Batch Settling of Flocculated Clay Slurry - American Chemical Society

equations properly interpreted the final sediment data. The null-stress solidosity was estimated using three different methods. Polyelectrolyte floccu...
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Ind. Eng. Chem. Res. 2002, 41, 1227-1233

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Batch Settling of Flocculated Clay Slurry C. P. Chu,† S. P. Ju,† D. J. Lee,*,† F. M. Tiller,‡ K. K. Mohanty,‡ and Y. C. Chang‡ Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, and Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792

This study employs a computerized axial tomography scanner (CATSCAN) to measure the spatiotemporal distributions of solidosity for a clay slurry flocculated with a cationic polyelectrolyte. Flocculation produces fast-settling sediment and a clear supernatant. Limited data revealed the finite role of sludge plasticity on rheological characteristics. However, owing to the deterioration of the sludge network structure during settling, the purely elastic constitutive equations properly interpreted the final sediment data. The null-stress solidosity was estimated using three different methods. Polyelectrolyte flocculation renders a low attainable solidosity at the settler bottom, the low null-stress solidosity, and a less-compressible sediment. Most of the sedimentation processes considering well-flocculated slurries is governed by sedimentation compaction. The solid flux in the sediment is not a unique function of solidosity. Introduction Slurry sedimentation characteristics are important to design a settler or thickener in industries. Theorists, like Coe and Clevenger,1 Kynch,2 and Talmadge and Fitch,3 ignored the role of the rising sediment. Tiller4 refined the Kynch theory to take into account the effect of increasing sediment during sedimentation. In consolidating sediment, the way the solidosity (volume fraction of solids phase, S) changes with solids pressure (pS) controls its rheological characteristics. As Koenders and Wakeman5 revealed, most related works assumed a purely elastic filter cake having the following powerlaw type constitutive equation:

(

S ) S0 a +

)

pS pa

β

(1)

where a can be taken as 0 or 1. S0 is the null-stress solidosity or the gel point if a ) 1,6 pa represents the fitting parameter,7 and β denotes the compressibility of the sediment subjected to external stress. Equation 1 assumes that S depends only on the local solids pressure pS. Hence, the solidosity in consolidating sediment would vary continuously along the vertical axis from the settler bottom. A purely elastic sediment would not exhibit a constant S regime except for an incompressible slurry (β ) 0). Buscall and White8 proposed a consolidation model considering the flocculated slurry as a purely plastic body that possesses a yield stress (Py(φ)). If the local pressure of sediment exceeds Py, the network structure would yield. They proposed the following constitutive equation:

DS ) κ(S,pS)[pS - Py(S)], Dt

(2)

if pS > Py(S). Otherwise, DS/Dt ) 0, that is, no solids consolidation would occur in the sediment. κ is called * Corresponding author. Fax: 886-2-2362-3040. E-mail: [email protected]. † National Taiwan University. ‡ University of Houston.

the “dynamic compressibility” of the suspension. This model had been extensively applied to sedimentation processes of flocculated suspensions.9-12 If the sediment is purely plastic, there should exist a constant solidosity portion in the sediment in which the solids stress has not exceeded the yield stress. Researchers have adopted nondestructive techniques such as γ-ray,10,13 NMR,14-16 and X-ray9,16-22 to obtain the relevant variable in the solid/liquid separation processes as a function of space and time. Auzerais et al.23 addressed a quantitative theory covering the full range of processes, from the transient settling of large stable particle to the slow consolidation of flocculated suspensions of submicron particles. Buscall24 reviewed the pertinent literature before 1990. Polyelectrolyte conditioning has long been utilized to pretreat the slurry in order to increase its filterability. Charge neutralization and interparticle bridging are the two major mechanisms to flocculating the constituting particles into larger flocs.25 A strong correlation exists between the polymer dose at which the particle surface charge had been neutralized and the maximum settling velocity.26,27 The effects of polyelectrolyte flocculation on the slurry settling characteristics must be thoroughly understood to effectively design and operate thickeners and clarifiers. To the authors’ best knowledge, there existed only two references that had employed the aforementioned, nondestructive techniques to monitor the spatiotemporal distributions of solidosity in a settling slurry with polyelectrolyte.28,29 These works had not discussed in detail the effects of the presence of flocculant molecules on sludge rheological characteristics, which are of essential importance to thickener performance. In addition, the implications of charge neutralization to the settling behavior had not been well-established. We discuss, in this work, the role of cationic polyelectrolyte flocculation on the batch settling behavior of clay slurry. Because the flocculated sludge settles rapidly, most of the settling process was controlled by sediment compaction. Also, we demonstrated herein that neither purely elastic nor purely plastic constitutive equations describe the whole sedimentation process.

