Page 14 - Percolation Models for Transport in Porous Media With

INTRODUCTION 3

Nevertheless some important cases can be handled analytically. The capilliary
dominant case of the oil-water flow in porous media with stochastic heterogeneity
has been solved analytically using the traditional percolation theory and effective
media model [14]. Viscous dominant case of the waterflood in stochastic porous
media was solved in [113] using the percolation model proposed in Chapters 1 and
2 of this book. In this study, a new approach to description of transfer processes in
stochastically heterogeneous media is presented. The origin of this approach can be
found in the series of studies [37-42]. A percolation model of a micro heterogeneous
medium is proposed, allowing for obtaining analytical formulas and solutions for
problems of the mentioned type. Methods for investigation of pore space structure
of different types of rocks are described, allowing for determination of the effective
radius probability density function for capillaries. Using this approach, effects of
pore space structure of a micro heterogeneous medium upon one- and multi-phase
flow are studied. A percolation theory for the two-phase flow developed in Chapter
4 can be used for the generalization of the relative permeabilities model for cases of
precipitation of paraffins and for chemical reactions in porous media [114]. Effects
of rearrangement of pore space structure resulting from different types of treatment
(acoustic, electric) are investigated. Methods for calculating phase permeabilities
are proposed, new physical effects due to certain properties of transfer processes
in micro heterogeneous media are described. In Part II, some of the technologies
based on such effects, are presented.
The examples shown demonstrate that use of percolation models are very
promising in investigation of the influence of pore space structure upon transfer
phenomena in micro heterogeneous media.
The authors wish to thank their colleagues and students, S.P. Glushko, N.S.
Rostovsky, and R.M. Musin, who took part in solving some of the problems
reflected in the book. Special thanks are owed to A.J. Greenberg for his great help
in preparing the manuscript.