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  • Articles  (15)
  • Articles: DFG German National Licenses  (15)
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  • 1996  (8)
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  • Articles  (15)
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  • Articles: DFG German National Licenses  (15)
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  • Springer  (15)
  • American Association for the Advancement of Science (AAAS)
  • American Geophysical Union
  • American Physical Society (APS)
  • Public Library of Science
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  • 1
    Electronic Resource
    Electronic Resource
    A resumé of nonlocal transport theories (1995)
    Springer
    Stochastic environmental research and risk assessment 9 (1995), S. 105-116 
    Details
    ISSN: 1436-3259
    Keywords: Nonlocal ; transport ; dispersion ; heterogeneity ; integro-differential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Analysis from a number of different perspectives has shown diffusion and dispersion in natural porous formations to generally be nonlocal in character, i.e., the mass balance involves integro-partial differential equations. Only in certain asymptotic limits do these laws localize to classical partial differential equations. Compiled within is a resume of nonlocal laws that our group has developed over the last few years for systems with physical, chemical and biological heterogeneity. Analytical tools used to obtain these laws are nonequilibrium and equilibrium statistical mechanics, and first-order spectral-perturbation methods. This paper is an expansion of the material presented at the Waterloo conference held in the memory of Dr. Unny.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585601
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  • 2
    Electronic Resource
    Electronic Resource
    Characteristics of whistler ducts recorded at Gulmarg (1996)
    Springer
    Earth, moon and planets 73 (1996), S. 181-186 
    Details
    ISSN: 1573-0794
    Keywords: Diffused whistler ; ducts ; electron density ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Morphological features of whistlers recorded at low latitude ground station Gulmarg (geomag. lat., 24
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00114150
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  • 3
    Electronic Resource
    Electronic Resource
    On the transient non-Fickian dispersion theory (1996)
    Springer
    Transport in porous media 23 (1996), S. 107-124 
    Details
    ISSN: 1573-1634
    Keywords: solute transport ; Fick's law ; dispersion ; dispersivity ; equation of motion ; non-Fickian dispersion equation ; scale effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The Fickian dispersion equation is the basic relationship used to describe the nonconvective mass flux of a solute in a porous medium. This equation prescribes a linear relationship between the dispersive mass flux and the concentration gradient. An important characteristic of the Fickian relationship is that it is independent of the history of dispersion (e.g. the time rate of change of the dispersion flux). Also, the dispersivities are supposed to be medium constants and invariant with temporal and spatial scales of observation. It is believed that in general these restrictions do not hold. A number of authors have proposed various alternative relationships. For example, differential equations have been employed that prescribe a relationship between the dispersion flux and its time and space derivatives. Also, stochastic theories result in integro-differential equations in which dispersion tensor grow asymptotically with time or distance. In this work, three different approaches, which lead to three different non-Fickian equations with a transient character, are discussed and their primary features and differences are highlighted. It is shown that an effective dispersion tensor defined in the framework of the transient non-Fickian theory, grows asymptotically with time and distance; a result which also follows from stochastic theories. Next, principles of continuum mechanics are employed to provide a solid theoretical basis for the non-Fickian transient dispersion theory. The equation of motion of a solute in a porous medium is used to provide a rigorous derivation of various dispersion relationships valid under different conditions. Under various simplifying assumptions, the generalized theory is found to agree with the conventional Fickian theory as well as several other non-Fickian relationships found in the literature. Moreover, it is shown that for nonconservative solutes, the traditional dispersion tensor is affected by the rate of mass exchange of the solute.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00145268
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  • 4
    Electronic Resource
    Electronic Resource
    The influence of free convection on soil salinization in arid regions (1996)
    Springer
    Transport in porous media 23 (1996), S. 275-301 
    Details
    ISSN: 1573-1634
    Keywords: free convection ; through flow ; vadoze zone ; salinization ; dispersion ; multigrid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Evaporation of groundwater in a region with a shallow water table and small natural replenishment causes accumulation of salts near the ground surface. Water in the upper soil layer becomes denser than in the depth. This is a potentially unstable situation which may result in convective currents. When free convection takes place, estimates of the salinity profile, salt precipitation rate, etc., obtained within the framework of a 1-D (vertical) model fail. Very simplified model of the process is proposed, in which the unsaturated zone is represented by a horizontal soil layer at a constant water saturation, and temperature changes are neglected. The purpose of the model is to obtain a rough estimate of the role of natural convection in the salinization process. A linear stability analysis of a uniform vertical flow is given, and the stability limit is determined numerically as a function of evaporation rate, salt concentration in groundwater, and porous medium dispersivity. The loss of stability corresponds to quite realistic Rayleigh numbers. The stability limit depends in nonmonotonic way on the evaporation rate. The developed convective regime was simulated numerically for a 2-D vertical domain, using finite volume element discretization and FAS multigrid solver. The dependence of the average salt concentration in the upper layer on the Rayleigh number was obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00167100
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  • 5
    Electronic Resource
    Electronic Resource
    Influence of capillary pressure, adsorption and dispersion on chemical flood transport phenomena (1996)
    Springer
    Transport in porous media 24 (1996), S. 275-296 
    Details
    ISSN: 1573-1634
    Keywords: chemical flooding ; ternary ; immiscible ; surfactant ; numerical simulation ; interfacial tension ; phase behavior ; miscibility ; capillarity ; numerical grid ; adsorption ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This is the second of two joint papers which study the influence of several physical properties on the transport phenomena in chemical flooding. To that aim, we use a previously reported ternary two-phase model into which representative physical properties have been incorporated as concentration-dependent functions. Physical properties such as phase behavior, interfacial tensions, residual saturations, relative permeabilities, phase viscosities and wettability have been analyzed in the first paper. In this paper, we discuss the influence of capillary pressure, adsorption of the chemical component onto the rock and dispersion. Although arising from different phenomenological sources, these transport mechanisms show some similar effects on concentration profiles and on oil recovery. They are studied for systems with different phase behavior. A numerical analysis is also presented in order to determine the relevance of the number of grid blocks taken in the discretization of the differential equations. This numerical analysis provides useful guidelines for the selection of the appropriate numerical grid in each type of displacement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00154094
