Page 9 - Percolation Models for Transport in Porous Media With

Foreword

It is an honour and pleasure to write a foreword to this useful and interesting book.
Authors are very well known researchers who pioneered percolation modelling of
transport in porous media in Russia from the early 80-th till nowadays.
The main scope of the work presented in the book was developed when bright
papers by A. Aharony, H.T. Davis, F.A.L. Dullien, A.A. Heiba, R.G. Larson, R.
Lenormand, M.Sahimi, L.E. Scriven, D. Stauffer, M. Yanuka, Y.C.Yortsos were
not available at the "other" side of the Iron Curtain.
Nowadays hundreds of works and papers with the "percolation" keywords ap-
pear in petroleum and related applied research areas. The book will take a re-
markable place in the "petroleum percolation" bibliography.
There are two important features of novelty in the monograph presented.
First of all the authors developed a generalization of percolation clusters theory
for grids with varying conductivity. Technique of representation of an infinite
cluster as an hierarchial set of trees (so called r-chain model) allows to present
conductivity of a stochastic grid in a closed form of explicit formulae.
This method differs from those known in the West, such as effective media
theory, solutions for the Bethe-lattice, etc. It has his own area of successful appli-
cations.
This technique was applied for modelling of transport of multiphase systems
in complex porous media. The majority of cases discussed have been investigated
by other authors in the West in more detail using other methods for conductivity
calculation (two- and three-phase flows, fractured media); some effects are pretty
new (flow of non-Newtonian fluids, deformable porous media).
Quasi static percolation models have been further developed into dynamic ones
(so-called model of the forest growth). Theory of non-equilibrium displacement
on the pore level in micro heterogeneous media is developed (Chapter 5). This
approach could give a hint for solution of a very desirable problem of dynamic
transport in fractals.
The second important novelty of the book is percolation modelling of electric
current in porous media. The theory provides basics for fast-developing methods

ix