Concentrating Dilute Sludge Wastes with High-Gradient Magnetic

Breakthrough curves for four different sludges containing a blend of paramagnetic metal hydroxides and oxides were measured at different feed velociti...
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Ind. Eng. Chem. Res. 2002, 41, 5049-5057

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Concentrating Dilute Sludge Wastes with High-Gradient Magnetic Separation: Breakthrough Experiments and Performance Armin D. Ebner and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208

High-gradient magnetic separation (HGMS) was successfully investigated for the concentration of dilute sludge wastes using a 0.3-T bench-scale system. Breakthrough curves for four different sludges containing a blend of paramagnetic metal hydroxides and oxides were measured at different feed velocities (0.0367-0.2754 cm s-1) and suspended insoluble solids feed concentrations (2.5-10.5 g L-1). With the aid of a dynamic model fitted to each of the breakthrough curves, the best bed utilizations of the HGMS unit and the highest enrichments of the feed were, respectively, on the order of 77% and 14 for the runs with lower feed velocities and concentrations. These results also corresponded to the HGMS unit producing on the order of 20 bed volumes of effluent free of suspended insoluble solids prior to breakthrough. Overall, the performance of the HGMS unit for this type of process was considered to be quite good, given the broad range of particle sizes, magnetic susceptibilities, and molecular species in each sludge waste. These results suggest that HGMS can be used as an effective and alternative treatment method for the concentration of a variety of dilute waste streams containing suspended solids of a diverse nature. Introduction High-gradient magnetic separation (HGMS) was introduced in the late 1960s to assist the kaolin clay industry1-3 in the beneficiation of clay. Since then, a great deal of attention has been placed on this separation process because of its particular ability to retain and segregate particles of relatively weak magnetism and microscopic size. For example, HGMS has other proven applications in the beneficiation of minerals such as coal,2,4-15 tin,16,17 bauxite,18 and rare metal ores.19,20 It also has proven applications in waste reclamation and recycling and in the ultrapurification of chemical refractories and powders.21-28 Other applications of HGMS include environmental remediation and nuclear waste treatment,27,28-33 particularly as a downstream collector of magnetically seeded nonmagnetic particles and ionic species.6,9,31,34-37 An excellent example of this kind of HGMS technology is the SIROFLOC process.38 The versatility of HGMS has also allowed for its expansion into phase separations,14,39-41 as well as into more novel uses such as the separation and segregation of biomolecules and cells by using bio-labeled magnetic carriers,42-47 a growing area. The equipment used for HGMS basically consists of a fine ferromagnetic wire matrix (e.g., ferritic stainless steel wool) inserted into the bore of a magnet, which is then energized by an externally applied magnetic field. When the external magnetic field is turned on, large magnetic field gradients are generated in the vicinity of the fine ferromagnetic wires that cause magnetic particles to be retained on the surface of the wires. At some point before the matrix is fully loaded, the field is turned off, and the particles are collected using a combination of back-flushing and gas sparging. Depending on the operating conditions (i.e., the magnetic field * To whom all correspondence should be addressed. Phone: (803) 777-3590. Fax: (803) 777-8265. E-mail: [email protected].

