Environ. Sci. Techno/. 1995, 29, 1032-1042
Introduction
ZAFAR ADEEL* A N D R I C H A R D G . LUTHY Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Sorption of nonionic surfactant onto aquifer sediment affects both surfactant transport and related surfactant solubilization properties as well as the potential for surfactant-aided mobilization of organic com pounds in sed ime nt-aq ueous systems. Column experiments were conducted to evaluate the transport and sorption of a nonionic surfactant, Triton X-100, onto an aquifer sediment material, Lincoln fine sand. Unusual two-step breakthrough curves were observed in the column tests, suggesting the existence of t w o sorption regimes dependent on the sorbed surfactant concentration and molecular conformation. Elution of the sorbed surfactant exhibited considerable tailing. A simplified two-stage, sorption kinetic model is proposed as a first approximation toward characterizing the sorption phenomena, where sorption in each stage is governed by a specific kinetic parameter. The results from this study indicate the importance of kinetic phenomena to describe surfactant transport in sediments.
Recent researchhas investigated the feasibilityof surfactant solutions in assisting the removal of organic contaminants from soils and aquifer sediments. Such work has addressed surfactant-facilitatedremoval of organic contaminants for possible applications in in-situ and ex-situ treatments (15). Much of the research performed to date has evaluated either the enhanced solubilizationof hydrophobic organic compounds (HOCs) by micellar surfactant solutions for applications in soil washing or flushingtreatment systems or the lowering of interfacial tension of organic liquids by surfactants in miscible displacement techniques (2-6). A few investigationshave examined the sorption of surfactant onto soils or sediments (7-10). It has been demonstrated by these studies that sorption of surfactant onto soil or aquifer sediment affectsthe micellar solubilization of HOCs. The research presented in this paper comprises experiments with a nonionic surfactant and a clean aquifer sediment. The primary objectiveof this work is to observe the transport of the nonionic surfactant through the aquifer sediment and to investigate the effect of sorption phenomena and related kinetics on surfactant transport. An empirical model is presented to describe the coupled sorption and transport of the nonionic surfactant. An understanding of surfactant sorption kinetics in flow situations would assist the prediction of micellar mobilization or facilitated transport of HOCs and the evaluation of surfactant applicationsin engineered remediation systems.
Nonionic Surfactant Sorption Nonionic surfactant molecules may sorb directly onto solid surfaces or may interact with sorbed surfactant molecules, the sorption mechanism being dependent on the nature of the sorbent and the surfactant dose (11). At low surfactant doses, the surfactant molecules maybe sorbing to amineral surface or to a clean sediment that has very few sorbed surfactant molecules, and sorption may occur mainly due to van der Waals interactions between the hydrophobic and the hydrophilic moieties of the surfactant and the surface (12). In comparison, at higher surfactant doses such sorption may entail the formation of more structured arrangements including the formation of monomer surfactant clusters on the surface or a second layer, for which these arrangements may be governed mainly by interactions between hydrophobic moieties of the surfactant molecules (12-14).
Figure 1 shows experimental batch test results for sorption of Triton X-100 onto Lincoln fine sand (11). The data are expressed as the logarithm of sorbed-phase concentration (mol/g of solid) versus the logarithm of the bulk aqueous-phasesurfactant concentration (mol/L).The sorption data reveal some complex relationships. At low surfactant concentrations in region 1, the sorption is Freundlich-type,up to the point at which the critical micelle concentration (cmc)is reached in the aqueous phase. There is an intermediate region beyond which the sorption appears to be Freundlich-type in region 2. The transition from the intermediate region to region 2 occurs at a bulk aqueous-phase surfactant concentration identified as Ci,,. * E-mail address:
[email protected]: Fax: 412-268-7813.
1032 1 ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, f i 0 . 4 , 1 9 9 5
0013-936X/95/0929-1032$09,00/0
@ 1995 American Chemical Society
7E-06
n - 4
-
m
TrltonX-100 Sorption 30 rnL bulk solution 5 g Lincoln fine sand
\
0
E
-5
ui u) -6
F
1
I
y
-" " 4
Log (Cln,)
Log (CMC)
0
-9
Region 1
+
Int. Reg.
14-
Region 2
-
i " ' ' l " " l " " l " " 1 " " i
-6
-5
-4
-3
-2
FIGURE 1. Batch experimental data for Triton X-100 equilibrium sorption onto Lincoln fine sand (source: ref 11).
Stage 1
P
r
d 0-
d
Aqueous phase
9
9
d Stage d A
0.00
-1
Log (Bulk Aqueous Conc., mol/L)
Aqueousphase
-
1E-06
0
0.01
Langmuir isotherm
0.02
0.03
Cs,mol/L FIGURE 3. Batch experimental data and the fitted nonlinear sorption model for Triton X-100 equilibrium sorption onto Lincoln fine sand.
micellizationin the aqueous phase and that surfaceclusters form prior to formation of aqueous-phase micelles. At present, it is not possible to determine the exact mechanism of these sorption phenomena or the precise molecular conformations of the sorbed surfactant monomers. A M e d mathematical expression describing the equilibrium surfactantsorption isothermrather than the discrete region-by-region Freundlich-type isotherms shown in Figure 1 is useful in modeling the surfactant transport in sediment-aqueous system. A Langmuir isotherm, as described by eq 1,provides a reasonable fit to the sorption data
where Ss is the sorbed concentration of the surfactant on the surface (mollg),Sm, is the maximum sorbed concentration (mol/@,Csis the aqueous-phase surfactant concentration (mollL), and 4 is the Langmuir constant (LI mol). Figure 3 shows the sorption data presented in Figure 1alongwith the fitted Langmuir isotherm; & and Sm, were estimated to be 967 (Llmol) and 6.5 x (mol/g), respectively ($ = 0.98).
