Transport in Porous Media

, Volume 112, Issue 1, pp 207–227 | Cite as

Impact of Surface Roughness on Capillary Trapping Using 2D-Micromodel Visualization Experiments

  • Helmut GeistlingerEmail author
  • Iman Ataei-Dadavi
  • Hans-Jörg Vogel


According to experimental observations, capillary trapping is strongly dependent on the roughness of the pore–solid interface. We performed imbibition experiments in the range of capillary numbers (Ca) from \(10^{-6}\) to \(5\times 10^{-5}\) using 2D-micromodels, which exhibit a rough surface. The microstructure comprises a double-porosity structure with pronounced macropores. The dynamics of precursor thin-film flow and its importance for capillary trapping are studied. The experimental data for thin-film flow advancement show a square-root time dependence. Based on the experimental data, we conducted inverse modeling to investigate the influence of surface roughness on the dynamic contact angle of precursor thin-film flow. Our experimental results show that trapped gas saturation decreases logarithmically with an increasing capillary number. Cluster analysis shows that the morphology and number of trapped clusters change with capillary number. We demonstrate that capillary trapping shows significant differences for vertical flow and horizontal flow. We found that our experimental results agree with theoretical results of percolation theory for \(Ca =10^{-6}\): (i) a universal power-like cluster size distribution, (ii) the linear surface–volume relationship of trapped clusters, and (iii) the existence of the cutoff correlation length for the maximal cluster height. The good agreement is a strong argument that the experimental cluster size distribution is caused by a percolation-like trapping process (ordinary percolation). For the first time, it is demonstrated experimentally that the transition zone model proposed by Wilkinson (Phys Rev A 30:520–531, 1984) can be applied to 2D-micromodels, if bicontinuity is generalized such that it holds for the thin-film water phase and the bulk gas phase.


2D-micromodel with rough surface Precursor thin-film flow Snap-off trapping Universal power law Ordinary bond percolation 



The authors gratefully acknowledge funding of the project Dynamically Capillary Fringe (DYCAP) by the German Research Foundation DFG. We thank Dr. Ralf Scholz and Dr. Freitag from Invenios Europe GmbH for developing, creatively improving and constructing the micromodels, as well as Dr. Christian Elsner from the Leibnitz Institute for Surface Modification IOM Leipzig for providing the SEM images.

Supplementary material

Supplementary material 1 (mp4 13836 KB)

Supplementary material 2 (mp4 14981 KB)


