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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapter
3 – P ressure Transient Analysis (PTA)- p71/743
To most engineers the replacement of manual techniques by computer based analysis in their
day-to-day work occurred in the 1980s, and came from three major breakthroughs:
Electronic downhole pressure gauges, either run with memory or on electric line, became
cheap and reliable, detecting repeatable behaviors far beyond what the previous generation
of mechanical gauges could offer.
The spread of Personal Computers allowed the development of PC-based pressure transient
analysis software. The first PC based programs appeared in the 1980’s, initially reproducing
the manual methods on a computer. Since then, new generations of tools have been
developed, with modern methodology at its core.
The Bourdet derivative is certainly the single most important breakthrough in the history of
Pressure Transient Analysis. It is still today (2016) the cornerstone of modern technology.
Let us start with the Bourdet derivative…
3.C.2
Definition of the Bourdet Derivative
As any breakthrough idea, the principle of the Bourdet derivative is very simple:
The Bourdet Derivative is the slope of the semilog plot displayed on the loglog plot…
… to be more accurate, it is the slope of this semilog plot when the time scale is the natural
log. It has to be multiplied by ln(10)=2.31 when the decimal logarithm is used in the semilog
plot. The semilog plot is not ‘any’ semilog plot (MDH, Horner, etc). To be correct the reference
logarithmic time scale must be the superposition time.
For the first drawdown:
td
pd
t
t
d
pd
p
ln
'
In the more general multirate case, and in particular for shut-ins:
t
d
pd
p
sup
'
Fig. 3.C.1 – Bourdet derivative, semilog plot