Pore-scale and continuum simulations of solute transport micromodel benchmark experiments


Four sets of nonreactive solute transport experiments were conducted with micromodels. Each set consisted of three experiments with one variable, i.e., flow velocity, grain diameter, pore-aspect ratio, and flow-focusing heterogeneity. The data sets were offered to pore-scale modeling groups to test their numerical simulators. Each set consisted of two learning experiments, for which all results were made available, and one challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the transverse dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice Boltzmann (LB) approach, and one used a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used the learning experiments to appropriately discretize the spatial grid representations. For the continuum modeling, the required dispersivity input values were estimated based on published nonlinear relations between transverse dispersion coefficients and Peclet number. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values, resulting in reduced dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models, which account for the micromodel geometry and underlying flow and transport physics, needed up to several days on supercomputers to resolve the more complex problems.

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  1. 1.

    Acharya, R.C., Valocchi, A.J., Werth, C.J., Willingham, T.W.: Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media. Water Resour. Res. 43, W10435 (2007). doi:10.1029/2007WR005969

    Article  Google Scholar 

  2. 2.

    Acharya, R.C., van der Zee, S.E.A.T.M., Leijnse, A.: Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks. Water Resour. Res. 41, W02020 (2005). doi:10.1029/2004WR003500

    Article  Google Scholar 

  3. 3.

    Bandara, U.C., Oostrom, M., Tartakovsky, A.M., Palmer, B.J., Zhang, C., Grate, J.W.: Comparison of pore-scale numerical simulations of unstable immiscible displacements in porous media with micromodel experiments. Adv. in Water Resour. 62, 356–369 (2013)

    Article  Google Scholar 

  4. 4.

    Bear, J.: Dynamics of fluids in porous media. Dover Publications, New York (1972)

    Google Scholar 

  5. 5.

    Bijeljic, B, Blunt, MJ: Pore-scale modeling of transverse dispersion in porous media. Water Resour. Res. 43, W12S11 (2007). doi:10.29/2006WR005700

    Article  Google Scholar 

  6. 6.

    Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Article  Google Scholar 

  7. 7.

    Boyd, V., Yoon, H., Zhang, C., Oostrom, M., Hess, N.J., Fouke, B., Valocchi, A.J., Werth, C.J.: The effect of magnesium on calcium carbonate precipitation during reactive transport in a model subsurface pore network. Geochimica Cosmochimica Acta 135, 321–335 (2014) doi:10.1016/j.gca.2014.03.018

    Article  Google Scholar 

  8. 8.

    Cardenas, M.B.: Three-dimensional vortices in single pores and their effects on transport. Geophys. Res. Lett., 35 (2008)

  9. 9.

    Carroll, K.C., Oostrom, M., Truex, M.J., Rohay, V.J., Brusseau, M.L.: Assessing performance and closure for soil vapor extraction: integrating vapor discharge and impact to groundwater quality. J. Contam. Hydrol. 128, 71–82 (2012)

    Article  Google Scholar 

  10. 10.

    Chiogna, G., Eberhardt, C., Grathwohl, P., Cirpka, O., Rolle, M.: Evidence of compound-dependent hydrodynamic and mechanical transverse dispersion by multitracer laboratory experiments. Environ. Sci. Techn. 44 (2), 688–693 (2012)

    Article  Google Scholar 

  11. 11.

    Chomsurin, C., Werth, C.J.: Analysis of pore-scale nonaqueous phase liquid dissolution in etched silicon pore networks. Water Resour. Res. 39 (9) (2003). doi:10.1029/2002WR001643

  12. 12.

    Cirpka, O., Olsson, A., Qingsong, J., Rahman, M.A., Grathwohl, P.: Determination of transverse dispersion coefficients from reactive plume lengths. Ground Water 44 (44), 212–221 (2006)

    Article  Google Scholar 

  13. 13.

    Crank, J., 2nd: The mathematics of diffusion. Oxford University Press, New York (1975)

    Google Scholar 

  14. 14.

