Modelling for small diameter hydrocyclones

Pergamon 0892-6875(94)00128-6

MineralsEngineering,Vol.8. No. 3, pp. 321-327, 1995 Copyright© 1995ElsevierScienceLtd Printed in GreatBritain.All rightsreserved 0892-6875/95 $9.50+0.00

TECHNICAL NOTE MODELLING FOR SMALL DIAMETER HYDROCYCLONES G. VALLEBUONA§, A. CASALI§, G. FERRARAt, O. LEAL§ and P. BEVILACQUAt § Mining Engineering Department, University of Chile, Santiago, Chile 1" DICAMP - - Process Eng. Div., University of Trieste, Trieste, Italy

(Received 1 July 1994; accepted 17 October 1994)

ABSTRACT

Small diameter ( 1 " - 2") hydrocyclones are used in different applications, in industrial minerals processing and in desliming ahead of flotation. The study of hydrocyclone performance, in terms of both fundamental and operational variables, has been undertaken by several authors. Empirical models are used for predicting the hydrocyclone performance in terms of capacity, cut size (dsoc), water split and partition curves. However, these models have been developed for larger hydrocyclones, while for smaller cyclones little modelling has been done. Only a few previous studies exist, which propose either new model equations or modifications to the existing ones. This paper reports experimental research on small hydrocyclones. The suitability of existing models has been checked and their accuracy compared. The experimental results show, in some aspects, coherency with what is already known. In other aspects, the results are in disagreement with previous findings. Accordingly, new model equations are proposed, which improve the predictive capability for small hydrocyclone performance.

Keywords Small diameters cyclones; modelling; partition curves

INTRODUCTION The study of hydrocyclone performance in classification by size, in terms of both fundamental and operational variables has been undertaken by several authors [1,2,3,4]. Empirical models have been developed [2,3,4,5] which are used for predicting hydrocyclone performance in terms of capacity, cut size (ds0c), water split and partition curve. Most of these models, for example those of Lynch and Plitt, have been developed for hydrocyclones with diameters larger than four inches. With respect to the empirical modelling of small diameter hydrocyclones, some studies [6,7,8] exist that describe hydrocyclone performance with new equations for the capacity, cut size and water split, using the Plitt equation for the corrected efficiency curve. Other studies [9,10,11,12], propose either new equations or modifications to the existing ones.

Poster presentation at MineralsEngineering "94,Lake Tahoe, USA, September 1994 321

322

Technical Note EXPERIMENTAL PROCEDURE

Details of the experimental set-up and procedures for size analysis, mass balance and data reconciliation have been presented before [9,10,11,12]. The equipment consisted of a Hydrocyclone Test Rig, with 50 mm and 25 mm diameter standard units. Three test ores were used. These were two copper flotation tailings (sample 1: density of 2.77 t/m 3 and 80% -150 prn, and sample 2: density of 2.78 t/m 3 and 80% -125 ~rn), and a copper fotation concentrate (sample 3: density of 4.44 t/m 3 and 80% -106 ~tm). The experimental conditions [11,12] were: F o r the 50 m m u n i t - - Vortex finder: 8-14 mm. Apex: 3.2-9.4 mm. Pressure drop: 10-40 psi. Solid concentration by volume: 0.13-0.32. For the 25 mm u n i t - - Vortex Finder: 5.5-7 mm. Apex: 2.2-3.2 mm. Pressure Drop: 10-40 psi. Solid concentration by volume: 0.1-0.3.

EXPERIMENTAL RESULTS

The results are presented and analysed on the basis of capacity, water split, partition curve and corrected cut point (ds0c). Capacity

Different equations, previously presented [9,11], were tested. These were those of Lynch and Rao [3], Bradley [7] and Vallebuona [11]. As the correlations were not good enough, other equations were tested. These were those of Plitt [4], Nageswararao [13] and a new one (Eq. 1) proposed by the authors. In the different approaches the capacity seems to depend on some of the following variables: pressure drop, vortex finder diameter, spigot diameter and feed solid % or slurry density. With respect to the pressure drop, the results [9,12] indicate a linear dependence. This confirms the findings of Heiskanen [14] and is included in one of the new equations proposed [9]. In the other models studied, there is not linearity. Dependence of capacity on the vortex finder diameter [12], independence on the spigot diameter [12] and on the feed solid concentration have been found [9,12]. Accordingly, Eq. 1 is selected, which combines only the two influential variables and represents the capacity better than all the other equations tested. The correlation between simulated and experimental data, for all data sets, is shown in Figure 1. Q

=

C1 , p + C2 , (Do)C3

(1)

where: Q = P = Do = C1, C2,

Slurry feed flowrate [l/s]. Pressure drop [psi]. Vortex finder diameter [mm]. C3 = parameters to be estimated for each set of data.

