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Transcript of 6.ShalySands
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
123
Velocity, Porosity, Clay Relations
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
124
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
Shaly Sands
125
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.
L.1
“Life Story” of a Clastic Sediment
Deposition
Burial
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
126
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
L.1
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
127
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
Shaly Sands
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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.
L.2
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
Shaly Sands
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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
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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L.4
Example of critical porosity behavior in sandstones.
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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Data from Anselmetti and Eberli, 1997, in Carbonate Seismology, SEG.
Stanford Rock Physics Laboratory - Gary Mavko
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Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
134
L.5
Chalks
Stanford Rock Physics Laboratory - Gary Mavko
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L.6
Stanford Rock Physics Laboratory - Gary Mavko
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Han’s Laboratory Study on Effects ofPorosity and Clay in Sandstones
Han (1986, Ph.D. dissertation, Stanford University)studied the effects of porosity and clay on 80 sandstonesamples represented here.
L.7
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
Han’s Study on Phi-Clay in Sandstones
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
138
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
Shaly Sands
139
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
L.9
Stanford Rock Physics Laboratory - Gary Mavko
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The critical porosity, modified Voigt bound incorporating Han's clay correction.
L.12
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
L.13
Unconsolidatedmixes of sandand kaolinite
Mixtures have a minimum in porosity that isless than either the sand or clay
observed
modeled
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
L.14
Unconsolidatedmixes of sandand kaolinite
Mixtures have a maximum in velocity
observed
modeled
Stanford Rock Physics Laboratory - Gary Mavko
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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
Dispersed sand-clay mixes tend toform “V”-shape in various domains
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
L.18
Dispersed Clay Model
Dispersed clay “V”-shape in nphi-rhobdomain
Stanford Rock Physics Laboratory - Gary Mavko
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0 0.2 0.4 0.6 0.8 11000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
Porosity
Vp
Statoil B, Brine Substituted
sandy leg
shaley leg
Example for fluvial sands
Each color represents adifferent fining-upwardsequence
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
146
Schlumberger, 1989
Density Porosity vs. NeutronPorosity in 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
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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Yin’s laboratory measurements on sand-claymixtures
L.20
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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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
L.21
Stanford Rock Physics Laboratory - Gary Mavko
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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.
L.22
Stanford Rock Physics Laboratory - Gary Mavko
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Yin's laboratory measurements onsand-clay mixtures.
L.23
Stanford Rock Physics Laboratory - Gary Mavko
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L.360
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.
Velocity-porosity trend is non-unique and is determinedby the geologic process that controls porosity
Stanford Rock Physics Laboratory - Gary Mavko
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152
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.
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
153
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
Stanford Rock Physics Laboratory - Gary Mavko
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154
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
L.37
Stanford Rock Physics Laboratory - Gary Mavko
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155
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
Stanford Rock Physics Laboratory - Gary Mavko
