Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

Fluid flow through geologic porous media is represented by Darcy's law and its inertial and nonlinear extension, the Forchheimer equation. These relationships equate the product of the driving potential gradient and phenomenological coefficients representing momentum resistance and dissipation to flux. From decades of research, the coefficient of viscous permeability ( k v ) in Darcy's law is largely predictable, but this is not the case for the coefficient of inertial permeability ( k i ) in the Forchheimer equation. Synthesizing results from thousands of laboratory and field flow tests and pore‐scale flow model results, we show that k i can be predicted from k v via the equation k i = 10 10 k v 3/2 across 12 and 20 orders of magnitude in k v and k i , respectively. Since it is related with k i , k v is thus sufficient for predicting flow across viscous to inertial regimes for most geologic porous media.