Desorption rate limitation in the extraction of organic molecules from unsaturated soils during soil venting operations

JOURNAL OF

Contaminant Hydrology ELSEVIER

Journal of ContaminantHydrology25 (1997) 21-37

Desorption rate limitation in the extraction of organic molecules from unsaturated soils during soil venting operations Farhad Nadim a,,, Ali Nadim b George E. Hoag Amine M. Dahmani a

a

a Environmental Research Institute, University of Connecticut, Storrs, CT 06269, USA b Department of Aeronautical & Mechanical Engineering, Boston University, Boston, MA 02215, USA

Received 15 August 1995; accepted 24 April 1996

Abstract A microscale mathematical model is developed to analyze the desorption rate limited extraction of volatile organic compounds in a soil column. By solving the diffusion equation in the liquid layer around the soil particles and incorporating the effects of slow desorption from the soil surfaces, it is found that the concentration of organics in the effluent is eventually given by the sum of two separate contributions. The first represents the removal of the compounds initially dissolved in the liquid layer by diffusion, providing an exponentially decaying concentration in the effluent. The second represents the removal of the organics, initially adsorbed onto the solid surfaces, by slow desorption producing the long-time tail which has been observed in the effluent concentration during soil vapor extraction. This model was applied to two bench-scale columns packed with soil contaminated by volatile organic compound (VOC) contaminated soil. The simplified results of the mathematical model allow such parameters as the effective diffusion length, area of gas-liquid contact, the desorption rate constant and the equilibrium partition coefficient, for trichloroethylene in the two soil columns to be determined. © 1997 Elsevier Science B.V. Keywords." Soils; Soil venting; Desorption;Trichloroethylene;Diffusion

1. I n t r o d u c t i o n Volatile and certain semi-volatile organic compounds can be removed from unsaturated soils by a process k n o w n as Soil Vapor Extraction (SVE). SVE brings fresh

* Corresponding author. 0169-7722/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0169-7722(96)00021-6

22

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 2 1 - 3 7

atmospheric air into contact with the contaminated subsurface by an induced vacuum. The continuous flow of air through the porous soil removes the non-aqueous phase liquid (NAPL), as well as the dissolved and the sorbed phases into the moving air. Experimental results have shown that the NAPL phase is extracted from the contaminated soil in the early stages of vapor extraction (Baehr et al., 1989; Hoag et al., 1989). Removal of the remaining portion of the compounds requires volatilization from the dissolved aqueous phase together with desorption from the solid surfaces into the dissolved aqueous phase (Armstrong et al., 1994). After the NAPL phase is depleted, the effluent concentration shows a roughly exponential decay which is followed by a long-time tail (with very small concentration) which persists for a much longer period as vapor extraction continues. Several researchers (e.g., Gierke, 1990; Armstrong et al., 1994) have attributed this long-time effluent tail to mass transfer rate limitation at the aqueous-air interface. Brusseau (1991) has described in detail solute transport by gas advection in the vadose zone using a numerical model that includes heterogeneity and rate-limited sorption in soil and has attributed the tailing effect to rate limited sorption. Grathwohl and Reinhard (1993) have studied desorption rate limitation for the removal of trichloroethylene (TCE) from aquifer material by soil vapor extraction. They observe that in wet soils, desorption of TCE from the soil particles was much slower than in dry soils and the rate of compound removal was independent of the air flow rate. They state that this phenomenon could be attributed to slow diffusion in water-filled pores a n d / o r slow desorption from the solid surfaces. Ball and Roberts (1991b) also suggest that intraparticle diffusion may be responsible for the slow sorptive uptake or desorption of organic molecules in aquifer systems. In this contribution we put forth an analytical solution which aims to provide a possible explanation for this phenomenon based on desorption rate limitation from the solid surfaces. The portion of compounds adsorbed to the solid particles is in a region of the aqueous phase called the "vicinal water", which is defined by Vesilind (1994) as the water molecules within about thirty to several hundred ~ngstriSms of the solid surfaces. In this region, due to enhanced hydrogen bonding, the water molecules tend to layer themselves in an orderly fashion and their properties appear to be much different from those of bulk water. Of relevance to the SVE process is the much larger apparent viscosity of this vicinal water. There is evidence to suggest that the viscosity of the water in the vicinal layer is as much as 30 times higher than the bulk. In most contaminated sites where the organic chemicals have remained in the soil for more than a few months, it is appropriate to assume that a portion of the organic molecules have diffused into the thin layer of viscous vicinal water and have either been adsorbed onto the solid surface or remain in solution within that layer. In either case, these molecules find it difficult to move back to the bulk water, resulting in a slow apparent desorption rate. Note that the molecular diffusivity, D, of the organic molecule is inversely proportional to the viscosity, /z, of the solvent, in accordance with the Stokes-Einstein relation (Atkins, 1978):

