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Separation of flocs in hydrocyclones—significance of floc breakage and floc hydrodynamics
Int. J. Miner. Process. 73 (2004) 239 – 249 www.elsevier.com/locate/ijminpro
Separation of flocs in hydrocyclones—significance of floc breakage and floc hydrodynamics D. Woodfield a, G. Bickert b,* b
a Comalco Research and Technical Support, PO Box 316, Thomastown, Victoria 3074, Australia School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, NSW 2052, Australia
Received in revised form 24 October 2002; accepted 29 April 2003
Abstract Improved understanding of the behaviour of flocs within a hydrocyclone is necessary to progress the use of hydrocyclones for the clarification and thickening of fine particles. This paper describes experimental and modelling work to investigate the separation behaviour of flocculated particles in a hydrocyclone to better understand the different mechanisms influencing separation. Flocculated pseudo-monodisperse and polydisperse alumina trihydrate in a 1 wt.% water slurry was separated in a 22-mm Mozley hydrocyclone. Floc structure properties, floc size distribution and also primary particle composition within those flocs were measured experimentally for all flows (feed, overflow and underflow). For the case study system at 100-kPa hydrocyclone-operating pressure, there was an improvement in reduced efficiency from 0.75 to 0.84 with flocculation. Contrary to the assumption of literature models, breakage was limited, with the effect of floc hydrodynamics determining the separation behaviour. With density being the most important hydrodynamic effect, the reduced density of flocs compared to primary particles is the main reason for the limited improvement flocculation could achieve in hydrocyclone separation and not, as often suggested, floc breakup. A micro-scale semiempirical model was developed to predict the separation performance of flocculated particles in hydrocyclones. The model represents the relationships between floc hydrodynamics and hydrocyclone classification as well as between floc strength and hydrocyclone shear. Comparison with the experimental results is used to highlight the areas where further work is required to progress understanding. D 2004 Elsevier B.V. All rights reserved. Keywords: hydrocyclone; flocculant; separation; floc structure
1. Introduction Abbreviations: OC1000, alumina trihydrate type (polydisperse); Hydra, alumina trihydrate type (pseudo-monodisperse); rpm, rotation per minute (1/min); PSD, particle size distribution; FSD, floc size distribution; PPPD, primary particle polydispersity (model). * Corresponding author. E-mail address: [email protected] (G. Bickert). 0301-7516/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/S0301-7516(03)00076-0
Hydrocyclones have typically been considered for application in particle classification. However, their small footprint and low capital cost make them potentially ideal candidates for plant retrofits to increase clarification or thickening capacity. The literature on floc – hydrocyclone interaction shows that
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improved separation is possible by flocculant addition, in some cases, up to f 50% of feed solids to cyclone underflow to over 90% to cyclone underflow for a fixed operating pressure (Yalcin, 1996; Williams and Roldan-Villasana, 1991; Poole and Beeson, 1997), suggesting that this is a worthwhile area to investigate. Svarovsky (1984) states ‘‘the effect of flocculation or other chemical agents on hydrocyclone performance cannot be in any way quantified. . . an art rather than a science. . . more test work and investigation in this area is needed’’. No measures of floc strength are given in the relevant literature and ‘‘applications should be tested experimentally’’ (Heiskanen, 1993). The fundamentals of flocculant usage to improve hydrocyclone efficiency are not well understood and further investigation is required. This paper sets out by a combination of experimentation and modelling to gain further insight into the mechanisms governing the separation behaviour of flocs in hydrocyclones.
2. Method The emphasis of the experimental work was to relate micro-properties (primary particle size, floc size, shape and structure) to macroscopic properties such as separation efficiency and operating pressure and flow. The experimental work was conducted using pseudo-monodisperse (Hydral) and polydisperse (OC1000) alumina trihydrate supplied commercially by Alcoa of Australia (size distributions are shown in Fig. 1). Particles were suspended in water (1 wt.% slurry), flocculated using a commercial polymer flocculant Magnafloc 800HP (CIBA specialty chemicals) and separated in a 22-mm Mozley hydrocyclone. The feed to the cyclone was via a 189-mm pressurised tank so that the effect of the pumping system on the floc size and structure was minimised. For all of the results presented in this paper, mixing was with an A310 impeller at 800 rpm operating speed using 100 g/ton Magnafloc 800HP. The nominal average shear was G = 364 s 1 (method discussed in Camp and Stein, 1943) and maximum shear G = 1417 s 1 (method discussed in Griffiths, 1996; Geisler et al., 1994).
Fig. 1. Primary particle size distributions measured with a Malvern Mastersizer E.
Mixing times used were 3 and 90 min. At 3 min, the approximate peak in average floc size is reached and 90 min represents the state when the distribution had reached close to a steady state. All experiments were single pass through the cyclone with no recirculation. The flocculant was made up using the procedure of Farrow and Swift (1996) using a bench top Orbital Shaker Incubator and left overnight before using. Flocculant solutions were discarded after 1 week. The flocculant was made up to 0.01 wt.% and shaken for 10 min on the orbital shaker prior to addition. The primary particles were suspended in the tank 30 min prior to the flocculant to ensure adequate particle dispersion. Floc size distribution was measured with a Malvern Mastersizer. Feed flocs were either sub-sampled directly from the stirred tank or by using a bypass line just prior to the cyclone entrance. Cyclone underflow and overflow were sampled using manual sampling with standard 600- and 1000-ml glass beakers and timed using a stopwatch. Combined product was collected by directing both streams into a single beaker. Flocs were sub-sampled from the beaker using specially designed wide-mouth pipettes and admitted to the Malvern Batch Cell for size determination. The sub-samples were taken by gently hand-swirling the beaker until there was no sediment visible on the bottom. This was as a compromise between minimising mixing which would encourage reflocculation and also introduce extra shear, and ensuring that all of the flocs were in suspension when the sample was taken.
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The measurements were found to be repeatable using this procedure. Only overflow size distributions were found to grow slightly if left to stand for 10 min for the short in-tank mixing time (3 min), possibly due to availability of free polymer. Consequently overflow measurements were made first for all of the test work and were completed after approximately 3 min. The overall separation efficiency of the cyclone was determined by filtering underflow and overflow samples using a double layer of pre-weighed GF/A Whatman filter papers and drying them overnight in a 105 jC oven. Mass balance closure was typically within 5%. To determine primary particle size distribution, these dried underflow and overflow samples were then re-dispersed using ultrasound and a small dose of dispersant (tetrasodiumpyrophosphate). Those samples were analysed in a Malvern Mastersizer E to determine the size distribution of primary particles within underflow and overflow flocs.
3. Experimental results and discussion Table 1 shows the overall separation efficiency results. A comparison is made between two different primary particle sizes (Hydral and OC1000), between two different floc formation times (3 and 90 min) and two different hydrocyclone pressure drops (100 and 230 kPa).
