Page 63 - Principles of Catalyst Development

44 Principles of Applied Reservoir Simulation

Qi =

where Q i is the cumulative pore volume of injected water. The slope of the water
fractional flow curve with respect to water saturation evaluated at the water
saturation at breakthrough gives Q ( at breakthrough.

Effects of Capillary Pressure and Gravity
In the absence of capillary pressure and gravity effects, the flood front
propagates as a "sharp" step function, or piston-like displacement. The presence
of capillary pressure leads to the imbibition of water ahead of the front. This
causes a change in the behavior of produced fluid ratios. Rather than an abrupt
increase in WOR associated with piston-like displacement, the WOR will
increase gradually as the leading edge of the mobile water reaches the well and
is produced. In addition, the WOR will begin to increase sooner than it would
have in the absence of capillary pressure. By contrast, gravity causes high S w
values to lag behind the front. The result is a smeared or "dispersed" flood front.

5.3 Miscible Displacement

Buckley-Leverett theory treats the displacement of one fluid by another
under immiscible, piston-like conditions. An immiscible displacement occurs
when the displaced and displacing fluids do not mix. The result is a readily
discernible interface between the two fluids. In a miscible displacement, the
fluids mix and the interfacial tension approaches zero at the interface. A miscible
displacement system is described by a convection-dispersion (C-D) equation.
As an illustration, consider the one-dimensional C-D equation for the concentra-
tion C of the displacing fluid:
2
d C BC dC
n
D v = — f5 16\
dx 2 dx dt IJ 10J
'
We assume here that dispersion D and velocity v are real, scalar constants. The
2
diffusion term has the Fickian form D'd C/dx 2 and the convection term is
vdC/dx. When the diffusion term is much larger than the convection term, the