Rock Petrophysical Properties and Modeling

Chert / Spicule
Wacke-Packstone
Schaben Field
Echinoderm
Pack-Wackestone
Spicule
Pack-Wackestone
Chert Breccia
6
8 10 12 14 16 18 20 22 24 >24
70
60
50
40
30
20
10
80
70
60
50
40
30
Echinoderm 150 ft
Echinoderm 50 ft
Spicule 150ft
Spicule 50 ft
20
10
0
0
0.001
0.01
0.1
1
10
100
0.001
80
1
10
10
k=100 md
k=50 md
k=10 md
k=5 md
k=1 md
90
0.1
100
Insitu Klinkenberg Permeability (md)
In situ Klinkenberg Permeability (md)
100
0.01
70
60
50
40
30
20
10
0
k=100 md
k=50 md
k=10 md
k=5 md
k=1 md
9
8
7
Generalized Capillary Pressure Curves
6
5
4
3
2
1
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cht0.189 f
ki = 0.746 e
Limestone
sl dol Limestone
Sucrosic Dolomite
Argillaceous Dolomite
Chert
Lm Pack-Suc Dol Mtx
cherty dol mudstone
arg Limestone
0.1
0.01
0.001
Regional Trend Boundaries
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34
Routine Porosity (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation (fraction)
Water Saturation (fraction)
Modeling Relative Permeability
Since relative permeability end point saturations change with permeability (e.g.,
“irreducible” water saturation changes with permeability), the relative permeability
curves also change with absolute permeability. Relative permeability curves for any
given permeability were modeled using Corey-type equations where Swi was obtained
from Pc-k relations and the average absolute permeability values assigned. Exponent
m and n values were initially obtained from measured data and were modified during
simulation to reproduce lease production data.
m
kro = a 1(1-SwD)
n
krw = a 2 SwD
SwD = (Sw-Swi)/(1-Swi-Sorw)
For moldic-porosity Mississippian rocks residual oil saturation to waterflood also
changes with permeability and/or Swi following the general trend: Sorw=(1-(Swi+0.5)).
Initial pseudo-Swi values were assigned to each layer using Pc-k relations discussed.
Figures show how kro and krw change with permeability. The lower figures on right
Lithofacies Key
Echinoderm Grainstone-Cemented
Echinoderm Packstone
Echinoderm Pack-Wackestone
Echinoderm Wacke-Packstone
Echinoderm Mud-Wackestone
Spicule Packstone
Spicule Pack-Wackestone
Spicule Pack-Wackestone-Echinoderm-rich
Spicule Pack-Wackestone-Cherty
Spicule Pack-Wackestone-Muddy
Spicule Wacke-Packstone
Spicule Wacke-Packstone-Echinoderm-rich
Spicule Mud-Wackestone
Bryozoan Packstone
Bryozoan Pack-Wackestone
Bryozoan Wacke-Packstone
Bryozoan Mud-Wackestone
Mudstone
Mudstone-Cherty
Chert Breccia
Chert/Cherty
Brecciated
Argillaceous
Evaporitic
Vuggy
0.1
0.01
0.001
2
4
6
8
10 12 14 16 18 20 22 24 26
10
1
0.1
0.01
Ness City Field
1
0.1
k=100 md
k=50 md
k=10 md
k=5 md
k=1 md
k=100 md-kro
k=50 md-kro
k=10 md-kro
k=5 md-kro
k=1 md-kro
0.01
Calculator for Wellington West
K(md)=
Krwmax=
Krw -m=
Kro - n=
water grad
oil grad
0.0
0
2
4
6
8
10 12 14 16 18
In situ Porosity (%)
20 22
24
0.1
0.2
26
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Echinoderm
Pack-Wackestone
10
Spicule Mixed
Wacke- Packstone
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
0.4000
0.4500
0.5000
0.5500
0.6000
0.6500
0.7000
0.7500
0.8000
0.8500
0.9000
0.9500
1.0000
1.0000
m=0.5
m=2
m=4
n=3.1
0.001
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Water Saturation (fraction)
1000
k=100 md
k=50 md
k=10 md
100
k=5 md
k=1 md
