Environ. Sci. Technol. 1997, 31, 461-466
Evaporation Phenomena during Thermal Decontamination of Soils P A T R I C K G I L O T , * ,† JACK B. HOWARD,‡ AND WILLIAM A. PETERS§ Laboratoire Gestion des Risques et Environnement, Universite´ de Haute Alsace, Ecole Nationale Supe´rieure de Chimie de Mulhouse, 25 rue de Chemnitz, 68200 Mulhouse, France, Department of Chemical Engineering and Center for Environmental Health Sciences, MIT, Cambridge, Massachusetts 02139, and Energy Laboratory, and Center for Environmental Health Sciences, MIT, Cambridge, Massachusetts 02139
Effects of thermal treatment conditions on removal of a low volatility aromatic contaminant from soil are quantified. Shallow beds (10 mg) of a clay soil pretreated with 8 ( 0.4 wt % pyrene were heated in a thermogravimetric analysis at 5, 25, or 50 °C/min or isothermally. Effects of temperature, time, initial soil mass, initial contaminant mass, heating rate, and flow rate of carrier gas (helium at standard conditions) were studied, as were weight loss of uncontaminated soil and evaporation rates of pure pyrene. Extensive pyrene removal from foil (85-90%) was found between 200 (at 5 °C/ min) and 300 °C (at 50 °C/min). Soil decontamination was modeled as pyrene transport without chemical reaction, i.e., (1) evaporation from a liquid sheath encasing each soil particle; (2) diffusion through the soil pile; and (3) diffusion to the ambient through a concentration boundary layer between the soil pile and the top of the thermobalance crucible. Evaporation is important in removing most, i.e., 70% or more, of the pyrene. However, rates of pyrene release from the soil bed are about 5-fold lower than those for evaporation of pure pyrene. Pyrene evaporation is confined largely to thin zones that recede downward through the soil pile as decontamination proceeds.
Introduction Thermal remediation technologies have been extensively used for treating contaminated soils during the last decade, especially in the United States (1). To help public acceptance of these technologies, a better fundamental understanding of the phenomena occurring during thermal decontamination is needed. Lighty et al. (2-5) reported experimental and theoretical results about characterization of the rate-controlling processes associated with the evolution of hazardous materials from soils. A bench-scale particle characterization reactor (PCR) and a bed characterization reactor (BCR) were used to study respectively intraparticle and interparticle transport of contaminants. The more complicated environment of a rotary kiln was studied by Lighty et al. in a rotary kiln simulator. The thermal treatment of organically con* Corresponding author telephone: (33) 89 32 76 55; fax: (33) 89 32 76 61. † Universite ´ de Haute Alsace. ‡ Department of Chemical Engineering and Center for Environmental Health Sciences, MIT. § Energy Laboratory and Center for Environmental Health Sciences, MIT.
S0013-936X(96)00293-3 CCC: $14.00
1997 American Chemical Society
taminated solids with rotary kiln incinerators has received attention (6-10). Heat and mass transfer were modeled to investigate the effect of design and operating parameters. The models show that interparticle mass transfer resistances were controlling in a bed of particles. Individual soil particles were also used to study non-isothermal desorption of toluene (11) or isothermal adsorption of toluene or carbon tetrachloride (12). Mass transfer mechanisms and equilibrium behavior of volatile organic substances in soil matrices were studied, leading to the determination of mass transfer parameters, equilibrium constants, and heats of adsorption (13). Simple models are available to predict extents of contaminant release during low-temperature thermal treatment of contaminated soils (14). The heatup of soil at a low temperature (less than 500 °C) in the absence of oxygen to remove volatile or semivolatile organic compounds before their incineration is a very promising decontamination methodology. Quite rapid surface, and for smaller particles, bulk heating rates and elevated temperatures may be obtained for certain treatment equipment, e.g., rotary kilns, fluidized beds, plasma arcs, vitrification furnaces, etc. Using a lab-scale electrically heated foil reactor, Bucala´ et al. (15) studied the removal of a complex organic mixture, i.e. no. 2 home heating oil from soils under rapid heating conditions (approximately 1000 °C/s). Decontamination, quantified as weight loss of oil-treated soil corrected for weight loss of neat soil, was completed by heating the soil to 300 °C at heating rates of 200 or 1000 °C/s and then continuing heating for about 25 s. The overall goal of this paper is to expand the current understanding of the underlying chemical and physical processes important to thermal removal of low volatility PAH compounds from soil. The specific objectives are to elucidate effects of treatment conditions, e.g., temperature, heating rate, treatment time, flow rate of ambient gas, and initial mass of soil and pollutant, on the overall rates and extents of pyrene removal from a clay soil.
