Abstract
In this study, we have developed a new method to generate a multi-directional pore network for representing a porous medium. The method is based on a regular cubic lattice network, which has two elements: pore bodies located at the regular lattice points and pore throats connecting the pore bodies. One of the main features of our network is that pore throats can be oriented in 13 different directions, allowing a maximum coordination number of 26 that is possible in a regular lattice in 3D space. The coordination number of pore bodies ranges from 0 to 26, with a pre-specified average value for the whole network. We have applied this method to reconstruct real sandstone and granular sand samples through utilizing information on their coordination number distributions. Good agreement was found between simulation results and observation data on coordination number distribution and other network properties, such as number of pore bodies and pore throats and average coordination number. Our method can be especially useful in studying the effect of structure and coordination number distribution of pore networks on transport and multiphase flow in porous media systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Acharya R.C., van der Zee S.E.A.T.M., 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, 707–723 (2004). doi:10.1016/j.advwatres.2004.05.002
Al-Kharusi, A.S., Blunt, M.J.: Permability prediction and network extraction from pore space images. Paper presented at CMWR XVI—Compitational Methods in Water Resources. Copenhagen, Denmark, June (2006). http://proceedings.cmwr-xvi.org/contributionDisplay.py?contribId=293&sessionId=9&confId=a051
Al-Raoush R.I., Willson C.S.: A pore-scale investigation of a multiphase porous media system. J. Contam. Hydrol. 77, 67–89 (2005). doi:10.1016/j.jconhyd.2004.12.001
Ambegaokar V., Halperin B.I., Langer J.S.: Hopping conductivity in disordered systems. Phys. Rev. B 4, 2612–2620 (1971). doi:10.1103/PhysRevB.4.2612
Arns J.-Y., Robins V., Sheppard A.P., Sok R.M., Pinczewaski W.V., Knackstedt M.A.: Effect of network topology on relative permeability. Transp. Porous Media 55, 21–46 (2004). doi:10.1023/B:TIPM.0000007252.68488.43
Bakke S., Øren P.E.: 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2, 136–149 (1997). doi:10.2118/35479-PA
Berkowitz B., Ewing R.P.: Percolation theory and network modeling applications in soil physics. Surv. Geophys. 19, 23–72 (1998). doi:10.1023/A:1006590500229
Blunt M., King M.J., Scher H.: Simulation and theory of twophase flow in porous media. Phys. Rev. A 46, 7680–7699 (1992). doi:10.1103/PhysRevA.46.7680
Blunt, M., King, M.J., Zhout, D.: What determines residual oil saturation in three phase flow. In: Proceedings of the SPE/DOE 9th Symposium on Improved Oil Recovery, Tulsa, OK (1994)
Chatzis, I., Dullien, F.A.L.: Modelling pore structures by 2D and 3D networks with application to sandstones. Can. J. Petroleum Technol, 97–108 (1977) (January–March)
Davis L.: The Handbook of Genetic Algorithms. Van Nostrand Reingold, New York (1991)
Dillard L.A., Blunt M.J.: Development of a pore network simulation model to study nonaqueous phase liquid dissolution. Water Resour. Res. 36(2), 439–454 (2000). doi:10.1029/1999WR900301
Dunsmoir, J.H., Ferguson, S.R., D’Amico, K.L., Stokes, J.P.: X-ray microtomography: a new tool for the characterization of porous media. SPE 22860. In: Proceedings of the 1991 SPE Annual Technical Conference and Exhibition, Dallas, October 6–9 1991
Fenwick D.H., Blunt M.J.: Three-dimensional modeling of three phase imbibition and drainage. Adv. Water Resour. 21(2), 121–143 (1998). doi:10.1016/S0309-1708(96)00037-1
Flannery B.P., Deckman H.W., Roberge W.G., D’Amico K.L.: Three-dimensional X-ray microtomography. Science 237, 1439–1444 (1987). doi:10.1126/science.237.4821.1439
