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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 kv via the equation k(i) = 10(10) kv 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.

Plain Language Summary Fluid flow through geologic porous media is dictated by permeability which is the resistance imparted by the medium. Flows in porous media are described by either Darcy's law or its extension for high flow rates, the Forchheimer equation. In both models, permeability represents the dissipation of mechanical energy by inertial losses and by fluid viscosity. Thus, permeability depends on both fluid properties and the configuration of pores. Decades of research has made the permeability in Darcy's law predictable from medium properties such as porosity and grain size, but the additional permeability in the Forchheimer equation has remained almost impossible to predict. This has hindered the application of the Forchheimer equation for many settings where it is potentially more appropriate. Through a broad synthesis of published data and through computational simulations, we were able to relate the permeability in Darcy's law to the permeability in the Forchheimer equation for the diversity of geologic porous media representing varied pore geometries and configurations. Thus, both kinds of permeability are now predictable and linked. This knowledge will help in many geophysical and engineering applications where it is necessary to consider flows at high rates.