Page 117 - Percolation Models for Transport in Porous Media With

110 CHAPTER 6. PORE SIZE DISTRIBUTION

The desired dependence rk(S) can be found from this equation, if the experi-
mental dependence p1{S) is known. At the time of trapping, the pressure in the
gas phase coincides with the pressure Po in the outer cross-section of the core;
therefore, the initial condition for the equation {6.12) is

rk(S') = 2x cosO
c Pl(S~)-po
When the displacement is over, the value of porosity cp can be found as the
ratio of the volume of mercury that has entered the pores to the volume of the
core. This quantity can be also calculated as the product of the average capillary
volume and the concentration of the edges of the network
00
cp = 1r;~z J f(r) dr {6.13)
2
r
0
The last expression represents another correlation between the constants z and
l of the network.
Thus the formulas {6.5), {6.8), {6.12) permit to find the dependencies X(rk)
and J(rk) for the given l and z. To determine the constants z and l from the
relationships {6.9) and {6.13), an iterative procedure is set up with respect to
these parameters. Once this is done, the quantity V is found from the relationship
{6.6), and the dependencies X(rk) and f(rk) are determined in the domain of the
macro-pores using this quantity at the first stage of displacement.
The presented algorithm of data interpretation in mercury porometry was ob-
tained for model II. Without drawing close attention to it, we note that the equa-
tions describing the sequence of stages for mercury injection in a porous medium
for model I can be derived in a similar fashion.
Results of the calculations using experimental data. To demonstrate
the efficiency of the outlined method for the experimental data interpretation,
we shall present the calculations for the experiment on the displacement of air
by mercury from a core extracted from the East-Poltavian layer (data given by
N. V. Savchenko). The plot of the X(S) relationship for this core appears in fig.
38. The obtained dependence proved to be stable with respect to small changes
of the initial conditions. The value of Sc close to zero and the value of S~ close to
unity are characteristic of this dependence. For the specimen under consideration,
Sc = 6.5 · w- , S~ = 0.964.
4
The curve I in fig. 39 corresponds to the initial experimental data. The curve
I I is obtained, if a relative error of 0.05 is allowed in determining the quantity
S. The greatest difference between the two curves is achieved at the values of rk
corresponding to the third stage of the experiment and makes 15%. For the first
two stages this difference does not exceed 5%. As the relative error goes down,