Table 1 Cyclone efficiency—22 mm Mozley hydrocyclone, feed—189 mm diameter pressure tank, A310 impeller, 800 rpm, 100 g/ton Magnafloc 800HP Operating conditions
Hydral
OC1000
Solids Reduced Solids Reduced fraction to efficiency fraction to efficiency underflow underflow
Primary particles 0.15 Pressure Floc mixing drop (kPa) (min) 3 100 0.14 90 100 0.15 90 230
0.04
0.75
0.72
0.05 0.05
0.86 0.86 0.86
0.84 0.84 0.84
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For Hydral, there is no significant improvement in the separation efficiency with flocculation. The OC1000 however, shows a distinct improvement by flocculation compared to the results using unflocculated primary particles. Changing the time for floc formation (and therefore the pre-exposure of the flocs to shear) and also changing the operating pressure of the hydrocyclone, both had no discernable effect on the separation. Table 2 shows floc size distribution properties for OC1000 and Hydral with flocculant under different mixing conditions and without flocculant. Fig. 2 shows these results graphically for OC1000 mixed for 3 min. The difficulties in conducting floc size distribution measurements on cyclone streams are identified by Williams and Roldan-Villasana (1991):
flocculated material that has been broken in high shear zones within the hydrocyclone will reflocculate in a low shear environment during size measurement if there is available flocculant presentation of the flocs to the measuring device involves sampling and suspension, both of which expose the flocs to a changed shear environment. As such, the floc sizes presented in this paper are indicative rather than absolute. The shift in size distribution from flocculated feed to underflow and overflow is discernable (Fig. 2 and Table 2) but not large, suggesting that there has definitely been breakage but it has been limited in extent. This is even though the cyclone is a small diameter operated at a reasonable pressure drop, for which a relatively high shear is expected. This is consistent with the published results for the size distributions of underflow and overflow from the breakup of polymer-based flocs within cyclones (Williams and Roldan-Villasana, 1991, 1999; Bidault et al., 1997; Flambeau, 1987) for the limited number of papers where this data has been reported. Flambeau (1987) even found for kaolin that in some cases the underflow flocs were actually smaller than the overflow flocs. However, the modelling in the literature suggests the separation efficiency is dependent on the breakage within the hydrocyclone (Williams and Roldan-Villasana, 1999) and similarly for centrifuges (Bell and Brunner, 1983). The results of these experi-
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Table 2 Floc size distributions for hydrocyclone feed, underflow and overflow and measures of the particle size distribution of the primary particles making up the flocs Experiment
Feed
Underflow
Flocs
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
OC1000 (no flocculant) OC1000 (3-min mix) OC1000 (90-min mix) OC1000 (90-min, 230 kPa) Hydral (no flocculant) Hydral (3-min mix) Hydral (90-min mix)
2.3 33.0 16.3 10.9 0.6 11.0 1.9
16.8 68.7 40.6 33.5 2.1 32.8 10.6
55.0 129.7 77.2 65.8 6.1 74.0 22.2
9.8 32.2 21.6 20.8
36.1 63.0 50.3 44.3
74.5 116.2 88.6 80.2
1.6 18.2 9.7 3.7
5.2 56.9 30.3 12.2
13.5 109.1 80.1 31.0
8.7 1.9
27.2 10.6
56.2 23.7
6.3 1.7
24.0 9.6
53.0 20.3
ments, confirmed by the limited extent of breakage in some literature data, suggest that this conclusion is incorrect for hydrocyclones. Another important aspect of the results comes from comparing the overflow and underflow distributions. A floc size distribution is formed in the mixing tank and presented to the hydrocyclone. At the mediumoperating pressure of 100 kPa, the flocs appear to report to the underflow and overflow almost independently of size. The increased separation efficiency for flocculation compared to primary particles shows that this is not because the cyclone is acting as a splitter (where the reduced efficiency would equal zero). Nevertheless, the aggregate size appears to be only a minor separation criteria. This suggests that floc density and hydrodynamics mostly determine separation performance for flocs, and not their size. To investigate the floc density further, measurements were made of the primary particle size distributions making up the underflow and overflow flocs, information that was not available in the literature.
Fig. 2. Floc size distributions for cyclone feed, underflow and overflow for OC1000 (Du = 3.2 mm, Do = 7.0 mm), 100-kPa cyclone-operating pressure, 3-min mixing time.
Overflow
The measured primary particle size distribution properties for the primary particles making up the OC1000 underflow and overflow flocs are given in Table 3 and shown for one case in Fig. 3. As both overflow and underflow contain large flocs, there must be a difference in the separation behaviour of these flocs. The results in Table 3 show that the primary particles that make up the overflow flocs are much smaller than those making up the underflow flocs. Underflow flocs are composed of a combination of fine particles and large particles, whereas overflow flocs appear to be made up of assemblages of fine particles only. The floc density is affected by the primary particle size distribution making up the floc, with finer particles forming less dense flocs (see Eq. (2)). The difference in floc density caused by differences in composition of primary particles explains the separation behaviour observed. These differences in floc makeup also show that there will be a distribution of density for any particular floc size of the flocculated feed. The results in Table 2 for 230-kPa operating pressure show that an array of effects are in play. The size distributions show more the expected behaviour with a much finer overflow than underflow and seem to reflect more floc breakup in the system, as would be expected at higher pressure. The overall separation efficiency remains the same, reflecting the effect of increased pressure on separation, but possibly also supporting that the measured size distributions may reflect breakup that occurs after the aggregates have already separated to the stream that will exit via the overflow or underflow within the hydrocyclone (Williams and Roldan-Villasana, 1999).
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Table 3 Particle size distribution of the primary particles making up the flocs for hydrocyclone feed, underflow and overflow Experiment
Feed
Primary particles
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
OC1000 OC1000 OC1000 OC1000
2.3 2.3 2.3 2.3
16.8 16.8 16.8 16.8
55.0 55.0 55.0 55.0
9.8 2.9 3.0 3.3
36.1 22.5 22.4 22.3
74.5 58.5 58.8 58.0
1.6 1.8 1.7 1.6
5.2 6.5 6.4 5.0
13.5 15.6 17.0 12.8
(no flocculant) (3-min mix) (90-min mix) (90-min, 230 kPa)
Underflow
Overflow
3.1. Carrier particles
3.2. Comparing 3- and 90-min floc mixing
It was found (see Table 2) that the underflow flocs contain significantly more small primary particles than the equivalent unflocculated underflow, thus giving an improved total solids to the underflow result for the flocculated material. It would appear that the large particles are acting as carrier particles for the smaller particle, increasing the floc density. Leadbetter and White (1986) deliberately induced this behaviour by adding coarse sand to metal precipitates to improve hydrocyclone separation. There are at least two commercial processes available for waste water treatment—Microsepk (US Filter, 1999) and Actiflok (Krueger, 1999), which use glass ballast as a carrier particle to which flocs are attached to give improved separation with a smaller unit area for the clarifier. Examples of carrier particles, used within other separation techniques, include coating particles on magnetic particles for subsequent separation (Kerbey and Williams, 1997), dry powder inhaler drug delivery, and flotation (the carrier particle is in this case a bubble).
The results in Table 1 demonstrate that although the flocs are much larger for 3-min mixing (Table 2), there is no corresponding improvement in the separation efficiency. The work above suggests that the separation is driven by the extent to which fine particles have attached themselves to coarse, something which presumably has already and mostly been reached at the 3-min mark. There are other interacting reasons and possibilities including:
Fig. 3. Flocculated size distributions and the size distributions of the particles making up the flocs—formed under the same conditions as above (Fig. 2), OC1000, 3-min mixing time, 100 kPa.
