This paper presents new models for partially penetrating wells with any number of perforated intervals in either layered, isotropic, anisotropic, or 3D, heterogeneous reservoirs. These models are applicable to both vertical and horizontal wells and are capable of accurately simulating non-uniform flux distributions along perforated intervals. For a partially penetrating well, the models generate a constant well index for each perforated layer based on the quasi-steady state conditions established early in unsteady state flows.
In general, the predicted flux distributions along the well in a coarse-grid simulation using the new models agree almost identically (within 1% error) with fine-grid solutions. It is shown that well indices depend only on the permeability distribution in the vicinity of the well, reservoir thickness, wellbore radius, and locations of perforated intervals. Finally, for a heterogeneous reservoir, the calculated well indices and the rate distribution along the well can be greatly influenced by the subgrid permeability distribution near the wellbore.