Page 308 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Fluid Movement in Waterflooded Reservoirs 975

- For a liquid-filled, linear system, the average water saturation at breakthrough,
Swbr, is:

(5-213)

where Siw is the irreducible or connate water saturation. If Equation 5-209 is
substituted into Equation 5-213:

- 1 s -siw
s,, - s, = - = wf
(df,l f, (5-214)

where S, is the water saturation at the flood front and fw, is the water cut at
the flood front. After breakthrough, water saturation is obtained from Equations
5-211 and 5-212 where, as mentioned earlier: (1) the tangent point, S,, repre-
sents the water saturation at the producing end of the system, (2) the value of
E, at the point of tangency is the producing water cut, (3) the saturation at which
the tangent intersects fw = 1.0 is the average water saturation, and (4) the inverse
of the slope of the tangent line is equal to the cumulative injected fluid in pore
volumes (Qi). If connate water is mobile, appropriate corrections need to be
made [133].
Oil production at breakthrough can be computed from [278]:

(5-215)

After water breakthrough, a number of saturations greater than Sw,are selected;
the slope of the tangent line and average water saturation are determined for
each value of Sw chosen. Oil production after breakthrough is then determined
by observing the change in water saturation [278]:

ANp = -(Sw - -3**)
Bo (5-2 16)

The incremental oil production from Equation 5-216 can be added to the
breakthrough production from Equation 5-215, and the resulting total production
for the linear system can be listed as a function of Sw, time, or other parameters.
If the pore volumes in these equations are in ft3, divide by 5.615 to get barrels.

Viscous Flngering

A problem often encountered in the displacement of oil by water is the
viscosity contrast between the two fluids. The adverse mobility ratios that result
promote fingering of water through the more viscous crude oil and can reduce the
oil recovery efficiency. An example of viscous fingering is shown in Figure 5-156.