Modelling Near-well Flow Performance for Horizontal Wells in Anisotropic Media

This paper presents a novel methodology to model flow performance in an anisotropic reservoir in the near-well region with an arbitrary well trajectory. It is based on an analytical productivity model describing coupled axial reservoir flow and radial well inflow. To apply this model in an anisotropic reservoir, the permeability field relative to the radial direction perpendicular to the well trajectory and the axial direction along the well trajectory must first be determined. A classical transformation is used to obtain a virtual isotropic model. The transformation preserves the volumes and average pressures. It is applied in the near-well region without modifying the outer boundary conditions. The use of this virtual isotropic model requires the Dietz shape factor for an ellipse, which is determined numerically. For example, in a circular-cylindrical near-well region, this transformation method maps the anisotropic reservoir onto an equivalent virtual isotropic media which is an elliptical cylinder. The coupled axial and radial productivity model is implemented in a numerical simulator incorporating formation anisotropy and wellbore hydraulics. The specific productivity index along the well trajectory is generated using the virtual configuration. Numerical results for different anisotropy ratios and also incorporating frictional losses in the well are presented.