Proposed models and analytical solutions of steady one- and three-dimensional (3D) air flow in partially saturated soil enable estimating air-injection sources in unsaturated soils and optimizing their application. The 3D modeling offers six solutions for air injection from a point source located in a: (i) laterally unconfined domain and (ii) at the center of a cylindrically confined domain, in (a) an infinite, vertically unconfined domain, (b) a vertically semi-infinite domain with a surface of constant pressure above the source, representing the effect of the atmosphere on air flow, and (c) with an impermeable surface below the source, representing the effect of a water table on the air flow. The 3D models were formulated using known mathematical solutions for water flow and adjusting them to describe air flow, assuming full analogy between the effect of gravitation on water flow to the effect of buoyancy on air flow. One-dimensional air injection simulations based on two types of air-permeability functions (a concaved exponential and a convex exponential) result in similar distributions of air pressure and capillary heads. Thus, the error caused by using the convex (of positive curvature) exponential function for linearizing the flow equation and for obtaining the 3D solutions is bounded, which justifies use of this function. Air flow patterns depend on a single soil characteristic parameter (α), indicative of the ratio between effects of buoyancy and capillary forces driving the air; high values indicate more upwardly oriented flow. The proposed analysis can be used for decision making regarding locations and depths of air-injection sources for aeration in the vadose zone. Based on the air pressure distribution and the streamlines outlined by the relevant solutions we conclude that the effect of the water table below the source on air flow is negligible, especially in cylindrical confinements. Furthermore, the effect of the atmosphere on air flow in a cylindrical domain is also negligible. The proposed models are applicable especially when the air-pressure gradient in the soil is relatively small, and the effect of air compressibility is negligible.

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