strength, fluid flow rate, and matrix wire size) and the type of material treated, HGMS can be used to achieve either separation between suspended species or total retrieval and concentration of unwanted species. Superficial velocities between 0.01 and 20 cm s-1, magnetic field intensities between 0.1 and 8 T, and wire diameters between 50 µm and 1 mm are commonly employed. Also, feed concentrations of suspended magnetic particles ranging up to a few weight percent, with particle sizes varying from 0.1 to 50 µm, can be handled easily. An area in which HGMS has significant but largely unexplored potential is nuclear waste remediation. Nuclear wastes normally consist of suspended solids made from a wide blend of paramagnetic and diamagnetic hydroxides and oxides of metals interconnected by van der Waals, electrostatic, and acid-base interactions. This intricate blend of compounds gives rise to a net paramagnetic nature that makes nuclear waste amenable to magnetic retrieval. HGMS also offers advantages over other more traditional techniques such as settling, ultrafiltration, or centrifugation. For example, back-flushing in HGMS is fast and efficient, and if carried out at small superficial velocities, large separation factors (i.e., sharp breakthroughs with clean initial elusions) can be achieved, which is essential in the treatment of suspensions containing highly hazardous substances, such as nuclear waste sludges. The objective of this work is to demonstrate the feasibility of using HGMS for the retrieval and concentration of suspended solids from sludge wastes. Breakthrough experiments were carried out in a bench-scale 0.3-T HGMS system with four different high-level radioactive waste (HLW) sludge simulants provided by the Savannah River Site (SRS). These sludge simulants were first diluted and then processed through the HGMS unit at varying superficial velocities and suspended solids concentrations. The resulting experimental breakthrough curves were also fitted to a dynamic

10.1021/ie020198r CCC: $22.00 © 2002 American Chemical Society Published on Web 09/04/2002

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by their appearance and large porosities (>0.8). The porosities were estimated by simply assuming that they were identical to the porosity of settled solids obtained upon centrifugation of 30-mL samples of the suspensions at accelerations of 800 000 G for 5 min with an Eppendorf centrifuge 5403. The final values were obtained simply by comparing the apparent volume of the deposited solids in the vial after centrifugation with that obtained by ultrapycnometry (Ultrapycnometer 1000, QuantaChrome) after membrane filtration (Gelman Sciences 0.45-µm Tuffryn) and vacuum-drying overnight at 80 °C. For each breakthrough run, diluted suspensions were prepared in 4-L batches (C) by dilution of the “asreceived” sludges with distilled water that had previously been adjusted to the initial pH of each sludge with either NaOH (AlfaAesar, 97%) or HNO3 (AlfaAesar, 6870%). The final concentrations of the suspensions ranged between 1 and 10 g L-1. While constantly being stirred with a magnetic stirrer (D), the suspensions were fed upward into the canister during each breakthrough run to ensure complete flooding of the magnetic matrix. The flow rates were controlled with a peristaltic pump (E) and varied between 20 and 150 mL min-1. Also, a settling column (F) was placed between the HGMS unit and the peristaltic pump to prevent silica and other large particles in the suspensions from entering the magnetic matrix. Because the amount of these particles was difficult to control, the exact concentrations of the suspensions were determined from the dynamic model, as explained later. The breakthrough behavior of the suspended insoluble solids through the matrix was monitored by collecting the effluent continuously in 30mL plastic bottles (G) until the 4-L feed solution was depleted. Because the volume in each 30-mL sample varied slightly, the actual amount collected was determined gravimetrically. The concentration of insoluble solids was also determined gravimetrically by weighing and then filtering each 30-mL sample through a tared Gelman Sciences 0.45-µm Tuffryn membrane and vacuum-drying the filtered material overnight at 80 °C.

Figure 1. Schematic of the 0.3-T HGMS bench-scale apparatus and experimental setup utilized for the measurement of breakthrough curves: (A) 0.3-T HGMS, (B) 1.37-in.i.d. canister, (C) magnetically stirred bottle with suspension, (D) magnetic stirrer, (E) peristaltic pump, (F) settling column, (G) plastic bottle with collected sample.

