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Mathematical Problems in Engineering
Volume 2009, Article ID 267964, 33 pages
Research Article

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

1College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
2Department of Petroleum Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

Received 8 October 2008; Accepted 2 January 2009

Academic Editor: Saad A. Ragab

Copyright © 2009 Jalal Farhan Owayed and Jing Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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