This sub-program consists of a wide
grouping of physicists, chemical and petroleum engineers, and geologists. The
program is attempting to answer questions such as: How do we describe and compare structures of complex - often
disordered - materials? Successful predictive modelling of the properties of
"real world" materials is reliant on accurate characterisation of
their micro and mesostructural morphologies. The objective of the program is to
develop and optimize HPC tools to analyse and characterise complex 3D
morphologies, and develop modelling software to relate morphology to material
properties. The program is split into two streams: one dealing with structure
and function of real materials at the meso-scale (including rocks, paper, wood
and bone); the other with enumeration of possible morphologies. In addition to numerical
modelling, the program contains a substantial visualisation component.
The Computational Mesoscale Physics
sub-program will develop a suite of software, to be made available to all
researchers, which will include software for structural analysis of 3D data
sets (that is useful to tomographic and confocal microscopy users) and physical
characterisation of those data.
The structural analysis will allow characterisation and display of
(surface) contours of 3D data sets (eg. according to density), including a
number of standard and novel integral and differential measures (porosity,
curvatures, Euler Characteristics), quasi-conformal circle maps, pore
skeletons. Physical
characterisation of arbitrary data will allow simulation of physical
properties, including conductivity, permeability, dielectric measures, linear
elastic moduli, NMR relaxation etc.
Those products are of immediate
interest to groups at the ANU (Research School of Physical Sciences, Faculty of
Engineering, Geology), CSIRO (Manufacturing Technology, Petroleum), Monash
University (Australian Paper and Pulp Institute, Chemical Engineering),
University of NSW (Petroleum Engineering), University of Queensland (Centre for
Microscopy and Microanalysis), as well as Australian Industry (BHP Petroleum,
SCOPE, APCRC, CSR). With the development of high resolution tomographic imaging
and confocal microscopy technologies, that client base is certain to broaden
once our capabilities become public.
The software will be in the areas of:
Imaging: Development
of parallel reconstruction and data analysis programs to run in real time to be
integrated with the high resolution X-ray Computed Tomography facility recently
funded by the ARC RIEF program.
Visualizing: The ability to manipulate and explore the
complex morphologies in real time within the 3-dimensional virtual environments
developed at ANU.
Modelling: Simulate transport, mechanical
and multi-phase flow properties directly on the image data sets and on complex
materials of arbitrary 3-dimensional geometry and topology. The prediction of flow transport and
mechanical properties in disordered materials on massive three-dimensional
grids is computationally very intensive and researchers utilising the software
will require access to APAC facilities.
With the power of the APAC National
Facility, the visualization and modelling components may be combined to provide
a Virtual Materials Laboratory for complex materials. The development has the potential to be a valuable aid for
research in a number of fields and industry as detailed below. (A graphical user interface that runs
on different platforms will also be written to make the software easily
accessible.)
Dr.
Mark Knackstedt, Applied Maths, ANU
Dr. Adrian P.
Sheppard, Applied Maths, ANU
Dr. Arthur Sakellariou, Applied Maths, ANU
Dr. Tim
Senden, Applied Maths, ANU
Dr. Vanessa
Robins, Applied Maths, ANU
Mr. Stuart J.
Ramsden, Visualisation Laboratory, ANUSF
Dr. Rob Sok,
Applied Maths, ANU/School of Petroleum Engineering, UNSW
Mr. C. Arns,
Visiting Fellow, School of Petroleum Engineering, UNSW
Mr. Gerd Schroeder, Applied Maths, ANU
Prof. S. F.
Cox, Geology, ANU
Reconstruction of tomographic image
data:
Work is almost complete on the development of an optimised parallel code which reconstructs cone-beam tomography data. The code is based on the Feldkamp algorithm and is designed to operate on massive data sets (up to 2048^3 voxels), which is necessary for the state-of-the-art X-ray CT facility operating at ANU. Additionally, this code is suitable for other CT instruments. The code has been written using the message passing interface, and engages up to 128 processors simultaneously. The code outputs three-dimensional images, typically of porous and multiphase materials. Once the code is complete and has reached production stage, is will be used continuously as long as the ANU X-ray CT facility is operational.