D-

kBT 67rtza

in which k B ( ~ 1.38 X 10 -23 kg m 2 s 2 K 1) is the Boltzmann constant; T is the

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37 Soil

Liquid

•

•

x=O

23

Air Flow

x= If

Fig. 1. A schematic drawing of the mass transport region. The organic molecules are initially dissolved in the liquid layer or adsorbed on the soil surface at x = O. As the venting gas comes into contact with the liquid, the organic molecules are extracted from the moist soil.

absolute temperature; and a is the effective radius of the diffusing molecule. In our simple model, we treat the molecules in the vicinal layer and those adsorbed to the soil surface as the same and assume a standard sorption rate expression for mass transfer between the bulk and the surface layer.

2. M a t h e m a t i c a l m o d e l

In order to model the transport of the organic molecules from the wet soil to the venting gas, consider the following one-dimensional microscale transport process. Referring to Fig. 1, suppose that a liquid layer of thickness l shields the surface of soil particle from the venting gas which is used to extract the dissolved organic molecules. Let the spatial coordinate normal to the solid surface be denoted by x and suppose that the liquid layer thickness 1 is small enough that the curvature of the soil particle is negligible, making the solid surface appear flat in this analysis. Initially, the organic molecules are dissolved in the liquid layer with a portion of them adsorbed on the solid surface at x = O. Denote the concentration of the species in the liquid layer by C ( x , t ) and that on the surface by Cs(t), where t is time. In the absence of flow in the liquid layer, C ( t ) is determined by solving the diffusion equation: OC --

Ot

i32 C =D--

~x 2

(1)

in which D is the molecular diffusion coefficient of the organic species in the liquid. At the solid surface an equation describing the exchange of the molecules between the liquid and the surface by adsorption and desorption is adopted in the form: OCs dt

k [ C s - a C(O,t)]

(2)

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37

24

in which k is the desorption rate constant; and a is the equilibrium partition coefficient which relates the equilibrium value of the surface concentration to that in the bulk. Note that the product k s can itself be thought of as the rate constant for the adsorption of the chemical onto the surface. For a " f a s t " sorption process (i.e. large k) the surface concentration Cs and the bulk concentration C(O,t) always maintain their equilibrium relation with the former given by the product of a and the latter. The limit that interests us here, however, is the case of " s l o w " desorption, which might be responsible for the long-time tail observed during SVE. In addition, the diffusive flux from the liquid onto the surface must be equated to the rate of increase of the surface concentration in the form:

~C

dC s

D-~x ( 0 ' t ) =

at

(3)

We will solve the above system of equations with the initial conditions that: C ( x , 0 ) = Co

(4)

q(0)

(5)

= ~ Co

which suggest an initial state with uniform concentration C o in the liquid layer, and with the surface concentration in equilibrium with the bulk. As the venting begins, the organics start to be transported to the air (at x = l) and the concentrations in the liquid layer and on the surface begin to decrease, until all the organics have been removed. Since the venting gas generally will contain a concentration of organics which is much less than its equilibrium value (determined by Henry's law) and if mass transfer resistance at the liquid-gas interface is neglected, the boundary condition at the interface is, to a good approximation, given by: C(l,t) = 0 (6) suggesting that any dissolved molecules which reach the interface are quickly removed by the venting gas, making the concentration of the organics in the liquid at that point vanish. The net rate of transfer of the organics to the air is thus determined by diffusion across the liquid layer and by desorption from the surface. The flux J of the chemicals into the venting air is given by: OC J= - D - - ( 1 , t ) (7) 0x To solve the above system of equations, it is convenient to render all quantities dimensionless. For this purpose, one can define the dimensionless quantities: C (c*,c;,x*,t*)

=-

C s, ,

"

x Dt)

C0 o~C0 ' l ' 12

(8)

in terms of which, the governing equations adopt the simplified forms (in which the superscript . . . . . is now dropped for convenience) OC 02 C at - ax 2

dCs

--

dt

-

k* [ C s -

(9) C(O,t)]

(10)

F. Nadim et al. / Journal of ContaminantHydrology 25 (1997) 21-37

25

C(x,O) = 1

(11)

Cs(O ) = 1

(12)

C(1,t) = 0 OC ~x (O,t) = k*a * [ C s - C(0,t)]

(13) (14)

where the two remaining dimensionless parameters are defined by k* =- k l 2 / D

(15)

a* =- a / l

(16)

The first parameter, k *, is a ratio of the characteristic diffusion time to the characteristic time for desorption. The limit k * << 1 which is of interest here is one in which diffusion across the liquid layer occurs relatively fast compared to the time it takes for desorption to take place. The second parameter, a *, is a dimensionless equilibrium partition coefficient. The solution to the system of Eqs. (9)-(14) can be found using Laplace transformation with respect to time (Hildebrand, 1976). If an overbar denotes the transformed dependent variable and s is the transformed parameter, the above equations reduce to: sC-l= sC s -

