Development and testing of a kinetic model for oxygen transport in porous media in the presence of trapped gas

The ability to predict the transport of dissolved gases in the presence of small amounts of trapped gas in an otherwise water-saturated porous medium is needed for a variety of applications. However, an existing model based on equilibrium partitioning of dissolved gas between aqueous and trapped gas phases does not accurately predict the shape of experimentally observed breakthrough and elution curves in column experiments. The objective of this study was to develop and test a kinetic model for dissolved gas transport that combines the advection-dispersion equation with diffusion controlled mass transfer of dissolved gas between the aqueous and trapped gas phases. The model assumes one-dimensional, steady-state ground-water flow, a single dissolved gas component, and a stationary trapped gas phase with constant volume. The model contains three independent parameters: the Peclet number, P, retardation factor, R, and dimensionless mass transfer parameter, omega. The model accurately described the shape of breakthrough and elution curves for dissolved oxygen in column experiments performed with a poorly graded sand and varying amount and composition of trapped gas. Estimated values of P for the bromide tracer increased from 5.92 to 174, corresponding to a decrease in dispersivity from 5.02 to 0.17 cm, as the trapped gas volume increased from ii to 30% of the pore space. It is speculated that this effect is due to a narrower pore size distribution (and hence more uniform pore scale velocity distribution) caused by trapped gas bubbles selectively occupying the largest pores. Estimated values of R increased from 1 to 13.6 as the trapped gas volume increased and confirmed earlier observations that even small amounts of trapped gas can significantly reduce rates of dissolved oxygen transport. Estimated values of omega ranged from 0.3 to 12.1. Although it was not possible to independently measure mass transfer coefficients or interfacial areas, values computed from flowrates and estimated omega values are consistent with values computed by assuming (1) that interfacial area is proportional to trapped gas volume, (2) that trapped gas bubbles are spheres with diameters the same size as soil particles, and (3) that mass transfer is limited by diffusion of dissolved oxygen through water films surrounding trapped gas bubbles.