model available in the literature to estimate both the column efficiency and the maximum enrichment that can be achieved with this HGMS process. Experimental Section A 0.3-T HGMS system from Advanced Environmental Systems, Inc., was used to carry out the breakthrough experiments. The experimental setup is depicted in Figure 1. The 0.3-T HGMS system (A) consists of a magnetic bore that is 4.75 in. long and 2.06 in. in diameter. A filter canister (B) with a diameter of 1.34 in. is placed inside this bore and contains the magnetic matrix and magnetic pole pieces that serve to distribute the magnetic field evenly over the matrix area. The matrix consists of steel wool disks (26.4 g) with a porosity of 0.926 that are stacked together and form a bed 1.97 in. in length and 1.34 in. in diameter. Breakthrough runs were carried out using suspensions of insoluble solids prepared by diluting the different SRS HLW sludge simulants. These simulants are identified here as drums 2, 4, 7, and 9. The compositions and some physical properties of these sludges are given in Table 1. Also, the number particle size distributions of these suspensions obtained with an optical particle sizer (Accusizer model 770A) are shown in Figure 2, along with log-normal distribution fits to these distributions. In general, all of the suspensions consisted of small particles between 2 and 5 µm in diameter, but with distributions skewed toward larger particles up to 10 µm in diameter. However, most of these suspensions had an amorphous flock-like morphology, as suggested

Theoretical Section To determine the performance parameters of the HGMS unit analyzed in this study, the experimental breakthrough curves were fitted to a well-known48-51 dynamic model that describes the mass balance through

Table 1. Chemical and Physical Properties of the HLW Sludge Simulants Prior to Dilution density (g cm-3)a pHa soluble solids, wt % nonsoluble solidsb content, wt % BET surface area, m2 g-1 mass susceptibilityc (cgs), cm3 g-1 × 106 skeleton density, g/cm3 porosity of retained solids effective volumetric susceptibility,d (SI) × 106 metal content, mg g-1 Fe Al Mn Ni Cu Cr a

Prior to dilution. b Sand previously removed. c Dry sample.

d

drum 2

drum 4

drum 7

drum 9

1.19 7.95 10.79

1.11 4.30 7.40

1.03 7.75 4.96

1.12 8.50 6.48

15.34 174.85 661.39 2.65 0.839 3546.0

9.93 155.73 1425.37 3.20 0.902 5617.1

2.68 171.79 1421.70 3.19 0.879 6895.9

10.73 103.75 959.71 3.92 0.854 6902.2

98.8 59.8 29.6 4.6 4.1 0.3

315.8 50.4 13.8 15.2 4.5 0.5

345.0 31.1 70.7 33.1 12.7 0.6

279.1 14.9 17.5 17.0 4.5 0.5

According to eq 11.

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Figure 2. Number particle size distributions of suspensions from (a) drum 2, (b) drum 4, (c) drum 7, and (d) drum 9.

an HGMS unit in terms of a monodisperse suspension, i.e., a suspension with particles of the same size and relative volumetric magnetic susceptibility. The solution and retained-phase mass balances are given by

conditions were applied to solve the above system of partial differential equations

c(t)0,z>0) ) 0

(4)

∂c (1 - ) ∂n Uo ∂c + Fc + )0 ∂t  ∂t  ∂z

c(t>0,z)0) ) co

(5)

n(t)0,z>0) ) 0

(6)

(1)

and

2fcUo ∂n λc)0 ∂t πacFc c

(2)

where t and z are the temporal and spatial coordinates of the bed, respectively; c is the mass concentration of suspended solids; n is the mass loading of the matrix; Uo is the superficial velocity in the bed; ac and Fc are the radius and density of the matrix wire, respectively; and  is the porosity of the matrix. The constant fc is the capture efficiency of the matrix. For random matrixes, fc is equal to 2/3,51,52 which simply indicates that the matrix behaves similarly to one having only twothirds of the wires perfectly oriented in the direction that favors retention (i.e., perpendicular to the field and flow). The parameter λc is the capture cross section of a wire placed perpendicular to both the fluid flow and the magnetic field. To account for the saturation of the bed, λc is assumed to have the following dependency on the loading of the matrix48,51

(

λc ) λc,o 1 -

n nT

)

(3)

where λc,o is the capture cross section of a clean wire and nT is the total mass loading at saturation [g/g of stainless steel (SS)]. The following initial and boundary

where co is the mass concentration of suspended solids in the feed. An iterative solution methodology was devised to solve this system of equations numerically using the Fortran code DDASPK.52 The combination of λc, co, and nT that best described each experimental breakthrough curve was determined by minimizing the root-meansquared error (RMSE), defined as