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  • 6
    Electronic Resource
    Electronic Resource
    Comment on ‘fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media’, by Muhammad Sahimi (1995)
    Springer
    Transport in porous media 21 (1995), S. 175-188 
    Details
    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; percolation ; fractals ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Two fundamental questions regarding the application of percolation theory to transport in porous media are addressed. First, when ‘critical path’ arguments (based on a sufficiently wide spread of microscopic transition rates) are invoked (in analogy to the case of transport in disordered semiconductors) to justify the application of percolation theory to the determination of relevant transport properties, then for long time scales (compared to the inverse of the ‘critical’ percolation rate), the fractal structure of the ‘critical’ path is relevant to transport, but not at short time scales. These results have been demonstrated concretely in the case of disordered semiconductors, and are in direct contradiction to the claims of the review. Second, the relevance of deterministic or stochastic methods to transport has been treated heretofore by most authors as a question of practicality. But, at least under some conditions, concrete criteria distinguish between the two types of transport. Percolative (deterministic) transport is temporally reproducible and spatially inhomogeneous while diffusive (stochastic) transport is temporally irreproducible, but homogeneous, and a cross-over from stochastic to percolative transport occurs when the spread of microscopic transition rates exceeds 4–5 orders of magnitude. It is likely that such conditions are frequently encountered in soil transport. Moreover, clear evidence for deterministic transport (although not necessarily percolative) exists in such phenomena as preferential flow. On the other hand, the physical limitation of transport to (fractally connected) pore spaces within soils (analogously to transport in metal-insulator composites) can make transport diffusive on a fractal structure, rather than percolative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00613755
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  • 7
    Electronic Resource
    Electronic Resource
    A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media (1996)
    Springer
    Transport in porous media 24 (1996), S. 1-33 
    Details
    ISSN: 1573-1634
    Keywords: unsaturated flow ; large-scale averaging ; dispersion ; high-resolution numerical simulations ; NAPL spills
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Infiltration of water and non-aqueous phase liquids (NAPLs) in the vadose zone gives rise to complex two- and three-phase immiscible displacement processes. Physical and numerical experiments have shown that ever-present small-scale heterogeneities will cause a lateral broadening of the descending liquid plumes. This behavior of liquid plumes infiltrating in the vadose zone may be similar to the familiar transversal dispersion of solute plumes in single-phase flow. Noting this analogy we introduce a mathematical model for ‘phase dispersion’ in multiphase flow as a Fickian diffusion process. It is shown that the driving force for phase dispersion is the gradient of relative permeability, and that addition of a phase-dispersive term to the governing equations for multiphase flow is equivalent to an effective capillary pressure which is proportional to the logarithm of the relative permeability of the infiltrating liquid phase. The relationship between heterogeneity-induced phase dispersion and capillary and numerical dispersion effects is established. High-resolution numerical simulation experiments in heterogeneous media show that plume spreading tends to be diffusive, supporting the proposed convection-dispersion model. Finite difference discretization of the phase-dispersive flux is discussed, and an illustrative application to NAPL infiltration from a localized source is presented. It is found that a small amount of phase dispersion can completely alter the behavior of an infiltrating NAPL plume, and that neglect of phase-dispersive processes may lead to unrealistic predictions of NAPL behavior in the vadose zone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00175602
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  • 8
    Electronic Resource
    Electronic Resource
    Double-camera measurements of plumes, applied to wind field characterization and dispersion studies (1996)
    Springer
    Boundary layer meteorology 79 (1996), S. 1-21 
    Details
    ISSN: 1573-1472
    Keywords: stereophotogrammetry ; visible plumes ; complex terrain ; tracers of opportunity ; dispersion ; wind shear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A stereophotogrammetric technique based on standard equipment to measure plume trajectories in sheared wind fields and/or complex terrain is shown here. The approach is to use existing visible plumes as tracers of opportunity of air flow. This technique was first developed as part of a multi-instrument field program intended for the experimental characterization of atmospheric dispersion in the complex coastal area of Bilbao in northern Spain. Emphasis is placed on the calibration method and the experimental procedures as well as on sources and margins of error. Finally, applications and joint usage with other techniques during several field programs are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00120072
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  • 9
    Electronic Resource
    Electronic Resource
    Advective and dispersive mixing in stratified formations (1995)
    Springer
    Transport in porous media 18 (1995), S. 231-243 
    Details
    ISSN: 1573-1634
    Keywords: Stratified formations ; kinematic mixing ; dispersion ; random fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The mixing process in fluid flow is presented as the bending and stretching of material lines or filaments. A mixing exponent, which quantifies their specific rate of stretching, is defined and analyzed for the case of groundwater flow though stratified formations characterized by a Gaussian autocovariance function. The analysis is performed for purely advective mixing as well as for advective-dispersive mixing. The mixing exponent was found to be proportional to the variance of hydraulic conductivity and inversely proportional to the correlation scale of hydraulic conductivity and to the pore-level dispersion coefficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00616933
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  • 10
    Electronic Resource
    Electronic Resource
    A stream tube model for miscible flow (1995)
    Springer
    Transport in porous media 18 (1995), S. 245-261 
    Details
    ISSN: 1573-1634
    Keywords: Porous media ; miscible flow ; tracer ; dispersion ; convective flow ; stochastic ; stream tube ; continuous time random walk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00616934
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