velocity, porosity, clay relations - stanford university · velocity, porosity, clay relations. ......

Stanford Rock Physics Laboratory - Gary Mavko

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Velocity, Porosity, Clay Relations

Stanford Rock Physics Laboratory - Gary Mavko

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Courtesy Per Avseth

What Controls Amplitude over thisNorth Sea Turbidite?

Lithology, porosity, pore fluids, stresses… but also sedimentation and diagenesis

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Velocity-porosity relationship in clastic sediments and rocks. Datafrom Hamilton (1956), Yin et al. (1988), Han et al. (1986). Compiled

by Marion, D., 1990, Ph.D. dissertation, Stanford Univ.

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“Life Story” of a Clastic Sediment

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We observe that the clastic sand-clay system is divided intotwo distinct domains, separated by a critical porosity φc.Above φc, the sediments are suspensions. Below φc , thesediments are load-bearing.

Critical Porosity

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Critical Porosity

Traditionally, bounding methods have been considered notvery useful for quantitative predictions of velocity-porosityrelationships, because the upper and lower bounds are sofar apart when the end members are pure quartz and purewater.

However, the separation into two domains above and belowthe critical porosity helps us to recognize that the bounds arein fact useful for predictive purposes.

• φ > φc, fluid-bearing suspensions. In the suspensiondomain the velocities are described quite well by the Reussaverage (iso-stress condition).

• φ < φc, load-bearing frame. Here the situation appears tobe more complicated. But again, there is a relatively simplepattern, and we will see that the Voigt average is useful.

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The first thing to note is that the clean (clay free) materialsfall along a remarkably narrow trend. These range fromvery low porosity, highly consolidated sandstones, to highporosity loose sand.

(Data from Yin et al., 1988; Han et al., 1986. Compiled andplotted by Marion, D., 1990, Ph.D. dissertation, StanfordUniversity.

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Amos Nur discovered that this narrow trend can bedescribed accurately with a modified Voigt bound. Recallthat bounds give a way to use the properties of the “pure”end members to predict the properties in between. The trickhere is to recognize that the critical porosity marks the limitsof the domain of consolidated sediments, and redefine theright end member to be the suspension of solids and fluids atthe critical porosity.

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Critical “Mush”

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The Modified Voigt Bound

Velocity in rocks

The usual Voigt estimate of modulus

Modified Voigt estimate of modulus

VP =M ρ

ρ = 1−φ( )ρmineral +φρfluid

M = 1− φ( )Mmineral + φMfluid

M = 1− φ ( )Mmineral + φ Mcritical"mush"

φ =φφc

0 ≤ φ ≤ φc 0 ≤ φ ≤ 1

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Example of critical porosity behavior in sandstones.

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Data from Anselmetti and Eberli, 1997, in Carbonate Seismology, SEG.

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Chalks

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Effects of Clay

Han (1986, Ph.D. dissertation, Stanford University)studied the effects of porosity and clay on 80 sandstonesamples represented here.

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Han (1986) found the usual result: velocities tend to decrease with porosity, but with a lot of scatter about the regressions when clay

is present (water saturated).

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Clean sand line

C=.05.15.25

.35

C=.05.15

.25.35

Vp = (5.6-2.1C) - 6.9φ

Vs = (3.5-1.9C) - 4.9φ

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Han’s Relations (40 MPa)Clean sandstones (10 samples)

Clay-bearing sandstones (70 samples)

Ignoring the clay

Including a clay term

R = correlation coefficient; % = RMS

VP = 6.08 – 8.06φVS = 4.06 – 6.28φ

VP = 5.02 – 5.63φVS = 3.03 – 3.78φ

VP = 5.59 – 6.93φ – 2.18CVS = 3.52 – 4.91φ – 1.89C

VP = 5.41 – 6.35φ – 2.87CVS = 3.57 – 4.57φ – 1.83C

R = 0.99 2.1%R = 0.99 1.6%

R = 0.80 7.0%R = 0.70 10%

R = 0.98 2.1%R = 0.95 4.3%

R = 0.90R = 0.90

dry

wat

er s

atur

ated

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Han’s water-saturated ultrasonic velocity data at40 MPa compared with his empirical relations

evaluated at four different clay fractions.