RMSE ) min

[

1

N

]

∑(cexp,i - cmodel,i)2 Ni)1

1/2

(7)

where cexp,i and cmodel,i are the experimental and predicted values, respectively, of the concentration at the time defined by the subscript i and N is the number of samples collected. However, the strong nonlinear nature of the model, as well as the presence of experimental scattering, assured the existence of multiple local minima, which made the traditional least-squares method rather inappropriate for finding the global minimum. Instead, a three-dimensional scan procedure was carried out with λc, co, and nT varied in discrete steps of 0.0001, 0.01 g L-1, and 0.0001 g g-1, respectively, to find the combination of these variables within suitable ranges that minimized the objective function in eq 7. These intervals corresponded to less than 0.5%

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Figure 3. Typical effect of the presence of the 0.3-T magnetic field on the breakthrough of a suspension made from drum 2 with co ≈ 8 g L-1

of full scale for co and less than 0.1% of full scale for both λc and nT. The results from the model were used to obtain the bed utilization (η) and the maximum enrichment (Emax) corresponding to the experimental breakthrough curves. The utilization is defined here as the ratio between the solids retained in the column at the breakthrough point and the solids that could be retained in the column at complete saturation according to nT. If the breakthrough volume (VBT) is defined as the volume of solution collected just prior to breakthrough of solids in the effluent, the bed utilization is given by

η)

VBT co Vb nT(1 - )Fc + co

(8)

where Vb () πdb2Lb/4) is the total bed volume. VBT was determined from the cumulative volume of effluent collected in the sample bottles that contained an insoluble solids concentration of less than 1% of co, with the minimum value of VBT assumed to be equal to Vb. Also, if one assumes that it takes only one bed volume of feed to flush the matrix fully, Emax is given by

Emax )

[

cf 1 co + nT(1 - )Fc ) 1+ η co 2 co

]

(9)

where cf is the enriched concentration of suspended solids. These definitions of Emax and the corresponding cf are equivalent to the values that would be obtained by back-draining the column after producing a solidsfree effluent volume of VBT, back-flushing the column with one column volume of feed, and collecting both effluents in the same container. Results and Discussion The effect of the magnetic field on the breakthrough of suspended solids from the HGMS unit is shown in Figure 3. Two identical experiments were carried out using diluted HLW sludge simulant from drum 2, one with the magnetic field turned on and one with it turned off. The experiment with the magnetic field turned on delivered 200 mL of clear effluent solution before sharp breakthrough of the suspended solids occurred. This transparent effluent, containing only dissolved or ionic

