Environ. Sci. Technol. 2004, 38, 4580-4586
Modeling of TCE Diffusion to the Atmosphere and Distribution in Plant Stems XINGMAO MA AND JOEL BURKEN* Department of Civil, Architectural and Environmental Engineering, Butler-Carlton Hall, 1870 Miner Circle, University of MissourisRolla, Rolla, Missouri 65409
Fate of chlorinated solvents in phytoremediation has been delineated by many discoveries made in recent years. Plant uptake, metabolism, rhizosphere degradation, accumulation, and volatilization were shown to occur to differing degrees for many organic contaminants including chlorinated solvents. Among these mechanistic findings, recent research confirmed that volatile organic compounds (VOCs) volatilize from stems and that the resulting diffusive flux to the atmosphere is related to exposure concentration and to height up the stem. A comprehensive model was developed based upon all identified fate and transport mechanisms for VOCs, including translocation in the xylem flow and diffusion. The dispersion and diffusion in the radial direction were considered as one process (effective diffusion) as the two could not be investigated individually. The mechanism-based model mathematically indicates an exponential decrease of concentrations with height. While an analytic solution for the comprehensive model was not attained, it can serve as a starting point for other modeling efforts. The comprehensive model was simplified in this work for practical application to experimentally obtained data on trichloroethylene (TCE) fate. Model output correlated well with experimental results, and effective diffusivities for TCE in plant tissues were obtained through the model calibrations. The simplified model approximated TCE concentrations in the transpiration stream as well as TCE volatilization to the atmosphere. Xylem transport, including advection, dispersion, and diffusion through cell walls with subsequent volatilization to the atmosphere, is a major fate for VOCs in phytoremediation.
Introduction Fate of organic contaminants in phytoremediation has been shown to include uptake and accumulation, rhizodegradation, and phytodegradation. When volatile organic compounds (VOCs) are treated with plants, their transfer to the atmosphere is possible based upon physicochemical properties, in particular, the Henry’s law constant (KH) and vapor pressure (VP) of the particular VOCs (1). Research at the Savannah River Site in South Carolina indicated decreasing TCE concentrations along the transpiration path (i.e., with height up the trunk), and a hypothesis was posed that diffusive loss was through stems rather than from leaves as previously assumed (2). TCE volatilization from stems was recently confirmed by direct measurement (3). Diffusive flux from stems was related to height, with lower TCE diffusion flux as height up the stem (trunk) increases. * Corresponding author phone: (573)341-6547; fax: (573)341-4728; e-mail:
[email protected]. 4580
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Uptake of organics by vegetation is well-documented, and numerous models describing such uptake have been developed (4-6). One of the most comprehensive models regarding chemical uptake and translocation was developed by Trapp, which described the uptake and translocation of ionized chemicals, nonionized chemicals, and acids and bases on the molecular level (7). An initial model concerning the accumulation of chemicals in plants was presented by Boersma et al. (8). The model was based on a soybean plant and conservation of mass law. The model divided plants into 18 compartments, and chemicals were assumed to transfer by diffusion and transport from one compartment to another (8). The model output matched well with data on bromacil (C6H13BrN2O2) uptake by soybean (9). A similar but simpler model was constructed by Trapp and colleagues from a different approachsfugacity (10). Fugacity describes the “escaping tendency” of a chemical substance from a phase, and the fugacity in different phases equals each other at equilibrium. Four compartments were identified in the model, namely, air, soil, roots, and shoots. Transfer processes were tracked between each compartment, and equilibrium was assumed by equaling the fugacity of each compartment. The final output of the simulation was the bioconcentration factor (BCF), which indicates the accumulation of contaminants in different compartments. Many of these models were developed on the basis of laboratory experiments conducted with small plants and agricultural chemicals. Therefore, mechanisms relating to volatility were not considered as the majority of agrochemicals are inherently nonvolatile. With respect to plant atmosphere interaction, only the aerial uptake by plant leaves has been considered at length, neglecting the possible volatilization of contaminants from plant shoots or plant stems to the atmosphere after uptake by roots. With phytoremediation, plants such as hybrid poplar trees have been intentionally used to treat soil and groundwater contaminated by VOCs such as TCE. In such directed interactions of plants and VOCs, the transfer of contaminants to the atmosphere has been proven (3). Research also showed that contaminants’ concentration in stems was related to height and radius of plants (2, 3, 11). In earlier work on modeling phytoremediation of methyl tert-butyl ether (MTBE), a mathematical model was developed to simulate the distribution of MTBE in alfalfa plants, and diffusion coefficients were estimated based on 50% decrease of MTBE concentrations in the transpiration stream (11). However, the work did not provide a quantitative model to estimate the diffusion of contaminants from stems. In addition, the flow patterns of transpiration stream in the alfalfa plants were neglected, assuming that the transpiration stream was conducted uniformly along the stem and the highest concentration was found in the center. Hence, new efforts to mathematically model contaminant transport and distribution in large, woody plants and contaminant transfer to the atmosphere are desired in order to better understand the phytoremediation of volatile compounds. The current understanding of the plant anatomy and flow patterns in stems constitutes the fundamental basis for the modeling. Flow patterns are closely related to the xylem structures and components. Three principal xylem anatomies exist, varying in the proportions and arrangements of vessel members, tracheids, fibers, and parenchyma cells, and anatomies are species dependent. The hybrid poplar trees fall into the category of “diffuse porous” species, which are featured by the presence of both tracheids and vessels, with vessels uniformly scattered among the tracheids and other 10.1021/es035435b CCC: $27.50
2004 American Chemical Society Published on Web 07/28/2004
FIGURE 1. Donut ring configuration of the model. Model element of tree stem (trunk) with flux terms for the contaminant TCE. cells of each annual growth ring (12). Conduction is primarily through the vessels scattered throughout several annual growth rings of the outer sapwood. Research on poplar and willow revealed sap flow and water transfer are dominated by the outermost 4 cm of sapwood (13). In other research with a hybrid poplar (Populus euramericana) with a 29 cm diameter stem, sap flow was also conducted primarily in the outermost 4 cm sapwood, with flow decreasing progressively inward, reaching zero at 8 cm from the outer surface of the trunk. For a Populus nigra tree with a 22 cm diameter stem, transpiration flow decreased abruptly at 4 cm. No transpiration was observed in deeper sapwood with the Granier technique for quantifying transpiration flow rate. For young trees, the active sapwood can represent roughly half of the trunk (13). As the water is dominantly transported in the most recent annual rings of the exterior, near the surface, the potential for diffusive loss to the atmosphere is high. For that reason, this paper models the migration of VOCs to the outer surface of the stems and the subsequent diffusion through the stem-atmosphere interface.
Materials and Methods Model Description. The main mechanisms considered in model formulation were (i) advective transport upward in xylem; (ii) advective transport downward in phloem; (iii) sorption and desorption between transpiration stream and biomass; (iv) dispersion and diffusion; and (v) metabolism. The term “effective diffusion” is used to describe the combined diffusion and dispersion processes, particularly in the radial direction. The downward transport of contaminants in phloem was neglected due to the relative insignificance as compared to the upward flow rate in xylem. The tree stem was also simplified as a cylinder in the model. When considering the geometry and the dominance of the outer annular rings, a “donut ring” model was considered with model element height of ∆z and effective conductive thickness in the radial direction of ∆r (Figure 1). ∆z and ∆r are interchangeable with ∂z and ∂r. To develop the mass balance for the model, each process involved was described mathematically as follows: Vertical TCE flux into the control volume:
J(z) )
Q(r)C(r,z) ∂C(r,z) - Dz 2πr∆r ∂zr,z
(1)
In eq 1, the flux in the vertical direction is composed of the water conduction and effective diffusion. 2πr∆r approximates the horizontal surface area of the element. Vertical TCE flux out of the system:
J(z + ∆z) )
Q(r)C(r,z + ∆z) ∂C(r,z + ∆z) - Dz 2πr∆r ∂zr,z+∆z
(2)