    Corapcioglu, M.Y., Chowdhury, S., Roosevelt, S.E.: Micromodel visualization and quantification of solute transport in porous media. Water Resour. Res 33, 2547–2558 (1997)

    Article  Google Scholar 

  15. 15.

    Corapcioglu, M.Y., Fedirchuk, P.: Glass bead micromodel study of solute transport. J. Contam. Hydrol. 36, 209–230 (1999)

    Article  Google Scholar 

  16. 16.

    DeHoff, K.J., Oostrom, M., Zhang, C., Grate, J.W.: Evaluation of two-phase relative permeability and capillary pressure relations for unstable displacements in a pore network. Vadose Zone J 12 (2012). doi:10.2136/vzj2012.0024

  17. 17.

    De Josselin de Jong, G.: Longitudinal and transverse diffusion in granular deposits. Eos Trans. Am. Geophys. Union 39, 67–74 (1958)

    Article  Google Scholar 

  18. 18.

    Degruyter, W., Burgisser, A., Bachmann, O., Malaspinas, O.: Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices. Geosphere 6, 470–481 (2010). doi:10.1130/GES00555.1

    Article  Google Scholar 

  19. 19.

    Fanizza, M. F., Yoon, H., Zhang, C., Oostrom, M., Wietsma, T.W., Hess, N.J., Bowden, M.E., Strathmann, T.J., Finneran, K.T., Werth, C.J.: Pore-scale evaluation of uranyl phosphate precipitation in a model groundwater system. Water Resour. Res. 49 (2013). doi:10.1002/wrcr.20088

  20. 20.

    Garmeh, G., Johns, R.T., Lake, L.W.: Pore-Scale simulation of dispersion in porous media. SPE J. 14 (4), 559–567 (2009). doi:10.2118/110228-PA. SPE-110228-PA

    Article  Google Scholar 

  21. 21.

    Grate, J.W., Dehoff, K.J., Warner, M.G., Pittman, J.W., Wietsma, T.W., Zhang, C., Oostrom, M.: Correlation of oil-water and air-water contact angles of diverse silanized surfaces and relationship to fluid interfacial tensions. Langmuir 28, 7182–7188 (2012). doi:10.1021/la204322k

    Article  Google Scholar 

  22. 22.

    Grate, J.W., Zhang, C., Wietsma, T.W., Warner, M.G., Anheier, N.C. Jr, Bernacki, B.E., Orr, G., Oostrom. M.: A note on the visualization of wetting film structures and a nonwetting immiscible fluid in a pore network micromodel using a solvatochromic dye. Water Resour. Res. 46, W11602 (2010). doi:10.1029/2010WR009419

    Article  Google Scholar 

  23. 23.

    Gutierrez-Neri, M.: Aspects of transverse dispersion in porous media, PhD thesis. Utrecht University, Netherlands (2009)

    Google Scholar 

  24. 24.

    He, X., Luo, L.S.: Lattice Boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys 88, 927 (1997)

    Article  Google Scholar 

  25. 25.

    Hess, N. J., Oostrom, M., Celia, M. A., Hilpert, M., Kang, Q., Pyrak-Nolte, L. J., Scheibe, T. D., Tartakovsky, A. M., Werth, C. J., Wildenschild, D., Zhang, C., Bialkowski, S. E., Ghezzehei, T. A., Tang, G., Doster, F., Kumar, J., Parashar, R., Gerlach, R., Yoon, H., Redden, G. D., Zhang, T., Huang, H., Nogues, J., Deng, W., Resat, H., Rod, K. A., Baer, D. R., Kelly, R. T., Um, W., Wang, G., Richmond, M. C., Rector, D. R., Stewart, M. L., Jung, H. B., Plata, C.: EMSL pore scale modeling challenge/workshop PNNL-1086. Pacific Northwest National Laboratory, Richland (2011)

    Google Scholar 

  26. 26.