restructuring so that the 90-min flocs are not just smaller versions of the 3-min flocs, but also more compact and therefore with higher density and lower drag from the shape of the particle size distributions, there are not only larger aggregates but also more primary particles not incorporated into flocs at 3 min compared to 90 min. Therefore, less primary particles participate in the improved separation of the flocs. 3.3. Model development: an overview There is limited previous modelling of the hydrodynamics of floc separation in hydrocyclones. The literature on floc behaviour in hydrocyclones showed mainly empirical approaches, with tabulated or graphical treatment of results rather than an equation based mathematical description. The most detailed modelling has been done by Williams and Roldan-Villasana (1999). They link measured feed and product size distribution information to performance through the use of an empirical– breakage relationship. The emphasis in their work is on the importance of breakage. The above experimental work shows that a much broader approach is needed to understand and predict performance. The most promising approach given the
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complexity of the underlying systems was to link micro-scale properties to overall separation performance by the use of semiempirical models. This involved developing or incorporating existing quantitative relationships for the following mechanisms influencing the separation:
floc structure and its relationship to floc density, hydrodynamics and strength hydrocyclone classification a link between floc hydrodynamics and classification behaviour in a hydrocyclone floc breakup behaviour and how that breakup is linked to the hydrocyclone flowfield and the hydrocyclone-feeding device. The model steps are detailed in Fig. 4 as a flowsheet. As the experimental data for floc size distribution for combined underflow and overflow streams is available, the complication of modelling the breakage step (Step 2) will not be illustrated in this paper. For
more detail on the development of the model equations for breakage within hydrocyclones (estimating maximum stable floc size, breakage rate and distribution of daughter fragments from experimental data), see Woodfield (2001). The modelling approach used is to let all breakage happen before the separation step. This approach is a conservative one, as the final product size distributions is likely to be more broken than the size distribution presented for classification within the cyclone, due to the high shear in the cyclone exits (Williams and Roldan-Villasana, 1999). The model developed attempts to predict the separation performance of flocs using the measured broken floc size distribution as feed to the cyclone, the feed primary particle size distribution and a Plitt model fitted (Flintoff et al., 1987 detail the Plitt equations) to the experimentally measured separation curve based on the separation of unflocculated primary particles. The concept used to link floc separation to the experimentally available data for the separation of unflocculated particles is the equivalent classification determined from equivalent terminal settling velocity, Ut (Eq. (1)). Ut2 ¼
4ðqp ql Þac da u XCD ðRe; /Þ 3ql
ð1Þ
This equation is the basis for the determination of separation behaviour. The primary particle density is known, the aggregate size is known from the measured floc size distribution, and the shape corrected drag coefficient as a function of Re number and sphericity CD(Re,/) can be solved iteratively (a sphericity value of / = 0.8 has been assumed for flocs from Tambo and Watanabe, 1979). The remaining equation terms need to be discussed in more detail. 3.4. Drag correction X
Fig. 4. Floc – hydrocyclone interaction model steps.
Floc drag corrections for mass fractals formed from monodisperse primary particles are discussed extensively in the literature (see Bushell et al., 2002 for a detailed review) though they do not model flow through effects well. For use with pseudo-monodisperse primary particles (Hydral), a new staged-fractal model for the permeability of fractal flocs has been
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developed which takes into account non-homogeneous porosity and is detailed elsewhere (Woodfield and Bickert, 2001). For polydisperse primary particles (OC1000), the Brinkman equation for drag (Brinkman, 1947) is used in conjunction with the permeability correction of Happel and Brenner (1973).
in turn is linked to the inlet velocity Vi by a, which for a range of cyclone types obeys Eq. (4). Vt rn ¼ Kt ¼ Vc Rnc a¼
3.5. Solids volume fraction u The floc density, in Eq. (1) expressed through the floc solids volume fraction u, is not easily available. For fractal aggregates, the solids volume fraction in the floc u is determined by a structure prefactor ks, floc to particle size ratio and mass fractal dimension Df: u ¼ ks
da do
ðDf 3Þ ð2Þ
While this model is useful for flocs composed of monodisperse primary particles, estimating the density of flocs composed of polydisperse primary particles required further model development. A simplified version of a Jackson’s (1998) population balance model has been developed to account for the effects of primary particle polydispersity (PPPD) on floc density. This PPPD model constructs the floc size distribution by adding together combinations of primary particles. Flocs and primary particles are assumed to be only able to be discrete sizes, such that each successive size is equal to the size of two combined flocs from the size class below. Flocs are assumed to be fractal. The model, while an advance, still gives only a single density value for each floc size. To use this model, it is necessary to measure structural information for aggregates. Details are given in Woodfield (2001). 3.6. Acceleration ac As non-Stokes flow is likely within small diameter hydrocyclones (Bradley, 1965), an explicit calculation of the acting acceleration is necessary. Within a hydrocyclone, the velocity profile is approximated by Eq. (3) (Bradley, 1965) where the tangential velocity Vt at any radius r can be estimated by knowing the velocity at the cyclone wall Vc, which
245
ð3Þ
Vc Di ¼ 3:7 Vi Dc
ð4Þ
The acceleration at any radial position, due to this tangential velocity is ac ¼
Vt2 r
ð5Þ
Typical values of n and a are in the range 0.5 –1 (Bradley, 1965). Having estimated the tangential velocity profile, the acceleration at any point within the cyclone can be estimated. The locus of zero vertical velocity, located at 0.43Dc (Bradley and Pulling, 1959) has been selected as the point at which acceleration is calculated for equivalent classification size comparison. This location is used as the basis for determining the d50 in the equilibrium orbit model (Bradley, 1965). As the part of the efficiency curve around the d50 cutsize is of most interest in the cyclone separation efficiency curve, the model will therefore correctly estimate the drag coefficient. For particles significantly larger than this size the relevant acceleration will be overestimated, and hence the particle Re overestimated, as large particles would have needed only a small acceleration to be effectively separated. For fine particles, Re will be underestimated. For a sharp separation efficiency curve, the impact of these effects will not be large. From Bradley (1965): dp ql Vt2 ¼ dr r
ð6Þ
and substituting from Eq. (3) and integrating gives pc pr a2 Vi2 ¼ ql 2n
"
Rc r
#
2n 1
where r is any nominal radial position.
ð7Þ
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To complete the calculation, the following assumptions are made:
Tangential velocity is the only significant velocity component—in general, axial velocity increases rapidly in the region where tangential velocity reduces next to the air core, but the absolute value is low, i.e. 1 m s 1 compared to 6 m s 1 at point of max tangential velocity (Lilge, 1962). That pressure equals 1 atm at the point of max tangential velocity. That velocity energy rather than pressure is what is lost through the underflow and overflow exit. Thus, pressure recovery occurs as velocity slows, but is lost due to frictional losses. Entry losses are negligible. These assumptions mean that the pressure drop pc pr will equal the overall pressure drop Dp at the maximum in tangential velocity. The modelling assumes the overflow radius r being approximately the overflow radius Ro in Eq. (7) as the calculated velocity profile of Dyakowski and Williams (1993) shows the maximum tangential velocity to be at approximately overflow radius Ro for a 22-mm Mozley cyclone. Knowing the entrance velocity from the flow rate, and the overall pressure drop and using the model of Bradley (Eq. (3)) and the value of the ratio of cyclone wall velocity Vc to inlet velocity a in Eq. (4), once the overall pressure to velocity conversion has been fixed, then for fixed cyclone dimensions the value for the empirical value n will also be fixed. The cyclone velocity at any radial position can then be estimated and hence the cyclone acceleration, a necessary step to estimating the terminal settling velocity.
4. Model results Having quantitatively determined all the relevant parameters, the entire floc size distribution curve, discretised into appropriate intervals can be translated to an equivalent classification size curve. Using the experimentally fitted Plitt model to model the separation behaviour, an overall separation efficiency can be estimated. Tables 4 and 5 show these calculations for Hydral and OC1000, respectively.
Table 4 Comparison of model and experiment—Hydral, 100 g/ton Magnafloc 800HP, 189-mm tank, 800 rpm, A310 impeller, Mozley hydrocyclone Dc = 22 mm, Du = 3.2 mm, Do = 7.0 mm Case
3-min mixing time
90-min mixing time
Measured % solids to underflow Predicted % solids to underflow Combined underflow and overflow distribution, density of aggregates is that of primary particlesa Flocs have variable densityb (Df = 1.91, kS = 2.88, do = 1.35, adjusted Plitt equations) Flocs have variable densityb (Df = 1.91, kS = 2.88, do = 1.35 Am, no shape correction, no flow through correction)
15
15
87
56
33
31
32
22
a This model applies the selectivity curve to the feed size distribution, without correcting for density or aggregate breakup. b This model uses a pseudo Df = 2.5, kS = 1 to fit the density equation until da = 6do (see Woodfield, 2001).