Experimental Section Soil decontamination was studied with a Cahn System 113 thermobalance. The experiment was designed to mimic practical-scale operating conditions, while providing sufficient control to allow the resulting observations to be interpreted quantitatively. A sample of a clay soil rich in montmorillonite (10) was supplied by the University of Utah. At MIT (16), a 63-90-µm fraction, prepared by sieving, was contaminated by exposing the soil to a dichloromethane (DCM) solution of pyrene and allowing the solvent to evaporate at ambient conditions. Pyrene deposited on the outer surface of the soil particles and caused them to agglomerate. The soil-pyrene mixture was ground to disperse the pyrene more uniformly. Weight loss of the resulting specimens upon DCM washing revealed a contamination level of 9.3 wt % based on uncontaminated soil (16). The soil moisture content was not determined but is probably no more than 1-2 wt % given that the weight loss from heating neat soil amounted to only 1-1.5 wt % at temperatures from 100 to 250 °C (Figure 1). Clay soil samples of about 10 mg were introduced into a crucible (5 mm deep and 9 mm of opened cross-sectional section diameter), which served as the hot stage during thermogravimetric analysis (TGA). Contaminated and uncontaminated (neat) samples were separately subjected to a preselected and continously measured temperature-time history, using heating rates of 5, 25, and 50 °C/min under a carrier ambient gas flow of helium of 105 cm3 min-1 (standard conditions). The TGA provides constant heating rates of e1
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FIGURE 1. Volatiles release by heating clay soil at 25 °C/min. Initial soil mass ) 9.50 ( 0.05 mg; initial pyrene contamination level, if present, 8.0 ( 0.4 wt %. (0) Soil and pyrene. (O) Soil without pyrene. °C/s and furnishes a continuous record of sample weight with a detectability of 0.01 mg. The nominal contamination level (CL) was 8% by weight of contaminated soil (16). For most of the present samples, the calculated CL values (see eq 3 below) fell in the range of 8.0 ( 0.4 wt %. Pyrene, a four-ring polycyclic aromatic (PAH) compound (MW 202, mp 156 °C, bp 395 °C) has been found in waste heavy oils, tars, and sludges (17) and is thus relevant to removal of low volatility PAH from contaminated soils. From thermogravimetric measurements, the total weight losses of contaminated soil (WLCT in % by weight) and uncontaminated soil (WLNCT in % by weight) were determined. Effects of temperature, time, initial sample mass, heating rate, and carrier gas flow rate on the rates of sample weight loss were separately investigated and, after correcting for weight loss of the soil itself, were associated directly with pyrene release. From eqs 1 and 2, it was possible to obtain the soil mass (contaminant not included) at time 0 (mS0) and the contaminant mass at time 0 (mC0). Time 0 was chosen just at the beginning of the heating process. The sample mass at time 0 (contaminant plus soil) is denoted by mCS0 and is known by a previous weighing:
mCS0 ) mS0 + mC0 WLCT ) WLNCT
(1)
mC0 mS0 + × 100 mCS0 mCS0
(2)
The contamination level of the soil CL is defined by eq 3, taking as a reference the mass mS0 of the soil only:
CL )
mC0 × 100 mS0
(3)
The decontamination level DL(t) (%) at any time t during the decontamination process can be evaluated using eq 4 in which WLCT(t) and WLNCT(t) (% by weight) are the weight losses measured at time t on the contamined soil and on the uncontaminated soil, respectively.
