Petrov-Galerkin finite element approximation for the three dimensional well model

作者：Zhang Ting^*

来源：Journal of Computational and Applied Mathematics, 2015, 277: 47-56.

DOI：10.1016/j.cam.2014.09.001

• Well model
• Error estimate
• Petrov-Galerkin finite element method

Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. In petroleum extraction and exploitation, the well is usually treated as a point or line source, due to its radius is much smaller comparing with the scale of the whole reservoir. Especially, in 3-dimensional situation, the well is regarded as a line source. To capture the well singularity, a Petrov-Galerkin finite element scheme is developed. With this in hand, we then derive the error estimates and obtain the wellbore pressure directly without post-processing. Some numerical tests are presented to demonstrate the effectiveness of the proposed method.

• 出版日期2015-3-15
• 单位兰州大学