(12) Darcy’s Law for the Oil Phase with Skin: , where, phase perm = ko = k∙kro
![Oil Gas Rel Perm Radial Darcy 1.png]()
For the reservoir section shown on the previous page, use this data:
k = 30 md o = 2 cp Bo = 1.3 RVB/STB
kro = 0.4 g = 0.05 cp Bg = 0.0011 RVB/SCF
krg = 0.1 pe = 2400 psi pw = 2000 psi
Rs = 720 SCF/STB
19) For this radial reservoir section, please calculate: (Use of kro, krg assumes average saturation in reservoir.)
1. The effective permeabilities (phase permeabilities) to oil and to gas (ko and kg): [ko = 12 md, kg = 3 md]
2. The producing rate of oil in RVB/day and in STB/day. [ qo = 58.5 RVB/day = 45.0 STB/day ]
3. The volume rate of free gas that is flowing in the reservoir, in RVB/day and in SCF/day.
[qg = 585 RVB/day = 531.83 MCF/day]
4. The reservoir GOR in [RVB gas/RVB oil]. [ GORres = 10 RVB gas/RVB oil ]
5. The instantaneous producing GOR [SCF gas/STB oil]. [ GOR = 12,538 SCF/STB ]
Basic skin concept and calculations:
20. Sketch the simple “skin” model we used, and label ks, rs, rw, k and re.
21. Positive skin corresponds to what? List three factors which produce positive skin.
22. Negative skin corresponds to what? List three ways that production engineers can enact negative skin in a well? In general, these actions to effect negative skin are called what?
23. (a) For a well we know k = 55 md, ks = 30 md, rw = .25 ft, and rs = 2.5 ft, calculate the skin factor, s.
[ Answer: s = 1.909 ]
(b) Given the following additional information for the well, calculate ps, the pressure drop due to skin.
[ ps = 7.10 psi ]
q = 100 STB/d B = 1.45 RB/STB
h = 70 ft = 0.7 cp
Productivity Index:
24. Take each term in the PI equation (k, kro, h, o, Bo, rw, and s) and explain how petroleum engineers can (or cannot) modify these to maximize production rate q for a given p.
226
oro
kkk
=×
(
)
[
]
s
r
r
p
p
B
h
k
q
w
e
w
e
o
o
o
o
+
-
×
=
-
/
ln
10
08
.
7
3
m
3
12
1.12710
o
o
oo
kA
pp
q
BL
m
-
-
=×
3
12
1.12710
g
g
g
kA
pp
q
L
m
-
-
=×
grg
kkk
=×
3
12
1.12710
g
g
gg
kA
pp
q
BL
m
-
-
=×
gggrggrgo
res
oooroorog
qkkk
GOR
qkkk
mmm
mmm
====
(
)
(
)
(
)
(
)
rggg
rgoo
surf
rogg
rooo
kB
kB
GOR
kB
kB
m
m
m
m
==
o
ro
o
o
o
k
k
k
m
m
l
×
=
=
wrw
w
ww
kkk
l
mm
×
==
grg
g
gg
kkk
l
mm
×
==
/
wwrwwrwo
reswo
ooroorow
kkk
WORM
kkk
mmm
mmm
====
/
ggrggrgo
resgo
ooroorog
kkk
GORM
kkk
mmm
mmm
====
(
)
(
)
(
)
(
)
/
rwww
rwoo
surfwo
roww
rooo
kB
kB
WORM
kB
kB
m
m
m
m
===
(
)
(
)
(
)
(
)
/
rggg
rgoo
surfgo
rogg
rooo
kB
kB
GORM
kB
kB
m
m
m
m
===
rgoo
s
rogg
kB
GORR
kB
m
m
=+
ro
o
k
k
k
×
=
rw
w
k
k
k
×
=
rg
g
k
k
k
×
=
k
k
k
o
ro
=
k
k
k
w
rw
=
k
k
k
g
rg
=
3
12
1.12710
pp
kA
q
L
m
-
-
=×
L
p
p
A
k
q
w
w
w
2
1
3
10
127
.
1
-
×
=
-
m
rw
w
k
k
k
×
=
L
p
p
B
A
k
q
w
w
w
w
2
1
3
10
127
.
1
-
×
=
-
m
(
)
3
7.0810
ln
ew
ew
pp
kh
q
rr
m
-
-
=×
(
)
3
7.0810
ln
oew
o
oew
khpp
q
rr
m
-
-
=×
3
12
1.12710
o
o
o
kA
pp
q
L
m
-
-
=×
(
)
3
7.0810
ln
oew
o
ooew
khpp
q
Brr
m
-
-
=×
(
)
3
7.0810
ln
g
ew
g
gew
kh
pp
q
rr
m
-
-
=×
(
)
3
7.0810
ln
g
ew
g
ggew
kh
pp
q
Brr
m
-
-
=×
(
)
[
]
s
r
r
B
h
k
k
p
p
q
PI
w
e
o
o
ro
wf
e
o
+
×
×
×
×
=
-
=
-
/
ln
10
08
.
7
3
m
1ln
s
sw
r
k
s
kr
æöæö
=-
ç÷ç÷
èøèø
(
)
141.270.6
2
s
qBqB
pss
khkh
mm
D=×=×
Jim_Ak
hw24.docx
0