0x 2 1= -k*[Cs-C(O,s)]

C(l,s) =0

(17) (18) (19)

i}x (O,s) = k*a * [ C s - C(O,s)]

(20)

in the s domain. The solution to Eq. (17) which satisfies boundary condition (19) at x = 1 is given by: 1

C ( x , s ) = s [ l -cosh{~ss(1 - x)}] +Asinh[~/J-(1 - x)]

(21)

in which A(s) is a constant of integration. Upon evaluating C and its derivative with respect to x at x = 0 and substituting the results into Eqs. (18) and (20), one obtains a system of two algebraic equations for two unknowns: A(s) and Cs(s). The solution to these equations is found to be: k *a* v~- coshv~- + k* sinhx/7 + s sinhfs A ( s ) = s(k* coshx/7 + s coshx/7 + k*a *~s sinhv~)

(22)

- k* + k* coshv~ + s coshx/7 + k *a* ~ sinhx/s-Css(S) =

s ( k * coshv~- + scoshv~- + k*a*v/7 sinhv/7)

(23)

The Laplace transforms of the bulk and surface concentrations, Eqs. (21) and (23), must then be inverted to yield the actual concentrations in the time domain. However, the quantity which is the most useful in the SVE process is the net flux of the chemical

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 2 1 - 3 7

26

across the liquid-gas interface. The dimensional flux J, given by Eq. (7), can be written in the form: J 0C -

-

DCo/1

-

Ox

(1,t)

which, upon evaluation of the right-hand side (RHS) using the solution found above yields J L - ' [ ~ s A ( s)] (24)

DCo/l

in which L -1 represents the inverse Laplace transform; and A(s) is given by Eq. (22). If either dimensionless group k * or a * zero, the last expression for the flux reduces to:

J

DCo/l

L-~

( si,h (- o hv7

= ~] 2 e x P It - , n(+~ _)

.-o

2"n'2tj]

(25)

where the inversion of the Laplace transform has been performed using method of residues (Hildebrand, 1976). In terms of the dimensional time, the long-time limit of the above is given by:

2DCo

J -~ ~ -

[ 7r2Dt1

exp~ ~ - T - )

(26)

valid for Dt/1z >> 1. When k * and a * are non-zero, we have not been able to invert the required Laplace transform (24) analytically. However, the long-time limit of the flux can be obtained using standard techniques for examining the asymptotic behavior of inverse Laplace transforms for large t (Davies, 1985). In that limit, the asymptotic behavior is dominated by the location of those poles in the complex s plane which have the most positive (or the least negative) real part. Here, we will consider the long-time behavior of the flux using this technique, in the limit when the dimensionless desorption rate k* is very small (i.e. the limit of slow desorption). It is convenient to write the expression for the flux (Eq. (24)) in the explicit form:

J L_l(s~/~sinhx/s+k*x/ssinhv~+a*scoshfs) DCo/1 scoshv~s[s+k*(1 + a *xTsstanh~s-s)]

(27)

Since ~ appears in the above, it may seem that the complex expression has a branch point at the origin. However, it can be verified that the apparent singularity at the origin s = 0 in the complex plane is "removable" and no branch cut is necessary. For small values of k *, one zero of the denominator on the RHS of Eq. (27) occurs when the term in the square brackets vanishes. In the limit k * << 1, this pole is approximately located at s = - k * and the contribution from the residue at that pole to the inverse Laplace transform can be calculated to be: k *c~* exp( - k ~ t) This represents the primary contribution to the net flux from the chemicals which were initially adsorbed on the solid surface. On the other hand, the contribution to the flux

F. Nadim et aL / Journal of Contaminant Hydrology 25 (1997) 21-37

27

from the diffusion of the chemicals in the liquid layer is primarily contained in the residue at the pole which would have been at s = - -rr2/4 when k * = 0 (cf. the first term in the sum on the RHS of Eq. (25)). For small but finite k *, this pole moves to s ----- -- ('n'2/4 + 2k *ce *) and the contribution from its residue to the flux becomes: 2

7r 2

exp -

~

+ 2 k *a * t

However, as long as k* << 1, the terms involving k* in the last expression are negligible and it produces a contribution of the form (26) to the flux. The long-time asymptotic form of the total flux J under these conditions is the sum of the two contributions obtained above, namely: J D C o / l = 2exp( - 7r2t/4) + k *ct* exp( - k * t)

(28)

which in terms of dimensional quantities takes the form 2DCo J=--~exp

( - ~ ' 2 Dt ) ~ 4l +kaCoexp(-kt

)

(29)

