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Effects of residence time and degree of water saturation on sorption nonequilibrium parameters
Journal of Contaminant Hydrology 36 Ž1999. 53–72
Effects of residence time and degree of water saturation on sorption nonequilibrium parameters Munjed A. Maraqa a , Roger B. Wallace b, Thomas C. Voice a
b,)
Department of CiÕil Engineering, United Arab Emirates UniÕersity, Al-Ain, United Arab Emirates Department of CiÕil and EnÕironmental Engineering, Michigan State UniÕersity, East Lansing, MI 48824, USA
b
Received 14 October 1997; revised 28 August 1998; accepted 28 August 1998
Abstract This study reports the impact of the degree of water saturation on sorption nonequilibrium parameters. Two nonionic organic compounds Žbenzene and dimethylphthalate. and three nonaggregated sandy soils were utilized. Local equilibrium assumptions were found to be invalid for describing the transport of these compounds even at pore-water velocities as low as 0.7 cmrh. Sorption nonequilibrium appeared to be of a diffusive nature rather than due to a slow chemical reaction. Sorption mass-transfer coefficients varied proportionally with pore-water velocity. A strong correlation between the mass-transfer coefficient and residence time was found utilizing present and previously reported laboratory data. A similar relationship was also found for the mass-transfer coefficient between mobile and immobile water regions. Field data indicate that the sorption mass-transfer coefficient may continue to decrease in a consistent way even at residence times as large as 5 = 10 3 h. Variations in the degree of water saturation had no impact on the value of the sorption mass-transfer coefficient other than what would be expected due to changes in the residence time. This suggested that movement into the solid grains of the large emptied pores through diffusion from the water-filled pores into stagnant water covering these grains was relatively fast compared to the sorption rate. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Pore-water velocity; Mass transfer; Benzene; Dimethylphthalate; Unsaturated flow
1. Introduction The need to consider nonequilibrium sorption in describing transport of dissolved nonionic organic compounds ŽNOCs. has been demonstrated by several laboratory )
Corresponding author. Tel.: q1-517-353-9178; fax: q1-517-355-0250; e-mail: [email protected]
0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 8 . 0 0 1 4 4 - 2
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M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
investigations ŽHutzler et al., 1986; Bouchard et al., 1988; Lee et al., 1988; Brusseau et al., 1991a; Brusseau, 1992; Ptacek and Gillham, 1992. and field studies ŽGoltz and Roberts, 1986, 1988; Bahr, 1989; Bowman, 1989.. Little of this work focused on partially saturated soils. Recently, Maraqa Ž1995. investigated the impact of water saturation on sorption of NOCs under dynamic conditions. The author argued that accessibility of the compounds to the grains in the emptied large pores occurs through diffusion from the water-filled pores into a stagnant water covering these grains ŽFig. 1.. Unless this diffusion process is fast, a higher degree of nonequilibrium can occur in the unsaturated soil than in the saturated soil. Assessment of the effects of water saturation on sorption nonequilibrium is important given that NOCs are commonly introduced in unsaturated zones. In most of the current nonequilibrium transport models, sorption kinetics have been simulated using a formulation that assumes a constant mass-transfer coefficient, one that is independent of pore-water velocity. Recent studies ŽBrusseau, 1992; Kookana et al., 1993. show that these two parameters may be correlated in saturated media. Since degree of water saturation is also typically correlated with pore-water velocity in laboratory experiments with unsaturated media, tracing the cause of any variations in the mass-transfer coefficient in unsaturated media requires separating the influence of pore-water velocity from that due to degree of water saturation. Analysis in unsaturated media is further complicated by the potential existence of an additional nonequilibrium process created by diffusion into and out of immobile water regions that are commonly observed under certain conditions including unsaturated flow Žvan Genuchten and
Fig. 1. Conceptualization of chemical diffusion from water-filled pores into stagnant water covering solid grains and subsequent sorption to the solid grains in the large emptied pores.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
55
Wierenga, 1977; De Smedt and Wierenga, 1979, 1984; De Smedt et al., 1986; Bond and Wierenga, 1990.. Another factor that needed to be considered was the change in the retardation coefficient associated with changes in the degree of water saturation. Maraqa Ž1995. observed that the retardation coefficients for both DMP and benzene increased as the degree of water saturation dropped, independent of pore-water velocity. Based on this observation, it was expected that at the same pore-water velocity a compound would have a higher residence time in unsaturated soils than when the soil was saturated. Brusseau et al. Ž1991a. suggested that differences in the value of the first-order mass-transfer coefficient Ž k . for a given compound at different flow rates could be a result of a time-scale effect, where the value of k is dependent on the length of time of the experiment. If this is the case, then k will be affected by not only pore-water velocity, but also the length of the system and the retardation coefficient of the compound. Our objective was to investigate the dependence of sorption kinetics on residence time and degree of water saturation. To achieve this, we investigated the dependence of k on pore-water velocity and residence time under saturated conditions using data from our experiments and that previously reported by others. The impact that degree of water saturation had on the sorption mass-transfer coefficient was evaluated by comparing values of k determined under both saturated and unsaturated conditions after isolating the effects of residence time.
2. Materials and methods Soil from the A and B horizons of Oakville sand and from the B horizon of a Pipestone sand were collected from North Star, Michigan. Soil samples were air-dried and ground to pass through a 0.85-mm sieve. Each soil sample was characterized for organic carbon using the wet-digestion technique ŽSchulte, 1988. and for particle-size distribution by the hydrometer method, as shown in Table 1. Other characteristics of these soils were reported by Maraqa et al. Ž1997.. Soil samples were packed in glass columns Ž5.45 cm ID. of 30.2 cm length with Teflon end-plates. Some characteristics of the packed soil columns are also presented in Table 1. A porous stainless-steel plate
Table 1 Properties of packed columns Soil
Organic carbon Ž%.
Texture Sand Ž%.
Silt Ž%.
Clay Ž%.
Oakville A Pipestone Oakville B
2.25 1.57 0.70
94.5 95.0 94.5
3.5 3.1 4.0
2.0 1.9 1.5
r Žg cmy3 .
u Žcm3 cmy3 .
1.587 1.636 1.587
0.408 0.383 0.353
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M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
ŽSoil Measurement Systems, Tucson, AZ. that functions as a capillary barrier was attached to the outflow end of each column. Two NOCs were chosen for study: benzene and dimethylphthalate ŽDMP.. 14 C-labeled benzene mixed with cold benzene was used in all the experiments and was analyzed by liquid scintillation counting. DMP was analyzed by high pressure liquid chromatography ŽHPLC. with a UV detector using 50% water: 50% acetonitrile as the mobile phase and a flow rate of 1.5 ml miny1 . Some properties of the two compounds were described by Maraqa et al. Ž1998. and the references cited therein. Pulse-type miscible displacement experiments were conducted under both saturated and unsaturated flow conditions. For the saturated-flow experiments, three different flow rates were employed. The unsaturated experiments were conducted at four levels of uniform saturation. Tensiometers ŽSoil Measurement Systems. were used to measure soil-water suction at one-third and two-thirds the column length. Uniform saturation was achieved by adjusting the flow rate and the applied suction at the bottom of the column until a unit hydraulic gradient was established Žsee Maraqa, 1995; Maraqa et al., 1997.. The two compounds were dissolved in a 0.005 M CaCl 2 solution prepared with deionized, deaired water containing 0.05% sodium azide to inhibit biodegradation ŽRussell and McDuffie, 1986.. The effectiveness of the biocide for benzene and DMP was verified by Maraqa et al. Ž1998.. Batch sorption isotherms of the two compounds using the same soils were also reported by Maraqa et al. Ž1998.. The compounds were injected into the column via a syringe pump using glass syringes. The concentration of benzene and DMP in the injected solution was approximately 30 mg ly1 . After introducing the pulse, the columns were displaced by an organic-compound-free solution. Effluent samples were collected using glass syringes attached to the outlet of the column prior to sample collection. The samples were analyzed for benzene and DMP shortly after collection. The experimental conditions applied in this study as well as the column setup and the sample collection device were exactly the same as those reported by Maraqa et al. Ž1997.. No adsorption, relative to tritium, of the two compounds to the column material was observed in a saturated control experiment using clean glass beads in place of soil. No evidence of DMP hydrolysis was detected as both DMP and phthalic acid Žthe product of DMP hydrolysis., which have different retention times in the HPLC method, were monitored in the effluent samples.
3. Model background and data analysis Two general types of models have been developed to simulate nonequilibrium during transport of solutes in the subsurface: Ž1. transport nonequilibrium models and Ž2. sorption-related nonequilibrium models. Transport nonequilibrium models assume the existence of mobile and immobile water regions with solute transfer between the two water regions ŽCoats and Smith, 1964; van Genuchten and Wierenga, 1976.. The presence of immobile water regions have been associated with aggregated soils Žvan Genuchten and Wierenga, 1976; Nkedi-Kizza et al., 1983. and unsaturated conditions
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
57
ŽBiggar and Nielsen, 1960; De Smedt and Wierenga, 1984; De Smedt et al., 1986; Bond and Wierenga, 1990.. Furthermore, transport nonequilibrium affects the transport of both sorptive as well as non-sorptive solutes. In this study, the two NOCs were injected into the soil columns concurrently with tritium. Based on the analysis of the tritium data ŽMaraqa et al., 1997., transport nonequilibrium was found not to be a factor in these systems. Sorption-related nonequilibrium models are usually categorized into two groups: chemical nonequilibrium models and diffusive mass-transfer models. Chemical nonequilibrium models assume that the sorption reaction is the rate-limiting process ŽCameron and Klute, 1977.. However, diffusive mass-transfer models describe the rate limiting process as physical rather than chemical. Two types of models have been developed in this regard: intraparticle diffusion ŽBall and Roberts, 1991. and intraorganic matter diffusion models ŽBrusseau et al., 1991b.. Generated breakthrough curves ŽBTCs. were analyzed using both equilibrium and nonequilibrium approaches. The equilibrium model for a linear sorption reaction is given as: R
1 E 2C
EC ET
s
P EZ
2
EC y
Ž 1.
EZ
where, C s crco
Ž 2a .
Z s zrL
Ž 2b .
T s Õo trL
Ž 2c .
P s Õo LrD
Ž 2d .
Rs1q
rKD
Ž 2e .
u
here c is the solute concentration, c o is the solute concentration in the influent solution, z is distance, L is the column length, t is time, T is the number of pore volumes, Õo is the average pore-water velocity, D is the hydrodynamic dispersion coefficient, P is the Peclet number, r is the soil bulk density, u is the moisture content, K D is the sorption distribution coefficient, and R is the retardation coefficient. The dimensionless equations of the two-site nonequilibrium models for linear sorption behavior are given as:
bR
EC ET
q Ž1yb . R
Ž1yb . R
E Q2 ET
E Q2 ET
1 E 2C s
P EZ
s v Ž C y Q2 .
2
EC y
EZ
Ž 3. Ž 4.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
58
where,
bs
u q Fr K D
Q2 s
vs
Ž 5a .
uqrKD 1
q2
Ž 1 y F . K D co
kL Õo
Ž1yb . R
Ž 5b . Ž 5c .
here q2 is the sorbed concentration in the rate-limited domain, F is the fraction of sorbent for which sorption is instantaneous, b and v are the dimensionless parameters that specify the degree of nonequilibrium in the system. BTCs of benzene and DMP were analyzed to determine the optimized parameter values, and their confidence intervals using the nonlinear least squares inversion program CXTFIT of Parker and van Genuchten Ž1984.. To achieve better accuracy in the numerical integration, the relative error in CXTFIT was reduced from 5 = 10y5 to 5 = 10y7 .
