The Network Generation Comparison Forum
A collaborative project for objective
comparison of network generation algorithms for 3D tomographic data
sets of porous media
This site aims to provide a forum for research groups working on network
representation of porous media to compare network generation algorithms
by testing against a number of "benchmark" images of porous
materials. Comparison is in terms of criteria relevant to modelling of
transport properties of porous materials, particularly for use of the
network in multiphase fluid flow simulations. Network modellers are
encouraged to run their algorithms on these data sets and submit the
resultant networks along with a description of the algorithm.
Contents
Overview
Network simulations have become established tools for the simulation of
two-phase fluid flow in porous materials. The method usually consists
of extracting a network and relevant pore size information from a 3D
data set of a porous material such as a rock, then using a
ball-and-stick network model to simulate the flow properties. The
guiding idea, for the situation where a non-wetting fluid invades the
rock pore space under external pressure (often called drainage), is that
the phase interface advances through the pore space according to the
relationship between capillary pressure and tunnel (or throat) diameter.
This approach assumes that the labyrinths of porous materials are well
represented by a ball-and-stick network. These assumptions are wrong,
as only rather special labyrinth geometries can be effectively
partitioned into the balls and sticks of a network. Additionally, it is
extremely rare to find a pore space for which there is only one suitable
network representation. A simple example is a throat with bone-like
cross-section; the location of the path of the network edge
corresponding to this throat can be defined in a variety of ways: in
either of the two maximally wide sides of the bone, through the narrow
center, or (if homotopy equivalence of network and pore space is
abandoned) there may even be two edges, one through either of the two
sides. Pore labyrinths where the definition is not unique are not an
exeption, but the general case. Because of this ambiguity, comparison of
different network algorithms that handle these cases differently is
imperative.
A second major difference between network generation algorithms is the
post-processing of the initially extracted network. Most networks
extracted from empirical data sets exhibit features that are induced by
noise or by details of the geometry that are irrelevant for the flow
(simulation). A typical example is that of a single non-convex pore that
yields a number of pores connected by very small edges, none of which
can be considered to represent a genuine throat. In this case, one may
want to merge these pores to a single pore. The details of
post-processing procedures such as these can however influence the
macroscopic properties of the eventual network.
As there is no perfect network definition or algorithm, it is paramount
to have independent and objective comparison of the networks generated
by the different proposed algorithms. This is what this forum aims to
provide.
Furthermore, it is often particular geometric labyrinth configurations
that cause problems for network algorithms. To provide a list of small
synthetic model datasets that capture geometrically peculiar situations
is an additional aim of this forum.
How to contribute
Participation is open to everyone. There are a number of ways to be involved:
- Participate in the development of network evaluation criteria:
We welcome criticism and suggestions regarding the criteria (measures) that this forum uses to evaluate and characterise networks, and would particularly welome code to be used for performing the evaluation. This is done through the email list adrian.sheppard@anu.edu.au.
- Presentation of results of a network extraction algorithm:
- Download the four reference datasets provided below
- Extract network representations of these datasets using your extraction algorithm
- Download the analysis software provided and use it to analyse your network
- Make your results and a description of your method available on this site.
- Contribute to the repository of pathological (interesting) cases:
Present model datasets of
situations with which your algorithm (or any algorithm) has had
trouble. These datasets shall be small synthetic model datasets that
capture the essence of the problematic geometry and shall be
accompanied by a description of how they were constructed what the
essence of the problem consists in.
Representative porous media data sets
The following four datasets were chosen as reference data sets because
they are reasonably different from one another, and span a reasonable
range of the materials that are traditionally analysed using network
simulations.
Each data set is a cubic segmented image 512 voxels to a side. It is
stored as a raw binary file, with one byte (or unsigned character) per
voxel. Byte ordering is therefore irrelevant, so the files can be read
without alteration on all CPU types. Voxels are set to 1 to indicate
solid phase, 0 to indicate void phase. The files are compressed with
gzip; the uncompressed files should be exactly 512x512x512 = 134217728
bytes, or 128MB.
Click on the images for more detailed descriptions and for download of the corresponding data files.
(1) Silica sphere pack
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(2) Castlegate sandstone
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(3) Unconsolidated Sand Pack
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(4) Mt Gambier Limestone
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Measuring network quality
The generated networks will be compared using the following measures
(currently six) that are generally accepted to be relevant to network
modeling of two-phase flow in porous materials. Discussion is invited
on the merits of these measures, and how best to characterise and
evaluate the networks that have been created. The forum hopes to develop
software to evaluate these measures.
Boundary conditions:
Depending on the geometry of the sample, the spatial characteristics of
the labyrinth and the network generation algorithm, the effect of the
boundary of the sample on the generated network will vary. Therefore the measures should only be calculated on those pores and throats that do not connect to the object boundary.
Results: Generated networks
| Author and date | Method | Brief description and reference |
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A repository of difficult (pathological?) cases
Network extraction algorithms are based on the assumption that a pore
space can be effectively decomposed into components, and thus
represented by a network of nodes and links. Typically, the
decomposition is more successful for pore spaces that consist of large
pore bodies connected to each other through narrow constrictions or
throats. As a consequence, there are numerous situations where network
extraction algorithms perform badly, or produce unexpected
results. Often such cases are then labelled as pathological,
although this term is misleading since the unambiguously partitionable
object is the exception rather than the rule.
A published list of such pathological cases is currently missing, yet it
would be a most valuable tool for network algorithm developers. The
following list aims to fill that gap.
The following examples are synthetic models, although they may be
derived from situations observed in empirical data sets of real porous
materials. Anyone wishing to contribute a pathological case to the
repository is asked to distill the essence of the problem, and create a
synthetic model that pin-points the difficulty.
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Three-periodic Gyroid labyrinth
A model
labyrinth with a well-defined three-connected network and the peculiar
property that the nodes of the network are inflection points (rather
than maxima) of the Euclidean distance map whereas the maxima are
located at the mid-points of the edges. The Gyroid labyrinth is
periodic in three dimensions with cubic symmetry and is very homogeneous in
terms of channel diameter variations. The interface between solid and
pore space is a minimal surface.
Contributed by Gerd Schroeder (Gerd.Schroeder@anu.edu.au) on Oct 6, 2005. |