Friedman S.P., Seaton N.A.: On the transport properties of anisotropic networks of capillaries. Water Resour. Res. 32, 339–347 (1996). doi:10.1029/95WR02830
Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison_Wesley (1989)
Heiba A., Sahimi M., Scriven L., Davis H.: Percolation theory of two-phase relative permeability. SPE Reserv. Eng. 7, 123–132 (1992)
Holland J.: Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor (1975)
Houck, C.R., Joines, J.A., Kay, M.G.: A Genetic Algorithm for Function Optimization: A Matlab Implementation. NCSU-IE TR 95, 09 (1995)
Ioannidis M.A., Chatzis I.: Network modelling of pore structure and transport properties of porous media’. Chem. Eng. Sci. 48, 951–972 (1993). doi:10.1016/0009-2509(93)80333-L
Ioannidis M.A., Chatzis I.: On the geometry and topology of 3D stochastic porous media. J. Colloid Interface Sci. 229, 323–334 (2000). doi:10.1006/jcis.2000.7055
Ioannidis, M.A., Kwiecien, M.J., Chatzis I., MacDonald, I.F. and Dullien, F.A.L.: Comprehensive pore structure characterization using 3-D computer reconstruction and stochastic modeling. Technical report, SPE Paper 38713 (1997a)
Ioannidis, M.A., Kwiecien, M.J., Chatzis, I., MacDonald, I.F., Dullien, F.A.L.: Comprehensive pore structure characterization using 3D computer reconstruction and stochastic modeling. In: Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX (1997b)
Jerauld G.R., Salter S.J.: The effect of pore-structure on hysteresis in relative permeability and capillary pressure: pore-level modelling. SPE Transp. Porous Media 5, 103–151 (1990). doi:10.1007/BF00144600
Jerauld G., Scriven L., Davis H.: Percolation and conduction on the 3D Voronoi and regular Networks: a second case study in topological order. J. Phys. Chem. 17, 3429 (1984)
Joekar-Niasar V., Hassanizadeh S.M., Leijnse A. (2007). Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modeling. Transp. Porous Med. (2007). doi:10.1007/s11242-007-9191-7
Knackstedt M.A., Sheppard A.P., Pinczewski W.V.: Simulation of mercury porosimetry on correlated grids: evidence of extended correlated heterogeneity at the pore scale in rocks. Phys. Rev. E. Rapid Commun. 58, R6923–R6926 (1998)
Lake L.W.: Enhanced oil recovery. In: Larson, R.G., Scriven, L.E., Davis, H.T. (eds) Percolation Theory of Residual Phases in Porous Media, Prentice Hall, Englewood Cliffs (1989)
Larson R., Scriven L.E., Davis H.T.: Percolation theory of residual phases in porous media. Nature 268, 409–413 (1977). doi:10.1038/268409a0
Larson R., Scriven L.E., Davis H.T.: Percolation theory of two-phase flow in porous media. Chem. Eng. Sci. 36, 57–73 (1991). doi:10.1016/0009-2509(81)80048-6
Lindquist B., Lee S.M., Coker D.: Medial axis analysis of void structure in threedimensional tomographic images of porous media. J. Geophys. Res. 101, 8297–8310 (1996). doi:10.1029/95JB03039
Lindquist W.B., Venkatarangan A., Dunsmuir J., Wong T.F.: Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainbleau sandstones. J. Geophys. Res. 105B, 21508 (2000)
Mayer A.S., Miller C.T.: The influence of porous medium characteristics and measurement scale on porescale distributions of residual nonaqueous-phase liquids. J. Contam. Hydrol. 11, 189–213 (1992). doi:10.1016/0169-7722(92)90017-9
Michalewicz Z.: Genetic algorithms + data structures = Evolution Programs. AI Series. Springer, New York (1994)
Øren P.E., Bakke S.: Process-based reconstruction of sandstones and prediction of transport properties. Transp. Porous Media 46, 311–343 (2002a). doi:10.1023/A:1015031122338
Øren, P.E., Bakke, S.: Reconstruction of Berea Sandstone and pore-scale modeling of wettability effects. In: Proceedings of the 7th International Symposium on Reservoir Wettability, Freycinet, Tasmania (2002b)
Øren P.E., Bakke S.: Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. J. Petrol. Sci. Eng. 39, 177–199 (2003). doi:10.1016/S0920-4105(03)00062-7
