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EM 1110-1-4001 <br /> 3 Jun 02 <br /> 1 Analyses of extracted vapors defining the decay trend prior to the initiation of the rebound test and <br /> the extraction rate during this period, <br /> 2 Measures of mobile soil concentrations during rebound up to equilibrium with the immobile soils, <br /> and <br /> 3 Analyses of extracted vapors defining the decay trend during extraction after the rebound test and <br /> the extraction rate <br /> Equations describing volume-averaged vapor concentrations in the mobile and immobile soils were <br /> presented in Section F-2 as equations (F-5) and(F-6) These equations were simplified under various <br /> assumptions to yield straightforward relationships for evaluating trends in the extracted concentration <br /> However, the equation pair can be solved exactly given an initial concentration in each soil region <br /> Equations (F-5) and (F-6)represent coupled, first-order, ordinary differential equations for the vapor <br /> concentrations If the extraction rate Q and the mass transfer coefficient ot are constant, coefficients in <br /> both equations are constant and the solution is easy to obtain If the extraction rate varies, such as the <br /> dormancy period during rebound,then the equations can be solved piecewise using the volume-averaged <br /> concentration in each region at the end of a constant extraction rate period as the initial condition for the <br /> next constant extraction rate period Solving the equations in terms of the vapor concentrations and <br /> designating the initial average vapor contaminant concentration in each region as C,,,o and C,o at some <br /> initial time to yields <br /> C,,,n = S21 exp[ r, (t-to)] + n2 exp[r2 (t -to}] (F-20) <br /> C,,, = S2, w, exp[ r, (t -to)] + 02 w2 exp[r2 (t -to)] (F-21) <br /> • where <br /> C,0 -(J)2Cm0 <br /> 1 - <br /> (01 -002 <br /> n _ COICm0 -C�0 <br /> 2 - <br /> wl _(02 <br /> Rmr, +0+a(D <br /> a(D <br /> Rmr2 +0+a(D <br /> m2 — <br /> (A) <br /> o = Q + 7MSM <br /> V. H(1—S. <br /> • <br /> F-12 <br />