Experimental Design
FIGURE 2. Schematic representation of the proposed model for sorption of Triton X-100 onto Lincoln fine sand.
The surface area of Lincoln fine sand was estimated to be 3 m2/g (14, from which the sorbed-phase surface concentration is estimated to be approximately 150 &/ molecule, corresponding to Cint and a maximum surface coverage of 75-80 &/molecule. The orientation of the sorbed surfactant molecules is envisioned to undergo a transition from a more or less flat-lying conformation to a bilayer conformation as surfactant concentration is increased from region 1 to region 2 (11). This process is illustrated schematicallyin Figure 2, where stages 1 and 2 correspond to the regions 1 and 2 shown in Figure 1. Levitz and van Damme (15) and Rupprecht and Gu (16) argue that the formation of such surface clusters is related to
The experimentalprocedures comprised one-dimensional column transport studies to elucidate the kinetics of nonionic surfactant onto a clean sand. The column transport experiments were performed with different innuent surfactant concentrations. Radiolabeled tracer techniques were used to observe surfactant transport and to estimate the hydrodynamic dispersivity of the sand columns. Materials. Triton X-100 (C~H17C~H40(CH2CH20)~,5H) was selected as a representative nonionic surfactant due to its abilityto enhance solubilizationof organic compounds (I1,I 7) and because of the surfactant being studied by other researchers (13-15, 17, 18) and its availability in radiolabeled form. i3H1 Triton X-100was obtained from New England Nuclear and in nonlabeled form from Aldrich Chemical Company. Triton X-100 is a commercially manufactured surfactant (purity 94-99%) and is polydisperse in nature. HPLC tests showed that the surfactant behaves as a single solute at supra-cmc concentrations with no observable chromatographic separation between molVOL. 29, NO. 4, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
1033
Influent solutions
Helium pressure
32cm
I
I
n a w
Stainless rocran,llir steel
I
.-"-'.-''
Stainless steel column
J
1 Waste flush FIGURE 4. Schematic layout of the equipment for the column experiments.
ecules with possible differentpolyoxyethylene chain lengths. The cmcofTritonX-100with0.01 M CaClzwasdetermined to be 1.8 x mol/L from surface tension measurements (11). The radiolabeled and nonlabeled surfactant were mixed in known proportions for all experiments. AU such solutions contained 0.01 M CaClz in order to prevent migration of fines by providing uniform ionic strength conditions. 3H20was obtained from DuPont NEN. Clean, Lincoln fine sand passing U S . standard sieve no. 10 (2 mm) was used as the sediment material. The sand was air-dried before shipment fromU.S. EPARohert S. Kerr Environmental Research Laboratory, Ada, OK. The fractional organic carbon was found to be 0.05% using the Walkley-Black method (19).which agrees with a value of 0.034% reported by Wilson et al. (20). The surface area for Lincoln fine sand was calculated from nitrogen adsorption data obtained with a Quantasorb sorption apparatus and was determined in accordance with the BET adsorption theory (21). The surface area was found to he 3.0 m2/g. Liquid Scintillation Counting. The aqueous-phase concentration of Triton X-100 in all liquid-phase samples was determined by measuring the 3H disintegrations per minute (dpm). The liquid samples ranged in volume from 0.1 to 1.0 mL and were mixed with 10.0 mL of Packard Optifluorscintillationcocktailin 20.0-mL polyethylenevials. These samples were then analyzed in a Beckman LS 5000 TD liquid scintillation counter for 3H activity. Column Transport Experiments. One-dimensional column transport experimentswere performedinastainless steel column with a transport length of 7.53 cm (3 in.) and an inner diameter of 2.20 cm (nominal 1 in. diameter), packed with 49.75 & 1.00 g of Lincoln fine sand. The sand was placed in the column in 18-20 layers, and the bulk densityofthesandwasdeterminedtobe 1.74+0.03g/cm3. The pore volume of the packed column was determined by 1034 m ENVIRONMENTAL SCIENCE &TECHNOLOGY I VOL. 29. NO. 4,1995
the weight difference ofthe water-saturated columnversus the dry column; the porositywasdetermined to be between 0.32 and0.38,assumingcompletesaturation.Stainlesssteel frits with 0.5-pm pore sue were used at both ends of the column to prevent migration of fine particles. Aschematic of the column-transport apparatus is shown in Figure 4. All aqueous solutions for column tests were kept in a stainless steel reservoir and were spargedwith helium prior to pumping in order to remove any entrapped air bubbles. A n SSI Model 350 HPLC pump was used to pump aqueous solutions from the reservoir. A 0.5-pm stainless steel inline filter was attached at the inlet to the pump in order to protect the pump head from damage by any spurious particles. The effluent from the column was collected by an Eldexfractioncollectorin10-mlglassNhes. The sample volume depended on the test conditions and the frequency of