10.1021/ie0103411 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/06/2002

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Table 1. ζ Potential of Original and Flocculated Clay Slurries flocculant dosage (g/kg DS) ζ potential (mV)

0 -22.1

0.5 -10.2

2.0 1.2

4.0 11.8

Experimental Section Sample. A ball clay slurry, whose initial solidosity φS0 was approximately 0.02 (5% w/w), was the testing material used in this study. The particle size distribution was determined by a Sedigraph 5100C (Micromeritics, Norcross, GA) as a monodispersed distribution with a mean diameter of approximately 4.6 µm. An Accupyc Pycnometer 1330 (Micromeritics) measured the true solid density as 2584 kg/m3. The slurry was prepared by mixing clay particles and 10-1 M NaClO4 in distilled water to provide a high ionic strength to prevent the interference of other ions that might be released from the clay particle surfaces. The pH value was fixed at 7. A cationic polyelectrolyte denoted as polymer T-3052 was obtained from Kai-Guan Inc. (Taiwan). The polymer T-3052 is a polyacrylamide with an average molecular weight of 107 and a charge density of 20%. The polymer solution was gradually poured into the original slurry with 200 rpm of stirring for 5 min, followed by 50 rpm for another 20 min. A small quantity of the clay-polymer aggregates was transferred into the fresh electrolyte solution at the same pH and electrolyte concentration as the original electrolyte after mixing and prior to settling. The ζ potentials of the clay-polymer aggregates were measured by the ζ meter (Zeta-Meter System 3.0, Zeta-Meter Inc., Staunton, VA). Table 1 lists the surface charge data, designating that charge reversal occurs around the dose of 2 g/kg DS (dried solids). The doses exceeding or below 2 g/kg DS are regarded as over- and underdosing, respectively. Computerized Axial Tomography Scanner (CATSCAN). Batch settling experiments were conducted in a settling cylinder that had a height of 20 cm and a diameter of 9.5 cm and were continuously monitored with the CT scanner (DeltaScan 2060; 100 kV, 75 mA). The X-ray attenuations, which are normally presented as a dimensionless scale (the CT number), could be obtained from a horizontal section.30 Bergstrom10 adopted similar procedures using their γ-ray apparatus. Preliminary tests revealed that the CT number for the solution that contained flocculant (no solid particles) is essentially zero because organic compounds do not absorb a significant amount of X-rays. Furthermore, the CT number was found to be proportional to the solidosity in the slurry (as demonstrated in Figure 1). The uncertainties in axial position measurement, and the local solid volume fraction were 2.5 mm and 0.1% because of the finite beam thickness and scanning time, which are close to those reported in Auzerais et al.9 Time Evolutions Figure 2a-d depicts the time evolutions of crosssectional average solidosity in the settling tube. The mean solidosity S,mea is interpreted as follows:

∫0h S dz 0

S,mea )

h0

(3)

where h0 in eq 3 is 20 cm, the height of the slurry. The calculated S,mea data all range from 1.85% to 2.10%,

Figure 1. Relationship between CT number and solidosity in clay slurry.