Han’s empirical relations between ultrasonic Vp and Vs in km/s with porosity and clayvolume fractions.

Clean Sandstones (determined from 10 samples) Water saturated40 MPa Vp = 6.08 - 8.06φ Vs = 4.06 - 6.28φ

Shaly Sandstones (determined from 70 samples)

Water saturated40 MPa Vp = 5.59 - 6.93φ - 2.18C Vs = 3.52 - 4.91φ - 1.89C30 MPa Vp = 5.55 - 6.96φ - 2.18C Vs = 3.47 - 4.84φ - 1.87C20 MPa Vp = 5.49 - 6.94φ - 2.17C Vs = 3.39 - 4.73φ - 1.81C10 MPa Vp = 5.39 - 7.08φ - 2.13C Vs = 3.29 - 4.73φ - 1.74C5 MPa Vp = 5.26 - 7.08φ - 2.02C Vs = 3.16 - 4.77φ - 1.64C

Dry40 MPa Vp = 5.41 - 6.35φ - 2.87C Vs = 3.57 - 4.57φ - 1.83C

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The critical porosity, modified Voigt bound incorporating Han's clay correction.

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Porosity vs. clay weight fraction at various confining pressures. FromDominique Marion, 1990, Ph.D. dissertation, Stanford University. Data

are from Yin, et al., 1988.

Sand, shaley sand Shale, sandy shale

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Velocity vs. clay weight fraction at various confining pressures. FromDominique Marion, 1990, Ph.D. dissertation, Stanford University. Data

are from Yin, et al., 1988.

Sand, shaley sand Shale, sandy shale

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Influence of clay content on velocity-porosity relationship at aconstant confining pressure (50 MPa). Distinct trends for shaly sandand for shale are schematically superposed on experimental data onsand-clay mixture. From Dominique Marion, 1990, Ph.D.dissertation, Stanford University. Data are from Yin, et al., 1988, andHan, 1986.

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Gulf of Mexico Well, Herron et al, 1992, SPE 24726

40

20

0

60

3

2

1

Clay (vol%)

Poro

sity

(vol

%)

Vp (k

m/s

)3780-4800 ft 3780-4800 ft

Poro

sity

(vol

%)

Clay (vol%)

Vp (k

m/s

)

3

2

1

60

40

40 40

20

20 200

00

4800-5895 ft4800-5895 ft

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Amoco's Well in the Hastings Field (On-Shore Gulf Coast)

Density vs. Neutron Porosity PoorlyConsolidated Shaly Sands

Laminar ClayModel

2.30

Marion Model

Increasing Clay Content

nphi

rhob

(g/c

m )

2.00

2.10

2.20

2.40

2.50

2.60

2.700.00 0.10 0.20 0.30 0.40 0.50

3

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Schlumberger, 1989

Density Porosity vs. Neutron Porosityin Shaly Sands

Sho

0.5

0.4

0.3

0.1

Q

QuartzPo in t

0.1

0.2

0.3 0.4 0.5

G asSand

Sd

C

ClSh

0.2

φN

φD

A

B

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To wate

r poin

t

To w

ater

poi

nt

To D

ry C

lay

poin

t

Clean Wate

r Sands

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Yin’s laboratory measurements on sand-claymixtures

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Yin’s laboratory measurements onsand-clay mixtures

10 - 2

10 - 1

10 0

10 1

10 2

10 3

10 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Permeability (Gas) vs. Porosity

Perm

eabi

lity

(mD)

Porosity

0 MPa

30 MPa

10 MPa

50 MPa 40 MPa

20 MPa

0%

5%

10%

15%20%

25%

30%

40%

50%

65%

85%

100%

% clay content by weight

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Permeability vs. porosity data in Gulf-Coast sandstones reflect the primary influence of clay content on both permeability and porosity. Kozeny-Carman relations for pure sand and pure shale are also shown (dashed lines) to illustrate the effect of porosity on permeability. FromDominique Marion, 1990, Ph.D. dissertation, Stanford University.

