Fazies Analysen mit

Kapillardruckkurven

Joachim Strobel, RWE Dea, May 2008

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Fazies Definitionen

� Gesamtheit aller biologischen und und lithologischenMerkmale (Geyer 1977).

� Jede Ausbildungs- oder Erscheinungsform einer in einem bestimmten Zeitraum erfolgten Ablagerung (Diener 1925).

� Fazies bezeichnet jene Eigenschaft der Gesteine die die Ablagerungsumstände widerspiegeln (Strausz 1928).

� Daher… ist unter Fazies keineswegs eine bestimmte Gesteinausbildung zu verstehen. (Geyer 1977).

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Petrophysik-Fazies

� Elektrofazies definiert über das Logantwortverhalten mögliche gruppierbare Abschnitte.

� Diese können- Korreliert werden mit geologischen Fazien.

- Benutzt werden um Bereiche gleicher Porositäts und Permeabilitätsverteilung einzugrenzen.

- Bereiche gleicher hydraulischer Eigenschaften zu definieren.

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Electrofazies

� Mit neuronalen Netzen oder Fuzzy Logic können Logs mit externe Kerninformationen kalibriert werden und so auch für ungekernteBohrungen ein Fazieslogerstellt werden.

� Mineral-Vergesellschaftungen können über Logs gefunden werden und eine Electrofazies definieren (ELAN).

� Über Crossplot und andere Klassifizierungs-Methoden können Logkurven statistisch gruppiert werden.

b a s i :VC L / co re :c kh _ c n

1 2 3 0 p o in t s p lo t t e d o u t o f 1 7 9 5 5

bas i:V CL

0 .80 .70 .60 .5

0 .40 .30 .20 .1

0- 0 .1

core

:ck

h_c

n

0 .01

0 .1

1

10

1 00

1 ,000 f az i:c lu s t_ f az

8

7

6

5

4

3

2

1

0

0 .

