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EM 1110-1-4001 <br /> 3 Jun 02 <br /> F-2 Theoretical Framework <br /> As described in the previous section, soils are often divided into two categories for remediation low <br /> permeability and high permeability,relative to each other Early models of pump-and-treat referred to <br /> the relatively low permeability soil as "immobile"since the water in the soil was practically stagnant(see <br /> Brusseau, 1991 for a review) Recent work has applied the approach to soil vapor extraction (Kalens <br /> and Croise, 1999)and air sparging(Rabsdeau and Blayden, 1998) The higher permeability soil is named <br /> "mobile" since the majority of flow occurs in these soils In the vadose zone, the mobile soils are the <br /> most permeable and appreciable air flow through these soils is induced when a practical pressure <br /> gradient is applied(e g ,air injection or extraction in a well) Immobile soils have relatively low <br /> permeabihties and air flow through these soils during the application of a pressure gradient is considered <br /> negligible Contaminant transport in immobile soils is dominated by diffusion in the vapor phase or <br /> liquid advection and diffusion if moisture contents are high <br /> As described in the previous example of SVE (see Figure F-1),the initial decay in contaminant <br /> concentration in the extraction well is governed by the transport of contaminants in flowing vapors <br /> through the mobile soils and is typically on the order of days or weeks In the immobile soils, <br /> contaminant transport occurs on a time scale proportional to the diffusion rate and the length scale <br /> associated with the immobile soil (e g , the thickness of a clay lens) and is typically on the order of <br /> months or years Because of these disparate time scales, the concentration in the mobile soils (equivalent <br /> to the extracted concentration during SVE) falls much faster than the concentration in the immobile soils <br /> Contaminant removal from the immobile soils relies on diffusion of contaminants to the interface with <br /> mobile soils where the contaminants are swept to extraction wells Hence the concentrations in the <br /> mobile and immobile soils are in dis-equilibrium and define the macro-scale mass transfer constraint <br /> resulting from soil heterogeneities This section develops mathematical relationships describing SVE <br /> using mass balances which can be employed to analyze rebound data and estimate field-scale mass <br /> transfer constraints The mass transfer constraints for various physical phenomena and length scales are <br /> lumped into a single, average mass transfer coefficient assumed relatively constant over time <br /> Consider the total mass of contaminant, m„ in a given volume,V, of soil type j where j can signify either <br /> "m" for mobile or"i"for immobile The total contaminant mass 1n the soil is equal to the sum of the <br /> mass adsorbed,the mass dissolved in pore water, and the mass volatilized <br /> mj = Cw,j [ (1-0j) psj Kd,j + �j Sj + Oj (1-S)H] f V <br /> mj = Cv,j Oj (I-SJ) f V Rj (F-1) <br /> The parameters are defined by <br /> CW J = mass of contaminant per unit volume of pore water;n soil type j <br /> CvJ = mass of contaminant per unit volume of soil gas in soil type j <br /> Cv j = H Cv j (Henry's Law) <br /> f = fraction of the treatment volume occupied by soil type j (NOTE fm+ f,= 1) <br /> F-3 <br />