4. Results and discussion 4.1. Saturated flow experiments Input parameter values for Õo , D, and the number of pore volumes of benzene and DMP solution injected ŽTo . used in the simulation of the saturated experiments are listed Table 2. Values of D used are those determined for tritium which was displaced concurrently with benzene and DMP. Discrepancy between R values determined by batch and column techniques, as reported by Maraqa et al. Ž1998. for benzene and DMP and the same soils, did not allow us to use independently determined batch retardation coefficients in the simulations. The best fit values of R for benzene and DMP using the equilibrium approach along with the sum of square errors ŽSSE. are also shown. Optimum values of R, b , and v along with their 95% confidence limits and the SSE values were obtained using the nonequilibrium approach ŽTable 3.; values of K D , F, and k calculated using Eqs. Ž2e., Ž5a. and Ž5c., respectively, and their 95% confidence limits are also listed. Example simulations based on the best fit R for the equilibrium model and the best fit values of R, b and v for the nonequilibrium model are shown in Fig. 2. The nonequilibrium model simulation closely matched the experimental results, while deviations between the equilibrium model simulation and the data points were significant. Comparison of corresponding SSE values ŽTables 2 and 3. revealed that the nonequilibrium model performed better than the equilibrium model, in all cases. The improvement in performance appeared to increase as the soil organic matter increased, consistent with the findings of Bouchard et al. Ž1988. and of Brusseau et al. Ž1991a.. This rate limitation appeared to be due to slow sorptive interactions and not due to slow diffusion into and
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
59
Table 2 Results of fitting the advection–dispersion model to the saturated experiments using independently determined dispersion coefficient Experiment
Tracer
OakÕille A soil SA1 Benzene DMP SA3 Benzene DMP SA6 Benzene DMP Pipestone soil SP1 Benzene DMP SP3 Benzene DMP SP6 Benzene DMP OakÕille B soil SB1 Benzene DMP SB3 Benzene DMP SB6 Benzene DMP a
Õo Žcm hy1 .
To
D for 3 H Žcm2 hy1 .
R
SSE a
31.55
1.95
20.88
6.30
1.96
5.37
0.62
1.91
0.222
1.98Ž"0.05. 2.14Ž"0.08. 2.05Ž"0.07. 2.50Ž"0.05. 2.19Ž"0.08. 2.86Ž"0.07.
0.214 0.635 0.354 0.980 0.445 1.405
33.60
2.08
18.78
6.72
2.09
2.88
0.67
2.05
0.156
2.09Ž"0.08. 1.95Ž"0.08. 2.15Ž"0.06. 2.14Ž"0.10. 2.32Ž"0.08. 2.55Ž"0.10.
0.185 0.419 0.432 1.060 0.377 0.702
36.47
2.18
18.04
7.29
2.20
3.27
0.73
2.17
0.204
1.36Ž"0.06. 1.41Ž"0.04. 1.43Ž"0.03. 1.54Ž"0.05. 1.44Ž"0.05. 1.52Ž"0.04.
0.540 0.368 0.250 0.350 0.260 0.310
SSE is the sum of square errors.
out of immobile water regions, since the simultaneous transport of tritium through the same soil columns ŽMaraqa et al., 1997. was described adequately using an equilibrium model. The values of R found by fitting the nonequilibrium model were higher than those produced with the equilibrium model ŽTables 2 and 3.. Moreover, equilibrium model R values appeared to decrease with increased flow rate. Dependence of R on the flow rate, as discussed by Brusseau et al. Ž1991a., is generally regarded as an indication of sorption-related nonequilibrium in which case retardation coefficients determined with the equilibrium model may not provide a good measure of actual retardation. The values of R predicted with the nonequilibrium model did not have this trend, except for DMP on Oakville A soil. Velocity dependent R may indicate the presence of an additional physical or chemical process not currently included in the adopted nonequilibrium model, but become apparent only at relatively large spatial or time scales. 4.2. Impact of pore-water Õelocity and residence time No functional relationship was found between F ŽTable 3. and pore-water velocity ŽTable 2. for the two compounds using the three soils. This is consistent with observations made by Brusseau et al. Ž1991a., but in conflict with those reported by
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M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 3 Results of fitting the nonequilibrium model to the saturated experiments using dispersion coefficient determined from tritium BTCs Experiment
Tracer
OakÕille A soil SA1 Benzene DMP SA3
Benzene DMP
SA6
Benzene DMP
Pipestone soil SP1 Benzene DMP SP3
Benzene DMP
SP6
Benzene DMP
OakÕille B soil SB1 Benzene DMP SB3
Benzene DMP
SB6
Benzene DMP
R
b
v
SSE
K D Žml gy1 . wEq. Ž2e.x
F wEq. Ž5a.x
k Žhy1 . wEq. Ž5c.x
2.45" 0.13 2.95" 0.16 2.78" 0.84 3.28" 0.25 2.73" 0.17 4.03" 0.19
0.787" 0.007 0.642" 0.032 0.693" 0.193 0.639" 0.033 0.755" 0.038 0.583" 0.023
0.265" 0.051 0.528" 0.068 0.204" 0.079 0.718" 0.168 0.383" 0.072 0.977" 0.117
0.018
0.373" 0.033 0.501" 0.041 0.458" 0.022 0.586" 0.064 0.445" 0.044 0.779" 0.049
0.64" 0.09 0.46" 0.08 0.52" 0.30 0.48" 0.10 0.61" 0.11 0.45" 0.06
0.534" 0.108 0.526" 0.084 0.050" 0.037 0.127" 0.033 0.011" 0.005 0.012" 0.002
2.76" 0.34 2.83" 0.29 2.74" 0.19 2.92" 0.21 2.75" 0.14 2.77" 0.06
0.733" 0.083 0.640" 0.050 0.750" 0.040 0.660" 0.030 0.797" 0.037 0.740" 0.020
0.220" 0.048 0.381" 0.064 0.302" 0.056 0.610" 0.130 0.342" 0.072 1.170" 0.320
0.027
0.412" 0.080 0.428" 0.068 0.407" 0.044 0.447" 0.049 0.410" 0.033 0.414" 0.014
0.58" 0.22 0.44" 0.15 0.61" 0.12 0.48" 0.10 0.68" 0.10 0.59" 0.04
0.334" 0.130 0.419" 0.094 0.099" 0.027 0.138" 0.034 0.014" 0.005 0.036" 0.011
1.64" 0.02 1.85" 0.17 1.61" 0.15 1.70" 0.06 1.65" 0.03 1.73" 0.04
0.850" 0.050 0.756" 0.034 0.894" 0.079 0.820" 0.024 0.870" 0.058 0.796" 0.016
0.110" 0.020 0.176" 0.032 0.161" 0.015 0.259" 0.045 0.225" 0.037 0.570" 0.170
0.184
0.142" 0.004 0.189" 0.038 0.136" 0.033 0.156" 0.013 0.145" 0.007 0.162" 0.009
0.62" 0.13 0.47" 0.19 0.72" 0.29 0.56" 0.10 0.67" 0.16 0.52" 0.06
0.544" 0.208 0.474" 0.116 0.229" 0.084 0.206" 0.050 0.026" 0.014 0.039" 0.014
0.012 0.104 0.048 0.030 0.015
0.033 0.028 0.059 0.029 0.022
0.049 0.164 0.049 0.026 0.016
Ninety-five percent confidence limits for K D , F and k were calculated by error propagation using first-order uncertainty analysis and assuming no error in L, u , r , and Õo .
Kookana et al. Ž1993.. As suggested by Schwarzenbach and Westall Ž1981., the F factor would likely be a function of velocity for a chemical nonequilibrium process involving a number of different reaction times. Conversely, F should be fairly independent of
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
61
Fig. 2. Selected BTCs of benzene Žtriangles. and DMP Žcircles.. Dashed lines are simulations using the equilibrium model and solid lines are simulations using the nonequilibrium model.
velocity for nonequilibrium caused by slow diffusion ŽBrusseau et al., 1991a.. Therefore, independence of F on velocity for the data presented here suggested that sorption nonequilibrium was due to slow diffusion. Fig. 3 plots the values of k ŽTable 3. versus pore-water velocity ŽTable 2.. Dependence of k on pore-water velocity was obvious and inconsistent with a constant mass-transfer coefficient for either compound on any of the three soils. While the values
Fig. 3. Dependence of mass-transfer coefficient on pore-water velocity. Circles for Oakville A, diamonds for Pipestone, and triangles for Oakville B soil, open symbols for DMP and closed ones for benzene.
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M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
of k were clearly dependent on pore-water velocity, it appeared that they were independent of compound or soil. The dependence of k on velocity cannot be attributed to changes in K D , since for all sorbate–sorbent combinations, with the exception of DMP on Oakville A, there was no apparent dependence of K D on pore-water velocity ŽTable 3.. Variation of k with pore-water velocity has been previously reported Žvan Genuchten et al., 1974; Brusseau et al., 1991a; Brusseau, 1992; Kookana et al., 1993.. Similar behavior has also been observed for mass transfer of nonsorbing solutes between mobile and immobile water regions Žvan Genuchten and Wierenga, 1977; Nkedi-Kizza et al., 1983; De Smedt and Wierenga, 1984; De Smedt et al., 1986; Schulin et al., 1987.. For nonsorbing solutes, the increase in mass-transfer coefficient Ž a . with increasing porewater velocity is attributed either to higher mixing in the mobile phase at high pore-water velocities Žvan Genuchten and Wierenga, 1977; De Smedt and Wierenga, 1984. or to shorter diffusion path lengths as a result of a decrease in the amount of immobile water Žvan Genuchten and Wierenga, 1977.. Since sorbate mass transfer occurs within either the sorbent or the intraparticle pores it is unlikely that k is affected by velocity induced mixing. Values of k reported by several investigators for NOCs, along with the relevant experimental conditions were summarized in Table 4. All the values of k ŽTable 4. were obtained using the same transport model as that used in this study. At comparable pore-water velocities, the values of k we determined were in agreement with those of Brusseau et al. Ž1991a. and Kookana et al. Ž1993.. Our values, however, were lower than those of Lee et al. Ž1988., Brusseau et al. Ž1990., Ptacek and Gillham Ž1992., and Brusseau Ž1992.. Inspection of Table 4 revealed that the agreement or disagreement between our values ŽTable 3. and those of other investigators ŽTable 4. was associated with the length of the column employed. To evaluate the importance of accounting for different column lengths, values of log k ŽTables 3 and 4. were regressed on values of log Õo and log LrÕo to obtain Eqs. Ž6a. and Ž6b. ŽTable 5.. Comparison of the coefficients of determination ŽTable 5. for the regression on log Õo Ž r 2 s 0.71. with that for the regression on log LrÕo Ž r 2 s 0.87. indicated that the hydraulic residence time Ž LrÕo . was a better parameter for explaining the observed variations in log k than was pore-water velocity alone. This suggests that the mass-transfer coefficient is a time dependent parameter. Since k was determined from BTCs of compounds having different retardation coefficients, it is perhaps more appropriate to characterize the time for mass transfer by the residence time Ž LRrÕo .. Values of log k were regressed on values of log LRrÕo ŽFig. 4. to obtain Eq. Ž6c. of Table 5. Eq. Ž6c. showed that there was a consistent trend for the mass-transfer coefficient to decrease as the residence time of the tracer increased. The equation suggested a linear log–log relationship between mass-transfer coefficient and inverse residence time. With the additional improvement in the coefficient of determination, variation in log LRrÕo explained 92% of the observed variation in log k. This strengthened the evidence that the mass-transfer coefficient is a time dependent parameter. Factors in addition to residence time would be required to reduce the remaining unexplained variation in log k. Since Eqs. Ž6a., Ž6b. and Ž6c. were developed by pooling all of the experimental data ŽTables 3 and 4., tracer and soil properties may
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
63
Table 4 Review of laboratory-determined mass-transfer coefficient for some organic compounds along with the experimental conditions Compounda Brusseau, 1992 PXY PXY NAP NAP PCE PCE 1,4-DCB 1,4-DCB NAP NAP PCE PCE Nkedi-Kizza et al., 1989 b Atrazine Diuron Brusseau et al., 1990 c BNZ CB DCB TCB Brusseau et al., 1991a CT TCE PCE PXY 1,4-DCB 1,2-DCB NAP BIP
Õo L Žcm hy1 . Žcm.
