Dual models of pore spaces

Glantz, Roland; Hilpert, Markus

doi:10.1016/j.advwatres.2005.11.017

Cited by 21 publications

(15 citation statements)

References 31 publications

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“…For a more formal treatment of polyhedral complexes, duality, and a justification of the term ''approximation" see [23]. In contrast to [23] we do not assume ''conformity of the widening relation with the pore boundary" -the reason being that we do not apply the widening relation anymore when constructing TDM. Finally, Section 2.3 deals with how and where we measure the widths of the pore space.…”

Section: Duality and Polyhedral Approximationmentioning

confidence: 98%

“…Finally, certain 1D Voronoi cells are fused which, through duality, yields the actual pore throats and fuses the slices into pore bodies. The pore throats and pore bodies derived in this paper are more realistic than those in Glantz and Hilpert [23], since the pore throats, which separate the pore bodies, now usually consist of more than one 2D Delaunay cell and extend all the way into the narrowing ends of the pore channel cross sections.…”

Section: Introductionmentioning

confidence: 97%

“…In an earlier paper [23] we (1) specified how a given pore space can be approximated by a Delaunay complex (in [23] the slightly more general term ''regular triangulation" is used instead of ''Delaunay complex"), (2) proved that the union of the cells in the Voronoi complex (denoted by Sk 0 in [23]) is homotopy equivalent to the pore space, and (3) described algorithms for computing the Delaunay and Voronoi complexes. The plan of this paper is as follows.…”

Section: Introductionmentioning

confidence: 98%

“…Second, we deal with relatively open Delaunay cells of dimensions one to three (see Section 2.1) and are thus able to represent and decompose open [29] pore spaces, i.e., pore spaces without the pore boundary. The pore spaces being open is an indispensable requirement for the pore network being homotopy equivalent [29] to the pore space [23]. Intuitively, this means that the pore network and the pore space can be transformed into one another by bending, shrinking and expanding operations in a way that preserves connectivity.…”

Section: Introductionmentioning

confidence: 99%

“…1a, i.e., the space inside the box not covered by the four spheres. Through a procedure explained in [23] and in Section 2.2 below we approximate this pore space by a polyhedral complex, the boundary of which is shown in Fig. 1b.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Tight dual models of pore spaces

Glantz

Hilpert

2008

Advances in Water Resources

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Section: Duality and Polyhedral Approximationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tight dual models of pore spaces

Glantz

Hilpert

2008

Advances in Water Resources

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A re‐examination of throats

Kim

Lindquist

2013

Water Resources Research

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[1] We critically re-examine the concept of a throat in a porous medium as a geometric quantity defined independently of an entry meniscus in a drainage process. To maintain the standard notion of a throat as a locally minimum-area cross section in the pore network, we demonstrate with examples that throats must intersect each other. Using flow simulation, we show that these intersecting throats correspond to capillary pressure controlled entry points during drainage. We have designed a throat-finding algorithm that explicitly locates intersecting throats, using a planar approximation for robustness and speed. The capability of the new algorithm was compared against an existing algorithm in the construction of pore-throat networks from X-ray computed tomography images of consolidated sandstones (7.5-22% porosity) and of an unconsolidated sand pack (32.5% porosity). We show that the probability of throat intersection increases significantly with porosity above 20%; in the sand pack, over 1/4 of all throats intersect with another.

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Percolating length scales from topological persistence analysis of micro‐CT images of porous materials

Robins

Saadatfar

Delgado‐Friedrichs

et al. 2016

Water Resources Research

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Topological persistence is a powerful and general technique for characterizing the geometry and topology of data. Its theoretical foundations are over 15 years old and efficient computational algorithms are now available for the analysis of large digital images. We explain here how quantities derived from topological persistence relate to other measurements on porous materials such as grain and pore-size distributions, connectivity numbers, and the critical radius of a percolating sphere. The connections between percolation and topological persistence are explored in detail using data obtained from micro-CT images of spherical bead packings, unconsolidated sand packing, a variety of sandstones, and a limestone. We demonstrate how persistence information can be used to estimate the percolating sphere radius and to characterize the connectivity of the percolating cluster.

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Dual models of pore spaces

Cited by 21 publications

References 31 publications

Tight dual models of pore spaces

Tight dual models of pore spaces

A re‐examination of throats

Percolating length scales from topological persistence analysis of micro‐CT images of porous materials

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