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

• Ting Zhang ^[1]
  1. [1] University of Lanzhou, China
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 277, Nº 1 (15 March 2015), 2015, págs. 47-56
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.09.001
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• Resumen

  • 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.