species that could not be retained magnetically, had a yellowish tint and contrasted markedly with the feed solution, which was opaque and looked like brown paint. When the experiment was carried out with the magnetic field turned off, the breakthrough happened almost immediately, and hence, hardly any retention took place. Identical results were observed with the other diluted suspensions from the other drums, confirming that they all had some magnetic character and that the matrix retained essentially no suspended particles by mechanical filtration. The effect of the superficial velocity on the breakthrough time and shape of the breakthrough curve is shown in Figure 4 for all four diluted HLW sludge simulants. For sludges from drums 2 and 9, the breakthrough curves for two different feed concentrations are depicted in parts a,b and e,f of Figure 4, respectively. These plots collectively confirm that all four HLW sludge simulants had some degree of magnetic character, in agreement with the magnetic susceptibilities shown in Table 1. Moreover, excellent separation factors were achieved under these conditions, i.e., all of the effluent solutions were initially free of suspended insoluble solids. As expected, however, earlier breakthrough occurred with higher superficial velocities, and it began almost immediately for the runs with Uo ) 0.2754 cm s-1 and co ≈ 10 g L-1, both values being at the higher ends of the parameter ranges investigated. The opposite behavior was observed for the runs carried out with the less-concentrated suspensions, as the matrix under such situations took more time to saturate. In Figure 4, for example, compare part a with part b for drum 2 sludge and part e with part f for drum 9 sludge. In both cases, when the feed concentrations were halved, the breakthrough took about twice as long to occur. Also, it is noteworthy that the sharpness of the breakthrough curves did not change substantially with the larger superficial velocities, suggesting that good separation factors can be achieved at larger flow rates, but only if suspensions with lower insoluble solids concentrations than those explored here are being treated. Nevertheless, these results clearly demonstrate the utility of HGMS for concentrating dilute sludge wastes of a diverse nature. The parameters used in the dynamic breakthrough model are presented in Table 2, which also includes the operating conditions under which the runs were performed. It is worth pointing out that the model presented in eqs 1 and 2 did not require values for the radii or magnetic susceptibilities of the particles as input. However, these variables were implicitly manifested through the magnitudes of λc and nT, which were obtained here by fitting the experimental breakthrough curves to the model. Also, the radii of the matrix wires, ac, were found to be highly irregular, which made the choice of a value for ac difficult and somewhat arbitrary. Figure 5 presents several SEM pictures of the matrix wires. In general, the wires exhibited radius distributions ranging between 10 and 80 µm. Moreover, this irregularity also extended to the wires themselves. Observe, for example, that the tip at the bottom part of the wire in Figure 5b was about 25 µm thick, whereas the main body of the wire was several times larger, with thicknesses varying between 80 and 130 µm. Because this model also did not account for a distribution in the matrix wire radii, as a first approximation, a wire radius of 50 µm was used as input to the model.

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Figure 4. Effect of the superficial velocity and suspended feed concentration on the breakthrough of suspensions made from (a) drum 2 with co ≈ 6-8 g L-1, (b) drum 2 with co ≈ 2.5-3.5 g L-1, (c) drum 4 with co ≈ 3-7 g L-1, (d) drum 7 with co ≈ 3.5-4.5 g L-1, (e) drum 9 with co ≈ 9-11 g L-1, and (f) drum 9 with co ≈ 3.5-4.5 g L-1. Table 2. Operating Conditions and Dimensions and Properties of the HGMS Matrix Uo, cm s-1  Lb, cm db, cm ac, µm Fc, g cm-3

0.0367, 0.0918, 0.1836, 0.2754 0.926 5.0 3.4 50 7.86

Figure 6 shows representative fits of the dynamic breakthrough model to four experimental breakthrough curves obtained with drum 9 sludge. Table 3 lists the results for the fits of the dynamic model to all of the experimental breakthrough curves. In particular, the values of λc, nT, and co were obtained by minimizing the RMSE, as explained earlier. The values of the RMSE, ranging from 0.14 to 0.53 g L-1, indicated that the model correlated relatively well with most of the experimental

breakthrough curves. However, because of the strongly asymmetric s-shape of the curves, the model failed to predict accurately the sharp changes observed at the bottom (or initial) part of some of the breakthrough curves. The main cause for this discrepancy was the fact that the capture cross section did not necessarily vary linearly with loading, as assumed in eq 3. Instead, the capture cross section seemed to decay more rapidly than linearly, suggesting that not all of the retention sites were equal in strength and that the strongest sites were filled first. In other words, as the wire retained more particles, the magnetic force holding the newly retained particles in place was lower, as these new particles were positioned farther from the wire by the particles already trapped underneath them. Also, but less significantly, the reason for the discrepancy between the experimental and modeling results might have been due to the wide

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Figure 6. Typical comparison of the experimental (symbols) and correlated (lines) breakthrough curves from the dynamic model for suspensions from drum 9 with co ≈ 8-10 g L-1.

