Effects Of Grid Systems on Predicting Horizontal Well Productivity

Abstract

Abstract This paper compares horizontal well performance simulated by a uniform coarse grid, a uniform fine grid, a nonuniform fine grid using the Peaceman's well model, and a non-uniform fine grid with explicit well modeling. An analytical solution is used to evaluate numerical solutions. We find that when a coarse grid is used to simulate a partially penetrating horizontal well, the fiow rate of the well is under-predicted, which means the well index calculated by Peaceman's method needs to be increased for the numerical simulator to predict the well productivity correctly. Peaceman's well model was developed for two-dimensional flow problems. Since these assumptions are violated for a partially penetrating horizontal well, Peaceman's formula does not accurately predict well performance. On the other hand, explicit modeling is a technique where the well blocks are of the same size as the well so that the well block pressure can be considered as the wellbore pressure. This eliminates the need for using a well index. However, our analysis shows that the non-uniform fine grid used for explicit modeling of wells, as reported in a recent paper, can lead to incorrect results. This is mainly because nonuniform grids can introduce large numerical errors into the computation of well block pressure which is made to be the same as the wellbore pressure, which is the explicit modeling technique. We demonstrate that the best way to obtain the correct well productivity is to use an appropriate analytical solution. When an analytical solution is not available, a uniform fine grid plus explicit well modeling can also yield correct results, but with large computational expense. We show that for such situations, use of non-uniform grids plus explicit modeling with uniform local grid refinement gives satisfactory results with reasonable computational costs. In this paper we also propose practical methods for calculating the correct well index.