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This chapter discusses water-oil displacement phenomena in two dimensions, either areal or vertical. The purpose of this chapter is to illustrate the characteristics of the water-oil displacement for 2D flow situations. In the early methods, various simplifying assumptions had to be made to solve each particular flow problem. For the 2D areal (XY) flow situations, the porous medium was assumed to be homogeneous, and then simple methods were developed that could be used to quantify the efficiencies of the displacement for particular injection/production-well geometries and reservoir descriptions. For the 2D cross-sectional (XZ) flow situations, the models studied were simple stratified layered systems, many with noncommunicating layers. Also described are the variety of historical methods developed to estimate oil recovery in noncommunicating 2D layered reservoirs. Although very simplified, these 2D methods allow rapid preliminary calculations for screening economic alternatives from improved oil recovery by means of waterflooding.

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