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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 5 – W ellbore models- p169/743
The following figures show a loglog response before and after pseudo time correction. The use
of pseudo time is detailed in the chapter on ‘
13.E - The use of pseudofunctions’
.
Fig. 5.C.3 – Without pseudo-time
Fig. 5.C.4 – With pseudo-time
5.C.3
Numerical pressure dependent wellbore storage
The principle is to use a wellbore model which, at any time, uses the pressure to define the
wellbore storage parameter. In order for the model to be stable, the wellbore storage has to
be calculated implicitly at each time step. As the problem is not linear, this can only be done
using a non linear model.
This is by far the most relevant way to simulate pressure related wellbore storage. The figure
below illustrates a buildup matched with the changing wellbore storage model (Hegeman), the
extracted buildup corrected for pseudo time and matched with this model, and the match with
the non linear numerical model with pressure dependent wellbore storage.
Fig. 5.C.5 – Changing wellbore storage match
Fig. 5.C.6 – Pseudo time match
Fig. 5.C.7 – Match with non linear numerical model:
Pressure dependent wellbore storage