(
)
mS0 WLCT(t) - WLNCT(t) mCS0 × mCS0 DL(t) ) mC0
(4)
Most of the decontamination processes will now be characterized by the variation of DL with temperature or time. To
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FIGURE 2. Comparison between model predictions and experiments for pyrene release for three different heating rates: 5 °C/min (9.56 ( 0.05 mg), 25 °C/min (9.50 ( 0.05 mg), and 50 °C/min (9.05 ( 0.05 mg). Initial soil charges are shown in brackets. Initial level of soil contamination with pyrene was 8.0 ( 0.4 wt % in all three cases. (0) Experiments. (- - -) model. aid in interpreting our data on soils, a systematic study of the evaporation kinetics of pure pyrene was carried out with the same apparatus for similar ranges of heating rates.
Results Figure 1 shows percent (by weight of soil) of volatiles released by heating samples of uncontaminated and contaminated soil at 25 °C/min up to 1000 °C. Clearly, most or all of the contaminant is released before 300 °C, since the subsequent weight loss appears to be primarily due to the soil itself. The use of eq 4 allows one to plot the percent of decontamination (DL) versus temperature, as is shown in Figure 2 for different heating rates. This figure shows that, given sufficient temperature, essentially complete removal of pyrene from the clay can be achieved over a wide range of relatively low heating rates and that most of this “decontamination” can be achieved by a temperature of 300 °C. For a fixed temperature, with increasing heating rate DL decreases, but the apparent average rate of decontamination increases. Also, 90% pyrene removal at 200 °C is indicated for heating at 5 °C/min. The reproducibility of the data (not shown here) was good. Figure 2 also suggests that as much as 5-10% of the pyrene removal may occur between 600 and 1000 °C, i.e., well above its normal boiling point. Quantitative interpretation of this region of the curves may not be straightforward. Our analysis (eqs 1 to 4) assumes that soil and pyrene do not affect each other’s volatilization behavior. However, at or even below 600 °C (if the clay is catalytic), pyrene may react chemically giving volatiles plus residual tar and coke. Some of these may in turn react with the soil, modifying its decomposition behavior. Thus, the last 5-10% of the DL may reflect a complex superposition of effects not covered in our analysis, including loss of monolayer coverage as DL approaches 100% (see below). Chemical analyses of the product off gas and residual soil are not available to experimentally test this proposition. For a fixed initial level of contamination, a larger mass of soil was found to require more severe thermal treatment to achieve the same DL. In particular when heating a 2.08- and a 9.50-mg sample from room temperature at 25 °C/min, 50% removal of the pyrene was achieved at a temperature 20 °C lower for the 2.08 mg sample. This is as expected because (see below) the rate of pyrene release is virtually unaffected
TABLE 2. Comparison of Measured Pyrene Release Rates (µg/s) temperature (°C)
evaporation of liquid, E
thermal treatment of thin beds of clay particles, Sa
E/ S
163-168 184-188
5.72 10.83
1.00 2.17
5.72 4.99
a For 163-168 °C, initial soil mass ) 9.48 ( 0.05 mg, and initial pyrene mass at start of isothermal heating ) 0.633 ( 0.008 mg. b For 184-188 °C, initial soil mass ) 9.29 ( 0.05 mg, and initial pyrene mass at start of isothermal heating ) 0.498 ( 0.008 mg.
FIGURE 3. Effect of initial pyrene mass and temperature on pyrene removal under isothermal conditions. Heating rate to the isothermal temperature was 5 and 25 °C/min for the 0.466 and 0.633 mg experiments, respectively. For 184-188 °C, pyrene mass at the start of isothermal heating was 0.498 mg, and the heating rate to the isothermal temperature was 25 °C/min. (0) 0.466 mg, 163-168 °C ; (O) 0.633 mg, 163-168 °C; (×) 0.498 mg, 184-188 °C.
