Prediction of preferential fluid flow in porous structures based on topological network models: Algorithm and experimental validation

  • Yang Ju
  • Peng Liu
  • DongShuang Zhang
  • JiaBin Dong
  • P. G. Ranjith
  • Chun Chang


The understanding and prediction of preferential fluid flow in porous media have attracted considerable attention in various engineering fields because of the implications of such flows in leading to a non-equilibrium fluid flow in the subsurface. In this study, a novel algorithm is proposed to predict preferential flow paths based on the topologically equivalent network of a porous structure and the flow resistance of flow paths. The equivalent flow network was constructed using Poiseuille’s law and the maximal inscribed sphere algorithm. The flow resistance of each path was then determined based on Darcy’s law. It was determined that fluid tends to follow paths with lower flow resistance. A computer program was developed and applied to an actual porous structure. To validate the algorithm and program, we tested and recorded two-dimensional (2D) water flow using an ablated Perspex sheet featuring the same porous structure investigated using the analytical calculations. The results show that the measured preferential flow paths are consistent with the predictions.


preferential flow porous structure topological networks flow resistance Darcy’s law experimental validation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Šimůnek J, Jarvis N J, van Genuchten M T, et al. Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone. J Hydrol, 2003, 272: 14–35CrossRefGoogle Scholar
  2. 2.
    Zhang Y, Yao F, Xu D, et al. Stochastic simulation on preferential seepage channels in water-flooding reservoirs. Electron J Geotech Eng, 2015, 20: 803–812Google Scholar
  3. 3.
    Birk S, Liedl R, Sauter M. Karst spring responses examined by process-based modeling. Groundwater, 2006, 44: 832–836CrossRefGoogle Scholar
  4. 4.
    Sinkevich M G, Walter M T, Lembo A J, et al. A GIS-based ground water contamination risk assessment tool for pesticides. Ground Water Monit Rem, 2005, 25: 82–91CrossRefGoogle Scholar
  5. 5.
    Wang Z, Jury W A, Tuli A, et al. Unstable flow during redistribution. Vadose Zone J, 2004, 3: 549–559Google Scholar
  6. 6.
    Gomez H, Cueto-Felgueroso L, Juanes R. Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium. J Comp Phys, 2013, 238: 217–239MathSciNetCrossRefGoogle Scholar
  7. 7.
    Beven K, Germann P. Macropores and water flow in soils revisited. Water Resour Res, 2013, 49: 3071–3092CrossRefGoogle Scholar
  8. 8.
    Jarvis N J. A review of non-equilibrium water flow and solute transport in soil macropores: Principles, controlling factors and consequences for water quality. Eur J Soil Sci, 2007, 58: 523–546CrossRefGoogle Scholar
  9. 9.
    Armstrong R T, Berg S. Interfacial velocities and capillary pressure gradients during Haines jumps. Phys Rev E, 2013, 88: 600–614CrossRefGoogle Scholar
  10. 10.
    Armstrong R T, Evseev N, Koroteev D, et al. Modeling the velocity field during Haines jumps in porous media. Adv Water Resour, 2015, 77: 57–68CrossRefGoogle Scholar
  11. 11.
    Kazemifar F, Blois G, Kyritsis D C, et al. Quantifying the flow dynamics of supercritical CO2-water displacement in a 2D porous micromodel using fluorescent microscopy and microscopic PIV. Adv Water Resour, 2015, 95: 352–368CrossRefGoogle Scholar
  12. 12.
    Kazemifar F, Blois G, Kyritsis D C, et al. A methodology for velocity field measurement in multiphase high-pressure flow of CO2 and water in micromodels. Water Resour Res, 2015, 51: 3017–3029CrossRefGoogle Scholar
  13. 13.
    Wehrer M, Slater L D. Characterization of water content dynamics and tracer breakthrough by 3-D electrical resistivity tomography (ERT) under transient unsaturated conditions. Water Resour Res, 2015, 51: 97–124CrossRefGoogle Scholar
  14. 14.
    Berg S, Ott H, Klapp S A, et al. Real-time 3D imaging of Haines jumps in porous media flow. Proc Natl Acad Sci USA, 2013, 110: 3755–3759CrossRefGoogle Scholar
  15. 15.
    Herring A L, Andersson L, Schlüter S, et al. Efficiently engineering pore-scale processes: The role of force dominance and topology during nonwetting phase trapping in porous media. Adv Water Resour, 2015, 79: 91–102CrossRefGoogle Scholar
  16. 16.
    Ptak T, Piepenbrink M, Martac E. Tracer tests for the investigation of heterogeneous porous media and stochastic modelling of flow and transport—A review of some recent developments. J Hydrol, 2004, 294: 122–163CrossRefGoogle Scholar
  17. 17.
    Amidu S A, Dunbar J A. Geoelectric studies of seasonal wetting and drying of a texas vertisol. Vadose Zone J, 2007, 6: 511CrossRefGoogle Scholar
  18. 18.
