9
    Electronic Resource
    Electronic Resource
    A Boundary Element-Finite Element Equation Solutions to Flow in Heterogeneous Porous Media (1998)
    Springer
    Transport in porous media 31 (1998), S. 293-312 
    Details
    ISSN: 1573-1634
    Keywords: heterogeneity ; Green element method ; boundary element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Abstract. A coupled boundary element-finite element procedure, namely, the Green element method (GEM) is applied to the solution of mass transport in heterogeneous media. An equivalent integral equation of the governing differential equation is obtained by invoking the Green's second identity, and in a typical finite element fashion, the resulting equation is solved on each generic element of the problem domain. What is essentially unique about this procedure is the recognition of the particular advantages and particular features possessed by the two techniques and their effective use for the solution of engineering problems. By utilizing this approach, we observe that the range of applicability of the boundary integral methods is enhanced to cope with problems involving media heterogeneity in a straightforward and realistic manner. The method has been used to investigate problems involving various functional forms of heterogeneity, including head variations in a stream-heterogeneous aquifer interaction and in all these cases encouraging results are obtained without much difficulty.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006529122626
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  • 10
    Electronic Resource
    Electronic Resource
    Boundary Integral Procedures for Unsaturated Flow Problems (1998)
    Springer
    Transport in porous media 31 (1998), S. 313-330 
    Details
    ISSN: 1573-1634
    Keywords: Boundary integral theory ; non-linearity ; heterogeneity ; unsaturated flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Abstract. A novel numerical scheme based on the singular integral theory of the boundary element method. (BEM) is presented for the solution of transient unsaturated flow in porous media. The effort in the present paper is directed in facilitating the application of the boundary integral theory to the solution of the highly non-linear equations that govern unsaturated flow. The resulting algorithm known as the Green element method (GEM) presents a robust attractive method in the state-of -the-art application of the boundary element methodology. Three GEM models based on their different methods of handling the non-linear diffusivity, illustrate the suitability and robustness of this approach for solving highly non-linear 1-D and 2-D flows which would have proved cumbersome or too difficult to implement with the classical BEM approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006525124289
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