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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapter
3 – P ressure Transient Analysis (PTA)- p73/743
3.C.4
Bourdet Derivative & Wellbore Storage
Pure wellbore storage effects are only observed at very early time when the well pressure
behavior is dominated by the well fluid decompression or compression.
In case of pure wellbore storage:
tCp
Even for multirate solutions at early time:
t
t
ln
sup
The derivative is therefore:
p tC
td
t dC
t
p
'
At early time, when pure wellbore storage is present, pressure and the Bourdet derivative
curves will merge on a unit slope straight line on the loglog plot.
Other early time flow regimes, such as linear and bilinear flow, covered in more detail later,
will exhibit a different and specific behavior for both pressure and the Bourdet derivative.
3.C.5
The original idea behind the Bourdet Derivative
The simplest and most frequently used analytical model in Pressure Transient Analysis is the
case of a vertical well, with wellbore storage and skin, producing a homogeneous reservoir of
infinite extent. This ‘new’ formulation of the derivative by Bourdet et al. was solving at once
this case, on a single loglog plot, and in a very accurate way:
When plotting the pressure and the Bourdet derivative on a loglog scale, at ‘late time’ the
derivative would stabilize, and the stabilization level would define the type-curve pressure
match (hence the permeability) in a unique way. The only possible movement then would be
left and right to define the time match.
At early time the Pressure and the Bourdet derivative would merge on a single unit slope, that
was also found on the type-curves, hence providing a unique value of this time match, and an
instant calculation of the wellbore storage.
Luckily enough, the shape of the derivative (drawdown) type-curve and the Bourdet derivative
of the data (multirate) was seldom affected by the superposition, unlike the pressure data, so
it was reasonably valid to match the data derivative with the type-curve derivative, hence
getting a unique identifier of the type-curve (generally C
D
e
2S
), which in turn would give the
value of Skin.
So, on a single action, a type-curve using the Bourdet derivative would provide the definitive
answer on a single, accurate diagnostic plot.
This was already brilliant, but it turned out that the Bourdet derivative could bring much more
for all type of models, whether by identification of other flow regimes or by the signature that
the Bourdet derivative would carry for such or such model…