6. Sedimentary Micro Structure

8/2/2019 6. Sedimentary Micro Structure

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Rock Physics Properties and

Sedimentary Microstructure-2Hilfan Khairy

UTP

Texture, and lithology: Rock physics basis


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Rock physics and AVO-Universiti Teknologi PETRONAS

Dr. Hilfan Khairy

Theory and Model

`

The information of rock microstructure can be extracted from the relation ofvelocity-porosity.

Avseth, 2003

Rock physics properties change with the depositional environmentand burial depth

Adjusting an effective-medium theoretical model


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Dr. Hilfan Khairy

A. Clean sandstones

1. Unconsolidated sand (friable model)

Model developed for this following contacttheory model of Hertz-Mindlin. The criticalporosity is relatively high about 0.4 and

very well sorted packing. The poorly sortedsand is accomplished by adding smallergrain deposited in the pore space. Thisadditional grain induced deterioratesorting thus decrease the porosity andslightly increase the velocity.

Avseth, 2007


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Dr. Hilfan Khairy

1/322 2

22

1

18 1

c

HM

nK P

1/322 2

22

3 15 4

5 2 2 1

c

HM

nP

3 2

2 3K

K

0

z

b flP g dz

220 34 14n

Bulk modulus at critical porosity (c)

Shear modulus at critical porosity (c)

Poissons ratio

Pressure at certain depth

Coordination number

Kand are solid bulk and shear modulus respectively


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Dr. Hilfan Khairy

1

/ 1 / 4

4 / 3 4 / 3 3

c cdry HM

HM HM HM

K

K K

1

/ 1 /c cdry

HM

zz z

9 8

6 2

HM HM HM

HM HM

Kz

K

Bulk and Shear modulusof friable sand

How to establish thesaturation model??

FLUID SUBSTITUTION BY USING GASSMANNS EQUATIONS

min1b fl


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Dr. Hilfan Khairy

2. Contact cement model

During burial, the sand becomecemented sandstone. The effect of cement provides the rock become stifferand rigid, due to the grains are mergedtogether.

1 / 6dry c c nK n M S

3 3 1

5 20

dry c c

dry

K n S

(Dvorkin and Nur., 1996)

Saturation model? Gassmanns equations

Morecement

Avseth, 2007


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Dr. Hilfan Khairy

3. Constant cement model

Constant cement model assumes that theporosity reduction come from noncontactpore-filling material, such asdeteriorating sorting. This model is a

combination of contact-cement andfriable sand model. At the beginning theporosity of sand-pack reduce to contact-cement porosity (b), and its continuesgoing down following the friable sandmodel. The friable sand model associates

with the sorting trend while the contactcement due toburial.

b

c

Avseth, 2007


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Dr. Hilfan Khairy

1

/ 1 / 4

4 / 3 4 / 3 3

b b

dry b

b b b bK K K

/ 1 /b bdry

b bz z

9 8

6 2

b b b

b b

KzK

1 / 6b c c nK n M S

3 135 20

c cbb

n SK

Kb and b following thecontact cement :

The effect of fluid ?? Gassmanns equations


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Dr. Hilfan Khairy

Avseth and Jrstad (2008)


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Dr. Hilfan Khairy

B. Shales

B1. Constant-clay model for sandy shales

Silts are commonly suspended in the clay matrix and not cemented. Thus, it isfeasible to use Friable-sand model to calculate bulk modulus of constant clay.

The critical porosity for model should be very high for shales about 60%-70%.

