2.6 CONTAMINATED SOIL MODELS


        Contaminated soil can be caused by leaks or spills of hazardous liquid or solid materials, or improper treatment, storage, or disposal of the such materials. Volatile components contained in the soil medium can be a major source of pollutant air emissions. The degree of volatile emissions from soil will depend upon the type of the contaminant, the chemical and physical properties of the contaminant, and the physical characteristics of the medium and the site.

        The rate of volatile emission from contaminated soil may be increased by remediation activities. Old hazardous waste sites containing volatile constituents may not emit vapors in significant amounts, but disturbing the soil in the process of remediation can redistribute the concentration profile across the soil depth, and can increase emission rates from the soil significantly.

        Hwang and Falco (1986) developed a model for estimating emission rates of volatile and semivolatile components in soil by solving a partial differential equation describing the process of diffusion and partitioning occurring within the soil. The solutions are presented for two cases: one case for predicting the emission rate from soil when there is no clean cover on top of soil and another case for predicting the emission rate when a clean soil cover is applied on top of soil immediately after remediation.

        This model based on Hwang and Falco (1986) is implemented as a volatilization source model referred to as "Contaminated Soil" (AG-VCASE = 5) in the user-interface of MEPAS 3.n versions. The "Contaminated Soil" model is one of the models recommended by the EPA (1990) for estimating emission rates from contaminated soil as part of the Superfund exposure and risk assessment process.

        The physical basis of the model is as follows. The contaminant in the soil is assumed to be initially distributed uniformly across the soil depth and across the depth up to the surface (e.g., without a clean soil cover on the surface). As emissions occur from the soil surface, the concentration gradient across the depth in the vertical direction is established. This concentration gradient limits the emission rate as time elapses. Under these conditions, Hwang and Falco (1986) present the following model for estimating the transient volatilization rate at some time, t:

(12)


where Ni = emission rate of contaminant i per unit surface area (g/cm2/s)

            e= air-filled porosity of soil (dimensionless)

         Dei = effective diffusivity defined as Di e1/3 (cm2/s)

           Di = molecular diffusivity of contaminant in soil air pore (cm2/s)

          Hc = concentration-based Henry's Law constant, or concentration in air/phase/concentration in water phase (dimensionless), which is computed as H / R T

            H = Henry's Law constant (atm m3/mole)

             R = gas constant (8.2 x 10-5 atm m3  /° K-mole

             T = temperature (° K)

           Kd = soil-water partition coefficient (cm3/g)

               t = time (s)

          Cso = initial (t=0) contaminant concentration in soil (g/g)

              a =  a term defined as (Dei e/[e+ Ps (1-e) Kd/Hc]) (cm2/s)

              Ps = true density of soil, g/cm3.

        The emission rate estimated by Equation 12 represents an instantaneous emission rate at any time t. The emission rate shown by this equation decreases as a function of time. The emission rate averaged over a long-term period can be obtained mathematically by integrating the instantaneous emission rate over the exposure period and dividing it by the exposure period. The result is

(13)


The total average emission is obtained by multiplying the emission rate in Equation 13 by the emission area,

(14)


where Ei = emission rate of constituent i (g/s)

          A = emission area (cm2).

 
        The emission rate from soil contaminated by organic compounds can be estimated from Equation 12 where the soil-air partition coefficient is defined by Hc/Kd and the value for Kd is related to the value of the octonal-water partition coefficient, Koc. In some special cases where the Koc values are not known and the compounds exert vapor pressures, Equation 12 can be modified to estimate the emissions. Examples of these special cases include soil contaminated with mercury or tritiated water in a mixture with water. Vapor pressures of the compounds in the soil pores provide a driving-force for air emissions and the driving-force term, (Hc/Kd) Cso, requires modification to estimate the transient emission rate. The term, (Hc/Kd) Cso, represents the concentration of a contaminant in the air space of soil pore at the beginning of contamination, and hence can be replaced by

(15)


 
 
where VPi = vapor pressure of constituent i (mmHg)

        MWi = molecular weight of constituent i (g/g-mole)

           Xi = weight fraction of constituent i in soil (g/g).
        Covering a contaminated soil site with a layer of clean soil may decrease the rate of volatile emissions. The extent to which the emission rate decreases depends upon several factors including the partitioning behavior of the contaminant between the soil and soil pore, volatility of the contaminant, the cover thickness, and contaminant diffusivity through the soil pores. For the case of having a clean soil cover, the partial differential equation describing the physical phenomena of the volatilization process could not be solved analytically at the appropriate boundary and initial conditions. Hwang and Falco (1986) presented the solution in form of a converging series using the techniques of the Fourier series.

(16)


 
 



    where        L = depth to the bottom of contamination from the soil surface (cm), including the depth of clean soil placed on top of contaminated layer

                     T = period over which emission rates are averaged (s)

                     k = depth of clean soil cover (cm)

                   N i = average emission rate of contaminant i over the exposure period T which is equal to t2-t1, g/cm2-s; when the initial exposure occurs at t1=0, the exposure period T is equal to t2 in Equation 15, and the integration starts from 0 to t2.

Other terms in Equation 16 are as defined in Equation 12. The summation in Equation 16 can be estimated with a computer. At the date of publication of this report, the above model for contaminated soil with a layer of clean soil is not implemented in MEPAS.