    Cuthbert M O, Mackay R, Tellam J H, et al. The use of electrical resistivity tomography in deriving local-scale models of recharge through superficial deposits. Q J Eng Geol Hydrogeol, 2009, 42: 199–209CrossRefGoogle Scholar
  19. 19.
    French H, Binley A. Snowmelt infiltration: Monitoring temporal and spatial variability using time-lapse electrical resistivity. J Hydrol, 2004, 297: 174–186CrossRefGoogle Scholar
  20. 20.
    Garré S, Koestel J, Günther T, et al. Comparison of heterogeneous transport processes observed with electrical resistivity tomography in two soils. Vadose Zone J, 2010, 9: 336–349CrossRefGoogle Scholar
  21. 21.
    Seven K, Germann P. Water flow in soil macropores II. A combined flow model. Can J Soil Sci, 1981, 32: 15–29CrossRefGoogle Scholar
  22. 22.
    Beven K. Micro-, meso-, macroporosity and channeling flow phenomena in soils. Soil Sci Soc Am J, 1981, 45: 1245CrossRefGoogle Scholar
  23. 23.
    Beven K, Germann P. Macropores and water flow in soils. Water Resour Res, 1982, 18: 1311–1325CrossRefGoogle Scholar
  24. 24.
    Skopp J. Comment on “micro-, meso-, and macroporosity of soil”. Soil Sci Soc Am J, 1981, 45: 1246CrossRefGoogle Scholar
  25. 25.
    Blunt M J, Bijeljic B, Dong H, et al. Pore-scale imaging and modelling. Adv Water Resour, 2013, 51: 197–216CrossRefGoogle Scholar
  26. 26.
    Wildenschild D, Sheppard A P. X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv Water Resour, 2013, 51: 217–246CrossRefGoogle Scholar
  27. 27.
    Nejad Ebrahimi A, Jamshidi S, Iglauer S, et al. Genetic algorithmbased pore network extraction from micro-computed tomography images. Chem Eng Sci, 2013, 92: 157–166CrossRefGoogle Scholar
  28. 28.
    Coon E T, Porter M L, Kang Q. Taxila LBM: A parallel, modular lattice Boltzmann framework for simulating pore-scale flow in porous media. Comput Geosci, 2014, 18: 17–27MathSciNetCrossRefGoogle Scholar
  29. 29.
    Muljadi B P, Blunt M J, Raeini A Q, et al. The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation. Adv Water Resour, 2016, 95: 329–340CrossRefGoogle Scholar
  30. 30.
    Al-Raoush R, Thompson K, Willson C S. Comparison of network generation techniques for unconsolidated porous media. Soil Sci Soc Am J, 2003, 67: 1687–1700CrossRefGoogle Scholar
  31. 31.
    Al-Raoush R I, Willson C S. Extraction of physically realistic pore network properties from three-dimensional synchrotron X-ray microtomography images of unconsolidated porous media systems. J Hydrol, 2005, 300: 44–64CrossRefGoogle Scholar
  32. 32.
    Lindquist W B, Lee S M, Coker D A, et al. Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J Geophys Res, 1978, 101: 8297–8310CrossRefGoogle Scholar
  33. 33.
    Nolan G T, Kavanagh P E. Computer simulation of random packing of hard spheres. Powder Tech, 1992, 72: 149–155CrossRefGoogle Scholar
  34. 34.
    Vogel H J. Topological characterization of porous media. In: Mecke K, Stoyan D, Eds. Morphology of Condensed Matter-Physics and Geometry of Spatially Complex Systems. Berlin Heidelberg: Springer Press, 2002. 75–92Google Scholar
  35. 35.
    Vogel H J, Roth K. Quantitative morphology and network representation of soil pore structure. Adv Water Resour, 2001, 24: 233–242CrossRefGoogle Scholar
  36. 36.
    Vogel H J, Roth K. Moving through scales of flow and transport in soil. J Hydrol, 2003, 272: 95–106CrossRefGoogle Scholar
  37. 37.
    Vogel H J, Cousin I, Ippisch O, et al. The dominant role of structure for solute transport in soil: Experimental evidence and modelling of structure and transport in a field experiment. Hydrol Earth Syst Sci, 2005, 10: 495–506CrossRefGoogle Scholar
  38. 38.
    Deurer M, Green S R, Clothier B E, et al. Drainage networks in soils. A concept to describe bypass-flow pathways. J Hydrol, 2003, 272: 148–162CrossRefGoogle Scholar
  39. 39.
    Yang G, Cook N G W, Myer L R. Analysis of preferential flow paths using graph theory. Int J Rock Mech Min Sci Geomech Abstr, 1993, 30: 1423–1429CrossRefGoogle Scholar
  40. 40.
    Gwo J P. In search of preferential flow paths in structured porous media using a simple genetic algorithm. Water Resour Res, 2001, 37: 1589–1601CrossRefGoogle Scholar
  41. 41.
