Transport by Oscillatory Flow in Soils with Rate‐Limited Mass Transfer: 1. Theory

Abstract

Oscillatory flow of fluid in a porous medium can generate a one‐way transport of heat or chemicals if there is a gradient of temperature or chemical concentration and a rate‐limited heat or mass transfer between the moving fluid and an immobile phase. For chemical transport in soils, the immobile phase can occur in stagnant porosity, by sorption, or by dissolution of a vapor in the pore water. As a function of oscillation frequency, the transport rate has a broad peak near the value ωτc = 1, where ω is the angular frequency of oscillation and τc is the characteristic equilibration time of the mobile phase. The transport rate is proportional to the gradient and to the square of the amplitude of periodic fluid displacement. A unique diffusivity derived from the analysis enables prediction of the long‐term transport by a diffusion calculation without fluid flow, thereby providing a tool for estimating the removal of contaminant vapors by passive soil vapor extraction (PSVE). We compared predictions of the analytic theory with numerical simulations of PSVE. The mobile–immobile model is also applicable to transport in other cases of oscillatory flow in porous media, including cyclic motion of water or gas due to tidal aquifers or earth tides.

Evidence for High Rates of Gas Transport in the Deep Subsurface

“…Our results have implications for the migration of gases linked to a range of scientific problems, including stable isotope analysis (Kwicklis et al, 2006), subsurface nuclear detonation gas migration (Jordan et al, 2015), and contaminated site remediation (Neeper & Stauffer, 2012a, 2012bYou et al, 2011). These data suggest that the site is impacted by barometric pumping, a phenomenon in which gases may be pulled and spread through the subsurface by barometric pressure fluctuations.…”

“…The model is built within the FEHM (Finite Element Heat and Mass) porous-flow simulator, developed at LANL, and used successfully to simulate barometrically pumped contaminant transport in fractured rock (Harp et al, 2018;Jordan et al, 2014Jordan et al, , 2015Neeper & Stauffer, 2012a, 2012b. The model is built within the FEHM (Finite Element Heat and Mass) porous-flow simulator, developed at LANL, and used successfully to simulate barometrically pumped contaminant transport in fractured rock (Harp et al, 2018;Jordan et al, 2014Jordan et al, , 2015Neeper & Stauffer, 2012a, 2012b.…”

“…Data collected during the tracer experiment are next used to create a numerical representation of the experiment. The model is built within the FEHM (Finite Element Heat and Mass) porous-flow simulator, developed at LANL, and used successfully to simulate barometrically pumped contaminant transport in fractured rock (Harp et al, 2018;Jordan et al, 2014Jordan et al, , 2015Neeper & Stauffer, 2012a, 2012b. FEHM simulates gas advection coupled to tracer transport using a standard form of the advection-dispersion equation (FEHM, 2019;Johnson, Otto, et al, 2019, Johnson, Zyvoloski, et al, 2019.…”

“…Periods of high atmospheric pressure push gases downward into the subsurface, while periods of low pressure draw gases upward toward the surface (Nilson et al, 1991). Broadly, barometric pumping has been shown to impact the mobility of volatile organic compounds (VOCs; Auer et al, 1996;Neeper & Stauffer, 2012a, 2012bYou & Zhan, 2013) and radionuclide gases (Bourret et al, 2018;Carrigan et al, 1996;Harp et al, 2018;Jordan et al, 2015). Broadly, barometric pumping has been shown to impact the mobility of volatile organic compounds (VOCs; Auer et al, 1996;Neeper & Stauffer, 2012a, 2012bYou & Zhan, 2013) and radionuclide gases (Bourret et al, 2018;Carrigan et al, 1996;Harp et al, 2018;Jordan et al, 2015).…”

“…Barometric pumping has been investigated thoroughly in the literature (Kuang et al, 2013;Scotter et al, 1967;Scotter & Raats, 1968;You et al, 2011)), and has been used to characterize the subsurface (Neeper, 2002;Rossabi, 2006). Broadly, barometric pumping has been shown to impact the mobility of volatile organic compounds (VOCs; Auer et al, 1996;Neeper & Stauffer, 2012a, 2012bYou & Zhan, 2013) and radionuclide gases (Bourret et al, 2018;Carrigan et al, 1996;Harp et al, 2018;Jordan et al, 2015). Deep drying and subsequent reductions in infiltration fluxes are hypothesized to result from pumping of dry air through fractured rock (Weeks, 2001).…”