Generally, the coefficient of the first exponential term in Eq. (29) is much larger than that of the second term. Therefore, the first term is initially dominant and an exponentially decreasing amount of chemicals appears to be extracted by the venting gas, with time constant 412/7r 2 D . But since the first exponential term decays much faster than the second, for sufficiently long times the first term becomes completely negligible and the flux is dominated by the second term (which, despite its small coefficient, decays over a much longer time) providing a possible explanation for the observed long-time tail in the experiments. The two main contributions to the flux of chemicals into the venting gas in our model are from the material which is initially dissolved in the moisture within the soil (first term on the RHS of Eq. (29), call this Jz), and that which is initially adsorbed on all the adsorption sites (second term on the RHS of Eq. (29), call it J2). in the simplified one-dimensional geometry embodied in Fig. 1, the area of adsorption sites (the surface at x = 0) is exactly the same as the area of liquid-gas contact (the surface at x = 1). In practice, however, the SVE process is more closely represented by Fig. 2, which suggests that as the air channels through the soil, the surface area of contact between the moist soil and the gas (AL~) can be very different from the total surface area available for adsorption (As). With this in mind, we generalize the result of the simplified model for the flux, Eq. (29), to the more general case of represented by Fig. 2 as follows. If the volumetric flow rate of the venting gas is given by Q, the total surface area where the gas and the liquid phases are in contact by ALe, and the total area of adsorption sites by A s , the measured concentration of chemicals in the outlet venting gas Gout would be given by: Gout(t) = Jl( t) A L ~ / Q + J2( t) A s / Q

(30)

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 2 1 - 3 7

28

© <

,<

<~

Area of A d s o r p t i o n Sites

;ORB

1/Gas Contact

ALG Fig. 2. A conceptual sketch of the Soil Venting Extraction (SVE) process. Venting air channels through the moist soil, creating an area of contact designated by ALG. Dissolved chemicals diffuse (with effective diffusivity D) through the soil over a characteristic length l to reach the venting gas. The total area available for adsorption, is typically much larger than the area of soil-air contact.

As,

where J~ and -/2 are the diffusion and desorption fluxes, respectively. Using the explicit forms of Jl and -/2, Eq. (30) can be written as:

C°ut(t)'~aLG 2DC°Q I

exp

(-Tr2Dt) a s 4 - ~+ - ~ - k a

C0 e x p ( - k t )

(31)

Thus, a measurement of the time evolution of the concentration of the chemicals in the outlet gas allows the time constants for the two exponential terms in Eq. (29) to be determined.

3. Experimental procedure The purpose of this laboratory experiment was to investigate the desorption and liquid diffusion behavior of volatile organic compounds under vapor extraction conditions in a contaminated soil, in order to validate the results of our simple model. Under laboratory conditions the desorption rate constant, k, and the b u l k / s u r f a c e partition coefficient, ~, can be estimated with the analytical model that was derived in the previous section. The diffusion length, 1, and the area of contact between air and water, AL~, can also be calculated with this model if the overall (apparent) diffusion coefficient

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37

29

of the target compound within the soil is known or estimated. Fig. 2 presents a conceptual sketch of the SVE process in a contaminated soil. As the venting air channels through the soil, the dissolved chemicals enter the air streams by diffusion, characterized by a diffusion coefficient D which represents not the molecular diffusivity of chemical in liquid, but the effective dispersion of the chemicals through the heterogeneous soil. The typical distance over which the chemicals have to diffuse in order to enter the air stream is denoted by l and the area of contact between the soil and the air streams by ALG. AS the concentration of dissolved chemicals in the soil decreases, those chemicals which had adsorbed on all available sites (area A s) begin to desorb and eventually make it to the air stream as well. In this simplified model, the resistance to mass transfer across the l i q u i d - a i r interface is neglected. In addition the processes of intraparticle (micropore) and intraparticle diffusion are all combined and characterized by a single effective diffusivity D for the whole medium. The apparent diffusion coefficient in soil can be estimated with batch sorption experiments (Grathwohl and Reinhard, 1991). In our study we did not carry out batch experiments; therefore, to estimate the values of ALG, and l we have used three values from a study by Grathwohl and Reinhard (1993) for the apparent diffusion coefficient of TCE in soil for fast, medium, and slow desorption (see Table 4). Our model has specifically been derived for moist soils that have a long history of contamination. The soil used in our column experiment was a contaminated soil taken from the bottom of a lagoon that had been a disposal site for volatile organic compounds and chlorinated solvents for more than 15 years. This lagoon is in a Superfund site in the state of Indiana. Soil vapor extraction wells were to be installed on site after complete drainage of the lagoon with the " p u m p - a n d - t r e a t " method. Soil samples were placed in sealed containers submerged in dry ice to prevent any possible loss of the chemicals during the shipping process. Grain size analysis was done for this soil using A S T M (1995) methods D421-85 and D422-63. Table 1 provides the results of this analysis and Table 2 lists the characteristics of the soil used in our study. Table 1 Grain size analysis and the specific area for the lagoon soil Sieve size % of bulk mass (mm)

