Porosity -permeability correlation
(data from Darling, 2005)
Core data:
Core description
Porosity and permeability
from Conventional Core Analysis
Depth in m
616.0 ... 622.5
Lithology
shale
622.5 ... 625.0
625.0 ... 626.5
626.5 ... 637.5
sandstone
limestone
sandstone
637.5 ... 639.0
639.0 ... 652.0
shale
sandstone
Depth in m
620
622
624
626
628
630
632
634
636
638
640
642
plug porosity
0.020
0.020
0.111
kh in md
0.01
0.02
22
0.095
0.156
0.150
0.075
0.105
0.060
0.179
0.156
10.5
135.6
120
11
15.3
0.8
350
130
plug porosity
0.010
Plot permeability versus porosity:
1000
f(x) = 553577.73 x^4.50
R = 0.98
kh in md
100
10
sandsto
ne
0.1
0.01
0.010
0.100
phi
1.000
00
kh in md
0.03
note: the data point for limestone is eliminated for regression
Derived regression:
k h =5 . 5410
4.5
where permeability is in md and porosity as fraction
sandsto
ne
Capillary Pressure Curves
(data from Darling, 2005)
Core data (SCAL):
permeability k
67
System:
Sample
porosity phi
permeability k
Air-Brine
4
0.179
278
Pressure Pc
in psi
3
Sw
0.861
10
25
50
125
200
0.617
0.388
0.290
0.239
0.216
Pressure Pc
in psi
3
10
25
50
125
200
0.730
0.430
0.282
0.214
0.176
0.144
Pc in psi .
Air-Brine
1
0.131
a) Capillary Pressure Curve
(laboratory data air-brine) in psi
200
150
1
4
100
50
0
0.000
above free water level in m .
System:
Sample
porosity phi
0.200
0.400 0.600
Sw
0.800
1.000
c) Water saturation from Capillary Pressure Curve versus elevation above FWL in m
200.00
150.00
1
4
100.00
above free water level in m .
c) Water saturation from Capillary Pressure Curve versus elevation above FWL in m
200.00
150.00
1
4
100.00
50.00
0.00
0.000 0.200 0.400 0.600 0.800 1.000
Sw
Conversion from air-brine (laboratory) to kerosene-brine (reservoir)
Depth of FWL (m) = 646
Parameter:
cos
System
Air/Brine
72
Kerosene/Brine
26
Capillary pressure in kPa
depth
in m
641.61
air-brine
20.68
kerosene/brine
7.47
above
FWL in m
4.39
68.94
172.35
344.70
861.75
1378.80
24.90
62.24
124.48
311.19
497.90
14.64
36.61
73.22
183.05
292.88
631.36
609.39
572.78
462.95
353.12
elevation
above
FWL in m
4.39
14.64
36.61
73.22
183.05
292.88
depth
Capillary pressure in kPa
air-brine
20.68
68.94
172.35
344.70
861.75
1378.80
kerosene/brine
7.47
24.90
62.24
124.48
311.19
497.90
in m
641.61
631.36
609.39
572.78
462.95
353.12
a)
1
4
b) Capillary Pressure Curve
(converted to kerosene-brine) in kPa
Sw - Sw,irr
Pc in kPa .
ressure Curve
a air-brine) in psi
500.00
1.000
f(x) = 0.826 x^
R = 0.973
400.00
1
300.00
200.00
100.00
0.800
0.00
0.000
1.000
e Curve versus elevation above FWL in m
0.100
1.00
0.200
0.400 0.600
Sw
0.800
1.000
d) Water saturation from Capillary Pressure Curve versus depth in m
depthl in m .