Effective diffusive flux to/from the inner circle:
J(r) ) -Dr
∂C(r,z) ∂rr,z
(3)
Effective diffusive flux to/from the outer circle:
∂C(r + ∆r,z) J(r + ∆r) ) -Dr ∂rr+∆r,z
(4)
Sorption/desporption:
dA ) KdC ′(r,z) × δ × 2πr∆r∆z - KaC(r,z) × 2πr∆r∆z dt (5) where A is the mass change of the contaminants in the liquid phase due to the sorption/desorption processes, C ′(r,z) is the sorbed contaminant concentration in the solid biomass, δ is the biomass density in the unit volume, Ka is the adsorption rate, and Kd is the desorption rate. Metabolism:
dM ) kC(r,z) × 2πr∆r∆z dt
(6)
where M is the mass of degradable contaminants in the system and k is the first-order degradation rate coefficient (s-1). On the basis of the conservation of mass law, the following equation was obtained:
dC ) J(z)2πr∆r + J(r)2πr∆z + KdC ′ × δ × dt 2πr∆r∆z - J(z + ∆z)2πr∆r - J(r + ∆r)2πr∆z KaC2πr∆r∆z - kC2πr∆r∆z (7)
2πr∆r∆z
Considering steady-state conditions, concentration is constant, and the left side in eq 7 is zero. Rates of sorption and desorption in eq 5 are equivalent, and the equation is equal to zero. Therefore, sorption processes cancel out. Metabolism was also considered to be negligible based upon previous 14C-labeled experiments that indicated metabolism, while clearly occurring, is small relative to fate and transport (1, 14, 15). Hence, eq 7 was simplified as
0 ) J(z)∆r + J(r)∆z - J(z + ∆z)∆r - J(r + ∆r)∆z (8) When the numerical expressions for each item in eq 8 were included and the effective diffusion in the vertical direction was assumed to be negligible as compared to dominant VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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advection term, which is reasonable for transpiring trees, eq 7 became
of which the solutions are
Z(z) ) e-λ (Dr/v)z
(20)
R(r) ) A sin λr + B cos λr
(21)
2
Q(r)C(r,z) Q(r)C(r,z + ∆z) ∂C(r,z) - Dr + 0) ∆z 2πr ∂rr,z 2πr ∂C(r + ∆r,z) Dr ∆z (9) ∂rr+∆r,z
This lead to the solution to eq 12 of the form:
C ) (A sin λr + B cos λr)e- λ (Dr/v)z 2
With the consideration that concentration is continuous and the assumption that its primary differential equation is also continuous, the following two equations were obtained at small ∆r and ∆z:
C(r,z + ∆z) ) C(r,z) +
∂C(r,z) ∆z ∂z
∂C(r + ∆r,z) ∂C(r,z) ∂C2(r,z) ) + ∆r ∂rr+∆r,z ∂rr,z ∂r2
(10) (11)
r,z
Substitution of eqs 10 and 11 into eq 9 yielded
Dr
∂2C(r,z) ∂r
2
∂C(r,z) ∂z
) v(r)
(12)
where v(r) is the water velocity of the transpiration stream. The boundary conditions for the modeling are listed as follows:
C(z, R) ) 0 C(0, r) ) C0 0ereR 0ezeT
(13)
Equation 12 is a linear differential equation of second order with two variables. An analytical solution for eq 12 is not available. To solve the equation, the concentration was approximated with the following equation to separate variables:
C ) R(r)Z(z)
(14)
where R and Z are functions of r and z, respectively. This approximation led to the following two equations by differential calculation:
dZ(z) ∂C ) R(r) ∂z dz
(15)
2 ∂2C d R(r) ) Z(z) ∂r2 dr2
(16)
Substituting eq 15 and 16 into eq 12 and assuming that v(r) is constant in the radial directions in the conduction channel, the following equation was obtained: 2 1 dZ(z) Dr d R(r) 1 ) v dr R(r) Z(z) dz
(17)
Because the left side equals the right side, they must be equal to the same constant. For the sake of subsequent algebra, -λ2Dr/v was taken as the constant. Then, two ordinary differential equations were obtained:
Dr 1 dZ ) -λ2 Z dz v
(18)
2
1dR ) -λ2 R dr2 4582
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(19)
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(22)
This equation was discussed in the Results and Discussion section. The modeling output was also compared with the experimentally collected data to evaluate the effectiveness of the models. Experimental Measurement. Wide-mouth glass bottles (1000 mL) fitted with Teflon-lined lids were used in the experiment. Silica sand (200 g) was used to fill the bottles. Hybrid poplar whips (P. deltoides × P. nigra, clone DN 34) were cut to an approximate length of 45 cm and inserted into reactors through holes in the lid. Holes were then sealed airtight. Detailed configuration of reactors was described elsewhere (3). Four diffusion traps were put around the tree cuttings. Each trap was a 2.5 cm section of 1-in. diameter glass tubing. One Teflon-lined septum was placed around the tree at each end of the tubes. The tubes and septa were then sealed around the cuttings with Teflon tape and Parafilm. One syringe needle was inserted into each Teflon-lined septum. The inlet needle was open to the atmosphere, and the other was connected to an activated carbon tube, which in turn was connected to a vacuum system. Details of the diffusion trap design were previously