Environ. Sci. Technol. 1994, 28, 1312-1319
Analysis of Diffusion and Sorption of Chlorinated Hydrocarbons in Soil by Single-Pellet Moment Technique Canan Cabbar and Gulgen Do&
Department of Chemical Engineering, Gazi University, Ankara, Turkey Timur Dog,.
Department of Chemical Engineering, Middle East Technical University 06531, Ankara, Turkey Ben J. McCoy and J. M. Smith
Department of Chemical Engineering, University of California, Davis, Davis, California 95616 The single-pellet moment technique was shown to be a powerful method for investigating the diffusion and adsorption of volatile hydrocarbons in the soil. The technique was used to evaluate effective diffusivities, adsorption equilibrium, and rate constants of chlorinated hydrocarbons (monochloroethane,1,2-dichloroethane,l,l,ltrichloroethane, and 1,1,2-trichloroethane). Results obtained in a dry system showed that adsorption rate constants of all these hydrocarbons on the soil pellet used are of the same order of magnitude (4.4-8.0cm3 g-l s-l). On the other hand, molecules having chlorine atoms bonded to the same carbon atom (monochloroethane, l,l,ltrichloroethane) have adsorption equilibrium constants about 1 order of magnitude smaller than these for molecules containing chlorine atoms bonded to different carbon atoms (1,l,Ztrichloroethane, 1,2-dichloroethane).
Introduction The contamination of the soil subsurface by volatile organic compounds has become an active area of environmental research (1-3). Among these pollutants, chlorinated and brominated hydrocarbons have attracted special attention (4-8) due to their frequent presence in the soil gas and groundwater and to their adverse health effects. The migration of pollutants in soil involves both transport (diffusion and convection) and adsorption processes. Transport by diffusion strongly depends on the pore structure of the soil. Adsorption depends on surface area (hence pore structure), composition, and moisture content. Because of the importance of soil remediation, transport and sorption studies for soil contaminants have attracted considerable attention in recent years (9,IO). Considering linear processes for the interaction of trace organics with soil, Pirvoni et al. (11) investigated the sorption of volatile organic compounds from aqueous solution onto soil surfaces. Rate processes, such as sorption or volatilization, may affect the spread of pollutant and may sometimes be difficult to distinguish from transport effect (12). In the recent literature, mathematical modeling studies for contaminant transport in soil have been published (2, 13-16). More recently, Doiu et al. (17)investigated irreversible and reversible adsorption of benzene in soil. Steinberg et al. (7) and Aochi et al. (18) reported detailed information for the
sorption, desorption, and entrapment of 1,2-dibromoethane in soils. They showed that a conceptual model of a clay as a dielectric medium was successful in explaining the observed results. The work of Brusseau et al. (19)provided strong evidence that intraorganic matter diffusion was responsible for the nonequilibrium sorption of hydrophobic organic chemicals by natural sorbents. Gschwend and Wu (2, 4) showed that hydrophobic sorption is reversible, and they proposed a radial diffusive penetration model to describe the microscale partitioning of sorbate between the pore fluid and the solid grains. In this work, a simple dynamic method previously used successfully for catalyst pellets (20,211 was proposed for studying diffusion and adsorption of contaminants in soil. It was shown that simultaneous evaluation of adsorption equilibrium and rate constants as well as effectivediffusion coefficients of organic pollutants in soil can easily be made with this technique. The technique was used to determine diffusion and sorption characteristics of monochloroethane, 1,2-dichloroethane, l,l,l-trichloroethane, and 1,1,2-trichloroethane in a soil pellet of known chemical and physical properties. The original method has been later modified to analyze diffusion and adsorption processes in bidisperse porous catalysts (22,23)and to evaluate diffusion and conduction in porous solids (24). More recently, the technique was adopted to investigate diffusion and viscous flow in porous media (25). Alkharasani and McCoy (26) showed that, using a moment technique in a chromatographic column the relative effects of gas-solid adsorption and gas-liquid absorption could be successfully investigated. Method and Theory
* To whom all correspondence should be addressed; e-mail:tdoiu at trmetu.