    Hochstetler, D.L., Rolle, M., Chiogna, G., Haberer, C. M., Grathwohl, P., Kitanidis, P.K.: Effects of compound-specific transverse mixing on steady-state reactive plumes: insights from pore-scale simulations and Darcy-scale experiments. Adv. Water Resour. 54, 1–10 (2013)

    Article  Google Scholar 

  27. 27.

    Joekar-Niasar, V., van Dijke, M.I.J., Hassanizadeh, S.M.: Pore-scale modeling of multiphase flow and transport: achievements and perspectives. Trans. Porous Media 94, 461–464 (2012)

    Article  Google Scholar 

  28. 28.

    Joekar-Niasar, V., Hassanizadeh, S.M.: Analysis of fundamentals of two-phase flow in porous media using dynamic pore-network models: a review. Crit. Rev. Environ. Sci. Technol. 42 (18), 1895–1976 (2012a)

    Article  Google Scholar 

  29. 29.

    Joekar-Niasar, V., Hassanizadeh, S.M.: Effect of initial hydraulic conditions on capillary rise in a porous medium: pore-network modeling. Vadose Zone J 11 (3) (2012b)

  30. 30.

    Kang, Q., Lichtner, P.C., Viswanathan, H.S., Abdel-Fattah, A.I.: Pore scale modeling of reactive transport involved in geologic CO 2 sequestration. Transp. Porous Media 82, 197–213 (2010). doi:10.1007/s11242-009-9443-9

    Article  Google Scholar 

  31. 31.

    Kang, Q., Lichtner, P.C., Zhang, D.: Lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media. J. Geophys. Res. 111, B05203 (2006)

    Google Scholar 

  32. 32.

    Karadimitriou, N.K., Hassanizadeh, S.M.: A review of micromodels and their use in two-phase flow studies. Vadose Zone J. 11 (2012). doi:10.2136/vzj2011.0072

  33. 33.

    Kim, D., Peters, C. A., Lindquist, W. B.: Upscaling geochemical reaction rates accompanying acidic CO2-saturated brine flow in sandstone aquifers. Water Resour. Res. 47 (1), W01505 (2011)

    Article  Google Scholar 

  34. 34.

    Klenk, I.D., Grathwohl, P.: Transverse vertical mixing in groundwater and the capillary fringe. J. Contam. Hydrol. 58, 111–128 (2002)

    Article  Google Scholar 

  35. 35.

    Knutson, C.E., Werth, C.J., Valocchi, A.J.: Pore-scale simulation of biomass growth along the transverse mixing zone of a model two-dimensional porous medium. Water Resour. Res. 41, W07007 (2005), available at doi:10.1029/2004WR003459

    Article  Google Scholar 

  36. 36.

    Lagrava, D., Malaspinas, O., Latt, J., Chopard, B.: Advances in multi-domain lattice Boltzmann grid refinement. J. Comput. Phys. 231 (14), 4808–4822 (2012). doi:10.1016/j.jcp.2012.03.015

    Article  Google Scholar 

  37. 37.

    Li, L., Peters, C. A., Celia, M. A.: Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Res. 29 (9), 1351–1370 (2006)

    Article  Google Scholar 

  38. 38.

    Lichtner, P.C., Kang, Q.J.: Upscaling pore-scale reactive transport equations using a multiscale continuum formulation. Water Resour. Res., 43 (2007)

  39. 39.

    Liu, Y., Zhang, C, Hilpert, M., Kuhlenschmidt, M.S., Kuhlenschmidt, T.B., Nguyen, T.H.: Transport of Cryptosporidium parvum oocysts in a silicon micromodel. Environ. Sci. Technol. 46 (3), 1471–1479 (2012). doi:10.1021/es202567t

    Article  Google Scholar 

  40. 40.

    Mehmani, A., Prodanović, M.: The effect of microporosity on transport properties in porous media. Adv. Water Resour. 63, 104–11 (2014)

    Article  Google Scholar 

  41. 41.

    Mehmani, Y., Oostrom, M., Balhoff, M.T.: A streamline splitting pore-network approach for computationally inexpensive and accurate simulation of species transport in porous media. Water Resour. Res., 50 (2014). doi:10.1002/2013WR014984

  42. 42.