correlating with φS0 of the original slurry (2%). This observation partially supports the accuracy of the solidosity distributions presented in Figure 2. The original slurry exhibits a slow settling velocity (Figure 2a) because the settling is not yet completed at 6000 s. A 1-cm thick sediment layer appears at the tube bottom after 100 seconds. A constant-concentration regime of the original volume fraction is noted above the sediment layer up to z ) 17 cm. In the subsequent 3000 s, the solidosity at z > 10 cm decays to a level of 0.5-1%, designating the existence of residual turbidity in the supernatant. The zone settling could not be visually differentiated from the supernatant. The solidosity slowly changes to half of the original slurry (1%) at z ) 4-10 cm in 6000 s of settling. The concentration and thickness of the sediment increases gradually. The original clay slurry needs more than 48 h to reach equilibrium, while the final thickness of the sediment was about 3 cm. The solidosity near the bottom increases to exceeding 28%, corresponding to approximately 55 wt %. The flocculated slurries exhibit a much better settleability than does the original slurry, as indicated in Figure 2b-d. The flocculated slurries usually settle faster with an increasing polyelectrolyte dose. For example, at a dose of 0.5 g/kg DS, the settling is completed within 4000 s, while it takes 2000 s at 2-4 g/kg DS. The fast-settling sediment is commonly observed for properly flocculated sludges in practice. A clear supernatant appears at the top 50% of the tube of flocculated slurry at 0.5 g/kg DS (Figure 2b) after 100 s of settling. A constant-concentration region only exists for 3 cm. A transition zone in which the solidosity increases to a second plateau region around 4.5% and then up to 12% exists beneath this regime. Only the compressing sediment and clear suspension exist at t ) 1000 s, and the settling is basically completed at t < 3000 s. The settling velocities were even faster than those illustrated in Figure 2a,b at a flocculant dose of 2-4 g/kg DS (Figures 2c,d). At t ) 100 s, a loose and thick sediment (5 cm) had already formed at bottom, above which is a settling slurry zone. The solidosity for flocculated slurries at z > 6 cm rapidly drop to zero in

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Figure 2. Solidosity distribution of clay slurry in the settler: (a) original slurry, (b) flocculated slurry (0.5 g/kg DS), (c) flocculated slurry (2.0 g/kg DS), (d) flocculated slurry (4.0 g/kg DS).

settling. The sediment was almost completely compacted within 500 s. The time evolutions of solidosity distributions for these two slurries almost coincide as the optimal polymer dose is identified as around 2 g/kg DS, which correlates with the charge neutralization point listed in Table 1. Charge neutralization thereby plays an essential role in the present flocculated system. The dramatic enhancement in settling velocity for wellflocculated slurries reveals that most of their sedimentation processes are governed by sediment compaction. Theories considering no rising sediment could not properly interpret the settling slurries after flocculation. Polyelectrolyte conditioning could yield a solidosity up to approximately 10% to ∼13%, which is much less than that observed for the original slurry (greater than 28%). The polyelectrolyte molecules would reduce the ultimate solidosity reachable by gravity settling. An increase in polyelectrolyte dose from 0.5 to 4 g/kg DS only further reduces the ultimate solidosity at bottom from 12.8% to 11.6%. Restated, although the polymer flocculation has markedly enhanced settling and yielded a clear supernatant, the ultimate solid concentration that could be achieved by settling is largely reduced.

Null-Stress Solidosity Null-stress solidosity (S0) is an essential parameter in eq 1. Figure 3 depicts the equilibrium solidosity distributions at different polyelectrolyte doses. No apparent jump in solidosity is noted on all curves. Previous studies could not illustrate such a jump.6,9,21,22,31 The length of the transition zone should be less than the resolution provided by the present CT scanner if a distinct interface exists because the X-ray beam is of a finite thickness. The Brownian motion of colloidal particles may provide a “diffusion” effect on the settling sediment. David and Russel32 incorporated a diffusion term into the Kynch theory to interpret such an occurrence. “Channels” and “volcano holes” appear in the sediment body and surface during settling tests of flocculated slurry.33,34 Such a surface “roughness” also prevents the exact determination of the position of interface. The aforementioned reasons may be responsible for the incapability of using CT scanner to directly measure S0 values for slurries. Although the exact value of S0 (if it really exists) is not known, some physical constraints can still be imposed on its range. Because all slurries exhibit the

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Figure 3. Solidosity distribution of the original and flocculated clay slurries in the final sediments. Black circles denote the corresponding null-stress solidosities.

