The Change Of Wor Vs. Dimensionless Time

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As Yortsos et al. (1999) have shown in their work, the change of WOR vs. dimensionless time is governed by the time regime. He distinguished four such time regimes: Early time, before water breaks through the layers of a reservoir (Fig. 1, b) in which WOR remains almost constant; The stage immediately following water breakthrough, when water saturation near the producer is low (Fig. 1, c). This regime can be analysed using the 1D displacement equation for intermediate values of water saturation (Eq. 8) which suggests that at intermediate values of water saturation at the producer,S_w^*≤0.5, the WOR-time relationship is described with a linear function of logW vs. logt with slope 1. Intermediate time between (ii) and (iv), reflecting…show more content…
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Figure 1: Four representative stages of a linear waterflood at interstitial water saturation. Injection of water causes oil to be displaced from the reservoir resulting in a water saturation gradient (Willhite,1986)

Figure 2: Areal X-ray shadowgraphs of flood progress in scaled five-spot patterns showing areal sweep efficiencies of two model floods for two mobility ratios (Willhite,1986)

Fig. 3 shows how WOR varies over time for one of the numerical wells created in a numerical simulation model for the Wytch Farm Field, UK.

Figure 3: Illustration of a typical WOR vs. dimensionless time dependence showing the four distinct time regimes Figure 4: A plot of log[(1+W)2/(Wt)] vs. log W showing that in the case of large M, the cross-plot conditions described by Eq. 8 apply over a wide range of WOR (b=2.0) (Yortsos et al., 1999)
Using diagnostic plots of log[(1+W)2/(Wt)] vs. logW Yortsos et al. (1999) showed numerically that for large water oil viscosity ratio and small Corey exponent to oil, the flood front water saturation is relatively low. As a result the behavior immediately following breakthrough described by Eq. 8 is valid over a wide range of WOR, in which case the ratio [(1+W)2/(Wt)] remains approximately constant for an extensive range of WOR. Conversely, for small viscosity ratios, the late time behavior becomes dominant at much lower values of WOR. His studies were supported by numerical
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