In this technique, a single-pellet cell was used to investigate diffusion and adsorption in soil pellets. The soil pellet was prepared by pressing the soil into a ringshaped stainless steel holder and then placing it into the single pellet cell. Details of the single-pellet cell are reported in the literature (17,20, 21, 24,27). Inert gas (e.g., nitrogen) streams passed over both end faces of the soil pellet (Figure 1). Adsorbing (chlorinated hydrocarbons in this work) or inert (helium) tracers were injected as pulses into the stream flowing over one end face (upper face) of the cylindrical pellet. A fraction of the tracer is expected to diffuse through the pellet to the other end face. In order to eliminate any convective transport through the pellet, the pressures of the carrier gas streams in the upper and lower chambers of the cell
1312 Environ. Sci. Technol., Vol. 28, No. 7, 1994
0013-936X/94/0928-1312$04.50/0
0 1994 American Chemical Society
Upper carrier gas- stream
r-
I
I
Tracer -------I Injection
I
bI
I
Table 1. Chemical Composition (Dry)of Soil Pellet.
I
4-I J
Si02 Ti02 Al2Oa Fez03 FeO
I
I
I I
I
-
P
MgO
6.36 0.41 2.02 0.68 0.34 0.09
S
x = 0 [CA = M 6(t)l and with a flux boundary condition at x = L:
I 1
CaO Na2O C H N
MnO a Clay types: simectite, kaolin, and illite.
I I
Detector
66.73 1.52 13.40 6.23 1.86 2.20 0.09
1
(5)
Detector
I
U Figure 1. Schematic dlagram of experlmental setup used In slnglepellet dynamic studies.
were adjusted to be the same, and pressure equality was observed by a U-tube manometer. Response peaks were measured, by FID or TCD detectors, in the carrier gas stream leaving the lower face of the pellet. From the time delay of the response curve, the effective diffusivity and adsorption equilibrium constant for the tracer in the soil can be determined. For an adsorbing tracer, the pseudohomogeneous differential speciesconservation equation for the porous pellet can be expressed as
ac,
-p at
a2cA
-De-ax2
ppNA
Here, De corresponds to the effective diffusion coefficient of the tracer in the pellet. For a linear, reversible process, the adsorption rate, NA,is given by
The moment expressions were then obtained using eq 4. Details of the derivation and boundary conditions and the assumptions involved are discussed by Do& and Smith (20)and Burghardt and Smith (28). The major assumptions of the boundary condition at x = L are complete mixing and negligible accumulation in the lower chamber of the cell. It was shown in the literature (20, 21) that these assumptions introduce negligible error for high flow rates of the carrier gas flowing through the lower chamber. First, the absolute moment expression for a reversibly adsorbed tracer is
By taking p & ~ = 0 in eq 6, the corresponding equation for an inert tracer can be obtained. The second moment expression for a reversibly adsorbed tracer is
(?)’(++Y( 1
$3.). +
($le,” + 6(3.
