Abstract
Classical models for flow and transport processes in porous media employ the so-called extended Darcy’s Law. Originally, it was proposed empirically for one-dimensional isothermal flow of an incompressible fluid in a rigid, homogeneous, and isotropic porous medium. Nowadays, the extended Darcy’s Law is used for highly complex situations like non-isothermal, multi-phase and multi-component flow and transport, without introducing any additional driving forces. In this work, an alternative approach by Hassanizadeh and Gray identifying additional driving forces were tested in an experimental setup for horizontal redistribution of two fluid phases with an initial saturation discontinuity. Analytical and numerical solutions based on traditional models predict that the saturation discontinuity will persist, but a uniform saturation distribution will be established in each subdomain after an infinite amount of time. The pressure field, however, is predicted to be continuous throughout the domain at all times and is expected to become uniform when there is no flow. In our experiments, we also find that the saturation discontinuity persists. But, gradients in both saturation and pressure remain in both subdomains even when the flow of fluids stops. This indicates that the identified additional driving forces present in the truly extended Darcy’s Law are potentially significant.
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References
Darcy, H.: Détermination des lois d’écoulement de l’eau à travers le sable. Pages 590–594 of: Les Fontaines Publiques de la Ville de Dijon. Victor Dalmont, Paris (1856)
Färber, A.: Wärmetransport in der ungesättigten Bodenzone: Entwicklung einer thermischen In-situ-Sanierungstechnologie. Ph.D. thesis, Universität Stuttgart (1997)
Gerthsen, C., Kneser, H.O., Vogel, H.: Physik. Springer, New York (1992)
Hassanizadeh, S.M., Gray, W.G.: Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour. 13(4), 169–186 (1990)
Hassanizadeh, S.M., Gray, W.G.: Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29(10), 3389–3405 (1993a)
Hassanizadeh, S.M., Gray, W.G.: Toward an improved description of the physics of two-phase flow. Adv. Water Resour. 16(1), 53–67 (1993b)
Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface. Springer, Berlin (1997)
Joekar-Niasar, V., Hassanizadeh, S.M., Leijnse, A.: Insights into the relationship among capillary pressure, saturation, interfacial area and relative permeability using pore-scale network modeling. Transp. Porous Media 74, 201–219 (2008)
Marshall, F.: Numerical solution of Philip’s redistribution problem. Dipl.-Ing. thesis, Institute of Hydraulic Engineering, University of Stuttgart (2009)
Philip, J.R.: Horizontal redistribution with capillary hysteresis. Water Resour. Res. 27, 1459–1469 (1991)
Pop, I.S., van Duijn, C.J., Niessner, J., Hassanizadeh, S.M.: Horizontal redistribution of fluids in a porous medium: the role of interfacial area in modeling hysteresis. Adv. Water Resour. 32(3), 383–390 (2009)
Richards, L.A.: Capillary conduction of liquids through porous mediums. Physics 1, 318–333 (1931)
Acknowledgments
We thank the German Research Foundation (DFG) for funding the International Research Training Group “Nonlinearities and Upscaling in Porous Media” (NUPUS). The authors are also grateful to Rudolf Hilfer for in-depth discussions on the physics of redistribution.
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Feuring, T., Braun, J., Linders, B. et al. Horizontal Redistribution of Two Fluid Phases in a Porous Medium: Experimental Investigations. Transp Porous Med 105, 503–515 (2014). https://doi.org/10.1007/s11242-014-0381-9
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DOI: https://doi.org/10.1007/s11242-014-0381-9