Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition

Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyn'ska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The well-posedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.Comment: 6 pages, 0 figure

Literature review on NAPL contamination and remediation

Remediation of polluted soils and groundwater is of major concern due to the increasing number of contaminated aquifers. Subsurface aquifers constitute one of the most important sources of drinkable water. In recent years, water needs have been increasing due to increases in development and human population. Several sorts of contaminants can be found in groundwater: metal ions, pesticides, aliphatic and aromatic hydrocarbons, polycyclic hydrocarbons, chlorinated hydrocarbons, etc. The toxicity of these compounds varies and so do guidelines that establish allowable concentration levels in drinking water. Among the aforementioned types of compounds, a particular importance is assumed by those which exist as a separate phase when their concentrations in water exceed a certain limit. The transport behavior and dynamics of multiphase contaminants are very different from their dissolved counterparts, and are very difficult both to describe and to model. Several phenomena can take place, such as organic phase trapping, formation of ganglia and pools of contaminant, sorption, hysteresis in both soil imbibition and drainage, capillarity, fingering, and mass-transfer. In such cases, our ability to describe and predict the fate of a contaminant plume in which a separate organic phase occurs is limited, and research within this field is quite open. Much effort has been devoted in trying to describe the characteristics of the phenomena occuring in multiphase systems, and several models and formulations have been proposed for predicting the fate of contaminants when present in such systems (see Miller et al. 1997) for a review on multiphase modeling in porous media). Work has also been done for modeling human intervention techniques for containing and/or reducing soil contaminantion (NRC, 1994), such as pumping, clean water-air-steam injection, soil heating, surfactants, biological methods, etc. Finally, much work has also been done on the numerical solution of mathematical models whose complexity does not allow for an analytical solution. Among the dozens of remediation methods which have been proposed and which are strongly dependent on site environmental conditions, biological methods are achieving increasing importance, due to their “naturalness" and their low costs (NRC, 1993) . It has been noticed that soil microorganisms are able to degrade several classes of compounds, in particular those which partition between an aqueous and an organic phase, or sometimes also gaseous phase, for e.g., hydrocarbons, chlorinated compounds, pesticides. These compounds, or better said, their fractions dissolved in water, are liable to be metabolized by subsurface microrganisms which have the capability to degrade the compounds and to transform them into carbon dioxide and/or other compounds, which are less toxic or unnoxious. Several laboratory and field studies have been conducted for assessing and evaluating the capability and the limits of soil microorganisms to degrade several classes of contaminants (Mayer et al., 1994, 1995, 1996, 1997) . Much work has also been devoted to modeling biodegration of groundwater contaminants. The outline of this report is as follows: section 2 gives a brief description of the characteristics and properties of NAPLs, including a review of the literature with regards to formulations and modeling; section 3 discusses biodegradation of contaminants and past efforts at modeling biodegradation; section 4 surveys specific remediation technologies and experiences; and section 5 discusses open issues for further research. In the final section possible lines of research for the second phase of the PhD program are indicated

Imaging spontaneous imbibition in full Darcy‐scale samples at pore‐scale resolution by fast X‐ray tomography

Spontaneous imbibition is a process occurring in a porous medium which describes wetting phase replacing nonwetting phase spontaneously due to capillary forces. This process is conventionally investigated by standardized, well-established spontaneous imbibition tests. In these tests, for instance, a rock sample is surrounded by wetting fluid. The following cumulative production of nonwetting phase versus time is used as a qualitative measure for wettability. However, these test results are difficult to interpret, because many rocks do not show a homogeneous but a mixed wettability in which the wetting preference of a rock varies from location to location. Moreover, during the test the flow regime typically changes from countercurrent to cocurrent flow and no phase pressure or pressure drop can be recorded. To help interpretation, we complement Darcy-scale production curves with X-ray imaging to describe the differences in imbibition processes between water-wet and mixed-wet systems. We found that the formation of a spontaneous imbibition front occurs only for water-wet systems; mixed-wet systems show localized imbibition events only. The asymmetry of the front depends on the occurrence of preferred production sites, which influences interpretation. Fluid layers on the outside of mixed-wet samples increase connectivity of the drained phase and the effect of buoyancy on spontaneous imbibition. The wider implication of our study is the demonstration of the capability of benchtop laboratory equipment to image a full Darcy-scale experiment while at the same time obtaining pore-scale information, resolving the natural length and time scale of the underlying processes

Новые клинические и диагностические стратегии при раке почки

Представлен анализ изменившейся клиники опухолей почки. Описаны динамика и последовательность использования новых визуализирующих методов диагностики.The analysis of the changed clinical picture of renal tumors is done. The dynamics and sequence of the new imaging techniques are described

Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour

The dissolution and microbial degradation of mobile aromatic hydrocarbons from a Pintsch gas tar DNAPL source zone

Source zones containing tar, a dense non-aqueous phase liquid (DNAPL), can contaminate groundwater for centuries. A common occurrence of tar is at former Pintsch gas factories. Little is known about the composition and fate of contaminants dissolving from Pintsch gas tar DNAPL. In this study, we determined the composition and water-soluble characteristics of mobile aromatic hydrocarbons and their biodegradation metabolites in the DNAPL contaminated groundwater at a former Pintsch gas tar plant. We assessed the factors that determine the fate of observed groundwater contaminants. Measured values of density (1.03–1.06 kg/m3) and viscosity (18.6–39.4 cP) were found to be relatively low compared to common coal tars. Analysis showed that unlike common coal tars phenanthrene is the primary component rather than naphthalene. Moreover, it was found that Pintsch gas tar contains a relatively high amount of light molecular aromatic hydrocarbon compounds, such as benzene, toluene, ethylbenzene and xylenes (BTEX). Less commonly reported components, such as styrene, ethyltoluenes, di-ethylbenzene, 1,2,4,5-tetramethylbenzene, were also detected in water extracts from Pintsch gas tar. Moreover, 46 relatively hydrophilic metabolites were found within the tar samples. Metabolites present within the tar suggest biodegradation of mobile aromatic Pintsch gas tar compounds occurred near the DNAPL. Based on eleven detected suspect metabolites, a novel anaerobic biodegradation pathway is proposed for indene. Overall, our findings indicate that Pintsch gas tar has higher invasive and higher flux properties than most coal tars due to its relatively low density, low viscosity and, high content of water-soluble compounds. The partitioning of contaminants from multi-component DNAPL into the aqueous phase and re-dissolution of their slightly less hydrophobic metabolites back from the aqueous phase into the DNAPL is feasible and demonstrates the complexity of assessing degradation processes within a source zone

Modeling anisotropic diffusion using a departure from isotropy approach

There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion. This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for two-dimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients