Page 275 - Fundamentals of Reservoir Engineering

OILWELL TESTING 212

At the end of the flow test the well is closed in for a pressure buildup from which the
permeability is estimated as 610 mD. The available reservoir data and fluid properties
are listed below.

Drainage area A = 80 acres

2

Geometry 1

φ =.22 B o = 1.35 rb/stb
h = 15 ft µ =1 cp

-6
= .33 ft c = 21 × 10 /psi
r w
1) Analyse the test data to determine k and S using equ. (7.69) with the p D functions
evaluated using equ. (7.42) or (7.46)
2) Repeat the analysis evaluating the p D function for transient flow conditions,
equ. (7.23).

EXERCISE 7.8 SOLUTION

1) The general multi-rate test analysis equation, (7.69) can be expressed as

p − p ) n q
( i wf n = m ∆ j p t − t ) + mS
q n j1 q n D ( D n D −
j 1
=
where m = 141.2 µ B o/kh

'
and p D t n − t D j 1 ) = p D ( t ) can be evaluated as
D
( D
−
4A
p D ( ) 2 t′ + 1 2 ln t′ + 1 2 ln − 1 2 p D(MDH) (t ) (7.46)
t′ =
′
π
D
DA
DA
DA
r γ w 2
i.e.
p D ( ) α − 1 2 p D(MDH) (t ) (7.73)
t′ =
′
DA
D
.000264kt .000264 610 t
×
in which t′ D = =
6
−
××
φµ cr w 2 .22 1 21 10 × (.33) 2
×
= 3.2 10 5 ( t hours )
×
2
and t DA = t × r / A = .01t (hours )
w
D
The p D functions, equ. (7.73), are evaluated in table 7.11 for all values of the time
argument required in the test, and for a variety of geometrical configurations of the
80 acre drainage area in order to investigate the sensitivity of the results to variation in
shape.