Abstract
In a finite difference scheme, continuous multi-phase flow variables that appear in conservation equations such as saturation are spacially discretized on grid blocks. When coarse grid blocks are used for reservoir simulation, the numerical solution tends to magnify the discretization error. This causes numerical errors called as coarse grid effect.
Through a coarse grid reservoir simulation, injection pressure showed quite difference with that of fine grid model.
This is because total mobility at the injection well is defined by the finite difference based average saturation in the injection well grid block. In other words, the saturation gradient that would appear in the near-well region is ignored in such coarse-grid system.
In this study, the areal average saturation in the injection well grid block was calculated analytically by the newly derived radial displacement approximation which was extende from the Buckley-Leverett linear displacement problem, taking account of pressure difference between the injection well and the injection well grid block. Consequently, the corrected total mobility was provided, by defining new value of total well index and transmissibility.
The injection pressure computed by this technique with for coarse grid model is reasonably agreed with the numerical solution of fine grid model. The practical application of the developed well-pseudo is validated through an actual reservoir simulation study.