+ F)2
where K A is the adsorption equilibrium constant and 12, is the adsorption rate constant. Adsorption linearity can be assumed for very low concentrations of the tracer. For an inert tracer, NAbecomes zero. The nth moment of the response peak at x = L is defined as Experimental Section m, = cCA(L,t)tndt
(3)
Theoretical moment expressions are obtained using the following relation between the nth moment and the Laplaceion of the tracer at x = L: (4)
Equations 1and 2 were solved in the Laplace domain for CA(X:,S) with a Dirac delta function boundary condition at
Aschematic diagram of the experimentalsetup is shown in Figure 1. The single-pellet cell was placed into the oven of a gas chromatograph (Varian Vista 6000) in place of the column. The length and cross-sectional area of the cylindrical pellet are 0.29 cm and 1.43 cm2, respectively. The soil was obtained from the Afyon region of Turkey. Its chemical composition (Table 1) was determined using spectrophotometric and analytical techniques. A Shimadzu ICPS (inductively coupled plasma source) spectrophotometer and a Unicam SP600 spectrophotometer were used for the analysis of the inorganic fraction of the Environ. Sci. Technol., Vol. 28, No. 7, 1994
1313
0.15681 0.1411 -
I
A
0 T = 90°C
*/
0. I255 -
b T = 70°C v T : 50°C
A T=35OC
7-
m
0.1098-
m '
E
"- 0.0941 -0" 0.0785 -
6-
L
>
I
C .E
-
0.0627-
u .0.0470-
15-
c
e
0.0314 -
E
0
0.0157 -
E 4 0)
V
-z c
0
VI
n o c
Pore radius, r ( p r n )
L
Figure 2. Differential pore size distribution of the soil pellet. ~
~ ~ ~ _ _ _ _ _ _
2-
Table 2. Physical Properties of Soil Pellet
total porosity (cm3/cm3) macro porosity (porosity corresponding to pores greater than 3.56 X 103 pm in radius (cmS/cm*) apparent density, pp (g/cm3) solid density (g/cm3) surface area (m2/g)
0.49 0.36
Environ. Scl. Technol., Vol. 28, No. 7, 1994
l -
01
0.4
1.52 2.91 23.9
clay (27). Elemental analysis of organic matter and total sulfur were determined using Leco total sulfur and carbonhydrogen-nitrogen analysis instruments. In this instrument, the organic fraction is burned, and gaseous effluents were analyzed. I t was also determined by X-ray diffraction that the soil contained simectite, illite, and kaolin-type clays. The clay fraction was separated, and X-ray diffraction patterns were determined for dried and treated (in ethylene glycol) samples (27). The total porosity, apparent density, and pore size distribution of the pellet were measured using a Quantachrome 60 mercury intrusion porosimeter, and the solid density was determined using a (Micrometrics) helium pycnometer. The pore size distribution obtained from the mercury intrusion porosimeter is given in Figure 2. The surface area of the pellet was also determined using a Quantachrome sorptometer. These techniques are described in the literature (37). Physical properties of the soil pellet are summarized in Table 2. The differential pore size distribution (Figure 2) shows a minimum for a pore radius of 3.56 X 10-3 pm. Pores larger than this size are considered as macropores. The macroporosity of the pellet was 0.36. The sorption and transport characteristics of monochloroethane, 1,2-dichloroethane, l,l,l-trichloroethane, and 1,1,2-trichloroethane were investigated with pulse-response measurements. These experiments were conducted at different lower stream flow rates and at different temperatures. Before these experiments, the pellet was dried at 110"C. All the results are based upon a dry system. Initial experiments were carried out to test the reversibility of adsorptin of these hydrocarbons on the soil sample. In these experiments, detectors (FID) were placed in the streams leaving both end faces of the pellet. Also, 1914
3-
.LL
I
0.8
I
I
I
I
2.0 2.4 Lower carrier flow rate, F, (crn3/s) 1.2
1.6
2.0
Figure 3. First absolute moment data for monochloroethane. Lines are model fitted (eq 6) based on the De and p,KA values reported In Tables 3 and 4.
the amount of the input tracer was measured by conducting pulse-response experiments in a system where the detector was placed to the flow line just after the injection port. A material balance around the single-pellet cell showed that for all these tracers the adsorption process is reversible for the temperature range 35-90 "C (27). A major assumption of moment analysis is the linearity of the processes involved. In order to satisfy this linearity, pulse-response experiments were conducted with a very small amount of the tracer for which linear adsorption isotherms are generally justified. This was confirmed by pulse-response experiments with different amounts of tracers (27).Results of these experiments indicated that the moments were not altered by the amount of the sample. Monochloroethane boils at 13 O C at atmospheric pressure, so it was kept at 0 "C in a closed bottle containing a septum. Samples were taken from the vapor space of the bottle using a gas-tight syringe. Most of the experiments were conducted with an injection volume of 0.1 mL for monochloroethane. For the other hydrocarbon tracers, 0.5 p L of liquid samples was injected to the injector of the chrornotograph where it evaporated before entering the single-pellet cell.