BET surface area a (m2/g)

2.38-4.76 1.18-2.38 0.6-1.18 0.3-0.6 O.15-0.3 0.074-0.15 < 0.074

3.7 2.7 1.5 1.6 1.4 1.3 2

0.04 0.04 0.058 0.0938 0.5804 0.12 0.07

Bulk surface area, A s (m2/g) < 0.075-4.76

100

Adapted from Ball and Roberts (1991a),

1.6

30

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37

Table 2 Characteristics of soil in columns I and I1 Soil characterization

Column I

Column II

Volume (cm3) Weight dry (g) Bulk density dry (g/cm 3) Moisture content by weight Total porosity Fraction of organic carbon

2303 3342 1.77 18% 32% 0.032%

2176 3056 1.61 12.8% 38% 0.032%

Three soil replicates ( 5 - 1 0 g) were taken from the sealed container and were analyzed for the total concentration of the target compounds using U.S. Environmental Protection Agency method 8240B (USEPA, 1992). The total organic carbon in the soil ( J ~ ) was measured with a Perkin Elmer CHN 2400 by the method of thermal conductivity. Applying the equilibrium partitioning relation between solid, gas and aqueous phases the concentration of the target compounds in the soil moisture C w was estimated via (Feenstra et al., 1991): Ct Pb C0---- Cw = ( K o c f o c P b + O w + H c O a ) in which C t is the total concentration of the organic compound in soil ( t x g / g dry weight); Pb is the dry bulk density of the soil sample ( g / c m 3 ) ; Koc is the partition coefficient between the organic compound and organic carbon; foc is the fraction of the organic carbon; 0a is the air-filled porosity (volume fraction); 0w is the water filled porosity (volume fraction); and H c is the dimensionless H e n r y ' s law constant. The value of Koc used for TCE was 126 m l / g (USEPA, 1986). The dimensionless H e n r y ' s law constant (20°C) used was 0.31 (Grathwohl and Reinhard, 1991). Two glass columns (90-cm long, 7.6-cm i.d.; Altech) were packed with the saturated lagoon soil. Packing was done with a stainless-steel scoop and in batches of ~ 1 kg. After each batch was delivered to the column, a stainless-steel rod was used to moderately compact the soil and bring its bulk density close to typical field values. The packing process was done as rapidly as possible to avoid excess loss of volatile compounds. After packing, the columns were immediately capped and the excess water was allowed to drain from the Teflon ~ valves connected to the gas sampling ports on the lower section of the columns for 4 h. Four water samples were collected in 20-ml V O A vials in the first, second, third and fourth hour, respectively, and were analyzed for the aqueous concentration of the target compounds. The average values of the measured concentrations were compared with the calculated concentration; the two values had a difference of less than 10%, therefore the estimated values were used as the initial aqueous concentration, C o , in the model. All tubing and fittings that were in contact with the vapor phase were made from stainless steel, glass, or Teflon ®. Other components where contamination a n d / o r adsorption were not of concern were made of nylon. The system was checked for leaks by closing the outlet valve and applying pressurized air (100 kPa) from the inlet. A

F. Nadim et al. // Journal of Contarainant Hydrology 25 (1997) 2 1 - 3 7

Pressurized Air

31

Activated C Humidifier

I o

oJ

Temperature Adjustment Apparatus

FlOWvalveCOntrol ~ ~

I

Manifold

I

Glass Wool ::i::ii:S

1 ~ Glass Wool

()

Soil

....... ~

Glass Beads

' ~ ' ~ Wire Mesh Gas Sampling Port and the drainage valve Pressure Gauge

Flow Meter

Activated Carbon

================================== ===================

ToVentHood

L

I

Flow Control Valve I

Vapor Liquid Separator

Manifold

Fig. 3. Bench-scale vapor extraction set-up.

soap-water solution was used to check for possible leaks; non was detected. Using pressurized air, flow for both columns started at the same time. A constant air flow rate of 12 m l / m i n was maintained for column I, and a constant flow rate of 25 m l / m i n was maintained for column II throughout the experiment (43 and 23 days for column I and II, respectively). Air was purified with an activated carbon filter (Supelco HC 2-2445) and humidified through a fine bubble diffuser immersed in water. The humid air was demisted with glass wool and entered the columns through a two-port manifold (Fig. 3). Samples were analyzed with a gas chromatograph equipped with a flame ionization detector (GC-FID). For quantitation of the volatile organics an HP-3365.GC.Chemstation integrator was used. Calibration of the FID was performed by a multi-point calibration curve using a 2000 / x g / m l standard solution (DWM-588, VOC-mix, Ultra

