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The Effect of Morphological and Topological Characteristics on Effective Diffusivity and Permeability of Dual-Structural-Scale Synthetic Porous Medium

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Abstract

Image-based simulations at pore scale provide direct insight into the impact of the microstructure on flow and transport processes in porous media. Diffusion is an important mechanism of mass transfer in gas or liquid phases, confined in porous media. Similar to fluid flow, the diffusive transport in porous media is a strong function of pore size and structure. Although the effect of porosity, pore connectivity and constrictivity of homogeneous porous media on macroscopic properties is clear, this is not well understood for heterogeneous porous media. This study uses a dual-structural-scale medium to analyze the effect of topological and morphological parameters on effective properties such as permeability and the effective diffusivity. A synthetic porous medium was created by two sizes of small and large glass beads, and 3D pore structure image of the sample was captured by X-ray computed tomography technique. The Stokes and diffusion equations were directly solved on the extracted pore geometry of sample, using a finite element method. The results show a strong nonlinear relationship between constrictivity, as a morphological parameter, with permeability and effective diffusivity. Based on the results obtained from pore-scale imaging and modeling, the connectivity of the pore space is increased by decreasing the Euler number and consequently the permeability and effective diffusivity is increased. Good agreement between image-based computed effective diffusivity with that estimated by van Brakel and Heertjes empirical relation confirms the reliability of this relation for heterogeneous porous medium, which includes constrictivity in addition to porosity and tortuosity, as three important morphological properties.

Article Highlights

  • The capability of X-ray CT technique was used to better understand the microstructural properties of porous media.

  • Porosity and constrictivity of a heterogeneous porous medium was correlated to its permeability and effective diffusivity.

  • The reliability of Van Brakel and Heertjes relation for estimating effective diffusivity in porous media was confirmed.

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Availability of Data and Material

Almost all data produced have been reported in the manuscript. More information is available on request.

Code Availability

No software was developed. The executive COMSOL files are available on request.

Abbreviations

\(A_{\text{void}}\) :

Void area

\(A_{\text{Total}}\) :

Total area

C 0 :

High concentration \(\left({\frac{\text{mol}}{{{\text{m}}^{3} }}} \right)\)

C :

Low concentration \(\left({\frac{\text{mol}}{{{\text{m}}^{3} }}} \right)\)

\(D_{\text{Eff}}\) :

Effective diffusion

D :

Molecular diffusion \(\left({\frac{{{\text{m}}^{2} }}{\text{s}}} \right)\)

\(D_{\text{w}}\) :

Water diffusion coefficient \(\left({\frac{{{\text{m}}^{2} }}{\text{s}}} \right)\)

J :

Diffusion flux \(\left[ {{\text{mol}}^{ - 1} \;{\text{s}}\;{\text{m}}^{ - 2} } \right]\)

K :

Permeability [darcy]

L :

Sample length

L e :

Effective path length

P :

Pressure [Pa]

D p :

Pore diameter [mm]

D t :

Throat diameter [mm]

u :

Velocity [m/s]

ΔC :

Concentration difference \(\left({\frac{\text{mol}}{{{\text{m}}^{3} }}} \right)\)

∆P :

Pressure drop

ΔZ :

Distance between the two faces

μ :

Viscosity of the fluid

δ :

Constrictivity

τ :

Tortuosity

ε :

Porosity

ρ :

Water density [kg/m3]

µ :

Water viscosity [kg/(m s)]

References

  • Aboufoul, M., Garcia, A.: Factors affecting hydraulic conductivity of asphalt mixture. Mater. Struct. 50(2), 116 (2017)

    Article  Google Scholar 

  • Akanji, L.T.: Simulation of pore-scale flow using finite element-methods (2010)

  • Akanji, L.T., Matthai, S.K.: Finite element-based characterization of pore-scale geometry and its impact on fluid flow. Transp. Porous Media 81(2), 241–259 (2010)

    Article  Google Scholar 

  • Apourvari, S.N., Arns, C.H.: Image-based relative permeability upscaling from the pore scale. Adv. Water Resour. 95, 161–175 (2016)

    Article  Google Scholar 

  • Arns, C.H., Bauget, F., Limaye, A., Sakellariou, A., Senden, T., Sheppard, A., Sok, R.M., Pinczewski, V., Bakke, S., Berge, L.I.: Pore scale characterization of carbonates using X-ray microtomography. Spec J. 10(04), 475–484 (2005)

