document preview

Abstract

The pressure behavior during buildup testing for a well located anywhere in a rectangular drainage area with constant pressure or mixed boundaries was investigated in this study. This study included the cases of 2:1 and 4:1 rectangular drainage area it was found that the buildup pressure behaviour varies from well location to another. Horner, MDH and pressure behaviour varies from well location to another. Horner, MDH and extended Muskat plots were obtained for different well locations and boundary conditions. Also, MBH average and boundary pressure functions were presented in graphical forms. It was found that most of drainage areas presented in graphical forms. It was found that most of drainage areas under complete or partial water drive may behave differently from the closed systems. The producing time before shut-in affects the pressure buildup behavior as long as the system did not reach steady state condition during production time.

Introduction

This paper is the fourth in a series of papers covering the pressure behavior of a well located anywhere in a rectangular drainage area with constant or mixed boundaries. The first two papers treated the transient pressure behavior of a well located in square drainage areas. The third pressure behavior of a well located in square drainage areas. The third paper 3 presented pressure drawdown testing of a well located in 2:1 and paper 3 presented pressure drawdown testing of a well located in 2:1 and 4:1 rectangular drainage areas. This paper treats the pressure buildup testing of a well located anywhere in a rectangular drainage area with constant/or mixed boundaries. The literature review presented in references 1-3 indicated that little attention was given to the case of transient pressure for a well located an here in a rectangle with constant or mixed pressure for a well located an here in a rectangle with constant or mixed boundaries. Kumar and Ramey resented a study dealing with a special case of a well located in the center of a constant pressure drainage area. The cases of a well located in a closed drainage shape of almost any geometry are treated extensively in the literature, Key in this development was the study published by Mathews, Brons and Hazebrock. In this paper, the three classical buildup testing methods (namely: Horner, MDK and Muskat) are established for the case of well located anywhere in a rectangular drainage area with constant or mixed boundaries. Also, MBH plots were developed.

Dimensionlesspressure Buildup

The fluid flow in a porous medium is described by the diffusivity equation. The porous medium is assumed to be homogeneous with constant permeability, porosity and thickness, and constant fluid viscosity and permeability, porosity and thickness, and constant fluid viscosity and compressibility. Also, effective compressibility and pressure gradient anywhere are assumed to be small anywhere in the reservoir. The line source solution of the diffusivity equation is presented as: