Environ. Sci. Technol. 2005, 39, 2267-2273
Optimizing Contaminant Desorption and Bioavailability in Dense Slurry Systems. 1. Rheology, Mechanical Mixing, and PAH Desorption WALTER J. WEBER, JR.* AND HAN S. KIM Department of Chemical Engineering, Energy and Environment Program, The University of Michigan, 4103 Engineering Research Building, Ann Arbor, Michigan, 48109-2099
Intermittently mixed batch reactor (IMBR) systems were employed to evaluate the effects of mechanical mixing and corresponding power consumption on rates of phenanthrene desorption from natural and synthetic model sorbent phases to the aqueous phase in dense slurry reactors. Sorbent slurries comprising 57-67% (w/w) solids exhibited non-Newtonian (pseudoplastic) fluid behaviors, with apparent viscosities varying with shear rate. Dimensionless power numbers varied inversely with the Reynolds number under laminar flow conditions, indicating that small increases in mixing revolution number and auger size effect significant increases in power and torque requirements for the mechanical mixing of dense slurries. Rates of release of phenanthrene associated with rapidly desorbing or labile fractions of sorbent organic matter (SOM) to the aqueous phase were markedly enhanced by relatively low-level auger mixing, but significantly less further enhancement was observed as higher levels of mixing were applied. Conversely, desorption of phenanthrene associated with slowly desorbing or resistant fractions of SOM was relatively unaffected by auger mixing, being limited as it is by slow intraparticle-scale diffusion processes that are not enhanced by reactor-scale mixing. The experimental results lead to and support a conclusion that auger mixing at relatively low intensity is an attractive strategy for optimizing dense slurry reactor systems for remediation of hydrophobic organic contaminants associated with labile (rapidly desorbing) fractions of SOM with respect to performance efficiency and cost-effectiveness.
in subsurface systems. A number of prior investigations have demonstrated convincingly that slow mass transfer processes limit the overall bioavailability and rates of biodegradation of sorbed-phase PAHs in such systems (1-3, 5). PAH biodegradation rates observed in contaminated soil and sediment field remediation scenarios are in fact generally much lower than corresponding rates observed in benchscale investigations. The work described here is predicated on the hypothesis that the mass transfer of critical reaction components (e.g., substrates, microbial nutrients, electron acceptors, and microorganisms) in the relatively high solids and initially stagnant fluid environments of saturated subsurface systems is controlled by very slow macro or reactor-scale mass transfer processes. Conversely, mass transfer under typical bench-scale test conditions is usually, by design, controlled by relatively fast micro or reactionscale mass transfer processes. We define reactor-scale mass transfer to be comprised essentially by transport processes having characteristic lengths determined by system-scale dimensions. Most laboratory experiments to determine rate behavior, however, are by design conducted in completely and continuously mixed batch reactors (CMBRs) specifically to reduce reactor-scale mass transfer processes to particlescale processes having essentially microscopic characteristic lengths. This is not a novel notion, for it is well-known that the rates and extents of mass transfer and associated reactions among system constituents are greatly influenced by the hydrodynamic dispersion of fluid elements containing those constituents, and that mixing is therefore a fundamental and universal factor in virtually all process operations (6-8). The objective of this work was to evaluate the effects of mechanical mixing on the mass transfer of sorbed PAHs from the solid phases of various natural geosorbents and synthetic model sorbents to the bulk aqueous phases of slurry systems containing high levels of solids. Laboratory-scale intermittently mixed batch reactors (IMBRs) were employed, and phenanthrene was selected as the target compound for the study. A motor-driven helical screw-type impeller (auger) was employed to mix the dense water-saturated sorbent slurries, and corresponding power requirements were quantitatively characterized using dimensional analyses. The results of the work should prove useful for establishing costeffective and performance-efficient mechanical mixing strategies for enhancement of mass transfer processes associated with both in-situ and ex-situ remediation of contaminated soils and sediments. Parallel studies on the effects of mechanical mixing on phenanthrene biodegradation in such systems are described in a companion investigation (9).