    Google Scholar 

  • Bear, J.: Dynamics of Fluids in Porous Media. Courier Corporation, New York (1988)

    Google Scholar 

  • Berg, C.F.: Permeability description by characteristic length, tortuosity, constriction and porosity. J. Transp. Porous Med. 103(3), 381–400 (2014)

    Article  Google Scholar 

  • Bijeljic, B., Muggeridge, A.H., Blunt, M.J.: Pore‐scale modeling of longitudinal dispersion. Water Resour. Res. 40(11) (2004)

  • Bini, F., Pica, A., Marinozzi, A., Marinozzi, F.: A 3D model of the effect of tortuosity and constrictivity on the diffusion in mineralized Collagen Fibril. J. Sci. Rep. 9(1), 2658 (2019)

    Article  Google Scholar 

  • 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 

  • Bourbatache, M.K., Bennai, F., Zhao, C., Millet, O., Aït-Mokhtar, A.: Determination of geometrical parameters of the microstructure of a porous medium. Appl. Cement. Mater. 117, 104786 (2020)

    Google Scholar 

  • Chen, Z., Espedal, M., Ewing, R.E.: Finite element analysis of multiphase flow in groundwater hydrology (1994)

  • Coenen, J., Tchouparova, E., Jing, X.: Measurement parameters and resolution aspects of micro X-ray tomography for advanced core analysis. In: Proceedings of the International Symposium on Society of Core Analysts, pp. 256–261 (2004)

  • Currie, J.A.: Gaseous diffusion in porous media Part 1. A non-steady state method. Br. J. Appl. Phys. 11(8), 314 (1960a)

    Article  Google Scholar 

  • Currie, J.A.: Gaseous diffusion in porous media. Part 2. Dry granular materials. Br. J. Appl. Phys. 11(8), 318 (1960b)

    Article  Google Scholar 

  • Dakhelpour-Ghoveifel, J., Shegeftfard, M., Dejam, M.: Capillary-based method for rock typing in transition zone of carbonate reservoirs. J. Petrol. Explor. Prod. Technol. 9(3), 2009–2018 (2019)

    Article  Google Scholar 

  • Davudov, D., Moghanloo, R.G., Zhang, Y.: Interplay between pore connectivity and permeability in shale sample. Int. J. Coal Geol. 220, 103427 (2020)

    Article  Google Scholar 

  • Dejam, M.: Advective-diffusive-reactive solute transport due to non-Newtonian fluid flows in a fracture surrounded by a tight porous medium. J. Int. J. Heat Mass Transf. 128, 1307–1321 (2019)

    Article  Google Scholar 

  • Dolado, J.S., Van Breugel, K.: Recent advances in modeling for cementitious materials. Cem. Concr. Res. 41(7), 711–726 (2011)

    Article  Google Scholar 

  • Flannery, B.P., Deckman, H.W., Roberge, W.G., Damico, K.L.: Three-dimensional X-ray microtomography. J. Sci. 237(4821), 1439–1444 (1987)

    Google Scholar 

  • Garrouch, A.A., Ali, L., Qasem, F.: Using diffusion and electrical measurements to assess tortuosity of porous media. Ind. Eng. Chem. Res. 40(20), 4363–4369 (2001)

    Article  Google Scholar 

  • Genabeek, O.V., Rothman, D.H.: Macroscopic manifestations of microscopic flows through porous media: phenomenology from simulation. J. Ann. Rev. Earth Planet. Sci. 24(1), 63–87 (1996)

    Article  Google Scholar 

  • Grathwohl, P.: Diffusion in natural porous media: contaminant transport, sorption/desorption and dissolution kinetics, p. 1. Springer, New York (2012)

    Google Scholar 

  • Gueven, I., Frijters, S., Harting, J., Luding, S., Steeb, H.: Hydraulic properties of porous sintered glass bead systems. J. Granul. Matter 19(2), 28 (2017)

    Article  Google Scholar 

  • Hu, W., Jiang, Y., Chen, D., Lin, Y., Han, Q., Cui, Y.: Impact of pore geometry and water saturation on gas effective diffusion coefficient in soil. J. Appl. Sci. 8(11), 2097 (2018)