TABLE 1. Effect of Initial Soil Mass on Rate of Pyrene Removal at 163-168 °C initial soil mass (mg)
initial rate of pyrene removal (µg/s)
1.50 4.57 9.48
0.50a 0.83 1.00
a This value has greater uncertainty and may be actually be closer to 1.00.
by initial soil mass or by initial pyrene loading for the present conditions of a relatively shallow soil bed and coverage of the soil by a film of pyrene equivalent to many monolayers. Thus, more pyrene must be removed from the larger mass sample, and more severe heating was needed to accomplish this. Figure 3 shows results for different cases where contaminated soil samples were heated for known times at essentially constant temperatures. At a fixed temperature, the absolute rate of pyrene release (the slope of the curve) during most of the period of isothermal decontamination does not exhibit a strong effect of the initial amount of pyrene present. Each curve shows some release of pyrene at “zero” time to account for the pyrene evolved during heatup to the indicated "constant" final temperature of 163-168 °C. The two different initial amounts of pyrene present when isothermal conditions are obtained (time 0) are due to the two different heating rates (5 and 25 °C/min) used before isothermal experiments were run. Table 1 implies at most a weak dependence of pyrene release rate on initial soil mass (the 1.50-mg entry has higher uncertainty, so all the rates are probably of the order of 1 µg/s). Temperature effects are much stronger. Figure 3 shows that even a modest increase in temperature (about 20-25 °C) more than doubles (from 0.06 to 0.13 mg min-1) the initial rate of pyrene release during isothermal heating. Pure samples of pyrene were also subjected to TGA at two different heating rates (5 and 25 °C/min). Pyrene was completely evaporated at a temperature less than 250 °C, with a large effect of the heating rate. Slower heating to the same temperature produced more evaporation, due to longer heating time. The evaporation of pure pyrene was also studied under isothermal conditions at the two temperatures of 167-168
and 188 °C, i.e., temperatures very close to those used with the contaminated soil. The results show increased rates of evaporation with increasing temperature. The weight loss is a linear function of time, except at the end of the process. No effect of the initial mass of pyrene was detected, which is characteristic of a process occurring at a liquid-vapor interface of constant area. The effect of the helium flow rate over the top of the TGA crucible was also investigated, using 105 and 250 cm3 min-1 (standard conditions) during heatup of pure pyrene from room temperature at 5 °C/min. No clear effect could be experimentally discerned. Table 2 compares for the same isothermal temperature and ambient gas flow rate the rates of pyrene evaporation from liquid pyrene and of pyrene release from thin beds of contaminated clay. Soil decontamination is about a factor of 5 slower than evaporation. Thus, evaporation can be considered as an upper bound on how fast pyrene can be eliminated from a soil at the same external pressure. Since the ratio of the rate of pyrene evaporation from liquid pyrene to the rate of pyrene release from thin beds of contaminated clay is about 5, evaporation is suspected to play an important role during the local decontamination process, i.e., the release of pyrene from each soil particle. This assumption is employed to advantage in our mathematical modelingssee below.
Mathematical Modeling Isothermal Evaporation Model for Pure Pyrene. Here is described a model for the release of pyrene vapor from pure liquid pyrene at a constant temperature. This release was modeled as evaporation from liquid pyrene followed by diffusive transport through a non-reactive concentration boundary layer. The model assumes that the pyrene vapor and helium both behave as ideal gases, that there is no volume change when they mix, and that any spatial variations in temperature can be ignored. Moreover, since most of the pyrene is evolved at low temperatures, chemical reactions of pyrene in the concentration boundary layer and in the packed bed of soil are ignored. If we further assume a one-dimensional diffusive transport of pyrene above the liquid surface, the molar flux density jP of pyrene is related to the pyrene mole fraction x by
jP ) -cD
dx dz
(5)
Integration of eq 5 between z ) 0, where the mole fraction was xsat, and z ) δ (the thickness of the concentration boundary layer), where the mole fraction is the bulk xb, leads to
jP xsat - xb ) δ cD
(6)
This equation allowed the thickness of the concentration boundary layer to be estimated, since jP was known from experiments.
