Page 302 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Fluid Movement in Waterflooded Reservoirs 269

FLUID MOVEMENT IN WATERFLOODED RESERVOIRS

Many of the principles discussed in this section also apply to immiscible gas
injection, primary recovery by gravity drainage, and natural bottom-water drive.
However, because of the importance of waterflooding in the United States, the
emphasis is placed on fluid movement in waterflooded reservoirs.
The importance of various factors that affect displacement of oil by water were
discussed in the first section. In particular, the discussion on the effect of
wettability on relative permeability characteristics is important in the under-
standing of oil displacement during waterflooding.
Several textbooks on waterflooding are available [ 133,254,276-2781. The
source most often referred to in this section is the excellent SPE monograph
by Craig [133]; many of the principles in this monograph are summarized in
the Interstate Oil Compact Commission text [277] and in an SPE paper [279].
The text by Smith [254] contains many useful aspects of waterflooding, and the
recent SPE text 12781 contains a more thorough and mathematical treatment of
the subject.

Displacement Mechanisms
Under ideal conditions, water would displace oil from pores in a rock in a
piston-like manner or at least in a manner representing a leaky piston. However,
because of various wetting conditions, relative permeabilities of water and oil
are important in determining where flow of each fluid occurs, and the manner
in which oil is displaced by water. In addition, the higher viscosity of crude oil
in comparison to water will contribute to nonideal displacement behavior.
Several concepts will be defined in order that an understanding of displacement
efficiencies can be achieved.

Buckley-Leverett Frontal Advance. By combining the Darcy equations for the
flow of oil and water with the expression for capillary pressure, Leverett [loo]
provided an equation for the fractional flow of water, fw,at any point in the
flow stream:

(5-204)

where f, = fraction of water in the flowing stream passing2ny point in the rock
(i.e., the water cut)
k = formation permeability
k, = relative permeability to oil
k, = effective permeability to oil
k, = effective permeability to water
p,, = oil viscosity
p, = water viscosity
vt = total fluid velocity (i.e., qJA)
Pc = capillary pressure = p, - p,, = pressure in oil phase minus pressure
in water phase
L = distance along direction of movement