R
k Compounda Õo L R Žhy1 . Žcm hy1 . Žcm.
89.0 5.0 45.0 5.0 45.0 5.0 90.0 5.0 53.0 6.0 93.0 5.0
7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 6.75 6.75
1.48 14.20 1.48 0.50 2.00 6.10 2.04 0.30 2.11 4.90 2.22 0.20 1.72 17.00 1.48 0.90 2.22 4.40 2.04 0.60 2.25 11.40 2.27 0.60
5.0 5.0
5.0 5.0
1.80 4.37
90.0 90.0 90.0 90.0
5.3 5.3 5.3 5.3
0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
30.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0
0.77 0.15
1.33 23.50 2.23 17.00 4.87 9.80 13.50 3.46 1.50 1.50 2.10 2.20 4.60 4.90 1.40 2.30
0.08 d 0.12 0.08 0.06 0.02 0.02 0.08 0.09
Lee et al., 1988 TCE 24.0 6.0 TCE 24.0 8.8 PXY 24.0 6.0 PXY 24.0 8.8 Ptacek and Gillham, 1992 BROM 12.08 10.0 CT 12.08 10.0 PCE 12.08 10.0 1,2-DCB 12.08 10.0 HAC 12.08 10.0 BROM 12.08 10.0 CT 12.08 10.0 PCE 12.08 10.0 1,2-DCB 12.08 10.0 HAC 12.08 10.0 BROM 0.75 10.0 CT 0.75 10.0 PCE 0.75 10.0 1,2-DCB 0.75 10.0 HAC 0.75 10.0 BROM 0.75 10.0 CT 0.75 10.0 PCE 0.75 10.0 1,2-DCB 0.75 10.0 HAC 0.75 10.0 Kookana et al., 1993 simazine 37.2 30.0 simazine 18.6 30.0 simazine 3.7 30.0 simazine 1.9 30.0
k Žhy1 .
1.61 1.43 2.65 2.02
5.23 d 4.52 d 2.81d 2.70 d
1.08 1.17 1.40 1.71 2.15 1.32 1.63 1.60 1.98 2.24 1.29 1.35 2.65 3.05 4.10 1.40 1.42 2.31 3.06 2.84
5.58 1.58 2.88 2.18 1.25 1.12 0.76 2.55 1.58 1.70 0.23 0.15 0.07 0.10 0.06 0.17 0.18 0.06 0.07 0.16
3.66 3.66 3.66 3.66
0.24 d 0.12 d 0.06 d 0.04 d
a
PXYs p-xylene, NAPs naphthalene, PCEs tetrachloroethylene, 1,4-DCBs1,4-dichlorobenzene, TCEs trichloroethylene, TC s carbon tetrachloride, 1,2-DCB s1,2-dichlorobenzene, BIP s biphenyl, BNZ s benzene, CBs chlorobenzene, DCBsdichlorobenzene, TCBs trichlorobenzene, BROMs bromoform, HAC s hexachloroethane. b Only the values for the experiments with aqueous phase Ži.e., f c s 0.. Reported velocity is 5–6 cm hy1 . A value of 5.0 cm hy1 is assumed here. c Values for the miscible displacement experiments. d Calculated using the reported v values and Eq. Ž5c..
still have an important influence beyond that described by residence time. For example, it has been observed that k depends on K D ŽKarickhoff and Morris, 1985; Brusseau and Rao, 1989; Brusseau et al., 1991a,b.. This was also noticed in our data ŽTable 3. at the low and intermediate flow rates, but it was not obvious at the high flow rate. Eq. Ž6c. accounts for the dependence of k on K D but only as the latter affects residence time.
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M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 5 Relationships between mass-transfer coefficient and some system parameters Relationship and equation number
r2
Na
Organic compounds log k s 0.99 log Õo y1.18Ž6a. log k sy0.90 logŽ Lr Õo .y0.08Ž6b. log k sy0.90 logŽ LR r Õo .q0.23Ž6c.
0.71 0.87 0.92
72 72 72
Ideal or near-ideal tracers log a s 0.79 log Õo y1.47Ž7a. log a sy0.82 logŽ LR r Õo .y0.56Ž7b.b
0.57 0.72
72 72
Unsaturated, nonaggregated media log a s 0.85 log Õo y1.22Ž8a. log a sy0.80 logŽ LR r Õo .y0.02Ž8b.c
0.71 0.91
13 13
Aggregated media log a s 0.71 log Õo y1.51Ž9a. log a sy0.79 logŽ LR r Õo .y0.70Ž9b.b
0.52 0.80
59 59
a
N is the number of data points. When an R value was reported, it was used. Otherwise, R was assumed to be 1.0. c Rs1.0. b
Fig. 4 also shows the relationship between a , the coefficient for mass transfer between mobile and immobile water regions of ideal or near ideal tracers, and residence time. The line was generated using two, previously reported, types of data. One set of data was obtained using unsaturated, nonaggregated media ŽKrupp and Elrick, 1968; De Smedt and Wierenga, 1984; De Smedt et al., 1986., while the other set was obtained
Fig. 4. Dependence of sorption mass-transfer coefficient on residence time based on this and previous studies.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
65
using aggregated media Žvan Genuchten and Wierenga, 1977; Rao et al., 1980b; Nkedi-Kizza et al., 1983.. All the values of a were determined using a transport model that was mathematically the same as that used in this study. The improvement in the fit achieved by using residence time rather than pore-water velocity was made obvious by comparing the coefficient of determination of Eq. Ž7a. with that of Eq. Ž7b. ŽTable 5.. The relationship between a and LRrÕo ŽEq. Ž7b.. was not as strong as for k ŽEq. Ž6c... This was partly due to differences in the nature of the data sets for a . When each data set was regressed separately to obtain Eqs. Ž8b. and Ž9b. both coefficients of determination increased. As compared to Eq. Ž6c., the low r 2 associated with Eq. Ž9b. may be due to unaccounted for variations in the size of aggregates employed. Nevertheless, the similarity between Eqs. Ž6c. and Ž7b. suggests a similar mechanistic behavior of the two mass transfer processes. This is not surprising given that both mass-transfer coefficients have been related to a molecular diffusion coefficient and a diffusion path length. For spherical aggregates a is given as ŽHarmon et al., 1992.:
as
15De u im b2
Ž 10a.
where De is the effective pore diffusion coefficient, u im is the immobile water content, and b is a characteristic diffusion length. Similarly, for the case where sorption nonequilibrium is due to intraorganic matter diffusion, the mass-transfer coefficient Ž k OM . is given as ŽBrusseau et al., 1991b.: k OM s
Sf DOM 2
l Ž1yF .
Ž 10b.
where sf is a shape factor, DOM is the effective diffusion coefficient in the organic matter matrix, and l is a characteristic diffusion length. Eqs. Ž10a. and Ž10b. do not account directly for changes in mass-transfer coefficient with residence time. Theoretical analysis and experimental data presented by Rao et al. Ž1980a. for non-sorbing tracers shows that a mass transfer model that only considers average concentration within mobile and immobile water regions, similar to the one used here, yields a mass-transfer coefficient that decreases with increasing time of diffusion and reaches a constant value for large times. By analogy, the dependence of k on residence time for sorbed tracers could be due to the inadequacy of the commonly used mass transfer model ŽEq. Ž4.. in that it does not account for variations in concentration along the diffusion path length. Nkedi-Kizza et al. Ž1983. observed that the mass-transfer coefficient is sensitive to solution concentration. Therefore, variations of k with time could be a result of changes in either the diffusion coefficient or in the characteristic diffusion length created by changes in the local aqueous solution concentration driving diffusive mass transfer. Schwarzenbach and Westall Ž1981. proposed using a continuous distribution of k’s to describe the effect of flow velocity on transport of chemicals affected by sorption nonequilibrium. The different k values, as indicated by the authors, would correspond to different diffusion path lengths. On the other hand, concentration-dependent diffusion coefficients have been reported ŽCussler, 1984.. If this is the case, then at a given flow
66
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
rate, the value of mass-transfer coefficient obtained represents a time-averaged value that corresponds to a time-averaged diffusion coefficient. Consequently, a different time-averaged mass transfer value would be obtained for a different residence time. 4.3. Applicability of Eq. (6c) to field data Although Eq. Ž6c. covers a wide range of residence times Ž0.1–195 h., the upper values in this range are still small compared to field residence times associated with contaminant plumes. Furthermore, the laboratory data from which Eq. Ž6c. was developed were obtained using homogenized, packed soil samples, and the influence of field heterogeneity on the values of the nonequilibrium parameters is unknown. Eq. Ž6c. was compared to two data sets ŽGoltz and Roberts, 1986; Ptacek and Gillham, 1992. collected at the Canadian Forces Base Borden in Southern Ontario, Canada. Ptacek and Gillham Ž1992. determined k for the same organic compounds utilized in their laboratory experiments ŽTable 4. at pore-water velocities of 11.25 and 15.8 cm hy1 . Their values were determined from BTCs generated by collecting samples over a short length scale Ž10 cm.. Residence times for their experiments Ž1.00–2.44 h. fall within the range of values observed ŽTables 3 and 4. in the laboratory used to obtain Eq. Ž6c.. Using the values of Õo , L, and R reported by Ptacek and Gillham Ž1992., the predicted k values based on Eq. Ž6c. were 2.2–6.4 times lower than the reported ones, but fell within or close to the 95% confidence limits of the predictive relationship ŽFig. 5.. Predicted values of k appeared to be in reasonable agreement with values obtained in the laboratory considering that the soil was not homogenized and the groundwater temperature was 8 " 28C in the field.