1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .f az i:c lus t_ f az

We ll Z one De pths

4 3 _ 1 9 A -0 4 Z (1 ) TWE S T_ A 4 5 3 1 .M - 4 7 3 8 .M

4 3 _ 1 9 A -0 4 Z (2 ) Intra _ We s t_ A 4 7 3 8 .M - 4 8 3 9 .M

4 3 _ 1 9 A -0 4 Z (3 ) N r_ Ba s e _ We s 4 8 3 9 .M - 4 8 9 9 .M

4 3 _ 1 9 A -0 4 Z (4 ) Tm a rs d 4 8 9 9 .M - 4 9 9 0 .M

4 3 _ 1 9 A -0 4 Z (5 ) Intra _ M a rs d 4 9 9 0 .M - 5 0 3 7 .M

4 3 _ 1 9 A -0 4 Z (6 ) Tk ind 5 0 3 7 .M - 5 1 3 2 .M

4 3 _ 1 9 A -0 4 Z (7 ) A lport 5 1 3 2 .M - 5 1 3 5 .M

4 3 _ 1 9 _ 0 2 A (1 ) TWE S T_ A 3 5 6 1 .M - 3 6 1 7 .M

4 3 _ 1 9 _ 0 2 A (2 ) Intra _ We s t_ A 3 6 1 7 .M - 3 7 3 0 .M

4 3 _ 1 9 _ 0 2 A (3 ) N r_ Ba s e _ We s 3 7 3 0 .M - 3 8 0 0 .M

4 3 _ 1 9 _ 0 2 A (4 ) Tm a rs d 3 8 0 0 .M - 3 8 9 9 .M

4 3 _ 1 9 _ 0 2 A (5 ) Intra _ M a rs d 3 8 9 9 .M - 3 9 4 0 .M

4 3 _ 1 9 _ 0 2 A (6 ) Tk ind 3 9 4 0 .M - 4 0 4 1 .M

4 3 _ 1 9 _ 0 2 A (7 ) A lport 4 0 4 1 .M - 4 1 3 4 .M

4 3 _ 1 9 _ 0 2 A (8 ) C hoc k ie ria n 4 1 3 4 .M - 4 2 1 6 .M

4 3 _ 1 9 _ 0 2 A (9 ) A rn s be rg 4 2 1 6 .M - 4 2 6 0 .M

4 3 _ 2 0 B -2 (1 ) TWE S T_ A 3 6 5 1 .M - 3 8 3 5 .M

4 3 _ 2 0 B -2 (2 ) Intra _ We s t_ A 3 8 3 5 .M - 3 9 0 1 .M

4 3 _ 2 0 B -2 (3 ) N r_ Ba s e _ We s 3 9 0 1 .M - 3 9 7 5 .M

4 3 _ 2 0 B -2 (4 ) Tm a rs d 3 9 7 5 .M - 4 0 8 2 .M

4 3 _ 2 0 B -2 (5 ) Intra _ M a rs d 4 0 8 2 .M - 4 1 3 2 .M

4 3 _ 2 0 B -2 (6 ) Tk ind 4 1 3 2 .M - 4 2 4 7 .M

4 3 _ 2 0 B -2 (7 ) A lport 4 2 4 7 .M - 4 3 2 0 .M

4 3 _ 2 0 B -2 (8 ) C hoc k ie ria n 4 3 2 0 .M - 4 6 3 3 .9 7 2 6 6 M

4 3 _ 1 9 _ 0 1 (1 ) TWE S T_ A 3 5 3 4 .5 M - 3 5 3 5 .M

4 3 _ 1 9 _ 0 1 (2 ) Intra _ We s t_ A 3 5 3 5 .M - 3 5 5 8 .M

4 3 _ 1 9 _ 0 1 (3 ) N r_ Ba s e _ We s 3 5 5 8 .M - 3 6 1 9 .M

4 3 _ 1 9 _ 0 1 (4 ) Tm a rs d 3 6 1 9 .M - 3 7 0 5 .5 M

4 3 _ 1 9 _ 0 1 (5 ) Intra _ M a rs d 3 7 0 5 .5 M - 3 7 8 3 .M

4 3 _ 1 9 _ 0 1 (6 ) Tk ind 3 7 8 3 .M - 3 8 7 9 .M

4 3 _ 1 9 _ 0 1 (7 ) A lport 3 8 7 9 .M - 3 9 5 0 .M

4 3 _ 1 9 _ 0 1 (8 ) C hoc k ie ria n 3 9 5 0 .M - 3 9 8 0 .M

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Main usage of Facies classification:Facies Model for modelling

� Facies modelled bei Truncated GaussianSimulation

Porous Limestone

Non Reservoir

Reservoir Sst

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Porosity Histograms by each Facies class

all facies

Non - ReservoirReservoir Sandstone Porous Limestone

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Petrophysical Modellingof Porosity by each facies type

� Porosity modelled by Sequentiell Gaussian Simulation for eachFazies

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Reservoir are made of hydraulic unit

Modified Lorenz Plot:KgxH (relative Gaspermeability) vs PhixH yields storage and producer areas.

l u m p : R P h i H / l u m p : K r v H

0 . 1

1 .

1 0 .

1 0 0 .

1 0 0 0 .

1 0 0 0 0 .

1 0 0 0 0 0 .

lum

p:K

rvH

0 . 2 . 4 . 6 . 8 . 1 0 .l u m p :R P h i H

PhixH

Kgx

H

Permeable Streak

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Porosity-Permeability Plot

SOLG_Z2

core:cpor_ccom / core:ck_c

0. 0.06 0.12 0.18 0.24 0.3core:cpor_ccom

0.001

0.01

0.1

1.

10.

100.

1000.

co

re:c

k_

c

A Plot of Porosity versus Permeability is usually taken as identification of hydraulic units.