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TABLE 3. Estimation of the Thickness of the Concentration Boundary Layer T (°C)
FHe (mol/s)
FP (mol/s)
xb
xsat
δ (cm)
7.18 × 2.83 × 3.94 × 1.65 × 1.81 × 10-4 3.41 × 10-8 1.88 × 10-4 1.65 × 10-3 7.18 × 10-5 5.36 × 10-8 7.46 × 10-4 4.07 × 10-3 10-5
168 168 188
10-8
10-4
10-3
a Using mathematical model described in text. isothermal heating at the stated temperature.
b
0.23 0.23 0.34
Data are for
The vapor phase mole fraction of pyrene at the surface of the liquid pyrene (xsat) was obtained, at a given temperature, by assuming thermodynamic equilibrium between pyrene in the two phases:
xsat )
Psat cRT
(7)
The quantity Psat is the vapor pressure of pyrene in equilibrium with liquid pyrene. This vapor pressure was obtained, at any temperature, by integrating the Clausius-Clapeyron equation, leading to
ln
( )
Psat ) P0
(
5
∫ 1.037RT× 10 T
2
Tb
1-
)
T 936
0.464
dT
(8)
where the term 1.037 × 105 (1 - T/936)0.464 is a correlation to account for the temperature variation of the latent heat of vaporization of pyrene (18). The bulk mole fraction of pyrene was calculated by assuming a dilution of the pyrene flux molar flow rate, FP, caused by the ambient helium flow (molar flow rate FHe):
xb )
FP FP + FHe
(9)
The diffusion coefficient of pyrene in helium was estimated (19) and can be represented as a function of temperature by
D ) 2.515 × 10-10 T 1.92
(10)
where T is in K and D is in m2/s. Using eq 6 plus eqs 7-10, the thickness of the concentration boundary layer was estimated at 168 °C for two different helium flow rates of 105 and 265 cm3/min and at 188 °C for 105 cm3/min. The values of key experimental quantities as well as the estimates for δ are given in Table 3. These estimates of the boundary layer thickness are of the same order of magnitude of the depth of the TGA crucible and, as expected, are affected by the temperature. However, to simplify the calculations a mean, temperature-independent value of 0.25 cm was used for δ in the model of non-isothermal release of pyrene. The only model parameter derived from the present data is the concentration boundary layer thickness δ, and this was estimated using only isothermal experiments. Another model of pure pyrene evaporation under transient, i.e., nonisothermal heating, not described in this paper, was carried out using the 0.25-cm value estimated from isothermal heating. Good quantitative agreement of predictions from this non-isothermal model with the data on non-isothermal evaporation of pyrene is a validation of this δ value. Soil Decontamination Model. A model was also developed for soil decontamination under non-isothermal heating. The pyrene release from the soil was modeled as evaporation from a liquid phase surrounding each soil particle followed by non-reactive diffusive transport through the soil pile and then through a non-reactive concentration boundary layer above the soil surface within the crucible.