10
1
0.1
0.01
100
m=0.5
m=2
m=4
10
1
0.1
0.01
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
Water Saturation (fraction)
1
Kromax=
Swi=
Sorw=
W sp grav=
Oil sp grav=
1
0.05
0.450
1.0111
0.8439
Pce=
Pcs=
PcSwiH(ft)=
input value
calc value
0.520
-0.879
60.0
0.2
0.3
0.4
0.5
0.6
0.7
Water Saturation (fraction)
0.8
0.9
1.0
KRW
KROW
0.0000
31.4960
44.6318
54.6992
63.1823
70.6541
77.4080
83.6182
89.3980
94.8262
99.9600
100.0000
100.0000
100.0000
100.0000
100.0000
100.0000
100.0000
100.0000
100.0000
100.0000
PCOW
1.0000
0.7233
0.5023
0.3322
0.2061
0.1172
0.0588
0.0241
0.0069
0.0008
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
SwD
7.236
3.934
99.94
54.34
2.755
38.05
2.139
29.55
1.758
24.29
1.498
20.69
1.308
18.07
1.163
16.07
1.049
14.49
0.956
13.21
0.879
0.814
0.759
0.711
0.669
0.633
0.600
0.570
0.544
0.520
0.520
12.14
11.25
10.49
9.82
9.25
8.74
8.28
7.88
7.51
7.18
7.18
0.00000
0.09920
0.19920
0.29920
0.39920
0.49920
0.59920
0.69920
0.79920
0.89920
0.99920
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
0.01
Spicule
Wacke-Packstone
0.001
0
2
4
6
8
10 12 14 16 18
In situ Porosity (%)
20
22
24
26
PPTD = 2.60ki
R2 = 0.93
1
0.1
0.01
0.0001
Spicule
Mud-Wackestone
Undifferentiated Sandstones
& Carbonates
Mississippian
0.001
0.01
0.1
1
10
100
In situ Klinkenberg Permeability (md)
Echinoderm
Wacke-Packstone
1000
Wellington
West dolomites
exhibit a
general
increase in
pore body size
with increasing
k as shown by
Nuclear
Magnetic
Resonance T2
times.
Archie Cementation
Exponent
Wellington Mississippian Composite
1.0
3179.1; 64.3 md
0.9
3180.0; 39.2 md
3176.2; 19.5 md
0.8
3692.3; 8.67 md
3190.2; 8.10 md
0.7
3196.6; 2.29 md
0.6
3973.2; 0.61 md
3764.2; 0.13 md
0.5
3758.0; 0.01 md
T2=80ms
0.4
0.3
0.2
0.1
0.0
1
10
100
Time (ms)
1000
0.1
0.1
0.001
0.1
0.001
0.1
1
10
100
1000
10000
Traditional wireline log calculation of
saturations use the Archie equation and
cementation (m) and saturation exponent (n)
values of 2. Formation resistivity factors (Ro/Rw)
measured at Rw=0.045 ohm-m (Figure) indicate
that the Archie cementation exponent (assuming
an Archie intercept of 1.0) averages
m=1.97+0.09 for all facies. Echinoderm-rich
facies can exhibit cementation exponents
between 2.0 and 2.1. Vuggy cherts can exhibit
cementation exponents between 2.1 and 2.2.
How to reconstruct oil
production history?
Used to estimate missing production data or to predict future
production provided production practices remain unchanged.
This method estimates reserve volumes that are in pressure
communication - ultimately recoverable by the wells.
Type curves, theoretical solutions to flow equations, are often
used for decline analyses.
Fetkovich decline type curves were used here.
Model assumptions
Well producing under constant BHP
Well is centered in a circular drainage area
No-flow occurs at drainage boundaries
100
10
0.01
0.1
1
10
100
1000
10000
0.01
0.1
1
10
100
1000
10000
0.01
0.1
Months
Months
1000.0
Missing oil production between 1983 to 1988 estimated for
Becker #1 - completed oil history.
Production history for Becker #4 completed between 1983
to 1988 by subtraction Becker #1 production from Becker
Lease.
Reconstructed Becker #4 history also falls on a
decline curve.
Waugh #2 - online Jun 1983
1000.0
100.0
Decline curves analyse production data from depletion period
only.