Fig. 5. Comparison between laboratory- and field-determined mass-transfer coefficients for organic compounds.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
67
Goltz and Roberts Ž1986. obtained identical values of k Ž1.7 = 10y4 hy1 . for carbon tetrachloride, and tetrachloroethylene by analyzing aqueous samples collected 5 m from a line of injection wells. The average-pore water velocity was 0.33 cm hy1 , and the retardation coefficients were 1.8 and 3.0, respectively. The mass-transfer coefficient was about 2 orders of magnitude lower that our lowest laboratory values, which were comparable to the lowest values obtained by Brusseau et al. Ž1991a.. Brusseau et al. Ž1991a. suggests that the low k value obtained by Goltz and Roberts Ž1986. could be due to heterogeneities in hydraulic conductivity and sorption capacity. Extrapolation of Eq. Ž6c. form the largest laboratory values of LRrÕo s 195 h to the much larger values of 2.7 = 10 3 h and 4.5 = 10 3 h encountered in Goltz and Roberts’ field experiment, shows that about 90% of the difference in k between the lowest laboratory values and Goltz and Roberts’ field values can be explained by accounting for the effect of the much larger residence time of the field experiment. On the bases of this large-scale field experiment, it appears that Eq. Ž6c. can be extended to large values of residence time. 4.4. Unsaturated flow experiments The nonequilibrium model was used to analyze the DMP data under unsaturated conditions. Fixed parameter values for Õo , To and D used in fitting are listed in Table 6. The values of D are those for tritium which was injected into the soil columns concurrently with DMP. The assumption was made here that physical nonequilibrium is not important during the transport of sorbing tracers based on the analysis presented by Maraqa et al. Ž1997. for the transport of non-sorbing tracers. The best fit values of R, b and v for DMP and their confidence intervals are also reported in Table 6. Values for F and k are estimated using Eqs. Ž5a. and Ž5c., respectively, along with the values of R and Õo that are listed in the table. An example of the fit achieved with the nonequilibrium model at two levels of saturation using Oakville A soil is shown in Fig. 6. For the saturated-flow experiments, the mass-transfer coefficient, k, was found to depend on residence time. Since saturation and pore-water velocity are coupled in the unsaturated experiments, the values of k determined under unsaturated-flow conditions were expected to vary with saturation. The impact of saturation on k was investigated by comparing the values of k for both saturated and unsaturated experiments at the same residence time ŽFig. 7.. Although the unexplained variation in k for the unsaturated experiments was greater than for the saturated case, the expected values of k for any given residence time were essentially the same for both saturated and unsaturated soils. This provides evidence that the mass-transfer coefficient retains the same value independent of the degree of water saturation, as long as changes in residence time with saturation have been accounted for. The values of F for DMP on Oakville A ŽTable 6. decreased with saturation although this trend was not obvious for the other soils. As saturation dropped, the solids concentration Ž rru . increased. Karickhoff and Morris Ž1985. reported a dependence of F on the parameter r K D ru . Therefore, to assess the impact of saturation on F, the effect of changes in the solids concentration should be accounted for. This was accomplished by plotting the parameter Ž r K D ru . versus F as presented in Fig. 8. As shown, F changes inversely with Ž r K D ru .. Furthermore, the unsaturated data coin-
68
To
u Žcm3 cmy3 .
D Ž 3 H. Žcm2 hy1 .
R
b
v
SSE
K D Žml gy1 .
F
k Žhy1 .
OakÕille A soil USA1 16.51 USA2 7.272 USA3 2.156 USA4 0.806
1.94 2.08 1.38 1.80
0.390 0.318 0.239 0.213
12.16 10.73 3.800 0.757
2.83"0.13 3.38"0.18 5.46"0.13 7.29"0.33
0.66"0.02 0.61"0.02 0.45"0.01 0.37"0.02
0.60"0.09 0.60"0.08 1.60"0.09 2.24"0.24
0.017 0.009 0.002 0.011
0.45"0.03 0.48"0.04 0.67"0.02 0.84"0.04
0.47"0.06 0.45"0.06 0.33"0.02 0.27"0.03
0.344"0.057 0.112"0.017 0.038"0.003 0.013"0.002
Pipestone soil USP1 USP2 USP3 USP4
17.50 8.397 2.562 1.026
2.12 2.42 1.64 2.30
0.378 0.276 0.212 0.167
11.84 14.42 2.797 0.665
2.64"0.25 3.36"0.20 4.55"0.12 5.86"0.12
0.73"0.06 0.69"0.04 0.57"0.02 0.55"0.02
0.28"0.06 0.45"0.09 1.91"0.28 2.01"0.24
0.033 0.014 0.009 0.006
0.37"0.06 0.40"0.03 0.46"0.02 0.50"0.01
0.56"0.17 0.56"0.09 0.45"0.04 0.46"0.03
0.231"0.073 0.121"0.030 0.084"0.013 0.026"0.003
OakÕille B soil USB1 18.74 USB2 9.180 USB3 2.735 USB4 1.014
2.16 2.56 1.69 2.21
0.337 0.251 0.179 0.169
8.052 7.853 2.089 0.705
1.55"0.08 1.57"0.04 2.21"0.09 2.88"0.28
0.84"0.03 0.86"0.02 0.71"0.02 0.67"0.06
0.19"0.02 0.24"0.09 0.49"0.08 0.27"0.04
0.074 0.011 0.016 0.022
0.12"0.02 0.11"0.01 0.15"0.01 0.23"0.03
0.56"0.16 0.66"0.08 0.50"0.07 0.52"0.14
0.479"0.125 0.309"0.125 0.066"0.014 0.009"0.003
Experiment
Õo Žcm hy1 .
Ninety-five percent confidence limits for K D , F and k were calculated by error propagation using first-order uncertainty analysis and assuming no error in L, u , r , and Õo .
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 6 Results of fitting the nonequilibrium model to DMP unsaturated experiments using dispersion coefficient determined from tritium BTCs
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
69
Fig. 6. Selected BTCs of DMP under unsaturated conditions. Open and closed circles are data of experiment USA2 and USA4, respectively. Lines are simulations using the nonequilibrium model.
cided with the saturated ones, and the low F values of DMP on Oakville A soil appeared to be a result of the high r K D ru associated with these values. These conclusions are based on our previous observations that F is independent of velocity under saturated conditions. This was confirmed by performing a multi-variable analysis that revealed no significant correlation between F and Õo on a 95% confidence level. In addition, the correlation between F and r K D ru ŽFig. 8. was statistically significant Ž95% level.. As the degree of water saturation drops, the large pores are emptied, and the water flow will be restricted to the narrower pore channels. Maraqa Ž1995. reported that desaturation did not cause any change in the retardation coefficient of DMP on these
Fig. 7. Relationship between mass-transfer coefficient and residence time under saturated Žclosed symbols. and unsaturated Žopen symbols. conditions. Circles for Oakville A, diamonds for Pipestone, and triangles for Oakville B soil. Solid line is the best fit of the DMP values under saturated conditions, and dotted one is the best fit of the values under unsaturated conditions.
70
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Fig. 8. Impact of solids concentration and sorption distribution coefficient on the fraction of instantaneous sorption sites for DMP. Open symbols for unsaturated experiments and closed ones for saturated experiments.
soils other than what would be expected as a result of a decrease in moisture content Žsee Eq. Ž2e... Based on this, the author concluded that accessibility of the compound to the solid grains constructing the large, emptied pores occurs through diffusion from the water-filled pores into stagnant water films covering the grains of the emptied pores. The data reported in this paper suggested that this diffusion process was relatively fast compared to the rate of sorption. More importantly, the data indicated that sorption nonequilibrium parameters can be estimated from more-easily-conducted saturated experiments.
5. Summary and conclusions The impact of residence time and degree of water saturation on the values of sorption nonequilibrium parameters was investigated using two NOCs and three soil materials. The assumption of local equilibrium during transport of benzene and DMP was found to be invalid even at low pore-water velocity. The two NOCs exhibit sorption nonequilibrium which appears to be of a diffusive nature rather than a result of slow reaction rates. This was supported by the fact that the fraction of instantaneous sorption sites was independent of the magnitude of the pore-water velocity. Diffusive mass-transfer coefficients varied proportionally with pore-water velocity. Hence, the assumption of a constant diffusion mass-transfer coefficient was not valid. At comparable pore-water velocities, previously reported values of mass-transfer coefficients varied significantly as compared to the ones found in this study. This was found to be a result of variations in the length-scales of the systems and to variations in the retardation coefficient of the organic compounds. A strong relationship between masstransfer coefficient and residence time was found among laboratory-determined values
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
71
of this and other studies. This relationship appears to extend to the much larger residence times of previously reported field values. Using the same soil materials utilized in this study, Maraqa et al. Ž1997. concluded that physical nonequilibrium under unsaturated conditions had not occurred in these experiments. This work further showed that there was no impact of water saturation on the value of the sorption mass-transfer coefficient other than that caused by changes in residence time.
Acknowledgements This research was supported by the National Institute of Environmental Health Sciences through grant number 08-P2ESO4911B.
References Bahr, J.M., 1989. Analysis of nonequilibrium desorption of volatile organics during field test of aquifer decontamination. J. Contam. Hydrol. 4, 205–222. Ball, W.P., Roberts, P.V., 1991. Long-term sorption of halogenated organic chemicals by aquifer material: 2. Intraparticle diffusion. Environ. Sci. Technol. 25, 1237–1249. Biggar, J.W., Nielsen, D.R., 1960. Diffusion effects in miscible displacement occurring in saturated and unsaturated porous materials. J. Geophys. Res. 65, 2887–2895. Bond, W.J., Wierenga, P.J., 1990. Immobile water during solute transport in unsaturated sand columns. Water Resour. Res. 26, 2475–2481. Bouchard, D.C., Wood, A.L., Campell, M.L., Nkedi-Kizza, P., Rao, P.S.C., 1988. Sorption nonequilibrium during solute transport. J. Contam. Hydrol. 2, 209–223. Bowman, B.T., 1989. Mobility and persistence of the herbicides atrazine, metolachlor and teruthylazine in plainfield sand determined using field lysimeters. Environ. Toxicol. Chem. 8, 485–491. Brusseau, M.L., 1992. Nonequilibrium transport of organic chemicals: the impact of pore-water velocity. J. Contam. Hydrol. 9, 353–368. Brusseau, N.L., Rao, P.S.C., 1989. Sorption nonideality during organic contaminant transport in porous media. Critical Rev. Environ. Control 19, 33–99. Brusseau et al., 1990. Brusseau, M.L., Larsen, T., Christensen, T.H., 1991a. Rate-limited sorption and nonequilibrium transport of organic chemicals in low organic carbon aquifer materials. Water Resour. Res. 27, 1137–1145. Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1991b. Nonequilibrium sorption of organic chemicals: elucidation of rate-limiting processes. Environ. Sci. Technol. 25, 134–142. Cameron, D.A., Klute, A., 1977. Convective–dispersive solute transport with a combined equilibrium and kinetic adsorption model. Water Resour. Res. 13, 183–188. Coats, K.H., Smith, B.D., 1964. Dead-end pore volume and dispersion in porous media. Soc. Pet. Eng. J. 4, 73–84. Cussler, E.L., 1984. Diffusion: Mass Transfer in Fluid Systems. Cambridge Univ. Press, New York. De Smedt, F., Wierenga, P.J., 1979. A generalized solution for solute flow in soils with mobile and immobile water. Water Resour. Res. 15, 1137–1141. De Smedt, F., Wierenga, P.J., 1984. Solute transfer through columns of glass beads. Water Resour. Res. 20, 225–232. De Smedt, F., Wauters, F., Sevilla, J., 1986. Study of tracer movement through unsaturated sand. J. Hydrology 85, 169–181. Goltz, M.N., Roberts, P.V., 1986. Interpreting organic solute transport data from a field experiment using physical nonequilibrium models. J. Contam. Hydrol. 1, 77–93.
