Tight dual models of pore spaces

Advances in Water Resources

Volumn 31, Issue 5, 2008, Pages 787-806

  Glantz, Roland ^a   Hilpert, Markus ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

3D image analysis; Drainage; Duality; Gradient vector fields; Homotopy equivalence; Modeling; Polyhedral pore space; Pore network; Tight pore throats

Indexed keywords

GRADIENT METHODS; IMAGE ANALYSIS; MATHEMATICAL MODELS; POROUS MATERIALS; THREE DIMENSIONAL; VECTORS;

GRADIENT VECTOR FIELDS; HOMOTOPY EQUIVALENCE; PORE NETWORK; PORE SPACES; TIGHT PORE THROATS;

DRAINAGE;

DRAINAGE; GRADIENT METHODS; IMAGE ANALYSIS; MATHEMATICAL MODELS; POROUS MATERIALS; THREE DIMENSIONAL; VECTORS;

COMPUTER SIMULATION; DRAINAGE; IMBIBITION; MODELING; PERMEABILITY; POROUS MEDIUM;

EID: 41749092306     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2008.01.015     Document Type: Article

References (52)

1. Acharya R.C., van der Zee S.E.A.T.M., and Leijnse A. Porosity-permeability properties generated with a new 2-parameter 3D hydraulic pore network model for consolidated and unconsolidated porous media. Adv Water Resour 27 7 (2004) 707-723
2. Ahronovitz E, Aubert J-P, Fiorio C. The star-topology: a topology for image analysis. In: Cinquième Colloque DGCI, LLAIC1, Université d'Auvergne, ISBN 2-87663-040-0, September 1995. p. 107-16.
3. Al-Raoush R., Thompson K., and Willson C.S. Comparison of network generation techniques for unconsolidated porous media. Soil Sci Soc Am J 67 (2003) 1687-1700
4. Aurenhammer F. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Comput Surv 23 3 (1991) 345-405
5. Björner A. Topological methods. Handbook of Combinatorics II (1995), Elsevier, Amsterdam 1819-1872
6. Blunt M.J. Flow in porous media - pore network models and multiphase flow. Curr Opin Colloid Interf Sci 6 (2001) 197-207
7. Blunt M.J., and Hilpert M. Editorial (to the special issue on pore-scale modeling). Adv Water Resour 24 3-4 (2001) 231-232
8. Boissonnat J.-D. Algorithmic geometry (1998), Cambridge University Press
9. Bryant S.L., Mellor D.W., and Cade C.A. Physically representative network models for transport in porous media. AIChE J 39 (1993) 387-396
10. Celia M.A., Reeves P.C., and Ferrand L.A. Recent advances in pore scale models for multiphase flow in porous media. Rev Geophys 33 Supplement (1995) 1049-1057
11. Cohen-Steiner D, Morvan J-M. Restricted Delaunay triangulations and normal cycle. In: Proc 19th Ann Sympos Comput Geom 2003. p. 312-21.
12. Delerue J.F., Perrier E., Yu Z.Y., and Velde B. New algorithms in 3D image analysis and their application to the measurement of a spatialized pore size distribution in soils. Physics and Chemistry of the Earth, Part A-Solid Earth and Geodesy 24 (1999) 639-644
13. Dey TK, Edelsbrunner H, Guha S. Computational topology. In: Chazelle B, Goodman JE, Pollack R. editors. Advances in discrete and computational geometry, vol. 223 of Contemporary mathematics, Americ. Math. Soc., 1999. p. 109-43. URL: http://citeseer.ist.psu.edu/dey99computational.html.
14. Dullien F.A.L. Porous media. Fluid transport and pore structure (1992), Academic Press, San Diego, USA
15. Edelsbrunner H. Algorithms in combinatorial geometry, volume 10 of EATCS monographs on theoretical computer science (1987), Springer
16. Edelsbrunner H., and Harer J. Persistent homology - a survey. In: Goodman J.E., Pach J., and Pollack R. (Eds). Twenty Years After (2007), AMS
17. Fatt I. The network model of porous media: I. Capillary pressure characteristics. Trans AIME 207 (1956) 144-159
18. Fatt I. The network model of porous media: II. Dynamic properties of a single size tube network. Trans AIME 207 (1956) 160-163
19. Fatt I. The network model of porous media: III. Dynamic properties of networks with tube radius distribution. Trans AIME 207 (1956) 164-181
20. Forman R. Morse theory for cell complexes. Adv Math 134 1 (1998) 90-145
21. Forman R. A user's guide to discrete Morse theory. preprint, 2001. URL citeseer.ist.psu.edu/485188.html.
22. Gladkikh M., and Bryant S. Prediction of interfacial areas during imbibition in simple porous media. Adv Water Resour 26 (2003) 609-622
23. Glantz R., and Hilpert M. Dual models of pore spaces. Adv Water Resour 30 2 (2007) 227-248