Conceptual Background Introduction Limitations associated with conventional in-situ bioremediation technologies for removal of strongly sorbed hydrophobic organic compounds (HOCs) such as polycyclic aromatic hydrocarbons (PAHs) from contaminated soils and sediments center about the conversion of these substances to a form or state conducive to microbial utilization (i.e., to a bioavailable form) and the effective delivery of appropriate electron acceptors and other nutrients (1-4). The highly hydrophobic characters and low aqueous solubilities of PAHs, and the high associated sorption capacities that soils and sediments exhibit for such contaminants usually result in only very slow decreases in solid-phase concentration levels * Corresponding author phone: 734-763-2274; fax: 734-936-4391; e-mail:
[email protected]. 10.1021/es049565b CCC: $30.25 Published on Web 02/04/2005
2005 American Chemical Society
Non-Newtonian Fluid Rheology. Rheological analysis embracing elasticity, viscosity, plasticity, and internal friction resulting from molecular interactions is required for nonNewtonian fluids because their properties change with fluid element location and history (10). The relationship between apparent viscosity (µa) and shear rate (γ˘ ) of non-Newtonian fluids can be described simply by a power law form as
µa ) K(γ˘ )p-1
(1)
in which K is referred to as a consistency parameter, and p is termed the exponential power law index. For Newtonian fluids p ) 1, for dilatant non-Newtonian fluids p > 1, and for pseudoplastic non-Newtonian fluids p < 1 (10, 11). Power Consumption. The power consumption (P, [M‚L2‚t-3]) involved in the impeller-driven mixing of a fluid VOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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can be characterized functionally by impeller revolution rate (N, [t-1]), impeller diameter (D, [L]), fluid density (FL, [M‚L-3]), viscosity (µ, [M‚L-1‚t-1]), and gravitational acceleration rate (g, [L‚t-2]). For simplicity of analysis, other variables associated with reactor geometry (e.g., impeller and reactor vessel shape factors and their locations) are not considered in this study. The Buckingham Π theorem approach to dimensional analysis (6) can then be applied to obtain the general correlation
( )( )
FLND P )C 3 5 µ FL N D
2 a
2
ND g
b
(2)
or, in terms of corresponding dimensionless group numbers
NP ) CNReaNFrb
(3)
where C is a characteristic reactor geometry parameter, a and b are empirical exponential coefficients, NP is the power number, NRe is the Reynolds number, and NFr is the Froude number (7, 11). Degree of Mixing. Mixing effectiveness is dependent on impeller revolution rate (N) and total mixing duration (total mixer operation time each day, (θT), which is the sum of homogenization time (referred to often as mixing time) and mixing duration. The homogenization time is the time required after onset of mixing to attain a homogeneous distribution of system constituents (12, 13), and the mixing duration is the period over which mixing continues after homogenization has been achieved. The product of impeller revolution rate and total mixing duration is thus defined as the dimensionless mixing revolution number (NRev), representing total revolution and corresponding to degree of mixing given by a specific mixing scheme: i.e.,
NRev ) NθT
(4)
Biphasic Desorption. The biotreatment of soils and/or sediments contaminated with high-molecular-weight HOCs is commonly observed to entail an initial relatively fast rate of sorbed substrate degradation (weeks to months) followed by an extended period of extremely slow degradation (years to decades, refs 14, 15). This phenomenologically biphasic nature of substrate mass transfer from the sorbed phase to the aqueous phase can be attributed to the essentially dual dominant reactive domain character of the organic matter typically associated with most natural geosorbents (16, 17). Johnson et al. (18) have demonstrated the utility of an empirical dual-reactive-domain model (DRDM) for describing the combined rapid and slow desorption rate processes, a model having the form
q(t) ) φs exp(- kst) + (1 - φs) exp(- krt) qo
(5)
The term q(t) in eq 5 is the sorbed-phase substrate concentration at any time, qo is the initial sorbed-phase substrate concentration, φs is the slowly desorbing fraction of sorbed substrate, (1 - φs) is the rapidly desorbing fraction, and ks and kr are, respectively, the apparent first-order rate coefficients (day-1) for the slowly and rapidly desorbing fractions. Correlation between Mass Transfer and Mixing. The dependence of substrate mass transfer (i.e., desorption) from the solid to the aqueous phases under mixing conditions can be described by an empirical correlation between the appropriate first-order desorption rate coefficient (either kr 2268
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or ks, day-1) and the mixing revolution number (NRev) defined previously. Thus, for the rapid desorption process
kr ) kr,R + βr NRevc
(6)
and for the slow desorption process
ks ) ks,R + βs NRevc
(7)
where kr,R and ks,R (day-1) are the respective corresponding values of kr and ks under quiescent conditions (i.e., no mixing), βr and βs (day-1) are the respective mixing sensitivity parameters representing impact capacities of mixing intensities on values of kr and ks, and c is an empirical exponential coefficient.
Materials and Methods Chemicals. Phenanthrene was obtained from Sigma-Aldrich (analytical grade, purity > 98%, Milwaukee, WI). Methanol and acetonitrile (HPLC analysis grade, purity > 99%) were purchased from Fisher Scientific (Chicago, IL). Sorbents. Two synthetic polymers and two natural soils that had been characterized well in prior studies (19-23) were employed as sorbents. These materials were selected on the basis of the different physical and chemical characteristics of their respective organic matter or SOM matrixes: i.e., the highly amorphous soft-carbon SOMs of cellulose and the Chelsea soil, and the chemically more condensed hard-carbon SOMs of poly(methyl methacrylate) (PMMA) and the Wagner soil (24). The cellulose and PMMA were purchased from Scientific Polymer Products, Inc. (Ontario, NY), and the Chelsea and Wagner soils were collected from uncontaminated upper-horizon deposits in the local area (Chelsea and Ann Arbor, MI). The two natural soils were ground and sieved to obtain uniform and similar particle size distributions. The characteristics of the four sorbents are summarized in Table 1. Sorption and Desorption Isotherms. An experimental protocol developed by Huang et al. (25) was employed to obtain the sorption/desorption equilibrium parameters. A one-month period of equilibrium was determined sufficient to ensure reasonable completion of sorption/desorption equilibria for the cellulose and Chelsea soil systems, and a three-month period was determined sufficient for those involving the PMMA and Wagner soil. The Freundlich isotherm model was employed to describe the sorption/ desorption equilibria for all systems studied. This model has the form
qe ) KFCen
(8)
where qe is the solid-phase substrate concentration at equilibrium, Ce is the liquid-phase substrate concentration at equilibrium, KF is a concentration-specific sorption capacity term, and the exponent n is a joint measure of the cumulative magnitude and distribution of energies associated with a particular sorption reaction (6). Laboratory Spiking of Sorbents. Table 1 provides a summary of the conditions under which selected sorbents were spiked with the target solute, phenanthrene, in preparation for the subsequent desorption experiments. Because of their relatively sticky physical characteristics and high sorption capacities for phenanthrene, the cellulose and Chelsea soil were premixed with glass beads purchased from Sigma-Aldrich (particle size 100d
a Solids composed of sorbent mixed with glass beads (1:4, w/w). acid-based soil SOM. d Tg value for kerogen-based soil SOM.
b
solids content (%, w/w)
final aqueous-phase phenanthrene concn (µg/L)
final solid-phase phenanthrene concn (µg/g)
57a 67a 60 67
107.97 ( 5.00b 95.03 ( 4.41 88.75 ( 4.66 96.61 ( 3.23
2.74 ( 0.08b 235.13 ( 7.84 31.67 ( 0.95 7.23 ( 0.14
Mean ( standard deviation for triplicate samples. c Tg value for humic-
TABLE 2. Intermittent Auger Mixing Conditions Set 1: Total Mixing Duration Each Day (θT) ) 12 h revolution rate (N, min-1) 9.3 18.4 26 57.8 75.3 108.5
intermittent mixing scheme each day 6 times, each of 2-hr duration
Set 2: Revolution Rate (N) ) 57.8 min-1
mixing revolution number (NRev, dimensionless)
total mixing duration each day (θT, hrs)
intermittent mixing scheme each day
mixing revolution number (NRev, dimensionless)
6696 13 248 18 720 41 616 54 216 78 120
2 4 6 12 18 24b
2 times, each of 1-hr durationa 2 times, each of 2-hr duration 3 times, each of 2-hr duration 6 times, each of 2-hr duration 6 times, each of 3-hr duration continuous
6936 13 872 20 808 41 616 62 424 83 232
a The same each idle period (no mixing period) between mixing operations (e.g., 2 times of each 11 h, 2 times of each 10 h, 3 times of each 6 h, 6 times of each 2 h, 6 times of each 1 h, and 0 h of idle period from the lowest NRev to the highest NRev, respectively). b Continuously mixed batch reactor (CMBR).
FIGURE 1. Schematic diagram of laboratory scale IMBR. Scientific). A predetermined amount of phenanthrene stock solvent (10 g/L methanol) was spiked to the each of the slurries (resulting in less than 0.2% of methanol concentrations by volume in the aqueous solution phases) to achieve an equilibrium aqueous phenanthrene concentration of approximately 100 µg/L. The glass bottles, each containing approximately 700 mL of sorbent slurry, were mixed topto-bottom continuously at 25 ( 0.5 °C on a laboratory tumbler operated at 12 rpm to ensure CMBR reaction conditions. As noted earlier, two different contaminant spiking equilibration periods were provided: i.e., one month for the cellulose and Chelsea soil slurries and three months for the PMMA and Wagner soil slurries. Intermittently Mixed Batch Reactor Design. As illustrated schematically in Figure 1, each bench-scale IMBR comprised a 500-mL glass kettle (Ace Glass, Vineland, NJ) equipped with a stainless steel auger driven by a motor (Dayton, Detroit, MI) having variable revolution rate and relatively high torque capabilities. Intermittent auger operation was achieved using a programmable timer (Intermatic, TN 811 Timer, Spring Grove, IL). The auger served to lift liquids and particles from the bottom of the reactor vessel to the slurry surface, from
which the lifted liquids and particles then return by gravity to the reactor bottom. Thus, in addition to lateral mixing, the auger provided effective vertical circulation of liquids and particles. To ensure uniform distribution of constituents in both the aqueous and solid phases of the slurries, concentrations of both a nonsorbing/nonreactive tracer (e.g., dye) and the PAHs spiked to each sorbent were monitored in separate batch tests to determine a 95%-operative homogenization time, the time required for concentrations of the aqueous-phase dye or the solid-phase PAHs to come within ( 5% of their respective leveling off concentrations (12, 13, 26). These times were observed to range from 2.5 to 41 min, depending on auger revolution rate and the sorbent slurry involved (data not presented). In general, inverse relationships were observed between homogenization time and revolution rate in all cases: i.e., the higher the revolution rate, the sooner was a uniform distribution of constituents established in the system. No evident “dead” (unmixed) zones were observed at any time in any of the reactors. Phenanthrene Desorption in Dense Slurries. Two sets of abiotic IMBRs were operated in parallel for each phenanthrene desorption experiment; the first set was operated at various impeller revolution rates and a fixed total mixing duration, and the second was operated at a fixed impeller revolution rate and various total mixing durations. Details regarding these mixing conditions are provided in Table 2. The phenanthrene-spiked sorbent slurries (approximately 600 mL) were each introduced to IMBRs, CMBRs, and nomix control reactors. Tenax TA polymer resin (Alltech, Deerfield, IL) was employed in each reactor to act as a phenanthrene sink and maintain an infinite-dilution condition in the aqueous phase. The dialysis membrane tube (molecular weight cutoff ) 10 000 Da, Sigma-Aldrich) containing the Tenax TA resins was supported by a brass rod (2-mm diameter) in each reactor. Two different reactor operation periods were employed: 40 days for the cellulose and Chelsea soil slurries and 100 days for the PMMA and Wagner soil slurries. While the reactors were operating in mixing mode, samples were withdrawn from a point 3 cm below the slurry surfaces using glass pipets (Fisher Scientific). VOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 3. Power Law Model Parameters
b
slurry
power law consistency parameter (K)
power law index (p)
R2
cellulosea Chelsea soila PMMA Wagner soil
2.08 ( 0.05b 1.26 ( 0.04 2.42 ( 0.04 1.80 ( 0.02
0.43 ( 0.01b 0.37 ( 0.01 0.39 ( 0.01 0.60 ( 0.01
0.994 0.992 0.997 0.992
a Solids composed of sorbent mixed with glass beads (1:4, w/w). Mean ( standard error (number of observations ) 55).
