Page 200 - Introduction to Petroleum Engineering
P. 200
SKIN 187
The radius r is the radius of the damaged zone. Equation 10.5 is Hawkin’s formula
d
for skin. It shows that skin depends on the change of permeability as well as the
size of the damaged zone relative to the well. Actual values of skin around wells are
usually found from analysis of well tests.
Example 10.1 Skin from Hawkin’s Formula
Use Hawkin’s formula to estimate the skin of a damaged zone around a well
with radius of 4 in., k = 20 md, and k = 2 md. The damaged zone extends 2 in.
d
beyond the radius of the well.
Answer
Substitute the physical values into Equation 10.5:
20md 6in.
s = −1 ln = 36 .
2md 4in.
Our next objective is to describe how skin affects well productivity. Consider a
well in a large cylindrical zone of radius r and thickness h. Here, r is the drainage
e
e
radius and p is the average pressure in the zone. For example, r is 745 ft for a well
ave
e
in a 40‐acre pattern. The difference in pressure between the average pressure of the
drainage zone and the well pressure is
qB
141 2 µ r 1
.
p ave − p = o ln e −+ s (10.6)
w
kh r w 2
for steady‐state flow. The units are field units: pressure (psi), flow rate (STB/D),
viscosity (cp), formation volume factor (RB/STB), permeability (md), and formation
thickness (ft). Petroleum engineers often rearrange this equation to obtain an expres-
sion for productivity index J:
q kh
J = = (10.7)
p ( ave − p ) 141 2 . µ B ln r e −+
1
w
s
o r w 2
Productivity index depends on properties and dimensions of the formation, fluid
properties, and skin. Productivity index is a handy term for comparing performances
of any group of wells. It should be clear that increasing skin will decrease produc-
tivity index. The magnitude of skin depends on the extent of near‐well damage.
Severe damage could translate to skin of about 20. Skin for mild damage might be
5 or so. Skin can be negative as noted in the discussion of hydraulic fracturing.
Negative skin corresponds to enhanced permeability in the near‐well region.
