The role of eddies inside pores in the transition from Darcy to Forchheimer flows

Abstract

We studied the role of intra-pore eddies, from viscous to inertial flows, in modifying continuum-scale flow inside pores. Flow regimes spanning Reynolds Number Re ∼ 0 to 1350 are divided into three zones-one zone follows Darcy flow, and the other two zones describe non-Darcy or Forchheimer flow. During viscous flows, i.e., Re < 1, stationary eddies occupy about 1/5 of the pore volume. Eddies grow when Re > 1, and their growth leads to the deviation from Darcy's law and the emergence of Forchheimer flow manifested as a characteristic reduction in the apparent hydraulic conductivity K a. The reduction in K a is due to the narrowing of the flow channel which is a consequence of the growth in eddies. The two zones of Forchheimer flow correspond to the changes in rate of reduction in K a, which in turn are due to the changes in eddy growth rate. Since the characteristics of Forchheimer flow are specific to pore geometry, our results partly explain why a variety of Forchheimer models are expected and needed for different porous media. Copyright 2011 by the American Geophysical Union.