Results and Discussion Experimental first moment values obtained at different temperatures with monochloroethane are given in Figure 3 (pellet length = 0.29cm). These values were corrected for the retention times in the dead volumes. The figure shows that the first moment values decreased from about 5 to 0.5 min as the temperature increased from 35 to 90 "C. This is caused by the temperature dependence of the
I2
Table 3. Effective Diffusivities of Helium and Monochloroethane in Soil Pellet Used (c = 0.49)
0 L = 2.99cm 0 L * 0.29cm
70 90 50 temperature ("C) 35 4.9 4.5 5.5 helium, Ap1,- (s) 5.6 0.129 0.132 0.148 0.161 helium, De (cm2/s) monochloroethane,4De (cm2/s) 0.021 0.022 0.025 0.028 4 De values of monochloroethane are evaluated based upon tortuosity factor determined from the He tracer.
1
-+-
0
0.4
0.8
1.2 1.6 2.0 2.4 2.8 Lower carrier flow r o t e , F,(ml/s)
3.2
Flgure 4. First absolute moment data for helium tracer ( T = 50 sample size = 0.25 mL).
3.6
"C;
adsorption equilibrium constant. The first absolute moment expression given in eq 6 is used to evaluate the adsorption equilibrium constant. The limit of eq 6 for high values of the lower stream flow rate, F,is
In eqs 6 and 8, there are two unknowns, namely, p& and De. These two unknowns can be evaluated from eq 6 using a regression analysis at a given temperature. A more accurate procedure is to determine De from independent diffusion data and then evaluate p&, by regression analysis of the first moment data for the hydrocarbon tracers. To evaluate the effective diffusion coefficients in the porous soil pellet, the tortuosity factor is required. For this purpose, pulse-response experiments were conducted with a helium (nonadsorbing) tracer in nitrogen carrier gas at different temperatures. Helium response peaks were detected using a thermal conductivity detector. Typical first, absolute moment data obtained with helium tracer are shown in Figure 4 for 50 "C. Experiments were repeated with two pellets of identical physical and chemical properties but of different lengths (2.99 and0.29 cm). Then, the differences between the first moments obtained with these two pellets (Ap1) were used to calculate the effective diffusivity. By taking the difference of first absolute moments, dead volume corrections, which are significant in inert tracer runs, cancel. For large values of the lower flow rate, F, the expression for Apl becomes
With the data in Figure 4, the effective diffusivity of helium was determined as 0.132 cm2/s a t 50 "C. The calculated curve for Apl with this diffusivity value was also illustrated in Figure 4. The results for helium at different temperatures are summarized in Table 3. The tortuosity factor of the pellet was determined from
where for a dilute system DT can be expressed (30) as
DT = 1 DAB
1 D,
In this calculation, the tortuosity factor was evaluated on the basis of macroporosity. By considering a porous solid with a bidispersed pore size distribution, it was shown in our previous papers (22,23)that the diffusion coefficient obtained from the first moment data corresponded to the macropore diffusion coefficient. Both molecular and Knudsen contributions might be significant in macro- and mesopores. On the other hand, in micropores, where mean free path is much greater than the pore size, Knudsen diffusion dominates (30). The effective diffusion coefficient is a very strong function of pore structure. The experimental