32

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37

Table 3 Conditions of gas chromatography Initial temperature Maximum temperature Initial time Temperature increasing rate Final time Run time Column Auxiliary gases Carrier gas Flow rate

35°C 180°C I rain 6°C/min 5 rain 30 rain DB-624 (J&W Scientific), 30 m × 2 mm air and hydrogen helium 2.9 ml/min

Scientific, North Kingstown, Rhode Island, U.S.A.). The FID response was linear in the concentration range used. Table 3 gives the set-up condition of this instrument. Gas samples were taken with 5- and 50-ml Hamilton glass air-tight syringes with Teflon * plungers equipped with Minert valves. Sampling frequency depended on the total amount of volatile compounds that remained in the soil column after a certain time. The concentration of the target compounds in the injected samples were within the range of FID's calibration curve. In the first few runs, where the concentrations were relatively high, each sample was followed by a blank to eliminate any possible carryover problem. Seventy-two hours after the beginning of operation, a sharp decline was observed in the overall concentration of the effluent gas for both columns. After decreasing to a certain level, the concentration of compounds in the discharged gas started to resemble a long tail which asymptotes the horizontal time axis (Figs. 4 and 5). In order to determine the starting point of the " t a i l " portion of the data points, the effluent concentration of each compound must be plotted separately. In this article, data for trichloroethylene have been employed and the same can be done for other target compounds.

4. Results and discussion

The soil used in this experiment was from a Superfund site where 18 volatile organic compounds have been identified by USEPA (1992) method 8240B. These compounds had been disposed of on site for nearly a decade, therefore the chemicals have had sufficient time to fully penetrate the micropores within the soil grains. The target compounds in this study were benzene, toluene, ethylbenzene, xylenes, trichloroethylene, tetrachloroethylene, chlorobenze, carbon tetrachloride and methylene chloride. For columns I and II, the concentration of trichloroethylene in the discharged gas was plotted as a function of time. Based on equilibrium partitioning of TCE between the aqueous, air and the adsorbed phases during the SVE process in the soil column, a short FORTRAN program was written to determine the starting point of the tailing part of the measured data points(Dahmani et al., 1994). Assuming equilibrium partitioning between the three phases mentioned above the estimated clean-up time for both soil columns was 72 h. As the plots of SVE effluent concentration for TCE suggest, the clean-up time is much longer than the estimated time by the equilibrium model, therefore the data points

33

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21-37

Pore Volume 250 350

500

750

1000

L

l

F

Diffusion and DesorDtion 300 - O - y " " !

i t

I

g 250

~

g

,

i - ! !

200 -

i

150 4~

,

-~

Diffusion

r~

A~"~

I

-

i

I

Desorption

i

i

,i

50000

60000

ox-

03

0

10000

20000

30000

40000

700(10

Time (minutes) Fig. 4. Soil column I, SVE effluent concentration of trichloroethylene as a function of time and pore volume. Diffusion and desorption flux (0), diffusion flux (A), and the desorption flux (O). Solid lines are best exponential fits through the data points. The first seven data points representing the diffusion and desorption flux and the last nineteen data points representing the desorption flux are the values obtained directly from experimental measurements. m e a s u r e d after 72 h of operation were considered as desorption fluxes of T C E to the f l o w i n g air. On the graph an exponential curve is fitted to the tailing part of the data points (Figs. 4 and 5). The equation o f this curve which represents desorption flux and is the same as the second term on the RHS of Eq. (31) is obtained. U s i n g this equation, desorption fluxes for the initial data points which represent the s u m o f the desorption and diffusion fluxes are estimated. W h e n the estimated desorption fluxes are subtracted from the initial data points, the diffusion fluxes are determined. A p p l y i n g a best exponential fit through the estimated diffusion points the first term on the RHS of Eq. (31) is determined. U s i n g the data presented in Figs. 4 and 5, for c o l u m n I Eq. (31) takes the form: Cga~ = 178.86 exp( - 0 . 0 0 0 2 6 7 t ) + 116.5 exp( - 0 . 0 0 0 0 6 9 t ) and for c o l u m n II it is given by Cgas = 76.2 exp( - 0 . 0 0 0 3 5 3 t ) + 36.9 exp( - 0 . 0 0 0 1 3 6 t ) where the concentrations have units of ( n g / m l ) and time is m e a s u r e d in minutes. In order to estimate a , the e q u i l i b r i u m partition coefficient, the total surface area available for adsorption A s , m u s t be k n o w n . A s is the soil specific area and for its estimation different methods are used. O n e of the c o m m o n techniques is the application

34

F, Nadim et a l . / Journal of Contaminant Hydrology 25 (1997) 21-37

Pore Volume

5OO

250

75O

120 Diffusion and Desorption !

100

i I

: .c

80

1

J !