FIGURE 2. Power curves for auger mixing of dense sorbent slurries.
TABLE 4. Parameters for the Power and Reynolds Number Correlation under Laminar Flow Conditions
b
slurry
reactor geometry parameter (C)
exponential coefficient (a)
R2
cellulosea Chelsea soila PMMA Wagner soil
266.99 ( 5.53b 230.55 ( 3.37 191.98 ( 0.75 232.63 ( 2.08
-1.00 ( 0.04b -1.00 ( 0.03 -1.13 ( 0.01 -1.21 ( 0.02
0.993 0.998 0.999 0.999
a Solids composed of sorbent mixed with glass beads (1:4, w/w). Mean ( standard error (number of observations ) 10).
The solids in these samples were separated by centrifugation at 16 000g for 20 min using 0.2-µm nylon microcentrifuge tube filters (Alltech), oven-dried overnight at 60 °C, and then placed in 40-mL glass vials containing methanol. The vials were capped with Teflon-lined septa and open-port screw caps (Fisher Scientific), and sonicated (50 Hz) for 4 h to extract phenanthrene, after which solid-phase phenanthrene concentrations were calculated by dividing the concentrations measured in methanol by the masses of associated dried solids. The same extraction technique was used at the end of reactor operation to quantify phenanthrene sorbed by the Tenax TA resins and dialysis membranes and evaluate phenanthrene recovery efficiencies. Analytical Procedures. Phenanthrene concentrations were analyzed by HPLC as described elsewhere (27). The total organic carbon contents of the sorbents were analyzed using a high-temperature combustion method (Leco, CHN1000 analyzer, St. Joseph, MI). Rheological measurements were performed using a rotational viscometer equipped with a small sample adaptor (Brookfield, Programmable DV-II+ Digital Viscometer, Middleboro, MA) at 25 ( 0.5 °C. Torques required to agitate the dense slurries were measured using a Servodyne high-torque and low-speed mixer system (ColePalmer, Vernon Hills, IL). Nonlinear regression analyses employed to determine model parameters by best fits to the experimental data were performed using a Kaleidagraph computer program (Synergy Software, Release 3.01, Reading, PA).
Results Fluid Characterization. Shear stress as a function of shear rate was measured for the four sorbent slurries studied.
Parameters required for determining µa values using the power law relationship given in eq 1 were obtained by nonlinear regression of the shear stress and shear rate data, and summarized in Table 3. Unlike Newtonian fluids, for which shear stress increases linearly with shear rate, the slurries exhibited pseudoplastic non-Newtonian fluid behavior (i.e., p < 1). Power Correlation. Power and Reynolds numbers obtained for auger mixing of the four sorbent slurries were logarithmically transformed to construct power curves encompassing a range from laminar to turbulent flow conditions (0.5 < NRe < 104), as illustrated in Figure 2. The Metzner and Otto method, known as an empirical but very useful way to estimate the average shear rate of nonNewtonian fluids, was employed in the calculation of both dimensionless numbers as described elsewhere (11). In turbulent flow regimes, apparent viscosity values measured by viscometer or estimated from such measurements were used as inputs under the assumption that the shear rate is the same as the auger revolution rate. A free surface vortex is not known to be produced on the fluid surface in cases of either: (i) mixing in self-baffled systems, in which an impeller edge is placed within a distance of less than 5% of the impeller diameter to the reactor wall (i.e., 0.25 cm for this study); or, (ii) mixing of viscous non-Newtonian fluids by helical screw impellers under laminar flow conditions (11, 28-31). In such cases, the Froude number in the functional correlation given earlier in eq 3 is not a variable because the impacts of gravitational acceleration (g) on power demand are negligible, in which case the correlation reduces to
NP ) CNRea
(9)
The power curve data for mixing of all sorbent slurries under laminar flow conditions (NRe < 20) were analyzed by nonlinear regression using eq 9, and the resulting correlation parameters are presented in Table 4. The power numbers were found to be essentially proportional to the inverse of the Reynolds numbers for all slurries. This finding has been well proven in a number of prior investigations for laminar mixing of non-Newtonian fluids (11, 32, 33). The deviations of a values from unity and the differences observed in the characteristic reactor geometry parameters (C) are likely
TABLE 5. Freundlich Isotherm Parameters Sorption sorbent cellulose Chelsea soil PMMA Wagner soil a
Log
-1.81 ( 0.05c 0.89 ( 0.01 0.11 ( 0.02 -0.67 ( 0.01
Units of (µg/g)‚(µg/L)-n.
