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Effect of Grain-Size Distribution on Temporal Evolution of Interfacial Area during Two-phase Flow in Porous Media

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Abstract

Interfacial area is an important factor during two-phase flow in porous media because mass-transfer mechanisms take place at the interfaces of immiscible phases. The objective of this work is to quantify how grain-size distribution affects the temporal development of interfacial area during two-phase flow through porous media. A two-phase lattice Boltzmann model (color gradient method) was used to simulate drainage (displacement of a wetting fluid by a non-wetting fluid) and imbibition (displacement of the non-wetting fluid by the wetting fluid) in an ensemble of two-dimensional porous media samples. Five groups of porous media, each comprising 20 realizations, were characterized by their median grain size (d50) and coefficient of uniformity (Cu). For all 100 realizations, simulations of drainage and imbibition were conducted until steady-state saturation was achieved, and interfacial area was monitored throughout the simulations. During both drainage and imbibition, the interfacial area initially increases with time until reaching a peak area, then decreases, and then plateaus at a steady-state value. Interfacial area is higher during imbibition than during drainage. The temporal evolution of interfacial area, as quantified by peak area and time to reach peak area, was similar in the three groups characterized by small grain size (d50 ≈ 7.7 lattice units) and relatively uniform grain-size distribution (Cu ≈ 1.21, 1.49, 1.85), for both drainage and imbibition. This suggests that, for the fluid conditions considered here, nonuniformity of grain size is not important below a certain threshold value of Cu. However, two groups with larger grain size (d50 ≈ 8.9 lattice units) and relatively nonuniform grain-size distribution (Cu ≈ 1.85, 2.29) exhibited differences from each other, suggesting that nonuniformity of grain size affects interfacial area when Cu is above a certain value. Furthermore, median grain size was observed to have important effects on temporal evolution of interfacial area.

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Availability of Data and Material

Measured values of interfacial area and fluid saturations are available from the corresponding author upon request.

Code Availability

MATLAB codes for the lattice Boltzmann model (color gradient model) are available from the corresponding author upon request.

References

  • Abriola, L.M., Pinder, G.F.: A multiphase approach to the modeling of porous media contamination by organic compounds: 1, Equation Development. Water Resour. Res. 21(1), 11–18 (1985)

    Article  Google Scholar 

  • Akai, T., Bijeljic, B., Blunt, M.J.: Wetting boundary condition for the color-gradient lattice Boltzmann method: validation with analytical and experimental data. Adv. Water Resour. 116, 56–66 (2018)

    Article  Google Scholar 

  • Al-Raoush, R.I.: Experimental investigation of the influence of grain geometry on residual NAPL using synchrotron microtomography. J. Contam. Hydrol. 159, 1–10 (2014)

    Article  Google Scholar 

  • Blunt, M.J.: Multiphase Flow in Permeable Media: A Pore-Scale Perspective. Cambridge University Press, Cambridge (2017)

    Google Scholar 

  • Brusseau, M.L., Peng, S., Schnaar, G., Costanza-Robinson, M.S.: Relationships among air-water interfacial area, capillary pressure and water saturation for a sandy porous medium. Water Resour. Res. 42, W03501 (2006)

    Google Scholar 

  • Brusseau, M.L., Peng, S., Schnaar, G., Murao, A.: Measuring air-water interfacial areas with X-ray microtomography and interfacial partitioning tracer tests. Environ. Sci. Technol. 41, 1956–1961 (2007)

    Article  Google Scholar 

  • Brusseau, M.L., Janousek, H., Murao, A., Schnaar, G.: Synchrotron X-ray microtomography and interfacial partitioning tracer test measurements of NAPL-water interfacial areas. Water Resour. Res. 44, W01411 (2008)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Brusseau, M.L., Taghap, H.: NAPL-water interfacial area as a function of fluid saturation measured with the interfacial partitioning tracer test method. Chemosphere. 260, 127562 (2020)

    Article  Google Scholar 

  • Chatzis, I., Morrow, N.R., Lim, H.T.: Magnitude and detailed structure of residual oil saturation. SPE J. 23(02), 311–326 (1983)

    Google Scholar 

  • Chen, D., Pyrak-Nolte, L.J., Griffin, J., Giordana, N.J.: Measurement of interfacial area per volume for drainage and imbibition. Water Resour. Res. 43, W12504 (2007)

    Google Scholar 

  • Chen, Y., Li, Y., Valocchi, A.J., Christensen, K.T.: Lattice Boltzmann simulations of liquid CO2 displacing water in a 2D heterogeneous micromodel at reservoir pressure conditions. J. Contam. Hydrol. 212, 14–27 (2018)

    Article  Google Scholar 

  • Cho, J., Annable, M.D.: Characterization of pore scale NAPL morphology in homogenous sands as a function of grain size and NAPL dissolution. Chemosphere 61, 899–908 (2005)

    Article  Google Scholar 

  • Costanza-Robinson, M.S., Harrold, K.H., Lieb-Lappen, R.M.: X-ray microtomography determination air-water interfacial area-water saturation relationships in sandy porous media. Environ. Sci. Technol. 42, 2949–2956 (2008)

    Article  Google Scholar 

  • Culligan, K.A., Wildenschild, D., Christensen, B.S.B., Gray, W.G., Rivers, M.L., Tompson, A.F.B.: Interfacial area measurements for unsaturated flow through a porous medium. Water Resour. Res. 40, W12413 (2004)

    Article  Google Scholar 

  • Culligan, K.A., Wildenschild, D., Christensen, B.S.B., Gray, W.G., Rivers, M.L.: Pore-scale characteristics of multiphase flow in porous media: a comparison of air-water and oil-water experiments. Adv. Water Resour. 29, 227–238 (2006)

    Article  Google Scholar 

  • Dalla, E., Hilpert, M., Miller, C.T.: Computation of the interfacial area for two-fluid porous medium systems. J. Contam. Hydrol. 56, 25–48 (2002)

    Article  Google Scholar 

  • Fakhari, A., Li, Y., Bolster, D., Christensen, K.T.: A phase-field lattice Boltzmann model for simulating multiphase flows in porous media: application and comparison to experiments of CO2 sequestration at pore scale. Adv. Water Resour. 114, 119–134 (2018)

    Article  Google Scholar 

  • Ferrari, A., Jimenez-Martinez, J., Borgne, T.L., Méheust, Y., Lunati, I.: Challenges in modeling unstable two-phase flow experiments in porous micromodels. Water Resour. Res. 51, 1381–1400 (2015)

    Article  Google Scholar 

  • Godinez-Brizuela, O.E., Karadimitriou, N.K., Joekar-Niasar, V., Shore, C.A., Oostrom, M.: Role of corner interfacial area in uniqueness of capillary pressure-saturation-interfacial area relation under transient conditions. Adv. Water Resour. 107, 10–21 (2017)

    Article  Google Scholar 

  • Gray, W.G., Miller, C.T.: Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 1. Motivation and overview. Adv. Water Resour. 28, 161–180 (2005)

    Article  Google Scholar 

  • Gunstensen, A.L., Rothman, D.H., Zaelski, S., Zanetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. E 43(8), 4320–4327 (1991)

    Article  Google Scholar 

  • Hassanizadeh, S.M., Gray, W.G.: Thermodynamics basis of capillary pressure in porous media. Water Resour. Res. 29(10), 3389–3405 (1993)

    Article  Google Scholar 

  • Huppert, H.E., Neufeld, J.A.: The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46, 255–272 (2014)

    Article  Google Scholar 

  • Ju, Y., Gong, W., Chang, W., Sun, M.: Effects of pore characteristics on water-oil two-phase displacement in non-homogenous pore structures: a pore-scale lattice Boltzmann model considering various fluid density ratios. Int. J. Eng. Sci. 154, 103343 (2020)

    Article  Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Physical Review E. 71, 056702 (2005)

    Article  Google Scholar 

  • Li, Z., Galindo-Torres, S., Yan, G., Scheuermann, A., Li, L.: A lattice Boltzmann investigation of steady-state fluid distribution, capillary pressure and relative permeability of a porous medium: effects of fluid and geometrical properties. Adv. Water Resour. 116, 153–166 (2018)

