Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction. To cite this article: A. Ern et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

Influence of particle concentration on initial collection efficiency and surface coverage in porous media filtration

Four sizes (0.095, 0.53, 1.0 and 2.01 μm) of polystyrene latex particles were used to prepare monodispersed suspensions at three different ionic strengths (10−3, 10−2.5 and 10−2M KCl). Filtration experiments were conducted using those suspensions in a filter column with glass beads as porous medium. The filter bed depth and the filtration velocity were kept at 5 cm and 1 m/h, respectively. When suspensions with equal mass concentrations (0.2 mg/L) or equal surface area concentrations (0.12 cm2/mL) were filtered through the system, the largest particles exhibited higher initial single collector efficiency, η. The difference between the η of largest particles and the smaller particles was prominent for suspensions with equal surface area concentrations at higher ionic strengths. The collision efficiency, α of those particles exhibits higher values at higher ionic strengths. Both at equal mass concentration and equal surface area concentration, α is only slightly dependent on particle sizes when compared to its dependence on ionic strength. Further, it was found that the specific surface coverage was similar for 0.095 μm, 0.53 μm and 1.0 μm particles during the transient stage of filtration at any ionic strength when the surface area concentrations of those suspension were equal.

A non-darcian numerical modeling in domed enclosures filled with heat-generating porous media

Numerical study of the natural-convection flow and heat transfer in a dome-shaped, heat-generating, porous enclosure is considered. The general conic equation for the top dome is used to consider various conical top sections such as circular, elliptical, parabolic, and hyperbolic. The individual effect of fluid Rayleigh, Darcy, and heat-generating parameters on flow patterns and heat transfer rates are analyzed and presented. The predicted results show that the heat-generating parameter has the most significant contribution toward the growth of bicellular core flow. Moreover, there is significant change in temperature distribution in comparison to rectangular enclosures, due to the existence of the domed-shape top adiabatic cover. The results also show that, regardless of Darcy and Rayleigh values, a flat adiabatic top cover tends to yield the highest value of Nusselt number, followed by circular, elliptical, parabolic, and hyperbolic top covers, respectively.

T2-T2 exchange in biofouled porous media

Recent two dimensional nuclear magnetic resonance (NMR) techniques access exchange in pore structures through surface relaxation and diffusion based relaxation [1-4]. This research applies these techniques to measure pore changes due to biofilm growth and the impact this growth has on diffusion transport. The porous media used in this study are model beadpacks constructed from borosilicate glass beads with diameters approximately 100 um. This research shows that through changes in the relaxation rates, NMR can be used to verity biofilm growth in porous media

Permeability mapping in porous media by magnetization prepared centric-scan SPRITE

The ability of porous media to transmit fluids is commonly referred to as permeability. The concept of permeability is central for hydrocarbon recovery from petroleum reservoirs and for studies of groundwater flow in aquifers. Spatially resolved measurements of permeability are of great significance for fluid dynamics studies. A convenient concept of local Darcy’s law is suggested for parallel flow systems. The product of porosity and mean velocity images in the plane across the average flow direction is directly proportional to permeability. Single Point Ramped Imaging with T 1 Enhancement (SPRITE) permits reliable quantification of local fluid content and flow in porous media. It is particularly advantageous for reservoir rocks characterized by fast magnetic relaxation of a saturating fluid. Velocity encoding using the Cotts pulsed field gradient scheme improves the accuracy of measured flow parameters. The method is illustrated through measurements of 2D permeability maps in a capillary bundle, glass bead packs and composite sandstone samples.

Measuring miscible fluid displacement in porous media with magnetic resonance imaging

The development of new quantitative magnetic resonance imaging (MRI) technologies open new opportunities for measurements of mass transport in porous media. The current work examines a simple miscible displacement process of H2O and D2O in porous media samples. Laboratory measurements of dispersion in porous media traditionally monitor the effluent intensity of an injected tracer. We employ MRI to obtain quantitative water saturation profiles, and to measure dispersion in rock core plugs. The saturation profiles are modeled with PHREEQC, a fluid transport modeling program. We demonstrate how independent magnetic resonance measurements can be employed to estimate three important input parameters for PHREEQC, mobile porosity, immobile porosity, and dispersivity. Bulk Carr Purcell Meiboom Gill (CPMG) T2 distribution measurements were undertaken to estimate mobile and immobile porosity. Bulk alternating-pulsed-gradient-stimulated-echo (APGSTE) measurements were undertaken to measure dispersivity. The imaging method employed, T2 mapping Spin Echo Single Point Imaging (SE-SPI), also provides information about the pore size distributions in the rock cores, and how the fluid occupancy of the pores changes during the displacement process.