I

I

I

I

iL

g 60

!

J

G

--

r--

i

Diffusion

Deso~tion I t

/

i

q 0 ~ v i

0

r ~

l

4~ i

5000

10000

15000

20000

25000

30000

Time (minutes) Fig. 5. Soil Column II, SVE effluent concentration of trichloroethylene as a function of time and pore volume. Diffusion and desorption flux (Q), diffusion flux (A), and the desorption flux (C)). Solid lines "are best exponential fits through the data points. The first ten data points representing the diffusion and desorption flux and the last nine data points representing the desorption flux are the values obtained directly from experimental measurements.

of the BET model (named after Brunauer, Emmett and Teller) which is based on a kinetic model of the adsorption process as suggested by Langmuir (Gregg and Sing, 1982). The BET method for calculation of specific area involves two steps: evaluation of the monolayer capacity to adsorb the adsorbing gas (nitrogen, argon, krypton, carbon monoxide, carbon dioxide, water or benzene) and conversion of this capacity into surface area by means of the molecular area (German, 1994). The BET model can produce results with a divergence of _+ 10% from the actual area of the solids and is a good tool for the measurement of intraparticle porosity. The specific surface area of the soil used in our study was measured using the valves reported by Ball and Roberts (1991a), for different size fractions. Table 1 shows the results of soil specific area estimation and Table 4 shows the estimated parameters for soil columns I and II. The area of air-liquid contact has been estimated with our model for three different values of overall diffusion coefficients (Table 4). Applying the equilibrium model developed by Dahmani et al. (1994), that assumes instantaneous equilibrium in solid-water and water-air phases during bench-scale vapor extraction at low flow rates (0.01-0.03 1/min), the clean-up level for soil columns I and II will be achieved after ~ 150 and ~ 200 pore volumes of air have passes through the columns. The experimental results indicate that 870 and 980 pore volumes of air are

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 2 1 - 3 7

35

Table 4 Soil column parameters Column I

ColumnII

5.35 × 107 12 714 7.6× 10 -7 7.6× 10-8 6x 10-9

4.9 X 107 25 286 7.6× 10 -7 7.6× 10-8 6x 10.9

a (cm) k (1/min)

5.3× 10 -4 6.9X 10 5

2.34× 10 -4

Fast desorption: 1(cm) diffusionlength ALG (cm2), area of liquid-gas contact

0.084 1.66 X 105

0.073 3.2 X 105

Medium desorption: l (cm) diffusionlength ALe (cm2), area of liquid-gas contact

0.026 5.24× 105

0.023 1.01X 106

Slow desorption: l (cm) diffusionlength AL~ (cm2), area of liquid-gas contact

0.0074 1.86 X 106

0.0065 3.6 X 106

Parameters estimated with existing data: A s " (cmz)

Q (ml/min) C o (ng/ml) Oap p (cm2/min), fast desorption b Dapp (cm2/min), mediumdesorption b Oap p (cm2/min), slow desorption b Parameters estimated with the model:

13.6× 10-5

a Total area of adsorption sites, estimated with values reported by Ball and Roberts (1991b). b Grathwohl and Reinhard (1993).

required to reach the standard cleanup levels for TCE in soil columns I and II, respectively.

S. Conclusions The microscale analysis of transport of volatile organic compounds from the dissolved and adsorbed states into the venting gas during soil vapor extraction suggests that if the characteristic desorption time is long compared to the diffusion time across the liquid layer, there will be a long-time tail in the measured concentration of organics in the effluent gas. The overall process is characterized by the rapid removal of the non-aqueous phase liquid (organics), followed by the dissolved organics from the liquid layer surrounding the soil particles (which produces an exponentially decreasing concentration with a time scale determined by the molecular diffusivity), and finally the slow removal of the organics initially adsorbed onto the soil particle surface or in the vicinal water layer by slow desorption, producing the long-time tail. In the present analysis, a simple first-order rate expression is taken to describe the sorptive process (cf. Eq. (2)), leading to a slow, exponentially decaying long-time tail.

F. Nadim et al. / Journal of Contaminant Hydrology 25 (1997) 21 37

36

The microscale model developed in this work can be used for bench-scale vapor extraction columns. This model may be used to indicate the extent of channeling in bench-scale soil venting systems by estimating the length across which the organic compounds must diffuse in order to reach the venting air. 6. Notation A(s) ALG

A~ a

C(x,t) Co Gout(I ) = Ggas

Cs(t) D or DTc E J k kB l Q S

T l X

a constant of integration area of liquid-gas contact [L2] total site available for adsorption[L2 effective radius of the molecule [L] concentration of dissolved organics [ M / L 3] initial concentration [ M / L 3] concentration of the chemical in the venting gas [ M / L 3] surface concentration of adsorbed organics [ M / L 2] apparent molecular diffusivity of trichloroethylene [LZ/T] flux of organics to the venting gas [M/LZT] desorption rate constant [1/T] Boltzmann constant thickness of the liquid layer [L] volumetric flow rate of the venting gas [L3/T] Laplace transform parameter absolute temperature time [Y] coordinate normal to the soil surface

Greek symbols: OL 7r

bulk/surface partition coefficient [L] viscosity [M/LT] 3.14159...