1000
0.001
Months
1000.0
Transient - decline caused by fluid expansion with
continually increasing drainage area
Depletion - decline after drainage radius reaches outer
boundaries
0.442
10
0.1
0.001
Waugh #1 - online Feb 1983
Production data normally includes both transient and
depletion declines
To facilitate simulator modification and history matching an Excel worksheet
was constructed that contained all relevant equations linked to porosity and/or
permeability. With this worksheet, if the simulator required an adjustment of the
permeability, the corresponding capillary pressure and relative permeability
properties could be calculated and input. This kept all petrophysical properties
“coupled.” This worksheet also provided easy changes to relative permeability
and immediate feed-back of the effect of a change on flow at a given saturation.
In situ Formation Resistivity
Factor (Ro/Rw)
0.1
1.0
0.01
st
10.0
1.0
100.0
10.0
1
10
Months
100
im We
ul ll
at
ed
1000
10000
St
100.0
im
ula
tio
10.0
ns
1.0
0.1
0.001
0.01
0.1
1
10
100
1000
10000
Months
Waugh #3 - online Sep 1983
1000.0
Waugh #4 - online Sep 1983
1000.0
100.0
10.0
Oil production histories reconstructed for
Wharton #1 & #2.
Oil production for Wharton #3 during
1985-89 estimated by subtracting
production from Wharton #1 & #2 from
lease production.
Reconstructed production history for
Wharton #3 falls on a decline curve and
indicates intermittent stimulations.
100.0
10.0
10.0
1.0
1.0
1.0
1.0
0.1
0.001
0.1
0.1
0.001
0.1
0.001
0.01
0.1
1
10
100
1000
10000
0.001
0.01
0.1
1
10
100
1000
10000
0.01
0.1
1
Months
10
100
1000
10000
0.01
0.1
1
10
100
1000
10000
Months
Months
Waugh #5 - online Sep 1983
1000.0
Inferences from Decline Curve Analyses
100.0
10.0
1.0
free water (ft)
10.0
1.0
Initial oil production history missing in each well
Match available production (rate/time) data with a model.
100
Fraction of Pore Volume
In situ Klinkenberg Permeability (md)
100
Principal Pore Throat Diameter (u m)
Echinoderm
Pack-Wackestone
0.01
0.0
krw/kro Relative Permeability Ratio
Cherty Spicule
Pack-Wackestone
Though permeability is shown correlated with porosity,
variables that control permeability in Mississippian rocks
include pore throat size and distribution, grain size
distribution, moldic pore size and packing, and moldic pore
connectivity. Porosity is only one of the variables
controlling permeability and bivariate correlation therefore
relies on the correlation between porosity and the other
controlling variables. A crossplot of permeability and
principal pore throat diameter (PPTD) illustrates the control
PPTD exerts on permeability.
krw/kro Relative Permeability Ratio
Bindley Field
0.1
Water Saturation (fraction)
Permeability and Pore
Throats
Echinoderm/Bryozoan
Pack-Wackestone
SW
1.0
1000
100
0.5
3.1
0.438
0.365
10.0
100.0
1.0
Field developed between 1977 to 1985
Majority of wells drilled in 1983
Advanced Decline Curve
Analyses
100
100.0
100.0
g
n
i
s
s ta
i
M da
1000.0
Wharton #3 - online Jul 1985
Height above
0.001
0.001
To provide capillary pressure curves for the reservoir simulation it was
necessary to develop generalized curves that represented the
specific permeabilities that might be assigned to a gridcell. Equations
to construct generalized capillary pressure curves were constructed
based on the relationships evident from the entry pressures and
curve shapes in the air-mercury capillary pressure curves, and from
the saturations evident in the air-brine capillary pressure analysis.
The relationships between increasing entry pressure, “irreducible”
wetting phase saturation, and the capillary curve curvature (reflecting
increasing pore throat size heterogeneity) with decreasing
permeability were utilized to develop equations that would predict the
capillary pressure curve using permeability as the independent
variable.
Entry pressure, or the first pressure at which wetting phase
desaturation begins and similar to R35, exhibits a strong correlation
with permeability and can be predicted using:
Pcowentry = 4.374 ki -0.4625
Where Pcowentry is the oil-water entry pressure and ki is the in situ
permeability. Using the above term and a function to model capillary
pressure curve shape synthetic capillary pressure curves could be
created for any permeability.
