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Description
It has been known for a long time that there are cases where Darcy’s law does not
apply, also for single phase flow with small capillary numbers [1–4]. The flow rate has for
some cases been found to be proportional to the pressure gradient raised to the power
1/n where n 6 = 1. For other cases it has been found to be a threshold pressure, below
which no flow occurs.
Non-equilibrium molecular dynamics simulation is an excellent tool to study flow in
porous media. We have used a modified Lennard-Jones/Spline potential which makes
it possible to model a wide range of systems with varying pore sizes, interface tensions
and fluid viscosity. The Reflective Particle Method has been used to create a pressure
difference across the porous medium [5]. The red particles are fluid and the blue particles are pore particles with a fixed
position.
We present results for single and two-phase flow varying the contect of wetting fluid,
porosity, average pore diameter, and interface tensions. The results are interpreted using
non-equilibrium thermodynamics for porous materials, a new theory. On this bases we
propose various reasons for deviations from Darcy’s law.
Acknowledgement
The calculation power is granted by The Norwegian Metacenter of Computational Science
(NOTUR). Thanks to the Research Council of Norway through its Centres of Excellence
funding scheme, project number 262644, PoreLab.
References
[1] D. Swartzendruber, “Non-Darcy flow behavior in liquid-saturated porous media,” Journal of Geo-
physical Research, vol. 67, no. 13, pp. 5205–5213, 1962.
[2] M. G. Bernadiner and A. L. Protonanas, “Progress on the Theory of Flow in Geologic Media with
Threshold Gradient,” Journal of Environmental Science and Health. Part A: Environmental Science
and Engineering and Toxicology, vol. 29, no. 1, pp. 249–275, 1994.
[3] L. Boersma, F. T. Lindstrom, and S. K. Saxena, “Limitations of Darcy’s law in Glass Bead Porous
Media,” no. 3351, pp. 1972–1974, 1972.
[4] R. J. Miller and P. F. Low, “Threshold Gradient for Water Flow in Clay Systems,” Soil Science
Society of America Proceedings, vol. 27, no. 6, pp. 605–609, 1963.
[5] J. Li, D. Liao, and S. Yip, “Coupling continuum to molecular-dynamics simulation: Reflecting particle
method and the field estimator,” Physical Review E, vol. 57, no. 6, pp. 7259–7267, 1998.
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