Page 121 - Percolation Models for Transport in Porous Media With

114 CHAPTER 6. PORE SIZE DISTRIBUTION

Figure 42: Modified scheme of measurements in the electric porometry method

capillaries of some effective radii.
Introduce some complimentary simplifying assumptions. Consider the network
simple cubic and the vector E of the applied electric field collinear to the vertical
edges of the network. For the chosen type and orientation of the network, only
vertical capillary chains play an essential part: the transverse bonds affect the
general picture of the current flow in the medium rather weakly, since they are
perpendicular to the vector E. In this model we can take the ICP approximation,
which proves to be more relevant and justified with EPM than with the mercury
porometry method. In this case it is possible, using the ICP model, to analytically
solve in the explicit form both the direct and the reverse problems of electric
porometry.
Suppose the pore space of the core consists of a system of vertical cylindrical
pores distributed with respect to radii with the PDF f(r). Establish the correlation
between the integral electric conductivity a of a specimen portion as a function
of height L and the radius PDF for capillaries. (The scheme of measurements is
represented in fig. 42.) Taking into account the fact that all pores are connected
successively, we obtain
J
N r(L)
L }
2
a(L) = ?= Ri Ti < r(L) = S* Nb1r f(r)ae(r /l) dr,
t=l 0
where S* is the cross-section of the specimen, N L is the total number of saturated
pores in the specimen at the height L.
Introduce the mean square radius at the height L