This is often very vague. It works seldom in high porosity regions where the relation becomes weak.

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FreeWaterLevel

GasWaterContact

Kapillarkraft

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80 90 100

WATER SATURATION (%PORE VOLUME)

CA

PIL

LA

RY

PR

ES

SU

RE

(P

SIG

)

Seal

Use of Capillary Pressure Curve for definition of hydraulic units

Quantification of the relation between a derived bundled tube permeability and the measured permeability yields a classification into units with similar pore structure connectivity

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Pore Size distribution from Capillary Pressure curves

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.01 0.1 1 10 100

Pore Size (um)

020

40

60

80

10

0

12

0

14

0

16

0

18

0

20

0

01

02

03

04

05

06

07

08

09

01

00

WA

TE

R S

AT

UR

AT

ION

(%

PO

RE

VO

LU

ME

)

CAPILLARY PRESSURE (PSIG)

The capillary pressure measurements yields the pore-throat neck distribution

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Darcy & Poiseuille

Darcy

capillaryofradiusr

cpityVis

cmLengthL

deltaPdp

cmflowq

L

prq

__

)(cos:

)(:

:

sec)(:

8

3

4

=

∗

∗∗

∆∗∗=

µ

µ

π

Poiseuille

26107.12 rk ∗∗=

Darcy = Poiseuille

R

This relation allows calculation of Permeability from tubes assuming circular pore throats of same length

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Caveat:

The true pore is no a tube and not onlywater wet

Pore Mixed Oil wet Full Oil Wet Water Wet

Oil Oil OilWATER

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Example:Permeabilty for each Radii

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

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Cummulative Tube Permeability

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

Pores are connected in a complex way. Building a true pore scale model from capillary pressure curves is impossible.As a first guess, the tube permeabilities are added up for a cumulative permeability.

Simple accumulation of tube-permeability assumes parallel flow in all tubes. This is of course wrong. The truth is a mixture of parallel and serial connectivity.

Plugpermeability

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Comparison core permeability versus cumulative tube permeability

Perm cum

0.1

1

10

100

1000

0.1 1 10 100 1000

Perm core

pe

rm C

ap

Perm corr

The comparison yields the PURCELL or litho-factor.

All plugs from the same hydraulic unit shows the same ratio

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Example

� The following example comes from carbonates.

� They are from two wells covering two main producing carbonate zones: One & Two.

� The question is, if the same zones in each well belong to the same hydraulic unit and if the two zone per well also belong to one hydraulic unit.

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Pore Size Distribution

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.01 0.1 1 10 100

Pore Size (um)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

DAHRA

Satal

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One:Permeabilty from Bundle Model from 2 wells.

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

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One:Ratio of cumulative Bundle Permeability to measured Perm. Average value 0.266

Phi

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Phi

Pe

rmc

ap

/pe

rm

Phi

0.27

Porosity

Tru

eP

erm

. /

Cum

Per

m.

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One:Measured Permability versus Purcell-Lithofactor corrected (0.27) Bundle-Permeabilty: Both wells see the same zone

Perm corr

0.1

1

10

100

1000

0.1 1 10 100 1000

Perm core

pe

rm C

ap

Perm corr

Perm Core

Per

m C

um.

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Two:Permeabilty from Bundle Model from 2 wells

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

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Well 1, Zone B:Ratio of cummulative Bundle Permeabilty to measured Perm. Averagae Value 0.31 or 0.1 after point exclusions.

Phi

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Phi

Pe

rmc

ap

/pe

rm

Phi

0.31

0.1

Porosity

Tru

eP

erm

. /

Cum

Per

m.

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Well 1, Zone B :Measured Perm. versus Purcell-Lithofactor corrected (0.1) Bundle Permeabilty. Doubts remain if both wells see the same zone.

Perm corr

0.1

1

10

100

1000

0.1 1 10 100 1000

Perm core

perm

Cap

Perm corr

Perm Core

Per

m C

um.

