Page 378 - Petrophysics 2E

346 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Pore size distributions are used to analyze reductions of permeability
caused by clay swelling; precipitations of organic matter in pores-for
example, asphaltenes and paraffins; particle migration; and growth of
microbes in pores [26-291.
The procedure to determine the pore size distribution of cores is to:

1. Obtain air-brine inlet capillary pressure (Equation 5.22) versus average
saturation data using the centrifuge method.
2. Obtain the three constants (A, B, and C) for the fit of the data to a
hyperbola using least-squares method.
3. Obtain the inlet saturation (Si) that corresponds to the inlet capillary
pressure (Pd), or obtain the exact solution (Equation 5.46 or
Equation 5.52); use the hyperbola to obtain the derivative (dS/dPc).
4. Use the least-squares fit of the Pd versus Si data to obtain the A, B, and
C constants for the hyperbola Pci = (A + BSi)/(l + CSi).
5. Extrapolate the Pci versus Si curve to Si = 1.0 to obtain the correct
threshold pressure (PD) that corresponds to the largest theoretical
pore entry size (rmax = 20/PD).
6. Obtain a table of rj versus Pcj for specific values of Sij (rj =
Z/Pcj from Si = 1 to Si,).
7. Differentiate the hyperbola to obtain dSij/dPcj at each point (j).
8. Calculate the pore throat size distribution from Equation 5.58.

EXAMPLE

Use the capillary pressure data for air displacing water from the Berea
Sandstone core presented in the Example on page 342 (Table 5.la) to
calculate the pore throat size distribution.
The inlet saturation and capillary pressure from the earlier Example are
listed in Table 5.2 together with the pore throat size distrubtion, D(ri),
as a function of the pore throat radius, 4, and the results are shown in
Figure 5.21.

SOLUTION

The maximum pore entry size (10.59 pm) occurs at S, = 1.0, and the
minimum pore size that will conduct fluid occurs at the irreducible water
saturation (0.27 pm).

VERTICAL SATURATION PROFILE IN A RESERVOIR

Welge and Bruce derived the capillary pressure equation from the
equilibrium of vertical forces in a capillary tube [30, 311. The weight