Page 213 - Petroleum Geology

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izontal reference plane to a plane inclined in the direction of motion, and its
normals are similarly rotated, of course, from the vertical. Surfaces of equal
potential (the equipotential surfaces) are normal to the direction of motion,
surfaces of equal pressure are inclined in the direction of motion, and a com-
ponent of lateral motion is imparted to migrating petroleum. The magnitude
of this component depends on the density difference between the petroleum
and the water, in such a way that as the density of the petroleum approaches
that of the water, the more nearly do their directions of motion coincide.
The direction of gas migration across a carrier bed will be more nearly vertical
than that of oil.
The direction of water movement is the resultant of two forces: the force
of gravity acting on unit mass of the water, and the force due to pressure act-
ing on unit mass of the water. The resultant is the impelling force acting on
unit mass of the water; and, like the others, it has the dimensions of an ac-
celeration (LT2), and it is the potential gradient (Fig. 9-6).
At any point in the water, and at any point capable of being occupied by
the water, the water has a potential. When the water is at rest, the potential
is constant through the body of water: when the water is in motion, the po-
tential is not constant but decreases in the direction of flow. The water flows
in a direction normal to the surfaces of equal potential, which can be mapped
through the body of water.
A measure of the water potential at a given point (eq. 8.12, p. 171) is:

P
h=-+z
Pg
where h is the total head, plpg is the pressure head, and z is the elevation
head (or simply, elevation) of the point relative to an arbitrary datum level
(negative downwards).
Oil in the water also has a potential, and it tends to move in a direction
normal to its equipotential surfaces. If we consider a small volume of oil
migrating, a measure of this potential is:

and since the capillary pressure is a very small part of the pressure in the oil
in an aquifer at the depths that we are concerned with, we can take the pres-
sure p to be the ambient water pressure that would exist at that point. Solving
eq. 9.2 for p, and substituting it into eq. 9.3, we get:

where z is, as before, positive when measured upwards above the arbitrary
datum.
Following Hubbert (1953, p. 1991, footnote 3) we divide eq. 9.4 by (p -pJ
Po: