Predicting wellbore production plays a crucial role in petroleum engineering. Therefore, the modeling of the ow in reservoir and in wellbore is fundamental in several problems in this area. In the overwhelming majority problems, Darcy s equation is the choice to predict the behavior of ow in reservoirs. The great success of Darcy s equation, unfortunately, took its application out of the scope of the problems for which it applies. The classic Darcy s equation presents limitations when applied in highly heterogeneous porous media, for example with cavities connected by fracture networks, with vugs and caves. Over the years, other models have been proposed and derived from other points of view to treat ow in porous media, for example through the average volume process or through mixture theory. The present work considers the average volume process in porous media. The developed model includes additional terms for the linear momentum equation that are relevant in several practical situations, and involves the joint solution of conservation equations. In the model developed in this work, the ow in the reservoir is solved coupled to the wellbore ow, considering the possibility of using different completion types. The pressure and velocity fields predictions as well as the productivity of oil wellbores using the developed model are compared with the predictions of the model based on the Darcy s equation. It is shown that for certain situations, especially in highly heterogeneous carbonate reservoirs, large differences can be obtained. The prediction of the productivity of a wellbore from the Darcy s equation can be significantly overestimated.