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Yin's laboratory measurements onsand-clay mixtures.

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0

1000

2000

3000

4000

5000

6000

0 0.1 0.2 0.3 0.4 0.5

Varied Velocity-Porosity Trends

Porosity

Gulf of Mexico (Han)

Vp

Troll

Oseberg

Cementing Trend

Han’s large data set spans a large range of depths andclearly shows the steep cementing trend, which would befavorable for mapping velocity (or impedance) to porosity.Other data sets from the Troll and Oseberg indicate muchshallower trends.

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0

1000

2000

3000

4000

5000

6000

0 0.1 0.2 0.3 0.4 0.5

Cementing vs. Sorting Trends

Porosity

Troll

Gulf of Mexico (Han)

Oseberg

Vp

Reuss Bound(Deposition)

Cementing Trend

SortingTrend

The slope of the velocity-porosity trend is controlled by thegeologic process that controls variations in porosity. Ifporosity is controlled by diagenesis and cementing, weexpect a steep slope – described well by a modified upperbound. If it is controlled by sorting and clay content(depositional) then we expect a shallower trend – describedwell by a modified lower bound.

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Generalized Sandstone Model

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0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5

Cementing vs. Sorting Trends

Vp

Porosity

clean cementing trend

Suspension Line(Reuss Bound)

sorting trend

New Deposition

Mineral point

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0

1

2

3

4

5

6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

North Sea Clean sands

shallow oil sand deeper water sand

Vp

Total Porosity

increasing cement

Suspension Line

poor sorting

• all zones converted to brine• only clean sand, Vsh <.05

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0

1

2

3

4

5

6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

North SeaClean vs. Shaly Sands

2508-2545 m, vsh<.052508-2545 m, Vsh>.32701-2750 m, vsh<.052701-2750 m, Vsh>.3

Vp

Total Porosity

increasing cement

Suspension Line

poor sorting

all zonesconverted to brine

more clay

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0 0.1 0.2 0.3 0.4 0.50

1000

2000

3000

4000

5000

6000

Porosity

Vp

Data Before (blue) and After (red) Cementing

Cementing Trend

0 500 1000 1500 2000 2500 3000 3500 40000

1000

2000

3000

4000

5000

6000

V s

Vp

Data Before (blue) and After (red) Cementing

Cementing Trend

Decrease porosity 5% by Cementing

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0 500 1000 1500 2000 2500 3000 3500 40000

1000

2000

3000

4000

5000

6000

V s

Vp

Data Before (blue) and After (red) Sorting

Sorting Trend

0 0.1 0.2 0.3 0.4 0.50

1000

2000

3000

4000

5000

6000

Porosity

Vp

Data Before (blue) and After (red) Sorting

Sorting Trend

Decrease porosity 5% by Sorting

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0 500 1000 1500 2000 2500 3000 3500 40000

1000

2000

3000

4000

5000

6000

V s

Vp

Data Before (blue) and After (red) Fluid Change

0 0.1 0.2 0.3 0.4 0.50

1000

2000

3000

4000

5000

6000

Porosity

Vp

Data Before (blue) and After (red) Fluid Change

Replace Oil with Water

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-0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

AVO PP Gradient

R(0)

P-P avo; cap: A, res: B

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

AVO PS Gradient

R(0)

P-S avo; cap: A, res: B

Porosity decreaseby Cementing

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

AVO PP Gradient

R(0)

P-P avo; cap: A, res: B

Porosity decreaseby Sorting

Replace Oil with Water