A quantitative design approach for multi-port distributors

Minerals Engineering,Vol. II, No. 12, pp. 1209-1218, 1998

Pergamon, @2--6875(98)00107-1

© 1998 El~vier Science Ltd All tights w.served

0892--6875/98/$- -

see front matter

A QUANTITATIVE DESIGN APPROACH FOR MULTI-PORT DISTRIBUTORS

S. HU and B. FIRTH CSIRO/Division of Energy Technology, P.O. Box 883, Kenmore, Qld. 4069, Australia E-mail: [email protected] (Received 11 June 1998; accepted 19 August 1998)

ABSTRACT

A simple n~tel has been developed to predict the extent of particle settling in a multi-port slurry feed distributor for given conditions. The model relates the degree of particle settling with particle size distribution, particle density, solids concentration, feed flowrate and geo~;tric parameters of the distributor. The parameter, Variation Index, has been introduced to provide a quantitative measurement of the bias on particle size distribution of substreams. A linear relationship has been found between the model prediction of the degree of particle settling and the Variation Index of experimental curves on particle size distributions of substreams. This relationship not only verifies the model prediction, but also provides a good description of the dependence of the degree of bias on operating conditions and design parameters of the distributor. A design procedure based on the model and the linear relationship has been established to determine the geometric parameters of a multi-port distributor for unbiased slurry subdivision. A laboratory and two industrial distributors have been used for case studies to validate the new design approach. It has been found that predictions are in good correspondence with experimerttal results and plant sampling data. © 1998 Elsevier Science Ltd. All rights reserved

Keywords Modelling;; particle size; mineral processing

INTRODUCTION The subdivision of slurry feed to a number of units operated in parallel (e.g. hydrocyclones or flotation units) is a common process in coal and mineral processing industry. The slurry subdivision is usually performed by a nmlti-port distributor. Unfortunately, the distributor is not always capable of producing substreams with the same flowrate, solids concentration and particle size distribution. This biased slurry subdivision leads ~Loa significant decrease in the operating efficiencies of the sizing and cleaning units in coal preparation plants. The problem is also recognised in other industries, e.g. distribution of coal-oil slurry into parallel pre-heaters in a coal liquefaction process [Segev and Kern, 1985].

1209

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S. Hu and B. