Search results for "Porous medium"
showing 10 items of 164 documents
Dimensional analysis of pore scale and field scale immiscible displacement
1996
A basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a ‘macroscopic capillary number’\(\overline {Ca}\) which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number\(\overline {Ca}\) is defined as the ratio between the macroscopic viscous pressure drop and the macroscopic capillary pressure.\(\overline {Ca}\) can be related to the microscopic capillary number Ca and the LeverettJ-function. Previous dimensional analyses contain a tacit assumption which amounts to setting…
Attenuation of the fourth sound in liquid helium II via extended thermodynamics
2004
Abstract This work continues a study begun in previous works, where a non-standard model of liquid helium II is proposed, in which a small entropy transfer is associated with the superfluid component. In this work the influence of this superfluid entropy on the propagation of the fourth sound is analyzed. From experimental data for velocities and attenuations of the first and second sound, the model provides speed and attenuation coefficient of the fourth sound in a porous medium as a function of the ratio ss/s between the superfluid entropy ss and the total entropy s. These values are determined in the two limiting cases ss/s=0 and =0.02, for various values of temperature and pressure.
Local-porosity theory for flow in porous media
1992
A recently introduced geometric characterization of porous media based on local-porosity distributions and local-percolation probabilities is used to calculate dc permeabilities for porous media. The disorder in porous media is found to be intimately related to the percolation concept. The geometric characterization is shown to open a possibility for understanding experimentally observed scaling relations between permeability, formation factor, specific internal surface, and porosity. In particular, Kozeny's equation k\ensuremath{\propto}\ensuremath{\varphi}\ifmmode\bar\else\textasciimacron\fi{} $^{\mathit{b}}$ between effective permeability and bulk porosity and the relation k\ensuremath{\…
WENO Schemes for Multi-Dimensional Porous Media Flow Without Capillarity
2016
In this work we derive a numerical technique based on finite-difference WENO schemes for the simulation of multi-dimensional multiphase flows in a homogeneous porous medium. The key idea is to define a compatible discretization for the fluxes of the convective term in order to maintain their divergence-free character not only in the continuous setting but also in the discrete setting, ensuring the conservation of the sum of the saturations through time evolution. The one-dimensional numerical technique is derived in detail for the case of neglected capillarity effects. Numerical results obtained with one-dimensional and two-dimensional standard tests of multiphase flow in a homogeneous poro…
Tortuous flow in porous media
1996
The concept of tortuosity of fluid flow in porous media is discussed. A lattice-gas cellular automaton method is applied to solve the flow of a Newtonian uncompressible fluid in a two-dimensional porous substance constructed by randomly placed rectangles of equal size and with unrestricted overlap. A clear correlation between the average tortuosity of the flow paths and the porosity of the substance has been found. \textcopyright{} 1996 The American Physical Society.
Coupled Multi-Field Continuum Methods for Porous Media Fracture
2015
The focus of the present contribution is on the numerical modelling of hydraulic fracture in fluid-saturated heterogeneous materials, which can be carried out on a macroscopic scale using extended continuum porous media theories. This accounts for the crack nucleation and propagation, deformation of the solid matrix and change in the flow of the interstitial fluid. In particular, fluid-saturated porous materials basically represent volumetrically interacting solid-fluid aggregates, which are modelled using the Theory of Porous Media. The hydraulic- or tension-induced fracture occurs in the solid matrix and is simulated using a diffusive phase-field modelling approach. This way of fracture t…
Permeability and effective porosity of porous media
1997
The concept of permeability of porous media is discussed, and a modification of Kozeny’s permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this two-dimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. …
Capillary pressure, hysteresis and residual saturation in porous media
2006
Abstract A macroscopic theory for capillarity in porous media is presented. The capillary pressure function in this theory is not an input parameter but an outcome. The theory is based on introducing the trapped or residual saturations as state variables. It allows to predict spatiotemporal changes in residual saturation. The theory yields process dependence and hysteresis in capillary pressure as its main result.
Silica-based macrocellular foam monoliths with hierarchical trimodal pore systems
2005
Abstract Silica-based large monoliths exhibiting a trimodal hierarchical pore system have been successfully prepared through a nanotectonic approach starting from sub-micro/nanometric mesoporous particles (as building blocks), and using a polyurethane foam as macrotemplate. Large trimodal pieces with macrocellular like interconnected macropores in the micrometer range are a mineralized replica of the polyurethane foam. Textural large-mesopores/macropores (in the 20–70 nm range) have their origin in the inter-particle voids. The small intra-particle mesopore system (with pore diameters around 2–3 nm) is due to the supramolecular templating effect of the surfactant.
Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section
2021
Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. …