Identifying Phase Distributions and
3D Visualization of Data Sets:
The tomographic image consists of a
cubic array of up to 8 billion reconstructed linear x-ray attenuation
coefficient values, each corresponding to a finite volume cube (voxel) of the
sample. Beam hardening artefact corrections have been developed for the data
sets. Phase separation techniques have also been developed to run on APAC
facilities. The simplest method is to choose a threshold attenuation which
matches a predetermined bulk measurement. In practice this is not a reasonable
method, due to peak overlap in the intensity histogram and due to the
uncertainty in the bulk measurements. It has been shown that a reliable method
of phase separation can be made through detection and localization of edges
between distinct phases. We have developed an edge-based kriging segmentation
algorithm to phase separate images.
Volume rendering on the 3D data sets is performed. wherein the data volume is rendered directly without decomposing it into geometric primitives. Typically the scalar density within the volume is assigned a colour and transparency depending upon lookup tables, rays are traced into the volume and they are attenuated and coloured depending on the transparency of their route through the volume. The 3D visualization is performed on a 2GHz Pentium 4 with 1Gb RAM. Typical rendering time is about 1 min. per image frame.
Network generation
Skeletonisation of the image (or
³medial axis extraction²) is required to quantify the network morphology of
each phase. The size of the data
sets mandates the development of parallel algorithms to perform the
skeletonisation. We have developed
several new algorithms for this purpose as rigorous testing has shown that all
previous parallel thinning algorithms do not correctly preserve topology. This
method is currently being implemented. We are developing additional codes to calculate other morphological
signatures, including the integral geometric Minkowski measures, described
below.
Stochastic reconstructions of
complex materials: Integral Geometric Approach.
These measures embody information from every order of the correlation
function but can be calculated simply by summing over local contributions. We
have computed the evolution of the measures with density for a range of
disordered microstructural models; particle-based models, amorphous
microstructures and cellular and foam-like structures. Analytic results for the
particle-based models have been derived and compared with computed values,
confirming the accuracy of the computational algorithm.
We have successfully developed
efficient finite difference codes for transport and finite element codes for
mechanical properties to run on the APAC facilities. The multiphase flow
software, has also been implemented on the APAC facility. Studies of
geophysical properties of petroleum reservoir rocks are now well-developed,
with extensive use of the APAC machine. Several milestones have been reached:
Permeability of Porous media
The permeability code based on the
lattice-Boltzmann method (LB) has been written. The LB approach is a mesoscopic
approach for computational fluid dynamics, where the macroscopic dynamics of
the solution of a discretized Boltzmann equation can be shown to match the
Navier-Stokes equation. Due to its simplicity in form and adaptability to
complex flow geometries, like the presence of solid-fluid and fluid-fluid
boundaries, one of the most successful applications of the LB method has been
to flow in porous media. In this method, the fluid is modelled as a collection of particles moving on a regular
lattice with each lattice point connected to its nearest and next-nearest
neighbours. In our implementation we use the D3Q19 (3 Dimensional lattice with
19 possible momenta components).
Poisson ratio of dry sandstone
morphologies. A finite element method was implemented
on the APAC facility to study the elastic properties of dry sandstone
morphologies obtained from microtomographic images of a clean sandstone and of
model microstructures. The elastic properties derived from the microtomographic
images agree well with those for the model structures for all porosities. We
show that the dry Poisson's ratio for the model sandstone morphology becomes
independent of Poisson's ratio of the solid phase at a critical porosity and
that this limiting behaviour holds for any number of solid phases and is
insensitive to the manner in which the phases are distributed. An empirical structure-property
relationship has been found, that holds for all systems independent of the
number of phases and Poisson's ratio of the solid phase. (Accepted by Geophysical
Research Letters, to
appear March 2002.)
Elasticity-Porosity Relationships:
Accurate velocity model for cemented sands and carbonates. Based on successful work modeling the elastic properties
of monomineralic cemented sandstone, we have subsequently generated elastic
property relationships for both the dry and water-saturated states for model cemented sandstone morphologies.
We find that for all porosities, the choice of microstructural model for
cementation has a minimal effect on the resultant modulus-porosity relationship.
Gassmann's equations are verified for the porous materials made up of multiple
solid constituents. Agreement of the predictions with experimental data sets
for clay-bearing consolidated sandstones is excellent. Results are compared to
currently employed theoretical and empirical relationships for deriving
moduli-porosity estimates. The empirical relationship used to derive the full
elasticity-porosity relationship for clean consolidated sands is extended to
cemented sands made up of multiple mineral phases. (Submitted to Geophysical
Prospecting.)
Network Modelling of Capillary
Dominated Fluid Displacements in
Porous Structures. The displacement of one immiscible
fluid by another inside a porous structure occurs in many places throughout the
earth's crust. In most cases the
rate of the fluid flow is slow enough that the displacement is governed purely
by the capillary forces acting at the fluid interfaces. Our understanding of what governs the
displacement is still poor. We are
using network modelling to better understand how the topology of the porous
structure affects the displacement, and also to investigate the role played by
long range correlations of the material properties.