Water Split

Three different equations, presented previously [9,11], were tested. These were those of Lynch and Rao [5], Brookes [8] and Vallebuona [9]. Additionally, other equations were tested. These were those of Nageswararao [13], Leal [12] and a new one (Eq. 2) proposed here. In these approaches the water split seems to depend on some of the following variables: vortex finder diameter, spigot diameter and, for some authors, on the feed flowrate and/or on the feed solid %.

Technical Note

323

1.0

0.8 0.7

I

+

I

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+

o,s 4

+

+

-*'+:~+

+---+.z'÷

I

+

"~ 0"41

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++

++

÷ +

~ + 4-

.S/

+.,/

:.1-' " I

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O0

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o.1

,

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,

o.a

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,

o.s

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ExperimentalC a p a c i t y

o17

o:a

ob

1.o

[I/s]

Fig. 1 Correlation Curve for the new Capacity Equation. All tests. Correlation: r = 0.884 The results [12] show a clear independence on the pressure drop. This fact is in disagreement with the Nageswararao Eq. and in agreement with the other models studied. A dependence on the feed solid concentration and on the water feed flowrate has been proved [12]. This is in disagreement only with the Brookes eq.. A clear dependence on the vortex finder diameter and on the spigot diameter has been found [ 10]. With these evidences, only the equations proposed by the authors remain. In Figure 2, the dependence on the Do/Du ratio is shown. Due to its better performance, Eq. 2 is selected. The correlation for all data sets, is shown in Figure 3.

R = C4 *

(Do)c 5 ~

. (GLA) C6 . (CpA)c7

(2)

where: R = Do = Du = GLA= CpA= C4, C5,

Water Split = water underflow rate/water feed flowrate. Vortex finder diameter [mm]. Spigot diameter [mm]. Water feed flowrate [Us]. Feed concentration, % solid by weight. C6, C 7 = parameters to be estimated for each set of data.

Partition C u r v e

For each one of the tests, the partition curves (normal and corrected) were determined. To represent them, the two more common efficiency equations were tested: Lynch [5] and Plitt [4]. The quality of both approaches is high and equivalent. The data processing using the Lynch model has been done and presented elsewhere [ 10,11,12].

324

Technical Note

0.350-

÷ c:~

÷

0.300-

P ~ 10 [p~i]

0.250-

+

P = 15 [psi]

pX 20[psi____]]

o.. 0.20003 0.1500.1000.0500.000 1.0

115

210

215

310

315

410

4.5

Do/Du Fig.2 The Effect of the Do/Du ratio on the Water Split. Sample 1, Dc=50 mm, Cv=24%.

0.40 0.350.30~L CO

"0 (1)

0.250.20-

E 0.15.D uJ

0.10-

I

0.00

0.()5

0.I0

I

0.15 O.:PO 0.25 0.30 Experimental Water Split

0.35

0.40

Fig.3 Correlation Curve for the new Water Split Equation. Samples 1 and 2. Correlation: r = 0.919. The data, shown in Figure 4, corresponding to two tests, are presented together with the predictions of the Plitt model, selected as the best one. Y/ = 1 - exp[-0.693 * ( ~ ) N ]

aso~

(3)

TechnicalNote

325

where: y

~

Corrected efficiency [%]. Particle size [pin]. Corrected cut point [tan]. Parameter to be estimated for each set of data.

d d50c N

j/'

100 908070-

)./ :..y ?/

60o E 0

5040-

UJ

3020-

Yl

.//_

10-

0

I

1

/

I

r'q'l

i

ii

I

si

I

I

I

1o

I

I

I I

160

., o o =

I

I

J

I

I

I

I

4 )00

Size [urn] Fig.4 Experimental and Simulated Corrected Efficiency. De=2": Sample 2, Do=ll ram, Du=6.4 mm, P=13 psi, Cp=39%. De=l": Sample 2, Do=5.5 ram, Du=3.2 mm, P=13 psi, Cp=27%.

