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

Between Rock and A Hard Place

Is rock that hard?

Quartzite Sandstone Metamorphism About.com

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

Reconstruction

Segmentation

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