observations. The column apparatus and the related equipment were designed in a way such that the surface contacted by the aqueous solutions were either stainless steel, Teflon, or glass. The column was cleaned and repacked for each separate run. A newly filled column was conditioned by pumping 500 mL (about 50 pore volumes) or more of 0.01 M CaC4 solution in order to obtain steady-state flow conditions and to remove any suspended colloids. After the conditioning, a 3Hz0 solution with 0.01 M CaCIz was pumped through the column and monitored at the outlet; subsequently, the column was flushed with 0.01 M CaC4 solution until 3H count was reduced to background level. The radiolabeled Triton X-100 solutions were then pumped, each run having a different influent concentration. After achieving a surfactant breakthrough, Le., obtaining an effluent concentration equal to influent concentration, pumping of the surfactant solution was stopped. The stainlesssteelreservouand the tubingleadingto thecolumn
0
0
3
0.6 0.4
On2 0.0
followed by a plateau in the effluent aqueous surfactant concentration, which persisted upto an “inflectionpoint”. The Mection point on the breakthrough curve was followed by a second-stage breakthrough curve with tailing of the effluent concentration as it approached the influent concentration value, C,. The elution curves, however, did not show a stage-wise behavior as was observed for the breakthrough curves. Considerable tailing was observed for surfactant elution. The column experiment for surfactant transport was repeated at C, = 50 x cmc at a much faster flow rate (1.4 mllmin). This breakthrough curve is plotted in Figure 10 along with the data for slower flow rate (0.03 mllmin). It can be observed that the two curves are very similar, although the inflection point appears to be less distinct at the faster flow rate. These observed surfactant transport phenomena are significantly different from those reported by Abdul and Gibson (23, who had conducted experiments with a nonionic alkyl ethoxylate surfactant (Witconol SN 70) in 30-46 cm long columns packed with a natural aquifer sediment. They had observed breakthrough curves for the surfactant to be regular S-shapedcurves. According to that study, as the surfactant concentration is reduced, the effluent breakthrough curves become more and more skewed, and the number of pore volumes of surfactant solution required to reach a complete breakthrough increases from 1.5to more than 5 as the influent surfactant concentration is decreased from 1% to 0.125%. The work of Abdul and Gibson (25) indicates that the degree of retardation as well as the degree of skewness in surfactant breakthrough is enhanced for lesser influent surfactant concentrations. It may be expected that the retardation would occur as a result of sorption of the surfactant onto the solid matrix, while the skewness in the breakthrough curve would indicate either mass transfer kinetics or a Langmuir-type sorption isotherm. The effect of sorption kinetics for the case of organic compounds has been discussed in a general fashion by Brusseau et al. (26). A sensitivity analysis by Brusseau et al. (26)has shown that the degree of skewness increases as the extent of nonequilibrium is increased for sorbing organic solutes. Magee et al. (27) have reported similarly retarded and skewed breakthrough curves for transport of natural dissolved organic matter, separated from clayey silty loam, through a dark quarry sand. Sabatini and Austin (28)have reported “two-legbreakthrough curves” for the transport of rhodamine WT through alluvial aquifer sand; the results are qualitativelysimilar to the observations for TritonX-100 transport. Some other researchers have considered surfactant sorption phenomenain laboratoryand field transport studies to be either equilibrium processes or to be negligible altogether (10, 29, 30). Surfactant Breakthrough Curves. Each of the breakthrough curves presented here can be considered to be composed of five characteristic features: the initial breakthrough, the plateau stage, the inflection point, the second breakthrough, and the elution curve. It is apparent from the first two segments of the breakthrough curves that sorption of Triton X-100 onto Lincoln fine sand is a nonequilibriumprocess for which the sorption kinetics are controlled in part by the influent surfactant concentration. The initial breakthroughoccurs slightly after 1pore volume and attains the plateau concentration after about 1.5 - 2.5 pore volumes. This initial portion of the breakthrough curve
* h
0.0
0.5
1.0
1.5
2.0
2.5
I
3.0
Pore volumes FIGURE 5. 3Hz0 breakthrough data and the fitted curve for column transport.
were cleansed with a methanol solution followedby distilled water; the process of switching from one influent solution to another took about 30 minor less. The pumping solution was then changed to distilled water with 0.01M CaC12, and surfactant desorption from the sand column was monitored to observe the elution characteristics.
