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Pore-Scale Simulations of Simultaneous Steady-State Two-Phase Flow Dynamics Using a Lattice Boltzmann Model: Interfacial Area, Capillary Pressure and Relative Permeability

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Abstract

The dynamics of simultaneous flow of immiscible two-phase fluids at the steady state in the capillary force-dominated regime were investigated. It was described by the key state variables, including interfacial area between fluids, capillary pressure and relative permeability, as functions of fluid saturation. Based on the two-dimensional pore-scale simulations using the Shan-Chen multi-component lattice Boltzmann model (SCMC-LBM), the steady-state interfacial area, capillary pressure and relative permeability versus saturation relationships subjected to flow conditions, such as initial fluid distribution, saturation history and magnitude of hydraulic gradient, were examined. Also, the intrinsic differences in the interfacial area and capillary pressure versus saturation curves between at dynamic equilibrium in the steady-state infiltration and at quasi-static equilibrium in the transient displacement were explored. As the SCMC-LBM simulations revealed, the relative permeabilities of both fluids were insensitive to initial fluid distribution or saturation history because of the simultaneous steady-state flow dynamics, but dependent on the magnitude of hydraulic gradient due to the existence of a threshold hydraulic gradient. The hysteresis behaviours of interfacial area-saturation and capillary pressure–saturation curves were captured in the transient displacement but absent in the steady-state infiltration, and the unique interfacial area-capillary pressure–saturation surface at dynamic equilibrium did not tend to overlap with the one at quasi-static equilibrium. The hysteretic capillary pressure behaviour for these two flow patterns was of great theoretical and practical significances.

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Acknowledgements

All the simulations using the SCMC-LBM model were executed based on the Mechsys open source library (http://mechsys.nongnu.org) and using the Macondo high performance computing cluster of the University of Queensland. The first author would like to acknowledge the support of International Postgraduate Research Scholarship (IPRS) and University of Queensland Centennial Scholarship (UQCent). The authors also thank the anonymous referees for their critical comments and constructive advices.

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Authors and Affiliations

  1. Research Group on Complex Processes in Geo-Systems, School of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Zi Li & Ling Li

  2. Department of Civil Engineering and Industrial Design, The University of Liverpool, Liverpool, L69 3BX, UK

    Sergio Galindo-Torres

  3. Geotechnical Engineering Centre, School of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Guanxi Yan & Alexander Scheuermann

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  1. Zi Li
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  2. Sergio Galindo-Torres
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  3. Guanxi Yan
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  5. Ling Li
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Correspondence to Zi Li.

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Li, Z., Galindo-Torres, S., Yan, G. et al. 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). https://doi.org/10.1007/s11242-019-01288-w

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