2270
9
KFa
b
Desorption a
n
R2
Log KF
1.09 ( 0.03c 0.74 ( 0.01 0.74 ( 0.01 0.76 ( 0.01
0.986 0.999 0.997 0.999
-1.92 ( 0.05c 0.92 ( 0.01 0.16 ( 0.01 -0.56 ( 0.01
n
R2
hysteresis index, HIb
1.14 ( 0.04c 0.75 ( 0.01 0.85 ( 0.01 0.83 ( 0.01
0.991 0.999 0.998 0.999
0 0.09 0.89 0.78
HI at Ce ) 100 µg/g. c Mean ( standard error (number of observations ) 27).
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attributable to inaccuracies associated with the measurements of torque. In the turbulent flow regime (NRe > 1000), which is impractical for mixing of highly viscous fluids or dense slurries, the power number is independent of the Reynolds number. Sorption and Desorption Isotherms. The phenanthrene sorption and desorption data were logarithmically transformed, the Freundlich isotherm parameters (eq 8) were determined via linear regression, and the results are summarized in Table 5. As evident from the tabulated values of n, nonlinear isotherm behaviors were observed for three of the four sorbents: i.e., Chelsea soil, PMMA, and Wagner soil. The Freundlich model parameters are in good agreement with those reported in earlier studies (19, 23). Slight differences between the parameter values obtained in this study and those reported previously may be attributed to different sorption/desorption periods, different particle size distributions, and/or the relatively more severe sorbent preparation procedures (e.g., crashing, grinding, and sieving) employed, which may have resulted in physical changes in the Chelsea and Wagner soil particles. Sorption/desorption hysteresis was quantified in terms of an index defined in prior studies (20, 25): i.e.,
Hysteresis Index (HI) )
qde - qse |Ce qse
(10)
where qde and qse are solid-phase substrate concentrations for single-cycle desorption and sorption isotherms, respectively. The same residual aqueous-phase concentration (Ce ) 100 µg/L) was used to obtain these values from the Freundlich isotherms for the four sorbents employed, and the HI values are summarized in Table 5. Hysteresis effects were more pronounced for the hard-carbon sorbents, PMMA and Wagner soil, while little or no hysteresis effects were observed for the soft-carbon sorbents, cellulose and Chelsea soil. Phenanthrene Desorption in IMBRs. Auger mixing effects on phenanthrene desorption rates were evaluated by monitoring its solid-phase concentrations as illustrated in Figure 3. It is evident that solid-phase phenanthrene concentrations decreased only slowly over the entire period of reactor operation when no mixing was provided. Conversely, desorption rates were markedly enhanced when the slurries were mixed. As the NRev increased, the desorption process began to exhibit increasing apparent biphasic behavior. These data presented in Figure 3 were analyzed by nonlinear regression fits (solid lines) using the DRDM rate relationship given in eq 5, and model parameters corresponding to equivalent CMBR system configurations are presented in Table 6. As evidenced by the model fits in Figure 3 and the corresponding regression R2 value range of 0.894-0.997 for all reactors, the model describes the desorption processes reasonably well over the entire range of mixing conditions and sorbent slurries tested. It is evident from Table 6 that the slowly desorbing fraction (φs) values of the sorbents were strongly related to the hardness of their respective associated organic matrixes, with φs increasing in the order cellulose, Chelsea soil, Wagner soil, and PMMA. The geologically young or soft-carbon SOM associated with Chelsea soil had a large rapidly desorbing fraction (1 - φs), while the geologically old or hard-carbon SOM associated with Wagner soil had a large slowly desorbing fraction. This trend was even more evident in the cases of the cellulose and PMMA, respectively, representing a relatively soft or rubbery biopolymer and a relatively hard or glassy carbon polymer. It is also to be noted that the DRDM rate parameters for the Chelsea and Wagner soil slurries in this study were statistically consistent with those reported by Johnson et al. (18), who obtained values
