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.

are very useful. Recently, Fassihi [291] provided correlations for the calculation of areal and vertical sweep efficiencies. For these correlations of areal sweep, the data of Dyes, Caudle, and Erickson [281] were curve-fitted and the resulting equation was:

where E, is the -areal sweep efficiency which is the fraction of the pattern area contacted by water, M is the mobility ratio, and the coefficients are as listed in Table 5-40 for the 5-spot, direct line drive, and staggered line drive. These coefficients are valid both before and after breakthrough, and apply to mobility ratios between zero and ten, which is within the range observed in many waterfloods. For the 5-spot pattern, these values of E, are generally higher than in later experiments, and a correction has been suggested by Claridge [292] that should be multiplied by the E, from the Dyes et al. data: