Effects of grid systems on predicting horizontal-well productivity

We compare horizontal-well performance for different grid types using a con ventional formula for the well index. These results are also compared with the results of explicit well modeling, which does not require a well index. To assess the accuracy of numerical solutions, examples chosen are those f or which exact analytical solutions are also available. These analytical so lutions are for horizontal wells in brick-shaped homogeneous (isotropic or anisotropic) reservoirs (or drainage volumes). When a horizontal well exten ds through the full length of the reservoir, the problem becomes two-dimens ional with uniform influx along the well. On the other hand, if the well is completed in only a part of the reservoir (partially penetrating) a three- dimensional (3D) solution is needed. The 3D solution also predicts the infl ux profile along the well, with higher influx at the two ends. Because the conventional well index calculation does not account for the 3D nature of f low, the how rate of the well may be incorrect. We have found that the well index obtained with the default procedure in most simulators (Peaceman's m ethod) needs to be increased for the numerical simulator to predict the pro ductivity of horizontal wells correctly. The correct well index can be obtained for any well if a suitable analytica l solution is available. When such solutions are not available, reference s olutions can also be obtained by explicitly modeling the well with blocks t hat are of the same size as the well. In this case, there is no need for a well index. However, our analysis shows that for correct results the grid-a spect ratio for blocks representing the well and surrounding blocks has to be close to 1.