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Goltz, M.N., Roberts, P.V., 1988. Simulation of physical nonequilibrium solute transport models: application to a large-scale field experiment. J. Contam. Hydrol. 3, 37–63. Harmon, T.C., Semprini, L., Roberts, P.V., 1992. Simulating solute transport using laboratory-based sorption parameters. J. Environ. Eng. 118, 666–689. Hutzler, N.C., Crittenden, J.C., Gierke, J.S., Johnson, A.S., 1986. Transport of organic compounds with saturated groundwater flows: experimental results. Water Resour. Res. 22, 285–295. Karickhoff, S.W., Morris, K.R., 1985. Sorption dynamics of hydrophobic pollutants in sediment suspensions. Environ. Toxicol. Chem. 4, 469–479. Kookana, R.S., Schuller, R.D., Aylmore, L.A.G., 1993. Simulation of simazine transport through soil columns using time-dependent sorption data measured under flow conditions. J. Contam. Hydrol. 14, 93–115. Krupp, H.K., Elrick, D.E., 1968. Miscible displacement in an unsaturated glass bead medium. Water Resour. Res. 4, 809–815. Lee, L.S., Rao, P.S.C., Brusseau, M.L., Ogwada, R.A., 1988. Nonequilibrium sorption of organic contaminants during flow through columns of aquifer materials. Environ. Toxicol. Chem. 7, 779–793. Maraqa, M.A., 1995. Transport of dissolved volatile organic compounds in the unsaturated zone. PhD diss., Michigan State Univ., E. Lansing ŽDiss. Abstr. 96-05907.. Maraqa, M.A., Wallace, R.B., Voice, T.C., 1997. Effects of water saturation on dispersivity and immobile water in sandy soil columns. J. Contam. Hydrol. 25, 199. Maraqa, M.A., Zhao, X., Wallace, R.B., Voice, T.C., 1998. Retardation coefficients of nonionic organic compounds determined by batch and column techniques. Soil Sci. Soc. Am. J. 62, 142–152. Nkedi-Kizza, P., Biggar, J.W., van Genuchten, M.Th., Wierenga, P.J., Selim, H.M., Davidson, J.M., Nielsen, D.R., 1983. Modeling tritium and chloride 36 transport through an aggregated oxisol. Water Resour. Res. 19, 691–700. Nkedi-Kizza, P., Brusseau, M.L., Rao, P.S.C., Hornsby, A.G., 1989. Nonequilibrium sorption during displacement of hydrophobic organic chemicals and 45 Ca through soil columns with aqueous and mixed solvents. Environ. Sci. Technol. 23, 814–820. Parker, T.C., van Genuchten, M.Th., 1984. Determining transport parameters from laboratory and field tracer experiments. Bull. 84-3, Va. Agric. Exp. Stn., Blacksburg. Ptacek, C.J., Gillham, R.W., 1992. Laboratory and field measurements of non-equilibrium transport in the Borden aquifer, Ontario, Canada. J. Contam. Hydrol. 10, 119–158. Rao, P.S.C., Jessup, R.E., Rolston, D.E., Davidson, J.M., Kilcrease, D.P., 1980a. Experimental and mathematical description of nonadsorbed solute transfer by diffusion in spherical aggregates. Soil Sci. Soc. Am. J. 44, 684–688. Rao, P.S.C., Jessup, R.E., Rolston, D.E., Jessup, R.E., Davidson, J.M., 1980b. Solute transport in aggregated media: theoretical and experimental evaluation. Soil Sci. Soc. Am. J. 44, 1139–1146. Russell, D.J., McDuffie, B., 1986. Chemodynamic properties of phthalate esters: partitioning and soil migration. Chemosphere 15, 1003–1021. Schulin, R., Wierenga, P.J., Fluhler, H., Leuenberger, J., 1987. Solute transport through a stony soil. Soil Sci. Soc. Am. J. 5, 36–42. Schulte, E.E., 1988. Recommended Chemical Soil Test Procedure for the Central Region. North Central Regional Pub. No. 221. North Dakota State University, Fargo, ND, pp. 29–32. Schwarzenbach, R.P., Westall, J., 1981. Transport of nonpolar organic compounds from surface water to groundwater: laboratory sorption studies. Environ. Sci. Technol. 15, 1360–1367. van Genuchten, M.Th., Wierenga, P.J., 1976. Mass transfer studies in sorbing porous media: I. Analytical solutions. Soil Sci. Soc. Am. J. 40, 473–480. van Genuchten, M.Th., Wierenga, P.J., 1977. Mass transfer studies in sorbing porous media: experimental evaluation with tritium. Soil Sci. Soc. Am. J. 41, 272–278. van Genuchten, M.Th., Davidson, J.M., Wierenga, P.J., 1974. An evaluation of kinetic and equilibrium equations for the prediction of pesticide movement through porous media. Soil Sci. Soc. Am. J. 38, 29–35.
Effects of residence time and degree of water saturation on sorption nonequilibrium parameters Munjed A. Maraqa a , Roger B. Wallace b, Thomas C. Voice a
b,)
Department of CiÕil Engineering, United Arab Emirates UniÕersity, Al-Ain, United Arab Emirates Department of CiÕil and EnÕironmental Engineering, Michigan State UniÕersity, East Lansing, MI 48824, USA
b
Received 14 October 1997; revised 28 August 1998; accepted 28 August 1998
Abstract This study reports the impact of the degree of water saturation on sorption nonequilibrium parameters. Two nonionic organic compounds Žbenzene and dimethylphthalate. and three nonaggregated sandy soils were utilized. Local equilibrium assumptions were found to be invalid for describing the transport of these compounds even at pore-water velocities as low as 0.7 cmrh. Sorption nonequilibrium appeared to be of a diffusive nature rather than due to a slow chemical reaction. Sorption mass-transfer coefficients varied proportionally with pore-water velocity. A strong correlation between the mass-transfer coefficient and residence time was found utilizing present and previously reported laboratory data. A similar relationship was also found for the mass-transfer coefficient between mobile and immobile water regions. Field data indicate that the sorption mass-transfer coefficient may continue to decrease in a consistent way even at residence times as large as 5 = 10 3 h. Variations in the degree of water saturation had no impact on the value of the sorption mass-transfer coefficient other than what would be expected due to changes in the residence time. This suggested that movement into the solid grains of the large emptied pores through diffusion from the water-filled pores into stagnant water covering these grains was relatively fast compared to the sorption rate. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Pore-water velocity; Mass transfer; Benzene; Dimethylphthalate; Unsaturated flow
1. Introduction The need to consider nonequilibrium sorption in describing transport of dissolved nonionic organic compounds ŽNOCs. has been demonstrated by several laboratory )
Corresponding author. Tel.: q1-517-353-9178; fax: q1-517-355-0250; e-mail: [email protected]
0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 8 . 0 0 1 4 4 - 2
54
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
investigations ŽHutzler et al., 1986; Bouchard et al., 1988; Lee et al., 1988; Brusseau et al., 1991a; Brusseau, 1992; Ptacek and Gillham, 1992. and field studies ŽGoltz and Roberts, 1986, 1988; Bahr, 1989; Bowman, 1989.. Little of this work focused on partially saturated soils. Recently, Maraqa Ž1995. investigated the impact of water saturation on sorption of NOCs under dynamic conditions. The author argued that accessibility of the compounds to the grains in the emptied large pores occurs through diffusion from the water-filled pores into a stagnant water covering these grains ŽFig. 1.. Unless this diffusion process is fast, a higher degree of nonequilibrium can occur in the unsaturated soil than in the saturated soil. Assessment of the effects of water saturation on sorption nonequilibrium is important given that NOCs are commonly introduced in unsaturated zones. In most of the current nonequilibrium transport models, sorption kinetics have been simulated using a formulation that assumes a constant mass-transfer coefficient, one that is independent of pore-water velocity. Recent studies ŽBrusseau, 1992; Kookana et al., 1993. show that these two parameters may be correlated in saturated media. Since degree of water saturation is also typically correlated with pore-water velocity in laboratory experiments with unsaturated media, tracing the cause of any variations in the mass-transfer coefficient in unsaturated media requires separating the influence of pore-water velocity from that due to degree of water saturation. Analysis in unsaturated media is further complicated by the potential existence of an additional nonequilibrium process created by diffusion into and out of immobile water regions that are commonly observed under certain conditions including unsaturated flow Žvan Genuchten and
Fig. 1. Conceptualization of chemical diffusion from water-filled pores into stagnant water covering solid grains and subsequent sorption to the solid grains in the large emptied pores.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
55
Wierenga, 1977; De Smedt and Wierenga, 1979, 1984; De Smedt et al., 1986; Bond and Wierenga, 1990.. Another factor that needed to be considered was the change in the retardation coefficient associated with changes in the degree of water saturation. Maraqa Ž1995. observed that the retardation coefficients for both DMP and benzene increased as the degree of water saturation dropped, independent of pore-water velocity. Based on this observation, it was expected that at the same pore-water velocity a compound would have a higher residence time in unsaturated soils than when the soil was saturated. Brusseau et al. Ž1991a. suggested that differences in the value of the first-order mass-transfer coefficient Ž k . for a given compound at different flow rates could be a result of a time-scale effect, where the value of k is dependent on the length of time of the experiment. If this is the case, then k will be affected by not only pore-water velocity, but also the length of the system and the retardation coefficient of the compound. Our objective was to investigate the dependence of sorption kinetics on residence time and degree of water saturation. To achieve this, we investigated the dependence of k on pore-water velocity and residence time under saturated conditions using data from our experiments and that previously reported by others. The impact that degree of water saturation had on the sorption mass-transfer coefficient was evaluated by comparing values of k determined under both saturated and unsaturated conditions after isolating the effects of residence time.
2. Materials and methods Soil from the A and B horizons of Oakville sand and from the B horizon of a Pipestone sand were collected from North Star, Michigan. Soil samples were air-dried and ground to pass through a 0.85-mm sieve. Each soil sample was characterized for organic carbon using the wet-digestion technique ŽSchulte, 1988. and for particle-size distribution by the hydrometer method, as shown in Table 1. Other characteristics of these soils were reported by Maraqa et al. Ž1997.. Soil samples were packed in glass columns Ž5.45 cm ID. of 30.2 cm length with Teflon end-plates. Some characteristics of the packed soil columns are also presented in Table 1. A porous stainless-steel plate
Table 1 Properties of packed columns Soil
Organic carbon Ž%.
Texture Sand Ž%.
Silt Ž%.
Clay Ž%.
Oakville A Pipestone Oakville B
2.25 1.57 0.70
94.5 95.0 94.5
3.5 3.1 4.0
2.0 1.9 1.5
r Žg cmy3 .
u Žcm3 cmy3 .
1.587 1.636 1.587
0.408 0.383 0.353
56
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
ŽSoil Measurement Systems, Tucson, AZ. that functions as a capillary barrier was attached to the outflow end of each column. Two NOCs were chosen for study: benzene and dimethylphthalate ŽDMP.. 14 C-labeled benzene mixed with cold benzene was used in all the experiments and was analyzed by liquid scintillation counting. DMP was analyzed by high pressure liquid chromatography ŽHPLC. with a UV detector using 50% water: 50% acetonitrile as the mobile phase and a flow rate of 1.5 ml miny1 . Some properties of the two compounds were described by Maraqa et al. Ž1998. and the references cited therein. Pulse-type miscible displacement experiments were conducted under both saturated and unsaturated flow conditions. For the saturated-flow experiments, three different flow rates were employed. The unsaturated experiments were conducted at four levels of uniform saturation. Tensiometers ŽSoil Measurement Systems. were used to measure soil-water suction at one-third and two-thirds the column length. Uniform saturation was achieved by adjusting the flow rate and the applied suction at the bottom of the column until a unit hydraulic gradient was established Žsee Maraqa, 1995; Maraqa et al., 1997.. The two compounds were dissolved in a 0.005 M CaCl 2 solution prepared with deionized, deaired water containing 0.05% sodium azide to inhibit biodegradation ŽRussell and McDuffie, 1986.. The effectiveness of the biocide for benzene and DMP was verified by Maraqa et al. Ž1998.. Batch sorption isotherms of the two compounds using the same soils were also reported by Maraqa et al. Ž1998.. The compounds were injected into the column via a syringe pump using glass syringes. The concentration of benzene and DMP in the injected solution was approximately 30 mg ly1 . After introducing the pulse, the columns were displaced by an organic-compound-free solution. Effluent samples were collected using glass syringes attached to the outlet of the column prior to sample collection. The samples were analyzed for benzene and DMP shortly after collection. The experimental conditions applied in this study as well as the column setup and the sample collection device were exactly the same as those reported by Maraqa et al. Ž1997.. No adsorption, relative to tritium, of the two compounds to the column material was observed in a saturated control experiment using clean glass beads in place of soil. No evidence of DMP hydrolysis was detected as both DMP and phthalic acid Žthe product of DMP hydrolysis., which have different retention times in the HPLC method, were monitored in the effluent samples.
