Page 404 - Fundamentals of Reservoir Engineering

IMMISCIBLE DISPLACEMENT 339

Consider a volume of water contained between two spherical sand grains, in a water
wet reservoir, as shown in fig. 10.2.

ROCK

WATER
r 1 x

OIL r 2

Fig. 10.2 Water entrapment between two spherical sand grains in a water wet reservoir

In applying equ. (10.1) to calculate the capillary or phase pressure difference at point X
on the interface, one of the principal radii of curvature, say, r 1, is positive, since it is
measured through the oil, while the other, r 2, which is measured through the water, is
negative. Since r 1 < r 2, however, the capillary pressure is positive. What is also evident
from fig. 10.2 is the fact that as the volume of water (water saturation) decreases, the

radii decrease, and therefore there must be some inverse relationship between P c
and S w.

This relationship is called the capillary pressure curve (function) and is measured
routinely in the laboratory. Typically, such experiments are conducted, for convenience,
using air-brine or air-mercury fluid combinations and the resulting capillary pressure
3,4
curve converted for the oil-water system in the reservoir . For the sake of consistency,
however, a hypothetical experiment will be considered, firstly for the (non-commercial)
case of oil displacing water, in a water wet core sample, and then the displacement
process will be reversed. The results of such an experiment are shown in fig. 10.3.

B

P
c

DRAINAGE

IMBIBTION

C C A

1 - S or 100%
S wc
S (% OF PORE VOLUME)
w
Fig. 10.3 Drainage and imbibition capillary pressure functions