Corrected Cut Point d5oc

Four different equations were previously tested and presented [ 11]: Lynch [5], Rouse [6], Plitt [4] and a new equation proposed by one of the authors [9]. Additionally, other equations were tested: Nageswararao [ 13] and another new one proposed here. In the different approaches, the ds0c depends on some of the following variables: vortex finder diameter, spigot diameter, pressure drop, feed (flowrate or slurry density or solid %) and, for some authors, on the overflow or underflow rates (outputs). The results [9,12] indicate a clear dependence of ds0c on the pressure drop (fact in disagreement only with the Rouse eq.), on the vortex finder and on the spigot diameter. A dsoc dependence on the feed solid concentration has been proved [12]. This fact is in disagreement with Lynch and one of the authors Eqs. In Figure 5, the dsoc dependence on the Do/(Du) 2 ratio is shown. This allows the deduction of Eq. 4, selected as the best one. The correlation for some of the data sets is shown in Figure 6. d~

= C8 * (19o)c, Du 2

• e[C,..c.,] • (Qra)C,,

(4)

326

Technical Note

where: dsoc= Corrected cut point [~rn]. 250 E '7 200 0 0 13 {,.-

150-

0 n

~5 o 10013

b o

5o-

0 0.0

012

014

016

018

Do / (Du)

1.'0

112

1,4

2

Fig.5 The Effect of the Do/(Du) 2 Ratio on the dsoc. Sample 1, Dc=50 mm, Cp=45%, P=10 psi. 180160-

:1:

140

E

4-

120-

o

0 LO

.44-

1004-

8O .

E -

-

ffl W

44-

60

,d

4O

4-

4-t-4-

,4

20 .J 0-~

0

2b

40

6'0 80 160 120 Experimental d50c [urn]

1'~0

Fig.6 Correlation Curve for the new dsoc Equation (Plitt modified) Sample 1 and 2. Correlation: r = 0.974

160

180

Technical Note

327

CONCLUSIONS

The present study, based on extended experimental research, has provided some useful information on the modelling of small diameter hydrocyclones. The results show, in some aspects, coherency with what is already known about conventional larger cyclones. In other aspects, the results are in disagreement with previous findings. Accordingly, modifications of existing equations and new equations are proposed, improving their predictive capability for the small cyclones performance. In summary the resulting new model is much better, for the description of the small hydrocyclones performance, than all the others analysed, including previous authors's models. Remarkable contribution is the finding about the dependence of the water split on the Do/Du ratio and of the d50c on the Do/Du 2.

ACKNOWLEDGEMENTS

The authors are indebted to CONICYT (Nat. Sc. and Tech. Research Council of Chile) for their financial support, derived from the FONDECYT Grant N°1931086.

REFERENCES

.

2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14.

Dahlstrom, D.A., Cyclones Operating Factors and Capacities on Coal and Refuse Slurries. Mining Transaction, 184, 331--422 (Sept. 1949). Yoshioka, N. & Hotta, Y., Liquid Cyclones as a Hydraulic Classifier. Chem. Eng. Japan, 19(12), 632-640 (1959). Lynch, A.J. & Rao, T.C., Modelling and Scale-up of Hydrocyclone Classifiers. 11th. Int. Min. Proc. Congress, Cagliari, (1975). Plitt, R., Mathematical Model of the Hydrocyclone Classifier. CIM Bulletin, 114-123 (Dec. 1976). Lynch, A.J., Mineral Crushing and Grinding Circuits, D.W. Fuerstenau, Ed., vol. 1, (1977). Rouse, G. et al., Confirmation of Modelling Techniques for Small Diameter Cyclones. 3rd International Conference on Hydrocyclones, P. Wood Ed., BHRA, Session A, (1987). Bradley, D. & Pulling, D.. Flow Patterns in the Hydraulic Cyclone and their Interpretation in terms of Performance. Trans. Inst. Chem. Eng., 37, (1959). Brookes, G., et al., Hydrocyclones Performance Related to Velocity Parameters. 2nd International Conference on Hydrocyclones, BHRA, Session C, (1984). Vallebuona, G., Studio per la Modellizzazione di Cicloni di Piccolo Diametro. Tesi di Dottorato, Trieste, Italia, (1992). Vallebuona, G. & Casali, A., et al., Influenza dei Parametri Operativi e Dimenzionali nella Classificazione con Cicloni di Piccolo Diametro. Analisi dei Processi Mineralurgici - - '93, Trieste - - Italia, (1993). Vallebuona, G. & Casali, A., et al., Small Diameter Hydrocyclones - - Performance Prediction by Empirical Models. SME (Mineral Processing) Annual Meeting, New Mexico, U.S.A., (Feb. 1994). Leal, O., Modelaci6n y Dimensionamiento de Hidrociclones de Pequefio DiLrnetro. Memoria de Ingeniero Civil de Minas, U. de Chile, (March 1994). Nageswararao, K., J.K. SIMMET, Steady State Mineral Processing Simulator, User Manual, Version 3.4, (1991). Heiskanen, K. & Vesanato, A., A New type of Hydrocyclone for Fine Separation. 7th European Symposium in Comminution, Preprints, Part 2, (June 1990).