Page 245 - Introduction to Petroleum Engineering

232 TRANSIENT WELL TESTING
12.2.1 Pressure buildup Test

The concepts of pressure transient test analysis can be exhibited by outlining the
analysis for the PBU test. The PBU test measures the pressure response at the well
when the well is shut in after the well has been producing. It is necessary to have an
average flow rate for the production period. Flow rates in real wells tend to fluctuate.
An average flow rate q is determined by producing the well for a period t ; thus
F
cumulativeproductionSTB
q STBD (12.9)
/
t F
After the well is shut in, the elapsed time measured from shut‐in is denoted Δt.
Bottom‐hole pressure is recorded as a function of time during the shut‐in period.
The PBU test is analyzed using the superposition principle. The superposition
principle says that the total pressure change at the location of the shut‐in well is
equivalent to a linear sum of the changes in pressure at two wells: the actual well and
an imaginary well. Both the actual well and imaginary well are located at the same
location. The pressure change at the real well is due to the production rate q for the
entire period of the test plus the production rate −q from the imaginary, or image,
well for the shut‐in period of the test. The rates for the PBU test are shown in
Figure 12.2. The solid line in the figure is the total rate obtained by adding the rates of
the real well and the image well.
Dimensionless pressure is a linear function of the logarithm of time during the
infinite‐acting time period as in Equation 12.8; thus

1
p ln t constant (12.10)
D 2 D
Applying the superposition principle and using oil field units give the shut‐in pressure
at the well p (psia) as
ws

Q

Actual rate
Well rate 0 t F t

–Q
Time
FIGURE 12.2 Rates for the PBU test.