    Article  Google Scholar 

  • Huang, J., Xiao, F., Dong, H., Yin, X.: Diffusion tortuosity in complex porous media from pore-scale numerical simulations. J. Comput. Fluids (2019)

  • Ibrahim, S.H., Skibinski, J., Oliver, G., Wejrzanowski, T.: Microstructure effect on the permeability of the tape-cast open-porous materials. Mater. Des. 167, 107639 (2019)

    Article  Google Scholar 

  • Koestel, J., Larsbo, M., Jarvis, N.: Scale and REV analyses for porosity and pore connectivity measures in undisturbed soil. J. Geoderma 366, 114206 (2020)

    Article  Google Scholar 

  • Kou, Z., Dejam, M.: Dispersion due to combined pressure-driven and electro-osmotic flows in a channel surrounded by a permeable porous medium. J. Phys. Fluids 31(5), 056603 (2019)

    Article  Google Scholar 

  • Lane, N.M.: Numerical studies of flow in porous media using an unstructured approach (2011)

  • Lewis, R., Sukirman, Y.: Geomechanics, A.M.i.: Finite element modelling of three-phase flow in deforming saturated oil reservoirs. Int. J. Numer. Anal. Methods Geomech. 17(8), 577–598 (1993)

    Article  Google Scholar 

  • Li, L., Mei, R., Klausner, J.F.: Multiple-relaxation-time lattice Boltzmann model for the axisymmetric convection diffusion equation. Int. J. Heat Mass Transf. 67, 338–351 (2013)

    Article  Google Scholar 

  • Lu, X., Armstrong, R.T., Mostaghimi, P.: Analysis of gas diffusivity in coal using micro-computed tomography. J. Fuel 261, 116384 (2020)

    Article  Google Scholar 

  • Luo, J.-W., Chen, L., Min, T., Shan, F., Kang, Q., Tao, W.: Macroscopic transport properties of Gyroid structures based on pore-scale studies: permeability, diffusivity and thermal conductivity. Int. J. Heat Mass Transf. 146, 118837 (2020)

    Article  Google Scholar 

  • Masciopinto, C., Palmiotta, D.: Flow and transport in fractured aquifers: new conceptual models based on field measurements. J. Transp. Porous Med. 96(1), 117–133 (2013)

    Article  Google Scholar 

  • Mostaghimi, P., Blunt, M.J., Bijeljic, B.: Computations of absolute permeability on micro-CT images. Math. Geosci. 45(1), 103–125 (2013)

    Article  Google Scholar 

  • Münch, B., Holzer, L.: Contradicting geometrical concepts in pore size analysis attained with electron microscopy and mercury intrusion. J. Am. Ceram. Soc. 91(12), 4059–4067 (2008)

    Article  Google Scholar 

  • NeithAlAth, N., Bentz, D.P., Sumanasooriya, M.S.: Predicting the permeability of pervious concrete. J. Concr. Int. 32(5), 35–40 (2010)

    Google Scholar 

  • Noble, D.R., Chen, S., Georgiadis, J.G., Buckius, R.O.: A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Phys. Fluids 7(1), 203–209 (1995)

    Article  Google Scholar 

  • Pisani, L.: Simple expression for the tortuosity of porous media. Transp. Porous Med. 88(2), 193–203 (2011)

    Article  Google Scholar 

  • Qu, Z., Yin, Y., Wang, H., Zhang, J.F.: Pore-scale investigation on coupled diffusion mechanisms of free and adsorbed gases in nanoporous organic matter. J. Fuel 260, 116423 (2020)

    Article  Google Scholar 

  • Renard, P., Allard, D.: Connectivity metrics for subsurface flow and transport. J. Adv. Water Resour. 51, 168–196 (2013)

    Article  Google Scholar 

  • Saboorian-Jooybari, H., Dejam, M., Chen, Z., Pourafshary, P.: Comprehensive evaluation of fracture parameters by dual laterolog data. J. Appl. Geophys. 131, 214–221 (2016)

    Article  Google Scholar 

  • Sato, M., Panaghi, K., Takada, N., Takeda, M.: Effect of bedding planes on the permeability and diffusivity anisotropies of berea sandstone. Transp. Porous Med. 127(3), 587–603 (2019)