values reported here correspond to a specific soil with a given pore structure (porosity 0.49). With the pore size distribution data given in Figure 2, Knudsen diffusivity of helium was calculated to vary between 4.34 and 4.72 cm2/s in the temperature range of 35-90 "C, respectively. The tortuosity factor of the pellet was then calculated as 1.8(27).No significant variation of tortuosity was observed with temperature. With this tortuosity factor, effective diffusivities of the hydrocarbon tracers were evaluated from eq 10 and are reported in Tables 3 and 5. KnowingDelp & ~values were determined from the first moment expression (eq 6). The adsorption equilibrium coefficients for monochloroethane at different temperatures are reported in Table 4. The temperature dependence of the adsorption equilibrium consant, p & ~ , of monochloroethane is illustrated in Figure 5. From the slope of this curve, the heat of adsorption was found as-7.9 kcal/mol. This result suggests that monochloroethane is physically but rather strongly adsorbed on the soil without chemical bonding. Adsorption equilibrium constants of different chlorinated hydrocarbons, namely, monochloroethane, 1,2dichloroethane, l,l,l-trichloroethane, and 1,1,2-trichloroethane, were evaluated from the pulse-response experiments conducted with these tracers at 90 "C. The effective diffusivities of these tracers are also evaluated from eq 10. The first absolute moment data obtained with these tracers are shown in Figure 6 , and the resultant p& values are shown in Table 5. In the same table (Table 51, adsorption rate constant values for the different tracers are also shown. These values were determined from the experimental second central momenta (Figure 7) evaluated from the response curves of the pulse-response experiments. In the evaluation of adsorption rate constant, eq 7 was used. With the effective diffusion coefficient and adsorption equilibrium constant from the first moment analysis, the rate constant is the only unknown in eq 7. Envlron. Scl. Technol., Vol. 28, No. 7, 1994
1315
Table 4. Adsorption Equilibrium Constants of Monochloroethane at Different Temperatures
temp ("C) 35 50
Table 5. Diffusion and Sorption Parameters of Different Chlorinated Hydrocarbons in Soil'
temp ("C)
P&A
460 256
tracer
P&A
204 56
70
90
De (cm2/s)
k , (cm3g' s-1)
P&A
monochloroethane 0.028 56 8.0 1,2-dichloroethane 0.022 568 4.9 l,l,l-trichloroethane 0.020 46 4.4 1,1,2-trichloroethane 0.020 896 6.5 De values are calculated based upon the tortuosity factor of 1.8, using eq 10. T = 90 "C; cp = 0.49; L = 0.29 cm.
' 00 O0I 10 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30
( I / T ) x IO3,
0 I, I, 2 Trichloroalhane
A i,2
Dichloroethane Trichloroelhane 0 Monochloroethane
OK-'
I
Figure5. Temperature dependenceof absorptionequilibrium constant of monochloroethane. ~
E 50-
~~~~
E
0 I, I , 2 -Trichloroethane A I, 2 Dichloroelhane I , i , I Trichioroethone 0 Monochloroethane
-
-;I
A
0
k 40-
0
\
,I, I
'.'.
W
U c 0
x
30-
A
v)
-2,
0.2
m
-- ----*-.'-e----- --- %-&-a---g-2,
0 e
e
e
-I
0
0
O . 1
-0 4
08
12
16
20
24
28
Lower carrier flow rote, F, (cm3/s) Flgure 7. Second central moment data for different chlorinated hydrocarbons (T = 90 O C ) .
0 0.4
0.8
1.2
1.6
2.0
2.0
2.8
Lower carrier fiow rate, F, (cm3/s) Flgure 8. First moment data for different chlorinated hydrocarbons (T = 90 "C). Lines are model fitted (eq 6) based on the De and p,KA values reported in Table 5.
