Page 199 - Introduction to Petroleum Engineering

186 WELL COMPLETIONS
10.1 SKIN

Fluids and particulates in the drilling mud invade the formation immediately around
the well during the drilling process. Drilling mud filtrate can change relative perme-
ability or lead to mineral precipitates and scale buildup as the filtrate reacts with
formation solids and native brine. Particulates in the drilling mud can plug pores in
the formation. The extent of invasion of fluids and particulates varies, but the general
result is reduced capacity for flow. Petroleum engineers refer to this as formation
damage, and they quantitatively describe the extent of permeability damage with a
dimensionless quantity “skin.” An objective of well completion is to reduce skin.
To explore the concept of skin, consider radial flow through a damage‐free
cylindrical zone of radius r around a well of radius r . Darcy’s law for state–state
w
radial flow is
µ
141 2 qB  r 
.
−
pp = o ln   (10.1)
w
r
kh  w 
The constant 141.2 in Equation 10.1 incorporates conversion factors so that field units
can be used for the various parameters. Specifically, p is the pressure (psi) at wellbore
w
radius r (ft), p is the pressure (psi) at radius r (ft), q is the liquid flow rate (STB/D), μ is
w
the viscosity (cp), B is the formation volume factor (RB/STB), k is the permeability
o
(md), and h is the formation thickness (ft). Imagine that this cylindrical zone is now
damaged such that its permeability k is less than the undamaged permeability k. The
d
pressure drop for the same flow rate q through the damaged zone is
µ
141 2 qB  r 
.
−
pp wd = o ln   (10.2)
r
kh  w 
d
Here, p is wellbore pressure when the formation is damaged. The pressure drop
wd
p − p must be greater than p − p when k is less than k. In other words, p must be
wd
d
wd
w
less than p . Solving the previous equations for the change in pressure as a result of
w
the change in permeability gives
qB 
141 2 µ k   r 
.
p − p wd = o  −  1 ln   (10.3)
w
kh  k d   r w 
d
or
µ
141 2 qB
.
p − p = o s (10.4)
w wd 2π h
in which the skin s is a dimensionless pressure drop given by the following
expression:
 k   r 
s =  −  1ln  d  (10.5)
r
 k d   w 