    Mason G, Morrow N R. Capillary behavior of a perfectly wetting liquid in irregular triangular tubes. J Colloid Interface Sci, 1991, 141: 262–274CrossRefGoogle Scholar
  42. 42.
    Wong P Z, Koplik J, Tomanic J P. Conductivity and permeability of rocks. Phys Rev B, 1984, 30: 6606–6614CrossRefGoogle Scholar
  43. 43.
    Dong H, Blunt M J. Pore-network extraction from micro-computerized-tomography images. Phys Rev E, 2009, 80: 1957–1974Google Scholar
  44. 44.
    Silin D B, Jin G, Patzek T W. Robust determination of the pore space morphology in sedimentary rocks. In: SPE Annual Technical Conference and Exhibition. Denver, Colorado, 2003Google Scholar
  45. 45.
    Blum H. A transformation for extracting new descriptors of shape. In: Wathen-Dunn W, Ed. Models for the Perception of Speech & Visual Form. Amsterdam: MIT Press, 1967. 362–380Google Scholar
  46. 46.
    Baldwin C A, Sederman A J, Mantle M D, et al. Determination and characterization of the structure of a pore space from 3D volume images. J Colloid Interface Sci, 1996, 181: 79–92CrossRefGoogle Scholar
  47. 47.
    Silin D, Patzek T. Pore space morphology analysis using maximal inscribed spheres. Physica A, 2006, 371: 336–360CrossRefGoogle Scholar
  48. 48.
    Vaswani K, Nori A V, Chilimbi T M. Preferential path profiling. SIGPLAN Not, 2007, 42: 351–362CrossRefMATHGoogle Scholar
  49. 49.
    Li B, Wang L, Leung H, et al. Profiling all paths: A new profiling technique for both cyclic and acyclic paths. J Syst Software, 2012, 85: 1558–1576CrossRefGoogle Scholar
  50. 50.
    Adler P. Porous Media: Geometry and Transports. Boston: Elsevier, 2013Google Scholar
  51. 51.
    Floyd RW. Algorithm 97: Shortest path. Communications of the ACM, 1969. 345Google Scholar
  52. 52.
    Ju Y Liu P, Yang Y, et al. Software of seepage network model and preferential flow analysis in porous media (in Chinese). Software Copyright Registration, CUMTB, Beijing, 081126, 2012Google Scholar
  53. 53.
    Keller A A, Blunt M J, Roberts A P V. Micromodel observation of the role of oil layers in three-phase flow. Transp Porous Media, 1997, 26: 277–297CrossRefGoogle Scholar
  54. 54.
    Sirivithayapakorn S, Keller A. Transport of colloids in saturated porous media: A pore-scale observation of the size exclusion effect and colloid acceleration. Water Resour Res, 2003, 39: SBH111Google Scholar
  55. 55.
    Ju Y, Xing M, Sun H. Computer program for extracting and analyzing fractures in rocks and concretes (in Chinese). Software Copyright Registration, CUMTB, Beijing, 0530646, 2013Google Scholar
  56. 56.
    Ju Y, Zheng J, Epstein M, et al. 3D numerical reconstruction of wellconnected porous structure of rock using fractal algorithms. Comput Methods Appl Mech Eng, 2014, 279: 212–226CrossRefGoogle Scholar
  57. 57.
    Handy L L. Determination of effective capillary pressures for porous media from imbibition data. Pet Trans, 1960, AIME 219: 75–80Google Scholar
  58. 58.
    Patzek T W. Verification of a complete pore network simulator of drainage and imbibition. SPE J, 2001, 6: 144–156CrossRefGoogle Scholar
  59. 59.
    Wang S, Feng Q, Dong Y, et al. A dynamic pore-scale network model for two-phase imbibition. J Nat Gas Sci Eng, 2015, 26: 118–129CrossRefGoogle Scholar
  60. 60.
    Nguyen V H, Sheppard A P, Knackstedt M A, et al. The effect of displacement rate on imbibition relative permeability and residual saturation. J Pet Sci Eng, 2006, 52: 54–70CrossRefGoogle Scholar
  61. 61.
    Lenormand R, Zarcone C, Sarr A. Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J Fluid Mech, 1983, 135: 337–353CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yang Ju
    • 1
    • 2
    • 3
  • Peng Liu
    • 1
    • 4
  • DongShuang Zhang
    • 5
  • JiaBin Dong
    • 2
  • P. G. Ranjith
    • 6
  • Chun Chang
    • 1
    • 3
  1. 1.State Key Laboratory of Coal Resources and Safe MiningChina University of Mining and TechnologyBeijingChina
  2. 2.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina
  3. 3.School of Mechanics and Civil EngineeringChina University of Mining & TechnologyBeijingChina
  4. 4.School of Resources and Safety EngineeringChina University of Mining & TechnologyBeijingChina
  5. 5.Institute of Mechanics, Chinese Academy of ScienceBeijingChina
  6. 6.Department of Civil EngineeringMonash UniversityMelbourne, VictoriaAustralia

Personalised recommendations