Page 314 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Fluid Movement in Waterflooded Reservoirs 281

Areal or Pattern Sweep Efficiency (E,)

Areal sweep efficiency of an oil recovery process depends primarily on two
factors: the flooding pattern and the mobilities of the fluids in the reservoir.
In the early work on sweep efficiency and injectivity, Muskat and coworkers
[25,280] presented analytical solutions for direct line drive, staggered line drive,
hpot, ?spot, and $spot patterns (patterns were discussed earlier; see Figure 5150).
Experimental studies on the effect of mobility ratio for different patterns were
presented by Dyes, Caudle, and Erickson [281] (5-spot and line drives); Craig,
Geffen, and Morse [282], Prats et al. [283], Caudle and Witte [284], and
Haberman [285] (5-spot); and Kimbler, Caudle, and Cooper [286] (9-spot). The
effect of sweepout beyond the pattern area was studied as well [287,288]. From
a mathematical study the breakthrough sweep efficiency of the staggered line
drive was presented by Prats [289]. A comparison of the areal sweep efficiency
and the ratio d/a is shown in Figure 5-159 for direct and staggered line drives
[25,289], and a review of the early work was provided by Crawford [290].
Areal sweep efficiency at breakthrough for a 5-spot pattern is shown in Figure
5-160, and the effect of mobility ratio on areal sweep is shown in Figure 5-161.
These figures show that areal sweep efficiency is low when mobility ratio is high
(note that the data in Figure 5-161 from Dyes, Caudle and Erickson are plotted
in terms of the reciprocal of mobility ratio as currently defined). Areal sweep
efficiencies at breakthrough, for different patterns and a mobility ratio of one,
are summarized in Table 5-39 [133,277,279].
Areal sweep efficiency is more important for considering rate vs. time
behavior of a waterflood rather than ultimate recovery because, at the economic
limit, most of the interval flooded has either had enough water throughput to
provide 100% areal sweep or the water bank has not yet reached the producing
well so that no correction is needed for areal sweep [133].
When waterflooding calculations are performed, especially with computers
or programmable calculators, the use of equations with adjustable coefficients

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z I
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k 0.6 - -
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5 0.4 - -
3 I Direct Line Drive - Muskat
in - 2 Staggered Line Drive- Muskat
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J 3 Staggered Line Drive - Prats
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