Extensions to biomaterials.
The success of this work in the field of geomaterials has led to a
collaboration with groups at University of New South Wales and National
University of Singapore working in the field of biomaterials. In particular we
have embarked on a study of the elastic properties of bone and tissue engineered
bone and cartilage. The
work has also led to a collaboration with a endocrinology group of Prof. E.
Seeman at the University of
Melbourne Medical school and the Austin Repatriation Hospital working in the
field of the assessment of bone quality and health. In particular we have
embarked on a study of the morphological and mechanical changes that occur in
bone during osteoporosis. A final collaboration has been mooted with Prof. M.
Swain from the School of Dentistry, University of Sydney, considering the mechanical
properties of teeth undergoing carification.
The linkage of the two
programs is progressing well:
Accurate estimation of permeability
from microtomographic image. Following on from previous work where
we have shown that very accurate predictions of transport properties can be
derived directly from digitised tomographic images we show that fluid
permeability can also be derived accurately. Simulation of permeability on
microtomographic images of sandstone are in excellent agreement with
experimental measurements over a wide range of porosity. This shows the
feasibility of combining digitised images with transport calculations to
accurately predict physical properties of complex materials. (to be submitted to Geophysical Research Letters).
Accurate estimation of permeability
on reservoir rock.
Simulation of permeability on
microtomographic images of sandstone from a commercial reservoir provided by
BHP Billiton has been undertaken. Results compare favourably with experiments.
Excitingly, we find that one can obtain useful data on small sample sizes (~1mm3).
This gives one the ability to generate a large ensemble of independent samples
from a single imaged core. For example, measurement at a scale of (200)^3
enables us to generate 64 independent data points for each (1000)^3 core. A
single core plug can in principle give one a full permeability:porosity curve,
rather than a single data point. The CT facility can obtain images at the same
resolution on cores of (1 cm3) or (20003 voxels). In
principle one could obtain 500 independent data points from a single core. In
an important industrial context, as sample sizes can be very small (~mm3)
it may be possible to predict properties from core material not suited for
laboratory testing (e.g., drill cuttings and damaged core).
Effect of network topology on
relative permeability. We consider the role of topology on the
drainage relative permeability derived from network models. We first describe
the topological properties of network models derived from a suite of
tomographic images of Fontainebleau sandstone. We then show the importance of
accurately reproducing the sample topology when deriving relative permeability
curves from network models. Comparison of the relative permeability curves
generated on networks derived from experimental images and those generated on a
regular cubic lattice with identical geometric characteristics (pore- and
throat-size distributions) leads to poor agreement. Relative permeability
curves generated on regular lattices and on diluted lattices with a similar
average coordination number as the original rock network also give poor
agreement. We find that relative permeability curves generated on stochastic
networks which honour the full coordination number distribution do give
reasonable agreement. We find that random and regular lattices with the same
coordination number distribution give equivalent relative permeabilities, and
that the introduction of longer-range topological bonds have a small effect.
Networks exhibiting correlations in pore- and throat-size and results on
systems up to the core-scale still exhibit a significant dependence on network
topology. The results show the importance of generating realistic 3D topologies
when attempting to develop predictive network models for multiphase flow.
(Submitted to J. Petroleum Sci. and Technology.)
This sub-program is dedicated to the
enumeration of networks and spatial partitions, to construct a comprehensive
catalogue of form against which real morphologies can be compared. A number of
conceptual approaches are being developed, all requiring advanced computation
and visualisation techniques:
Euclidean 3D Networks and spatial
partitions. The project has matured in the past
twelve months considerably, with all mathematical details now in place for
systematic enumeration of 3d networks deduced from tilings of triply periodic
hyperbolic surfaces. A couple of preliminary publications have appeared,
directed at the solid state chemistry and physics communities, with examples of
the technique. We have now incorporated all aspects of the program into a single
Python code, including analysis of groups and sub-groups relevant to particular
projections, allowable tilings, network relaxation subject to simple force
fields as well as visualization of relevant discrete hyperbolic groups in the
2D hyperbolic plane (Klein or Poincaré models), their projection onto
3-periodic hyperbolic surfaces in 3D Euclidean space and decoration of the
groups with vertices and edges. The resulting package is a unique teaching and
research resource for visual exploration of hyperbolic group theory, complex
spatial partitions and networks.
