Page 64 - Percolation Models for Transport in Porous Media With

56 CHAPTER 3. PERCOLATION MODEL OF FLUID FLOW

for g0 (r) = C0r-h(h = 1.5; 2; 2.5; 3) and of f(r) in the form (3.46) showed that in
this range of G, changes of the permeability are very notable (by tens of times),
and the greater h, the sharper the changes.
Using the experimental distribution function of [48], which corresponds to
{3.46) for i = 4 and a* = 25JLm, numerical calculations were carried out for
the change of permeability of the medium when the relative elastic deformation of
all capillaries in the conducting r 1-chains is the same {Hooke's law). The value of
Young's modulus was taken as usual for sandstones, E = 10 4 MPa (fig. 15).
Such sensitivity of the specimen's permeability towards its squeezing even with
a small pressure (when the majority of deformations is elastic) is due to the fact
that a good deal of r 1-chains, where the thinnest capillaries become completely
filled with the bounded fluid, is excluded from the fluid flow. The described
sensitivity is higher when the variance of f(r) is less.
Also note that the calculations carried out for the model in which the pore space
of the medium is presented as a body of parallel tubes with constant radii gives
a low (several per cent) change of the permeability, if the layers of the bounded
fluid in thin tubes are taken into account, and deformations caused by squeezing
the specimen are mostly elastic.
Thus the structure of the pore space of the medium can notably affect laws for
macroscopic fluid flow, since various types of flow can take place at the micro level
in such a medium. Therefore knowledge of merely the macroscopic parameters of a
heterogeneous medium (i.e., some average coefficients of permeability and porosity
or the average pore size) does not suffice to describe the fluid flow for different
pressure gradients.