3. Model background and data analysis Two general types of models have been developed to simulate nonequilibrium during transport of solutes in the subsurface: Ž1. transport nonequilibrium models and Ž2. sorption-related nonequilibrium models. Transport nonequilibrium models assume the existence of mobile and immobile water regions with solute transfer between the two water regions ŽCoats and Smith, 1964; van Genuchten and Wierenga, 1976.. The presence of immobile water regions have been associated with aggregated soils Žvan Genuchten and Wierenga, 1976; Nkedi-Kizza et al., 1983. and unsaturated conditions
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
57
ŽBiggar and Nielsen, 1960; De Smedt and Wierenga, 1984; De Smedt et al., 1986; Bond and Wierenga, 1990.. Furthermore, transport nonequilibrium affects the transport of both sorptive as well as non-sorptive solutes. In this study, the two NOCs were injected into the soil columns concurrently with tritium. Based on the analysis of the tritium data ŽMaraqa et al., 1997., transport nonequilibrium was found not to be a factor in these systems. Sorption-related nonequilibrium models are usually categorized into two groups: chemical nonequilibrium models and diffusive mass-transfer models. Chemical nonequilibrium models assume that the sorption reaction is the rate-limiting process ŽCameron and Klute, 1977.. However, diffusive mass-transfer models describe the rate limiting process as physical rather than chemical. Two types of models have been developed in this regard: intraparticle diffusion ŽBall and Roberts, 1991. and intraorganic matter diffusion models ŽBrusseau et al., 1991b.. Generated breakthrough curves ŽBTCs. were analyzed using both equilibrium and nonequilibrium approaches. The equilibrium model for a linear sorption reaction is given as: R
1 E 2C
EC ET
s
P EZ
2
EC y
Ž 1.
EZ
where, C s crco
Ž 2a .
Z s zrL
Ž 2b .
T s Õo trL
Ž 2c .
P s Õo LrD
Ž 2d .
Rs1q
rKD
Ž 2e .
u
here c is the solute concentration, c o is the solute concentration in the influent solution, z is distance, L is the column length, t is time, T is the number of pore volumes, Õo is the average pore-water velocity, D is the hydrodynamic dispersion coefficient, P is the Peclet number, r is the soil bulk density, u is the moisture content, K D is the sorption distribution coefficient, and R is the retardation coefficient. The dimensionless equations of the two-site nonequilibrium models for linear sorption behavior are given as:
bR
EC ET
q Ž1yb . R
Ž1yb . R
E Q2 ET
E Q2 ET
1 E 2C s
P EZ
s v Ž C y Q2 .
2
EC y
EZ
Ž 3. Ž 4.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
58
where,
bs
u q Fr K D
Q2 s
vs
Ž 5a .
uqrKD 1
q2
Ž 1 y F . K D co
kL Õo
Ž1yb . R
Ž 5b . Ž 5c .
here q2 is the sorbed concentration in the rate-limited domain, F is the fraction of sorbent for which sorption is instantaneous, b and v are the dimensionless parameters that specify the degree of nonequilibrium in the system. BTCs of benzene and DMP were analyzed to determine the optimized parameter values, and their confidence intervals using the nonlinear least squares inversion program CXTFIT of Parker and van Genuchten Ž1984.. To achieve better accuracy in the numerical integration, the relative error in CXTFIT was reduced from 5 = 10y5 to 5 = 10y7 .
4. Results and discussion 4.1. Saturated flow experiments Input parameter values for Õo , D, and the number of pore volumes of benzene and DMP solution injected ŽTo . used in the simulation of the saturated experiments are listed Table 2. Values of D used are those determined for tritium which was displaced concurrently with benzene and DMP. Discrepancy between R values determined by batch and column techniques, as reported by Maraqa et al. Ž1998. for benzene and DMP and the same soils, did not allow us to use independently determined batch retardation coefficients in the simulations. The best fit values of R for benzene and DMP using the equilibrium approach along with the sum of square errors ŽSSE. are also shown. Optimum values of R, b , and v along with their 95% confidence limits and the SSE values were obtained using the nonequilibrium approach ŽTable 3.; values of K D , F, and k calculated using Eqs. Ž2e., Ž5a. and Ž5c., respectively, and their 95% confidence limits are also listed. Example simulations based on the best fit R for the equilibrium model and the best fit values of R, b and v for the nonequilibrium model are shown in Fig. 2. The nonequilibrium model simulation closely matched the experimental results, while deviations between the equilibrium model simulation and the data points were significant. Comparison of corresponding SSE values ŽTables 2 and 3. revealed that the nonequilibrium model performed better than the equilibrium model, in all cases. The improvement in performance appeared to increase as the soil organic matter increased, consistent with the findings of Bouchard et al. Ž1988. and of Brusseau et al. Ž1991a.. This rate limitation appeared to be due to slow sorptive interactions and not due to slow diffusion into and
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
59
Table 2 Results of fitting the advection–dispersion model to the saturated experiments using independently determined dispersion coefficient Experiment
Tracer
OakÕille A soil SA1 Benzene DMP SA3 Benzene DMP SA6 Benzene DMP Pipestone soil SP1 Benzene DMP SP3 Benzene DMP SP6 Benzene DMP OakÕille B soil SB1 Benzene DMP SB3 Benzene DMP SB6 Benzene DMP a
Õo Žcm hy1 .
To
D for 3 H Žcm2 hy1 .
R
SSE a
31.55
1.95
20.88
6.30
1.96
5.37
0.62
1.91
0.222
1.98Ž"0.05. 2.14Ž"0.08. 2.05Ž"0.07. 2.50Ž"0.05. 2.19Ž"0.08. 2.86Ž"0.07.
0.214 0.635 0.354 0.980 0.445 1.405
33.60
2.08
18.78
6.72
2.09
2.88
0.67
2.05
0.156
2.09Ž"0.08. 1.95Ž"0.08. 2.15Ž"0.06. 2.14Ž"0.10. 2.32Ž"0.08. 2.55Ž"0.10.
0.185 0.419 0.432 1.060 0.377 0.702
36.47
2.18
18.04
7.29
2.20
3.27
0.73
2.17
0.204
1.36Ž"0.06. 1.41Ž"0.04. 1.43Ž"0.03. 1.54Ž"0.05. 1.44Ž"0.05. 1.52Ž"0.04.
0.540 0.368 0.250 0.350 0.260 0.310
SSE is the sum of square errors.
out of immobile water regions, since the simultaneous transport of tritium through the same soil columns ŽMaraqa et al., 1997. was described adequately using an equilibrium model. The values of R found by fitting the nonequilibrium model were higher than those produced with the equilibrium model ŽTables 2 and 3.. Moreover, equilibrium model R values appeared to decrease with increased flow rate. Dependence of R on the flow rate, as discussed by Brusseau et al. Ž1991a., is generally regarded as an indication of sorption-related nonequilibrium in which case retardation coefficients determined with the equilibrium model may not provide a good measure of actual retardation. The values of R predicted with the nonequilibrium model did not have this trend, except for DMP on Oakville A soil. Velocity dependent R may indicate the presence of an additional physical or chemical process not currently included in the adopted nonequilibrium model, but become apparent only at relatively large spatial or time scales. 4.2. Impact of pore-water Õelocity and residence time No functional relationship was found between F ŽTable 3. and pore-water velocity ŽTable 2. for the two compounds using the three soils. This is consistent with observations made by Brusseau et al. Ž1991a., but in conflict with those reported by
60
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 3 Results of fitting the nonequilibrium model to the saturated experiments using dispersion coefficient determined from tritium BTCs Experiment
Tracer
OakÕille A soil SA1 Benzene DMP SA3
Benzene DMP
SA6
Benzene DMP
Pipestone soil SP1 Benzene DMP SP3
Benzene DMP
SP6
Benzene DMP
OakÕille B soil SB1 Benzene DMP SB3
Benzene DMP
SB6
Benzene DMP
R
b
v
SSE
K D Žml gy1 . wEq. Ž2e.x
F wEq. Ž5a.x
k Žhy1 . wEq. Ž5c.x
2.45" 0.13 2.95" 0.16 2.78" 0.84 3.28" 0.25 2.73" 0.17 4.03" 0.19
0.787" 0.007 0.642" 0.032 0.693" 0.193 0.639" 0.033 0.755" 0.038 0.583" 0.023
0.265" 0.051 0.528" 0.068 0.204" 0.079 0.718" 0.168 0.383" 0.072 0.977" 0.117
0.018
0.373" 0.033 0.501" 0.041 0.458" 0.022 0.586" 0.064 0.445" 0.044 0.779" 0.049
0.64" 0.09 0.46" 0.08 0.52" 0.30 0.48" 0.10 0.61" 0.11 0.45" 0.06
0.534" 0.108 0.526" 0.084 0.050" 0.037 0.127" 0.033 0.011" 0.005 0.012" 0.002
2.76" 0.34 2.83" 0.29 2.74" 0.19 2.92" 0.21 2.75" 0.14 2.77" 0.06
0.733" 0.083 0.640" 0.050 0.750" 0.040 0.660" 0.030 0.797" 0.037 0.740" 0.020
0.220" 0.048 0.381" 0.064 0.302" 0.056 0.610" 0.130 0.342" 0.072 1.170" 0.320
0.027
0.412" 0.080 0.428" 0.068 0.407" 0.044 0.447" 0.049 0.410" 0.033 0.414" 0.014
0.58" 0.22 0.44" 0.15 0.61" 0.12 0.48" 0.10 0.68" 0.10 0.59" 0.04
0.334" 0.130 0.419" 0.094 0.099" 0.027 0.138" 0.034 0.014" 0.005 0.036" 0.011
1.64" 0.02 1.85" 0.17 1.61" 0.15 1.70" 0.06 1.65" 0.03 1.73" 0.04
0.850" 0.050 0.756" 0.034 0.894" 0.079 0.820" 0.024 0.870" 0.058 0.796" 0.016
0.110" 0.020 0.176" 0.032 0.161" 0.015 0.259" 0.045 0.225" 0.037 0.570" 0.170
0.184
0.142" 0.004 0.189" 0.038 0.136" 0.033 0.156" 0.013 0.145" 0.007 0.162" 0.009
0.62" 0.13 0.47" 0.19 0.72" 0.29 0.56" 0.10 0.67" 0.16 0.52" 0.06
0.544" 0.208 0.474" 0.116 0.229" 0.084 0.206" 0.050 0.026" 0.014 0.039" 0.014
0.012 0.104 0.048 0.030 0.015
0.033 0.028 0.059 0.029 0.022
0.049 0.164 0.049 0.026 0.016
Ninety-five percent confidence limits for K D , F and k were calculated by error propagation using first-order uncertainty analysis and assuming no error in L, u , r , and Õo .