Barrel test (Oil & Water) data available from
1989 to date - 1 test per year
10.0
Months
1
Relative Permeability (fraction)
1
Relative Permeability (fraction)
Echinoderm
Mud-Wackestone
10
Echinoderm
Pack-Wackestone
For cores near Wellington West the following relations predicts Sw60:
Sw60(%) = -28.8 log10 kinsitu + 62.6.
100.0
1000.0
Bopd
4
80
90
1000.0
Bopd
0
90
1000.0
Bopd
5
100
Becker #4 - online Jun 1983 Wharton #1 - online Apr 1981 Wharton #2 - online Sep 1982
Becker #1 - online Feb 1977
Bopd
8 10 12 14 16 18 20 22 24 26
Bopd
6
In situ Porosity (%)
100
10
1
Cherty Mudstone
Echinoderm Grainstone
Cemented
4
100
In situ Porosity (%)
Chert Breccia
2
Bopd
Dol0.189 f
ki = 0.746 e
10
Ls0.569 f
ki = 0.00198 e
Spicule
Wacke-Packestone
0
Bryozoan
Pack-Wackestone
0
1000
Bopd
100
Water Saturation at Oil Column
Height (%)
Percent of Population (%)
10
15
Porosity (%)
In situ Klinkenberg Permeability (md)
In situ Klinkenberg Permeability (md)
Echinoderm Grainstone
Cemented
1
Field production recorded by lease
Wharton Lease - 3 wells
Becker Lease - 2 wells
Waugh Lease - 6 wells
ng
si
is a
M dat
Spicule
Mud-Wackestone
0.1
100
0
100
0.01
In situ Klinkenberg Permeability (md)
0.0001
Cherty Spicule
Pack-Wackestone
10
ng
si
is a
M dat
(%) - 3.78
20
ng
si
is a
M dat
in situ
30
ng
si
is a
M dat
log kin situ (md) =0.24 f
40
ng
si
is a
M dat
log kin situ = 0.25 f in situ - 4.5
!Between these bounding trends each lithofacies exhibits a
generally unique range of k and f which together define a
continuous trend with k decreasing with decreasing grain/mold
size for any given porosity. Each individual lithofacies exhibits a
unique sub-parallel trend to the general trend. Statistically the
general trend is dominated by the large number of spicule-rich
samples and is strongly influenced by mudstone and cemented
echinoderm grainstone properties:
50
0
0.001
20
60
Reconstruct Oil Production History
Advanced Decline Curve Analyses
Production data
Bopd
2.5
10
70
Fluid saturations in the Wellington West field were determined
using electrical wireline logs and capillary pressure relations.
Capillary pressure curves show a relationship of increasing threshold
entry pressure with decreasing permeability that is consistent with
decreasing pore throat size with decreasing permeability (Figure).
Capillary pressure properties of Mississippian carbonates differ
between lithofacies. Structural closure in many Mississippian
Kansas fields is less than 60 feet limiting oil column heights and
necessitating understanding of the exact capillary pressure
relationships.
Air-brine capillary pressure measurements indicate that water
saturations at 45-50 ft (Sw45,Sw50) above free water increase with
decreasing porosity and permeability (Figures). Because of the
close correlation between lithofacies and k-f , Sw also increase with
decreasing grain/mold size from packstone to mudstone. Sw45 in
Schaben can be predicted within + 14% (saturation %) using:
Sw45(%) = -20*log kinsitu + 61. Within the echinoderm-rich facies in
Ness Field, Sw50 is correlated with f and k: Sw50(%) = -3.21 f insitu +
87.6l (SE=+19%) and Sw50(%) = -17.5 log10 kinsitu + 42.1 for
Echinoderm-rich facies (SE=+8.7).
Bopd
in situ -
20
Oil-Brine Capillary Pressure (psia)
log kin situ = 0.25 f
30
Height Above Free Water (ft)
The permeability-porosity trend for all lithofacies are approximately
bounded within two orders of magnitude by trendlines defined by:
40
0
Wireline log response was able to to identify dolomite, limestone,
and chert facies but could not distinguish lithofacies (mudstonegrainstone). Permeability-porosity (k-f ) trends for cores from eight
wells in nearby fields were consistent with regional Mississippian
trends. It was assumed that these trends were most representative
of the Wellington West field. Permeability for the carbonates was
predicted from porosity using:
0.189 f
Dolomite:
ki = 0.746 e
0.569 f
ki = 0.00198 e
Limestone:
Local cherts exhibit a k-f trend (light blue line) that is subparallel to
the regional chert trend (blue line). Because of limited local
sampling the regional trend was considered more robust and was
utilized for modeling.