Figure 5. Scanning electron microscopy (SEM) images showing the variability of the matrix wires inside the HGMS unit.

particle size distributions of the samples (Figure 2), as well as the diverse magnetic character associated with

the wide range of molecular species in these sludges (Table 1). The use of an exponential parameter, γ, has been suggested51 to correct the loading term for this behavior, i.e., (1 - n/nT)γ, which appeared to be larger than unity in these results. In contrast, the model did very well in predicting nT for each of the experimental breakthrough curves; the values of nT were subsequently used to predict experimental bed utilizations (η) from eq 8 and the values of VBT obtained from each experimental breakthrough curve. Then, the maximum enrichments (Emax) and corresponding cf values were predicted from eq 9. The resulting values of VBT, η, Emax, and cf are listed in Table 3. The values of the breakthrough volume, VBT, ranged from the lowest possible value of essentially one bed volume (Vb ) 45.5 cm3) to about 1100 cm3, which corresponds to about 20 bed volumes. The higher values were obtained, in general, at the lower feed velocities and concentrations. The corresponding bed utilizations ranged from about 9 to 77%. These results were very

Table 3. Correlation of the Dynamic Model to the Experimental Breakthrough Curves and Prediction of the Bed Utilizations and Maximum Enrichments run

drum

flow (cm3/min)

Uo (cm/s)

nT (g/g of SS)

λc,o

co (g/L)

RMSE (g/L)

VBT (cm3)

η (%)

Emax

cf (g/L)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2 2 2 2 2 2 2 2 4 4 4 4 7 7 7 7 9 9 9 9 9 9 9 9

20 20 50 50 100 100 150 150 20 50 100 150 20 50 100 150 20 20 50 50 100 100 150 150

0.0367 0.0367 0.0918 0.0918 0.1836 0.1836 0.2754 0.2754 0.0367 0.0918 0.1836 0.2754 0.0367 0.0918 0.1836 0.2754 0.0367 0.0367 0.0918 0.0918 0.1836 0.1836 0.2754 0.2754

0.1371 0.1807 0.1017 0.1226 0.0831 0.1040 0.0702 0.0856 0.1378 0.1219 0.1169 0.1067 0.1515 0.1109 0.0763 0.0683 0.2650 0.2661 0.1883 0.2058 0.1405 0.1800 0.1116 0.1515

0.2760 0.3174 0.0951 0.1401 0.1128 0.0801 0.0825 0.0675 0.2721 0.1119 0.0714 0.0714 0.4578 0.2541 0.1776 0.1320 0.2535 0.3501 0.1752 0.1740 0.1170 0.1164 0.1212 0.0846

2.73 6.84 3.04 7.01 3.20 7.99 3.43 7.98 2.74 5.32 6.02 6.68 3.98 4.22 4.03 3.99 3.99 8.80 3.83 9.46 4.11 9.73 4.16 10.50

0.1396 0.2334 0.2015 0.3775 0.1976 0.5335 0.1978 0.3510 0.1408 0.3518 0.4622 0.3852 0.1956 0.2557 0.1718 0.2478 0.2397 0.4352 0.1964 0.4466 0.2004 0.3809 0.2732 0.4418

1056.83 489.79 382.29 241.00 379.33 143.65 155.19 42.04a 1057.76 352.49 158.81 42.04a 804.41 523.58 317.62 254.85 1145.39 621.95 687.29 311.46 280.26 147.14 318.55 42.04a

77.25 66.23 41.31 47.83 52.13 37.24 26.64 12.94 77.21 54.48 28.63 9.06 76.82 71.15 58.61 51.59 63.79 74.00 51.28 50.52 29.67 27.74 42.45 9.94

13.07 6.33 5.05 3.37 5.01 2.21 2.35 1.00 13.08 4.69 2.39 1.00 10.07 6.73 4.28 3.53 14.12 7.90 8.67 4.20 3.83 2.25 4.29 1.00

35.68 43.27 15.34 23.60 16.04 17.65 8.05 7.98 35.84 24.96 14.38 6.68 40.07 28.39 17.24 14.09 56.35 69.50 33.22 39.78 15.76 21.89 17.84 10.50

a Because of dispersive mechanisms along the bed, breakthrough was observed in the first 30 mL-bottle. In this case, the lower theoretical limit of Vb () 42.04 cm3) was used to evaluate VBT.