The results given in Table 5 show that adsorption rate constants of the different chlorinated hydrocarbons investigated in this work are all in the same order of magnitude, ranging from 4.4 to 8.0 cm3 g-l s-l. The adsorption rate constant of monochloroethane was also determined at different temperatures by Cabbar (27) and ranged from 7.3 cm3 g-l s-l at 35 OC to 8.0 cm3 g-l s-l at 90 "C.This small variation indicated that the activation energy of the adsorption rate is small, again suggesting 1316 Envlron. Sci. Technol., Vol. 28, No. 7, 1994
physical adsorption. For all these tracers, the rates of adsorption are close to each other. On the other hand, significant differences were found for the adsorption equilibrium constants. Adsorption equilibrium constant (p&d values of monochloroethane and l,l,l-trichloroethane are in the order of magnitude of 50 at 90 "C while the corresponding values of p&, for 1,Zdichloroethane and l,l,Ztrichloroethane are 10-15 times larger, respectively (Table 5). Although the dipole moment of monochloroethane (1.99 x 10-18 esu) is higher than the mean dipole moment of 1,2-dichloroethane r1.12 X 10-18 esu at 305 OK (3211, its adsorption equilibrium constant is 10 times less. As it was discussed by Mizushima (32),Duthiewicz et ai. (33), and Aochi et al. (18), 1,2-dichloroethane has two stable configurations, namely, the trans (anti) and gauche forms (Figure 8). The relative abundance of trans form is about three times larger than the gauche form in vapor phase (18). On the other hand, in the liquid phase the ratio of gauche form to trans form is higher (about 1.3). In the
CI
CI
CI
b
QA trons form
gauche form
I, 2 dichloroethane
0
b
H
CI
H
2.00
2.50
1.50
Lower flow rote, F, (cm3/s)
CI
H
I
1.00
Figure 9. Zeroth moment data for different chiorlnated hydrocarbons ( r = 90 "c).
' H
H
I, I, 2 trichloroethane Flgure 8. Stable configurations of 1,2dichloroethane and 1,1,2trichloroethane.
recent work of Aochi et al. (18), the sorption of 1,2dibromomethane on clay mineral surfaces was investigated by diffuse reflectance infrared spectroscopy. Their results indicated that gauche form is the major configuration in the adsorbed state. Similarly, in the adsorption of 1,2dichloroethane on cationized zeolyte, it was reported that the population ratio of the gauche and trans forms is about 5-fold that of the pure liquid (33, 34). This effect is attributed to the strong field existing at the phase boundary. All these results indicate that the most stable form of 1,2-dihalogenoethane in the adsorbed state is the gauche configuration. The measured dipole moment of 1,2-dichloroethane (1.12 X 10-l8esu) is the mean value of trans and gauche configurations. The dipole moment of the trans configuration is considered as zero. Mizushima (32) reported the calculated value of the dipole moment of the gauche form of lY2-dichloroethaneas 2.55 X 10-l8 esu. This result shows that the gauche form of 1,2dichloroethane is more polar than monochloroethane. As a result, the gauche form of 1,2-dichloroethane is much more strongly adsorbed than monochloroethane on soil. The presence of the gauche form as the major configuration in the adsorbed state of 1,Zdichloroethane indicates that the rotation of the molecule along the carbon-carbon axis is considerably hindered in the adsorbed state. It might as well be that lY2-dichloroethaneis adsorbed on the surface from both ends by the involvement of both chlorine atoms connected to different carbon atoms. Two adjacent sites on the surface might participate in this sorption process. Of course, steric effects and pore and surface structure of the clay as well as the forces of attraction may have influence on the preferential sorption of the gauche form. The difference of adsorption equilibrium constants of l,l,l-trichloroethane and 1,1,2-trichloroethane can also be explained with a similar discussion. The dipole moment of l,l,l-trichloroethane (1.79 X lP1*esu) is larger than the mean dipole moment of 1,1,2-trichloroethane (1.22 x 10-l8esu), but yet its adsorption equilibrium constant is about 15 times less than the adsorption equilibrium
