Page 252 - Fundamentals of Reservoir Engineering

OILWELL TESTING 189

7.7 PRESSURE BUILDUP ANALYSIS TECHNIQUES

The remaining sections of this chapter concentrate on the practical application of the
theory developed so far to the analysis of well tests. It is considered worthwhile at this
stage to change from Darcy to field units since, in practice, tests are invariably
analysed using the latter and the majority of the literature on the subject employs these
units. All equations in the remainder of this chapter will therefore be formulated using
the field units specified in table 4.1. Since a great many of the equations are expressed
in dimensionless parameters they remain invariant, or at least partially invariant in
form. For instance, the most significant equation in the present subject of pressure
buildup analysis is that describing the theoretical linear buildup, which in Darcy units, is

2kh t +∆ t 4t D
π
t
−
=
p −
D
( i p ws(LIN) ) ½ ln + p D () ½ ln (7.37)
q µ t ∆ γ
and which, on conversion to field units becomes
kh t +∆ t 4t
7.08 10 -3 (p − p ) 1.151 log + p () − ½ ln D (7.48)
t
=
×
qB o i ws(LIN) t ∆ D D γ
µ
The conversion of the left hand side of this equation has already been described in
exercise 7.3 and is necessary to preserve this expression as dimensionless, in field
units. The only change to the right hand side is that the natural log of the
dimensionless time ratio has been replaced by log 10, which is mainly required for

plotting purposes, the remainder of the equation is invariant in form. Thus the p D
function is still

4t
π
p(t ) = 2 t DA + ½ ln D − ½ p D(MBH) (t ) (7.42)
D
D
DA
γ
which is totally invariant, although in evaluating this expression it must be remembered
that now
kt
t = 0.000264 2 (t-hours) (7.20)
D
φµ cr w

and

kt
t DA = 0.000264 (t-hours) (7.49)
φµ cA

The p D(MBH) term is, in the majority of cases, just a number read from the MBH charts
corresponding to t DA evaluated in field units. Only when used to calculate p using the
MBH method does it require interpreting as

kh
p D(MDH) = 0.01416 ( p * p )
−
qB o
µ
The Horner plot for a typical buildup is shown as fig. 7.18.