published (3). The bottom tube was 2 cm above the lid, and the other tubes were 6 cm apart from top to bottom. Reactors were watered with 200 mL of one-quarter strength modified Hoagland solutions initially to a target point of 80% field capacity and weighed. Reactors were put in a growth room fitted with a 1000 W metal halide lamp (Metalarc) with an approximate PAR (photo active range) intensity of 190 µmol m-2 s-1, on a 13-h photoperiod. The temperature in the laboratory was 26 ( 4 °C. After transpiration rates stabilized at about 1 month, the Hoagland solutions were replaced with 440 ppm of TCE solution, made by diluting DI water saturated TCE with Hoagland’s solution. For watering, reactors were weighed, transpiration rate was recorded, and transpiration was replaced with fresh TCE-containing solution. The reactors were fed every 2 d, and the activated carbon tubes from each collecting trap were changed every 6 d on days 6, 12, 18, and 24. Background controls (Orbo Tubes) placed in the growth room with the same configurations revealed no measurable TCE, proving that the TCE mass collected from the traps was from the stem and not the ambient air in the growth room. After the experiment was terminated, the poplar cuttings above the lid were cut into 1-cm sections and put into 20-mL vials. The vials were closed immediately with a Teflon rubber septum and sealed with crimp top seal. Headspace samples were injected into a HP 5890 gas chromatograph through a Tekmar 7000 headspace autosampler after reaching equilibrium. The activated carbon in each Orbo tube was extracted with CS2 (2 mL) and analyzed via the same HP 5890 GC after a 24-h desorption period. TCE concentrations in the transpiration stream were then calculated from measured headspace concentrations using relationships described elsewhere (16).
Results and Discussion Model Solution and Application. Equation 22 indicates that concentration of contaminants is related to the location of stems, demonstrating that concentrations decrease exponentially with height, as is consistent with the reported data
FIGURE 2. Configuration for the simplified model. R is the radius of the stem, and Ra is the representative diffusion path length. Q was measured as the transpiration rate. earlier (3). The vertical distribution of contaminants is related to the diffusivity, transpiration velocity (V) or transpiration rate (Q). The concentration change in radial directions includes trigonometric functions and is not as simple. Since eq 17 is a linear equation, the most general solution is obtained by summing solutions bearing the form of
(
∞
Dr C) (Am sin λmr + Bm cos λmr) exp -λm z v m)1
∑
)
(23)
where the constants Am, Bm and λm are determined from the boundary conditions. The determination of these constants was not attained in this work. The trend of concentration change in the radial direction was indeterminate in an unspecified range of r due to the inclusion of two alternating trigonometric functions. However, if a specific solution rather than the general solution to eq 19 was sought, the following equation satisfies eq 19:
R(r) ) -e-λr
(24)
Equation 24 demonstrated that, under certain conditions, concentration in the radial direction decreases in an exponential manner moving from the center outward. The exponential functions and trigonometric functions are interrelated to each other through Euler’s formula mathematically. The decreasing concentrations of both TCE and 1,1,2,2tetrachloroethane (TeCA) in radial directions were observed in field site settings (3). The difficulty in precisely mimicking concentration changes in radial directions with mathematical equations was attributed to the advective flows in both xylem and phloem and nonuniform diffusion in radial directions. In addition, the xylem flow velocity profile, while dominated by flow in the outer, recent annular rings, is not known. To solve the model requires the determination of constants involved in the solutions. Unfortunately, the complexity of eq 23 prevents a simple determination of constants. Thus, the model mentioned above is of more qualitative significance than quantitative importance in this case. Solving the model explicitly was not accomplished. To attain quantitative model output for comparison to experimental data, the model was simplified by using an average effective diffusion path length, neglecting the complex, unknown concentration profile in radial directions. The simplified model was developed considering a small element of tree stem, as configured in Figure 2. On the basis
of the conservation of mass law, the following equation was obtained:
dCi ) CiQ - Ci-1Q - JiA - kCiV - kfCi1/nm dt
(25)
V
