pore-scale modelling of macroscopic rock properties
TRANSCRIPT
9th Euroconference on
Rock Physics and Geomechanics
Trondheim, Norway
17 – 21 October 2011
Pore-scale modelling of
macroscopic rock properties
Cathrine Ringstad
Pål-Eric Øren
Thomas Ramstad
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK SIZE AND RESOLUTION
Typical grid size
10003 – 12003 voxels
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK SIZE AND RESOLUTION
Pore space
Quartz
Feldspar
Resolution = 10 mm
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK SIZE AND RESOLUTION
Pore space
Quartz
Feldspar
Resolution = 10 mm
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK SIZE AND RESOLUTION
Pore space
Quartz
Feldspar
Resolution = 10 mm
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK SIZE AND RESOLUTION
Typical grid size = 10003 – 12003 voxels
Typical voxel resolution = 2 – 5 µm
Typical sample size = 2 – 6 mm3
Low resolution High resolution
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK PROCESS BASED
PROPERTIES
SEM analyses
Geological modelling
SEM imaging
Sample preparation
WORKFLOW
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK PROCESS BASED
SEM analyses
Geological modelling
SEM imaging
Sample preparation
WORKFLOW
µCT IMAGE
Image processing
Interpretation
µCT imaging
Sample preparation
WORKFLOWPROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK PROCESS BASED µCT IMAGE
Micro-structure
Weakly consolidated
Analogue
Sandstone and carbonate
PROS and CONSPROPERTIES
Segmentation
Consolidated only
Direct model
All types of rocks
PROS and CONS
Pore-scale modelling of macroscopic rock properties
1
10
100
1000
10000
0,0 0,1 0,2 0,3
Porosity [fraction]
Per
mea
bilit
y [m
Dar
cy]
Elasticity
Formation resistivity factor
Absolute permeability
NMR relaxation time
krw_exp1kro_exp1krw_exp2kro_exp2krw_exp3kro_exp3krw simkro simkrw avgkro avg
Rel
ativ
e pe
rmea
bilit
y
1.0
0.8
0.6
0.4
0.2
0.01.00.80.60.40.20.0
Sw [fraction]
Relative permeability
Capillary pressure
Resistivity index
DIGITAL ROCK PETROPHYSICAL FLUID FLOW
PROPERTIES
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK
FLUID FLOW
GRID PORE NETWORK
Resolution limited by grid
Computer intensive
Capillary and viscous flow
Exact pore space
PROS and CONS
Infinite resolution
Capillary flow
Simplified pore space
Fast
PROS and CONSPROPERTIES
Pore-scale modelling of macroscopic rock properties
0.0
1.0
0.8
0.6
0.4
0.2
0.01.00.80.60.40.2
Water saturation Sw [fraction]
krw
kroPrimary drainage
Re
lati
ve p
erm
ea
bil
ity
k r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
krw =kwater
kabs
kro =koil
kabs
Swi
Pore-scale modelling of macroscopic rock properties
0.0
1.0
0.8
0.6
0.4
0.2
0.01.00.80.60.40.2
Water saturation Sw [fraction]
krw
kroImbibition
Re
lati
ve p
erm
ea
bil
ity
k r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
krw =kwater
kabs
kro =koil
kabs
Swi Sor
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Grid Network
Process based µCT image
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Primary drainage
PBM model of Sandstone B
Network
Grid
Lab data
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Primary drainage
PBM model of Sandstone B
Network
Grid
Lab data
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Primary drainage
PBM model of Sandstone B
Network
Grid
Lab data
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Grid Network
Process based µCT image
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Imbibition
Sandstone A – Network simulations
µCT model
PBM model
Lab data
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Imbibition
Sandstone A – Network simulations
µCT model
PBM model
Lab data
Pore-scale modelling of macroscopic rock properties
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Water saturation Sw [fraction]
Rela
tive p
erm
eabil
ity k
r
DIGITAL ROCK
FLUID FLOW
PROPERTIES
RELATIVE PERMEABILITY kr
Imbibition
Sandstone A – Network simulations
µCT model
PBM model
Lab data
Pore-scale modelling of macroscopic rock properties
DIGITAL ROCK
FLUID FLOW
PROPERTIES
CONCLUSIONS
1) Pore scale derived properties are
comparable to laboratory data
2) Both µCT imaging and process based
modelling (PBM) may be used to generate
representative digital rock models
3) Grid and network calculations of relative
permeability produce similar results
THANK YOU FOR YOUR ATTENTION!