0.600
Sw
elevation
350.00
400.00
450.00
500.00
550.00
1
4
0 1.000
depthl in m .
e Curve versus elevation above FWL in m
d) Water saturation from Capillary Pressure Curve versus depth in m
350.00
400.00
450.00
1
4
500.00
550.00
600.00
650.00
0.000 0.200 0.400 Sw0.600 0.800 1.000
Analyse using Leverett function
J (Sw )=Pc(Sw )
Analyse using Thomeer's equation
k
1
cos
V b, Pc
=e
V b , P
Sw,irr = 0.05
J-function calculated
Sw-Sw,irr
0.811
0.567
0.338
0.240
0.189
0.166
( )
Input parameters
from laboratory data (in kPa)
air-brine
kerosine-brine
0.94
6.50
3.14
7.85
15.71
39.26
62.82
G
P
log c
Pd
(iterative approximation)
sample 1
G
-1.5
pd in psi
1
21.65
54.14
108.27
270.68
433.08
V b ,
1.64
5.47
13.68
27.37
68.42
109.47
V b , pc
=e
1. 5
log ( p
0.08
V b , pc
0 . 08
=e
1. 5
log ( p
6.50
21.65
54.14
108.27
270.68
433.08
b) Thomeer (air-brine s ys tem )
a) J-function
300
1.000
f(x) = 0.826 x^-0.440
R = 0.973
Pc in ps i
Sw - Sw,irr
0.12
0 . 12
0.680
0.380
0.232
0.164
0.126
0.094
sample 4
-1.5
Lab-data sample 1
250
Thomeer curve set 1
Lab-data sample 4
200
Thomeer curve set 4
150
0.100
1.00
100
10.00
J-function
100.00
50
0
0.000
0.200
0.400
Sw
0.600
0.800
1.000
V b , pc
0 . 08
=e
1. 5
log ( p
ys tem )
ata sample 1
eer curve set 1
ata sample 4
eer curve set 4
600
0.800
1.000
Variable
Sample 1
Sample 2
Pc
Vb,Pc
Vb,Pc
5
10
1.026
0.538
0.684
0.359
15
20
25
25
30
40
50
70
100
150
200
250
300
0.430
0.380
0.351
0.351
0.331
0.306
0.290
0.271
0.254
0.239
0.230
0.224
0.220
0.286
0.253
0.234
0.234
0.221
0.204
0.193
0.180
0.169
0.159
0.154
0.150
0.147
Archie parameter
Part 1: Formation factor (F) vs. Porosity (phi)
Scal analyses data
For regression with two parameters (a and m) the first table (SCAL data) is used and plotted in plot a)
For regression with one parameters (m) the second table (logarithms of data) is used and plotted in plot b)
porosity
0.10
0.15
0.17
0.08
0.14
0.13
F
89.3
44.0
33.4
133.4
43.3
58.2
f(x) = 1.28 x^-1.84
R = 0.99
log por
-1.000
-0.824
-0.770
-1.097
-0.854
-0.886
log F
1.951
1.643
1.524
2.125
1.636
1.765
f(x) = N.aN x^N.aN
R = N.aN
a)
2.000
log (F)
1000.0
100.0
1.800
f(x) = - 1.958x
R = 1.000
1.600
1.400
10.0
1.200
1.0
0.01
0.10
phi
1.00
1.000
-1.000
-0.900
-0.8
Part 2: Resistivity index (IR) vs.water saturation (Sw)
used and plotted in plot a)
Plug 1 Scal analyses data
a) is used and plotted in plot b)
f(x) = 1.00 x^-2.19
R = 1.00
b)
1000.000
2.000
1.800
f(x) = - 1.958x
R = 1.000
100.000
1.600
IR
log (F)
x) = N.aN x^N.aN
= N.aN
phi = 0.17
Sw
I=Rt/Ro
1
1.000
0.8
1.612
0.6
2.956
0.4
8.056
0.35
10.150
0.3
12.890
0.28
16.200
1.400
10.000
1.200
1.000
-1.000
-0.900
-0.800
-0.700
log (phi)
-0.600
-0.500
1.000
0.1
Sw
Result: For Log Analysis is used:
a=
m=
n=
vs.water saturation (Sw)
Sw
Analysis is used:
1.00
1.96
2.19
phi
0.02
0.1
1
F
2121.208059
90.78205302
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