New Numerical Schemes for Near-Well Modeling Using Flexible Grids

Abstract

Summary Control-volume schemes are discussed for the modeling of vertical wells using flexible grids. The main difficulty of well modeling in reservoir simulation is the problem of the difference in scale between the reservoir size (several kilometers) and the wellbore radius (several centimeters). In applications, although the wellbore boundary can be discretized using flexible grids, the gridblocks in the vicinity of the well 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 commonly used linear approach (that is linear with respect to coordinates of physical space) inefficient for near-well flow modeling. In this paper, new numerical schemes, based on logarithmic approach, are proposed to improve the linear approach for nearwell modeling. In particular, a multipoint and a two-point flux approximation scheme are presented. These schemes can reduce the calculation errors for the dominant "singular" well flow and consequently give good results. The proposed approach can be used for any kind of flexible grid for near-well modeling.