Pressure Drop Equations for a Partially Penetrating Vertical Well in a Circular Cylinder Drainage Volume

摘要

Taking a partially penetrating vertical well as a uniform line sinkin three-dimensional space, by developing necessary mathematicalanalysis, this paper presents unsteady-state pressure drop equationsfor an off-center partially penetrating vertical well in a circularcylinder drainage volume with constant pressure at outer boundary.First, the point sink solution to the diffusivity equation isderived, then using superposition principle, pressure drop equationsfor a uniform line sink model are obtained. This paper also gives anequation to calculate pseudoskin factor due to partial penetration.The proposed equations provide fast analytical tools to evaluate theperformance of a vertical well which is located arbitrarily in acircular cylinder drainage volume. It is concluded that the well off-center distance has significanteffect on well pressure drop behavior, but it does not have any effect onpseudoskin factor due to partial penetration. Because the outerboundary is at constant pressure, when producing time issufficiently long, steady-state is definitely reached. When wellproducing length is equal to payzone thickness, the pressure dropequations for a fully penetrating well are obtained.