Øren, P.E., Pinczewski, W.V.: The effect of film flow in the mobilization of waterflood residual oil by gas flooding. In: 6th European IOR-Symposium, Houston, USA (1991)
Øren P.E., Pinczewski W.V.: Effect of wettability and spreading on recovery of waterflood residual oil by immiscible gasflooding. SPE Form. Eval. 8, 149–156 (1994)
Øren P., Billiotte J., Pinczewski W.V.: Mobilisation of waterflood residual oil by gas injection of water-wet conditions. SPE Form. Eval. 7, 70–78 (1992). doi:10.2118/20185-PA
Øren, P.E., Billiotte, J., Pinczewski, W.V.: Pore scale network modelling of waterflood residual oil recovery by immiscible gas flooding. In: SPE Improved Oil Recovery Symposium, Houston, USA (1994)
Øren P.E., Bakke S., Arntzen O.J.: Extending predictive capabilities of network models. SPE J. 3, 324–336 (1998a). doi:10.2118/52052-PA
Øren P.E., Bakke S., Arntzen O.J.: Extending predictive apabilities to network models. SPE J. 3, 324–336 (1998b). doi:10.2118/52052-PA
Paterson L., Painter S., Knackstedt M., Pinczewski W.V.: Patterns of fluid flow in naturally heterogeneous rocks. Physica A 233, 619–628 (1996a). doi:10.1016/S0378-4371(96)00199-9
Paterson, L., Painter, S., Zhang, X., Pinczewski, W.V.: Simulating residual saturation and relative permeability in heterogeneous formations. In: Proceedings of the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado (1996b)
Pereira G., Pinczewski W.V., Chan D., Paterson L., Øren P.: Pore-scale network model for drainage dominated three-phase flow in porous media. Transp. Porous Media 24, 167–201 (1996). doi:10.1007/BF00139844
Reeves P.C., Celia M.A.: A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale model. Water Resour. Res. 32(8), 2345–2358 (1996). doi:10.1029/96WR01105
Renault P.: The effect of spatially correlated blocking up of some bonds or nodes of a network on the percolation threshold. Transp. Porous Media 6, 451–468 (1991). doi:10.1007/BF00136352
Silin, D.B., Jin, G., Patzek, T.W.: Robust determination of the pore space morphology in sedimentary rocks. In: SPE 84296, Annual Technical Conference and Exhibition, Denver, Colorado, USA (2003)
Sok R.M., Knackstedt M.A., Sheppard A.P., Pinczewski W.V., Lindquist W.B., Venkatarangan A., Paterson L.: Direct and stochastic generation of network models from tomographic images; effect of topology on two phase flow properties. Transp. Porous Media 46, 345–372 (2002). doi:10.1023/A:1015034924371
Spanne P., Thovert J.F., Jacquin C.J., Lindquist W.B., Jones W., Adler P.M.: Synchrotron computed microtomography of porous media: topology and transports. Phys. Rev. Lett. 73, 2001–2004 (1994). doi:10.1103/PhysRevLett.73.2001
Thompson K.E., Willson C.S., Zhang W.: Quantitative computer reconstruction of particulate materials from microtomography images. Power Technol. 163, 169–182 (2006). doi:10.1016/j.powtec.2005.12.016
Thovert J.-F., Salles J., Adler P.: Computerised characterization of the geometry of real porous media: their description, analysis and interpretation. J. Microsc. 170, 65–79 (1993)
Wilkinson D., Willemsen J.F.: Invasion percolation: a new form of percolation theory. J. Phys. Math. Gen. 16, 3365–3376 (1983). doi:10.1088/0305-4470/16/14/028
Acknowledgments
Valuable discussions with Prof. Toon Leijnse are acknowledged. We also thank Prof. Ruud Schotting (Utrecht University) for his useful comments. As the members of the International Research Training Group NUPUS, financed by the German Research Foundation (DFG) and the Netherlands Organization for Scientific Research (NWO), the authors thank the DFG (GRK 1398) and NWO (DN 81-754) for their valuable support.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Raoof, A., Hassanizadeh, S.M. A New Method for Generating Pore-Network Models of Porous Media. Transp Porous Med 81, 391–407 (2010). https://doi.org/10.1007/s11242-009-9412-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9412-3