Digital
computation of medial surfaces and axes. The
development of rigorous numerical theory for generation of medial surface and
medial axis transforms of surfaces in 3D Euclidean space is now complete. The
work is about to be published and has been presented in international for a in
2002. The package is now being applied to novel spatial partitions generated by
the group, with particular interest in deriving accurate, mathematically meaningful
networks characteristic of multi-handled hyperbolic surfaces.
Complex systems and networks. Developments in the network enumeration project and the
expertise of our incoming fellow researcher, Dr. T. Di Matteo in econophysics,
has led to the spawning of a new effort, combining our extant understanding of
networks with complex data sets found for example in financial markets. New
tools for characterizing and visualizing such complex multi-dimensional data
are being developed, that extend the techniques used for 3D networks. A
powerful feature of our approach is the use of 2D hyperbolic space, as this can
project into Euclidean spaces of arbitrarily high dimensions. The work offers a
complementary view of the nature of complex random networks, of real interest
to a range of scientist recently, following the explosion of Small Worlds
Theory and Scale-Free networks results in the statistical physics
community.
Ramsden presented examples of the
Mesoscale Physics program to the national VR community at the second National
Visualization Workshop (U Sydney, December 2001). Informal links were
established and renewed due to that exposure, particularly within the
visualisation community.
Research Collaborations:
Prof. W.V. Pinczewski, Mr. C. Arns, Ms.
J.-Y. Lee, Mr. V. Nguyen, School of Petroleum Engineering, UNSW: Development of
CT Facility. Development of skeletonization algorithms. Multi-phase flow in
sedimentary rocks. Geophysical properties of petroleum reservoir rocks.
Prof. Ian White, Centre for Resources
and Environmental Sciences and Dr. R. Greene, Geography, ANU: Characterisation
of pore structure in deep regolith materials.
Prof. S. F. Cox, Department of Geology,
ANU: Fluid flow in ore forming systems.
Dr.
R.N. Mantegna, Dip. di Fisica e Tecnologie Relative, Observatory of Complex
Systems, Universita' di Palermo: Systems behaviour of fininacial markets.
Dr.
Christophe Oguey, Cergy-Pontoise University, France: Polycontinuous networks.
Dr. K.
Mecke, Max Planck Institute for Metallurgy, Stuttgart, Germany:
Characterisation of complex materials.
Prof. W. B. Lindquist, Applied Maths,
State University of New York, Stony Brook: Development of skeletonisation
algorithms
Prof. B. Milthorpe, School of
Biomedical Engineering, UNSW and Dr. D. Hutmacher, Orthopaedics, National
University of Singapore: Developing optimal scaffold technology for tissue
engineered bone and cartilage.
Dr. Thomas H. Rich, Museum of Victoria,
Visualisation of fossils within rock matrices.
Assoc. Prof. Ego Seeman, Dept. of
Endocrinology, University of Melbourne: Assessing Bone Quality and Health.
Industrial Collaborations:
Statoil: WAG Injection into North Sea
Sandstones.
Statoil: Imaging and characterization
of carbonate core.
BHP Petroleum: Interpretation of
laboratory core measurements. Imaging, visualising and modelling laboratory
core floods
BASF A.G.: Imaging and analysis of foam
morphologies.
International Paper: Imaging fluid
penetration into sized and unsized paper.
PUBLICATIONS
AND INTELLECTUAL PROPERTY
Nonuniversality of invasion percolation
in two-dimensional systems, M. A. Knackstedt, M. Sahimi and A. P. Sheppard,
Phys. Rev. E, 65, 2002, 035101(R).
Direct and Stochastic generation of
network models from tomographic images: Effect of topology on two phase flow
properties, Robert M. Sok, Mark A. Knackstedt, A. P. Sheppard, W.V. Pinczewski,
W.B. Lindquist, A. Venkatarangan and L. Paterson, Transport in Porous Media 46,345-371 (2002).
Computation of linear elastic
properties from microtomographic images: Methodology and agreement between
theory and experiment, C. Arns, M. A. Knackstedt, W. V. Pinczewski and E.
Garboczi, Geophysics, 67(5),
1396-1405 (2002).
Accurate
Vp:Vs relationships for sandstones, C. Arns, M. A. Knackstedt, and W.V.
Pinczewski, Geophys. Res. Letters, 29(8), paper number:
29(8), art. No. 1202 (April 15, 2002).
Trapping
Thresholds in Invasion Percolation, L. Paterson, M. Knackstedt and A. P.
