Transient Pressure Behavior of Partially Penetrating Wells Subject to Bottomwater Drive
Authors: Buhidma Ismail M. , Raghavan Rajagopal 
Published: December 2007

This paper examines the characteristics of the wellbore pressure drop vs. time curves for a partially penetrating well located at the center of a square drainage region and subject to bottomwater drive. The effects of the penetration ratio and reservoir anisotropy on the transient behavior of the system are investigated. Edgewater- and bottom water-drive systems are compared.

Introduction
It is a common practice in the petroleum industry to drill wells through a limited portion of the formation or to penetrate the entire thickness and then selectively perforate a limited interval. These two completion techniques are known as partial penetration and restricted entry, respectively. The purpose of partial penetration or limited entry is to avoid or partial penetration or limited entry is to avoid or delay the intrusion of unwanted fluids into the wellbore. Partial penetration is probably the rule in geothermal systems since reservoirs can be extremely thick.Virtually all studies on the transient pressure behavior of both types of wells assume that the top and bottom boundaries are sealed. The objective of these studies has been to determine the horizontal and vertical permeability of the reservoir and/or the productivity loss that results from limiting the productivity loss that results from limiting the interval open to flow. Suprisingly, the pressure transient behavior of wells subject to fluid influx across the bottom boundary has not been investigated until now. The goal of this study was to examine the drawdown and buildup behavior of partially penetrating wells subject to bottomwater partially penetrating wells subject to bottomwater drive and to draw conclusions about pressure transients in these cases. The results obtained in this study also could be used to examine the pressure behavior of partially penetrating wells in a tall steam column supported by a boiling vapor/liquid interface. More specifically, the objectives of this study are to (1) investigate the applicability of conventional techniques for estimating formation flow characteristics, particularly horizontal and vertical permeabilities in systems subject to bottomwater drive, permeabilities in systems subject to bottomwater drive, (2) examine the interaction between the sealed lateral boundaries and the constant-pressure bottom boundary and its implication on well test analysis, and (3) determine the special characteristic features of the shapes of drawdown and buildup curves so that they can be used to identify bottomwater-drive systems.

Mathematical Formulation
The isometric and top views of the system under study are shown in Fig. 1. The following assumptions are made.1. The reservoir is a parallelepiped with a square drainage area A, uniform thickness h, and porosity phi. It has horizontal and vertical permeabilities k and phi. It has horizontal and vertical permeabilities k and kz, respectively - i.e., an orthotropic (anisotropic) system is considered. The well, which partially penetrates the formation, is at the center of the penetrates the formation, is at the center of the drainage area. It has an infinitesimally small radius rw and length hw.2. A single-phase slightly compressible liquid with compressibility c and viscosity mu flows from the reservoir into the wellbore at a constant reservoir rate qB.3. Initially, the pressure pi is uniform throughout the reservoir. While the upper and the lateral boundaries are sealed, the bottom boundary is kept at a constant pressure equal to the initial pressure. Gravity effects are not included.
JPT
P. 1251