Concerning the Value of Producing Time Used in Average Pressure Determinations from Pressure Buildup Analysis
Authors: Pinson A.E. 
Published: December 2007

Introduction

Average drainage volume pressures calculated by the Horner -Matthews, Brons, and Hazebroek (H-MBH) method have frequently been accepted with suspicion because of the apparently arbitrary method for determining the value of producing time that is normally used in the Horner plot. However, it will be shown here that for certain common conditions the value of producing time can be chosen arbitrarily. producing time can be chosen arbitrarily.

Horner-Matthews, Brons, and Hazebroek Method

As pointed out by Dietz, in the H-MBH method, the production time enters twice: when the buildup production time enters twice: when the buildup pressures are plotted against log [(t + ) to determine pressures are plotted against log [(t + ) to determine p*, and again when the area dimensionless time is p*, and again when the area dimensionless time is used to determine the MBH pressure correction function . It will be shown here that, if semistate flow prevails before shut-in, the use of producing time in these two ways precisely compensates producing time in these two ways precisely compensates for errors that may be made in estimating this time. This means that the correct value of average drainage volume pressure is calculated, even though errors are made in estimating the producing time. One additional requirement is that t &gt;&gt; delta t so that log(t + delta t ) logt, which is almost always the case. After a producing well has been shut in, the bottomhole pressure rise during the transient buildup period is described by the following equation :

The derivation of Eq. 1 is based on the assumption that the well has been produced at a constant rate, q, for a period of time, before shut-in. Rate is seldom constant, and Horner' suggested the use of a "corrected time" obtained by dividing the total cumulative production by the last established production rate. This corrected time was suggested for use in place of the theoretically correct but laboriously place of the theoretically correct but laboriously applied principle of superposition. Failure to satisfy the assumption of constant producing rate and the obvious effect of t on p* has resulted in a lack of confidence in drainage volume pressures calculated by the H-MBH method. It will be shown that a lack of confidence for this reason is unfounded if the well was producing at semisteady-state before shut-in. producing at semisteady-state before shut-in. Dietz" has represented the MBH relationship by

.............(2)

for semisteady-state flow before shut-in.

Combining Eqs. 1 and 2, we obtain

..............(3)

Eq. 3 represents a combination of the Homer plot and the MBH expression for average drainage volume pressure. This combination eliminates t as a pressure. This combination eliminates t as a parameter, thereby showing that p calculated from the parameter, thereby showing that p calculated from the H-MBH method is independent of the value used for t. An article by Russell contains an example that will demonstrate the lack of dependence of p on t. Example Well C of the Russell paper provides both Horner and extended Muskat plot (Russell's Figs. 9 and 10), reproduced here as Figs. 1 and 2, respectively.

JPT

P. 1369