Application of Dimensional Analysis to Water Flooding Problems

Abstract

The author applied method of dimensional analysis to 2-fluid flooding problems in dipping reservoirs. The principal results obtained are as follows.1) Applying the method to 2-well system (Fig. 2), we can see the outlines of these following items. Pressure distribution (Eq. 1), well-pressure difference (Eq. 2) and breakthrough time (Ep. 3) are obtained when both injection rate and production rate are constant. Pressure distribution (Eq. 4), injection rate, production rate (Eq. 5) and breakthrough time (Eq. 6) are as well obtained when injection pressure and production pressure are constant.2) Similarly when the method is applied to multiple-well system (Fig. 3) the following items come into our possible insight. Pressure distribution (Eq. 7), well-pressure difference (Eq. 8), break-through time (Eq. 9) and sweep efficiency (Eq. 10) are obtained when injection rate and production rate are constant. And, again, pressure distribution (Eq. 11), injection rate, production rate (Eq. 12), breakthrough time (Eq. 13) and sweep efficiency (Eq. 14) are obtained when injection pressure and production pressure are constant.3) Dimensions of various quantities in general flooding problems are shown in Table 1.4) Dimensionless quantities in general flooding problems are enumerated in § 6.1 and § 6.2.