Pressure and Compaction in theRock Physics Space

Jack Dvorkin

June 2002

Compaction of Shales

Freshly deposited shales and clays may have enormous porosity of ~80%. The speed of sound is close to that in water ~ 1500 m/s. The S-wave velocity is small but not negligible. As a result, Poisson’s ratioapproaches 0.5.

As the overburden increases, the shale compacts. Porosity decreasesand velocity increases.

Compaction in on-shore shale andin GOM.

50 100 150

0

200

600

800

1000

GR

Dep

th (m

)

1.6 1.8 2.0 2.2 2.4

RHOB (g/cc)

2.0 2.5

Vp (km/s)

NPP

GOM

2

3

4

5

6

7

0.2 0.4 0.6

Ip (

km

/s

g/cc

)

NPP

GOM

Porosity

CompactionIp

(km

/s g

/cc)

Dep

th (

m)

Difference in Compaction of Shales and Sands

Sands are much less compactable than shales (unless the grains break ordiagenesis sets in).

Compaction in dry kaolinite,Ottawa sand, and a 50/50

mixture thereof (Yin, 1992).

1.0

1.5

2.0

0.1 0.2 0.3 0.4 0.5

Vp (

km

/s)

Porosity

10 MPa

40 MPa

Clay

Sand

50% Sand50% Clay

DRY

Vp

(km

/s)

2

3

4

5

6

7

0.2 0.4 0.6

Ip (

km

/s

g/cc

)

NPP

GOM

Porosity

Compaction

YIN 50/50

YINKaolinite

Compaction of Shales

As long as shale is load-bearing, the compaction trend in the impedance-porosity space seems to be universal among wells logs and lab data.

Compaction in on-shore shale and in GOM + Yin's clay andsand/clay data.

Ip (

km/s

g/c

c)

Compaction and Undercompaction Due to PorePressure

Abnormal pore pressure results in undercompaction and porosityand velocity reversals

0.2

0.3

0.4

Por

osit

y

SHALE: 120 > GR > 90

2

3

Vp (

km

/s)

SHALE: 120 > GR > 90

Porosity Reversal

Velocity Reversal

1 km

Po

rosi

tyV

p (

km/s

)

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6

Ip (

km

/s

g/cc

)

GOM

Porosity

YIN 50/50

YINKaolinite

Compaction and Undercompaction Due to PorePressure -- Same Rock Physics Trend

Normally- and over-pressured parts of the well project onto thesame rock physics trend, same as the lab data.

Ip (

km/s

g/c

c)

Moreover, well log data from different wells worldwide fall onto thesame Ip-porosity trend. Different color means different well.

Universality of Compaction and Undercompactionin Rock Physics Space

50 100 150

500

1000

1500

2000

2500

3000

3500

GR

Dep

th (m

)

0 .2 .4 .6Porosity

3 4 5 6 7 8 9 10Ip (km/s g/cc)

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6

Ip (

km

/s)

Porosity

Ip (

km/s

g/c

c)

Dep

th (m

)

Universality of Compaction and Undercompactionin Rock Physics Space

The curves are from “unconsolidated sediment” model that relates elasticproperties to porosity, lithology, and pore fluid compressibility.

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sh

ear

Mod

ulu

s (G

Pa)

Porosity

NPPC =100%

30%50%

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Com

pre

ssio

nal

Mod

ulu

s (G

Pa)

Porosity

NPP

C =100%

30%

50%

Co

mp

ress

ion

al M

od

ulu

s (G

Pa)

Sh

ear

Mo

du

lus

(GP

a)

Rational Effective-Medium ModelUncemented Particles

Hertz-Mindlin Theory + Modified Lower Hashin-Shtrikman

Hertz-Mindlin theory provides expressions for the contact stiffness betweentwo elastic particles. Based on these expressions, we can derive the elasticmoduli for uncemented sediment at critical porosity depending on pressure

and pore fluid.

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4

M-M

odu

lus

(GPa)

Porosity

SOLID

HERTZ-MINDLIN

IncreasingPressure

MODIFIEDLOWER

HASHIN-SHTRIKMANWITH

HERTZ-MINDLIN

Co

mp

ress

ion

al M

od

ulu

s (G

Pa)

Compaction and Undercompaction Due to PorePressure in AI-EI Space

Abnormal pore pressure also results in AI and Poisson's ratioreversals

Ip Reversal

PR Reversal

3

456

78

Ip (

km

/s

g/cc

)

ALL

0.2

0.3

0.4

10 15 20 25 30

Poi

sson

's R

atio

ALL

Differential Pressure (MPa)

PR Reversal

1 km

Hi-P Gas

Ip (

km/s

g/c

c)P

R

5

6

7

0.3 0.4 0.5

Ip (

km

/s

g/cc

)

Poisson's Ratio

PR is very sensitive to mineralogy. We may want to use it todetect mineralogical changes associated with onset ofoverpressure. May help resolve the non-uniqueness ofuniversality of Ip-φφφφ trends

Compaction and Undercompaction Due to PorePressure in AI-EI Space

AbovePressure

Zone

BelowPressure

Zone

PressureZone

JustShales

Ip (

km/s

g/c

c)

High pore pressure in rock with gas results in smaller Poisson’s ratio.Velocity may vary a lot among rocks but PR behavior is universal.

Plots based on lab data.