Results and Discussion Column Tests for Tracer Transport. Conservative tracer transport, with 3H20as the tracer, was used to describe the dispersive characteristicsof each column used for surfactant transport studies. A typical breakthrough and flushing curve is shown in Figure 5, which presents the relative concentration of the effluent with respect to the influent (CIC,) versus the pore volumes of the 3H20solution flushed through the column at an average pore water velocity of 0.1 cmlmin. It is noted that the midpoint of the breakthrough curve (CIC, = 0.50) arrived after flushing 1 pore volume and that the breakthrough curvewas symmetrical about its midpoint. Such behavior is expected of a conservative tracer (22,231. Considering 3H20 to be a conservative tracer with no retardation in the breakthrough curve, an estimate of the longitudinal dispersivity (a) was obtained for each column by fitting the one-dimensional advection-dispersion equation (221, for which the result is shown as a solid line in Figure 5. The measured longitudinal dispersivity ranged from 0.07 to 0.15 cm, which agrees well with reported a values (24). Surfactant Transport in Columns. Several different column tests were conducted to evaluate surfactant transport at various influent surfactant concentrations. These experiments were conducted at flow rates such that the residence time in the column was in the range of 45-325 min. Unusual, but similar, breakthrough curves were observed in each of the surfactant transport studies. Figures 6-9 show four breakthrough curves for four different influent concentrations of the surfactant, ranging from 15 to 150 times the cmc (1.8 x mollL). The surfactant concentrations have been presented here as multiples of cmc, and the breakthrough curves have been normalized to a nondimensionalform to depict relative concentrations (CJC,) plotted against pore volumes of aqueous solution flushed through the column, where C, is the effluent surfactant concentration and C, is the influent surfactant concentration. The first breakthrough of surfactant was observed after flushing slightly more than 1 pore volume. This was
VOL. 29, NO. 4,1995 / E N V I R O N M E N T A L SCIENCE & TECHNOLOGY 1 1035
1.4
I I
1.2
-
Model
0 Experiment
kfl = 0.03/min kb2 = 0.0005 /min FI. rate = 0.23 mumin
1.o
8
0.8
\
#
0 0.6 0.4 0.2
0.0 0
a
4
12
16
Pore volumes FIGURE6. Surfactant breakthrough curve for transport of Triton X-100 through a column packed with Lincoln fine sand, C, = 150 cmc (0.0267 MI.
1.4
1-
1.2
50 CMC kfl= 0.0035 /min kb2 = 0.00001 /min FI. rate = 0.03 mumin Disp. = 0.1 5 cm Porosity = 0.34 cm Pore volume = 9.7 mL
Model 0 Experimental
1.o 0.8 0.6
0
0.4 0.2 0.0 0
2
6
4
8
10
12
Pore volumes FIGURE 7. Surfactant breakthrough curve for transport of Triton X-100 through a column packed with Lincoln fine sand, C. = 50 cmc (0.0089 MI.
is asymmetrical, and it took more than 1 pore volume for the midpoint to arrive; such behavior would indicate retardation due to surfactant sorption (25). It can also be observed that this retardation is relatively small in magnitude and that the mass of the surfactant sorbed in this early step of the breakthrough is small compared to that occurring during the plateau stage. The second feature of the breakthrough curve is a flat, plateau-like region for which the effluent concentration 1036 = ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 4,1995
(C,) remains relatively constant for each column test. The existence of a plateau region in this portion of the breakthrough curve suggests that depletionof the surfactant from the aqueous phase attains a constant value which is dependent on C,, and that the sorption rate in this segment is rapid relative to the flow rate. This concept can be qualitativelycorroborated by the results observed by Abdd and Gibson (27) in which the mass of surfactant lost from the aqueous phase during the flushing of a surfactant
kfl = 0.0125/min kb2 = 0.0002/min FI. rate = 0.13 ml/min Disp. = 0.12cm Porosity = 0.38 Pore volume = 10.9mL
0
12
8
4
16
Pore volumes FIGURE 8. Surfactant breakthrough curve for transport of Triton X-100 through a column packed with Lincoln fine sand,
& = 25 cmc (0.0045
MI.