    Article  Google Scholar 

  • Li, Z., Galindo-Torres, S., Yan, G., Scheuermann, A., Li, L.: Pore-scale simulations of simultaneous steady-state two-phase flow dynamics using a lattice Boltzmann model: interfacial area, capillary pressure and relative permeability. Transp. Porous Med. 129, 295–320 (2019)

    Article  Google Scholar 

  • Liu, T., Wang, M.: Critical REV size of multiphase flow in porous media for upscaling by pore-scale modeling. Transp Porous Med (2021). https://doi.org/10.1007/s11242-021-01621-2. (in press)

    Article  Google Scholar 

  • Liu, H., Zhang, Y., Valocchi, A.J.: Lattice Boltzmann simulation of immiscible fluid displacement in porous media: Homogenous versus heterogeneous pore network. Phys. Fluids. 27, 052103 (2015)

    Article  Google Scholar 

  • Liu, H., Kang, Q., Lenonardi, C.R., Schmiescheck, S.M.P., Narvaez Salazar, A.E., Jones, B.D., Williams, J.R., Valocchi, A.J., Harting, J.D.R.: Multiphase lattice Boltzmann simulations for porous media applications: a review. Comput. Geosci. 20, 777–805 (2016)

    Article  Google Scholar 

  • Lou, Q., Guo, Z., Shi, B.: Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation. Phys. Rev. E 87, 063301 (2013)

    Article  Google Scholar 

  • Marafini, E., La Rocca, M., Fiori, A., Battiato, I., Prestininzi, P.: Suitability of 2D modelling to evaluate flow properties in 3D porous media. Transp. Porous Med. 134, 315–329 (2020)

    Article  Google Scholar 

  • Mayer, A.S., Miller, C.T.: The influence of porous medium characteristics and measurement scale on pore-scale distributions of residual nonaqueous phase liquids. J. Contam. Hydrol. 11, 189–213 (1992)

    Article  Google Scholar 

  • McClure, J.E., Berrill, M.A., Gray, W.G., Miller, C.T.: Tracking interface and common curve dynamics for two-fluid flow in porous media. J. Fluid Mech. 796, 211–232 (2016)

    Article  Google Scholar 

  • McDonald, K., Carroll, K.C., Brusseau, M.L.: Comparison of fluid-fluid interfacial areas measured with X-ray microtomography and interfacial partitioning tracer tests for the same samples. Water Resour. Res. 52, 5393–5399 (2016)

    Article  Google Scholar 

  • Meakin, P., Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. 47, RG3002 (2009)

    Article  Google Scholar 

  • Mollon, G., Zhao, J.: Fourier-Voronoi-based generation of realistic samples for realistic modeling of granular materials. Granul. Matter. 14, 621–638 (2012)

    Article  Google Scholar 

  • Mora, P., Morra, G., Yuen, D.A., Juanes, R.: Optimal wetting angles in lattice Boltzmann simulations of viscous fingering. Transp. Porous Med. 136, 831–842 (2021a)

    Article  Google Scholar 

  • Mora, P., Morra, G., Yuen, D.A., Juanes, R.: Influence of wetting on viscous fingering via 2D lattice Boltzmann simulations. Transp. Porous Med. 138, 511–538 (2021b)

    Article  Google Scholar 

  • National Library of Medicine: PubChem. https://pubchem.ncbi.nlm.nih.gov/. Accessed 28 January 2021

  • Niessner, J., Hassanizadeh, S.M.: Modeling kinetic interphase mass transfer for two-phase flow in porous media including fluid-fluid interfacial area. Transp. Porous Med. 80, 329–344 (2009)

    Article  Google Scholar 

  • Peng, S., Brusseau, M.L.: Impact of soil texture on air-water interfacial areas in unsaturated sandy porous media. Water Resour. Res. 41, W03021 (2005)

    Article  Google Scholar 

  • Porter, M.L., Schaap, M.G., Wildenschild, D.: Lattice-Boltzmann simulations of the capillary pressure-saturation-interfacial area relationship for porous media. Adv. Water Resour. 32, 1632–1640 (2009)

    Article  Google Scholar 

  • Qin, F., Zhao, J., Kang, Q., Derome, D., Carmeliet, J.: Lattice Boltzmann modeling of drying of porous media considering contact angle hysteresis. Transp. Porous Med. 140, 395–420 (2021)

