`Mathematical Problems in EngineeringVolume 2009, Article ID 626154, 34 pageshttp://dx.doi.org/10.1155/2009/626154`
Research Article

## Productivity Formulas for a Partially Penetrating Vertical Well in a Circular Cylinder Drainage Volume

1The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates
2Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma T-301 Sarkeys Energy Center, 100 E. Boyd Street, Norman, OK 73019-1003, USA
3Department of Petroleum Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 26 December 2008; Accepted 6 July 2009

Academic Editor: Francesco Pellicano

Copyright © 2009 Jing Lu et al. 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.

#### Abstract

Taking a partially penetrating vertical well as a uniform line sink in three-dimensional space, by developing necessary mathematical analysis, this paper presents steady state productivity formulas for an off-center partially penetrating vertical well in a circular cylinder drainage volume with constant pressure at outer boundary. This paper also gives formulas for calculating the pseudo-skin factor due to partial penetration. If top and bottom reservoir boundaries are impermeable, the radius of the cylindrical system and off-center distance appears in the productivity formulas. If the reservoir has a gas cap or bottom water, the effects of the radius and off-center distance on productivity can be ignored. It is concluded that, for a partially penetrating vertical well, different productivity equations should be used under different reservoir boundary conditions.