slurry settling and the formation of sediment, the nullstress solidosity should exceed that of φS0 (2%). Furthermore, S0 should be less than the solidosity developed at the bottom, for example, 10% as displayed in Figure 3a. Three proposed methods for estimating S0 at equilibrium are as follows (the equilibrium sediment height is denoted as l0 at which S ) S0). (1) The solidosity at height z, at which the accumulated solidosity per unit area of settler becomes ω ) ∫z0S dz ) 0.975 ωC is labeled as S0, where ωC is the total accumulated solidosity per unit area of settler. The corresponding axial position is labeled as the sediment height, l0. (2) One cannot differentiate the sediment and the supernatant within the 0.1% maximum error for solidosity. Moving from the top surface of the slurry, the “interfacial zone” between the suspension and the sediment was interpreted in the region from the height where S ) 0.1% to 1 cm below. The average solid fraction over this 1-cm zone is determined as S0. (3) Ideally, a sudden jump in solidosity exists at the interface. Consequently, S0 is determined as the solidosity at which the slope of the S versus z curve (dS/ dz) has a maximum value. Table 2 lists the estimated S0 values based on the three proposed methods. The choices of the cutoff accumulative solidosity (0.975 ωC) in method 1 and the minimum solidosity (0.1%) and 1 cm of zone length in method 3 are apparently arbitrary. However, the estimated S0 values are rather close in most cases, especially for the flocculated slurries. Furthermore, most estimated S0 values are in the physically feasible range (greater than φS0 and less than the solidosity at sediment bottom). In addition, the average solidosity in the sediment S,av is defined as (1/l0)∫l00S dz. The definition of S,av is similar to the mean solidosity S,mea in eq 3. However, the latter is evaluated on the basis of both the sediment and the suspension phases. Table 2 also illustrates that S0 for the original clay slurry ranges from 5% to 10%. Restated, the possible range of null-stress solidosity for the original slurry is very large. This is attributed to the ill-developed sediment and the supernatant for the original slurry. The possible ranges for the flocculated slurries become much

Figure 4. The null-stress solidosity S0, average solidosity S,av in sediment, and solid pressure at bottom pS|z)0 at different flocculant doses. Table 2. Null-Stress Solidosity, Sediment Height, Average Solidosity in Sediment, and Compressive Pressure Estimated on the Basis of the Three Proposed Methods method S0 sediment height (cm) S,av pS|z)0 (Pa)

0 g/kg DS 1 0.049 2.05 0.185 60.14

2 0.079 1.87 0.199 58.36

3 0.102 1.75 0.205 56.65

method S0 sediment height (cm) S,av pS|z)0 (Pa)

0.5 g/kg DS 1 0.045 3.6 0.11 60.3

2 0.058 3.4 0.11 59.3

3 0.046 3.6 0.11 60.3

method S0 sediment height (cm) S,av pS|z)0 (Pa)

2 g/kg DS 1 0.037 3.9 0.10 61.5

2 0.045 3.8 0.10 60.9

3 0.048 3.8 0.10 60.5

method S0 sediment height (cm) S,av pS|z)0 (Pa)

4 g/kg DS 1 0.039 4.0 0.098 61.8

2 0.048 3.9 0.099 62.0

3 0.016 4.4 0.093 63.1

narrower as the estimated S0 values range from 4.5% to ∼5.8%, 3.7% to ∼4.8%, and 3.9% to ∼4.8% at 0.5, 2, and 4 g/kg DS, respectively. It is easier to define the top surface of the sediment after flocculation, which closely corresponds to the visual observation. The estimated S0 values based on method 1 are the lowest among the three methods. Furthermore, method 2 is utilized in the subsequent discussion as method 3 produces a too-low estimation (1.6%) for the slurry conditioned at 4 g/kg DS. These values are also presented as circles in Figure 3 for clarity sake. Figure 4 illustrates the estimated S0 and S,av values as functions of the flocculant dose. The increase in flocculant dose would yield a lower S0 and thicker sediment (lower S,av). Both S0 and S,av values reach a plateau value at the charge neutralization point. No significant changes in these values were noted in the overdosing regime.

