Next Article in Journal
Maximum Entropy Learning with Deep Belief Networks
Previous Article in Journal
Thermoeconomic Coherence: A Methodology for the Analysis and Optimisation of Thermal Systems
Article Menu

Export Article

Open AccessArticle
Entropy 2016, 18(7), 249; doi:10.3390/e18070249

Modeling Fluid’s Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks

1
International Center for Mathematical Modelling in Physics and Cognitive Sciences, Mathematical Institute, Linnaeus University, Vaxjo SE-351 95, Sweden
2
Centro de Geociencias, Universidad Nacional Autonoma de Mexico (UNAM), Campus UNAM Juriquilla, Blvd. Juriquilla 3001, Queretaro, Qro. 76230, Mexico
3
Coordinación del Grupo Multidisciplinario de Especialistas Técnicos de Diseño de Proyectos, Suptcia de caracterizacion de Yacimientos, Activo de Produccion Ku-Maloob-Zaap, Ed. Kaxan, Av. Contadores, Carretera Carmen Puerto Real, Cd. Del Carmen, Camp. 24150, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 1 May 2016 / Revised: 22 June 2016 / Accepted: 23 June 2016 / Published: 7 July 2016
View Full-Text   |   Download PDF [8337 KB, uploaded 7 July 2016]   |  

Abstract

We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces. View Full-Text
Keywords: tree-like geometry; ultrametric spaces and analysis; capillary networks in random porous media; master equations; ultrametric pseudo-differential operators and diffusion; fluids flows; p-adic numbers; fractals; non-Archimedean theoretical physics tree-like geometry; ultrametric spaces and analysis; capillary networks in random porous media; master equations; ultrametric pseudo-differential operators and diffusion; fluids flows; p-adic numbers; fractals; non-Archimedean theoretical physics
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Khrennikov, A.; Oleschko, K.; Correa López, M.J. Modeling Fluid’s Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks. Entropy 2016, 18, 249.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top