0.166 f
ki = 0.0309 e
Chert regional:
0.273 f
ki = 0.000894 e
Chert:
Insitu Klinkenberg Permeability (md)
Lithofacies and early diagenesis are major controls on permeability
(k) and porosity (f ) despite complex diagenetic overprinting by subPennsylvanian subaerial exposure and burial processes.
!k and f decrease significantly and continuously with decreasing
grain/mold size from packstone to mudstone ( a trend exhibited by
many other carbonates) and from echinoderm-rich to spicule-rich
facies
50
25
Wellington West Equations
Lithofacies, Permeability,
Porosity
60
80
ng
si
is a
M dat
As with many smaller Mississippian fields, core was not available from within the
field. To provide models for predicting permeability, oil-water relative permeability,
capillary pressure properties, and connate water saturations, regional
petrophysical trends for the Mississippian and trends obtained from analysis of
eight cores from nearby fields were used.
70
90
ng
si
is a
M dat
Porosities for the Wellington West
field average 16+4%. Porosities
are interparticle, intraparticle and
moldic. Properties of the moldic
porosity rocks are largely controlled
by original depositional fabric with
permeablity increasing from
mudstones to grainstones.
80
"Irreducible" Water Saturation at
~50' Oil Column (%)
Sources for Core Analysis Data
Porosity Distribution
30
90
Bopd
Rock Petrophysical Properties and Modeling
Capillary Pressure
100
"Irreducible" Water Saturation
at ~50' Oil Column (%)
Water Saturation at ~45 ft Above
Free Water (%)
100
0.1
0.001
0.01
0.1
1
Months
10
100
1000
10000
Oil production histories were completed using initial production (IP) rates and barrel test data recorded
since 1989.
Reconstructed oil production data from wells in a lease when added together closely approximated
recorded lease production.
Available production data, for most of the productive life of each well, could be modeled by a decline
curve. This means that bottom hole producing pressures (Pwfs) at the wells remained mostly unchanged.
Recorded production data at some of the wells indicated that wells underwent intermittent stimulations.
A very short transient decline is visible when the recorded production data is plotted on Fetkovich’s
Type Curve. This is indicative of low effective permeabilities existing in the reservoir.
Water Production data
Available water production data consisted of IP (initial production)
records from Scout cards and annual barrel test results from 1989.
The IP records show that measureable amounts of water were
recorded in only 4 wells - Waugh #5, #6, #7, and Wharton #3.
Of these 4 wells, water rates greater than 2 bbls/day were recorded
in only 2 wells. It appears that initial water production from remaining
wells were not significant enough to merit measurement and record.
Based on this limited water production data, it is not unreasonable
to assume that initial water saturation in the reservoir was at
“critical water saturation”, Swcrit, where the relative permeability
to water, Krw,is effectively zero (or close to zero as perhaps is the
case in this field).
Summary of IP rates from Scout Cards
Well
KB
Perforation
from, ft
Perforation
to, ft
Perf from Perf to
IP bopd IP bwpd Acidization
Subsea, ft Subsea, ft
Wharton 1
Wharton 2
Wharton 3
1237
1244
1246
3644
3646
3654
3658
3660
3664
-2407
-2402
-2408
-2421
-2416
-2418
15
Yes
25 No Water Yes
25
10 Yes
Becker 1
Becker 4
1246
1248
3790
3652
3800
3670
-2544
-2404
-2554
-2422
50
25 Water
Yes
Yes
Waugh 1
Waugh 2
Waugh 3
Waugh 4
Waugh 5
Waugh 6
Waugh 7
1258
1252
1248
1259
1245
1257
1256
3654
3652
3644
3672
3660
3655
3680
3670
3656
3662
3686
3670
3656
3685
-2396
-2400
-2396
-2413
-2415
-2398
-2424
-2412
-2404
-2414
-2427
-2425
-2399
-2429
25
25 Water
15 Water
15
30
25
25
Yes
Yes
Yes
Yes
2 Yes
25 Yes
1 Yes
1
1
10
In situ Porosity (%)
100
Bhattacharya et al, AAPG Salt Lake City, May 11-14, 2003 Panel 2