where Ci and Ci-1 are respectively the concentrations of influent and effluent and are only a function of z, Ji is the effective diffusion flux, kf and 1/n are isothermal constants in the Freundlich adsorption isotherm, and m is the mass of the biomass within the model element. All other parameters are as described earlier. Equation 25 was simplified by assuming that the system is at steady state, and the metabolism and sorption processes are minor relative to the other terms. Equation 25 was simplified as
0 ) CiQ - Ci-1Q - JiA
(26)
Applying Fick’s first law to the diffusion term and integrating the equation in the vertical direction, the following equation was obtained:
∆Ci Ci dCiQ ) JiA ) -Dr A ) -Dr 2πRa dz (27) ∆R (R - Ra) or
C ) C0e-((Ra/R-Ra))*(2Drπ/Q)z
(28)
where Ra is the effective diffusion path length, an approximation of the nonuniform diffusion paths as indicated in Figure 2. Equation 28 demonstrates the exponential decline of contaminant’s concentration with height. As indicated in the comprehensive model, the transpiration rate (Q) and the diffusivity influence the concentration change with height. The simplified model also indicates that the effective diffusion path impacts the vertical concentration change. The average diffusion path (Ra) was designated as 0.85R in the model. As indicated, the active sapwood can represent half of the trunk for young trees, meaning that contaminated water is mainly conducted in the outer ring from 0.7R to R (13). Due to variances of diffusion path, the median value Ra ) 0.85R was used in the model to approximate the average diffusion path length. The concentration in the transpiration stream at ground surface (Co) is taken as the measured concentration in the transpiration stream and is assumed to be constant across the entire cross section. The impact of bulk solution VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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concentration (i.e., the groundwater contamination) on the contaminant concentrations in stems is clearly due to the connection between groundwater, root xylem and stem xylem. Previous work proposed that Co can be estimated by multiplying the concentration of the bulk solution with the transpirations stream concentration factor (TSCF). While there was a clear relationship, use of TSCF for volatile organic compounds such as TCE appears to be problematic as it does not consider possible vapor phase interactions in the root zone. TSCF was first put forward to describe the uptake and movement of nonvolatile, bio-recalcitrant herbicides and insecticides from hydroponic solutions to plants, neglecting vapor-phase interactions. Recent research has demonstrated that TCE effectively diffuses to/from roots and stems and therefore concentrations can change between the water table and ground surface (3, 17). In addition, metabolism in or around roots can further confound the use of TSCF. Therefore, direct measurement of Co from partitioning coefficients as describe earlier is preferred (16). The effective diffusion of contaminant from stems was estimated using the following equation:
FIGURE 3. Accumulation of TCE diffusion to atmosphere vs height. The error bars represent standard deviation for four individual collection periods. Each period was 6 d long.
Ci 2πRa dz Ji ) D r 2πRa dz ) Dr C e-(Ra/R-Ra)*(2Drπ/Q)z R - Ra R - Ra o (29) or
J ) -CoQe-(2RaDrπ/Q(R-Ra))zz1
z2
(30)
where z1 and z2 are two relative heights of stem. Diffusion of contaminants to the atmosphere from a tree stem can be estimated via eq 30 by integrating the equation throughout the height. All parameters are measured experimentally, with the exception of Dr and Ra. Ra was designated as 0.85R in this work, and Dr is the lone fitting parameter. By using variable Dr values and comparing the model output with the experimentally measured values, the effective diffusivity of TCE in poplar stems could be estimated. Experimental Results. No acute phytotoxicity, in terms of decreased water transpiration or chlorosis, was observed throughout the short-term experiment. In a former study, no acute phytotoxicity was observed when similar setup reactors were dosed with 550 ppm of TCE (3). However, acute phytotoxicity signs such as wilting leaves and decreasing water uptake were reported for one reactor dosed with 820 ppm of TCE after 24 d, and one plant died at day 36. In a hydroponic study, TCE concentration causing zero growth of plants was found to be 0.9 mM (131 mg/L) (18). TCE was detected in all collecting traps for trees exposed to TCE. The traps at the lower portion of the cuttings usually accumulated greater TCE mass than upper traps for a given tree. Collection systems were designated as traps 1-4 from bottom to top. TCE accumulation along height during the sampling period is exhibited