Post on 27-Dec-2021
Poromechanics Investigation at Pore-scale Using
Digital Rock Physics Laboratory
Shawn Zhang1,*, Nishank Saxena2, Patrick Barthelemy1, Mike Marsh1, Gary Mavko2, Tapan Mukerji2 1Visualization Sciences Group, Burlington, MA, USA; 2Stanford University, Stanford, CA, USA
Session: Multiphysics October 13, 2011
Agenda
Introduction
Motivation
Goal of study
Theory
Approach – digital rock physics lab
3D Imaging
Avizo digital rock analysis
Comsol simulation
Results
500nm
Shale Gas Reservoir, 70,000x Magnification
70nm or .07µm
7.2
µm
Motivation: porous rock network
Ø 2.57% K ~0.0003mD
Convention Sandstone Reservoir
Tight-Gas Sandstone Reservoir
Ø 10% - K 0.052mD 50µm
Ø 33.0% - K 753mD 200µm
500nm
Shale Gas Reservoir, 70,000x Magnification
70nm or .07µm
7.2
µm
Motivation: porous rock network
Ø 2.57% K ~0.0003mD
Convention Sandstone Reservoir
Ø 33.0% - K 753mD 500µm
Important
• Oil and Gas
• Geology
• Hydrology
500nm
Shale Gas Reservoir, 70,000x Magnification
70nm or .07µm
7.2
µm
Motivation: porous rock network
Ø 2.57% K ~0.0003mD
Convention Sandstone Reservoir
Ø 33.0% - K 753mD 500µm
Complex
• Multiscale
• Multiphase
• Multiphysics
Goal: Validate Pore Filling Theory
This Presentation,
Validates the use of solid material filling to
replace more commonly used fluid filling
theory;
Designs the validation framework using
digital rock physics.
Work in progress,
Derives generic pore filling theory;
Validates new theory in a similar framework
with more complex physics.
Pore filling Theories: Substitution Equation
Solid B
Solid A
Solid B
Empty
Solid A
drydry,K
AA,K
satsat,K
BB,K
Material A
Fluid Substitution:
• Brine Sand, Oil Sand, Gas Sand
Solid Substitution:
• Heavy oil, Bitumen filled
Pore filling Theories: Substitution Equation
Solid B
Solid A
Solid B
Empty
Solid A
drydry,K
AA,K
satsat,K
BB,K
Material A
Fluid Substitution:
• Gassmann, 1951
Solid Substitution:
• Ciz & Shapiro,
1997
dry
BBAB
dry
A
dry
BAB
A
sat
KKKKKK
KKKKK
11111
1111
0
0
Solid Substitution equation
dry
BBAB
dry
A
dry
BAB
A
sat
KKKKKK
KKKKK
11111
1111
0
0
where Ksat Effective bulk modulus η0 Porosity Kdry Dry (drained) rock bulk modulus KA Bulk modulus of the pore-filling mineral KB Bulk modulus of the solid matrix
Digital Rock Physics Lab An escape from the flat land. Edward Tufts, 1981
Image Import and
Processing
3D Volume
Reconstruction
3D Visualization
Segmentation
Geometry
Reconstruction Statistical analysis
Enhanced
Visualization
Presentation
Publication Numerical Modeling
FEA/CFD
Discovery
Experiment
Modification
Custom Processing, Automation
Matlab, LabVIEW, Script, C++
3D
Image Stack
Multiple
Modalities,
Scales or
Channels
Registration / Fusion
Avizo workflow
3D Imaging
Imaging Data
• Electron microscopy
• S/TEM tomography
• TEM serial sectioning
• FIB-SEM Nanotomography
• Light microscopy
• Confocal
• Polish and view 3D (e.g. Robo-MET)
• X-ray tomography
• Industrial
• Material sciences (micro and nano)
• MRI
• Ultrasound
• GPR
• LIDAR
• Remote Sensing Satellite Imagery
Petrophysical parameters derived from image
based simulation
Porosity 0.168
Permeability X 1x10-3 Darcy
Permeability Y 0.89x10-3 Darcy
Permeability Z 0.57x10-3 Darcy
Mesh reconstruction & Comsol BC
Boundary conditions,
Normal displacement at
external surface with
strain 10^-3.
Continuity of
displacement and traction
at pore/rock interface.
Quasi-static simulation
(inertial effects are
negligible).
Different Pore-filling Material: Pressure
0 0.01x1010
1 0.41x1010
2 0.81x1010
3 1.21x1010
4 1.61x1010
5 2.01x1010
6 2.41x1010
7 2.81x1010
8 3.21x1010
dry
BBAB
dry
A
dry
BAB
A
sat
KKKKKK
KKKKK
11111
1111
0
0
Different KA (Pa)
Different Pore-filling Material: Strain
0 0.01x1010
1 0.41x1010
2 0.81x1010
3 1.21x1010
4 1.61x1010
5 2.01x1010
6 2.41x1010
7 2.81x1010
8 3.21x1010
dry
BBAB
dry
A
dry
BAB
A
sat
KKKKKK
KKKKK
11111
1111
0
0
Different KA (Pa)
Different Pore-filling Material: Validation
0 0.01x1010
1 0.41x1010
2 0.81x1010
3 1.21x1010
4 1.61x1010
5 2.01x1010
6 2.41x1010
7 2.81x1010
8 3.21x1010
dry
BBAB
dry
A
dry
BAB
A
sat
KKKKKK
KKKKK
11111
1111
0
0
Different KA (Pa)
5 10 15 20 25 30 35
0
5
10
15
20
25
30
35
40
Pore Solid Bulk Modulus (GPa)
Sa
tura
ted
Bu
lk M
od
ulu
s (G
Pa)
Finite Element Simulation
Present Theoretical Work
Approximate Ciz and Shapiro (2007)
HS Upper Bound
HS Lower Bound
Concluding remarks
A theoretical rock pore material
substitution model is validated with a
digital rock physics framework.
We are working on,
Derives generic pore filling theory;
Validate it in a similar framework but with
more complex physics, e.g., shear traction,
fluid structure interaction, etc. Solid B
Solid A
0PP
A
drypseudoK
Applied Stress
Deformed body
Reference body
Internal traction
Solid B
Empty
dryK
Stress to maintain0
PPA