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Research Papers: Petroleum Wells-Drilling/Production/Construction

# Steady State Productivity Equations for a Vertical Well in Anisotropic Sector Fault, Channel, and Rectangular Reservoirs

[+] Author and Article Information
Jing Lu1

Department of Petroleum Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAEjilu2@yahoo.com

Djebbar Tiab

Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma, 100 East Boyd Street, SEC T310, Norman, OK 73019dtiab@ou.edu

Jalal Farhan Owayed

College of Engineering and Petroleum, University of Kuwait, P.O. Box 5969 Safat 13060 Kuwaitjalal@kuc01.kuniv.edu.kw

1

Corresponding author.

J. Energy Resour. Technol 131(1), 013102 (Feb 05, 2009) (6 pages) doi:10.1115/1.3066429 History: Received June 05, 2007; Revised May 20, 2008; Published February 05, 2009

## Abstract

This paper presents steady state productivity equations for a fully penetrating vertical well in the following three anisotropic systems: (a) sector fault, (b) channel, and (c) rectangular reservoir using a uniform line sink model. The new equations, which are based on conformal mapping method, are simple, accurate, and easy to use in field practice. If the well is in a sector fault reservoir, the productivity is a function of the angle of the sector, wellbore location angle, off-vertex distance, and drainage radius. If the well is in a channel reservoir with two parallel impermeable lateral boundaries, well flow rate reaches a maximum value when the well is located in the middle of the channel width. If the well is in a rectangular reservoir with constant pressure lateral boundaries, a new equation is provided to calculate the productivity of the well arbitrarily located in the anisotropic reservoir for the case where the flow rate of an off-center well is bigger than that of a centered well. It is concluded that, for a vertical well, different steady state productivity equations should be used in different reservoir geometries.

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## Figures

Figure 1

Sector fault reservoir model

Figure 2

Channel reservoir model

Figure 3

Rectangular reservoir model

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