FIGURE 3. Phenanthrene desorption as a function of time in IMBRs containing cellulose (A), Chelsea soil (B), PMMA (C), and Wagner soil (D) slurries for different mixing revolution number (NRev). Additional data for auger operations at NRev values of 18 720, 20 808, 54 126, and 62 424 not presented. Error bars denote standard deviation of triplicate samples. of 0.41 (Chelsea soil) and 0.74 (Wagner soil) for φs, 1.29 (Chelsea soil) and 0.13 day-1 (Wagner soil) for kr, and 12.4 × 10-3 (Chelsea soil) and 1.38 × 10-3 day-1 (Wagner soil) for ks, respectively, under similar experimental conditions (i.e., three-month pre-aging of phenanthrene-spiked sorbents, VOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 6. Desorption Rate Parameters and Associated Correlations to Mixing Revolution Number for Rapidly Desorbing Organic Fractions DRDM Rate Parameters for Equivalent CMBR Systems
slurry cellulosea Chelsea Soila PMMA Wagner Soil
slowly desorbing fraction (Os)
desorption rate coefficient for rapidly desorbing fraction (kr, day-1)
desorption rate coefficient for slowly desorbing fraction (ks × 103, day-1)
0.15 ( 0.48 ( 0.02 0.75 ( 0.03d 0.74 ( 0.03
0.38 ( 0.54 ( 0.01 0.07 ( 0.01d 0.12 ( 0.02
52.78 ( 30.54 ( 0.07 0.73 ( 0.61d 1.00 ( 0.35
0.04b
0.04b
4.87b
Correlation Parameters value of kr under quiescent conditions (kr,r × 103, day-1) 18.85 ( 13.68 ( 7.38 16.49 ( 4.19 25.83 ( 5.45
12.07c
mixing sensitivity parameter (β × 103, day-1)
exponential coefficient (c)
R2
0.72 ( 1.72 ( 0.71 0.21 ( 0.18 0.23 ( 0.19
0.56 ( 0.51 ( 0.04 0.51 ( 0.08 0.53 ( 0.07
0.994 0.968 0.866 0.898
0.34c
0.04c
a Solids composed of sorbent mixed with glass beads (1:4, w/w). b Mean ( standard error (number of observations ) 14). c Mean ( standard error (number of observations ) 36). d Mean ( standard error (number of observations ) 20).
in a statistically similar range, supporting the hypothesis that desorption of phenanthrene from the rapidly desorbing fractions of SOM in the absence of mechanical mixing is controlled by the same mass transfer process: i.e., interparticle pore-scale diffusion.
Discussion
FIGURE 4. First-order rate coefficients for the rapidly (kr) and slowly (ks) desorbing fractions of cellulose and Chelsea soil slurries as a function of mixing revolution number (NRev). similar initial phenanthrene loadings, and ampule-type CMBRs). The mass recovery of desorbed phenanthrene collected from the Tenax TA resins and dialysis membranes ranged from 85.1 to 107.9 wt % of the amounts initially spiked for all reactors tested. Desorption rate coefficients for the rapidly and slowly desorbing fractions were correlated to the NRev. The results for the cellulose and Chelsea soil slurries are illustrated in Figure 4, in which the kr values are in both cases observed to increase sharply with auger mixing in the relatively lowlevel NRev range (0-20 808), followed by much more gradual increases with further mixing in the relatively high-level NRev range (41 616-83 232). Moreover, it is clear from Figure 4 that mechanical mixing had essentially no impact on ks values, suggesting a transition during desorption from reactor-scale rate control to reaction-scale rate control. Very similar relative patterns of kr and ks values were observed in IMBRs containing PMMA and Wagner soil slurries (data not illustrated). Rapidly desorbing fraction rate dependencies on degree of auger mixing were then evaluated using the empirical correlation between kr and NRev values given in eq 6, and model parameters obtained by nonlinear regression of those data are provided in Table 6. As indicated by the R2 values, closer model fits were achieved for the cellulose and Chelsea soil slurries than for the PMMA and Wagner soil slurries. This is likely related to the larger fractions of rapidly desorbing SOM associated with the former sorbents, resulting in more evident kr value dependence on NRev. The highly nonlinear correlations confirm that desorption of phenanthrene associated with the rapidly desorbing SOM was enhanced more significantly and effectively by relatively low-level auger mixing rather than by relatively high-level mixing. It is also to be noted that kr,R values obtained from the empirical correlations for auger mixing of the four sorbent slurries were 2272
