Skin Effect and Formation Damage - KSU...
Transcript of Skin Effect and Formation Damage - KSU...
By
Dr. Mohammed A. Khamis
02-02-2016
Well Stimulation and Sand Production
Management (PGE 489 )
Skin Effect and Formation Damage
Skin Factor
• A formation damage model is a dynamic relationship expressing the
fluid transport capability of porous medium undergoing various
alteration processes.
• Modeling formation damage in petroleum reservoirs has been of
continuing interest. Although many models have been proposed,
these models do not have the general applicability.
Hawkins’ Formula
idealreals ppp
Hawkins’ Formula
w
s
s
realwfsrealr
r
hk
qppp ln
2,
w
sidealwfsideal
r
r
kh
qppp ln
2,
skh
qps
2
idealreals ppp
Steady-state pressure drop due to skin is given by:
w
s
w
s
s r
r
kh
q
r
r
hk
qs
kh
qln
2ln
22
w
s
w
s
s r
r
kr
r
ks
kln
1ln
11
w
s
s r
r
k
ks ln1
Hawkins’
Formula
Ps
pwf
rsrw
Hawkins’ Formula
Ps
pwf
rsrw
s
w
r
r
realrrk
dr
h
qp
)(2
w
sideal
r
r
kh
qp ln
2
skh
qps
2
idealreals ppp
Steady-state pressure drop due to skin is given by:
w
s
r
rr
r
kh
q
rrk
dr
h
qs
kh
q s
w
ln2)(22
General
Hawkins’
Formula
w
s
r
rr
r
krrk
drs
k
s
w
ln1
)(
1
w
s
r
rr
r
rrk
drks
s
w
ln)(
Hawkins’ Formula - Example
Hawkins’ Formula - Example
Example: assume that a well has a radius rw equal to 0.25 ft, and the
damage beyond the well is 5 ft. What would be the skin effect if the
permeability impairment results in k/ks equal to 6 and 12, respectively.
Solution:
22.1525.0
25.5ln16ln1
w
s
s r
r
k
ks
49.3325.0
25.5ln112ln1
w
s
s r
r
k
ks
non-Darcy Skin (S)
2
1.05106
perfw
s
hr
hkD
Where, is the gas gravity, ks is the
near-wellbore permeability in md, h
and hperf are the net and perforated
thicknesses in ft and is the gas
viscosity in cp.
Dqs
Skin due to turbulence is additional
pressure drop caused by high gas
velocity near the wellbore and applies
only to gas wells.
This shows the apparent skin from well testing.
Dqss
non-Darcy Skin (S)
Example: Calculate the non-Darcy coefficient for well with wellbore radius
of 0.25 ft. Assume that ks is the same as the reservoir permeability (0.1 md)
and hperf is half of the reservoir thickness. Use a viscosity of 0.01 cp, gas
gravity of 0.6, and reservoir thickness of 80 ft. What will happen if the near-
wellbore permeability reduced by damage to one-fifth?
Solution:
19
2
1.05
2
1.05
/1006.9
)40)(25.0)(01.0(
)80()1.0()6.0(106106
dMSCF
hr
hkD
perfw
s
18
2
1.05
2
1.05
/1006.1
)40)(25.0)(01.0(
)80()02.0()6.0(106106
dMSCF
hr
hkD
perfw
s
Slanted/Partial Penetration
Partial Completion Skin
• Skin due to partial penetration
is always greater than 0 and
typically ranges from 0 to 30.
• Partial penetration with
vertical permeability (kv)
equal to zero is the limiting
case. Skin factor can be
estimated using Hawkins’
formula.
Partial Completion Skin
1
2cos71
1ln
5.0h
hh
rh
r
rs
ww
epp
Muskat’s Model
zw
hw h
h = Reservoir height
hw = Perforation height
zw = The elevation of the
perforation midpoint from the base
of the reservoir
Completion Ratio
This model did not consider the permeability anisotropy
h
hh w
95.1lnln1.049.0ln135.1
825.0
wc
V
H
V
H
w
pp rk
kh
k
kh
h
hs
Odeh Model
zw
hw h
0
0753.22126.0exp
yforr
yforh
zr
r
w
mw
wc
2
wm
hyz y
h = Reservoir height
hw = Perforation height
zw = The elevation of the perforation midpoint from
the base of the reservoir
y = The distance from top of reservoir to top of
perforation
Where,
Partial Completion Skin
Papatzacos Model
zw
hw h
y
h = Reservoir height
hw = Perforation height
zw = The elevation of the
perforation midpoint from the base
of the reservoir
y = The distance from top of
reservoir to top of perforation
Where,
5.0
1
1
1
1
2ln1
1
B
A
h
h
hrhs
pD
pD
pDDpD
pp
43
1
4
1
1
1
1
5.0
pDD
pDD
D
H
VwD
wpD
hhB
hhA
y
hh
k
k
h
rr
h
hh
All models assumed kx = ky
Partial Completion Skin
Partial Completion Skin
Ref. Yildiz (2006), SPE-82249
Partial Completion Skin
Example:
A well with a radius rw = 0.328 ft is completed in a 33-ft reservoir.
In order to avoid severe water coning problems, only 8 ft are completed
and the midpoint of the perforations is 29 ft above the base of the
reservoir.
1. Calculate the skin effect due to partial completion for a vertical well.
What would be the composite skin effect if Ɵ = 45°?
2. Repeat this problem for h = 330 ft, hw = 80 ft and zw = 290 ft.
Partial Completion Skin - Example
Solution:
The dimensionless reservoir thickness hD is h/rw = 33/0.328 = 100.
The elevation ratio is zw/h = 29/33 = 0.875
The completion ratio is hw/h = 8/33 = 0.25.
From Table 5-1 for a vertical well,
Ɵ = 0°and Sc + Ɵ = 8.6, Sc = 8.6 and SƟ = 0.
If Ɵ = 45° , then
Sc = 8.6 but SƟ = -2.7 resulting in Sc + Ɵ = 6.
If hD = 330/0.328 = 1000 and the other ratios are the same.
From Table 5-2
Sc + Ɵ = 15.7 for the vertical well and
Sc + Ɵ = 10.4 for the 45°slant well.
Partial Completion Skin - Example
Solution:
Ɵ hD zw/h hw/h S Ɵ + c Sc S Ɵ
• When the angle of inclination
through the formation is
significant (> 10°), a reduction in
pressure drop can occur due to
the angle of inclination.
• This pressure drop is defined as
skin due to inclination
• The skin is negative and the
larger the angle of slant, the
larger the negative contribution
to the total skin effect.
100log
5641
865.1'
06.2'
Dw hs
w
V
Hw
k
k tantan 1'
V
H
w
Dk
k
r
hh
Does s negative all the time?
Skin due to Inclination
Perforation Skin