Page 351 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 286

flow period at rate Q 2. The main purpose of this type of test is to determine the current
average pressure within the drainage boundary of the well, p. Theoretically, this can
be done by using either the method of Matthews, Brons and Hazebroek, or Dietz (refer
Chapter 7, sec. 7), but the difficulty is to determine at what pressure the µc product
should be evaluated which is required to calculate t DA for use with either of these
methods. For the initial well tests described in exercises 8.1-3, the product (µc) i
evaluated at the initial equilibrium pressure could be used but for a survey made, say,
several years after the well has started to produce this can lead to serious error. The
basic problem is that for very long flowing times the calculation of m D using the semi-
steady state equation (8.33) with the (µc) i product does not accurately correlate with
the similar p D function for liquid flow, equ. (7.27).

10
Kazemi has presented an iterative method for determining the pressure at which, µc
should be evaluated and hence the correct value ofp. The method is applicable for
wells producing under semi-steady state conditions at the time of the survey. In this
case, as shown in Chapter 7, sec. 7, the value of the flowing time used to plot the
buildup is immaterial providing that t ≥ t SSS, the time required for semi-steady state
conditions to be reached for the particular geometrical configuration of the drainage
area. Strictly speaking, this statement is only valid when applied to a liquid, in which
case the MBH plots, figs. 7.11-15, are linear functions of the dimensionless flowing

time t DA. For a real gas, however, the m D(MBH) functions deviate from the linear p D(MBH)
functions for large values of t DA, as shown in fig. 8.16. This implies that using the MBH
charts, for a large value of the (effective) flowing time, can lead to an error in the
determination ofp in the analysis of a routine buildup survey in a gas well.

Kazemi argues, and substantiates his argument with detailed numerical simulation, that
if the buildup is plotted for a flowing time t SSS,where

(c)
φµ p A
t = SSS (t ) (8.61)
SSS
0.000264k DA SSS
and the MBH method applied for a dimensionless flowing time (t DA) SSS, then the portion
of the MBH charts for which the liquid and gas MBH functions correlate is used and this
should result in the correct determination of p. Of course, in order to calculate t SSS,

using equ. (8.61), requires a knowledge of p SSS, the average pressure at a time t SSS
prior to the buildup and the evaluation of the µc product at this pressure. A simple
iterative scheme for calculating p SSS, t SSS and hence p is shown in fig. 8.17.