30 20 10 0Pp (MPa)

Sand35% Porosity

30 20 10 0Pp (MPa)

Sand27% Porosity

30 20 10 00

.1

.2

Pp (MPa)

PR

Sand36% Porosity

High Pressure in Gas SandsP

R

Normal Compaction in ShalesLog data show monotonic compaction versus depth.

0 50 100 150

2000

2500

3000

GR

Dep

th (m

)

2.0 2.2 2.4 2.6RHOB (g/cc)

2 3 4 5Vp (km/s)

Dep

th (

m)

Normal Compaction in ShalesLog data show monotonic compaction versus depth.

0 .1 .2 .3 .4 .53

4

5

6

7

8

9

10

11

12

13

Porosity

Ip (

km

/s

g/cc

)

GR

20

40

60

80

100

120

140

160

0 0.1 0.2 0.3 0.4 0.53

4

5

6

7

8

9

10

11

12

13

Porosity

Ip (

km

/s

g/cc

)

TVD

1800

2000

2200

2400

2600

2800

3000

3200

Left -- color coding by GR highlights compaction trends for shale and sand.Right -- color coding by depth shows porosity collapse and impedance increase.

Ip (

km/s

g/c

c)

Ip (

km/s

g/c

c)

0.1 0.2 0.3 0.44

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

Porosity

Ip (

km

/s

g/cc

)

TVD2500

2550

2600

2650

2700

2750

2800

2850

Undercompaction in ShalesLog data show reverse compaction versus depth.

Color coding by depth shows porosity and impedance reversal.Overpressured shales stay on the same rock physics trend as normally

pressured shales.

Reversal -- DeeperShale Plots to

Low-Right

Ip (

km/s

g/c

c)

40 60 80 100

8

9

10

11

12

13

14

15

16

GR

MD

(kft

)

AT_136_1

.2 .4 1 3

Rt

.1 .2 .3 .4

Porosity

UPS

CA

LE

D

2.0 2.5 3.0

Vp (km/s)

UPS

CA

LE

D

5 6 7

Ip (km/s g/cc)

UPS

CA

LE

D

10 11 12 13

MW (lb/gal)

Mudweight Steps Approximately Match Porosity and Velocity Flattening

4 5 6 7 8 9 10

Pp (kpsi)

1 2 3 4

Peff (kpsi)

2 kf

tUndercompaction in Shales -- Example 2

Undercompaction in Shales -- Example 2

0.15 0.2 0.25 0.3 0.35

4

4.5

5

5.5

6

6.5

7

7.5

Porosity

P-I

mped

ance

Depth (km)

2.5

3

3.5

4

4.5

SAND

OverpressuredShale

Color-Coded by Depth

Overpressured shales stay on the same rock physics trend as normallypressured shales.

Ip (

km/s

g/c

c)

Undercompaction and Vp/Vs Ratio

In overpressured (softer) sediments, the Vp/Vs ratio is high and deviatesfrom the established Vp/Vs relations.

In overpressured gas sands the opposite is true -- the Vp/Vs ratio is small.

1.5

2.0

2.5

3.0

3.5

2.0 2.5 3.0 3.5 4.0

Vp

/V

s

Vp (km/s)

Mudrock

WilliamsShale

WilliamsSand

OverpressuredGas Sand

OverpressuredShale

Pore PressureIncrease

Figure shows a Vp/Vs versusVp plot for a well with an

overpressured shale section(green) and overpressured

gas sand (red). Blacksymbols are for normallypressured shales. Blue

curves show establishedrelations for water-saturated

sediment.

Vp

/Vs

Compaction and Unloading in Sands

Loading and unloading produce different strain paths in sand

Compaction and elastic unloading in a sand.

0 5 10 15 200.39

0.4

0.41

0.42

0.43

Pressure (MPa)

Galveston

Por

osit

y

0.39 0.40 0.41 0.42 0.430

1

2

Porosity

Galveston

Envelope

Vp (

km

/s)

0.39 0.40 0.41 0.42 0.430

0.2

0.4

0.6

0.8

1.0

1.2

Porosity

Galveston

Envelope

Vs

(km

/s)

Po

rosi

ty

Vp

(km

/s)

Vs

(km

/s)

Compaction and Unloading in Sands

Static and Dynamic Moduli

StaticUnloading

StaticLoading

0

1

2

3

4

0 5 10 15 20

Bu

lk M

odu

lus

(GPa)

Effective Pressure (MPa)

Dynamic

Static

0 5 10 15 20Effective Pressure (MPa)

Dynamic

Static

StaticUnloading

StaticLoading

SAND 1 SAND 2

Bu

lk M

od

ulu

s (G

Pa)

Conclusion

The projection of compaction (loading) process intothe impedance-porosity plane produces a universaltrend typical for many soft shales and independentof depth.

AI/EI technique may help detect pressure-associated lithology changes in shales. But what todo in frontier areas where impedance inversion isdifficult?

Unloading (uplift) is different from loading(compaction) and will produce a different trendbecause of irreversible porosity reduction.

Pore Fluid and Pressure Diagnostic from AI and EI

The softer the rock with liquid the larger the Poisson’s Ratio. The softer therock with gas the smaller the Poisson’s ratio.

0

0.1

0.2

0.3

0.4

2 3 4 5 6

Poi

sson

's R

atio

P-Impedance (km/s g/cc)

BRINE

PorePressure

PorePressure

GAS

NORTH SEASAND

PR