The Forchheimer Approach for Soil Air Permeability Measurement

Abstract

Core Ideas We developed an apparatus with automatic registration of flow (Q) and pressure (ΔP). A curvilinear Q–ΔP relation was found for seven of eight soil samples tested. Ignoring non‐linear pressure loss gave permeability errors up to 65% at ΔP=100 Pa. We suggest an index for pore tortuosity based on the non‐linear Q–ΔP relation. Air permeability affects a range of soil functions and is useful in the quantification of soil pore characteristics. Measurements of air flow used to quantify air permeability are mostly performed at a fixed pressure difference, assuming a linear relation between flow and pressure. However, evidence exists that nonlinear pressure losses may occur even at low pressure gradients. We constructed an apparatus that allows automatic measurement of air flow at a range of pressures. The new methodology was applied to eight soil samples deriving from a loamy, Stagnic luvisol. Three artificial cores were also tested: a solid cylinder of plastic with drilled, vertical holes; a cylinder of autoclaved aerated concrete (AAC), and an AAC cylinder with drilled holes. The historical Forchheimer approach, including a polynomial regression of flow–pressure data, was applied to derive the true Darcian flow based on the coefficient to the linear part of the relation. Flow‐pressure data appeared to be curvilinear for all test specimens, except for one of the soil samples. The results showed up to 65% errors in estimates of air permeability if the nonlinear pressure losses were ignored when applying a pressure difference as low as 100 Pa. Our results strongly suggest use of the Forchheimer approach based on measurements of flow and pressure difference at a range of air pressures. We suggest an index for soil pore tortuosity, which appears to reflect the pore characteristics of the artificial samples tested. More studies are needed to evaluate the applicability of the index for soil samples.

Ratio of Non‐Darcian to Darcian Air Permeability as a Marker of Soil Pore Organization

“…In the laboratory, the soil cores were saturated on tension tables, then drained first to –30 then –100 hPa matric potential. At each matric potential, air permeability was measured via the Forchheimer approach described by Schjønning and Koppelgaard (2017). In brief, air flow was measured consecutively at four pneumatic pressures (D P : ∼0.5, ∼1, ∼2, and ∼5 hPa).…”

“…[2] for b = 0 reveals that the laminar (Darcian) permeability, k Darcy , may be calculated from the coefficient, a [Eq. 1], deriving from a quadratic regression: The k app corresponding to a pneumatic pressure of 5 hPa was similarly estimated from these regression results by – erroneously – assuming a linear relationship between the pressure gradient and superficial air velocity at that pneumatic pressure [please see figure 4 of Schjønning and Koppelgaard (2017)]. The pneumatic pressure of 5 hPa was chosen to reflect the conditions often applied in standard air permeability measurements (e.g., Iversen et al, 2001; Peng and Horn, 2008; Simojoki et al, 2008; Martínez et al, 2016).…”

“…The pneumatic pressure of 5 hPa was chosen to reflect the conditions often applied in standard air permeability measurements (e.g., Iversen et al, 2001; Peng and Horn, 2008; Simojoki et al, 2008; Martínez et al, 2016). Please consult Schjønning and Koppelgaard (2017) for a detailed explanation of the measurement and calculation procedures. The Forchheimer approach for estimating Darcian air permeability has recently been validated (Schjønning, 2019).…”

“…In previous studies, we have shown that air flow in soil pores may become non‐Darcian at quite low pressure gradients (Schjønning et al, 2013; Schjønning and Koppelgaard, 2017). These studies also indicate that the ratio between k app measured at some specific pneumatic pressure gradient and the estimate of k Darcy may be useful as an indicator of soil pore characteristics.…”

“…The soil samples also analyzed by Pulido‐Moncada and co‐authors were drained initially to –30 hPa and subsequently to –100 hPa matric potential. Air permeability was measured via the Forchheimer approach (Schjønning and Koppelgaard, 2017), which allows estimates of k Darcy , as well as the k app , measured at a pneumatic pressure of 5 hPa. The purpose was to evaluate the potential of the ratio R = k app / k Darcy for revealing the characteristics of the soil pore systems not obtained from k Darcy .…”