constant of 1,1,2-trichloroethane. The only difference between these two molecules is the position of the third chlorine atom. As it is reported by Mizushima (33),1,1,2trichloroethane has two stable configurations (Figure 8), and one of these configurations is much more polar than the other. The more polar configuration is expected to be adsorbed on the surface more strongly. All these results indicated that, for the chlorinated hydrocarbons investigated in this work, the molecules having chlorine atoms bonded to the single carbon atom are less strongly adsorbed to the clay surface than the molecules containing chlorine atoms bonded to different carbon atoms. Since the adsorption rate constant of all the chlorinated hydrocarbons investigated in this study are in the same order of magnitude, it was concluded that the desorption rate constants of 1,Zdichloroethane and 1,1,2-trichloroethane are an order of magnitude smaller than the desorption rate constants of monochloroethane and l,l,l-trichloroethane. In the previous analysis, the effective diffusion coefficients were evaluated from eq 10using a tortuosity factor of 1.8. I t is also possible to evaluate the effective diffusion coefficients from zerothmoment data. For both inert and adsorptive tracers, the rearranged form of the zeroth moment expression is
M _ - 1+-FL
*,
*De
The effective diffusivity may in principle be determined from the slope of this relation. Even a single M/m0value obtained at a high value of F is sufficient in this analysis. However, an independent measurement of M is required. For this purpose, pulse-response experiments were carried out by placing an impermeable Teflon plate over the pellet and by detecting the response peak leavingthe top chamber of the single-pellet cell. The area under the curve of this peak corresponds to M. These calibration experiments were repeated for different hydrocarbons. Results obtained at 90 "C with different chlorinated hydrocarbons are shown in Figure 9. As discussed in the Method and Theory section, the boundary conditions of the model are justified only at high flow rates of carrier gas. For this reason, data obtained for F values greater than 1.4 cm3/s were used. From the slopes of the linear relations with an intercept of unity, the effectivediffusivitieswere evaluated, and the results are tabulated in Table 6. For monochloroethane, similar analysis was made with the data obtained a t different temperatures. For instance, at 35 "C,the D, Environ. Scl. Technol.. Vol. 28, No. 7, 1994
1317
14
Table 6. Effective Diffusion Coefficients of Different Chlorinated Hydrocarbons Obtained by Two Different Approachesa
tracer
De(cmZ/s)*
De(cm2/s)c
monochloroethane 1,2-dichloroethane l,l,l-trichloroethane 1,1,2-trichloroethane
0.028 0.022 0.020 0.020
0.029
0.034 0.020
0.022
T = 90 OC,tp = 0.49;L = 0.29 cm. Using tortuosity, eq 9. From zeroth moment data, eq 12.
0 l , l , 2 Trichloroelhanetpure I , l , Z Trichloroeihanelmixl 1,l.I Trichloroethane(pure I,I,I Trichloroethane ( m i x :
1.
0
I3
c .-
12
E
-E < I
II
a
value evaluated from zeroth moment analysis is 0.022 cmz/s while the corresponding value evaluated from eq 10is 0.021 cm2/s. The effective diffusivities determined from the zeroth moment data and the corresponding values evaluated from eq 10are in good agreement, except for 1,2-dichloroethane. For this hydrocarbon tracer, the value from the zeroth moment data is about 50% larger than the corresponding value from eq 10. Surface diffusion might be a possible explanation for this difference. 1,2-Dichloroethane is rather strongly adsorbed on the soil (Table 5), and surface diffusion might play a significant role, especiallyfor tracers having high adsorption equilibrium constants. In a recent work, Miller an Pedit (29) explained the hysterysis of adsorption-desorption processes by a surface diffusion model. It was interesting to note that 1,1,2-trichloroethane, which is more strongly adsorbed than 1,2-dichloroethane, did not show a significant difference in diffusion coefficients evaluation by the two procedure. Surface diffusion is generally considered to become significant with appreciable adsorption, yet if adsorbed molecules are held so strongly as to be essentially immobile, surface diffusion will be insignificant. All the previous data correspond to single tracers. To assess interference