Semi-analytical Solutions for Wellbores with Graded Skin Zones in Poroelastic Media

Abstract

In analyzing the complex interaction between the wellbore and the reservoir formation, the hydromechanical properties of the region proximal to the wellbore, referred to as the “wellbore skin zone”, play a pivotal role in determining flow dynamics and the resulting formation deformation. Existing models of the wellbore skin zone generally assume a constant permeability throughout, resulting in a sharp permeability discontinuity at the skin-reservoir interface. This paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic medium. Analytical solutions are derived using the Laplace transform method, addressing both positive and negative skin zones. Numerical results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a wellbore. The results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.