Post on 12-Jan-2017
DIGITAL ROCK PHYSICS:
A NEW TOOLS FOR BETTER UNDERSTAND OF
RESERVOIR PROPERTIES
Umar Fauzi - umarf@fi.itb.ac.id
Fourier D. E. Latief - fourier@fi.itb.ac.id
HAGI LUNCHEON TALK - 2015
ROCK GOES DIGITAL
OUTLINES
Introduction Characterization and Estimation of Physical Properties of Rocks Permeability, Elastic constants, Electric conductivity Digital reconstruction techniques Fluid flow in reconstructed porous rocks Discussion
INTRODUCTION
Terminologi Petrofisika dan Fisika Batuan
Petrophysics Rock Physics
Petro => batuan batuan
Archie (1950)
SPWLA (1959)
Archie Conference (1990)
SRB – (1990-an)
Nur, Schoen, Gueguen
1st IWRP – 2011 di CSM
http://www.rockphysicists.org/
Dewar (2001) Seismik: sedikit Seismik: utama
DIGITAL ROCK PHYSICS
Abbasi, N. (EAGE, Amsterdam, 2014):
-Evaluation of digital rock physics for routine and special core
analysis-
“DRP is an emerging technology with a wide spectrum of
applications for different conventional and unconventional
reservoirs.”
Saenger, dkk (2nd EAGE Workshop on Rock Physics 2014 ):
-Towards a representative rock model from a micro-CT image-
“Digital rock physics combines modern imaging with advanced
numerical simulations to analyze the physical properties of
rocks.”
INTRO. CONT.
Quote: “(The) Truth (is) in the Detail”
Field Well Core Micro-sample
Bulk properties Detail components
„inner beauty‟
Field – Well - Core Micro-images
Bulk properties Detail microstructures
Porosity Pore structure
Pore connectivity (connected, isolated)
Pore/throat size distribution
Saturation Fluid distribution
Type of fluids Type of fluids
Saturation processes Mechanism of saturation processes
Permeability Percolation (Pc, l)
Connectivity (z,th)
Relative permeability Relative permeability
Conductivity Detail components (z, te)
Elasticity (Velocity) Components (grains, fluids): K, m
Mechanisms (grain contacts, Sw, etc)
Map of physical
properties
What do cause change in
-Physical properties (AI, s ,etc)?
Physical properties of rocks depend on:
Solid/Matrix
Pore structures
Fluid content
gas
water
Complexity of rocks
Earth-Science Reviews 123 (2013), V. Cnudde and M.N. Boone
High-resolution X-ray computed tomography in geosciences: A
review of the current technology and applications
….Driven by the technological and computational progress, the
technique is continuously growing as an analysis tool in geosciences
and is becoming one of the standard techniques, …….
It is foreseen that this number will continue to rise, and micro-CT
will become an indispensable technique in the field of geosciences….
Leading Edge, June 2012, Vernik, L. and Kachanov, M.
On some controversial issues in rock physics
….. The misconceptions seem to be rooted in the fact that this
broader discussion has remained largely unknown in the exploration
and development geophysics community…….
