Page 133 - Percolation Models for Transport in Porous Media With

126 CHAPTER 6. PORE SIZE DISTRIBUTION

"one-humped"
2
/in(r) = (2xfro) exp( -x )
and "two-humped"
2
2
/in(r) = (0.3y'iT0)- {exp[-(x- Xt) fa)+ exp[-(x- x2) fa]},
1
x = rfro; ro =10- m; x1 = 0.4; x2 = 0.8; a= 0.15
4
are presented in fig. 47 to illustrate the efficiency of the method. In both cases
/in(r) are shown by continuous lines and the recovered distributions, by dotted
lines. The curves f(r) are compared in the interval of recovering 0 ::; r ::; rc. To
the right of rc, the function f(r) can be merged with the exponential dependence
f(r)- r-j, as it was mentioned in §6.3.
The scheme of the electric porometry method (see fig. 41) was used to recover
the PDFC for an actual sandstone rock with different degrees of cementation.
These rocks are grained media with twofold (capillary and pore) porosity. Exper-
imental data were processed according to the procedure described in §6.2 (using
the effective medium model) by means of solving the system (6.26) using the reg-
ularization method. Examples of the recovered PDFC are shown in fig. 48. In the
same figure, the functions f(r), obtained using the ICP model according to the
analytical formula (6.18), are presented. It can be seen that the formula (6.18)
permits to correctly estimate the characteristic radii of capillaries and the variance
of PDFC, but rather roughly describes the true distribution f(r).
Thus the presented results of the numerical simulation and model data pro-
cessing demonstrate the efficiency of the ways used for interpretation of the ex-
perimental data for the recovering of the radius probability density function for
capillaries in media with porosity of different scale described in this chapter.