The results for Hydral show the importance of density and floc hydrodynamic in correctly predicting performance where breakage is limited. A value of 86% separation efficiency would be predicted based on floc size distribution alone, compared to a reality of 15%. The model based on floc structural properties is a lot closer to the experimental value, though still high. With breakage limited, floc hydrodynamics are therefore dominant in explaining the separation behaviour. The limited effects on the model outcomes of varying the shape-based drag correction and the flow through drag correction suggest that density is by far the most important aspect of the hydrodynamics affecting separation. For OC1000, a similar set of results, though in a much narrower band, is shown in Table 5. Again the model predicts efficiency closer to reality than modelling without allowing for floc density and hydrodynamics, but again the result is higher than the experimental value. The developed overall predictive model is an improvement on previous work but it still tends to overestimate the separation efficiency. The earlier discussion of the experimental data shown in Table 2 and Fig. 2 suggests the probable reason for this is that each floc size will exhibit a range of den-
D. Woodfield, G. Bickert / Int. J. Miner. Process. 73 (2004) 239–249 Table 5 Comparison of model and experimental results—OC1000, 100 g/ ton Magnafloc 800HP, 189-mm tank, 800 rpm, A310 impeller, Mozley hydrocyclone Dc = 22 mm, Du = 3.2 mm, Do = 7.0 mm Case
3-min mixing time
90-min mixing time
Measured % solids to underflow Predicted % solids to underflow Feed distribution, density of aggregates is that of primary particlesa Combined broken product, density of aggregates is that of primary particles Primary Particles only Flocs have variable densityb— PPPD (Df = 2.3, kS = 1, do = 1 Am, adjusted Plitt equations)
86
86
98
94
98
94
73 93
73 86
a
This model applies the selectivity curve to the feed size distribution, without correcting for density or aggregate breakup. b Happel correction for permeability, sphericity = 0.8.
sities depending on the primary particle composition, whereas the modelling only gives one density for each size. To correctly predict separation requires a model of the distribution of density for each floc size. The approximation of the PPPD and literature models of a single density for each size is inadequate, though an improvement on modelling which ignores these effects.
5. Conclusions Limited floc breakage occurs within hydrocyclones for flocs formed using appropriate polymeric flocculants. Further, the overflow floc size distribution is quite similar to the underflow floc size distribution. The reason for the differing separation of the underflow and overflow, even though the floc size distribution is similar, is the difference in floc density caused by differences in composition of primary particles within the flocs. The reason for the improvement in overall separation is the inclusion of fine particles in underflow flocs containing coarse particles. The experimental results suggest that floc hydrodynamics and density are more important than breakage in determining hydrocyclone separation performance. Floc hydrodynamic and density models gave improved prediction compared to models which ignored
247
these effects, but the experimental and model results highlight that more detailed models accounting for floc density distribution are needed to be truly predictive of the floc separation behaviour seen in this system. Notation ac Particle acceleration. Equivalent to g for a gravity field [ms 2] CD(Re,/) Shape-corrected drag coefficient of Haider and Levenspiel (1989) able to be used across multiple flow regimes. This is necessary due to the possibility of non-Stokes flow within the 22-mm Mozley hydrocyclone (Bradley, 1965) d[v,0.5] Median diameter from light scattering instrument. 50% of the volume of the distribution is below this size [m] d[v,0.1] 10% of the volume of the distribution is below this size [m] d[v,0.9] 00% of the volume of the distribution is below this size [m] da Diameter of a floc [m] do Diameter of a primary particle used to make flocs [m] Dc Cyclone diameter (cylindrical section) [m] Df Mass fractal dimension of a self-similar particle or floc (range: 1– 3) Di Cyclone inlet diameter [m] Do Cyclone overflow diameter [m] Du Cyclone underflow diameter [m] G Shear rate [s 1] kS Structure prefactor for mass fractal objects Kt Constant in relationship between tangential velocity and radius n Numerical exponent used in relationship between tangential velocity and radius, typical value 0.4 –0.9 (Bradley, 1965) p Pressure [Pa] pc Pressure at cyclone wall [kPa] pr Pressure at nominal radial position r within the cyclone [kPa] r Radius co-ordinate measured from the cyclone centreline [m] Rc Cyclone radius [m] Re Reynolds number for the floc Ut Terminal velocity of particle moving in a fluid [m s 1]
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Vc Vi Vt
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Peripheral velocity –tangential velocity at the cyclone wall [m s 1] Average velocity in the inlet [m s 1] Tangential velocity [m s 1]
Greek symbols a Ratio of cyclone wall velocity Vc to inlet velocity Vi / Sphericity (Wadell/Heywood shape factor) = surface of a sphere having the same volume as the particle divided by the actual surface area of the particle u Solids volume fraction in a floc ( = 1 for primary particles) ql Fluid density [kg m 3] qp Primary particle density [kg m 3] X The ratio of resistance experienced by a permeable sphere (floc) to an equivalent solid sphere that has the same diameter and density Acknowledgements The authors would like to acknowledge Comalco Aluminium for funding this work and Professor Richard Williams for valuable discussions and input regarding experimental and theoretical understanding of the behaviour of flocs in hydrocyclones. References Bell, D.J., Brunner, K.H., 1983. A method for the evaluation of floc break-up in centrifuges. Filtration and Separation 20 (4), 274 – 278. Bidault, A., Clauss, A., Helaine, D., Balavoice, C., 1997. Floc agglomeration and structuration by a specific talc mineral composition. Water Science and Technology 36 (4), 57 – 68. Bradley, D., 1965. The Hydrocyclone. Pergamon, Oxford. Bradley, D., Pulling, D.J., 1959. Flow patterns in the hydraulic cyclone and their interpretation in terms of performance. Transactions of the Institute of Chemical Engineers 37, 34 – 45. Brinkman, H.C., 1947. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research. Section A. Mechanics, Heat Chemical Engineering Mathematical Methods A1, 27 – 34. Bushell, G.C., Yan, Y.D., Woodfield, D., Raper, J., Amal, R., 2002. On techniques for the measurement of the mass fractal dimension of aggregates. Advances in Colloid and Interface Science 95, 1 – 50.
