The balance between advection and diffusion in reactive gas transport in the unsaturated zone

Oxygen diffusion has long been held to be the rate limiting factor on aerobic reactions in the unsaturated zone and models of these systems have been driven by this assumption. However, oxygen comprises 23.2% by mass of dry air. When oxygen is consumed at depth in the unsaturated zone a pressure gradient is created between the reactive zone and the soil surface. This causes substantial air flow into the subsurface. To determine the balance between advective and diffusive transport, a one-dimensional unsaturated zone gas transport model is developed. The model includes advection, diffusion and dispersion in the oxygen and nitrogen gas components. Density and viscosity are dependent on the gas composition and the flux determined using Darcy’s law. The equations are cast in terms of the total gas pressure and the nitrogen mass fraction. This formulation is chosen because the total gas pressure is slowly varying and the total gas equation and nitrogen transport equation are only weakly coupled. Boundary conditions are driven by atmospheric conditions at the top of the column. At the bottom of the column a zero flux of nitrogen and unit mass fraction of nitrogen are imposed. Equations are solved using a backward Euler linear Galerkin finite element scheme with an iterative decoupling of the equations.

The model is used to investigate the balance between advective and diffusive oxygen transport in the unsaturated zone in both steady and transient states. Barometric forcing at the top boundary can also induce advective flow in the unsaturated zone and is also investigated. Finally, the model is compared with existing field data and results from current approaches.