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EM 1110-1-4001 3 Jun 02 region Fitting SVE and rebound concentration data generally requires varying only four parameters in equation(F-20) C,o,V,f.,and a Case studies of site-specific parameter fitting are presented in the next section After fitting equation(F-20)to a series of extraction well concentrations associated with a rebound test, values for the fitted parameters can be checked for consistency with other existing data Vapor concentrations are often measured in monitoring points constructed in the vadose zone around extraction wells The monitoring points are frequently installed in low permeability soils which correspond to the immobile soil region These measured concentrations at the start of a rebound period should correspond roughly to the fitted average initial concentration in the immobile region Data from a number of monitoring points can be used to calculate an order-of-magnitude estimate for the total contaminated volume This volume can be compared with the fitted representative volume A review of boring logs or vertical flow profiles from PneuLoe can also yield an estimate for the fraction of soil which is mobile For example, a site with distinct sand and silt intervals would only require an estimate for the total thickness of sand divided by the total thickness of the vadose zone to arrive at an estimated mobile fraction in the soil for comparison with the fitted fraction Finally, the mass transfer coefficient can be estimated from vaporous diffusion theory in a slab Again, a review of well logs may reveal an average thickness for immobile soil regions (e g, thin clays or thick moist silts interbedded in sands)and previous measurements may yield the water saturation Looking at the leading term in the linear diffusion solution leads to the following estimate for the mass transfer coefficient, D o4/3 (1-S.)10/3 �2 a ; (F-22) R, a 2 where D is the vapor phase diffusion coefficient of the contaminant in free air and a is the half-length over which diffusion occurs (t e , half the thickness of typical immobile region intervals) The fitted and calculated mass transfer coefficients should be of the same order of magnitude As stated above, one of the goals of the rebound test is to evaluate the mass of contaminant remaining in the subsurface After fitting the model above to the concentrations observed with the rebound test, equation(F-1) can be used to generate an order-of-magnitude estimate for the total residual contaminant mass, mtotal —mm+in, = Cv,mRmOm(I-Sm)fmV+ Cv jRjOj(1-Sj)(1-fm)V (F-23) If the field conditions are adequately modeled by the two-region concept and the fitted parameters are consistent with other information, then the model of the rebound data yields powerful information regarding closure or optimization of the existing system For example,the calculations may yield estimates for a small residual mass and/or the attainment of cleanup goals For optimization,the model can predict durations of extraction to reach cleanup goals for various extraction rates F-6 Case Studies This section presents two case studies for the evaluation of SVE and rebound concentration data using the mathematical models descnbed in this appendix Both sites are located in California's Central • F-14 I