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Zone B:Ratio of cumulative Bundle Permeability to measured Perm. Litho-Factor as function of PHI

Diagrammtitel

y = 2.4606x - 0.5385

R2 = 0.1127

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Phi

Pe

rmc

ap

/pe

rm

Phi

Linear (Phi)

Porosity

Tru

eP

erm

. /

Cum

Per

m.

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Zone B:Measured Perm. Versus Purcell-Lithofactor corrected (as function of PHI) Bundle Permeabilty:Both wells see same zone

Perm corr

0.1

1

10

100

1000

0.1 1 10 100 1000

Perm core

perm

Cap

Perm corr

Perm Core

Per

m C

um.

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Result

� Zone A shows an average Purcell ratio which can be used well to correct all cumulative permeabilities.

� Zone B shows a weak average Purcell Ratio. A strong correlation between Purcell Ratio and Porosity exists for both wells. Hence both wells see the same zone.

� Zone A and B exhibit different Purcell correlations and thus can not be treated as similar fazies units.

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One Step further towards pore scale modeling

� The portion of pore sizes filled during each capillary pressure step yields the number of tubes available for flow by the intrusive fluid (wetting or non-wetting, depending on experiment).An incremental cumulative permeability therefore yields the relative permeability for the intrusive fluid and also for the retreating media

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Big Pores are invaded first and have high permeability

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

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.. then smaller

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

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And even smaller ones

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

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Raw data: Simple cumulating of wetting and non-wetting phase versus core measured rel. Perm.

KrLb_corey_core

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SW

Kw

Krw_raw

Krhc_raw

Core_krw

Core_Kro

Core

This simple model fails because no fluid path or asymmetry between wetting and non-wetting fluid is used.

It can be improved by assuming values for irreducible water (Swir) or Oil (Sor) or by pore scale modeling

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Simple Pore structure Model though comparison with measured rel. Perm. curve

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.01 0.1 1 10 100

Pore Size (um)

Reihe1

Reihe2

Reihe3

Reihe4

Reihe5

Reihe6

Reihe7

Reihe8

Reihe9

Reihe10

Reihe11

Reihe12

Reihe13

Reihe14

Reihe15

Reihe16

Reihe17

Reihe18

Reihe19

Reihe20

Reihe21

Reihe22

Reihe23

Reihe24

Reihe25

Reihe26

Reihe27

Reihe28

Reihe29

Reihe30

Reihe31

Reihe32

Reihe33

Reihe34

Reihe35

Reihe36

Reihe37

Poresizeclasses: 0.8 um

Small Poresize: permeabilityis reduced

Large Poresize: permabilityis modelledhigher

Above: Original pore size permeability

Below: Modified version.

Final:18% of the Small pores are mixed with the big pores in a serial method to yield a total cumulative Permeability

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Result of the changes to pore size permeability: Synthetic Prel. Perm is much closer to Core data

KrLb_corey_core

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SW

Kw

KrW_Lbd

KrHC_Lbd

Core_krw

Core_Kro

Could we not use log data to derive a pore-scale class based model ?

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Possible source of a continuous capillary pressure curve profile:NMR T2 to Poresize conversion

T2 T2 Cap T2 Pore Size Core Pore Size

ft

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Possible source for irreducible water and oil saturation

and rel. Perm parameters:

Invasion Model

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Future Work

Capillary pressure and relative permeability data yield enough data to create a coarse pore scale model.

The task would be, to set up a method for matching permeability and relative permeability from a crude pore scale mode with true measurements based on the pore size distribution.

For core-free application, additional information can be extracted from the behavior of the mud invasion front (Swirr, Sor, transition zone length and shape). Continues capillary pressure curves can be obtained from NMR T2 inversion. Draw down mobilities from formation tester can act as true permeability calibrator.The results can then be grouped in hydraulic facies units.