Page 176 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 114

particles suspended in the mud can partially plug the pore spaces, reducing the
permeability, and creating a damaged zone in the vicinity of the wellbore.

The situation is shown in fig. 4.5, in which r a represents the radius of this zone. If

q

p e
pressure

∆
p skin

r
r w r a r e
Fig. 4.5 Radial pressure profile for a damaged well

the well were undamaged, the pressure profile for r < r a would be as shown by the
dashed line, whereas due to the reduction in permeability in the damaged zone,
equ. (4.25) implies that the pressure drop will be larger than normal, or that p wf will be
reduced. This additional pressure drop close to the well has been defined by van
7
Everdingen as

qµ
∆ p skin = 2kh S (4.26)
π

in which the ∆p skin is attributed to a skin of reduced permeability around the well and S
is the mechanical skin factor, which is just a dimensionless number. This definition can
be included in equ. (4.25) to give the total steady state inflow equation as
qµ r
p − p wf = ln e + S (4.27)
e
2kh r w
π
in which it can be seen that if S is positive then p e - p wf the pressure drawdown,
contains the additional pressure drop due to the perturbing effect of the skin.

Since equ. (4.27) is frequently employed by production engineers, it is useful to
express it in field units rather than the Darcy units in which it was derived. The reader
should check that this will give

qB r
µ
p − p wf = 141.2 kh o In r w e + S (4.28)
e

in which the geometrical factor 2π has been absorbed in the constant. This equation is
frequently expressed as