1.2
-
kfl = 0.0168 /min kb2= 0.00052/min FI. rate = 0.09 mUmin
1.o
Experimental
Model
0
8
10
0.8 Pore volume = 9.6mL
0.6 0.4
0.2 0.0 0
2
4
solution in a column study was dependent on the influent surfactant concentration. The third feature of the breakthrough curve is the inflection point. The mass of surfactant sorbed onto the sediment up to the inflection point can be computed by numerically integrating the area to the left of the breakthrough curve and subtracting the equivalent of 1 pore volume representing the displacement of clean aqueous solution (0.01 M CaC12) that was initially present in the column. The sorbed surfactant mass up to the inflection
6
12
14
point for the four curves shown in Figures 6-9 is determined to be in the range of 2.0-2.7 pmollg (see Table 1). This concentrationcorrespondsto a computed surface coverage of approximately 180-250 &/surfactant molecule. These data suggest that a transition in sorbed surfactant conformation and in sorption kinetics might occur as the sorption density approaches an average value of about 2.4 pmollg (200&/molecule). The surface coverage at the inflection point on the breakthrough curve is very similar in value to the surface VOL. 29, NO. 4,1995 / ENVIRONMENTAL SCIENCE &TECHNOLOGY
1037
1
Triton X-100 (50 CMC)
0.03 mumin 0.8 lmO B 1.43 mumin 0
%(
00 B o 0
0.2
Om4
1 0
2
1
3
4
5
Pore Volumes FIGURE 10. Comparison of surfactant breakthrough curves for transport of Triton X-100 through Lincoln fine sand at different flow rates, C, = 50 cmc (0.0089 M). TABLE 1
S o ~ e dConcentrations of Triton X-100 onto Lincoln Fine Sand total amt. sorbed at complete breakthrough influentamt. sorbed at inflection point concn sorbed mass sorption density sorbed mass sorption density ( x cmc) (pmollg) (AZ/molecule) (pmol/g) (&/molecule) 150 50 25 15
2.7 2.4 2.0 2.5
185 210 250 202
3.1 2.8 2.4 3.4
160 180 210 150
coverage corresponding to Ci,, shown in Figure 1. For this reason, it is proposed that the inflection point reflects a change in the sorption regime from a patchy monolayer to partial bilayers. Based on equilibrium sorption experiments, several researchers have proposed that admicelles or partial bilayers are created on silica surfaces and Lincoln fine sand (11-13, 15). The second-stage breakthrough curve is S-shaped with effluent concentration starting at the plateau value and approaching Co in a finite number of pore volumes. The number of pore volumes required after the inflectionpoint to achieve a complete breakthroughvaries from 0.5 to more than 4 depending on C,,. The apparent retardation in the second-stage breakthrough curve appears to be dependent on C,; the extent of retardation and skewness increases with decreasing C, values. This result qualitatively matches those reported by Abdul and Gibson ( 2 3 , where the retardation and skewness was observed to be greater for low surfactant concentrations. The total mass of surfactant sorbed at complete breakthrough can be estimated by numerically integrating the area to the left of the entire breakthrough curve and subtracting the equivalent of 1 pore volume representing
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1038 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 4, 1995
the displacement of clean aqueous solution (0.01 M CaC12) that was initially present in the column, as summarized in Table 1. It was observed that the maximum sorbed surfactant mass in the column studies was somewhat less than that observed for the batch sorption studies. The lesser amount of surfactant sorbed per unit weight of the sand in the column tests indicates that the sorption process is affectedby the nature of the column experiment. Possible explanationsfor this difference in sorption behavior include lesser accessible surface area in a packed column and significantkinetic limitations to sorption in a column test compared to a well-mixed system. The elution curves for the column studies depicted in Figures 6-9 show a rapid drop in the effluent concentration within the first two eluted pore volumes, after which the elution curve approaches the abscissa asymptotically. Similar results have been reported by Abdul and Gibson (25) for elution of a nonionic surfactant from a natural sediment. Two interestingobservationscan be made about the elution curves: (a) the elution curves did not display the step-wisebehavior observed in the breakthrough curves and (b) owing to the limited duration of the elution test, the mass of surfactant desorbed during the elution process is much smaller compared to the total mass sorbed. It may be surmised that the removal of the sorbed surfactantwould require prolonged flushingwith clean water. Such elution characteristicshave been previouslyreported for HOCs with nonequilibrium sorption characteristics (31).
Mathematical Model for Surfactant Sorption Kinetics Some attempts have been made to experimentally observe the conformation of sorbed surfactant molecules on silica and quartz particles using atomic force microscopy (32). Such a direct observation is not feasible for materials like Lincoln fine sand, which is heterogeneous in its mineral composition and contains some small amount of naturally-
occurring organic material. Some researchers have utilized flotation and fluorescencetechniquesto infer the molecular conformationson solid surfaces (14,15),but such indirect observations lack verification at the molecular scale. In the absence of molecular scale informationfor sorption of Triton X-100 onto Lincoln fine sand, an empirical, macroscale model of the sorption phenomena is proposed. Such a model is supported by existing information about equilibrium surfactant sorption onto solid media. In this investigation,an empirical, two-stage sorptionkinetic model is proposed for sorption ofTritonX-100onto Lincoln fine sand. This model envisions that at low, subcmc concentrations, Le., stage 1 of Figure 2, the surface coverage is sparse and the maximum surface area per molecule for sorption of Triton X-100 onto the sand may be around 700-800 &, as determined from Figure 1 (11). The surfactant molecules at such surface coverage may be visualized as more or less flat-lying on the surface of the solid. As the concentration of the surfactant is increased such that the aqueous-phase concentrations are in excess of the cmc, a much greater surface coverage is observed, corresponding to stage 2 of Figure 2. This categorization of sorption behavior has been proposed by several researchers studying sorption of nonionic surfactants onto silica gels, silica sols, and sands. Clunie and Ingram (12) have proposed five stages of nonionic surfactant sorptim onto a solid surface, where the sorbed molecules transform from a sparse flat-lying coverage to a denser monolayer, followed by formation of multilayers and surface clusters as the surfactant concentration is increased. Partyka et al. (13)have described a similar sorption process in three distinct stages. Levitz and van Damme (1.9 have also explored the possibility of formation of close-packed assemblies on the surface that presumably act as precursors to the micellization process. All of these studies point toward two broad categories of surfactant sorption phenomena: monomer-surface interactions and monomer-monomer interactions. This concept forms the basis of the two-stage, sorption kinetic model proposed in this paper. It is proposed that the rate of surfactant sorption can be described conceptuallyby four first-order kinetic parameters (kn,kbl, kn,and k b 2 ) as shown in Figure 2. It is further proposed that in stage 1the sorbed surfactant concentration is sparse and the sorption process is governed by surfactant-surface interactions, whereas the sorption process in stage 2 is governed by surfactant-surfactant interactions. This proposition simplifies the model to two kinetic parameters, kfl and kb2, as explained below. Other conventional sorption models,such as the bicontinuum model (22, 26), failed to adequately fit the observed data. The model comprisestwo first-order sorption reactions which work sequentially, i.e., the first reaction is valid up to the inflection point on the breakthrough curve, where surface coverage is less than 2.4 pmol/g, and the second reaction is valid only for higher surface coverage. Mathematically
(3)
where kf and
kb
are the first-order forward and reverse
(backward)reaction constants for the sorption reaction and the subscripts 1 and 2 indicate the controlling sorption regime, i.e., stage 1 or 2. The total mass of surfactant sorbed (S,) on the sand at equilibrium is given as
s, = g(CJ = s, + s,
(4)
where the isotherm function, g(C,), is described by eq 1. The controlling differential equation for the first-stage sorption process can be obtained from eq 2:
where e is the bulk density (g/L) and n is the porosity (LIL). It has already been observed that the sorption in this region is rapid, suggesting that kbl may be very Small. Further, the surface coverage in the first region is relatively sparse. Thus, as a first approximation,the second term on the left side of eq 5, which is the product of two comparatively small values, can be ignored.
