Bounds to Air-Flow Patterns during Cyclic Air Injection into Partially Saturated Soils Inferred from Extremum States

Abstract

Soil-aeration procedures are widely used as an environmental practice for soil and groundwater remediation (removal of volatile compounds and enhancement of biological treatment) and less frequently as an agricultural practice to prevent root O deficiency. Analytical solutions to problems of air flow in the soil allow a phenomenological analysis of the physical problem and the effects of the governing parameters, which in turn enables a more systematic design tool for soil-aeration systems. We present solutions for the air-pressure distributions resulting from harmonic (sinusoidal) or square-wave (step-pulse) air injection into infinite and semi-infinite (with an atmospheric pressure at the soil surface) soil domains. The approach presented here suggests using exact (analytical) solutions to extreme (unrealistic) conditions, setting the boundaries of the physical span of the flow problem. The simplified analytical solutions, based on assuming instantaneous water relaxation or, alternatively, assuming stagnant water are used to analyze the effects of different air-injection modes (constant, harmonic, and step-pulse) on the air-pressure distribution and radius of influence (ROI) for different values of the governing parameters: source depth, cycle period, and the soil’s air-conductivity parameters. For long cycle periods, square-pulse and harmonic air injection can increase the maximal ROI compared with that resulting from steady air injection.