174 / 743
Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 6 – W ell models -p174/743
6.C
Vertical Well with Changing Skin
In this section, we keep the assumption of a vertical well fully penetrating the formation.
However we now allow the skin factor to be changing over time and/or as a function of the
producing rate.
6.C.1
Rate dependent skin
In high rate wells, especially but not only in gas wells, the flow velocity may become
considerable and in some cases the flow becomes turbulent. When this happens, Darcy’s law
no longer applies and will be replaced by Forchheimer’s equation:
2
u
u
k dx
dP
,
5.0 5.5
1
005 .0
k
Sw
The exact problem is nonlinear and can be solved numerically, as described in chapter on
‘Numerical models’.
However, it can be simplified and analytical models can be used with a fair approximation by
adding a rate dependent component to the skin factor. Under these conditions, the effective
skin factor S’ for a given rate q will be given by:
q
dq
dS
S Sor Dq S S
0
0
'
'
D is called the non-Darcy flow coefficient. In order to assess the rate dependency the skin has
to be solved for several rates.
In gas well testing the most common method is to plan for an isochronal or modified
isochronal test, but this is done mainly to determine the deliverability of the well. Such a test
procedure includes multiple buildups after different flowrates and the engineer can then profit
for ‘free’ the fact that the buildups can be analyzed for skin and define the rate dependency.
This can then be used in the model.
The following figures illustrate the loglog plot with four buildups with different skins and the
corresponding history match using a constant skin in the model. It can be seen that the match
is not consistent with the measured data.
Fig. 6.C.1 – Loglog plot
Fig. 6.C.2 – History match, constant skin