KAPPA DDA Book v5.12

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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017 Chapte - p24/743
A way to model a positive skin effect is to consider an equivalent composite system, with
an invaded zone, or skin damage zone of radius rws larger than rw and permeability ks lower
than k.
Darcy’s law gives the relation between the equivalent skin factor, rs and ks:
Skin from a radial composite equivalent: 











 
w
ws
S r
r
k
k
S ln1
Fig. 2.D.3 – Equivalent composite system
Another way to model skin is the notion of equivalent radius, applicable to both positive and
negative skins. The idea is to consider that the well with skin has the same productivity as a
larger or smaller well with no skin. If the skin is positive, the equivalent wellbore radius will be
smaller than rw . If the skin is negative, the equivalent wellbore radius will be larger than rw.
The equation, again, straight from Darcy’s law, can also be found at the limits when the
permeability S k above tends to infinity (open hole), and will be given by:
Equivalent wellbore radius: 








w
we
r
r
S ln or S
w weer r

Fig. 2.D.4 – Skin: equivalent wellbore radius