    Article  Google Scholar 

  • Ramstad, T., Berg, C.F., Thompson, K.: Pore-scale simulation of single- and two-phase flow in porous media: approaches and applications. Transp. Porous Med. 130, 77–104 (2019)

    Article  Google Scholar 

  • Reeves, P.C., Celia, M.A.: A functional relationship between capillary pressure, saturation and interfacial area as revealed by a pore-scale network. Water Resour. Res. 32(8), 2345–2358 (1996)

    Article  Google Scholar 

  • Reis, T., Phillips, T.N.: Lattice Boltzmann model for simulating immiscible two-phase flows. J. Phys. A Math. Theor. 40(15), 4033–4053 (2007)

    Article  Google Scholar 

  • Saripalli, K.P., Rao, P.S.C., Annable, M.D.: Determination of specific NAPL–water interfacial areas of residual NAPLs in porous media using the interfacial tracers technique. J. Contam. Hydrol. 30, 375–391 (1998)

    Article  Google Scholar 

  • Schnaar, G., Brusseau, M.L.: Pore-scale characterization of organic immiscible-liquid morphology in natural porous media using synchrotron X-ray microtomography. Environ. Sci. Technol. 39, 8403–8410 (2005)

    Article  Google Scholar 

  • Sukop, M.C., Thorne, D.T., Jr.: Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Verlag-Berlin (2006)

    Book  Google Scholar 

  • 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. 51, 217–246 (2013)

    Article  Google Scholar 

  • Xu, Z., Liu, H., Valocchi, A.J.: Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resour. Res. 53, 3770–3790 (2017)

    Article  Google Scholar 

  • Zahid, F.: Impact of grain morphology on the temporal evolution of interfacial area during multi-phase flow in porous media. Doctoral dissertation, University of South Florida, Tampa, Fl, USA (2021)

  • Zhao, B., MacMinn, C.W., Primkulov, B.K., Chen, Y., Valocchi, A.J., Zhao, J., Kang, Q., Bruning, K., McClure, J.E., Miller, C.T., Fakhari, A., Bolster, D., Hiller, T., Brinkmann, M., Cueto-Felgueroso, L., Cogswell, D.A., Verma, R., Prodanović, M., Maes, J., Geiger, S., Vassvik, M., Hansen, A., Segre, E., Holtzmann, R., Yang, Z., Yuan, C., Chareyre, B., Juanes, R.: Comprehensive comparison of pore-scale models for multiphase flow in porous media. PNAS 116(28), 13799–13806 (2019)

    Article  Google Scholar 

  • Ziegler, D.P.: Boundary conditions for lattice Boltzmann simulations. J. Stat. Phys. 71(5–6), 1171–1177 (1993)

    Article  Google Scholar 

  • Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9, 1591–1598 (1997)

    Article  Google Scholar 

Download references

Acknowledgements

This paper is based upon the funding and support of the Foreign Fulbright PhD Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Fulbright Association. The authors are grateful for the valuable help and comments received from Dr. Sebastian Leclaire and Dr. Yu Chen during two-phase model development and coding. The computations for the work were performed on the Research Computing Resources of the University of South Florida (USF). The authors thank Dr. Amy Stuart of USF for her assistance with deploying the codes on USF’s Research Computing Resources.

Funding

This paper is based upon the funding and support of the Foreign Fulbright PhD Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Fulbright Association.

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  1. Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL, USA

    Fizza Zahid & Jeffrey A. Cunningham

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  1. Fizza Zahid
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  2. Jeffrey A. Cunningham
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Fizza Zahid had primary responsibility for generating the porous media realizations, wring the lattice Boltzmann codes, testing and validating the codes, running the drainage and imbibition simulations, collecting data, and analyzing data. Jeffrey Cunningham directed the project and supervised Fizza Zahid and was involved in all of the above-named steps. The two authors contributed equally to the writing of the manuscript.

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Correspondence to Jeffrey A. Cunningham.

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Zahid, F., Cunningham, J.A. Effect of Grain-Size Distribution on Temporal Evolution of Interfacial Area during Two-phase Flow in Porous Media. Transp Porous Med 144, 283–300 (2022). https://doi.org/10.1007/s11242-022-01767-7

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