24. Glantz R, Hilpert M. Invasion percolation through minimum weight spanning trees. Phys Rev E, in press.
25. Glantz R, Schuler U. Pore networks of granular filters. In: Jean Lafleur L, André Rollin, editors. Proceedings of Geofilters'96, Montreal, Canada, May 1996. BITECH. p. 75-84.
26. Golden K.M., Eicken H., Heaton A.L., Miner J.E., Pringle D.J., and Zhu J. Thermal evolution of permebility and microstructure in sea ice. Geophys Res Lett 34 16 (2007) L16501
27. Hilpert M., Glantz R., and Miller C.T. Calibration of a pore-network model by a pore-morphological analysis. Transport Porous Media 51 (2003) 267-285
28. Hilpert M., McBride J.F., and Miller C.T. Investigation of the residual-funicular nonwetting-phase-saturation relation. Adv Water Resour 24 2 (2001) 157-177
29. Jänich K. Topology (1984), Springer, New York
30. Kovalevsky V.A. Finite topology as applied to image analysis. CVGIP 46 (1989) 141-161
31. Lee T.-C., Kashyap R.L., and Chu C.-N. Building skeleton models via 3D medial axis/surface algorithms. CVGIP 56 (1994) 462-478
32. Lindquist W.B. The geometry of primary drainage. J Colloid Interf Sci 296 2 (2006) 655-668
33. Lindquist W.B., Lee S.-M., Coker D.A., Jones K.W., and Spanne P. Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J Geophys Res 101B (1996) 1163-1173
34. Lindquist W.B., and Venkatarangan A. Investigating 3D geometry of porous media from high resolution images. Phys and Chem Earth, Part A - Solid Earth Geodesy 24 7 (2000) 593-599
35. Lindquist W.B., Venkatarangan A., Dunsmuir J., and Wong T.-f. Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones. J Geophys Res 105 B9 (2000) 21509-21527
36. Lowry M.I., and Miller C.T. Pore-scale modeling of nonwetting-phase residual in porous media. Water Resour Res 31 3 (1995) 455-473
37. Mason G., and Mellor D.W. Analysis of the percolation properties of a real porous material. In: Rodríguez-Reinoso F., Rouquerol J., Sing K.S.W., and Unger K.K. (Eds). Characterization of porous solids. Studies in surface science and catalysis vol. II (1991), Elsevier 41-50
38. Mayer A.S., and Miller C.T. The influence of porous medium characteristics and measurement scale on pore-scale distributions of residual nonaqueous-phase liquids. J Contamin Hydrol 11 3/4 (1992) 189-213
39. Mellor DW Random close packing (RCP) of equal spheres: Structure and implications for use as a model porous medium. PhD thesis, Open University, 1989.
40. Okamoto I., Hirai S., and Ogawa K. MRI velocity measurements of water flow in porous media containing a stagnant immiscible liquid. Meas Sci Technol 12 (2001) 1465-1472
41. Oxley J.G. Matroid theory (1992), Oxford University Press, New York, USA
42. Prodanović M., Lindquist W.B., and Seright R.S. 3D Image-based characterization of fluid displacement in a Berea core. Adv Water Resour 30 2 (2007) 214-226
43. Schneider R. Convex bodies: the Brunn-Minkowski theory. Encyclopedia of Mathematics vol. 44 (1993), Cambridge University Press, Cambridge, NY
44. Seright R.S., Liang J.-T., Lindquist W.B., and Dunsmuir J.H. Characterizing disproportionate permeability reduction using synchrotron X-ray computed microtomography. PE Reserv Eval Eng 5 (2002) 355-364
45. Sethian J.A. Level set methods and fast marching methods (1999), Cambridge University Press, New York
46. In: Stapf S., and Han S. (Eds). NMR imaging in chemical engineering (2006), WILEY-VCH, Weinheim
47. Thompson K.E., and Fogler H.S. Modeling flow in disordered packed beds from pore scale fluid mechanics. AIChE J 43 (1997) 1377-1389
48. Thulasiraman K., and Swamy M.N.S. Graphs: theory and algorithms (1992), J. Wiley & Sons, New York, USA
49. Toussaint G.T. A simple linear algorithm for intersecting convex polygons. Visual Comput 1 (1985) 118-123
50. Vogel H.J., and Roth K. A new approach for determining effective soil hydraulic functions. Euro J Soil Sci 49 4 (1998) 547-556
51. Wildenschild D., Hopmans J.W., Vaz C.M.P., Rivers M.L., Rikard D., and Christensen B.S.B. Using X-ray computed tomography in hydrology: Systems, resolutions, and limitations. J Hydrol 267 3-4 (2002) 279-285
52. Yang A., Miller C.T., and Turcoliver L.D. Simulation of correlated and uncorrelated packing of random size spheres. Phys Rev E 53 2 (1996) 1516-1524