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encouraging because the higher bed utilizations (lower feed flow rates and concentrations) gave rise to maximum enrichments of around 14. Recall, however, that Emax was predicted by allowing breakthrough to occur up to VBT and then mixing together one column volume of drained effluent from the bed containing both the retained and suspended solids in the liquid phase with one column volume of feed (presumably used as back flush) containing suspended solids at a concentration of co. Hence, the values of Emax reported in Table 3 might be difficult to attain in practice unless the draining and back-flushing are carried out simultaneously with strong gas sparging, ultrasound, or even both to ensure that the column is cleaned sufficiently. Nevertheless, the results strongly indicate that HGMS can be used effectively to retrieve and concentrate suspended solids from simulated HLW sludges of a diverse nature that some researchers even considered to be nonmagnetic. It is also interesting to observe an appreciable dependence of the maximum solids holdup on the liquid velocity, particularly in the low-velocity range. With minor differences, the holdup values decreased in all of the sludges between 40 and 60% when the velocity was increased from 0.0367 to 0.2754 cm s-1. This result was in opposition to the high loadings observed by Friedlaender et al.53 in single-wire experiments at velocities much larger than 1 cm s-1 with sample susceptibilities of about one-fourth of those of the sludges. The main reason for this behavior was probably the large porosity of the suspensions (Table 1), which gave the sludges a floc-like character that most likely reduced their effective magnetic susceptibility. Also, it is worth pointing out a behavior that was not taken into account by the model utilized here, i.e., the observed consistent and direct dependence of nT on the feed concentration co. Notice in Table 3 that, with all other conditions constant, the runs with the higher feed concentrations also exhibited higher values of nT (e.g., compare runs 2, 4, 5, 8, 18, 20, 22, and 24 with runs 1, 3, 5, 7, 17, 19, 21, and 23, respectively). It is suspected that, in the regions on the wires where weak magnetic interactions prevail, a dynamic equilibrium was established, with the same number of particles being retained as released. According to this dynamic equilibrium scenario, higher feed concentrations would necessarily correspond to higher net loadings and vice versa for lower feed concentrations, as observed experimentally. This would not be the case in the regions where strong magnetic forces prevail. In the latter, the particles would be retained irreversibly, regardless of the concentration of the suspended solids. Future HGMS models will attempt to account for this phenomenon. As a final remark, even though these experiments were carried out at relatively low superficial velocities, the results reported in Table 3 are quite remarkable, particularly for an HGMS unit with a relatively small magnetic field of 0.3 T. A simple theoretical calculation of the relative strength of the force that the matrix wires subjected the particles to can be obtained from the following expression (in terms of the gravitational force) where Bo ) 0.3 T; f is the relative distance (in terms of

[(

)]

χp Bo2 1 1 1 F ) 2R +1 Fs - Ff µo acg f 3 f 2

(10)

wire radii) to the axis of the wire at the angle of largest attraction; µ is the permeability of free space; R is the

demagnetizing factor of the wire (assumed here to be unity because of the large saturation magnetization of stainless steel); and Fp and Ff are the skeletal density of the particles (Table 1) and the density of the fluid, respectively. χp is the effective volumetric susceptibility of the particles and given by

χp ) 4π(1 - p)Fpχm,p (cgs)

(11)

