The 3-D and 2-phase flow of oil and water in non piston-like displacement of horizontal and vertical well patterns was studied by using the pseudo three-dimensional methodology and on the basis of theoretical analysis with the 1-D and 2-phase percolation theory of oil and water. By adopting a suitable conformal transformation, the complex 2-D and 2-phase flow in XY plane of horizontal wells can be changed into a simple 1-D and 2-phase flow to determine the seepage flow resistance in this plane. The liquid production rate and dimensionless liquid production rate of horizontal well can be determined by each parts of resistances. According to the dimensionless pre-water and after-water breakthrough time and dimensionless time in 1D and 2-phase flow, the dimensionless water breakthrough time and dimensionless time under the well-pattern condition can be deduced. The variations of dimensionless water-injection rate and injection rates in the vertical well are determined by dimensionless liquid production rate in horizontal well. This theory can provide valuable basis for dynamic analysis and prediction of integral water-flooding development.
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