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
2Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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)
3Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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%
4Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
5Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
Relationship between size distribution and floating grain fraction
well #1well #2well #3
well #1well #2well #3
6Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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)
well #1well #2well #3
log( perm in mD) = 0.198 * porosity in % - 0.325 * floating in % - 1.76 + - 0.37x / 2.3
well #1well #2well #3
7Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
8Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
9Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
10Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
11Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
12Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
13Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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)
14Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
15Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
16Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
17Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
Permeability can be simulated given 3D rock matrix from CAT
small capillary pressure large capillary pressure
18Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
19Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
Layer based model derived from blocking for well #2
20Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
Multiple stack inversion Bayesian inversion is used
before inversion, ignore seismicafter inversion, honour
seismic to within noise level
near far
21Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
22Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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
23Monday, 25 January 2010
CSIRO. Estimation of Permeability with Seismic “I really did mean to say permeability not porosity”
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).
24Monday, 25 January 2010