New Correlations for Calculation of Vertical Coverage and Areal Sweep Efficiency
- M.R. Fassihi (Arco Resources Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1986
- Document Type
- Journal Paper
- 604 - 606
- 1986. Society of Petroleum Engineers
- 6.5.2 Water use, produced water discharge and disposal, 5.7.2 Recovery Factors, 5.4.1 Waterflooding
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Summary. This paper presents two new correlations for calculating vertical coverage and areal sweep efficiency. Use of these correlations can facilitate the waterflood performance calculations.
The determination of coverage (vertical sweep efficiency) is an important step in forecasting the performance of any waterflood project. This parameter is a function of the mobility of the injected fluid to the mobility of reservoir oil, M; the WOR, F and the Dykstra-Parsons permeability variation, V. The coverage curves first permeability variation, V. The coverage curves first introduced by Dykstra and Parsons have been widely used in the oil industry. Generally, these curves are available at each WOR as a function of V and M (Fig. 1). Thus for any coverage calculations, a set of curves at WOR's of 0.1, 0.2, 0.5, 1, 2, 5, 10, 25, 50, and 100 is needed.
For numerical simulation studies, it is most efficient to use equations of these curves or to find a correlation parameter that can reduce these curves into one curve. parameter that can reduce these curves into one curve. Recently, the latter task was accomplished by desouza and Brigham, 2 who grouped the coverage curves for 0 less than M less than 10 and 0.3 less than V less than 0.8 into one curve by regression analysis. These authors used a combination of F , V, and M in a parameter henceforth referred to as the Y correlation parameter. The equation for Y is
Fig. 2 shows the data of Dykstra and Parsons plotted against the Y parameter. The curve suggested by desouza and Brigham is also plotted in this figure. As shown, the Y parameter effectively groups these data together.
To simplify the calculations further, this graph was curve-fitted. The following equation was found to match this curve very closely:
where a =3.334088568, a =0.7737348199, and a = - 1.225859406. The comparison between the
Dykstra-Parsons coverage curves and C calculated with Eq. 2 is shown in Table 1 and Fig. 2. In this table, C was calculated for different F , M, and V with both Eq. 2 and the coverage curves. As shown, there is a close agreement between the C values calculated with Eq. 2 and deSouza and Brigham's curve. Notice that the same restrictions that are imposed on desouza and Brigham's curve are also true for Eq. 2 (i.e., this equation is valid only for 10 greater than M greater than 0 and 0.8 greater than V greater than 0.3).
Areal Sweep Efficiency
Areal sweep efficiency, E, is the fraction of the pattern area contacted by water. E is a function of the pattern geometry, mobility ratio, M, and the amount of water injected, W . Dyes et al . measured E for five-spot, direct line drive, and staggered line drive in a homogeneous, two-dimensional (2D) model with the X-ray shadowgraph technique. Their data are currently used as the standard procedure for calculating E in the waterflood monograph . The Dyes et al. data were curve-fitted by use of a nonlinear regression program. The equation used was
The coefficients of Eq. 3 for patterns such as five-spot, staggered line drive, and direct line drive are provided in Table 2. These coefficients are valid both before and after breakthrough for mobility ratios in the range of 0 less than M less than 10. This restriction is caused by the limitation of their experimental data to these mobility ratios. The comparison between the actual and the correlated sweep efficiencies is very good, as shown in Fig. 3.
Notice that the Dyes et a 1. 3 data for the five-spot pattern approaches 1 at a mobility ratio of 0.17, contrary to the fact that E should reach 1.0 only at zero M. Also, these data are generally higher than those reported by later investigators in better-scaled experiments, especially at higher mobility ratios.
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