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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017 Chapte - p167/743
5.C Changing wellbore storage
The most frequent case of changing wellbore storage is related to the compressibility change
of the wellbore fluid.
A classic example is gas. When the well is flowing the pressure in the wellbore will decrease,
and the gas compressibility will increase. In this fixed volume this will result in an increase of
the wellbore storage parameter. The opposite will occur during the shut-in, where the increase
of pressure will result in a decrease of the wellbore storage. Though it occurs in any gas test,
this behavior will be visible, and become a nuisance, in the case of tight gas, where the high
pressure gradient in the formation results in a high pressure drop in the wellbore.
Another typical example is an oil well flowing above bubble point pressure in the reservoir. At a
stage (sometimes immediately) there will be a point in the wellbore above which the pressure
gets below bubble point. In this place the oil compressibility will be progressively dominated by
the compressibility of the produced gas, hence an increase of the wellbore storage which will
evolve in time.
In both cases, the wellbore storage will be increasing during the production and decreasing
during the shut-in.
Other sources of changing wellbore storage may be various PVT behaviors, change of
completion diameter of a rising or falling liquid level, phase redistribution, falling liquid level
during a fall-off, etc.
In some cases the wellbore effect will be so extreme that any modeling is hopeless. In this
case the engineer will focus on matching the derivative response after the wellbore effect has
faded, accepting that the early time response cannot be matched and may induce a
(cumulative) incorrect value of the skin factor.
There are three main ways today to model changing wellbore storage:
 Analytical, time related wellbore storage
 PVT correction using the pseudotime function and a constant storage value
 Numerical, pressure dependent storage model
5.C.1 Analytical models
Most analytical formulations of changing wellbore storage involve an initial value of wellbore
storage Ci, a final value C f, some assumption for a transition function (Hegeman, Fair, etc) and
a time at which this transition occurs. The main characteristic of these models is that the
transition occurs at a given value of t, and is NOT related to the value of the pressure.
The figures below illustrate increasing and decreasing wellbore storage as modeled by the
Hegeman model of changing wellbore storage.
The matching consists in setting the wellbore storage straight line on the FINAL value of
wellbore storage, pick a second position corresponding to the INITIAL value of storage, and
then pick the median time when the transition occurs. The initial model generation will seldom
match the response perfectly, but this model, combined with a robust nonlinear regression,
has the capacity to adjust to virtually any single trend early time response.