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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
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The principle of traditional real gas analysis is to replace the pressure by the pseudopressure
and interpret the data as if the fluid was slightly compressible.
However, there is an important shortcoming in this method. Although the equation looks the
same, it will only be linear as long as we can consider the diffusion term k/
c
t
constant. This
is valid as long as the average reservoir pressure does not substantially decrease which is a
reasonable assumption for a standard, relatively short, well test. In the case of extended tests
such as limit tests and production well tests, this may not be the case.
2.I.3.b
Normalized pseudopressures
The gas diffusion equation remains valid if we multiply the pseudopressures by a fixed
number. Because the unit and orders of value of the standard pseudopressures are not
intuitive, one possibility is to use normalized pseudopressures by selecting a reference
pressure p
ref
, with the condition:
Normalized pseudopressures:
ref
ref
Norm
pm
pm
p p m
Normalized pseudopressure at:
p
ref
:
ref
ref
Norm
p p m
The normalized pseudopressures have the dimension and unit of the pressure, it follows the
same diffusion equation and it coincides with the pressure at p
ref
:
Normalized pseudopressures:
) (
0002637
.0
) (
2
p m
c
k
t
p m
Norm
t
Norm
2.I.4
Non-Darcy flow
The diffusion equation used as the basis of the methodology in Dynamic Data Analysis is based
on three components: the conservation of mass, a PVT equation and Darcy’s law. We have
seen above that the gas PVT required some adjustments in the equations and the method:
pseudopressures, changing storage, material balance. In complement there are some cases,
and especially for gas, where the assumption of Darcy flow is invalid. Sections of the reservoir,
generally close to the well, will flow at such speed that turbulence will occur and have a strong
impact on the well response. We now need to add a turbulence component to the flow
equation, replacing Darcy’s law by a second degree equation, such as Forchheimer’s.
Darcy’s law expressed in terms of speed, in SI units:
u
k x
P
Forchheimer’s equation, same references and units:
2
u
u
k x
P
is called the turbulence factor. There are two main options to address non-Darcy flow:
The first is to focus on the impact of non-Darcy flow on the well productivity. This is what
was done historically using rate dependent skin. Normal diffusion is used, but an additional,
rate related skin component is added.
The other way is to model non-Darcy flow by numerically integrating the Forchheimer
equation in the model.