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Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”

Michael Glinsky

1Monday, 25 January 2010

CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”

Outline

• rock physics model• supporting measurements (log and core)• numerical rock assembly model• model based seismic inversion & practical detectability• conclusions



Floating grain model - the link of deposition physics to grain scale properties, permeability

Load-Supporting

Floating

Abundance of potential floating grains in the system is due to two factors• overall abundance of silt/mud-sized particles (related to nature of clastic input and system-scale proximal vs distal position)• local variation due to depositional processes (e.g. rapid fallout vs traction)



Capture Ratio = 1 – (1/1.5) = 33% ie 1/3 of small grains are captured in to the load bearing matrix of the rock. The capture ratio will depend on the

geometries of the original grains.

Capture ratio is another key concept

At a constant Effective Stress - For every 3 small grains, 1 becomes part of matrix and 2 will float

porosity (%) = -1.5*float(%) + B (B is a constant for a particular constant Pe)

Bimodal grain sizes (big and small)

porosity in % = -1.54 * float in % - 88% * ( 1 – exp( - Pe / 800 psi ) ) + 110% +- 0.2%



Petrophysical evidence for the floating grain model

Vp (ft/s)

dens

ity (g

m/c

c)

well #2

well #5

well #6

well #3

well #4

well #1



Relationship between size distribution and floating grain fraction

well #1well #2well #3




Good regression found between the permeability, porosity, and floating grains

10% 30%porosity0

3.5

log(

perm

in m

D)

10% 30%log(perm in mD)0

3.5

log(

pred

icte

d pe

rm)


log( perm in mD) = 0.198 * porosity in % - 0.325 * floating in % - 1.76 + - 0.37x / 2.3




Acoustic resonance measurements on well #2 core confirm trend seen in logs

2

2.05

2.1

2.15

2.2

2.25

2.3

2.35

2.4

2000 2500 3000 3500 4000

vp (m/s)

den

sity

(g

m/

cc)

6% float0% floatmeasurment6% float

0% float moderate sorting

moderately poor

poor



No change in shear velocity as seen on logs and predicted by theory

1800

2000

2200

2400

3000 3200 3400 3600 3800

vp (m/s)

vs

(m/

s)

0% float

6% float

Ps correctedaverage

6% float

0% float

moderate sorting

moderately poor

poor



Floating grains seen in CAT scan and SEM of well #2

sample #3, moderate sorting, 300 mD, 24%

50 micron500 micron

#1, poor, 10 mD, 20%500 micron

#2, moderately poor, 100 mD, 22%500 micron

5 mm



Guide to AVO interpretation

Increasing NG0% to 100%

Brine to Oil

Decreasing Float6% to 0%Increasing perm1 mD to 1000 mD

Decreasing Effective Stress1000 psi

Dimming AVO

Brightening AVO

good

bad



Numerical rocks give important understanding of floating grain model

• Create sphere packings (two size) representative of unconsolidated sediment through “cooperative rearrangement” algorithm

• Quantify the number of loose grains in packings• Understand capture fraction



Mono-dispersed packing validation

• Single grain size• Comparison with Finney packing• Quality checks:

• Porosity• 36.3% Finney v. 36.2% simulation

• Percent of loose grains• 1.8% Finney v. 1.6% simulation

• Radial distribution function



Floating grain fraction & capture ratio demonstrated

Little dependence on RR5 vol% 40 vol%

RR = radius ratio

float

ing

grai

n pe

rcen

t

critical point

(small grain load support)

(large grain load support)

capture fraction0

1/3

2/3

1

“Thermodynamics of random packing”, Physics Today (June 2007)



Phase diagram for random packing of binary mixture of spheres

(large grain load support, small grains float)

(small grain load support)

(large grain load support, small grains part of matrix)

RRc VFc

note: volume fraction dominates over radius ratio critical point

“Statistical mechanics of dense granular media”, Coniglio et al., J. Cond. Matter 17, S2557 (2005).

Rc ≈ 4VFc ≈ 0.45



Critical scaling for radius ratio critical point (RRc)

y =

0.0103x2.2609

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

-1 0 1 2 3

RRc-RR

fmax -

f(p

eak)

fit data

data

Power (fit data)

y =

0.0102x2.1708

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

-1 0 1 2 3

RRc-RR

Dp

oro

sity

(max)

- D

po

rosi

ty(p

eak)

fit data

data

Power (fit data)

y =

0.1467x1.8419

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3

RRc - RR

CF0

= C

F(V

F=

0)

fit datadataPower (fit data)

capture fraction @ volume fraction = 0

peak decrease in porosity

peak floating fraction



Critical scaling for volume fraction critical point (VFc)

y = 2.4516x1.31

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

-0.10 0.00 0.10 0.20 0.30 0.40 0.50

VFc-VF

CFmax*(CFmax-CF)/(CFmax-CF0)

fit dataRR=1.5RR=2RR=3RR=4Power (fit data)

capture fraction



Permeability can be simulated given 3D rock matrix from CAT

small capillary pressure large capillary pressure



Implementation of floating grain model in DELIVERY

• φ = Aφ+Bφ vp+Cφφflt +εφ – (from numerical inversion of above, using clusters)

• vp= Ap +Bpd + Cp LFIV + Dp φflt+εp – (inverted from this regression, direct from log data and clusters)

φ =A’+B’d+C’ φflt+ εφ, with d←(1-exp(-σeff/P0))

C=-1/(1-fc), fc is ‘capture fraction’

• Vs= As+Bs vp+ εs

- direct from log data



Layer based model derived from blocking for well #2



Multiple stack inversion Bayesian inversion is used

before inversion, ignore seismicafter inversion, honour

seismic to within noise level

near far



Floating grain fraction and porosity are determined by seismic

time of layer boundary - seismic determines N/G - seismic does not determine

float fraction & porosity - seismic determines ==> permeability



Conclusions

• floating grain model:• explains well log measurements• relates seismic to the sorting and the permeability• strong link between the microscopic picture and the mesoscopic effective

media model• support given by:

• standard core measurements (laser grain size, permeability)• acoustical core measurements• CAT scan & SEM of core• numerical rock assembly modelling showing critical behaviour

• practical application shown to be feasible• deployed in stochastic model based inversion• applied to case of deepwater turbidite• porosity and floating grain percentage determined by seismic, therefore

permeability



Acknowledgments

• CSIRO• Michael Glinsky, James Gunning

• University of Texas• Stephen Bryant, Cynthia Thane

• Lone Star Geophysical• David DeMartini

• Australian National University• Mark Knackstedt

• Colorado School of Mines• John Scales, Brian Zadler

• Down Under Geosolutions• Troy Thompson

• BHP Billiton Petroleum• Stanislav Kuzmin, Kai Soon Tan, Chris Lerch, Dean Stoughton, Bruce Asher, Gabriela

Schell

“A model for variation of velocity versus density trends in porous sedimentary rocks”, Demartini & Glinsky, J. Appl. Phys. 100, 014910 (2006).“Critical grain-size parameters for predicting framework and floating grains in sediments”, Bryant et al., J. Sedimentary Research 79, 817 (2009).“Detection of reservoir quality using Bayesian seismic inversion”, Gunning & Glinsky, Geophysics 72, R37 (2007).


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