The governing equation for the second-stage sorption process can similarly be obtained from eq 3 (7) At equilibrium, dC,/dt = 0, which simplifies eq 7 as (8)
Equation 8 is qualitativelyjustified by other researchers, who have used similar mathematicaltreatment for defining the reverse first-order rate constant in terms of forward first-order rate constant for two-box sorption models for HOCs (e.g., ref 26). Assuming the system to be in the proximity of equilibrium, eq 7 can be modified by substituting the value of kn from eq 8 and the value of SZ from eq 4 and considering S1 to be a constant at 2.4 pmollg correspondingtothe surface coverage at the innectionpoint
whereas the term g(Cs) - S1 represents the maximum second-stage sorption corresponding to equilibrium, and thus the term in brackets on the right side of the equation may be visualized as a driving force term. In order to model the sequential two-stage kinetic sorption of Triton X-100, estimation of two parameters is required: kfl and kt,~.The sorption process for Triton X-100 can be defined based on eqs 6 and 9; the Euler method is used to solve these differential equations, respectively. C
r
= C - Atkf,C
when Si -= 2.4pmol/g
when 2.4 pmol/g
(10)
Si < 6.5 pmol/g (11)
Also, a mass conservation computation has to be performed at the end of each time step in each cell VOL. 29, NO. 4, 1995 / ENVIRONMENTAL SCIENCE &TECHNOLOGY
1099
(12)
where Mis the total mass of surfactant in a cell (mol).Either eq 10 or eq 11 is solved simultaneously with eq 12, and updated concentrations CY+', S;"', and S y 1 are determined. A segregated transport-sorption/solubilization (STSS) modeling technique is used here to simulate surfactant transport. It is a numerical approach in which a solute is transported in small but discrete time steps and sorption or solubilizationis allowed to occur at the end of each time step (33). This means that spatial and temporal variations of concentration of a solute can be explicitly accommodated in the model. At the onset, the transport module is used to transport the solute in the solid medium according to the one-dimensional advection-dispersion equation, considering the solute to be conservative and nonreactive.
where Dis the hydrodynamic dispersion coefficient (L2/T), v is the average pore water velocity (L/T),x is the distance along the direction of flow (L),and tis time (TI. A flux-type (Cauchytype) boundary condition is used at the inlet end, and a concentration-type (Dirichlet type) boundary condition is used at outlet end for solvingeq 13. The flow domain is divided into a number of small cells of length Ax, and the length of time steps is correlated to the cell size and the flow velocity (At = Ax/v). A Crank-Nicolson approach centrally-differencedin space and forward-differenced in time is employed to solve eq 13. During each time step, the transport module provides updated values for the aqueous-phase concentrations and the total mass of solute in a cell. The aqueous-phase and the sorbed-phase concentrations are then reequilibrated with each other in the sorption module according to the partitioning behavior of the solute and mass conservation (eqs 10-12). These updated concentrations are then used as initial concentrations for the transport module in the next time step. The numerical accuracy of the program code was evaluated by comparing its output to that from a conventional analytical method for transport of organic solutes (22, 33). Additionally, increasing the time step (At) by a factor of 10over that computed from At = Ax/ vstill provided very reasonable results (33).