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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
Stanford Rock Physics Laboratory - Gary Mavko
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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
L39
Stanford Rock Physics Laboratory - Gary Mavko
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158
L.37
Sand, Shale Depth Trends
What about intermediate facies?3000
2000
20 40 60
P –
Vel
ocity
Porosity (%)
Clean Sand Compaction
Shale Compaction
Stanford Rock Physics Laboratory - Gary Mavko
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159
0 0.2 0.4 0.6 0.8 11000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
Porosity
Vp
Statoil B, Brine Substituted
sandy leg
shaley leg
Sand-Clay “V” Mixing Law
Sandpoint
Sandpoint
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
160
3000
2000
20 40 60
P –
Velo
city
Porosity (%)
Clean SandShale
0 MPa5 MPa
50 MPaShaleySand
Sand, Shale Depth Trends
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
161
Clean SST
Clayey Shale
Depth Progression in a Fluvial Sequence
Stanford Rock Physics Laboratory - Gary Mavko
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162
Diagenetic Trend
DepositionalTrend
Porosity
Vp
Diagenetic Trend
DepositionalTrend
Reservoir quality
GR
Porosity ( Density)
Vp
Florez, Stanford University, 2002
Stanford Rock Physics Laboratory - Gary Mavko
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GrainContactcement
A B
R a a
Non-contactcement Scheme 1 Scheme 2
C
Dvorkin’s Cement Model
M c = ρcVPc2
is the cement's density; and and are its P- and S-wave velocities. Parameters and are proportional tothe normal and shear stiffness, respectively, of a cementedtwo-grain combination. They depend on the amount of thecontact cement and on the properties of the cement and thegrains. (see next page)
ρc VPc VSc S n
S τ
Jack Dvorkin introduced a cement model that predicts thebulk and shear moduli of dry sand when cement is depositedat grain contacts. The model assumes that the cement iselastic and its properties may differ from those of the grains. It assumes that the starting framework of cemented sand isa dense random pack of identical spherical grains withporosity , and the average number of contacts pergrain C = 9. Adding cement reduces porosity and increasesthe effective elastic moduli of the aggregate. The effectivedry-rock bulk and shear moduli are (Dvorkin and Nur, 1996)
where
φ0 ≈ 0.36
€
Keff =16
C 1−φ0( )Mc
) S n
€
µeff =35
Keff +320
C 1−φ0( )µc
) S τ
€
µC = ρcVSc2
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
164
where and are the shear modulus and the Poisson's ratio of the grains, respectively; and are the shear modulus and the Poisson's ratio of the cement; a is the radius of the contact cement layer; R is the grain radius.
Dvorkin’s Cement ModelConstants in the cement model:
ν νc
€
) S n = An (Λn )α
2 + Bn (Λn )α + Cn (Λn )
€
) S τ = Aτ (Λτ ,ν )α
2 + Bτ (Λτ ,ν)α + Cτ (Λτ ,ν ),
€
Aτ (Λτ ,ν ) = −10−2 ⋅ (2.26ν 2 + 2.07ν + 2.3) ⋅ Λτ0.079ν 2 +0.1754ν −1.342,
€
Bτ (Λτ ,ν ) = (0.0573ν 2 + 0.0937ν + 0.202) ⋅ Λτ0.0274ν 2 +0.0529ν −0.8765,
€
Cτ (Λτ ,ν ) =10−4 ⋅ (9.654ν 2 + 4.945ν + 3.1) ⋅ Λτ0.01867ν 2 +0.4011ν −1.8186;
€
Λn = 2µc (1−ν )(1−ν c ) /[πµ(1− 2ν c )]€
An (Λn ) = −0.024153 ⋅ Λn−1.3646,
€
Cn (Λn ) = 0.00024649 ⋅ Λn−1.9864
€
Bn (Λn ) = 0.20405 ⋅ Λn−0.89008
€
Λτ = µc /(πµ )
€
α = a /R
€
µc
€
µ
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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The amount of the contact cement can be expressed through the ratio of the radius of the cement layer a to the grain radius R:
α α = a/R
The radius of the contact cement layer a is not necessarily directly related to the total amount of cement: part of the cement may be deposited away from the intergranular contacts. However by assuming that porosity reduction in sands is due to cementation only, and by adopting certain schemes of cement deposition we can relate parameter to the current porosity of cemented sand . For example, we can use Scheme 1 (see figure above) where all cement is deposited at grain contacts:
α φ
α = 2 φ0 – φ
3C 1 – φ0
0.25= 2 Sφ0
3C 1 – φ0
0.25
or we can use Scheme 2 where cement is evenlydeposited on the grain surface:
α = 2 φ0 – φ
3 1 – φ0
0.5= 2Sφ0
3 1 – φ0
0.5
In these formulas S is the cement saturation of the porespace - the fraction of the pore space occupied by cement.
Dvorkin’scement model
GrainContactcement
A B
R a a
Non-contactcement Scheme 1 Scheme 2
C
Stanford Rock Physics Laboratory - Gary Mavko
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166
If the cement's properties are identical to those of the grains,the cementation theory gives results which are very close tothose of the Digby model. The cementation theory allowsone to diagnose a rock by determining what type of cementprevails. For example, it helps distinguish between quartzand clay cement. Generally, Vp predictions are much betterthan Vs predictions.
Predictions of Vp and Vs using the Scheme 2 model for quartz and clay cement, compared with data from quartz and clay cemented rocks from the North Sea.