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FIGURE 4. Geometry used in the mathematical model to approximate the arrangement of the soil pile and the pyrene concentration boundary layer in the crucible of the thermobalance. To justify this hypothesis of an evaporation process, following Tognotti et al. (12), the pyrene concentration in the soil (kg of pyrene/kg of soil) was used to estimate the fraction of the pyrene present on the soil surface as the first monolayer, assuming that all the pyrene was uniformly adsorbed, i.e., in successive monolayers each of an area equivalent to the BET surface area of the soil. The BET surface area of the present clay soil was found to be 1.54 × 103 m2 kg-1, a low value for many clays, probably due to the presence here of aggregates of particles. Assuming the projected surface area of the pyrene molecule to be Sm ) 2.4 × 10-19 m2, we obtained a pyrene monolayer concentration (mole of pyrene/kg of contaminated soil) of roughly 10-2 mol kg-1. When compared to the initial pyrene concentration of 0.396 mol kg-1 corresponding to 8% contamination, only a small fraction (i.e., about 2.5%) of the pyrene could be adsorbed as a monolayer over the BET surface. This calculation further implies that most of the pyrene is deposited on each soil particle in loosely bound liquid lamellae that are many (perhaps up to 40) monolayers thick. In this case, evaporation must be the main process for pyrene release from the soil particles during most of the decontamination process. This hypothesis will be further discussed in relation to the model predictions. When around 10 mg of contaminated soil was deposited within the crucible of the thermobalance, the soil pile did not cover the bottom of the crucible, and at the center of the pile, the depth was greater than 1 mm. Since the soil sample was present as a compact pile at the bottom of a wide shallow crucible, the geometric arrangement represented in Figure 4 was adopted for modeling purposes. The soil and crucible were respectively represented by cylinders of cross-sectional area S1 and S (S ) 0.64 × 10-4 m2 and S1 ) 1.26 × 10-5 m2). The contaminant was assumed to be transported in the z direction (one dimensional transport), first within the soil pile, and then in the particle-free region above the bed surface, i.e., in the concentration boundary layer. Pyrene transport within individual soil particles was not considered. The evaporation of pyrene from each soil particle was assumed to occur according to spherical symmetry. From Lighty et al. (5), the evaporation rate of pyrene rp (moles of pyrene per unit of volume of particles per second) is given by
rP )
12Dc (xsat - x) dP2
(11)
The equivalent diffusivity De of pyrene in the soil bed is given by
De )
D τ
(12)
Assuming a non-compact stacking of particles, a value of 0.35 was taken for the porosity (20). A tortuosity of 4 was assumed. It was checked that the value of the tortuosity (between 2 and 8) did not affect significantly the results given by the model. The evaluation of the mean free path of pyrene within the assumed cylindrical pores of the packed bed led to the conclusion that this mean free path is lower than the average pore diameter so that the pyrene transport from the surface of each particle and through the bed voids to the soil bed surface is by ordinary Fickian diffusion. Thus, D was still given by eq 10. A vapor phase mole balance within the bed, which does not account for sorbed pyrene, led to the following equation that applied for 0 e z e h (Figure 4):
De
δx 12D (1 - ) δ2 x -R (xsat - x) ) 0 + δT δz2 dP2
(13)
A mole balance of pyrene, under unsteady conditions, corresponding to non-isothermal diffusion within the concentration boundary layer (i.e., h e z e h + δ) led to eq 14, with R ) δT/δt the heating rate: 2
δx )0 (δxδz) + δδzx - DR δT 2
(14)
2
The boundary conditions are
x(z,0) ) xsat
t)0
δx )0 δz
z)0 z)h+δ
(T ) 150 °C)
(15) (16)
(dx dz)
xbFHe ) -cDS
z)h+δ
(17)
Equation 14 for pyrene transport inside the concentration boundary layer and eq 13 are solved simultaneously using eqs 16 and 17 (boundary conditions), eq 15 (initial conditions), and eq 18 expressing the continuity of pyrene flux at the bed surface:
z)h
-cDeS1
δx δx | - ) -cDS |z)h+ δz z)h δz
(18)
A finite difference method was used with 60 mesh nodes in the soil bed and 10 mesh nodes in the concentration boundary layer. The temperature step was taken as 0.1 K. During the calculations, the evaporation process was taken as complete when the local contamination level between two adjacent nodes was less than 0.04 wt % . This resolution provided the vertical (z) distribution of pyrene mole fraction in the soil bed and in the concentration boundary layer and, in particular, the pyrene mole fraction in the bulk gas, xb. Using xb in eq 19, the weight loss of pyrene and hence the percent decontamination was then calculated as affected by temperature for different heating rates:
FHeM d(WL) ) xb dT R
(19)
Results and Discussion of Soil Decontamination Model In Figure 2, three curves showing the percent pyrene removal predicted by the model, corresponding to 9.56-, 9.50-, and 9.05-mg charges of contaminated soil respectively heated at 5, 25, and 50 °C/min, are compared to our corresponding experimental data. The agreement is good over much of the decontamination range, e.g., roughly 10-80%, 5-85%, and 2-70% respectively for the three stated heating rates. This supports the hypothesis that evaporation is important in removing most, i.e., the first 70-85% or more, of the pyrene.
