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GFREE RESEARCH PROJECT
Everything you always wanted to know aboutPickett Plots*
* BUT WERE AFRAID TO ASK
Roberto Aguilera
Schulich School of Engineering
University of Calgary
April 24, 2011
Roberto Aguilera (2012)
GFREE
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OUTLINE
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Pickett plots, basic equations
Clean formations, shaly formations
m, n and Sw
k, rp35, Pc, h
In the case of shale formations:
Sw, TOC, LOM, viscous vs. diffusion-like flow Conclusions
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BASIC EQUATIONS (1942)
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PICKETT PLOT (CLEAN FORMATIONS)
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PICKETT PLOT (CLEAN FORMATIONS)
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PICKETT PLOT (CLEAN FORMATIONS)
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CARBONATE EXAMPLE
Integrate in a Pickett Plot:
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Porosity and water saturationPermeability and process speed
Capillary pressureHeight above free water tablePore throat aperture and particle size
KozenisconstantRock fabric number (grainstones, packstones, wackstones)
Range of initial flow rates
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PROCESS or DELIVERY) SPEED
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IS THE RATIO OF PERMEABILITY AND
POROSITY (k / )AND IS RELATED
DIRECTLY TO PORE THROATAPERTURE. IT PROVIDES A RELATIVE
INDICATION OF HOW QUICKLY FLUIDS
CAN MOVE THROUGH POROUS MEDIA(Chopra et al., 1987; Gunter et al., 1997)
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PERMEABILITY
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K1/2= 250 3/ Swi1AT IRREDUCIBLE
CONDITIONS (MEDIUM
GRAVITY OIL)(Source: Morris and Biggs)
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PORE THROAT RADIUS (m)
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r = 108.1 / PcHg-Air
ASSUMING:
INTERFACIAL TENSION:Hg-Air= 480 Dyne/cm
AIR/MERCURY CONTACT ANGLE:
Hg-Air= 140 Degrees
(Aguilera, AAPG, 2004)
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HEIGHT ABOVE
FREE WATER TABLE h)
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h (ft) 0.705 PcHg-Air
ASSUMING A MEDIUM
GRAVITY OIL RESERVOIR(Aguilera, AAPG, 2004)
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HEIGHT ABOVE
FREE WATER TABLE h)
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h (ft) 0.405 PcHg-Air
ASSUMING A DRY GAS OIL
RESERVOIR(Aguilera, AAPG, 2004)
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HEIGHT ABOVE
FREE WATER TABLE h)
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h (ft) 0.205 PcHg-Air
ASSUMING A GEOTHERMAL
RESERVOIR(Aguilera, AAPG, 2004)
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CARMAN-KOZENY EQUATION
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(k/) = 1014 [2
/(1-)2
].[1/(Fst
2
Sgv2
)]rmh= / [Sgv(1-)]
(k/) = 1014 rmh2/ Fst
2
rmh rp35
rp35= 2.665 (0.01k/)0.45Fst
2= 114.14 (k/)-0.1
Fst2= 89.543 rp35
-0.2222
Fs
t2= Kozenysconstant
Sgv2 = surface area per unit grain volume, microns
rmh= mean hydraulic radius, microns
rp35=pore throat aperture at 35% cumulative pore volume
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ROCK FABRIC ()
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(Aguilera, AAPG, 2004)
Rock fabric () refers to the geologic
description of particle size (dpin
microns) and sorting (Lucia, 1983,1995). Pore size distribution is
related to rock fabric and controls
permeability and saturation.
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Porosity and permeability relationship for
various particle size groups in uniform
cemented non-vuggy rocks (After Lucia, 1983)
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(Aguilera, AAPG, 2004)
Grainstone
Packstone
Wackstone
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Lucias straight lines (1983) intersect at porosity of
3.5% and permeability of 0.0015 md.