Camp, T.R., Stein, P.C., 1943. Velocity gradients and internal work in fluid motion. Journal of the Boston Society of Civil Engineers 30 (4), 219 – 237. Dyakowski, T., Williams, R.A., 1993. Modelling turbulent flow within a small-diameter hydrocyclone. Chemical Engineering Science 48 (6), 1143 – 1152. Farrow, J.B., Swift, J.D., 1996. A new procedure for assessing the performance of flocculants. International Journal of Mineral Processing 46, 263 – 275. Flambeau, M., 1987. Effect of flocculation on the separation of fine particles in a hydrocyclone. Chemical Engineering. UMIST, Manchester, pp. 70 – 80. Flintoff, B.C., Plitt, L.R., Turak, A.A., 1987. Cyclone modelling: a review of present technology. Canadian Institute of Mining Bulletin 80 (905), 39 – 50. Geisler, R., Krebs, R., Forschner, P., 1994. Local turbulent shear stress in stirred vessels and its significance for different mixing tasks. Eighth European Conference on Mixing: IChemE. Griffiths, S., 1996. The effect of agitator impeller design on maximum shear stress, and the resulting impact on the flocculation process. Water and Environmental Management 10 (5), 324 – 331. Haider, A., Levenspiel, O., 1989. Drag coefficient and terminal velocity of spherical and non-spherical particles. Powder Technology 58, 63 – 70. Happel, J., Brenner, H., 1973. Low Reynolds Number Hydrodynamics. Noordhoff International, Leyden. Heiskanen, K., 1993. Particle Classification. Chapman & Hall, London. Jackson, G.A., 1998. Using fractal scaling and two-dimensional particle size spectra to calculate coagulation rates for heterogeneous systems. Journal of Colloid and Interface Science 202, 20 – 29. Kerbey, M.H., Williams, R.A., 1997. Magnetic tagging technology—extending the potential of magnetic separation. Innovation in Physical Separation Technologies—Richard Mozley Memorial Volume. The Institution of Mining and Metallurgy, Falmouth, UK, pp. 231 – 244. Kruger, 1999. The Actiflo Process, http://www.vivendiwatersystems. dk. Leadbetter, T., White, D.A., 1986. Use of coarse sand particles to aid ferric hydroxide floc dewatering by hydrocyclones. Transactions Institution Mining Metallurgy. Section C. Mineral Processing, Extractive Metallurgy 95, C209 – C211 (Dec.). Lilge, E.O., 1962. Hydrocyclone fundamentals. Transactions Institution Mining Metallurgy 71 (285), 285 – 337. Poole, C., Beeson, S.A., 1997. Hydrocyclone recovery of flocculated sylvite from potash ore. Innovation in Physical Separation Technologies—Richard Mozley Symposium Volume. The Institution of Mining and Metallurgy, Falmouth, UK, pp. 171 – 182. Svarovsky, L., 1984. Hydrocyclones. Technomic, Lancaster, PA. Tambo, N., Watanabe, Y., 1979. Physical characteristics of flocs: I. The floc density function and aluminium floc. Water Research 13, 409 – 419. US-Filter, 1999. MicroSep-Technology, http: //www.water.usfilter. com/microsep.html. Williams, R.A., Roldan-Villasana, E.J., 1991. Opportunities for
D. Woodfield, G. Bickert / Int. J. Miner. Process. 73 (2004) 239–249 dewatering aggregated colloidal materials using small diameter hydrocyclones. In: Williams, R.A., de Jaegar, N.C. (Eds.), Advances in Measurement and Control of Colloidal Processes. Butterworth, Oxford, pp. 18 – 34. Williams, R.A., Roldan-Villasana, E.J., 1999. Classification and breakage of flocs in hydrocyclones. Minerals Engineering 12 (10), 1225 – 1243. Woodfield, D.L., 2001. The separation behaviour of aggregates in hydrocyclones. School of Chemical Engineering and Industrial
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Chemistry. University of New South Wales, Sydney, pp. 70 – 93 and pp. 157 – 163. Woodfield, D.L., Bickert, G., 2001. An improved permeability model for fractal aggregates settling in creeping flow. Water Research 35/16, 39 – 44. Yalcin, T., 1996. Tailings disposal using flocculant-assisted hydrocyclones. Canadian Institute of Mining Bulletin 89 (1005), 98 – 100.
Separation of flocs in hydrocyclones—significance of floc breakage and floc hydrodynamics D. Woodfield a, G. Bickert b,* b
a Comalco Research and Technical Support, PO Box 316, Thomastown, Victoria 3074, Australia School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, NSW 2052, Australia
Received in revised form 24 October 2002; accepted 29 April 2003
Abstract Improved understanding of the behaviour of flocs within a hydrocyclone is necessary to progress the use of hydrocyclones for the clarification and thickening of fine particles. This paper describes experimental and modelling work to investigate the separation behaviour of flocculated particles in a hydrocyclone to better understand the different mechanisms influencing separation. Flocculated pseudo-monodisperse and polydisperse alumina trihydrate in a 1 wt.% water slurry was separated in a 22-mm Mozley hydrocyclone. Floc structure properties, floc size distribution and also primary particle composition within those flocs were measured experimentally for all flows (feed, overflow and underflow). For the case study system at 100-kPa hydrocyclone-operating pressure, there was an improvement in reduced efficiency from 0.75 to 0.84 with flocculation. Contrary to the assumption of literature models, breakage was limited, with the effect of floc hydrodynamics determining the separation behaviour. With density being the most important hydrodynamic effect, the reduced density of flocs compared to primary particles is the main reason for the limited improvement flocculation could achieve in hydrocyclone separation and not, as often suggested, floc breakup. A micro-scale semiempirical model was developed to predict the separation performance of flocculated particles in hydrocyclones. The model represents the relationships between floc hydrodynamics and hydrocyclone classification as well as between floc strength and hydrocyclone shear. Comparison with the experimental results is used to highlight the areas where further work is required to progress understanding. D 2004 Elsevier B.V. All rights reserved. Keywords: hydrocyclone; flocculant; separation; floc structure
1. Introduction Abbreviations: OC1000, alumina trihydrate type (polydisperse); Hydra, alumina trihydrate type (pseudo-monodisperse); rpm, rotation per minute (1/min); PSD, particle size distribution; FSD, floc size distribution; PPPD, primary particle polydispersity (model). * Corresponding author. E-mail address: [email protected] (G. Bickert). 0301-7516/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/S0301-7516(03)00076-0
Hydrocyclones have typically been considered for application in particle classification. However, their small footprint and low capital cost make them potentially ideal candidates for plant retrofits to increase clarification or thickening capacity. The literature on floc – hydrocyclone interaction shows that
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improved separation is possible by flocculant addition, in some cases, up to f 50% of feed solids to cyclone underflow to over 90% to cyclone underflow for a fixed operating pressure (Yalcin, 1996; Williams and Roldan-Villasana, 1991; Poole and Beeson, 1997), suggesting that this is a worthwhile area to investigate. Svarovsky (1984) states ‘‘the effect of flocculation or other chemical agents on hydrocyclone performance cannot be in any way quantified. . . an art rather than a science. . . more test work and investigation in this area is needed’’. No measures of floc strength are given in the relevant literature and ‘‘applications should be tested experimentally’’ (Heiskanen, 1993). The fundamentals of flocculant usage to improve hydrocyclone efficiency are not well understood and further investigation is required. This paper sets out by a combination of experimentation and modelling to gain further insight into the mechanisms governing the separation behaviour of flocs in hydrocyclones.
2. Method The emphasis of the experimental work was to relate micro-properties (primary particle size, floc size, shape and structure) to macroscopic properties such as separation efficiency and operating pressure and flow. The experimental work was conducted using pseudo-monodisperse (Hydral) and polydisperse (OC1000) alumina trihydrate supplied commercially by Alcoa of Australia (size distributions are shown in Fig. 1). Particles were suspended in water (1 wt.% slurry), flocculated using a commercial polymer flocculant Magnafloc 800HP (CIBA specialty chemicals) and separated in a 22-mm Mozley hydrocyclone. The feed to the cyclone was via a 189-mm pressurised tank so that the effect of the pumping system on the floc size and structure was minimised. For all of the results presented in this paper, mixing was with an A310 impeller at 800 rpm operating speed using 100 g/ton Magnafloc 800HP. The nominal average shear was G = 364 s 1 (method discussed in Camp and Stein, 1943) and maximum shear G = 1417 s 1 (method discussed in Griffiths, 1996; Geisler et al., 1994).
Fig. 1. Primary particle size distributions measured with a Malvern Mastersizer E.