Model Predictions A sensitivity analysis was performed to assess the impact
of the two fitting parameters, kfl and kb2, on shape of the breakthrough curves. In order to achieve this, one parameter was held at a constant value while the other was varied. Figures 11 and 12 show the effluent relative concentrations (CJC,) from simulated column tests plotted against the number of pore volumes flushed through the column. Figure 11 depicts the simulated breakthrough curves for surfactant transport at various kn values, while kb2 was kept equal to zero. It is shown that kfl has averysignificant impact on the shape of the first plateau and the number of pore volumes of the surfactant solution required to achieve a complete breakthrough. Such a behavior would be anticipated because a faster reaction means a stronger retardation of the effluent concentrations. It may also be
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1040 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 4,1995
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inferred that as kn 0, with kb2 equal to zero, the surfactant effluent breakthrough curve would be similar to that for a conservative tracer. Figure 12 depicts the variations in the simulated breakthrough curves with kfl constant at 0.0035 min-l and kb2 varied. The rate of sorption and desorption in stage 2 does not affect the earlier part of the breakthrough curve. This is a result of the modeling approach, for which the first limb of the curve and the plateau concentrations are controlled by the stage 1 sorption. The predictions from the STSS model as fitted to the experimental data are shown in Figures 6-9. The curves were fitted to the experimental data by varying the values of kfl &?d kb2 until a good agreement between the fitted curves and the experimental data was observed. In essence, the search process was sequential in which kfl was varied to fit the first stage of the breakthrough curve, and then kb2 was varied to fit the second stage of the breakthrough curve and the elution curve. Some observations from these predictions are as follows: (a) In general, the modeling approach captures most of the salient features of the experimental data, i.e., an early breakthrough curve followed by a plateau region, and the prolonged tailing in the elution curve. (b) The value of kfl represents the rate of sorption in region 1, whereas the value O f kb2 represents the desorption rate as well as the sorption rate (eq 8) in region 2. A comparison of the two kinetic parameters reveals that sorption rate in stage 1 is much faster than the desorption rate in stage 2, as the kb2 values are about 2 orders of magnitude smaller than the kfl values in all four cases. (c) The sorption rate coefficients in both the regimes appear to be dependent on the influent concentration of the surfactant solutions. The prolonged tailing associated with the surfactant elution is principallyattributable to the small values of kb2. The kfl and kb2 values are similar for the breakthrough curves with C, = 150, 25, and 15 cmc (0.0125 < kfl < 0.03 min-I and0.0003 < kb2 < 0.0005 min-'1. In contrast, the fitted values for C, = 50 cmc do not agree with the trend seen for other experiments. This divergence for C, = 50 cmc cannot be explained with the available data. (d) The comparison of surfactant breakthrough curves at different flow rates yields similar results. However, the slight differences in the shape of breakthrough curves suggest a dependence of sorption phenomena on rate of sorption versus the rate of transport via advection and dispersion. (e)The model predictions are not able to provide a good fit in the transition zone between the two stages. Ideally, a more mechanistic model may be needed to accurately predict such transitions. It may be argued that one approach for such modeling is to exclude the simplifymg assumptions made earlier for solving the differential equations, Le., the assumption of neglectingthe desorption in stage 1, and the assumption that the system is in the proximity of equilibrium in stage 2. Such a detailed approach would lead to the use of four kinetic fitting parameters: kfl, kn, k b l , and kb2. Such an approach is not likely to be any more generalizable given the degree of empiricism. These experiments have provided insights into the sorption and transport phenomena involving a nonionic surfactant and a clean sand. First, surfactant sorption onto aquifer sediments is not an equilibrium process but is rate-
1.2 1.o
1
0.8
0.6 0.4
- kfl 0.0175 /min E
.". k f l = 0.0035 lmin
0.2
kfl=O.O007 /min
0.0
0
6
4
2
8
10
Pore Volumes FIGURE 11. Sensitivity analysis of the proposed sorption-transport model by varying kn with kb~set at 0 min-l.
1.2
1
1.o
-1
1
0.8
0.6
4
0.4 kb2=0.001 /min ...
0.2
kb2=0.0001 /min
- kb2=0.00001 /min I
I
0.0
I
I
0
2
I
4
1
6
I
I
I
8
10
12
Pore Volumes FIGURE 12. Sensitivity analysis of the proposed sorption-transport model by varying ku with kn set at 0.0035 min-l.
limited and depends on the influent surfactant concentration. Second, it is proposed in this paper that Triton X- 100 sorption onto Lincoln fine sand is controlledby two different sorption regimes: a first regime where surface coverage is sparse and sorption is rapid, and a second regime where some surfactantclusters,such as partial bilayers, are formed and sorption is relatively slower. Such a sorption kinetic behavior has not been reported previously for surfactants, and it indicates the need for development of techniques for observation of time-dependent sorption phenomena at a molecular scale. Third, the elution of the nonionic
surfactant also appears to a slow, rate-limited process, and extremely long time periods may be required for complete removal of the sorbed surfactant by flushing. This means that a residual sorbed surfactant mass may be left behind in practical surfactant-aided remediation schemes.
Acknowledgments Portions of this work were supported by the Aluminum Company of America, Environmental Technology Center, Pittsburgh, PA. Carl Enfield, U.S. EPA, Robert S. Kerr VOL. 29, NO. 4, 1995 / ENVIRONMENTAL SCIENCE &TECHNOLOGY
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EnvironmentalResearch Laboratory,Ada, OK, provided the Lincoln fine sand. Author-Supplied CAS Regfstry Number: Triton X-100, 9002-93-1.