  1. Adler, P.M.: Multiphase flow in porous media. Ann. Rev. Fluid Mech. 20, 35–59 (1988)CrossRefGoogle Scholar
  2. Bico, J., Tordeux, C., Quéré, D.: Rough wetting. Europhys. Lett. 55, 214 (2001)CrossRefGoogle Scholar
  3. Blunt, M.J., King, M.J., Scher, H.: Simulation and theory of two-phase flow in porous media. Phys. Rev. A 46, 7680 (1992)CrossRefGoogle Scholar
  4. Blunt, M.J., Scher, H.: Pore-level modeling of wetting. Phys. Rev. E 52, 6387–6403 (1995). doi: 10.1103/PhysRevE.52.6387 CrossRefGoogle Scholar
  5. Brooks, M.C., Wise, W.R., Annable, M.D.: Fundamental changes in in situ air sparging flow patterns. Ground Water Monit. Rem. 19, 105–113 (1999)CrossRefGoogle Scholar
  6. Brusseau, M.L., Narter, M., Schnaar, G., Marble, J.: Measurement and estimation of organic-liquid/water interfacial areas for several natural porous media. Environ. Sci. Technol. 43, 3619–3625 (2009)CrossRefGoogle Scholar
  7. Buchgraber, M., Kovscek, A.R., Castanier, L.M.: A study of microscale gas trapping using etched silicon micromodels. Transp. Porous Med. 95, 647–668 (2012). doi: 10.1007/s11242-012-0067-0 CrossRefGoogle Scholar
  8. Burlatsky, S.F., Oshanin, G., Cazabat, A.M., Moreau, M.: Microscopic model of upward creep of an ultrathin wetting film. Phys. Rev. Lett. 76, 86–89 (1996)CrossRefGoogle Scholar
  9. Cazabat, A.M., Gerdes, S., Valignat, M.P., Villette, S.: Dynamics of wetting: from theory to experiment. Interface Sci. 5, 129–139 (1997)CrossRefGoogle Scholar
  10. Cazabat, A.M., Cohen Stuart, M.A.: Dynamics of wetting: effects of surface roughness. J. Phys. Chem. 90, 5845 (1986)CrossRefGoogle Scholar
  11. Chatzis, I., Morrow, N.R., Lim, H.T.: Magnitude and detailed structure of residual oil saturation. Paper SPE/DOE-10681, Presented at the 3rd Symposium on Enhanced Oil Recovery, Tulsa, April 4–7 (1982)Google Scholar
  12. Constantinides, G.N., Payatakes, A.C.: Effects of precursor wetting films in immiscible displacement through porous media. Transp. Porous Media 38, 291–317 (2000)CrossRefGoogle Scholar
  13. Constanza-Robinson, M.S., Harrold, K.H., Lieb-Lappen, R.M.: X-ray microtomography determination of air-water interfacial area-water saturation relationships in sandy porous media. Environ. Sci. Technol. 42, 2949–2956 (2008)CrossRefGoogle Scholar
  14. de Gennes, P.G.: Wetting: statics and dynamics. Rev. Mod. Physics 57, 827 (1985)CrossRefGoogle Scholar
  15. Fisher, M.E.: The theory of condensation and the critical point. Physics 3, 255–283 (1967)Google Scholar
  16. Geistlinger, H., Ataei-Dadavi, I.: Influence of the heterogeneous wettability on capillary trapping in glass-beads monolayers: comparison between experiments and the invasion percolation theory. J. Colloid Interface Sci. 459, 230–240 (2015)Google Scholar
  17. Geistlinger, H., Lazik, D., Krauss, G., Vogel, H.-J.: Pore-scale and continuum modeling of gas flow pattern obtained by high-resolution optical bench-scale experiments. Water Resour. Res. 45, W04423 (2009). doi: 10.1029/2007WR006548 CrossRefGoogle Scholar
  18. Geistlinger, H., Mohammadian, S., Schlueter, S., Vogel, H.-J.: Quantification of capillary trapping of gas clusters using X-ray microtomography. Water Resour. Res. 50, 4514–4529 (2014). doi: 10.1002/2013WR014657 CrossRefGoogle Scholar
  19. Geistlinger, H., Mohammadian, S.: Capillary trapping mechanism in strongly water wet systems: comparison between experiment and percolation theory. Adv. Water Resour. 79, 35–50 (2015)CrossRefGoogle Scholar
  20. Georgiadis, A., Berg, S., Makurat, A., Maitland, G., Ott, H.: Pore-scale micro-computed-tomography imaging: nonwetting-phase cluster-size distribution during drainage and imbibition. Phys. Rev. E 88, 033002 (2013)CrossRefGoogle Scholar
  21. Hashemi, M., Dabir, B., Sahimi, M.: Dynamics of two-phase flow in porous media: simultaneous invasion of two fluids. AIChE J. 45, 1365–1382 (1999a)CrossRefGoogle Scholar