where p and χm,p are the porosity and the mass susceptibility (cgs), respectively, of the particles (given in Table 1). From the above two expressions, it is simple to show that, for this HGMS system, the particles were subjected to accelerations between 100 and 1000 G within 2 radii from the axis. Although these values are somewhat low, with larger magnetic fields, such as 1 T, they can be increased 10-fold, which makes them comparable to or even higher than those associated with some currently available continuous centrifuges and decanters. Conclusions High-gradient magnetic separation (HGMS) was investigated for the treatment of dilute sludge wastes. Four simulated HLW sludges from the Savannah River Site containing different mixtures of metal oxides and hydroxides were diluted and processed through a 0.3-T bench-scale HGMS unit. The feed concentration of the suspended solids was varied from 2.5 to 10.5 g L-1, and the feed velocity was varied from 0.0367 to 0.2754 cm s-1. Twenty-four breakthrough experiments were carried out under these conditions. A relatively simple dynamic model was correlated successfully with all of these breakthrough curves to obtain three parameters: the capture cross section, the maximum solids holdup, and a back prediction of the feed concentration. The results from this model were then used to predict experimental bed utilizations and maximum enrichments. In all cases, the sludges exhibited significant magnetic character, with the point of breakthrough of the suspended solids depending strongly on both the feed velocity and the feed concentration. The best results, i.e., process performances, were obtained at the lower values of both of these parameters. For example, this HGMS unit was able to process on the order of 20 bed volumes of feed prior to breakthrough of suspended solids, with corresponding bed utilizations and maximum enrichments on the order of 77% and 14, respectively. These very positive results were quite surprising, especially considering that the magnetic field strength was only 0.3 T and the feed streams consisted of a diverse mixture of metal oxide and hydroxide species with a wide range of particle sizes and magnetic susceptibilities. It was also encouraging that the relatively simple dynamic model was able to correlate the experimental data, even though it did not account for these particle size and magnetic susceptibility distributions or the marked variation in the matrix wire radii. Overall, this work clearly demonstrates the feasibility of HGMS for concentrating dilute sludge wastes of a diverse nature. The modeling results might also be useful for the design and scale-up of such HGMS processes and the further development of other HGMS processes being considered with similar applications in mind. In fact, it is surmised that HGMS has the potential to compete with other technologies such as

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centrifugation and traditional filtration, in terms not only of performance but also of economics when sharp separation factors and high enrichments are desired. Acknowledgment The authors gratefully acknowledge financial support from the National Science Foundation under Grant CTS-9985489 and from the Argonne National Laboratory under Contract 970552401. The authors also appreciate the assistance of Lorena S. Ortiz for obtaining most of the experimental results. Nomenclature ac ) wire radius, m Bo ) applied magnetic field strength, T cexp ) concentration of insoluble solids obtained from the experimental results, kg m-3 cmodel ) concentration of insoluble solids estimated from the dynamic model, kg m-3 c ) concentration of insoluble solids, kg m-3 co ) feed concentration of insoluble solids, kg m-3 cf ) concentration of insoluble solids in the eluted effluent if only one bed volume of feed is needed to flush the bed matrix fully, kg m-3 db ) bed diameter, m dp ) diameter of the suspended particles, m Emax ) maximum enrichment achieved by the bed if one bed volume of feed is needed to flush the bed matrix fully f ) relative distance to the axis of a wire in terms of wire radii fc ) capture efficiency for randomly distributed wires F ) magnetic force relative to gravitational force upon a particle by a wire at the point of maximum retention strength g ) acceleration of gravity, m s-2 Lb ) bed length, m n ) solids holdup, kg (kg of wire)-1 nT ) solids holdup at saturation, kg (kg of wire)-1 t ) temporal variable, s Uo ) superficial velocity, m s-1 Vb ) total bed volume, m3 VBT ) collected effluent volume of suspended solids prior to breakthrough, m3 z ) spatial variable, m Greek Letters R ) demagnetization factor of the wire χp ) effective volumetric susceptibility of the particles (SI) χm,p ) mass susceptibility of the particles (cgs), cm3 g-1  ) porosity of the matrix p ) porosity of the retained suspended particles λc ) capture cross section of a wire with loading nT λc,o ) capture cross section of a clean wire η ) bed utilization µo ) permeability of free space, 4π × 10-7 T m A-1 Fc ) density of the wire, kg m-3 Fp ) skeletal density of the suspended particles, kg m-3 Ff ) density of the fluid, kg m-3

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Received for review March 18, 2002 Accepted July 24, 2002 IE020198R