New Numerical Schemes for the Near-Well Modelling with Discretization Around the Wellbore Boundary Using Flexible Grids

Abstract

Abstract The control-volume schemes are discussed for the modelling of vertical wells using flexible grid. The main difficulties of the well modelling in the reservoir simulation is the problem of the scale between the reservoir size (several kilometers) and the wellbore radius (several centimeters). In applications, although the wellbore boundary can be discretized using the flexible grid, the gridblocks in the well vicinity are usually not small enough compared to the wellbore radius, and the gridblock sizes vary usually geometrically in the radial direction from the well. This kind of grid makes the standard linear approach inefficient for the near-well flow modelling. In this paper, new numerical schemes, which are based on logarithmic approach, are proposed to improve the standard linear approach for the near-well modelling. In particular, a multi-point and a two-point flux approximation scheme are presented. These schemes can reduce the calculation errors for the dominating "singular" well flow. Consequently, good results are obtained with these new schemes. The proposed approach can be used for any kind of flexible grid for the near-well modelling.