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Plastic Behavior A purely plastic sediment should exhibit a constant solidosity regime at S ) S0 in the settling sediment.8 Over the constant solidosity regime, the relation between position of supernatant-sediment interface (y) and the “height” of the constant solidosity regime (y Lc) could be stated as follows:35

uS(S0) ) -

[

]

Py(S0) dy (4) ) -U0K(S0) 1 dt ∆FgS0(y - LC)

where U0 is the terminal velocity of the individual particle, K is the hindered factor, and Lc is the height where S deviates from S0.11 At z ) y, pS ) 0, and at z ) Lc, pS ) Py. If the dy/dt versus 1/(y - Lc) plot yields a straight line, then the parameters U0K and Py at S ) S0 could be estimated. Another constraint for eq 4 is that the consolidating sediment has a fixed S0. For the original slurry, no constant S regime close to the estimated S0 (ca. 0.08) is noticeable during the settling. The inconsistency is partially owing to the very blurred interface observed for the original slurry. Furthermore, the flocculated slurries at 2 or 4 g/kg DS settle too fast to have possible interpretation of eq 4. Only the 0.5 g/kg DS slurry exhibits a constant S regime in the sediment over the first 1000 s settling. However, the corresponding constant S value shifts from around 4.5% at 100s to more than 7% at 1000 s, indicating a continuous deterioration of sludge network. Therefore, although the settling sediment of the investigated slurry might exhibit certain plastic characteristics as Buscall and White8 suggested (the existence of constant S regime), the network structure changes continuously with time. We cannot estimate the Py or U0K values according to the present experimental data using eq 4 because the corresponding S0 value is a time-dependent variable. Final Sediment Information on the sediment rheology could be obtained using the final sediment data. At equilibrium, uS ) uL ) 0, and the solid pressure gradient in the final sediment could be stated as follows:

∂pS ) -∆FgS ∂z

(5)

The local solid pressure is expressed as

pS ) ∆Fg

∫lzS dz 0

Figure 5. The solidosity in sediment versus solid pressure at different flocculant doses. The dotted curves are the best fitted curves based on eq 1. Table 3. Compactibility Parameters Obtained for the Slurriesa

a

flocculant dose (g/kg DS)

pa (Pa)

S0

β

0 0.5 2.0 4.0

1.2 0.50 0.41 0.97

0.079 0.058 0.045 0.048

0.33 0.17 0.21 0.24

S0 values are based on method 2.

1, for interpreting the final sediment data. The parameter pa and β in eq 1 are nonlinearly regressed on the basis of the Marquardt-Levenberg algorithm and are listed in Table 3. The parameter pa is rather low, generally around or less than 1 Pa. Polyelectrolyte flocculation would yield a lower pa. In addition, the parameter β is greater for the original slurry (0.33) than those for the flocculated slurries (0.17-0.24). Both the pa and β values reach the minimum values at charge neutralization. The compressibility of the flocculated sediment is, hence, lower than that of the original slurry, with its most important effect to occur at the charge neutralization point (lower β value). Moreover, the S versus pS curves do not depend on the flocculant dose. The value of uS at height z could be evaluated as follows:

(6)

The solid pressure at bottom (pS|z)0) could be estimated based on the solidosity data and eq 6. Figure 4 also represents the estimated pS|z)0 data as a function of the polyelectrolyte dose. All pS|z)0 data at equilibrium are around 60 Pa regardless of the presence of polyelectrolyte, corresponding to the total buoyant weight of the solid particles (∆Fgl0 ) 60.1 Pa). This partially confirms the accuracy of the present experimental measurement. Local solid pressure data could be evaluated on the basis of eq 6. Figure 5 illustrates the S versus pS curves at equilibrium condition. These curves present a continuously varying manner without the existence of a constant S regime, as proposed by the purely plastic models. We hereby employ the purely elastic model, eq

uS )

() ∂z ∂t

ω

( )( )

)-

∂z ∂ω -1 ) ∂ω ∂t z S

∫0z

( )

∂S dσ ∂t σ

(7)