Sheppard, Phys. Rev. E., 66(5), art. No. 056122,
(November, 2002).
Characterising
the morphology of disordered materials², Christoph H. Arns and Mark A.
Knackstedt and Klaus R. Mecke, in Morphology of Condensed Matter --- Physics
and Geometry of spatially complex Systems, Springer Lecture Notes in Physics,
Vol. 600, pp. 37-74, (2002).
Velocity/Porosity relationships: I.
Accurate velocity model for clean consolidated sandstones, M. A. Knackstedt, C.
Arns and W.V. Pinczewski, Geophysics, (to appear).
Spreading of aqueous liquids in unsized
papers is by film flow", R. Roberts, Tim J. Senden, Mark A. Knackstedt and
M. Bruce Lyne, J. Pulp and Paper Science, (to appear, cover article April, 2003
issue).
³Some novel three-dimensional Euclidean crystalline network derived
from two-dimensional hyperbolic tilings², European Physical Journal B, vol. 31,
pp. 273-284 (2003).
³Ab initio construction of some crystalline 3D Euclidean networks²,
S.T. Hyde, S. Ramsden, T. Di Matteo and J. Longdell, Journal of Solid State
Sciences (cover article), in press (March 2003).
³Novel surfactant mesostructural topologies: between lamellar and columnar
forms², S.T. Hyde and G.E. Schröder, Current Opinion in Colloid and Interface
Science, in press (March 2003).
'Medial surfaces of hyperbolic structures', G.E. Schröder, S.J.
Ramsden, A.G. Christy and S.T. Hyde, submitted to European Journal of Physics
B, Jan 2003.
"How
does the Eurodollar Interest Rate behave?", T. Di Matteo and T. Aste,
(cond-mat 0101009), International Journal of Theoretical and Applied Finance,
vol. 5, No.1 (2002) 1-16.
"Scaling
behaviours in differently developed markets", T. Di Matteo, T. Aste and M.
M. Dacorogna, Physica A (2003) in press.
"Using
the scaling analysis to characterize financial markets", T. Di Matteo, T.
Aste and M. M. Dacorogna, Journal of Empirical Finance (2003) submitted.
Invited Lectures:
Knackstedt:
Stochastic
Geometry and Statistical Physics, ³Characterisation of complex materials²,
German Mathematical Society, Oberwolfach, Germany, (February 10-16, 2002).
Workshop on The Physical and
Engineering of Underground Reservoirs: Oil and Gas Fields and Groundwater
Aquifers, Ministry of Education, Iran, Zanjan, Iran (December 2001-January
2002).
Hyde:
2 lectures; ³Hyperbolic and Euclidean
networks² and ³Mean and Gaussian curvature of triply periodic minimal surfaces²
at the ³Foams and Minimal Surfaces² Workshop, Isaac Newton Mathematics
Institute, Cambridge University, July-August 2002.
Di Mattero:
"Using
the scaling analysis to characterize financial markets", International
Econophysics conference (IEC 2002) August 28-31, Bali, INDONESIA.
Ramsden:
"Computation
and Visualization of Hyperbolic Tilings on Minimal Surfaces", Dec 3rd-4th
2002, OzViz 2, Sydney University.
"Combinatorial
Tiling Theory", Dec 9th, 2002, ACT ANZIAM Australian and New
Zealand Industrial and Applied Mathematics seminar.
Schroeder:
'Medial
Surface Analysis of hyperbolic structure','Geometry and Mechanics of Structured
Materials', Sept 29 - Oct 25, 2002, Max-Planck-Institut fuer die Physik
komplexer Systeme.
'Structure
and morphology studies using the medial surface transform' at the
Max-Planck-Institut fuer Metallphysik, Stuttgart, July 3rd, 2002.
RESOURCES
To date, APAC funds are being used to
support personnel only. Student support has been extended to C. Arns in 2001.
Arns joined with the Mesoscale Physics program (Virtual Materials Lab.
project), with 100% funding from APAC (from Jan 1, 2002). We have also employed
Dr T. Di Matteo, from Salerno University, Italy, to work on the Networks
sub-project (100% APAC funding, from January 2002). Dr Di Matteo comes to us
with extensive computational expertise, and the Mesoscale Physics program has
expanded into computational aspects of complex systems (particularly complex
network models of financial markets) as a result of her interests. APAC support
has also been extended to a postgraduate student, Michael Turner, to develop
analysis of the numerical physics of flow through permeable Australian soils.