of these tracers when they are injected into the adsorption cell simultaneously, a set of experiments was carried out with a mixture of tracers containing 20 % l,l,l-trichloroethaneand 80 % 1,1,2-trichloroethane. These experiments were done at 90 "C with a sample size of 0.5 pL. As discussed in the previous section, adsorption equilibrium constants of these two tracers are very different. The first moments of these two tracers are more than an order of magnitude different, and consequently, almost complete separation of the peaks was possible. Comparison of first moment data obtained with pure components and the mixture (Figure 10) indicated that the simultaneous presence of the hydrocarbons did not effect the sorption parameters. The amount of the tracer is very small, and the system is sufficiently dilute so that independent linear adsorption of hydrocarbons is a justifiable assumption. Similar conclusionswere obtained from the second moment data. The adsorption equilibrium and rate constants of l,l,l-trichloroethaneand 1,1,2trichloroethane obtained from pure tracer and mixture experiments are summarized Table 7. Results of this work showed that adsorption equilibrium and rate constants of volatiile hydrocarbons can easily be determined by the single-pellet technique and that significant information can be extracted about the sorption process. All the experimental data reported in this paper correspond to a dry system. Yet, the use of the singlepellet moment technique is not limited to dry systems. The experimental system can easily be modified to conduct pulse-response experiments with pellets and carrier gas 1318
Envlron. Sci. Technol., Vol. 28, No. 7, 1994
al
1.2
f 0 Y) 9 0 c Y)
;.
0.0
0.4
0 0
0.0
1.2 1.6 2 .O 2.4 Lower carrier gas flow rate, F, (cm3/s)
2 .e
Figure 10. First moment data for pure components and mixture of
1,1,2-trichloroethaneand l,l,l-trichloroethane. Table 7. Adsorption Equilibrium and Rate Constants of l,l,l-Trichloroethane and 1,1,2-Trichloroethane (Pure Tracer and Mixture Data)a
tracer (pure) l,l,l-trichloroethane (mixture) l,l,l-trichloroethane (pure) 1,1,2-trichloroethane (mixture) 1,1,2-trichloroethane a T = 90 "C.
P&A
46 41 896 884
k , (cm3/g18-l)
4.4 4.5
6.5 6.6
streams containing controlled amounts of moisture. For a moist pellet, the theoretical model equations require modification. Partitioning and adsorption in gas-liquidsolid chromatography are considered in recent literature (31), and moments are reported for a packed column. Similar derivations are required for the single-pellet system. For nonlinear adsorption isotherms, perturbation procedures suggested by Allal et al. (35)and by Dogu (36) might be used in the modification of theoretical analysis. Acknowledgments
The experimental work conducted as part of the Ph.D. thesis of C.C. in Gazi University is partially supported by Turkish State Planning Organisation. NSF Grant INT9108455 made possible the collaboration between researchers at Gazi University in Turkey, Middle East Technical University in Turkey, and University of California at Davis and is gratefully acknowledged. No tat ions
area of end face of pellet (cm2) concentration of tracer (mol/cm3) € A ( x , s ) Laplace transform of function C A ( x , t ) DAB molecular diffusivity of A in B (cm2/s) DKA Knudsen diffusivity of tracer (cm2/s) De effective diffusivity (cm2/s) A
CA
F
k, KA L
M mn
nA s t
lower stream volumetric flow rate (cm3/s) adsorption rate constant (cm3 g1s-l) adsorption equilibrium constant (cm3/gof catalyst) length of pellet (cm) strength of the input pulse (mol s cm-9 nth moment defined by eq 6 adsorbed concentration of the tracer (mol adsorbed/g) Laplace variable (8-l) time (s)
Greek Letters tP 111 112
A111 PP T
porosity of the pellet first absolute moment, ml/m, (8) second central moment as defined by eq 10 difference of first absolute moments (8) pellet density (g/cma) tortuosity factor
(82)
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Received for review November 3, 1993.Revised manuscript received March 31, 1994.Accepted April 5, 1994." ~
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Abstract published in Advance ACS Abstracts, May 1, 1994.
Environ. Scl. Technol., Vol. 28, No. 7, 1994 1919
