A Note on the Forchheimer Approach for Estimating Soil Air Permeability

Abstract

Important soil pore characteristics may be revealed from air permeability data. Recent research has quantified significant bias in estimates of the true Darcian permeability when frequently reported pneumatic pressure differences to drive the convective flow are used. An alternative to measurement at infinitesimal pressure differences is the Forchheimer approach, including a polynomial regression of corresponding values of the superficial air velocity (v) and the pressure gradient (G) applied. However, in situations with Darcian flow at low pressure gradients, this procedure may theoretically give an overestimation of the Darcian permeability. We constructed sample plastic cores (∼3.5 cm high) with different numbers (n = 1–19) of drilled tubes (holes of 1, 2, 4.5, and 5.8 mm diameter). Gas diffusivity was measured with a transient‐state method. Air permeability was measured at four pneumatic pressure differences (0.5, 1, 2, and 5 hPa), and the Darcian permeability was estimated with the Forchheimer approach. The ratio of apparent permeability at 5 hPa pneumatic pressure difference to the Forchheimer‐estimated Darcian permeability was significantly lower than unity (0.06–0.52) for all test samples. For all 1‐ and 2‐mm hole samples and for all four levels of G, the Reynolds number indicated nonturbulent flow, whereas turbulence was predicted for samples with 4.5‐ and 5.8‐mm diameters. A model combining relative gas diffusivity, air permeability, and the space available for gas transport indicated that the Forchheimer estimates of Darcian permeability were correct in situations with nonturbulent flow, whereas erroneous estimates were generated for the larger tubes with turbulence.Core Ideas We tested the Forchheimer approach for simple samples with straight tube pores. For nonturbulent flow conditions, the Forchheimer approach provides accurate results. Air flow at 5 hPa pressure difference implies significant underestimation of permeability.