Page 12 - Percolation Models for Transport in Porous Media With

Introduction

Creation of essentially new technologies in the recovery of mineral resources is im-
possible without a thorough research in fluid transfer phenomena in rocks. How-
ever it appears unreasonable to expect discovery of new physical effects in fluid
flow in porous media if traditional continuous media models are applied. In these
models, the huge variety of rock types is taken account of by varying the coeffi-
cients of permeability and porosity in the equations describing fluid flow. With this
approach, the coefficient of phase permeability is the only parameter that bears
information about pore space structure of rocks; experimental determination of
this coefficient, however, is of considerable technical difficulty.
At the same time, it is obvious that the pore space structure has a great
influence upon the nature of fluid flow in micro heterogeneous media. Notable
pressure gradients during the fluid flow or electric field potential during the electric
current flow can emerge at the micro level because of the heterogeneity of the
medium; those, in their turn, can bring about more physical effects. For example,
as it exceeds a certain threshold value, the high density of energy release in thin
capillaries can cause destruction of the cement and result in reconstruction of the
pore space structure of the medium. This effect was predicted theoretically and
confirmed experimentally in the mid 70s. Based on this effect, an essentially new
technology for stimulation of wells was developed, allowing for increase of well
rates in recovery of mineral resources (water, oil, metals).
Obviously, to describe a transfer in micro heterogeneous media and related
effects, one has to use 3D network models. Solving such problems (both static and
dynamic) by means of numerical simulation requires huge amounts of computer
time. In this case obtaining approximate analytical solutions using percolation
models is of a great interest.
More papers on fluid flow theory, purely computative [1-9] as well as both
computative and theoretical [10-16], using methods of percolation theory, began
to appear quite frequently in the last years. Experimental investigations in this
field come in a series of purely experimental [17 -22] or experimental and com pu-
tative [23, 24] studies, which combine numerical calculations with experimental

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