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