Pickett Plots

8/11/2019 Pickett Plots

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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


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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CARBONATE EXAMPLE

Integrate in a Pickett Plot:


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


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


K1/2= 250 3/ Swi1AT IRREDUCIBLE

CONDITIONS (MEDIUM

GRAVITY OIL)(Source: Morris and Biggs)


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PORE THROAT RADIUS (m)


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)


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)



ASSUMING A DRY GAS OIL

RESERVOIR(Aguilera, AAPG, 2004)


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HEIGHT ABOVE

FREE WATER TABLE h)



ASSUMING A GEOTHERMAL

RESERVOIR(Aguilera, AAPG, 2004)


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CARMAN-KOZENY EQUATION


(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 ()



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)



Grainstone

Packstone

Wackstone


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Lucias straight lines (1983) intersect at porosity of

3.5% and permeability of 0.0015 md.



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 ()


(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)



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


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


-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%


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)


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)


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)


0.01

0.1

1

0.01 0.1 1 10 100

Rt(m)

vs Rt

0%


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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)


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)


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)


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


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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Thank you

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