Mixing times used were 3 and 90 min. At 3 min, the approximate peak in average floc size is reached and 90 min represents the state when the distribution had reached close to a steady state. All experiments were single pass through the cyclone with no recirculation. The flocculant was made up using the procedure of Farrow and Swift (1996) using a bench top Orbital Shaker Incubator and left overnight before using. Flocculant solutions were discarded after 1 week. The flocculant was made up to 0.01 wt.% and shaken for 10 min on the orbital shaker prior to addition. The primary particles were suspended in the tank 30 min prior to the flocculant to ensure adequate particle dispersion. Floc size distribution was measured with a Malvern Mastersizer. Feed flocs were either sub-sampled directly from the stirred tank or by using a bypass line just prior to the cyclone entrance. Cyclone underflow and overflow were sampled using manual sampling with standard 600- and 1000-ml glass beakers and timed using a stopwatch. Combined product was collected by directing both streams into a single beaker. Flocs were sub-sampled from the beaker using specially designed wide-mouth pipettes and admitted to the Malvern Batch Cell for size determination. The sub-samples were taken by gently hand-swirling the beaker until there was no sediment visible on the bottom. This was as a compromise between minimising mixing which would encourage reflocculation and also introduce extra shear, and ensuring that all of the flocs were in suspension when the sample was taken.
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The measurements were found to be repeatable using this procedure. Only overflow size distributions were found to grow slightly if left to stand for 10 min for the short in-tank mixing time (3 min), possibly due to availability of free polymer. Consequently overflow measurements were made first for all of the test work and were completed after approximately 3 min. The overall separation efficiency of the cyclone was determined by filtering underflow and overflow samples using a double layer of pre-weighed GF/A Whatman filter papers and drying them overnight in a 105 jC oven. Mass balance closure was typically within 5%. To determine primary particle size distribution, these dried underflow and overflow samples were then re-dispersed using ultrasound and a small dose of dispersant (tetrasodiumpyrophosphate). Those samples were analysed in a Malvern Mastersizer E to determine the size distribution of primary particles within underflow and overflow flocs.
3. Experimental results and discussion Table 1 shows the overall separation efficiency results. A comparison is made between two different primary particle sizes (Hydral and OC1000), between two different floc formation times (3 and 90 min) and two different hydrocyclone pressure drops (100 and 230 kPa).
Table 1 Cyclone efficiency—22 mm Mozley hydrocyclone, feed—189 mm diameter pressure tank, A310 impeller, 800 rpm, 100 g/ton Magnafloc 800HP Operating conditions
Hydral
OC1000
Solids Reduced Solids Reduced fraction to efficiency fraction to efficiency underflow underflow
Primary particles 0.15 Pressure Floc mixing drop (kPa) (min) 3 100 0.14 90 100 0.15 90 230
0.04
0.75
0.72
0.05 0.05
0.86 0.86 0.86
0.84 0.84 0.84
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For Hydral, there is no significant improvement in the separation efficiency with flocculation. The OC1000 however, shows a distinct improvement by flocculation compared to the results using unflocculated primary particles. Changing the time for floc formation (and therefore the pre-exposure of the flocs to shear) and also changing the operating pressure of the hydrocyclone, both had no discernable effect on the separation. Table 2 shows floc size distribution properties for OC1000 and Hydral with flocculant under different mixing conditions and without flocculant. Fig. 2 shows these results graphically for OC1000 mixed for 3 min. The difficulties in conducting floc size distribution measurements on cyclone streams are identified by Williams and Roldan-Villasana (1991):
flocculated material that has been broken in high shear zones within the hydrocyclone will reflocculate in a low shear environment during size measurement if there is available flocculant presentation of the flocs to the measuring device involves sampling and suspension, both of which expose the flocs to a changed shear environment. As such, the floc sizes presented in this paper are indicative rather than absolute. The shift in size distribution from flocculated feed to underflow and overflow is discernable (Fig. 2 and Table 2) but not large, suggesting that there has definitely been breakage but it has been limited in extent. This is even though the cyclone is a small diameter operated at a reasonable pressure drop, for which a relatively high shear is expected. This is consistent with the published results for the size distributions of underflow and overflow from the breakup of polymer-based flocs within cyclones (Williams and Roldan-Villasana, 1991, 1999; Bidault et al., 1997; Flambeau, 1987) for the limited number of papers where this data has been reported. Flambeau (1987) even found for kaolin that in some cases the underflow flocs were actually smaller than the overflow flocs. However, the modelling in the literature suggests the separation efficiency is dependent on the breakage within the hydrocyclone (Williams and Roldan-Villasana, 1999) and similarly for centrifuges (Bell and Brunner, 1983). The results of these experi-
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Table 2 Floc size distributions for hydrocyclone feed, underflow and overflow and measures of the particle size distribution of the primary particles making up the flocs Experiment
Feed
Underflow
Flocs
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
OC1000 (no flocculant) OC1000 (3-min mix) OC1000 (90-min mix) OC1000 (90-min, 230 kPa) Hydral (no flocculant) Hydral (3-min mix) Hydral (90-min mix)
2.3 33.0 16.3 10.9 0.6 11.0 1.9
16.8 68.7 40.6 33.5 2.1 32.8 10.6
55.0 129.7 77.2 65.8 6.1 74.0 22.2
9.8 32.2 21.6 20.8
36.1 63.0 50.3 44.3
74.5 116.2 88.6 80.2
1.6 18.2 9.7 3.7
5.2 56.9 30.3 12.2
13.5 109.1 80.1 31.0
8.7 1.9
27.2 10.6
56.2 23.7
6.3 1.7
24.0 9.6
53.0 20.3
ments, confirmed by the limited extent of breakage in some literature data, suggest that this conclusion is incorrect for hydrocyclones. Another important aspect of the results comes from comparing the overflow and underflow distributions. A floc size distribution is formed in the mixing tank and presented to the hydrocyclone. At the mediumoperating pressure of 100 kPa, the flocs appear to report to the underflow and overflow almost independently of size. The increased separation efficiency for flocculation compared to primary particles shows that this is not because the cyclone is acting as a splitter (where the reduced efficiency would equal zero). Nevertheless, the aggregate size appears to be only a minor separation criteria. This suggests that floc density and hydrodynamics mostly determine separation performance for flocs, and not their size. To investigate the floc density further, measurements were made of the primary particle size distributions making up the underflow and overflow flocs, information that was not available in the literature.
Fig. 2. Floc size distributions for cyclone feed, underflow and overflow for OC1000 (Du = 3.2 mm, Do = 7.0 mm), 100-kPa cyclone-operating pressure, 3-min mixing time.
Overflow
The measured primary particle size distribution properties for the primary particles making up the OC1000 underflow and overflow flocs are given in Table 3 and shown for one case in Fig. 3. As both overflow and underflow contain large flocs, there must be a difference in the separation behaviour of these flocs. The results in Table 3 show that the primary particles that make up the overflow flocs are much smaller than those making up the underflow flocs. Underflow flocs are composed of a combination of fine particles and large particles, whereas overflow flocs appear to be made up of assemblages of fine particles only. The floc density is affected by the primary particle size distribution making up the floc, with finer particles forming less dense flocs (see Eq. (2)). The difference in floc density caused by differences in composition of primary particles explains the separation behaviour observed. These differences in floc makeup also show that there will be a distribution of density for any particular floc size of the flocculated feed. The results in Table 2 for 230-kPa operating pressure show that an array of effects are in play. The size distributions show more the expected behaviour with a much finer overflow than underflow and seem to reflect more floc breakup in the system, as would be expected at higher pressure. The overall separation efficiency remains the same, reflecting the effect of increased pressure on separation, but possibly also supporting that the measured size distributions may reflect breakup that occurs after the aggregates have already separated to the stream that will exit via the overflow or underflow within the hydrocyclone (Williams and Roldan-Villasana, 1999).
