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
Stanford Rock Physics Laboratory - Gary Mavko
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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
Stanford Rock Physics Laboratory - Gary Mavko
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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.
Stanford Rock Physics Laboratory - Gary Mavko
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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.
L.3
Critical “Mush”
Stanford Rock Physics Laboratory - Gary Mavko
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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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L.4
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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L.5
Chalks
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L.6
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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.
L.7
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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).
L.8
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
Stanford Rock Physics Laboratory - Gary Mavko
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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
Stanford Rock Physics Laboratory - Gary Mavko
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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.
L.15
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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
L.17
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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
L.19
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
L.36
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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L.37
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
L39
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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