Kookana et al. Ž1993.. As suggested by Schwarzenbach and Westall Ž1981., the F factor would likely be a function of velocity for a chemical nonequilibrium process involving a number of different reaction times. Conversely, F should be fairly independent of
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
61
Fig. 2. Selected BTCs of benzene Žtriangles. and DMP Žcircles.. Dashed lines are simulations using the equilibrium model and solid lines are simulations using the nonequilibrium model.
velocity for nonequilibrium caused by slow diffusion ŽBrusseau et al., 1991a.. Therefore, independence of F on velocity for the data presented here suggested that sorption nonequilibrium was due to slow diffusion. Fig. 3 plots the values of k ŽTable 3. versus pore-water velocity ŽTable 2.. Dependence of k on pore-water velocity was obvious and inconsistent with a constant mass-transfer coefficient for either compound on any of the three soils. While the values
Fig. 3. Dependence of mass-transfer coefficient on pore-water velocity. Circles for Oakville A, diamonds for Pipestone, and triangles for Oakville B soil, open symbols for DMP and closed ones for benzene.
62
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
of k were clearly dependent on pore-water velocity, it appeared that they were independent of compound or soil. The dependence of k on velocity cannot be attributed to changes in K D , since for all sorbate–sorbent combinations, with the exception of DMP on Oakville A, there was no apparent dependence of K D on pore-water velocity ŽTable 3.. Variation of k with pore-water velocity has been previously reported Žvan Genuchten et al., 1974; Brusseau et al., 1991a; Brusseau, 1992; Kookana et al., 1993.. Similar behavior has also been observed for mass transfer of nonsorbing solutes between mobile and immobile water regions Žvan Genuchten and Wierenga, 1977; Nkedi-Kizza et al., 1983; De Smedt and Wierenga, 1984; De Smedt et al., 1986; Schulin et al., 1987.. For nonsorbing solutes, the increase in mass-transfer coefficient Ž a . with increasing porewater velocity is attributed either to higher mixing in the mobile phase at high pore-water velocities Žvan Genuchten and Wierenga, 1977; De Smedt and Wierenga, 1984. or to shorter diffusion path lengths as a result of a decrease in the amount of immobile water Žvan Genuchten and Wierenga, 1977.. Since sorbate mass transfer occurs within either the sorbent or the intraparticle pores it is unlikely that k is affected by velocity induced mixing. Values of k reported by several investigators for NOCs, along with the relevant experimental conditions were summarized in Table 4. All the values of k ŽTable 4. were obtained using the same transport model as that used in this study. At comparable pore-water velocities, the values of k we determined were in agreement with those of Brusseau et al. Ž1991a. and Kookana et al. Ž1993.. Our values, however, were lower than those of Lee et al. Ž1988., Brusseau et al. Ž1990., Ptacek and Gillham Ž1992., and Brusseau Ž1992.. Inspection of Table 4 revealed that the agreement or disagreement between our values ŽTable 3. and those of other investigators ŽTable 4. was associated with the length of the column employed. To evaluate the importance of accounting for different column lengths, values of log k ŽTables 3 and 4. were regressed on values of log Õo and log LrÕo to obtain Eqs. Ž6a. and Ž6b. ŽTable 5.. Comparison of the coefficients of determination ŽTable 5. for the regression on log Õo Ž r 2 s 0.71. with that for the regression on log LrÕo Ž r 2 s 0.87. indicated that the hydraulic residence time Ž LrÕo . was a better parameter for explaining the observed variations in log k than was pore-water velocity alone. This suggests that the mass-transfer coefficient is a time dependent parameter. Since k was determined from BTCs of compounds having different retardation coefficients, it is perhaps more appropriate to characterize the time for mass transfer by the residence time Ž LRrÕo .. Values of log k were regressed on values of log LRrÕo ŽFig. 4. to obtain Eq. Ž6c. of Table 5. Eq. Ž6c. showed that there was a consistent trend for the mass-transfer coefficient to decrease as the residence time of the tracer increased. The equation suggested a linear log–log relationship between mass-transfer coefficient and inverse residence time. With the additional improvement in the coefficient of determination, variation in log LRrÕo explained 92% of the observed variation in log k. This strengthened the evidence that the mass-transfer coefficient is a time dependent parameter. Factors in addition to residence time would be required to reduce the remaining unexplained variation in log k. Since Eqs. Ž6a., Ž6b. and Ž6c. were developed by pooling all of the experimental data ŽTables 3 and 4., tracer and soil properties may
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
63
Table 4 Review of laboratory-determined mass-transfer coefficient for some organic compounds along with the experimental conditions Compounda Brusseau, 1992 PXY PXY NAP NAP PCE PCE 1,4-DCB 1,4-DCB NAP NAP PCE PCE Nkedi-Kizza et al., 1989 b Atrazine Diuron Brusseau et al., 1990 c BNZ CB DCB TCB Brusseau et al., 1991a CT TCE PCE PXY 1,4-DCB 1,2-DCB NAP BIP
Õo L Žcm hy1 . Žcm.
R
k Compounda Õo L R Žhy1 . Žcm hy1 . Žcm.
89.0 5.0 45.0 5.0 45.0 5.0 90.0 5.0 53.0 6.0 93.0 5.0
7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 6.75 6.75
1.48 14.20 1.48 0.50 2.00 6.10 2.04 0.30 2.11 4.90 2.22 0.20 1.72 17.00 1.48 0.90 2.22 4.40 2.04 0.60 2.25 11.40 2.27 0.60
5.0 5.0
5.0 5.0
1.80 4.37
90.0 90.0 90.0 90.0
5.3 5.3 5.3 5.3
0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
30.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0
0.77 0.15
1.33 23.50 2.23 17.00 4.87 9.80 13.50 3.46 1.50 1.50 2.10 2.20 4.60 4.90 1.40 2.30
0.08 d 0.12 0.08 0.06 0.02 0.02 0.08 0.09
Lee et al., 1988 TCE 24.0 6.0 TCE 24.0 8.8 PXY 24.0 6.0 PXY 24.0 8.8 Ptacek and Gillham, 1992 BROM 12.08 10.0 CT 12.08 10.0 PCE 12.08 10.0 1,2-DCB 12.08 10.0 HAC 12.08 10.0 BROM 12.08 10.0 CT 12.08 10.0 PCE 12.08 10.0 1,2-DCB 12.08 10.0 HAC 12.08 10.0 BROM 0.75 10.0 CT 0.75 10.0 PCE 0.75 10.0 1,2-DCB 0.75 10.0 HAC 0.75 10.0 BROM 0.75 10.0 CT 0.75 10.0 PCE 0.75 10.0 1,2-DCB 0.75 10.0 HAC 0.75 10.0 Kookana et al., 1993 simazine 37.2 30.0 simazine 18.6 30.0 simazine 3.7 30.0 simazine 1.9 30.0
k Žhy1 .
1.61 1.43 2.65 2.02
5.23 d 4.52 d 2.81d 2.70 d
1.08 1.17 1.40 1.71 2.15 1.32 1.63 1.60 1.98 2.24 1.29 1.35 2.65 3.05 4.10 1.40 1.42 2.31 3.06 2.84
5.58 1.58 2.88 2.18 1.25 1.12 0.76 2.55 1.58 1.70 0.23 0.15 0.07 0.10 0.06 0.17 0.18 0.06 0.07 0.16
3.66 3.66 3.66 3.66
0.24 d 0.12 d 0.06 d 0.04 d
a
PXYs p-xylene, NAPs naphthalene, PCEs tetrachloroethylene, 1,4-DCBs1,4-dichlorobenzene, TCEs trichloroethylene, TC s carbon tetrachloride, 1,2-DCB s1,2-dichlorobenzene, BIP s biphenyl, BNZ s benzene, CBs chlorobenzene, DCBsdichlorobenzene, TCBs trichlorobenzene, BROMs bromoform, HAC s hexachloroethane. b Only the values for the experiments with aqueous phase Ži.e., f c s 0.. Reported velocity is 5–6 cm hy1 . A value of 5.0 cm hy1 is assumed here. c Values for the miscible displacement experiments. d Calculated using the reported v values and Eq. Ž5c..
still have an important influence beyond that described by residence time. For example, it has been observed that k depends on K D ŽKarickhoff and Morris, 1985; Brusseau and Rao, 1989; Brusseau et al., 1991a,b.. This was also noticed in our data ŽTable 3. at the low and intermediate flow rates, but it was not obvious at the high flow rate. Eq. Ž6c. accounts for the dependence of k on K D but only as the latter affects residence time.
64
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 5 Relationships between mass-transfer coefficient and some system parameters Relationship and equation number
r2
Na
Organic compounds log k s 0.99 log Õo y1.18Ž6a. log k sy0.90 logŽ Lr Õo .y0.08Ž6b. log k sy0.90 logŽ LR r Õo .q0.23Ž6c.
0.71 0.87 0.92
72 72 72
Ideal or near-ideal tracers log a s 0.79 log Õo y1.47Ž7a. log a sy0.82 logŽ LR r Õo .y0.56Ž7b.b
0.57 0.72
72 72
Unsaturated, nonaggregated media log a s 0.85 log Õo y1.22Ž8a. log a sy0.80 logŽ LR r Õo .y0.02Ž8b.c
0.71 0.91
13 13
Aggregated media log a s 0.71 log Õo y1.51Ž9a. log a sy0.79 logŽ LR r Õo .y0.70Ž9b.b
0.52 0.80
59 59
a
N is the number of data points. When an R value was reported, it was used. Otherwise, R was assumed to be 1.0. c Rs1.0. b
Fig. 4 also shows the relationship between a , the coefficient for mass transfer between mobile and immobile water regions of ideal or near ideal tracers, and residence time. The line was generated using two, previously reported, types of data. One set of data was obtained using unsaturated, nonaggregated media ŽKrupp and Elrick, 1968; De Smedt and Wierenga, 1984; De Smedt et al., 1986., while the other set was obtained
Fig. 4. Dependence of sorption mass-transfer coefficient on residence time based on this and previous studies.
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
65
using aggregated media Žvan Genuchten and Wierenga, 1977; Rao et al., 1980b; Nkedi-Kizza et al., 1983.. All the values of a were determined using a transport model that was mathematically the same as that used in this study. The improvement in the fit achieved by using residence time rather than pore-water velocity was made obvious by comparing the coefficient of determination of Eq. Ž7a. with that of Eq. Ž7b. ŽTable 5.. The relationship between a and LRrÕo ŽEq. Ž7b.. was not as strong as for k ŽEq. Ž6c... This was partly due to differences in the nature of the data sets for a . When each data set was regressed separately to obtain Eqs. Ž8b. and Ž9b. both coefficients of determination increased. As compared to Eq. Ž6c., the low r 2 associated with Eq. Ž9b. may be due to unaccounted for variations in the size of aggregates employed. Nevertheless, the similarity between Eqs. Ž6c. and Ž7b. suggests a similar mechanistic behavior of the two mass transfer processes. This is not surprising given that both mass-transfer coefficients have been related to a molecular diffusion coefficient and a diffusion path length. For spherical aggregates a is given as ŽHarmon et al., 1992.:
as
15De u im b2
Ž 10a.
where De is the effective pore diffusion coefficient, u im is the immobile water content, and b is a characteristic diffusion length. Similarly, for the case where sorption nonequilibrium is due to intraorganic matter diffusion, the mass-transfer coefficient Ž k OM . is given as ŽBrusseau et al., 1991b.: k OM s
Sf DOM 2
l Ž1yF .