Literature Gied (1) Vigon, B. W.; Rubin, A. J. J. Water Pollut. Control Fed. 1989,61, 1233-1240. (2) Abdul, A. S.; Gibson, T. L.; Rai, D. N. Ground Water 1990,28, 920-926. (3) Fountain, J. C.; Klimek, A.; Beikirch, M. G.; Middleton, T. M. J , Hauzrd. Mater. 1991,28,295-311. (4) Rixey, W. G.; Johnson, P. C.; Deeley, G. M.; Byers, D. L.; Dortch, I. J. In Hydrocarbon Contaminated Soils, 1; Calabrese, E. J., Kostechki, P. T., Eds.; Lewis Publishers: Chelsea, MI, 1991; pp 387-409. (5) Ellis, W. D.; Payne, J. R.; McNabb, G. D. Treatment ofContaminated Soils with Aqueous Surfactants; Final Report EPA/6OO/ 2-85/129; U.S. EPA Washington, DC, 1986. (6) Lake, L. W. Enhanced Oil Recove% Prentice Hall: Englewood Cliffs, NJ, 1989. (7) Liu, Z.; Edwards, D. A,; Luthy, R. G. Water Res. 1992,26,13371345. (8) Jafvert, C. T.; Heath, J. K. Enuiron. Sci. Technol. 1991,25, 10311038. (9) PenneU, K.D.;Abriola,L. M.; Weber,W. J., Jr. Environ. Sci. Technol. 1993,27,2332-2340. (10) Abriola, L. M.; Dekker, T. J.; Pennell, K. D. Environ. Sci. Technol. 1993,27,2341-2351. (11) Edwards, D. A.; Adeel, Z.; Luthy, R. G. Environ. Sci. Technol. 1994,28,1550-1560. (12) Clunie, J. S.; Ingram, B. T. In Adsorption from Solution at the SolidlLiquid Interface; Parfitt, G. D., Rochester, C. H., Eds.; Academic Press: New York, 1983; pp 105-152. (13) Partyka, S.; Zaini, S.; Lindheimer, M.; Brun, B. Colloids Surf: 1984,12,255-270. (14) Somasundaran, P.; Snell, E. D.; Xu, Q. J. Colloid Interface Sci. 1991,144,165-173. (15) Levitz, P.; van Damme, H. J. Phys. Chem. 1986,917, 1302-1310. (16) Rupprecht, H.; Gu, T. Colloid Polym. Sci. 1991,269,506-522. (17) Edwards, D. A.; Liu, Z.; Luthy, R. G. J. Environ. Eng. ASCE 1994, 120,23-41. (18) Robson, R. J.; Dennis, E. A. J. Phys. Chem. 1977,81, 1075-1078.
1042 ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, NO. 4, 1995
(19) Nelson, D. W.; Sommers, L. E. In Methods of Soil Analysis, Part 2, Chemical and Microbiological Properties; Page, A. L., Ed.; American Society of Agronomy, Inc.: Madison, WI, 1986; pp 539-579. (20) Wilson, J. T.; Enfield, C. G.; Dunlap, W. J,; Cosby, R. L.; Foster, D. A.; Baskin, L. B. J. Environ. Qual. 1981,10, 501-506. (21) Gregg, S. J.; Sing, K. S. W. Adsorption Surfaces Area and Porosiv, Academic Press: London, 1967. (22) Parker, J. C.; van Genuchten, M. Th. Determining Transport Parameters from Laboratory and Field Tracer Experiments; Bulletin 84-3, Virginia Agricultural Experiment Station, Blacksburg; Virginia Polytechnic Institute and State University: Blacksburg, VA, 1984. (23) US. Environmental Protection Agency. Transport and Fate of Contaminants in the Subsurface; Seminar Publication EPA/625/ 4-89-019; U.S. EPA Washington, DC, 1989. (24) Liu, K.-H.; Enfield, C. G.; Mravik, S. C. Ground Water 1991,29, 685-692. (25) Abdul, S.A,; Gibson, T. L. Environ Sci. Technol. 1991,25,665671. (26) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. Res. 1989,25,1971-1988. (27) Magee, B. R.; Lion, L. W.; Lemley, A. T. Environ. Sci. Technol. 1991,25,323-331. (28) Sabatini, D. A,; Austin, T. A. Ground Water 1991,29,341-349. (29) Wilson, D. J. Sep. Scz. Technol. 1989,24,863-892. (30) Thurman, E. M.; Barber, L. B., Jr.; LeBlanc, D.J. Contam. Hydrol. 1986,1, 143-161. (31) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Environ. Sci. Technol. 1990,24,727-735. (32) Hayes, K. F.; Morton, J. D. Proceedings of the 68th ACS Colloid and Surface Science Symposium, Stanford University, Stanford, CA, June 19-22,1994; American Chemical Society: Washington, DC, 1994. (33) Adeel, Z.; Edwards, D. A,; Luthy, R. G. Department of Civil and Environmental Engineering, Carnegie Mellon University, submitted to Water Resour. Res.
Received for review July 25, 1994. Revised manuscript received January 4, 1995. AcceptedJanuary 6, 1995.@ ES9404633 ~~~~
@
Abstract published in Advance ACSAbstracts, February 15,1995.
