底水油藏水平井的合理位置多目标优化

Multi-Objective Optimization of Optimum Location of Horizontal Wells in Bottom Water Reservoir

底水油藏水平井垂向位置是影响水平井开发效果的重要因素。利用有限Fourier正弦变换和源函数理论求解三维稳态渗流方程,得到了圆柱形底水油藏水平井的产能、临界产量和见水时间公式。以水平井垂向位置为决策变量,建立了以其产量、临界产量和见水时间为目标函数的多目标优化模型。实例计算结果表明,水平井在底水油藏中的合理位置约为油藏厚度的4/5。这为水平井开采底水油藏的优化设计提供了理论基础,对实现水平井的稳产及延长无水开采期具有重要的理论和现实意义。

The vertical location of a horizontal well in the bottom water reservoir is an important factor affecting the effective exploitation of the well. Based on the finite Fourier sine transform method and the source function method, the three-dimensional steady-state seepage equation is solved for the pressure in a cylindrical reservoir with no-flow at the top and lateral boundary and constant pressure at the low boundary. From the pressure solution, the production equation, the critical production formula and the water breakthrough time formula of the horizontal well in the bottome water reservoir are developed. From the theory of multi-objective optimization, a multi-objective optimization model is proposed, in which the production, the critical production and the water breakthrough time of the horizontal well are treated as an objective function and the vetical location of the well as a decision-making variable. For a given example, the optimum vertical location of the horizontal well in the bottom water reservoir is located at about 4/5 times the thickness of the reservoir. This research result provides the theoretical basis for the optimization design of horizontal wells in reservoirs with bottom water,with theoretical and practical significance for stable production and longer water free production period.