    Mehmani, Y., Sun, T., Balhoff, M. T., Eichhubl, P., Bryant, S.: Multiblock pore-scale modeling and upscaling of reactive transport: application to carbon sequestration. Transp. Porous Media 95, 305–326 (2012). doi:10.1007/s11242-012-0044-7

    Article  Google Scholar 

  43. 43.

    Mostaghimi, P, Bijeljic, B., Blunt, M.J.: Simulation of flow and dispersion on pore-space images. Soc. Pet. Eng. J. 17, 1131–1141 (2012)

    Google Scholar 

  44. 44.

    Molins, S., Trebotich, D., Steefel, C.I., Shen, C.P.: An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation, Vol. 48 (2012)

  45. 45.

    Nitsche, J.M., Chang, H.C., Weber, P.A., Nicholson, B.J.: A transient diffusion model yields unitary gap junctional permeabilities from images of cell-to-cell fluorescent dye transfer between Xenopus oocytes. Biophysical J. 86, 2058–2077 (2004)

    Article  Google Scholar 

  46. 46.

    Noble, D. R., Chen, S., Gerogiadiis, J.G., Buckius, R.O.: A consistent hydrodynamic boundary-condition for the lattice Boltzmann method. Phys. Fluids 7, 203–209 (1995)

    Article  Google Scholar 

  47. 47.

    Oostrom, M., Truex, M.J, Carroll, K.C., Chronister, G.B.: Perched-water analysis related to deep vadose zone contaminant transport and impact to groundwater. J. Hydrol. 505, 228–239 (2013). 10.1016/j.jhydrol.2013.10.001

    Article  Google Scholar 

  48. 48.

    Palabos: Parallel lattice Boltzmann solver (2012). http://www.lbmethod.org/palabos/

  49. 49.

    Parmigiani, A., Huber, C., Bachmann, O., Chopard, B.: Pore scale mass and reactant transport in multiphase porous media flows. J. Fluid Mech. 686 (10), 40–76 ((2011)). doi:10.1017/jfm.2011.268

    Article  Google Scholar 

  50. 50.

    Richmond, M.C., Perkins, W.A., Scheibe, T.D., Wood, B.D.: Flow and axial dispersion in a wavy-walled tube: effects of inertial and unsteady flows. Adv. Water Resour. 62, 215–226 (2013)

    Article  Google Scholar 

  51. 51.

    Rolle, M., Hochstetler, D., Chiogna, G., Kitanidis, P., Grathwohl, P.: Experimental investigation and a pore-scale modeling interpretation of compound-specific transverse dispersion in porous media. Transp. Porous Media 93 (3), 347–62 (2012)

    Article  Google Scholar 

  52. 52.

    Saffman, P.G.: A theory of dispersion in porous media. J. Fluid Mech. 6, 321–349 (1959)

    Article  Google Scholar 

  53. 53.

    Taymaz, I., Aslan, E., Benim, A.B.: Numerical investigation of incompressible fluid flow and heat transfer across a bluff body in a channel flow. Therm. Sci. 145 (2012). doi:10.2298/TSCI120220145T

  54. 54.

    Thompson, K. E.: Pore-scale modeling of fluid transport in disordered fibrous materials. AIChE J. 48 (7), 1369–1389 (2002)

    Article  Google Scholar 

  55. 67.

    Wang, Y., Zhang, C.,Wei, N., Oostrom,M.,Wietsma, T.W., Li, X., Bonneville, A.: Experimental study of crossover from capillary to viscous fingering for supercritical CO2 – water displacement in a homogeneous pore network. Environ. Sci. Technol. 47, 212–218 (2013). doi:10.1021/es3014503

  56. 55.

    Werth, C. J., Cirpka, O. A., Grathwohl, P.: Enhanced mixing and reaction through flow focusing in heterogeneous porous media. Water Resour. Res. 42 (12) (2006). doi:10.1029/2006WR005326

  57. 56.

