三维多孔介质中应力与渗流的摄动有限元分析

Perturbation and Finite Element Analysis for Stress-Seepage Coupled Problems in Three Dimensional Porous Media

提出了一个较为实际的石油油藏的三维力学模型。以已有的三维介质中应力与渗流耦合问题的变分原理为基础，用摄动法证明了当油藏厚度变化为小量时，三维问题可简化为平面应变问题，并可采用不同厚度的平面应变单元进行有限元分析，所得到的解即是该三维问题的零阶摄动解。此外，给出了摄动法的推导和有限元格式。

This paper presents a practical model of oil formation for oil field recovery. Based on stress-seepage coupled variational principles, we prove by using the perturbation method that the three-dimensional probem can be simplified to a modified plane-strain problem with variable thickness of the oil formation if the thickness varies slightly in the horizontal plane. The solution then obtained is the zero-order perturbation solution. The elemental matrices and global finite element equations are given for the modified plane-strain problem.