Ž 10b.
where sf is a shape factor, DOM is the effective diffusion coefficient in the organic matter matrix, and l is a characteristic diffusion length. Eqs. Ž10a. and Ž10b. do not account directly for changes in mass-transfer coefficient with residence time. Theoretical analysis and experimental data presented by Rao et al. Ž1980a. for non-sorbing tracers shows that a mass transfer model that only considers average concentration within mobile and immobile water regions, similar to the one used here, yields a mass-transfer coefficient that decreases with increasing time of diffusion and reaches a constant value for large times. By analogy, the dependence of k on residence time for sorbed tracers could be due to the inadequacy of the commonly used mass transfer model ŽEq. Ž4.. in that it does not account for variations in concentration along the diffusion path length. Nkedi-Kizza et al. Ž1983. observed that the mass-transfer coefficient is sensitive to solution concentration. Therefore, variations of k with time could be a result of changes in either the diffusion coefficient or in the characteristic diffusion length created by changes in the local aqueous solution concentration driving diffusive mass transfer. Schwarzenbach and Westall Ž1981. proposed using a continuous distribution of k’s to describe the effect of flow velocity on transport of chemicals affected by sorption nonequilibrium. The different k values, as indicated by the authors, would correspond to different diffusion path lengths. On the other hand, concentration-dependent diffusion coefficients have been reported ŽCussler, 1984.. If this is the case, then at a given flow
66
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
rate, the value of mass-transfer coefficient obtained represents a time-averaged value that corresponds to a time-averaged diffusion coefficient. Consequently, a different time-averaged mass transfer value would be obtained for a different residence time. 4.3. Applicability of Eq. (6c) to field data Although Eq. Ž6c. covers a wide range of residence times Ž0.1–195 h., the upper values in this range are still small compared to field residence times associated with contaminant plumes. Furthermore, the laboratory data from which Eq. Ž6c. was developed were obtained using homogenized, packed soil samples, and the influence of field heterogeneity on the values of the nonequilibrium parameters is unknown. Eq. Ž6c. was compared to two data sets ŽGoltz and Roberts, 1986; Ptacek and Gillham, 1992. collected at the Canadian Forces Base Borden in Southern Ontario, Canada. Ptacek and Gillham Ž1992. determined k for the same organic compounds utilized in their laboratory experiments ŽTable 4. at pore-water velocities of 11.25 and 15.8 cm hy1 . Their values were determined from BTCs generated by collecting samples over a short length scale Ž10 cm.. Residence times for their experiments Ž1.00–2.44 h. fall within the range of values observed ŽTables 3 and 4. in the laboratory used to obtain Eq. Ž6c.. Using the values of Õo , L, and R reported by Ptacek and Gillham Ž1992., the predicted k values based on Eq. Ž6c. were 2.2–6.4 times lower than the reported ones, but fell within or close to the 95% confidence limits of the predictive relationship ŽFig. 5.. Predicted values of k appeared to be in reasonable agreement with values obtained in the laboratory considering that the soil was not homogenized and the groundwater temperature was 8 " 28C in the field.
Fig. 5. Comparison between laboratory- and field-determined mass-transfer coefficients for organic compounds.
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67
Goltz and Roberts Ž1986. obtained identical values of k Ž1.7 = 10y4 hy1 . for carbon tetrachloride, and tetrachloroethylene by analyzing aqueous samples collected 5 m from a line of injection wells. The average-pore water velocity was 0.33 cm hy1 , and the retardation coefficients were 1.8 and 3.0, respectively. The mass-transfer coefficient was about 2 orders of magnitude lower that our lowest laboratory values, which were comparable to the lowest values obtained by Brusseau et al. Ž1991a.. Brusseau et al. Ž1991a. suggests that the low k value obtained by Goltz and Roberts Ž1986. could be due to heterogeneities in hydraulic conductivity and sorption capacity. Extrapolation of Eq. Ž6c. form the largest laboratory values of LRrÕo s 195 h to the much larger values of 2.7 = 10 3 h and 4.5 = 10 3 h encountered in Goltz and Roberts’ field experiment, shows that about 90% of the difference in k between the lowest laboratory values and Goltz and Roberts’ field values can be explained by accounting for the effect of the much larger residence time of the field experiment. On the bases of this large-scale field experiment, it appears that Eq. Ž6c. can be extended to large values of residence time. 4.4. Unsaturated flow experiments The nonequilibrium model was used to analyze the DMP data under unsaturated conditions. Fixed parameter values for Õo , To and D used in fitting are listed in Table 6. The values of D are those for tritium which was injected into the soil columns concurrently with DMP. The assumption was made here that physical nonequilibrium is not important during the transport of sorbing tracers based on the analysis presented by Maraqa et al. Ž1997. for the transport of non-sorbing tracers. The best fit values of R, b and v for DMP and their confidence intervals are also reported in Table 6. Values for F and k are estimated using Eqs. Ž5a. and Ž5c., respectively, along with the values of R and Õo that are listed in the table. An example of the fit achieved with the nonequilibrium model at two levels of saturation using Oakville A soil is shown in Fig. 6. For the saturated-flow experiments, the mass-transfer coefficient, k, was found to depend on residence time. Since saturation and pore-water velocity are coupled in the unsaturated experiments, the values of k determined under unsaturated-flow conditions were expected to vary with saturation. The impact of saturation on k was investigated by comparing the values of k for both saturated and unsaturated experiments at the same residence time ŽFig. 7.. Although the unexplained variation in k for the unsaturated experiments was greater than for the saturated case, the expected values of k for any given residence time were essentially the same for both saturated and unsaturated soils. This provides evidence that the mass-transfer coefficient retains the same value independent of the degree of water saturation, as long as changes in residence time with saturation have been accounted for. The values of F for DMP on Oakville A ŽTable 6. decreased with saturation although this trend was not obvious for the other soils. As saturation dropped, the solids concentration Ž rru . increased. Karickhoff and Morris Ž1985. reported a dependence of F on the parameter r K D ru . Therefore, to assess the impact of saturation on F, the effect of changes in the solids concentration should be accounted for. This was accomplished by plotting the parameter Ž r K D ru . versus F as presented in Fig. 8. As shown, F changes inversely with Ž r K D ru .. Furthermore, the unsaturated data coin-
68
To
u Žcm3 cmy3 .
D Ž 3 H. Žcm2 hy1 .
R
b
v
SSE
K D Žml gy1 .
F
k Žhy1 .
OakÕille A soil USA1 16.51 USA2 7.272 USA3 2.156 USA4 0.806
1.94 2.08 1.38 1.80
0.390 0.318 0.239 0.213
12.16 10.73 3.800 0.757
2.83"0.13 3.38"0.18 5.46"0.13 7.29"0.33
0.66"0.02 0.61"0.02 0.45"0.01 0.37"0.02
0.60"0.09 0.60"0.08 1.60"0.09 2.24"0.24
0.017 0.009 0.002 0.011
0.45"0.03 0.48"0.04 0.67"0.02 0.84"0.04
0.47"0.06 0.45"0.06 0.33"0.02 0.27"0.03
0.344"0.057 0.112"0.017 0.038"0.003 0.013"0.002
Pipestone soil USP1 USP2 USP3 USP4
17.50 8.397 2.562 1.026
2.12 2.42 1.64 2.30
0.378 0.276 0.212 0.167
11.84 14.42 2.797 0.665
2.64"0.25 3.36"0.20 4.55"0.12 5.86"0.12
0.73"0.06 0.69"0.04 0.57"0.02 0.55"0.02
0.28"0.06 0.45"0.09 1.91"0.28 2.01"0.24
0.033 0.014 0.009 0.006
0.37"0.06 0.40"0.03 0.46"0.02 0.50"0.01
0.56"0.17 0.56"0.09 0.45"0.04 0.46"0.03
0.231"0.073 0.121"0.030 0.084"0.013 0.026"0.003
OakÕille B soil USB1 18.74 USB2 9.180 USB3 2.735 USB4 1.014
2.16 2.56 1.69 2.21
0.337 0.251 0.179 0.169
8.052 7.853 2.089 0.705
1.55"0.08 1.57"0.04 2.21"0.09 2.88"0.28
0.84"0.03 0.86"0.02 0.71"0.02 0.67"0.06
0.19"0.02 0.24"0.09 0.49"0.08 0.27"0.04
0.074 0.011 0.016 0.022
0.12"0.02 0.11"0.01 0.15"0.01 0.23"0.03
0.56"0.16 0.66"0.08 0.50"0.07 0.52"0.14
0.479"0.125 0.309"0.125 0.066"0.014 0.009"0.003
Experiment
Õo Žcm hy1 .
Ninety-five percent confidence limits for K D , F and k were calculated by error propagation using first-order uncertainty analysis and assuming no error in L, u , r , and Õo .
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
Table 6 Results of fitting the nonequilibrium model to DMP unsaturated experiments using dispersion coefficient determined from tritium BTCs
M.A. Maraqa et al.r Journal of Contaminant Hydrology 36 (1999) 53–72
69
Fig. 6. Selected BTCs of DMP under unsaturated conditions. Open and closed circles are data of experiment USA2 and USA4, respectively. Lines are simulations using the nonequilibrium model.
cided with the saturated ones, and the low F values of DMP on Oakville A soil appeared to be a result of the high r K D ru associated with these values. These conclusions are based on our previous observations that F is independent of velocity under saturated conditions. This was confirmed by performing a multi-variable analysis that revealed no significant correlation between F and Õo on a 95% confidence level. In addition, the correlation between F and r K D ru ŽFig. 8. was statistically significant Ž95% level.. As the degree of water saturation drops, the large pores are emptied, and the water flow will be restricted to the narrower pore channels. Maraqa Ž1995. reported that desaturation did not cause any change in the retardation coefficient of DMP on these
Fig. 7. Relationship between mass-transfer coefficient and residence time under saturated Žclosed symbols. and unsaturated Žopen symbols. conditions. Circles for Oakville A, diamonds for Pipestone, and triangles for Oakville B soil. Solid line is the best fit of the DMP values under saturated conditions, and dotted one is the best fit of the values under unsaturated conditions.
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Fig. 8. Impact of solids concentration and sorption distribution coefficient on the fraction of instantaneous sorption sites for DMP. Open symbols for unsaturated experiments and closed ones for saturated experiments.
soils other than what would be expected as a result of a decrease in moisture content Žsee Eq. Ž2e... Based on this, the author concluded that accessibility of the compound to the solid grains constructing the large, emptied pores occurs through diffusion from the water-filled pores into stagnant water films covering the grains of the emptied pores. The data reported in this paper suggested that this diffusion process was relatively fast compared to the rate of sorption. More importantly, the data indicated that sorption nonequilibrium parameters can be estimated from more-easily-conducted saturated experiments.
5. Summary and conclusions The impact of residence time and degree of water saturation on the values of sorption nonequilibrium parameters was investigated using two NOCs and three soil materials. The assumption of local equilibrium during transport of benzene and DMP was found to be invalid even at low pore-water velocity. The two NOCs exhibit sorption nonequilibrium which appears to be of a diffusive nature rather than a result of slow reaction rates. This was supported by the fact that the fraction of instantaneous sorption sites was independent of the magnitude of the pore-water velocity. Diffusive mass-transfer coefficients varied proportionally with pore-water velocity. Hence, the assumption of a constant diffusion mass-transfer coefficient was not valid. At comparable pore-water velocities, previously reported values of mass-transfer coefficients varied significantly as compared to the ones found in this study. This was found to be a result of variations in the length-scales of the systems and to variations in the retardation coefficient of the organic compounds. A strong relationship between masstransfer coefficient and residence time was found among laboratory-determined values
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of this and other studies. This relationship appears to extend to the much larger residence times of previously reported field values. Using the same soil materials utilized in this study, Maraqa et al. Ž1997. concluded that physical nonequilibrium under unsaturated conditions had not occurred in these experiments. This work further showed that there was no impact of water saturation on the value of the sorption mass-transfer coefficient other than that caused by changes in residence time.
Acknowledgements This research was supported by the National Institute of Environmental Health Sciences through grant number 08-P2ESO4911B.
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