Page 176 - Well Logging and Formation Evaluation

166 Well Logging and Formation Evaluation

Exercise 11.3. Radial Flow

Calculate the time taken for the flowing pressure to fall by 30 bar in the
vicinity of a well subject to the following flowing conditions: k = 300md,
-4
h = 30m, R w = 15cm, f= 0.20, m= 10cp, C = 2*10 /bar, Q =
3
200res.m /day,

11.5 WELL TESTING

The equations given in the previous section can be used to predict flow
performance in ideal cases. However, in reality, flow near the wellbore is
influenced by formation damage caused by drilling and production
processes (precipitation, fines moving, gas blocking, water dropout, etc.).
The pressure difference between the bottomhole well flowing pressure and
the reservoir pressure, DP, relates to formation properties via a formula
of the form:

k h)
DP = Q** J ( ** * (11.5.1)
m
p
2
where J may be considered a dimensionless productivity. In the case of
steady state flow, J = ln(r e /r w) - 1/2; and for semi-steady state flow, it is
ln(r e /r w) - 3/4. The productivity index (PI) is defined as:

PI = Q D P. (11.5.2)

The effect of formation damage is that the PI is smaller than one would
expect from theoretical values, or DP is greater than one would expect for
a given Q. This damage may be quantified by introducing a term called S
such that:

p
+
DP = Q** ( J S) ( ** * (11.5.3)
m
2
k h).
If the radius of the damaged zone is r 1, and it has permeability k 1, it may
be shown theoretically that S is given by:
S = ( k k - ) 1 *ln ( 1 (11.5.4)
r r w ).
1