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EM 1110-1-4001 <br /> 3 Jun 02 <br /> where the factor of ln(IO)represents a decrease in concentration by one order of magnitude After the <br /> initial flush of the mobile zone, the extracted concentration is determined primarily by the transport of <br /> contaminants from the immobile soil and the extraction rate To simplify the discussion,assume <br /> degradation in the immobile soils is negligible If we assume extraction from the mobile soils continues <br /> and that the extraction rate is sufficient to maintain the vapor concentration in the mobile zone much less <br /> than the concentration in the immobile soils,mass transfer from the immobile to the mobile soils can be <br /> estimated by <br /> R, d- —ocC,, (F-11) <br /> dt <br /> If the average initial concentration in the contaminated volume is designated as C,o,equation(F-11)may <br /> be solved to find an estimate for the average concentration in the immobile soil, <br /> at <br /> C , =C,o exp — R (F-12) <br /> An expression for the vapor concentration in the mobile zone during the late period of soil vapor <br /> extraction can be estimated by substituting equation(F-12) into(F-5), again neglecting degradation for <br /> brevity of discussion, <br /> Rm dCVm + Q C,,m =�' aCo, exp — a t (F-13) <br /> dt V. V. R, <br /> The solution to this equation subject to an initial condition of C„M=O at t=0 is, <br /> =CG- <br /> a V. Q a at Qt <br /> CVM Ca R V R V —R exp —R —exp — R V (F-14) <br /> m m m m i , m m <br /> The initial condition of zero for the mobile soil zone is valid at late times because the initial <br /> contamination in this region has been swept away The volume parameter for the mobile region, Vm, is <br /> determined from the initial period of extraction as described previously and the volume parameter for the <br /> immobile region, V„ can be estimated from soil properties and the expression <br /> V, (1—S,xl—fm)V = V. (I (1S,S1- fm) (F-15) <br /> ml .Yin <br /> If the retardation coefficients can be estimated, the only remaining unknown in(F-14) is the mass <br /> transfer coefficient, a Therefore, fitting(F-14)to later extracted concentration data yields an estimate <br /> for the mass transfer coefficient The mass transfer coefficient determines the rate of rebound and hence <br /> the anticipated dormancy period and the vapor sampling frequency to assess the vapor concentration in <br /> F-6 <br />