  22. Hashemi, M., Sahimi, M., Dabir, B.: Monte Carlo simulation of two-phase flow in porous media: invasion with two invaders and two defenders. Phys. A 267, 1–33 (1999b)CrossRefGoogle Scholar
  23. Hay, K.M., Dragilab, M.I., Liburdyc, J.: Theoretical model for the wetting of a rough surface. J. Colloid Interface Sci. 325, 472–477 (2008)CrossRefGoogle Scholar
  24. Herman, B., Lemasters, J.J.: Optical Microscopy: Emerging Methods and Applications. Academic Press, New York, NY (1993)Google Scholar
  25. Herring, A.L., Andersson, L., Schlüter, S., Sheppard, A.P., Wildenschild, D.: Efficiently engineering pore-scale processes: the role of force dominance and topology during nonwetting phase trapping in porous media. Adv. Water Resour. 79, 91–102 (2015). doi: 10.1016/j.advwatres.2015.02.005 CrossRefGoogle Scholar
  26. Hunt, A.G., Sahimi, M.: Flow and transport in porous media: percolation scaling, critical-path analysis, and effective-medium approximation. Rev. Geophys. in print (2015)Google Scholar
  27. Iglauer, S., Favretto, S., Spinelli, G., Schena, G., Blunt, M.J.: X-ray tomography measurements of power-law cluster size distributions for the nonwetting phase in sandstones. Phys. Rev. E 82, 056315 (2010)CrossRefGoogle Scholar
  28. Iglauer, S., Paluszny, A., Pentland, C.H., Blunt, M.J.: Residual CO2 imaged with X-ray microtomography. Geophys. Res. Lett. 38(L21403), 2011G (2011). doi: 10.1029/L049680 Google Scholar
  29. Iglauer, S., Paluszny, A., Blunt, M.J.: Simultaneous oil recovery and residual gas storage: a pore-level analysis using in situ X-ray micro-tomography. Fuel 103, 905–914 (2013)CrossRefGoogle Scholar
  30. ImageJ, Rasband, W.S.: ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA., pp. 1997–2014
  31. ISO-standard 4287 (1997) Geometrical Product Specifications (GPS)—Surface Texture: Profile Method-Terms, Definitions and Surface Texture ParametersGoogle Scholar
  32. Jeong, S.W., Corapcioglu, M.Y.: Force analysis and visualization of NAPL removal during surfactant-related floods in a porous medium. J. Hazard. Mater. 126, 8–13 (2005)CrossRefGoogle Scholar
  33. Johnson, P.C., Johnson, R.L., Brucea, C.L., Leeson, A.: Advances in in situ air sparging/biosparging. Bioremediation J. 5, 251–266 (2001)CrossRefGoogle Scholar
  34. Juanes, R., Spiteri, E.J., Orr Jr., F.M., Blunt, M.J.: Impact of relative permeability hysteresis on geological CO2-storage. Water Resour. Res. 42, W12418 (2006). doi: 10.1029/2005WR004806 CrossRefGoogle Scholar
  35. Kaoa, C.M., Chena, C.Y., Chenb, S.C., Chiena, H.Y., Chen, Y.L.: Application of in situ biosparging to remediate a petroleum-hydrocarbon spill site: field and microbial evaluation. Chemosphere 70, 1492–1499 (2008)CrossRefGoogle Scholar
  36. Karadimitriou, N.K., Hassanizadeh, S.M., Joekar-Niasar, V., Kleingeld, P.J.: Micromodel study of two-phase flow under transient conditions: quantifying effects of specific interfacial area. Water Resour. Res 50, 8125–8140 (2014)CrossRefGoogle Scholar
  37. Karpyn, Z., Piri, M., Singh, G.: Experimental investigation of trapped oil clusters in a water-wet bead pack using X-ray microtomography. Water Resour. Res. 46, W04510 (2010)CrossRefGoogle Scholar
  38. Kibbey, T.C.G.: The configuration of water on rough natural surfaces: implications for understanding air-water interfacial area, film thickness, and imaging resolution. Water Resour. Res. 49, 4765–4774 (2013)CrossRefGoogle Scholar
  39. Krummel, A.T., Datta, S.S., Münster, S., Weitz, D.A.: Visualizing multiphase flow and trapped fluid configurations in a model three-dimensional porous medium. AIChE J. 59, 1022–1029 (2013)CrossRefGoogle Scholar
  40. Landry, C.J., Karpyn, Z.T., Piri, M.: Pore-scale analysis of trapped immiscible fluid structures and fluid interfacial areas in oil-wet and water-wet bead packs. Geofluids 11, 209–227 (2011)CrossRefGoogle Scholar