The term ∂S/∂t in eq 7 could be computed by numerical differentiation of the experimental data. The numerical differentiation, however, introduces larger uncertainty in the solid velocity data than those in the previously mentioned solidosity distributions do. The results discussed herein, thereby, should be taken as preliminary. Figure 6 represents solid flux (qS ) SuS) versus solidosity data for the original and the flocculated slurry at 2 g/kg DS. The solid flux is noted to decrease with increasing solidosity in both slurries. The solid velocity of the original slurry decays slowly in the range of 1006000 s, which closely corresponds to the slow evolution

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ing the finite role of sludge plasticity on rheological characteristics. However, the sludge network deteriorated continuously during settling, which eliminated its contribution to the final sediment. Purely elastic constitutive models interpreted the final sediment data. Flocculation could largely increases the solid flux in sediment. The solid flux is not a unique function of solidosity as adopted in conventional settler design method. Acknowledgment The authors wish to acknowledge support for this work from National Science Council, ROC. The assistance from Wenping Li with CATSCAN experiments is highly appreciated. Nomenclature

Figure 6. Solid velocity uS versus solidosity of original and flocculated clay slurry. (Open symbols: original slurry. Solid symbols: flocculated slurry.)

in solidosity profiles displayed in Figure 2a. On the other hand, the solid velocity of the flocculated slurry at t ) 100 s is an order of magnitude greater than that of the original slurry at the same solidosity. As time proceeds, the solid velocity soon decays to less than that of the original slurry. The local solid flux is not a unique function of local solidosity, which contradicts with the common assumptions adopted in settler design method, like the Kynch theory. This observation is not surprised because the sludge network changes continuously with time, as demonstrated in the Plastic Behavior Section. The solid velocity at S ) φS0 gives an index for the zone settling velocity (ZSV) of the slurry. The result for slurries at t ) 100 s are 100 µm/s (original slurry), 700 µm/s (0.5 g/kg DS), 1500 µm/s (2 g/kg DS), and 1800 µm/s (4 g/kg DS), respectively. The data for flocculated slurries closely correspond to the ZSV data observed by a direct measurement of the sediment height versus time relationship (data not shown). Conclusions Polyelectrolyte conditioning has been widely adopted to pretreat the slurry in order to increase its settleability. This study has utilized a CATSCAN to measure the spatiotemporal distributions of solidosity for a clay slurry, with special attention to the effects of flocculation with cationic polyelectrolyte. Charge neutralization is essential for the present slurry system. The original slurry exhibits a slow settling velocity and a turbid supernatant during settling. The solidosity near the bottom could increase to more than 28%. Polyelectrolyte application produces a fast-settling sediment with a clear supernatant. Most of the settling process of well-flocculated slurry is, hence, sediment compaction. However, the highest solidosity attainable also decreases (12-13%). No sudden jump in solidosity is noted at all interfaces with distinctly different regimes. The three methods proposed herein to estimate the null-stress solidosity produced very similar results. Polyelectrolyte flocculation yields a lower null-stress solidosity and a less-compactible sediment. A constant solidosity regime was noted to temporarily exist in the settling sediment of weakly flocculated slurries, indicat-

a ) parameter in eq 1 g ) gravitational acceleration (m/s2) h0 ) height of the slurry (m) K ) hindered coefficient Lc ) height of sediment starts to yield (m) l0 ) sediment height (m) pa ) characteristic pressure in eq 1 (Pa) pS ) solids pressure (Pa) Py ) yield stress (Pa) qS ) solid flux (m/s) t ) settling time (s) U0 ) stokes velocity (m/s) uS ) solid velocity (m/s) uS ) liquid velocity (m/s) y ) the height of supernatant-slurry interface z ) vertical distance from the coordinate positioning downward with its origin located at the top of sediment (m) Greek Letters β ) empirical constant in eq 1 κ ) dynamic compressibility in eq 2 (m‚s/kg) S ) solidosity s,av ) average solidosity S0 ) null-stress solidosity φS0 ) initial solids concentration of clay slurry ∆F ) density difference between solids and liquid (kg/m3) σ ) dummy variable of length used in eq 12 (m) ω ) material coordinate (m) ωC ) solid volume per unit area of settler (m)

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Received for review April 16, 2001 Accepted November 21, 2001 IE0103411