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EM 1110-1-4001 <br /> 3 Jun 02 <br /> Equations describing the vapor concentrations in the mobile and immobile soils can be determined by <br /> substituting Equation (F-1)into (F-3)and(F-4) <br /> dCYm _ r r S 1—S 11 <br /> Rn, dt —0m(1-Qm)fmVCv,m (I—S )HCv,m + O��(1-Sm ma�Cvi —Cvm1 (F-5) <br /> W, _ 'YA r( l <br /> R, dt —(1—S,)HCv� —alCvi —Cvml (F-6) <br /> The initial decay rate shown in the example of Figure F-1, can be estimated from equation(F-5) and <br /> (F-6)can be used to estimate the"asymptotic" decay toward zero During the initial extraction period, <br /> mass transfer from the immobile zone plays a small role and degradation generally takes much longer <br /> Therefore, for the initial decay in concentration, equation(F-5) may be simplified <br /> dC v,,, _ Q ) <br /> Rm dt — m{1—`Sm)fmV C (vm F-7 <br /> If the average initial concentration in the contaminated volume is designated as C,,,,o,equation (F-7)may <br /> be solved to find, <br /> C„ =C,n o expQ t (F-8) <br /> — <br /> Rm V <br /> where V. [_� (1—Sm Y,,,V] is the air-filled pore volume within the mobile fraction of the total <br /> contaminated volume By fitting equation (F-8)to the initial observed decay in vapor concentration, an <br /> approximation for the mobile volume is obtained if the retardation coefficient is estimated from equation <br /> (F-2) This volumetric parameter will be employed in the evaluation of rebound data Rearranging(F-8) <br /> and utilizing the initial condition yields, <br /> Q I In Cm,O (F-9) <br /> R m Vm t measure C m,measure <br /> where the subscript measure designates a time and concentration measurement before the mobile region <br /> has been fully swept If the air-filled volume in the mobile zone can be estimated independently(e g, <br /> from vapor monitoring wells and boring logs), then the time required for the initial flush of the mobile <br /> region by SVE can be determined from, <br /> t flush . R Q m In(10) = 23 <br /> ..V,,, (F-10) <br /> F-5 <br />