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Table 3 Particle size distribution of the primary particles making up the flocs for hydrocyclone feed, underflow and overflow Experiment
Feed
Primary particles
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
d[v,0.1]
d[v,0.5]
d[v,0.9]
OC1000 OC1000 OC1000 OC1000
2.3 2.3 2.3 2.3
16.8 16.8 16.8 16.8
55.0 55.0 55.0 55.0
9.8 2.9 3.0 3.3
36.1 22.5 22.4 22.3
74.5 58.5 58.8 58.0
1.6 1.8 1.7 1.6
5.2 6.5 6.4 5.0
13.5 15.6 17.0 12.8
(no flocculant) (3-min mix) (90-min mix) (90-min, 230 kPa)
Underflow
Overflow
3.1. Carrier particles
3.2. Comparing 3- and 90-min floc mixing
It was found (see Table 2) that the underflow flocs contain significantly more small primary particles than the equivalent unflocculated underflow, thus giving an improved total solids to the underflow result for the flocculated material. It would appear that the large particles are acting as carrier particles for the smaller particle, increasing the floc density. Leadbetter and White (1986) deliberately induced this behaviour by adding coarse sand to metal precipitates to improve hydrocyclone separation. There are at least two commercial processes available for waste water treatment—Microsepk (US Filter, 1999) and Actiflok (Krueger, 1999), which use glass ballast as a carrier particle to which flocs are attached to give improved separation with a smaller unit area for the clarifier. Examples of carrier particles, used within other separation techniques, include coating particles on magnetic particles for subsequent separation (Kerbey and Williams, 1997), dry powder inhaler drug delivery, and flotation (the carrier particle is in this case a bubble).
The results in Table 1 demonstrate that although the flocs are much larger for 3-min mixing (Table 2), there is no corresponding improvement in the separation efficiency. The work above suggests that the separation is driven by the extent to which fine particles have attached themselves to coarse, something which presumably has already and mostly been reached at the 3-min mark. There are other interacting reasons and possibilities including:
Fig. 3. Flocculated size distributions and the size distributions of the particles making up the flocs—formed under the same conditions as above (Fig. 2), OC1000, 3-min mixing time, 100 kPa.
restructuring so that the 90-min flocs are not just smaller versions of the 3-min flocs, but also more compact and therefore with higher density and lower drag from the shape of the particle size distributions, there are not only larger aggregates but also more primary particles not incorporated into flocs at 3 min compared to 90 min. Therefore, less primary particles participate in the improved separation of the flocs. 3.3. Model development: an overview There is limited previous modelling of the hydrodynamics of floc separation in hydrocyclones. The literature on floc behaviour in hydrocyclones showed mainly empirical approaches, with tabulated or graphical treatment of results rather than an equation based mathematical description. The most detailed modelling has been done by Williams and Roldan-Villasana (1999). They link measured feed and product size distribution information to performance through the use of an empirical– breakage relationship. The emphasis in their work is on the importance of breakage. The above experimental work shows that a much broader approach is needed to understand and predict performance. The most promising approach given the
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complexity of the underlying systems was to link micro-scale properties to overall separation performance by the use of semiempirical models. This involved developing or incorporating existing quantitative relationships for the following mechanisms influencing the separation:
floc structure and its relationship to floc density, hydrodynamics and strength hydrocyclone classification a link between floc hydrodynamics and classification behaviour in a hydrocyclone floc breakup behaviour and how that breakup is linked to the hydrocyclone flowfield and the hydrocyclone-feeding device. The model steps are detailed in Fig. 4 as a flowsheet. As the experimental data for floc size distribution for combined underflow and overflow streams is available, the complication of modelling the breakage step (Step 2) will not be illustrated in this paper. For
more detail on the development of the model equations for breakage within hydrocyclones (estimating maximum stable floc size, breakage rate and distribution of daughter fragments from experimental data), see Woodfield (2001). The modelling approach used is to let all breakage happen before the separation step. This approach is a conservative one, as the final product size distributions is likely to be more broken than the size distribution presented for classification within the cyclone, due to the high shear in the cyclone exits (Williams and Roldan-Villasana, 1999). The model developed attempts to predict the separation performance of flocs using the measured broken floc size distribution as feed to the cyclone, the feed primary particle size distribution and a Plitt model fitted (Flintoff et al., 1987 detail the Plitt equations) to the experimentally measured separation curve based on the separation of unflocculated primary particles. The concept used to link floc separation to the experimentally available data for the separation of unflocculated particles is the equivalent classification determined from equivalent terminal settling velocity, Ut (Eq. (1)). Ut2 ¼
4ðqp ql Þac da u XCD ðRe; /Þ 3ql
ð1Þ
This equation is the basis for the determination of separation behaviour. The primary particle density is known, the aggregate size is known from the measured floc size distribution, and the shape corrected drag coefficient as a function of Re number and sphericity CD(Re,/) can be solved iteratively (a sphericity value of / = 0.8 has been assumed for flocs from Tambo and Watanabe, 1979). The remaining equation terms need to be discussed in more detail. 3.4. Drag correction X
Fig. 4. Floc – hydrocyclone interaction model steps.
Floc drag corrections for mass fractals formed from monodisperse primary particles are discussed extensively in the literature (see Bushell et al., 2002 for a detailed review) though they do not model flow through effects well. For use with pseudo-monodisperse primary particles (Hydral), a new staged-fractal model for the permeability of fractal flocs has been
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developed which takes into account non-homogeneous porosity and is detailed elsewhere (Woodfield and Bickert, 2001). For polydisperse primary particles (OC1000), the Brinkman equation for drag (Brinkman, 1947) is used in conjunction with the permeability correction of Happel and Brenner (1973).
in turn is linked to the inlet velocity Vi by a, which for a range of cyclone types obeys Eq. (4). Vt rn ¼ Kt ¼ Vc Rnc a¼
3.5. Solids volume fraction u The floc density, in Eq. (1) expressed through the floc solids volume fraction u, is not easily available. For fractal aggregates, the solids volume fraction in the floc u is determined by a structure prefactor ks, floc to particle size ratio and mass fractal dimension Df: u ¼ ks
da do
ðDf 3Þ ð2Þ
While this model is useful for flocs composed of monodisperse primary particles, estimating the density of flocs composed of polydisperse primary particles required further model development. A simplified version of a Jackson’s (1998) population balance model has been developed to account for the effects of primary particle polydispersity (PPPD) on floc density. This PPPD model constructs the floc size distribution by adding together combinations of primary particles. Flocs and primary particles are assumed to be only able to be discrete sizes, such that each successive size is equal to the size of two combined flocs from the size class below. Flocs are assumed to be fractal. The model, while an advance, still gives only a single density value for each floc size. To use this model, it is necessary to measure structural information for aggregates. Details are given in Woodfield (2001). 3.6. Acceleration ac As non-Stokes flow is likely within small diameter hydrocyclones (Bradley, 1965), an explicit calculation of the acting acceleration is necessary. Within a hydrocyclone, the velocity profile is approximated by Eq. (3) (Bradley, 1965) where the tangential velocity Vt at any radius r can be estimated by knowing the velocity at the cyclone wall Vc, which
245
ð3Þ
Vc Di ¼ 3:7 Vi Dc
ð4Þ
The acceleration at any radial position, due to this tangential velocity is ac ¼
Vt2 r
ð5Þ
Typical values of n and a are in the range 0.5 –1 (Bradley, 1965). Having estimated the tangential velocity profile, the acceleration at any point within the cyclone can be estimated. The locus of zero vertical velocity, located at 0.43Dc (Bradley and Pulling, 1959) has been selected as the point at which acceleration is calculated for equivalent classification size comparison. This location is used as the basis for determining the d50 in the equilibrium orbit model (Bradley, 1965). As the part of the efficiency curve around the d50 cutsize is of most interest in the cyclone separation efficiency curve, the model will therefore correctly estimate the drag coefficient. For particles significantly larger than this size the relevant acceleration will be overestimated, and hence the particle Re overestimated, as large particles would have needed only a small acceleration to be effectively separated. For fine particles, Re will be underestimated. For a sharp separation efficiency curve, the impact of these effects will not be large. From Bradley (1965): dp ql Vt2 ¼ dr r
ð6Þ
and substituting from Eq. (3) and integrating gives pc pr a2 Vi2 ¼ ql 2n
"
Rc r
#
2n 1
where r is any nominal radial position.
