Page 228 - Fundamentals of Reservoir Engineering

OILWELL TESTING 166

EXERCISE 7.4 TRANSITION FROM TRANSIENT TO SEMI-STEADY STATE FLOW

Determine the pressure response at the wellbore due to the production of a well which
is situated at the centre of a square drainage area with sides measuring

a) L = 100ft

b) L = 500ft
The relevant reservoir and fluid properties are as follows

k = 50 mD

φ = 0.3

µ = 1 cp
-6
c = 15 × 10 /psi
= 0.3 ft
r w
= 30.9
C A
When does the transition from transient to semi-steady state flow occur for both these
drainage areas?

EXERCISE 7.4 SOLUTION

If the real time is expressed in days, then t D can be determined as

0.00634kt
t D = (days) (7.21)
φµ cr w 2

with all the other parameters in field units, i.e.

0.00634 × 50 × t 5
t = = 7.827 10 t
×
D
-6
.3 ×× 10 × .09
1 15 ×
The dimensionless pressure response in the well can be determined using the
following functions
Transient flow p (t ) = ½ (ln t + 0.809) (7.24)
D
D
D
4A t r 2
SSS flow p (t ) = ½ ln + 2 π D w (7.25)
D
D
γ Cr 2 A
Aw
Transient flow
Equation (7.24) is independent of the reservoir geometry and will give the same value
of p D (t D) irrespective of the magnitude of the area drained. Furthermore p D (t D ) is a
linear function of t D when plotted on semi log paper. Using the following equations,
values of p D and log t D have been calculated and the results listed in table 7.2 and
plotted in fig. 7.5