-
Article
Open AccessPercolativity of Porous Media
Connectivity and connectedness are nonadditive geometric functionals on the set of pore scale structures. They determine transport of mass, volume or momentum in porous media, because without connectivity ther...
-
Article
Open AccessA Brief Review of Capillary Number and its Use in Capillary Desaturation Curves
Capillary number, understood as the ratio of viscous force to capillary force, is one of the most important parameters in enhanced oil recovery (EOR). It continues to attract the interest of scientists and eng...
-
Article
Open AccessEffective transport coefficients of anisotropic disordered materials
A novel effective medium theory for homogenized transport coefficients of anisotropic mixtures of possibly anisotropic materials is developed. Existing theories for isotropic systems cannot be easily extended,...
-
Article
Open AccessOn extremal domains and codomains for convolution of distributions and fractional calculus
It is proved that the class of c-closed distribution spaces contains extremal domains and codomains to make convolution of distributions a well-defined bilinear map**. The distribution spaces are systematica...
-
Article
Open AccessFractional glassy relaxation and convolution modules of distributions
Solving fractional relaxation equations requires precisely characterized domains of definition for applications of fractional differential and integral operators. Determining these domains has been a longstand...
-
Article
Open AccessConvolution operators on weighted spaces of continuous functions and supremal convolution
The convolution of two weighted balls of measures is proved to be contained in a third weighted ball if and only if the supremal convolution of the corresponding two weights is less than or equal to the third ...
-
Article
Stable Propagation of Saturation Overshoots for Two-Phase Flow in Porous Media
Propagation of saturation overshoots for two-phase flow of immiscible and incompressible fluids in porous media is analyzed using different computational methods. In particular, it is investigated under which ...
-
Article
Erratum to: Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media
-
Article
Open AccessNon-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media
Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations re...
-
Article
Influence of Initial Conditions on Propagation, Growth and Decay of Saturation Overshoot
A sequence of drainage and imbibition shocks within the traditional theory of two-phase immiscible displacement can give rise to shallow non-monotone saturation profiles as shown in Hilfer and Steinle (Eur Phy...
-
Article
Saturation overshoot and hysteresis for twophase flow in porous media
Saturation overshoot and hysteresis for two phase flow in porous media are briefly reviewed. Old and new challenges are discussed. It is widely accepted that the traditional Richards model for twophase flow in...
-
Article
Open AccessTraveling Wave Solutions in a Generalized Theory for Macroscopic Capillarity
One-dimensional traveling wave solutions for imbibition processes into a homogeneous porous medium are found within a recent generalized theory of macroscopic capillarity. The generalized theory is based on th...
-
Chapter and Conference Paper
Applications and Implications of Fractional Dynamics for Dielectric Relaxation
This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on “Broadband Dielectric Spectroscopy and its Advanced Technological Applications”, held in Perpignan...
-
Article
Percolation as a Basic Concept for Macroscopic Capillarity
The concepts of relative permeability and capillary pressure are crucial for the accepted traditional theory of two phase flow in porous media. Recently, a theoretical approach was introduced that does not req...
-
Article
Review on Scale Dependent Characterization of the Microstructure of Porous Media
The paper discusses local porosity theory and its relation with other geometric characterization methods for porous media such as correlation functions and contact distributions. Special emphasis is placed on ...
-
Chapter and Conference Paper
Effective Physical Properties of Sandstones
In this paper we continue the investigation of the effective transport parameters of a digitized sample of Fontainebleau sandstone and three reconstruction models discussed previously in Biswal et. al., Physic...
-
Chapter and Conference Paper
Fractional Evolution Equations and Irreversibility
The paper reviews a general theory predicting the general importance of fractional evolution equations. Fractional time evolutions are shown to arise from a microscopic time evolution in a certain long time sc...
-
Chapter and Conference Paper
On fractional diffusion and its relation with continuous time random walks
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship...
-
Chapter and Conference Paper
Fractional Derivatives in Static and Dynamic Scaling
A derivative or integral of fractional order is usually defined by analytically continuing a suitable definition of the derivative or integral of integer order n ∈ ℕ to real or complex values of n.
-
Article
Dimensional analysis of pore scale and field scale immiscible displacement
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’ ...