ð7Þ
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To complete the calculation, the following assumptions are made:
Tangential velocity is the only significant velocity component—in general, axial velocity increases rapidly in the region where tangential velocity reduces next to the air core, but the absolute value is low, i.e. 1 m s 1 compared to 6 m s 1 at point of max tangential velocity (Lilge, 1962). That pressure equals 1 atm at the point of max tangential velocity. That velocity energy rather than pressure is what is lost through the underflow and overflow exit. Thus, pressure recovery occurs as velocity slows, but is lost due to frictional losses. Entry losses are negligible. These assumptions mean that the pressure drop pc pr will equal the overall pressure drop Dp at the maximum in tangential velocity. The modelling assumes the overflow radius r being approximately the overflow radius Ro in Eq. (7) as the calculated velocity profile of Dyakowski and Williams (1993) shows the maximum tangential velocity to be at approximately overflow radius Ro for a 22-mm Mozley cyclone. Knowing the entrance velocity from the flow rate, and the overall pressure drop and using the model of Bradley (Eq. (3)) and the value of the ratio of cyclone wall velocity Vc to inlet velocity a in Eq. (4), once the overall pressure to velocity conversion has been fixed, then for fixed cyclone dimensions the value for the empirical value n will also be fixed. The cyclone velocity at any radial position can then be estimated and hence the cyclone acceleration, a necessary step to estimating the terminal settling velocity.
4. Model results Having quantitatively determined all the relevant parameters, the entire floc size distribution curve, discretised into appropriate intervals can be translated to an equivalent classification size curve. Using the experimentally fitted Plitt model to model the separation behaviour, an overall separation efficiency can be estimated. Tables 4 and 5 show these calculations for Hydral and OC1000, respectively.
Table 4 Comparison of model and experiment—Hydral, 100 g/ton Magnafloc 800HP, 189-mm tank, 800 rpm, A310 impeller, Mozley hydrocyclone Dc = 22 mm, Du = 3.2 mm, Do = 7.0 mm Case
3-min mixing time
90-min mixing time
Measured % solids to underflow Predicted % solids to underflow Combined underflow and overflow distribution, density of aggregates is that of primary particlesa Flocs have variable densityb (Df = 1.91, kS = 2.88, do = 1.35, adjusted Plitt equations) Flocs have variable densityb (Df = 1.91, kS = 2.88, do = 1.35 Am, no shape correction, no flow through correction)
15
15
87
56
33
31
32
22
a This model applies the selectivity curve to the feed size distribution, without correcting for density or aggregate breakup. b This model uses a pseudo Df = 2.5, kS = 1 to fit the density equation until da = 6do (see Woodfield, 2001).
The results for Hydral show the importance of density and floc hydrodynamic in correctly predicting performance where breakage is limited. A value of 86% separation efficiency would be predicted based on floc size distribution alone, compared to a reality of 15%. The model based on floc structural properties is a lot closer to the experimental value, though still high. With breakage limited, floc hydrodynamics are therefore dominant in explaining the separation behaviour. The limited effects on the model outcomes of varying the shape-based drag correction and the flow through drag correction suggest that density is by far the most important aspect of the hydrodynamics affecting separation. For OC1000, a similar set of results, though in a much narrower band, is shown in Table 5. Again the model predicts efficiency closer to reality than modelling without allowing for floc density and hydrodynamics, but again the result is higher than the experimental value. The developed overall predictive model is an improvement on previous work but it still tends to overestimate the separation efficiency. The earlier discussion of the experimental data shown in Table 2 and Fig. 2 suggests the probable reason for this is that each floc size will exhibit a range of den-
D. Woodfield, G. Bickert / Int. J. Miner. Process. 73 (2004) 239–249 Table 5 Comparison of model and experimental results—OC1000, 100 g/ ton Magnafloc 800HP, 189-mm tank, 800 rpm, A310 impeller, Mozley hydrocyclone Dc = 22 mm, Du = 3.2 mm, Do = 7.0 mm Case
3-min mixing time
90-min mixing time
Measured % solids to underflow Predicted % solids to underflow Feed distribution, density of aggregates is that of primary particlesa Combined broken product, density of aggregates is that of primary particles Primary Particles only Flocs have variable densityb— PPPD (Df = 2.3, kS = 1, do = 1 Am, adjusted Plitt equations)
86
86
98
94
98
94
73 93
73 86
a
This model applies the selectivity curve to the feed size distribution, without correcting for density or aggregate breakup. b Happel correction for permeability, sphericity = 0.8.
sities depending on the primary particle composition, whereas the modelling only gives one density for each size. To correctly predict separation requires a model of the distribution of density for each floc size. The approximation of the PPPD and literature models of a single density for each size is inadequate, though an improvement on modelling which ignores these effects.
5. Conclusions Limited floc breakage occurs within hydrocyclones for flocs formed using appropriate polymeric flocculants. Further, the overflow floc size distribution is quite similar to the underflow floc size distribution. The reason for the differing separation of the underflow and overflow, even though the floc size distribution is similar, is the difference in floc density caused by differences in composition of primary particles within the flocs. The reason for the improvement in overall separation is the inclusion of fine particles in underflow flocs containing coarse particles. The experimental results suggest that floc hydrodynamics and density are more important than breakage in determining hydrocyclone separation performance. Floc hydrodynamic and density models gave improved prediction compared to models which ignored
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these effects, but the experimental and model results highlight that more detailed models accounting for floc density distribution are needed to be truly predictive of the floc separation behaviour seen in this system. Notation ac Particle acceleration. Equivalent to g for a gravity field [ms 2] CD(Re,/) Shape-corrected drag coefficient of Haider and Levenspiel (1989) able to be used across multiple flow regimes. This is necessary due to the possibility of non-Stokes flow within the 22-mm Mozley hydrocyclone (Bradley, 1965) d[v,0.5] Median diameter from light scattering instrument. 50% of the volume of the distribution is below this size [m] d[v,0.1] 10% of the volume of the distribution is below this size [m] d[v,0.9] 00% of the volume of the distribution is below this size [m] da Diameter of a floc [m] do Diameter of a primary particle used to make flocs [m] Dc Cyclone diameter (cylindrical section) [m] Df Mass fractal dimension of a self-similar particle or floc (range: 1– 3) Di Cyclone inlet diameter [m] Do Cyclone overflow diameter [m] Du Cyclone underflow diameter [m] G Shear rate [s 1] kS Structure prefactor for mass fractal objects Kt Constant in relationship between tangential velocity and radius n Numerical exponent used in relationship between tangential velocity and radius, typical value 0.4 –0.9 (Bradley, 1965) p Pressure [Pa] pc Pressure at cyclone wall [kPa] pr Pressure at nominal radial position r within the cyclone [kPa] r Radius co-ordinate measured from the cyclone centreline [m] Rc Cyclone radius [m] Re Reynolds number for the floc Ut Terminal velocity of particle moving in a fluid [m s 1]
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Vc Vi Vt
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Peripheral velocity –tangential velocity at the cyclone wall [m s 1] Average velocity in the inlet [m s 1] Tangential velocity [m s 1]
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