Benefit of digital rock physics (practical):
> repeatable,
> non-destructive,
> easy and quick,
> easy to transfer
> sample „flexible‟
Conceptual:
> Hypothesis => reality
> „manipulation scheme‟
> “visible”
ADVANTAGES
DIGITAL IMAGING EQUIPMENTS
EQUIPMENTS: LOM: Light Optical Microscopy
SEM: Scanning Electron Microscope
STM: Scanning Tunneling Microscope
SAXS: Small Angle X-ray Scattering
SANS: Small Angle Neutron Scattering
3-D Reconstruction
(FAUZI & NOMEIRA, 2008) Optical Microscopy
Scanning Electron Microscope
X-ray micro-CT
4 mm
CHARACTERIZATION AND
ESTIMATION OF PHYSICAL PROPERTIES OF ROCKS
TWO POINT CORRELATION FUNCTIONS
T(0) =f
T’(0) ~ S
Pore radius
Grain radius
T m nN
f fi ij j
ij i m j n( , )max
max
,
1
11
T r r f x r f x r( , ) ( ) ( ) 1 2 1 2
Poreinxif
Matrixtheinxiffij
1
0
SIMPLE ANALYTICAL FORMULA Simple capillary model:
L
l
Electrical conductivity of rock:
sr: effective electrical conductivity of rock se: electrical conductivity of fluid f : porosity te : electrical tortuosity (l/L)
F : Formation factor
2
e
frt
fss
2
3
Sfk
ht
f
Permeability: f: shape factor
S: Specific surface area
th : hydraulic tortuosity
r
fF
s
s
Fauzi (1997) – 2D
PERMEABILITY
f k
keq
z
zkp
k
kp
kz
keq
dk( )
( )
( )
( )
( ) ( )
21
21
21
0
l
2
3)(
S
ckff
k ko p pct ( )
0.40 0.60 0.80 1.00percolation probability
1E+1
1E+2
1E+3
1E+4
perm
eabili
ty (
mD
)
LPT EMA
measured k
2 4 6 8
coordination number (z)
1E+3
k (
mD
)
EMA (UC_62)
measured k
LPT-Approach
EMA
PERKOLASI DAN KONEKTIVITAS
Hilfer (1991):
Mavko & Nur (1997):
Fauzi dkk (2002):
Fauzi (1997)
(LATIEF ET AL., 2008)
PERCOLATION PROBABILITY
See also:
Kalam, 2012, Digital Rock Physics for fast and accurate special core analysis in corbonates, Intech
TRACER INLET
TRACER OUTLET
Tortuosity
(flow path) TORTUOSITY VS POROSITY (FAUZI ET AL., 2007)
References for
Capillary pressure:
Kalam, 2012, Digital Rock Physics for fast and accurate special core
analysis in corbonates, Intech
Elastic constants:
- Prokopiev and Sevostianov, Int J Fract, 2007;
- Andra et al, 2013, Computer and Geosciences 50;
- dan lain-lain.
8 12 16 20 24
measured formation factor
0.10
1.00
10.00
rati
o e
sti
ma
ted
/meas
ure
d F
Fauzi (1997): 2D – EMA & Archie
FORMATION FACTOR
ANISOTROPY
0
50
250
1000
2000
0
50
250
1000
2000
Low
High
mD
500 1500 25000 1000 2000
measured k (mD)
0.8
1.2
1.6
2.0
ratio
k_m
ax/k
_min
(Fauzi, 2009)
DISCUSSION
Km
100 Hz m
30 kHz mm
100 kHz mm
Scaling problems:
Complexity: heterogeneity,
anisotropy
10-2
10-1
100
101
102
103
104
105
Scale of measurement (m)
10-6
10-9
10-12
10-15
10-18
10-21
10-24
P
E
R
M
E
A
B
I
L
I
T
Y
(m2)
Laboratory In situ (field)
Borehole regional
k ~ L2 k ~ L
-1
10-2
10-1
100
101
102
103
104
105
106
107
frekwensi (Hz)
Seismic akustik Ultrasonik K
E
C
G
E
L
S
E
I
S
M
I
K
Low-porous, low permeable rocks
high-porous, high permeable rocks
Renshaw (1998), Vila et al. (1996), Moerig (1994), etc.
ALTERNATIVES REV: Representative Elementary Volume
Representative models
Up-scaling techniques:
Averaging
Homogenization (EMA)
Renormalization
Simplification:
- Tensor => Scalar
- Heterogeneous => Homogoneous
- Anisotropic => Isotropic
- „variation‟ => „trends‟
1E+1 1E+2
pixel width (µm)
1E-3
1E-2
1E-1
1E+0
po
ros
ity
& s
pe
cif
ic s
urf
ac
e a
rea (
1/µ
m)
PorositySlope = -0.18
Specific surface areaSlope = -0.463
UC_3
Fauzi (1997)
Latief & Fauzi (2012)
The Statistical Physics of Sedimentary Rocks:‘The complexity of million-year-old sedimentary rock is being unraveled by such modern concepts of random systems as fractals, percolation and diffusion-limited growth’ (Wong P. Z., Physics Today, 1988)
Imbibition
Drainage
Drainage
Imbibition Drainage
Drainage
Imbibition
Imbibition
HYSTERISIS IN FLUID SATURATION
ILLUSTRATION OF FLOWS IN PORE
TERIMA KASIH