Calculate Kmixed and mixed (quartz-clay)

Input into Friable sand model to get Kdryand dry

Performing Gassmanns fluid substitution for saturationmodeling scenario


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Dr. Hilfan Khairy

1 1

mixed qz clay

C C

K K K

1 1

mixed qz clay

C C

Elastic moduli of clay minerals

1/322 2

22

1

18 1

c

HMclay

nK P

1/322 2

22

3 15 4

5 2 2 1

c

HMclay

n

P

3 2

2 3

mixed mixed

mixed mixed

K

K

0

z

b flP g dz

220 34 14n


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Dr. Hilfan Khairy

1

_

/ 1 / 4

4 / 3 4 / 3 3

c cdry ssh HM

HM HM HM

K

K K

1

_

/ 1 /c cdry ssh

HM

zz z

9 8

6 2

HM HM HM

HM HM

Kz

K

Bulk and Shear modulusSandy Shale



min1b fl


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Dr. Hilfan Khairy

B2. Dvorkin-Gutierrez silty shale model

shC

1

1 4

4 / 3 4 / 3 3

sat sh

sh sh q sh

C CK

K K

1

1sat sh

sh sh sh sh

C Cz

z z

9 8

6 2

sh sh shsh

sh sh

Kz

K

Porosity of shale as a function of clay content

Ksh and sh are saturatedelastic moduli of shale andthey are derived from well-log measurement of Vp, Vsand density in a pure shalezone.


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Dr. Hilfan Khairy

C. Shaly sandstones

C1. Constant-clay model for shaly sand

Since this model has the assumption of clay mineral dispersed in the grainand fill the pores between grains, thus it can be modeled the prediction ofelastic modulus by using Friable-sand model. The process has a similartechnique with the constant-clay model for sandy shale. However, the critical

porosity should be adjusted in between 10% to 40%, depending on the claycontent. Mineral modulus of mixed between quartz grain and shale can beestimated by applying lower bound ofHashin-Shtrikman or average of

Voigt-Reuss model. Special note should be addressed if the claycomposition is very soft such as smectite and illite (please refer to the elasticmoduli of clay minerals) and mixed with relatively stiff quartz.

Because the quartz grain are cemented and stiffer than the shale (smectiteand illite), the mixed of those two mineral should be stiffest possiblealternative. Thus, it is recommended to useVoigt bounds.


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Rock physics and AVO-Universiti Teknologi PETRONASDr. Hilfan Khairy

Calculate Kmixed and mixed (quartz-clay)

Input into Friable sand model to get Kdryand dry

Performing Gassmanns fluid substitution for saturationmodeling scenario

1

mixed q clayK C K CK

1

mixed q clayC C

1/322 2

22

1

18 1

c

HMclay

nK P

1/322 2

22

3 15 4

5 2 2 1

c

HMclay

nP

3 2

2 3

mixed mixed

mixed mixed

K

K

0

z

b flP g dz

220 34 14n


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1

_

/ 1 / 4

4 / 3 4 / 3 3

c cdry ss HM

HM HM HM

K

K K

1

_

/ 1 /c cdry ss

HM

zz z

9 8

6 2

HM HM HM

HM HM

Kz

K

Bulk and Shear modulusSandy Shale



min1b fl


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C2. Yin-Marion shaly sand model

The model is dedicated to predict the elastic modulus with the increasing ofclay content. By assuming the total porosity will decrease with the increasingof clay content (C) , and again it increases after threshold point, the totalporosity can be formulated as follows:

1 for C

s sh s

s sh s

sh s

C

Shaly sand

Sandy shale


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Marion et.al., 1992


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dry pf sat

q sat q dry s q pf

K KK

K K K K K K

1 1

pf clay fluidK K K

sat dry

1 1 1s q sh clay s sh flC C

Kdry= dry sand frame bulk modulus

dry= dry sand frame shear modulusKq = quartz bulk modulusKpf= bulk modulus pore filling material (fluid and clay)


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Marion et.al., 1992


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Avseth, 2007

Clean sand line

Shale line

Unconsolidated sand

Shaly sand

Silty sand

Clean sand line:constant-cement model

Shale line:constant clay model


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Chi and Han., 2009


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Chi and Han., 2009


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Quantifying cement from Vs-porosity graph


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Rock physics and AVO-Universiti Teknologi PETRONASD Hilf Kh i


Quantifying sorting from Vs-porosity graph

6. Sedimentary Micro Structure

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