A comparative study of some well-reservoir coupling models in the numerical simulation of oil reservoirs

In reservoir simulation, the most known well-reservoir coupling technique is based on the Peaceman's equivalent radius, which is applied on the productivity index computation, that is used to relate flow rate, wellbore pressure, and the mesh block pressure. Original Peaceman's model considers the assumption of steady-state flow, leading to an artifact on the calculation of the wellbore pressure, called numerical wellbore storage. This artifact is more significant for coarser meshes and initial time instants, and it is also a function of fluid and rock properties. In this context, we have implemented and compared different Peaceman's technique extensions for productivity index calculation incorporating transient effects to prevent numerical wellbore storage. We have also considered some production scenarios for a vertical well and single-phase oil flow.