Page 177 - Well Logging and Formation Evaluation

Reservoir Engineering Issues 167

This is subject to the following assumptions:

• Flow is radially symmetric.
• Porosity and compressibility are not affected by the damage.
• Pressure is continuous over the boundary between the damaged and
virgin zones.
• The damaged zone is in the steady state and the region outside is in
either the steady or semi-steady state.

The effect of stimulation through acid, steam, reperforation, etc., will
be to reduce S. Of particular interest to the petrophysicist is how the
product k*h is derived from a well test, since this will have to be recon-
ciled with values derived from logs. During the initial phase of testing a
well, the semi-steady state has not been reached, and a transient state will
prevail. In this regime the following equations apply:

D (
)
p
kh
2* * * * P Q *m) = ( 1 2 *ln( 4*t d g)+ S (11.5.5)
where t d is the dimensionless time given by:
2
k t ( * * *
t d = * fm C R w ). (11.5.6)
If two measurements are made of P and t, kh can be derived from:

)
Q
m
t t ) (2* *
kh = (12 ** *ln ( 1 2 p ( P - P ). (11.5.7)
2
1
Having determined kh, S may be determined from equation 11.25. Note
that in the equations presented, SI units must be used throughout, and Q
is in reservoir volume, not standard volume.
In reservoir limit testing, a well is produced sufficiently long for the
semi-steady state to be reached. Once semi-steady state is reached, the
well pressure will decline linearly with time, and the rate of change of
pressure with time will be constant. In the semi-steady state:

f
Q =- C A h* * ( dP dt). (11.5.8)
**
Hence if measurements of P vs. t are made, the drainage area A can be
deduced. Most commonly, wells are tested by letting them flow for a