    Werth, C. J., Zhang, C. Y., Brusseau, M. L., Oostrom, M., Baumann, T.: A review of non-invasive imaging methods and applications in contaminant hydrogeology research. J. Contam. Hydrol. 113, 1–24 (2010)

    Article  Google Scholar 

  58. 57.

    Willingham, T.W., Werth, C.J., Valocchi, A.J.: Evaluation of the effects of porous media structure on mixing-controlled reactions using pore-scale modeling and micromodel experiments. Environ. Sci. Technol. 42, 3185–3193 (2008)

    Article  Google Scholar 

  59. 58.

    Willingham, T.W., Zhang, C., Werth, C.J., Valocchi, A.J., Oostrom, M., Wietsma, T.W.: Using dispersivity values to quantify the effects of pore-scale flow focusing on enhanced reaction along a transverse mixing zone. Adv. Water Res. 33 (4), 525–535 (2010). doi:10.1016/j.advwatres.2010.02.004

    Article  Google Scholar 

  60. 59.

    Yang, X., Scheibe, T.D., Richmond, M.C., Perkins, W.A., Vogt, S.J, Codd, S.L., Seymour, J.D., McKinley, M.I.: Direct numerical simulation of pore-scale flow in a bead pack: validation against magnetic resonance imaging observations. Adv. Water Resour. 54, 228–241 (2013). doi:10.1016/j.advwatres.2013.01.009

    Article  Google Scholar 

  61. 60.

    Yoon, H., Dewers, T.: Nanopore structures, statistically representative elementary volumes, and transport properties of chalk. Geophys. Res. Lett. 40 (16), 4294–4298 (2013). doi:10.1002/grl.50803

    Article  Google Scholar 

  62. 61.

    Yoon, H., Valocchi, A.J., Werth, C.J., Dewers, T.: Pore-scale simulation of mixing-induced calcium carbonate precipitation and dissolution in a microfluidic pore network. Water Resour. Res. 48, W02524 (2012). doi:10.1029/2011WR011192

    Google Scholar 

  63. 62.

    Zhang, C., Dehoff, K.J., Hess, N.J., Oostrom, M., Wietsma, T.W., Valocchi, A.J., Fouke, B., Werth, C.J.: Pore-scale study of transverse mixing induced CaCO 3 precipitation and permeability reduction in a model subsurface sedimentary system. Environ. Sci. Technol. 44 (20), 7833–7838 (2010). doi:10.1021/es1019788

    Article  Google Scholar 

  64. 63.

    Zhang, C., Oostrom, M., Grate, J.W., Wietsma, T.W., Warner, M.G.: Liquid CO 2 displacement of water in a dual-permeability pore network micromodel. Environ. Sci. Technol. 45 (17), 7581–7588 (2011a). doi:10.1021/es201858r

    Article  Google Scholar 

  65. 64.

    Zhang, C., Oostrom, M., Wietsma, T.W., Grate, J.W., Warner, M.G.: Influence of viscous and capillary forces on immiscible fluid displacement: pore-scale experimental study in a water-wet micromodel demonstrating viscous and capillary fingering. Energy Fuels 25 (8), 3493–3505 (2011b). doi:10.1021/ef101732k

    Article  Google Scholar 

  66. 65.

    Zhang, D.X., Kang, Q.J.: Pore scale simulation of solute transport in fractured porous media. Geophys. Res. Lett. 31 (2004)

  67. 66.

    Zhang, T., Shi, B., Guo, Z., Chai, Z., Lu, J.: General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method. Phys. Rev. E 85, 016701 (2012)

    Article  Google Scholar 

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Oostrom, M., Mehmani, Y., Romero-Gomez, P. et al. Pore-scale and continuum simulations of solute transport micromodel benchmark experiments. Comput Geosci 20, 857–879 (2016). https://doi.org/10.1007/s10596-014-9424-0

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  • Pore-scale modeling
  • Olute transport
  • Icromodel
  • Ispersion
  • Enchmarking