Page 373 - Petrophysics

CENTRIFUGE MEASUREMENT OF CAPILLARY PRESSURE 34 1

data that have an increasing negative error as the wetting-phase saturation
decreases. Curve 4 shows the results of the Van Domselaar’s equation that
is apparently more accurate than the Hassler and Brunner approximate
solution at the higher wetting-phase saturations. But as the wetting-phase
saturation decreases, it introduces an increasing positive error in the
calculated capillary pressure. It is apparent that the accurate calculation
of (Pc)i versus Si can be obtained using Rajan’s equation, which is
theoretically exact because it correctly models the physics of the problem
and does not contain simplifying assumptions.
The recommended procedure is to:

(1) fit the experimental (Pc)i versus S data to the least-squares hyperbolic
expression;
(2) evaluate the derivatives at specific values of S and their corresponding
(Pc)i;
(3) obtain Si corresponding to each (PJi, from a computer solution of
Equation 5.52; and
(4) establish a table of values of (Pc)i versus Si to plot the capillary
pressure curves and to evaluate wettability and the thermodynamic
energy required for immiscible fluid displacements.

EXAMPLE

Prepare the capillary pressure versus inlet saturation curve based on the
centrifuge displacement of water by air. Data: L = 2.0 cm; d = 2.53 cm;
Vp = 1.73cm3; k = 144mD; centrifuge arm - = 8.6cm; water-air
density difference = 0.9988; porosity = 0.17. The experimental data for
an air-displacing-water capillary pressure experiment and the calculated
capillary pressure (in psi) obtained from Equation 5.31 are presented in
Table 5. la.

SOLUTION

Table 5. lb presents the least-squares regression procedure for
calculation of Pc as a function of S, whereas Figure 5.20 shows a
comparison of the raw data versus the smoothed data obtained from
the hyperbolic function.

The hyperbolic function (A + B x S)/(l.O + C x S) was then used to
obtain the inlet saturation using the Hassler-Brunner method. The data
presented in Table 5.lc and Figure 5.20 shows a comparison between
the average and the inlet saturation.