Page 32 - Percolation Models for Transport in Porous Media With

Chapter 2

Percolation Models of

One-Phase Flow in Rocks of

Different Types

There are many types of pore space structure in natural rocks. We consider oil
and gas reservoirs as well as hydrogenous water- and ore-bearing strata. These
formations break up in three fundamental groups, namely grained, cavernous,
and fractured reservoirs. There also exist rocks of a mixed type, e.g., fractured-
cavernous, fractured-porous, etc. Inside each group, it is possible to describe
conductivity of the reservoir rocks using the model of a heterogeneous medium
(see chapter 1), if the distribution of conducting structural elements with respect
to intrinsic conductivities is defined.

2.1 Conductivity of Grained Media

Consider a specimen of an infinite grained medium with grain centers arranged
in cyclic symmetry and whose grains have equal diameters (see fig. 5). In such
a medium fluid can flow only along the thin channels which connect the large
pores. The channels between the pores can be partially or entirely trapped by
a cementing substance, and therefore channels have different cross-sections. It is
possible to characterize conducting properties of each channel by the parameter r,
the effective radius of the channel. Suppose the conducting channels with different
rare distributed randomly with the probability density function f(r). Percolation
theory treats large pores as sites and the thin channels as bonds between them.
When centers of grains are arranged in cyclic symmetry, the system of channels

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