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(Aguilera, AAPG, 2004)
0.001
0.01
0.1
1
10
100
1000
10000
0.01 0.1 1
INTERPARTICLE POROSITY (fraction)
PERMEABIL
ITY(md)
=0.5 1.0 1.5 2.0 2.5 3.0
4.0
dp=500 m
100 m 20 m
1.8
mGrainstone
Packstone
Wackstone
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ROCK FABRIC ()
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(Jennings and Lucia, 2002)
= - 0.6213 ln (dp) + 4.3614
k = e a( ) b( )
a() = 22.5612.08 ln ()
b() = 8.671 3.603 ln ()
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PICKETT PLOT (MISSION CANYON CARBONATES)Little Knife field, North Dakota. Flow units after Martin et al. (1997)
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(Aguilera, AAPG, 2004)
0.01
0.1
1
0.01 0.1 1 10 100
RESISTIVITY, Ohm-m
POROSI
TY
Sw=
100% 90% 50% 30%
10md
1 md
100 md
1000 md
k/
=10000 md
15%
Pc=10 psi
rp=10.8 m Pc=25 psi
rp=4.32 m
Pc=50 psi
rp=2.16 m
Pc=100 psi
rp=1.08 m
Pc=200 psi
rp=0.54 m
Pc=400 psi
rp=0.27 m
Pc=800 psi
rp=0.14 m
Pc=1600 psi
rp=0.07 m
46
3
2
9
107
85
1311
15
1412
65%
m=2.0
n=2.0
Pcand rpare valid between
Sw=30% and 90%
=0.5
1.5=2.0
=2.5
=4.0
=
h=18'
h=35'
h=71'
h=141'
h=282'
h=7'
45.4
57.2
72.0
91.5
117.2
Fst2
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SHALY FORMATIONS
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PICKETT PLOT (SHALY FORMATIONS)
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SHALE GAS: log R Technique
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Fine-grained, non-source rock
Clast with a
mean grain size
of less than
0.0625 mm
includingsiltstone,
mudstone,
claystone and
carbonates
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PASSEY ET AL CURVES FOR Sw =100%
from log R Technique
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-1
0
1
2
3
50 60 70 80 90 100 110 120 130 140 150
L
R
m
)
t s/ft)
Log R
t
) vs t
Shale
Sandstone
Limestone
Dolomite
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PICKETT PLOT USING PASSEY ET AL
DATA FOR Sw =100%
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1
10
100
0.1 1 10 100
m
f
R
t
m)
t-tm
) vs R
t
Dolomite
Shale
Sandstone
Limestone
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PICKETT PLOT (HAYNESVILLE SHALE)
Sw data from Ramirez et al. (2011)
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0.01
0.1
1
0.01 0.1 1 10 100
R
t
m)
vs R
t
25%
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TOC on Pickett Plot
TOC=total organic carbon
LOM=level or organic metamorphism(Yu and Aguilera, 2011)
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log= 0.02 0.02+ 0.02 + log, + 100.16882.297
Bc= correction between density porosity and core crushed sample
Rov= vitrinite reflectance, m= porosity exponent
Baseline: The transit time and resistivity logs are scaled in such a way thattheir relative scaling is -50s/ft per logarithmic resistivity cycle.
These two logs need to be overlain and baselined in a
fine-grained, non-source rock.
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Prediction of TOC and LOM
with the Use of Pickett Plot
(TOC and LOM Data from Passey et al., 1990)
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0.01
0.1
1
0.01 0.1 1 10 100
Rt(m)
vs Rt
0%
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GFREE RESEARCH PROJECT
0.01
0.1
1
0.01 0.1 1 10 100
R
t
m)
vs R
t
Kn = 0.01
Kn = 0.1
Kn = 0.001
5%
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Integrated Pickett Plot
(TOC Data from Passey et al., 1990)
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0.01
0.1
1
0.01 0.1 1 10 100
R
t
m)
vs R
t
Log Data
Log. (TOC=0%)
Log. (TOC=5%)
Log. (TOC=10%)
Log. (TOC=15%)Power (Sw=100%)
Power (Sw=50%)
Power (Sw=25%)
Power (Kn=0.1)
Power (Kn=0.01)
Power (Kn=0.001)
5%
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Conclusion (1)
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Pickett plots are not a panacea but are useful
for estimating:
Porosity and water saturation
Permeability and process speed
Capillary pressure
Height above free water table
Pore throat aperture and particle size
Kozenisconstant
Rock fabric number (grainstones, packstones,wackstones)
Range of initial flow rates
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Conclusion (2)
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Pickett plots are not a panacea but are useful
for estimating:
Porosity and water saturation
Permeability and process speed
Capillary pressure
Height above free water table
Pore throat aperture and particle size
Kozenisconstant
In carbonates: Rock fabric number (grainstones,packstones, wackstones)
In shales: TOC, LOM, viscous vs. diffusion-like flow
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Acknowledgement
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Parts of this work were funded by
ConocoPhillips, the Natural Sciences and
Engineering Research Council of Canada(NSERC), and the Alberta Innovates
Energy and Environmental Solutions
(formerly AERI). Their contributions aregratefully acknowledged.
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GFREE RESEARCH PROJECT
Thank you