  41. Lenormand, R., Zarcone, C.: Role of roughness and edges during imbibition in square capillaries, SPE-paper No. 13264. In: Proceedings of the 59th Ann. Tech. Conf. of the SPE, Houston, TX (SPE, Richardson, TX, 1984) (1984)Google Scholar
  42. Levinson, P., Cazabat, A.M., Cohen Stuart, M.A., Heslot, F., Nicolet, S.: The spreading of macroscopic droplets. Revue Phys. Appl. 23, 1009–1016 (1988)CrossRefGoogle Scholar
  43. Mohammadian, S., Geistlinger, H., Vogel, H.-J.: Quantification of gas phase trapping within the capillary fringe using micro-CT, Special section: dynamic processes in capillary fringes. Vadose Zone J. doi: 10.2136/vzj2014.06.0063
  44. Mohammadian, S.: A micro-CT-study of capillary trapping and pore-scale quantification of effective mass transfer parameters. PhD-thesis, Faculty of Geosciences. Technical University Freiberg (2015)Google Scholar
  45. Pan, C., Dalla, E., Franzosi, D., Miller, C.T.: Pore-scale simulation of entrapped non-aqueous phase liquid dissolution. Adv. Water Resour. 30, 623–640 (2007)CrossRefGoogle Scholar
  46. Papadopoulos, P., Mammen, L., Deng, X., Vollmer, D., Butt, H.-J.: How superhydrophobicity breaks down. PNAS 110, 3254–3258 (2013)CrossRefGoogle Scholar
  47. Prodanovic, M., Lindquist, W.B., Seright, R.S.: 3D-image based characterization of fluid displacement in a Berea core. Adv. Water Resour. 46, 214 (2007)CrossRefGoogle Scholar
  48. Ronen, D., Magaritz, M., Paldor, N., Bachmat, Y.: The behavior of groundwater in the vicinity of the water table evidence by specific discharge profiles. Wat. Resour. Res. 22, 1217–1224 (1986)CrossRefGoogle Scholar
  49. Stauffer, D., Aharony, A.: Introduction to Percolation Theory, Revised, 2nd edn. Taylor and Francis, Philadelphia (1994)Google Scholar
  50. Suekane, T., Zhou, N., Hosokawa, T., Matsumoto, T.: Direct observation of trapped gas bubbles by capillarity in sandy porous media. Transp. Porous Med. 82, 111–122 (2010). doi: 10.1007/s11242-009-9439-5 CrossRefGoogle Scholar
  51. Vizika, O., Avraam, D.G., Payatakes, A.C.: On the role of the viscosity ratio during low-capillary number forced imbibition in porous media. J. Colloid Interface Sci. 165, 386–401 (1994)CrossRefGoogle Scholar
  52. Voburger, T.V., Raja, J.: Surface Finish Metrology Tutorial. US Department of Commerce, National Institute of Standards and Technology, NISTIR 89-4088 (1999)Google Scholar
  53. Washburn, E.W.: Phys. Rev. 17, 273 (1921)CrossRefGoogle Scholar
  54. Wenzel, R.N.: Ind. Eng. Chem. 28, 988 (1936)CrossRefGoogle Scholar
  55. Wenzel, R.N.: J. Phys. Colloid Chem. 53, 1466 (1949)CrossRefGoogle Scholar
  56. Werth, C.J., Zhang, C., Brusseau, M.L., Oostrom, M., Baumann, T.: A review of non-invasive imaging methods and applications in contaminant hydrogeology research. J. Cont. Hydrol. 113, 1–24 (2010)CrossRefGoogle Scholar
  57. Wiesendanger, R.: Scanning Probe Microscopy: Methods and Applications. Cambridge University Press, New York, NY (1994)CrossRefGoogle Scholar
  58. Wildenschild, D., Armstrong, R.T., Herring, A.L., Young, I.M., Careyc, J.W.: Exploring capillary trapping efficiency as a function of interfacial tension, viscosity, and flow rate. Energy Procedia 4, 4945–4952 (2011)CrossRefGoogle Scholar
  59. Wildenschild, D., Shepard, A.P.: X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv. Water Resour. 51, 217–246 (2013)CrossRefGoogle Scholar
  60. Wilkinson, D.: Percolation model of immiscible displacement in the presence of buoyancy forces. Phys. Rev. A 30, 520–531 (1984)CrossRefGoogle Scholar
  61. Zhou, D., Sten, E.J.: Displacement of trapped oil from water-wet reservoir rock. Transp. Porous Med. 11, 1 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Helmut Geistlinger
    • 1
    Email author
  • Iman Ataei-Dadavi
    • 1
  • Hans-Jörg Vogel
    • 1
  1. 1.UFZ-Environmental Research CentreHalle/SaaleGermany

Personalised recommendations