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The mass transfer of solutes in the dense slurries studied was observed in the absence of mechanical mixing to be controlled by pore/particle-scale diffusion processes. The introduction of even modest mechanical mixing was demonstrated to facilitate markedly improved interchange of interparticle pore-scale fluid elements and associated solutes with those in the bulk fluid. Phenanthrene association with rapidly desorbing fractions of labile or soft-carbon SOM is known to exhibit partitioning-like equilibrium behavior and relatively fast sorption/desorption rates (16, 18). It is in fact desorption from that type of SOM that can most readily and markedly be enhanced by the sharpened solute concentration gradients resulting from hydrodynamic mixing. Slow or resistant desorption processes are generally associated with the highly cross-linked macromolecular structures of hardcarbon SOM, and relate to both strong interactions between solutes and sorbing sites and intraparticle or intra-SOM matrix diffusion processes that proceed extremely slowly (20). It is thus not surprising that the introduction of mechanical mixing, because it cannot influence intraparticle diffusion processes, does not significantly enhance rates of sorbed phenanthrene release from solids containing principally such hard carbon SOM. The auger employed in this study (i.e., helical screw-type impeller) was able, under laminar flow conditions, to provide a relatively efficient homogenization of the dense slurries employed, and thus able to minimize reactor-scale transport limitations via competent bulk mixing of interparticle pore fluids. Given the rheological complexities of non-Newtonian fluids, which include sticky and viscous liquids involved in many industrial and biological processes and most dense slurries of 40% (w/w) or more solids, it is difficult via mixing or any other means to obtain a truly homogenized state of constituents (11, 32, 33, 35, 36). High viscosity, a representative characteristic of non-Newtonian fluids, increasingly dampens mechanical energy introduced by mixing through increasing deformation of fluid elements and increasing interference of particles, resulting in large power consumption (11, 37). The mixing of highly viscous fluids is thus usually performed under laminar flow conditions, in which viscous effects dominate over inertial effects (12, 35). Correlations between the power and Reynolds numbers for the systems studied illustrate the dependence of power and torque requirements on associated reactor design parameters. The rearrangement of eq 9 and the exponential coefficients (a) given in Table 4 clearly indicate that power
and torque for a given mixing system can depend heavily upon impeller revolution rate and mixer geometry (i.e., power ∝ N1.79-2.00D2.58-3.01 and torque ∝ N0.79-1.00D2.58-3.01, a values used in this calibration expressed as the low-high values obtained for the four different slurries studied). Given that both capital and operating costs of mixing systems are proportional to torque and power requirements (38), small increases in auger size or mixing revolution number can result in significant increases in system costs. In those cases where mechanical mixing enhanced overall desorption rates, it did so as evidenced by the nonlinearity of empirical correlations between degree of mixing and rate coefficients for desorption processes associated with rapidly desorbing fractions of SOM. This is a fortuitous reality of the gain in mass transfer effected by a relatively simple shift from pore-scale to reactor-scale control, and a significant finding of this work. In other words, high-level mixing that entails significant increases in capital and operational costs as results of dramatically increased torque and power requirements as discussed earlier is unnecessary for the performance-efficient and cost-effective design and operation of dense slurry systems.
Acknowledgments We appreciate the invaluable comments and suggestions given by the three anonymous reviewers. Funding for this research was provided by the Strategic Environmental Research and Development Program (a consortium comprising the Department of Defense, the Department of Energy, and the U.S. Environmental Protection Agency) through a grant from the Army Corps of Engineers Waterways Experiments Station to the Great Lakes and Mid-Atlantic Center (GLMAC) for Hazardous Substance Research, which operated under U.S. Environmental Protection Agency baseline Grant R-825539. Baseline support of the activities of GLMAC was also provided by the State of Michigan Department of Environmental Quality.
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Received for review March 19, 2004. Revised manuscript received December 10, 2004. Accepted December 21, 2004. ES049565B
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