Category: review article

A Brief Review of Capillary Number and its Use in Capillary Desaturation Curves

Post author By R Hilfer
Post date August 9, 2021

H. Guo, K. Song, R. Hilfer

Transport in Porous Media 144, 3-31 (2022)
https://doi.org/10.1007/s11242-021-01743-7

submitted on
Monday, August 9, 2021

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 engineers, because the nature and quantification of macroscopic capillary forces remains controversial. At least 41 different capillary numbers have been collected here from the literature. The ratio of viscous and capillary force enters crucially into capillary desaturation experiments. Although the ratio is length scale dependent, not all definitions of capillay number depend on length scale, indicating potential inconsistencies between various applications and publications. Recently, new numbers have appeared and the subject continues to be actively discussed. Therefore, a short review seems appropriate and pertinent.

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Fractional Calculus Mathematics review article

Threefold Introduction to Fractional Derivatives

Post author By R Hilfer
Post date January 2, 2008

R. Hilfer

in: Anomalous Transport: Foundations and Applications
edited by: R. Klages and G. Radons and I. Sokolov
Wiley-VCH, Weinheim, 17-74 (2008)
ISBN: 978-3-527-40722-4

submitted on
Wednesday, January 2, 2008

Historical, mathematical and physical introduction to fractrional derivatives.

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image analysis Porous Media review article

Review on Scale Dependent Characterization of the Microstructure of Porous Media

Post author By R Hilfer
Post date February 8, 2000

R. Hilfer

Transport in Porous Media 46, 373 (2002)
https://doi.org/10.1023/A:1015014302642

submitted on
Tuesday, February 8, 2000

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 the charcterization of geometric observables through Hadwigers theorem in stochastic geometry. The four basic Minkowski functionals are introduced into local porosity theory, and for the first time a relationship is established between the Euler characteristic and the local percolation probabilities. Local porosity distributions and local percolation probabilities provide a scale dependent characterization of the microstructure of porous media that can be used in an effective medium approach to predict transport.

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Porous Media review article Transport Processes

Local Porosity Theory and Stochastic Reconstruction for Porous Media

Post author By R Hilfer
Post date February 23, 1999

R. Hilfer

in: Räumliche Statistik und Statistische Physik
edited by: D. Stoyan and K. Mecke
Springer, Berlin, 203 (2000)
10.1007/3-540-45043-2
ISBN: 978-3-642-08725-7

submitted on
Tuesday, February 23, 1999

The paper reviews recent developments in local porosity theory, and discusses its application to the analysis of stochastic reconstruction models for sedimentary rocks. Special emphasis is placed on the geometric observables in local porosity theory and their relation with the Hadwiger theorem from stochastic geometry. In addition recent results for the exact calculation of effective physical transport properties are given for a Fontainebleau sandstone. The calculations pertain to potential type problems such as electrical conduction, dielectric relaxation, diffusion or Darcy flow. The exact results are compared to the approximate parameterfree predictions from local porosity, and are found to be in good agreement.

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Tags local porosity theory

Fractional Calculus review article

Fractional Derivatives in Static and Dynamic Scaling

Post author By R Hilfer
Post date March 11, 1997

R. Hilfer

in: Scale Invariance and Beyond
edited by: B. Dubrulle and F. Graner and D. Sornette
Springer, Berlin, 53 (1997)
10.1007/978-3-662-09799-1
978-3-540-64000-4

submitted on
Tuesday, March 11, 1997

The paper is a brief review of recent applications of fractional calculus in physics with emphasis on static and dynamic scaling.

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Tags scaling