in Figure 3. The accumulation was the average of four collection periods, 6 d per period. The results indicated decline of TCE volatilization with height in all cases. TCE concentrations in the transpiration stream and biomass were calculated from measured headspace concentrations using relationships described elsewhere (16).The concentrations in the transpiration stream also declined with height of the cuttings, exhibiting an exponential trend in all three trees. TCE concentrations in the transpiration stream along height of tree 2 are shown in Figure 4. Comparison of Modeling and Experimental Data. The model was capable of approximating effective TCE diffusion to the atmosphere and TCE distribution in plant stems. The model-generated TCE concentration profile, output of eq 28, could be fit well with the experimental data with Dr as 4584
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FIGURE 4. TCE concentrations in the transpiration stream of tree 2 vs height. The calculated concentration is the output of eq 28, using measured Co values and effective diffusivity of 4.5 × 10-7 cm2/s the fitting parameter. The comparison of the modeling output and the experimental measurement of the concentrations in the transpiration stream of tree 2 is shown in Figure 4. The transpiration rate (Q) of tree 2 was measured as 44 mL/d. The comparison was accomplished with the effective diffusivity Dr as the lone fitting parameter. Using sum of leastsquares method to evaluate the best correlation of the experimental and model data, an effective diffusivity was determined for each data set. The values of the parameters used in this modeling calculation are listed in Table 1, including a range of effective diffusivities from 4.0 to 5.0 × 10-7 cm2/s. Model output of diffusion and volatilization from eq 30 were relatively low compared with the accumulation of TCE in diffusion traps from stems collected experimentally. The model output did however exhibit the exponential curve of TCE volatilization with height, and values were similar to experimentally measured values. The results for tree 2 are shown in Figure 5, where z1 and z2 were taken as the height of the bottom and top of each glass tube. The low output may result from the variations in the measurement of parameters used in the equations. This model approach assumed constant R with height, which tends to underestimate the volatilization because the thinner stem with increasing height favors diffusion. The selection of Ra may be another contributing factor. Ra was selected based upon studies of xylem flow for much larger trees. Xylem flow has not been studied at this scale. The parameters used in the calculation are also tabulated in Table 1. The water transpiration rate used in the modeling calculations for TCE concentrations in the transpiration stream was the average of the final 2 d, while the water usage applied in the effective diffusion simulation was the average of the associated sampling collection period (6 d). The effective diffusivity values in Table 1 for TCE volatilization were the best fit for the last sampling event of each tree. The average of the
TABLE 1. Parameters Used in the Modeling Calculations calculations of TCE in transpiration stream
calculations of TCE volatilization
parameters
tree 1
tree 2
tree 3
tree 1
tree 2
tree 3
(mL/d)a
38 5.0 × 10-7
44 4.5 × 10-7
55 4.0 × 10-7
78 2.0 × 10-6
64 1.9 × 10-6
74 2.5 × 10-6
Q Dr (cm2/s)b
a Transpiration rates for the calculating plant concentrations were for a 2-day period prior to sampling, and transpiration rates for volatization were recorded over a 6-day average. b Effective diffusivities were obtained from best correlation of model output and experimental data.
above the septa was calculated to be less than 0.22% of the total TCE mass added to the reactors. The percentage of TCE found in three trees were 0.17% for tree 1, 0.22% for tree 2, and 0.05% for tree 3. Measured concentrations in the leaves and new stem growth suggest that volatilization also occurred from these tissues, but any volatilization from the newly grown stems was not measured nor included in model calculations. Potential metabolites were not assayed, but metabolite accumulation has been shown to be minimal as mentioned above, indicating that transfer of TCE from groundwater and soil to the atmosphere may be the major fate of VOCs in phytoremediation applications. FIGURE 5. Comparison of measured and model-generated TCE diffusion during in the first sampling event, 6 d, of tree 2. Each data represents the capture in a 2.5 cm long diffusion trap and is plotted at the average height of that trap. The model output was the output of eq 30, using measured values for Co and effective diffusivity of 1.9 × 10-6 cm2/s.
