Page 182 - Petroleum Geology

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if it were, it would be thick enough to flow and would drain to leave virtually
zero water saturation. It therefore follows that this water must be largely
concentrated around the grain contacts in pendular rings (Fig. 8-4) that are
not in hydraulic continuity with each other - as can be seen in drained pack-
ings of glass spheres.
This leads to two other questions: how big can such pendular rings be
without impinging upon neighbouring pendular rings? and, what is the maxi-
mum water saturation due to these rings?
Versluys (1916) approximated the shape of a pendular ring as a solid of
revolution of the area bounded by the arcs of three circles (Fig. 8-5), and
Rose (1958) showed this to be a close approximation. It can be shown
(Chapman, 1982) that the half-volume of a pendular ring so approximated,
relative to the volume of a single sphere (again, we must idealize the geometry)
is given by :
3 1 ff
v /2 = - (- -1)Z (1--) (8.3)
pr 4 sin (Y tan (Y
where (Y = (n/2) - 0. And it can also be shown by an argument similar to that
used for the specific surface, that the saturation is then given by:
(8.4)

Fig. 8-4. Water is concentrated as pendular rings around the grain-contacts.
Fig. 8-5. Idealized pendular ring geometry.