Page 411 - Petrophysics 2E

EVALUATION OF WETTAElILITY 379

2. the free energy change resulting from the change in pressure which
is experienced by the element of water when it is transferred from h
to h + dh:

(6.18)

6F
- =AV (6.19)
FPW

The expression for the total change of free energy, resulting from
the change in the height of the element of water, is obtained by taking
the total derivative with respect to the height and pressure and then
substituting Equations 6.18 and 6.19 into it:

(6.20)

pwgc AVdh + AVdp, = 0 (6.21)

pwgc dh + dp, = 0 (6.22)

Since the same derivation can be made for any phase:

When the capillary pressure expressed by Equation 6.24 is zero, one
of two conditions exists: either the two phases are completely miscible
or a single phase exists. Because two immiscible phases are considered
in Equation 6.24, the only condition in which the capillary pressure may
be zero is when there exists only one phase at some point within the
column. If the column is sufficiently high and enough time is allowed
for equilibrium to be attained between the two fluids, no oil will be
found below some level in the column due to gravity segregation. This
is the free liquid surface (h = 0 at this point as a boundary condition for
Equation 6.19).