TABLE 2. Diffusivities (cm2/s) for Volatile Organic Compounds in Wood or Plant Tissues chemicals
diffusivities (cm2/s)
TCE TCE benzene toluene o-xylene TCE
5 × 10-7-2 × 10-6 a 3 × 10-8-10-7 b 6 × 10-8 c 5 × 10-8 c 0.6 × 10-8 c 10-7-10-6 d
a Data were measured by authors of this work for hybrid poplar stems with 0.9-1.0 cm diameter. b Data were cited from Trapp et al (19). The diffusivity was calculated for poplar stems with 4-8 mm diameters. c Data were cited from Mackay and Gschwend (20). The diffusivity was measured for dried Douglas fir sticks (2 cm × 2 cm × 0.2 cm). d Data were cited from Davis et al. (21). The diffusivity was measured for poplar stems.
parameters best-fitting the four sampling periods of three trees ranged from 1.9 × 10-6 to 2.5 × 10-6 cm2/s. The average Dr was 2.2 × 10-6 ( 3.5 × 10-7 cm2/s. The average diffusivity was slightly higher than previously reported values for organic contaminant diffusion in plant tissues. The higher effective diffusivity may result from the dispersion process in the active transpiration stream of this experiment when compared to stagnant conditions of other experiments. A summary regarding diffusivities of organics passing through plants or biomass is listed in Table 2. The reported values vary by more than an order of magnitude. The significant variances were attributed to the differences of chemicals, plant structures, ages, and measuring methods. For example, the percentage of polymers (lignin, cellulose, hemicellulose) varies at different ages of plants, and researchers have noted that the diffusivities of salt in longitudinal and transverse directions of wood can differ by more than an order of magnitude (22). Efforts specifically designated to measure the diffusivity of TCE passing through poplar tree tissues will increase the accuracy of the models presented here. Accumulation of TCE in biomass was not significant as has been demonstrated previously. Parent compound was detected in most plant tissues, but total TCE in tree biomass
Limitations of the Modeling. The modeling showed capability in predicting effective TCE diffusion and distribution in stems of poplar trees. However, as mentioned above, such models cannot be applied indiscriminately to other plants and organics. The organic chemicals should have certain physicochemical properties including intermediate octanol-water partitioning coefficients and relatively high Henry’s law constant and vapor pressure to be readily taken up by plants and then volatilized to the atmosphere. Flow patterns in different plant anatomies vary considerably; therefore, modeling presented here cannot be quantitatively used to phytoremediation systems with other plants of nonporous or ring porous anatomies. When the fitting parameters were examined, the average values of Dr utilized to model contaminant profiles were roughly 4 times smaller than those used to model diffusion processes. These differences may in part be ascribed to the estimated partitioning coefficients from which concentrations in the transpiration stream were derived. In addition, assumptions regarding xylem flow structure and simplifications of the plant structure to make the modeling possible may contribute further to the inherent imprecision expected. The model was not calibrated with data from field sites, therefore, the parameters fitted data from a lab-scale experiment might not best reflect the field conditions even though both exponential decrease of TCE in the transpiration streams and TCE diffusion from stems were observed in field sites (3).
Acknowledgments We thank Dr. Glenn Morrison for the valued discussions in the development of this model and Dr. D. Marshall Porterfield for helpful insight regarding plant physiology. Our gratitude also goes to Dr. Vy K Le for his assistance in mathematical insight to solving the differential equations.
