Abstract The accurate modeling of wells that exhibit arbitrary trajectories and/or multiple laterals (i.e., nonconventional wells) is critical for obtaining reliable well performance predictions. Modeling strategies need to account for both well geometry and reservoir heterogeneity effects, especially in the near-well region. Multiblock grids offer the ability to model complex wells more accurately than standard finite difference procedures. Such grids are globally unstructured, yet maintain structure locally, making them a reasonable compromise between standard (fully structured) techniques and fully unstructured procedures. In this paper, we develop a near-well upscaling procedure suitable for use with multiblock grids. The technique is applicable for grids that are radial (or nearly so) in the near-well region rather than rectangular. The method is well-suited for models in which the general well trajectory is resolved by the simulation grid and is capable of modeling reservoir heterogeneity down to the scale of the wellbore itself. The high degree of accuracy of the upscaling technique is demonstrated through comparison to fine grid calculations for two different types of reservoir heterogeneity. It is shown that the effects of near-well heterogeneity can be significant and that the new procedure provides much better accuracy than simpler well models that assume near-well homogeneity and isotropy.