Dvorkin’s Cement Model
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
167
Sand models can be used to “Diagnose” sands
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
168
Dvorkin’s Uncemented Sand ModelThis model predicts the bulk and shear moduli of dry sandwhen cement is deposited away from grain contacts. Themodel assumes that the starting framework of uncementedsand is a dense random pack of identical spherical grainswith porosity , and the average number of contactsper grain C = 9. The contact Hertz-Mindlin theory gives thefollowing expressions for the effective bulk ( ) andshear ( ) moduli of a dry dense random pack ofidentical spherical grains subject to a hydrostatic pressureP:
φ0 = 0.36
KHM GHM
KHM = C2 1 – φ0
2 G2
18 π2 1 – ν 2 P1/3
GHM = 5 – 4ν
5 2 – ν3C2 1 – φ0
2 G 2
2π2 1 – ν 2 P1/3
where is the grain Poisson's ratio and G is the grain shear modulus.
ν
Stanford Rock Physics Laboratory - Gary Mavko
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Dvorkin’s Uncemented Sand ModelIn order to find the effective moduli at a different porosity, a heuristic modified Hashin-Strikman lower bound is used:
Keff = φ / φ0
K HM + 43 G HM
+ 1 – φ / φ0
K + 43 G HM
–1– 4
3 GHM
G eff = [ φ / φ0
G HM + G HM6
9KHM + 8G HMK HM + 2GHM
+ 1 – φ / φ0
G + GHM6
9K HM + 8GHMKHM + 2GHM
]–1
– GHM6
9KHM + 8G HMKHM + 2GHM
Illustration of the modified lower Hashin-Shtrikman bound for various effectivepressures. The pressure dependence follows from the Hertz-Mindlin theory
incorporated into the right end member.
Stanford Rock Physics Laboratory - Gary Mavko
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170
Dvorkin’s Uncemented Sand ModelThis model connects two end members: one has zeroporosity and the modulus of the solid phase and the otherhas high porosity and a pressure-dependent modulus asgiven by the Hertz-Mindlin theory. This contact theoryallows one to describe the noticeable pressure dependencenormally observed in sands.The high-porosity end member does not necessarily have tobe calculated from the Hertz-Mindlin theory. It can bemeasured experimentally on high-porosity sands from agiven reservoir. Then, to estimate the moduli of sands ofdifferent porosities, the modified Hashin-Strikman lowerbound formulas can be used where KHM and GHM are set atthe measured values. This method provides accurateestimates for velocities in uncemented sands. In the figuresbelow the curves are from the theory.
Prediction of Vp and Vs using the lower Hashin-Shtrikman bound, compared with measured velocities from
unconsolidated North Sea samples.
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
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This method can also be used for estimating velocities in sands of porosities exceeding 0.36.
Stanford Rock Physics Laboratory - Gary Mavko
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2 3
2 .1
2 .2
2 .3
Vp (km/s)
Dep
th (
km)
Well #1
A40 80 120
G RB2 3 4
1 .7
1 .8
1 .9
Vp (km/s)
Well #2
Dep
th (
km)
C
Marl
Limestone
40 80 120G RD
2 .5
3
3 .5
0.25 0 .3 0.35 0 .4
Vp
(km
/s)
Porosity
Contact CementL i n e
UnconsolidatedL i n e
ConstantCement Fraction (2%) Line
Well #1
Well #2
North Sea Example
Study by Per Avseth, along with J. Dvorkin, G. Mavko, and J. Rykkje
Stanford Rock Physics Laboratory - Gary Mavko
Shaly Sands
173
Sorting Analysis of Thin-Sections
0.4mm0.4mm
0.4mm0.4mm
Stanford Rock Physics Laboratory - Gary Mavko
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174
Thin-Section and SEM Analyses
Well #2 Cemented
0.25 mm
Well #1 Uncemented
0.25 mm
SEM cathode-luminescent image:Well #2
0.1 mm0.1 mm
SEM back-scatter image: Well #2
Unconsolidated(Facies IIb)
Cemented(Facies IIa)
Back-scatter light Cathode lum. light
Qz-cement rim Qz-grain