Abstract: 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 1-D 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.

Key words: multilateral horizontal well, vertical well, well pattern, water-flooding development, productivity calculation, oil-water 2-phase percolation theory

摘要： 根据拟三维原理,将理论分析方法和一维油水两相渗流理论相结合,求解分支水平井和直井混合井网三维两相非活塞渗流问题。采用适当的保角变换,将XY平面二维两相复杂渗流问题转化为一维两相问题求解,从而确定出水平井在油水两相流条件下XY平面内的渗流阻力,根据各部分的渗流阻力,确定出水平井的产液速度和无因次产液速度;根据一维渗流条件下见水前后的无因次时间和无因次见水时间,确定出井网条件下见水前后的无因次时间和无因次见水时间。根据水平井的无因次产液速度确定出直井的注水速度,无因次注水速度随时间的变化规律。该理论的建立为水平井整体注水开发油田的动态分析和预测提供了依据。

关键词: 分支水平井, 直井, 井网, 注水开发, 产能计算, 油水两相渗流理论