Introduction
In most well tests, a measurement is made of
the pressure response at the formation face of a well to a stimulus within that
same well. In the case of
interference testing, the pressure response to a stimulus at one well is
measured at another well. The
second well is relatively remote from the active well (the well where the
stimulus is applied).
Interference tests are carried out to test
for reservoir continuity, to detect directional permeability and other major
reservoir heterogeneities and to estimate reservoir volume.
A pulse test is a modification of standard
interference testing that is designed to assist in identification of the signal
produced by the stimulus.
In an interference test, a long duration
rate modification in one well creates a pressure interference in an observation
well that can be analyzed for reservoir properties.
Interference and pulse testing require at
least one active (producing or injecting) well and at least one pressure
observation well. The observation
well is shut-in while the testing is performed.
Usually, both the mobility-thickness
product, kh/m, and
the porosity-compressibility-thickness product, fcth, can be estimated.
In reservoirs with fluid contacts in the
zone of influence, results may be unreliable.
Single Injecting Well and a Passive Monitoring Well
Consider that there is an injector (the active well) and there is a monitoring well (the passive well). Assume further that the monitoring well has never been produced from or injected into. The theoretical response for measurement at the passive well is:
In oilfield units, this can be expressed as:
Two Well Interference with Flow/Injection
If there is a history of injection/production
in both the active and the passive wells, the situation is more complex. Assuming single phase, small
compressibility liquid and a uniform, homogeneous, infinite, horizontal
reservoir:
where:
d is the distance between the two wells.
Analysis
For infinite acting situations there is a
set of available type curves (Mueller and Witherspoon, JPT, April 1965;
Earlougher, 1977). These are
developed using the following nondimensionalization.
Deviations from fits on the type curves can
be indicative of reservoir heterogeneity.
Finally, be aware that there is no real guarantee of a unique fit to the
type curves. Unless the reservoir
is homogeneous and isotropic, the interpretation is ambiguous.
For bounded systems, dimensionless data have
been published. In either case,
software packages can facilitate analysis.
If the wells are much closer together than
the nearest boundary or to another active well (by a factor of ~10) and the
stimulus is long lasting, it may be possible to use the logarithmic
approximation. Under these
circumstances:
Plotting pws versus logt and
taking the slope gives:
For one shut-in observation well and multiple producing/injecting wells around it, the superposed relationship for the observation well is:
where:
q .............. production/injection rate at the observation well before it was closed in,
qj ...................................................................... production/injection rate at Well j,
tj ......................... producing/injecting time at the jth interfering well prior to shut-in
of the observation well,
Dtj ................................... producing/injecting time interval of the jth interfering well
since the observation well was shut-in,
n ......................................................................... number of interfering wells, and,
aj ............................... distance of the jth interfering well from the observation well.
Precautions
1. Additional considerations are required if
boundaries are close.
2. The rates at the active wells should be
fairly constant.
3. WATCH your signs – Injection is negative.
4. Wellbore storage and skin effects at the pulser
and the responder (active and passive wells) can lead to complexities and
uncertainties in the results, especially if the dimensionless distance between the two wells
is less than 1,000 or if the duration of the pulse is too short.
5. There are other complicating factors for
pulse testing (lunar-solar tides, oilfield activities, natural or hydraulic
fractures, multi-layering, the presence of gas ….Lunar and ocean tides are
periodic. In an inland reservoir,
these can cause pressure variations of ±0.015 psi. In near-shore and offshore reservoirs, the pressure
fluctuations due to tides can be ±1
psi. The high compressibility of
gas tends to suppress or attenuate the pressure signal at the observation well.
6. Unless, and even if, the reservoir is
homogeneous, isotropic and infinite, interpretation can be ambiguous and
conjectural.
References
1. Daltaban, T.S., and Wall, C.G.: Fundamental
and Applied Pressure Analysis, Imperial College Press, London (1998).
2. Earlougher, R.C. Jr.: Advances in Well
Test Analysis, Henry L. Doherty Memorial Fund of AIME, SPE, Dallas (1977).
3. Matthews, C.S. and Russell, D.G.: Pressure
Buildup and Flow Tests in Wells, Henry L. Doherty Memorial Fund of AIME,
SPE, Dallas (1967).
4. Sabet, M.A.: Well Test Analysis, Gulf
Publishing Company, Houston (1991).
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