    Article  Google Scholar 

  • Shamsi, F., Norouzi-Apourvari, S., Jafari, S.: Engineering: image-based simulation of formation damage during suspension injection in homogeneous and heterogeneous porous media: the impact of pore-scale characteristics on macroscopic properties. J. Petrol. Sci. Eng. 186, 106786 (2020)

    Article  Google Scholar 

  • Shen, K.-H., Brown, J.R., Hall, L.M.: Diffusion in lamellae, cylinders, and double gyroid block copolymer nanostructures. ACS Macro Lett. 7(9), 1092–1098 (2018)

    Article  Google Scholar 

  • Spangenberg, E., Spangenberg, U., Heindorf, C.: An experimental study of transport properties of porous rock salt. J. Phys. Chem. Earth 23(3), 367–371 (1998)

    Article  Google Scholar 

  • Stenzel, O., Pecho, O., Holzer, L., Neumann, M., Schmidt, V.: Predicting effective conductivities based on geometric microstructure characteristics. AIChE J. 62(5), 1834–1843 (2016)

    Article  Google Scholar 

  • Succi, S., Foti, E., Higuera, F.: Three-dimensional flows in complex geometries with the lattice Boltzmann method. EPL (Europhys. Lett.) 10(5), 433 (1989)

    Article  Google Scholar 

  • Takahashi, H., Seida, Y., Yui, M.: 3D X-ray CT and diffusion measurements to assess tortuosity and constrictivity in a sedimentary rock. Diffus. Fundam. 11, 1–11 (2009)

    Google Scholar 

  • Tan, Q., You, L., Kang, Y., Zhang, X., Meng, S.: Changes in pore structures and porosity-permeability evolution of saline-lacustrine carbonate reservoir triggered by fresh water–rock reaction. J. Hydrol. 580, 124375 (2020)

    Article  Google Scholar 

  • Ukrainczyk, N., Koenders, E.: Representative elementary volumes for 3D modeling of mass transport in cementitious materials. J. Modell. Simul. Mater. Sci. Eng. 22(3), 035001 (2014)

    Article  Google Scholar 

  • Van Brakel, J., Heertjes, P.M.: Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor. Int. J. Heat Mass Transf. 17(9), 1093–1103 (1974)

    Article  Google Scholar 

  • Vilcáez, J., Morad, S., Shikazono, N.: Pore-scale simulation of transport properties of carbonate rocks using FIB-SEM 3D microstructure: implications for field scale solute transport simulations. J. Nat. Gas Sci. Eng. 42, 13–22 (2017)

    Article  Google Scholar 

  • Vogel, H.-J., Weller, U., Schlüter, S.: Quantification of soil structure based on Minkowski functions. J. Comput. Geosci. 36(10), 1236–1245 (2010)

    Article  Google Scholar 

  • Wang, Y.D., Armstrong, R.T., Mostaghimi, P.: Boosting resolution and recovering texture of 2D and 3D micro-CT images with deep learning. J. Water Resour. Res. 56(1), e2019WR026052 (2020)

    Article  Google Scholar 

  • Yoshida, H., Nagaoka, M.: Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comput. Phys. 229(20), 7774–7795 (2010)

    Article  Google Scholar 

  • Yong, Y., Lou, X., Li, S., Yang, C., Yin, X.: Direct simulation of the influence of the pore structure on the diffusion process in porous media. J. Comput. Math. Appl. 67(2), 412–423 (2014)

    Article  Google Scholar 

  • Yuan, Y., Doonechaly, N.G., Rahman, S.: An analytical model of apparent gas permeability for tight porous media. J. Transp. Porous Med. 111(1), 193–214 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Petroleum Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Fateme Shamsi & Saeid Norouzi-Apourvari

  2. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Saeed Jafari

Authors
  1. Fateme Shamsi
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  2. Saeid Norouzi-Apourvari
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  3. Saeed Jafari
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FS handled data, ran simulations and wrote the original draft; SNA took part in conceptualization and supervision, and edited the original draft; SJ contributed to supervision and validation.

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Correspondence to Saeid Norouzi-Apourvari.

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Shamsi, F., Norouzi-Apourvari, S. & Jafari, S. The Effect of Morphological and Topological Characteristics on Effective Diffusivity and Permeability of Dual-Structural-Scale Synthetic Porous Medium. Transp Porous Med 136, 657–676 (2021). https://doi.org/10.1007/s11242-020-01535-5

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