Scripts: Overbar

dimensionless quantity represents Laplace transform of the variable

Acknowledgements We thank Dr. Shili Liu, Dr. Jiang Shi Kang and Mr. Robert J. Carley for their technical support and laboratory assistance. References Armstrong, J.E., Frind, E.O. and McClellan, R.D., 1994. Non-equilibrium mass transfer between the vapor, aqueous, and solid phases in unsaturated soils during vapor extraction. Water Resour. Res., 30(2): 353-368.

F. Nadim et aL / Journal of Contaminant Hydrology 25 (1997) 21-37

37

ASTM (American Standards of Testing Materials), 1995. Standard practice for dry preparation of soil samples for particle-size analysis and determination of soil constants. Am. Stand. Test. Mater., Washington, DC, Designation: D 421-85, pp. 92-93. Atkins, P.W., 1978. Physical Chemistry. W.H. Freeman, San Francisco, CA. Baehr, A.L., Hoag, G.E. and Marley, M.C., 1989. Removing volatile contaminants from the unsaturated zone by inducing advective air-phase transport. J. Contam. Hydrol., 4: 1-26. Ball, W.P. and Roberts, P.V., 1991a. Long-term sorption of halogenated organic chemicals by aquifer material, 1. Equilibrium. Environ. Sci. Technol., 25: 1223-1236. Ball, W.P. and Roberts, P.V., 1991b. Long-term sorption of halogenated organic chemicals by aquifer material, 2. Intraparticle diffusion. Environ. Sci. Technol., 25:1237-1249. Brusseau, M.L., 1991. Transport of organic chemicals by gas advection in structured or heterogeneous porous media: Development of a model and application to column experiments. Water Resour. Res., 27(12): 3189-3199. Dahmani, A.M., Nadim, F., Hoag, G.E. and Carley, R.J., 1994. Soil vapor extraction treatability tests in support of remedy selection. In: Proceedings of Superfund XV, Federal Environmental Restoration and Waste Minimization. Hazard. Mater. Control Resour. Inst., Rockville, MD, pp. 1047-1056. Davies, B., 1985. Integral Transforms and Their Applications, Springer, New York, NY. Feenstra, S., Mackay, D.M. and Cherry, J.A., 1991. A method for assessing residual NAPL based on organic chemical concentrations in soil samples. Ground Water Monit. Rev., Spring Ed., pp. 128-136. German, R.M., 1994. Powder Metallurgy Science. Metal Powder Industries Federation, Princeton, NJ. Gierke, J.S., 1990. Modeling the transport of volatile organic chemicals in unsaturated soil and their removal by vapor extraction. Ph.D. Dissertation, Michigan Technological University, Houghton, MI, 220 pp. Grathwohl, P. and Reinhard, M., 1991. Sorption and desorption kinetics of trichloroethylene in aquifer material under saturated and unsaturated conditions. Western Region Hazardous Substance Research Center, Tech. Rep. No. 2, Stanford Univ., Stanford, Cal. Grathwohl, P. and Reinhard, M., 1993. Desorption of trichloroethylene in aquifer material: Rate limitation at the grain scale. Environ. Sci. Technol., 27: 2360-2366. Gregg, S.J. and Sing, K.S.W., 1982. Adsorption, Surface Area and Porosity. Academic Press, London. Hildebrand, F.B., 1976. Advanced Calculus for Application. Prentice Hall, Englewood Cliffs, NJ. Hoag, G.E., Baehr, A.L. and Marley, M.C., 1989. Induced soil venting for recovery/restoration of gasoline hydrocarbons in the vadose zone. In: Proceedings of Oil Pollution in Freshwater, Edmonton, Alberta, Canada. Pergamon, New York, NY, pp. 175-194. USEPA (United States Environmental Protection Agency), 1986. Superfund public health evaluation manual. Off. Solid Waste Emergency Response, U.S. Environ. Prot. Agency, Washington, DC, EPA 540/186/060. USEPA (United States Environmental Protection Agency), 1992. Test methods for evaluating solid waste. Physical/chemical Methods: Methods 8240B and 8260A. U.S. Environ. Prot. Agency, Washington, DC, SW-846, 3rd ed. Vesilind, A.P., 1994. The role of water in sludge dewatering. Water Environ. Res., 66: 4-11.