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 Ka. The reduction in Ka 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 Ka, 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.


Civil, Architectural and Environmental Engineering


This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security (CFSES)at the University of Texas at Austin, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under award DE-SC0001114. Additional support was provided by the Geology Foundation of the University of Texas.

Keywords and Phrases

Porous materials; Darcy flows; Darcy's law; Flow channels; Flow regimes; Forchheimer models; Inertial flow; Pore geometry; Pore volume; Rate of reduction; Reynolds number; Darcy law; Eddy; Hydraulic conductivity; Numerical model; Porous medium; Viscous flow; Volume

International Standard Serial Number (ISSN)

0094-8276; 1944-8007

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2011 American Geophysical Union (AGU), All rights reserved.

Publication Date

01 Dec 2011