Indoor Air as a Source of VOC Contamination in Shallow Soils - GSI ...
Indoor Air as a Source of VOC Contamination in Shallow Soils - GSI ...
Indoor Air as a Source of VOC Contamination in Shallow Soils - GSI ...
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110 T. E. McHugh et al.Q gb = Volumetric flow rate <strong>of</strong> air from the soil underly<strong>in</strong>g the foundation <strong>in</strong>to thebuild<strong>in</strong>g (L 3 T −1 ).Q bg = Volumetric flow rate <strong>of</strong> air from the build<strong>in</strong>g <strong>in</strong>to the soil underly<strong>in</strong>g the foundation(L 3 T −1 ).Under positive pressure conditions, air flows from the build<strong>in</strong>g to the subsurface soil,and Q gb and Q ag are 0. A m<strong>as</strong>s balance on the build<strong>in</strong>g <strong>in</strong>door air and subsurface soil yieldsa set <strong>of</strong> two ord<strong>in</strong>ary differential equations:M<strong>as</strong>s balance on build<strong>in</strong>g (positive pressure):dC bV b = Q ab C a − Q ba C b − Q bg C b + ṁ b (3)dtM<strong>as</strong>s balance on subsurface soil (positive pressure):dC gV gdtWith <strong>in</strong>itial conditions specified <strong>as</strong>:= Q bg C b − Q ga C g (4)C b,0 = 0 and C g,0 = 0 at t = t 0 (5)where:V b = <strong>Air</strong> volume <strong>of</strong> build<strong>in</strong>g (L 3 ).V g = <strong>Air</strong> volume <strong>of</strong> subsurface soil beneath foundation (L 3 ).C a = Concentration <strong>in</strong> ambient air and subsurface soil surround<strong>in</strong>g the build<strong>in</strong>g (butnot beneath the foundation), usually <strong>as</strong>sumed to be constant (ML −3 ).C b = Concentration <strong>in</strong> build<strong>in</strong>g <strong>in</strong>door air (ML −3 ).C g = Concentration <strong>in</strong> subsurface soil beneath the foundation (ML −3 ).ṁ b = Transient m<strong>as</strong>s rele<strong>as</strong>e rate <strong>of</strong> <strong>VOC</strong> from an <strong>in</strong>door source (MT −1 ).The <strong>VOC</strong> m<strong>as</strong>s rele<strong>as</strong>e rate, ṁ b ,isatime-dependent variable that can be used to describethe transient rele<strong>as</strong>e <strong>of</strong> <strong>VOC</strong>s from a variety <strong>of</strong> <strong>in</strong>door sources. For example, a first-orderdecay function could be used for the rele<strong>as</strong>e <strong>of</strong> <strong>VOC</strong>s from dry<strong>in</strong>g pa<strong>in</strong>t, or a step functioncould be used to describe the sublimation <strong>of</strong> a volatile solid (see “Simulation <strong>of</strong> <strong>Indoor</strong><strong>VOC</strong> <strong>Source</strong>s” below).Under negative pressure conditions, air flows from below the foundation <strong>in</strong>to the build<strong>in</strong>g,and Q bg and Q ga are 0. A m<strong>as</strong>s balance on the build<strong>in</strong>g <strong>in</strong>door air and subsurface soilyields a similar set <strong>of</strong> equations:M<strong>as</strong>s balance on build<strong>in</strong>g (negative pressure):dC bV b = Q ab C a − Q ba C b + Q gb C g + ṁ b (6)dtM<strong>as</strong>s balance on subsurface soil (negative pressure):dC gV g =−Q gb C g + Q ag C a (7)dtKey model variables are illustrated <strong>in</strong> Figure 3. The foundation pore space is <strong>as</strong>sumed tooccupy a negligible volume relative to the build<strong>in</strong>g and sub-foundation soil, so that theconcentration <strong>of</strong> <strong>VOC</strong>s with<strong>in</strong> the foundation is <strong>as</strong>sumed to be at a pseudo steady state. Theconcentration <strong>of</strong> <strong>VOC</strong>s with<strong>in</strong> the cracks <strong>in</strong> the foundation is equal to the build<strong>in</strong>g concentrationunder positive pressure conditions and equal to the subsurface vapor concentration
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