However, rates of pyrene removal from the soil bed are about 5-fold lower than those for evaporation of pure pyrene. Figure 2 illustrates the ability of the present model to describe well the heating rate effects over a 10-fold variation in that parameter. These data and modeling curves also imply that beyond some level of decontamination (DL) removal of the remaining pyrene is strongly impacted by processes not accounted for in the present analysis, e.g., at elevated temperatures, chemical reactions (possibly catalyzed by the clay), and at surface coverages approaching one monolayer, desorption. In support of the latter, a residual pyrene contamination level of 10% (i.e., DL ) 90%) would correspond to about four monolayers on this clay, or possibly even lower surface coverage, if the BET surface area of the soil particles has been underestimated. Our results imply that, for shallow soil beds with pyrene contamination levels corresponding to coverages of several monolayers, the rate of pyrene release shows little or no effect of soil mass or contaminant mass. Thus, for a fixed initial level of contamination and the same thermal treatment schedule, the amount of pyrene removal, i.e., the DL, should vary inversely with soil mass. This expectation is supported by predictions from the current model and experimentally. Assuming a fixed initial level of contamination and illustrative cases where initial soil charges of 4.96 and 9.50 mg are heated at 25 °C/min, the model predicts that the DL is, to a reasonable approximation, proportional to the reciprocal of the soil mass, e.g., at 200 °C the predicted DL for the 4.96-mg charge was 1.94 times that for the 9.50-mg soil pile, while the soil mass ratios are 0.52 (1/0.52 ) 1.92). Satisfying agreement with the reciprocal soil mass ratio of 1.92 was found for predicted and experimental DL ratios for other temperatures between 150 and 200 °Csexperimental values of the DL ratio ranged from 1.4 to 2.0 while the corresponding model predictions are slightly higher. This in turn suggests that decontamination of the soil pile occurs as pyrene evaporates from successive, relatively thin flat sheets of soil normal to the crucible axis. This evaporation begins at the top of the pile and proceeds downward layer by layer. Thus, at any time, (or equivalent temperature during non-isothermal heating), only a small upper layer of that portion of the soil bed yet to be decontaminated contributes significantly to pyrene release by evaporation. The vertical (i.e., z) profiles of pyrene concentration through the soil bed predicted by the model support this picture. At any time, the calculated mole fractions of pyrene in the yet to be decontaminated portion of the bed are all equal to xsat, except in a thin layer at the top of the still polluted portion of the bed. This local saturation of the vapor phase region around most of the still polluted soil with pyrene prevents pyrene from evaporating from the surface of the soil particles except in the stated top zone. Because the local release rate of pyrene is, for a given temperature, about the same regardless of the absolute mass of soil present, the decontamination level subjected to the same thermal treatment protocol should vary inversely with the total amount of soil to be cleaned. The proposition that pyrene evaporation occurs primarily in a thin layer at the top of the yet to be decontaminated portion of the soil bed is also consistent with results obtained during our isothermal experiments. Those measurements show that at 163-168 °C (Table 1) the rate of pyrene removal was at best only modestly affected by the initial mass of the soil sample. Clearly, the results given by the present soil decontamination model are relevant if there is enough soil to form several layers of particles, in effect at least a shallow packed bed. When the masses of soil become sufficiently small, e.g.,