Nomenclature D
diffusivity (cm2/s)
r
radius (cm)
z
height (cm)
∆z
height of the donut ring model (cm)
∆r
effective conduction thickness of model (cm)
Q(r)
transpiration flow rate (cm3/s)
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C(r,z)
contaminant concentration in tree stems (mg/ L)
Co
TCE concentration in transpiration stream at height zero (mg/L)
C′(r,z)
contaminant concentration in solid biomass (mg/g)
v
velocity of transpiration flow (cm/s)
m
mass of small pieces of tree cores/cuttings (mg)
δ
dry weight of unit volume (g/cm3)
J(z)
TCE advective flux into system (mg/cm2‚s)
J(r)
diffusive flux from inner circle (mg/cm2‚s)
J(r + ∆r) diffusive flux out of system (mg/cm2‚s) diffusivity in vertical direction (cm2/s)
Dz
J(z + ∆z) TCE flux out of system (mg/cm2‚s)
Literature Cited (1) Burken, J. G.; Schnoor, J. L. Int. J. Phytorem. 1999, 2, 139-151. (2) Vroblesky, D. T.; Neitch, C. T.; Morris, J. T. Environ. Sci. Technol. 1999, 33, 510-515. (3) Ma, X.; Burken, J. G. Environ. Sci. Technol. 2003, 37, 2534-2539. (4) Briggs, G. G.; Bromilow, R. H.; Evans, A. A. Pestic. Sci. 1982, 13, 495-504. (5) Burken, J. G.; Schnoor, J. L. Environ. Sci. Technol. 1998, 32, 3379-3385. (6) Hsu, F. C.; Marxmiller, R. L.; Yang, A. Y. S. Plant Physiol. 1990, 93, 1573-1578. (7) Trapp, S. Pest Manage. Sci. 2000, 56, 767-778. (8) Boersma, L.; McFarlane, C.; Lindstrom, F. T.; McCoy, E. L. Soil Sci. 1988, 146, 403-417. (9) Boersma, L.; McFarlane, C.; Lindstrom, F. T. J. Environ. Qual. 1991, 20, 137-146. (10) Trapp, S.; Matthies, M.; Scheunert, I.; Topp, E. M. Environ. Sci. Technol. 1990, 24, 1246-1252. (11) Zhang, Q.; Davis, L. C.; Erickson, L. E. Environ. Sci. Technol. 2001, 35, 725-731. (12) Chaney, W. R. Anatomy and physiology related to chemical movement in trees. In Annual Conference of International Society of Arboriculture; Milwaukee, 1985; http://www.fnr.purdue.edu/ extension/SpecTop/anatomy_and_physiology_related_t.htm. (13) Lambs, L.; Muller, E. Ann. For. Sci. 2002, 59, 301-315. (14) Newman, L. A.; Strand, S. E.; Choe, N.; Duffy, J.; Ekuan, G.; Ruszai, M.; Shurtleff, B. B.; Wilmoth, J.; Heilman, P.; Gordon, M. P. Environ. Sci. Technol. 1997, 31, 1062-1067. (15) Orchard, B. J.; Doucette, W. J.; Chard, J. K.; Bugbee, B. Environ. Toxicol. Chem. 2000, 19, 895-903. (16) Ma, X.; Burken, J. G. Environ. Sci. Technol. 2002, 36, 4663-4668. (17) Schumacher, J. G.; Struckhoff, G. C.; Burken, J. G. Assessment of Subsurface Chlorinated Solvent Contamination Using Tree Cores at the Front Street Site and Former Dry Cleaning Facility at the Riverfront Superfund Site, New Haven Missouri, 19992003; U.S. Geological Survey Investigative Report 2004-5049; USGS: Denver, 2004; p 35. (18) Dietz, A. C.; Schnoor, J. L. Environ. Toxicol. Chem. 2001, 20, 389-393. (19) Trapp, S.; Miglioranza, K.; Mosebek, H. Environ. Sci. Technol. 2001, 35, 1561-1566. (20) Mackay, A. A.; Gschwend, P. M. Environ. Sci. Technol. 2000, 34, 839-845. (21) Davis, L. C.; Castro-Diaz, S.; Zhang, Q.; Erickson, L. E. Crit. Rev. Plant Sci. 2002, 21, 457-491. (22) Behr, E. A.; Briggs, D. R.; Kaufert, F. H. J. Phys. Chem. 1953, 57, 476-480.
Dr
diffusivity in radical direction (cm2/s)
A
mass reduction of contaminants in liquid phase (mg)
Ka
adsorption rate (s-1)
A′
mass reduction of contaminants in solid phase (mg)
Kd
desorption rate (s-1)
S
concentration on surface of solid cell membranes (mg/cm2)
Sav
surface area of unit volume of system (cm-1)
M
mass of degradable contaminants in system (mg)
k
degradation rate (s-1)
T
height of stem (cm)
R(r)
function of TCE concentration distribution in radial directions
Z(z)
function of TCE concentration distribution in vertical directions
λ
mathematical parameter
R
radius of stem (cm)
Ra
average effective diffusion path in stem (cm)
Ci
TCE concentration entering into simplified modeling system (mg/L)
Ci-1
TCE concentration going out simplified modeling system (mg/L)
V
volume of modeling systems (L)
Ji
diffusive flux (mg/cm2‚s)
kf
adsorption coefficient in Freundlich adsorption curve
Received for review December 20, 2003. Revised manuscript received June 7, 2004. Accepted June 16, 2004.
1/n
adsorption index in Freundlich adsorption curve
ES035435B
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 17, 2004
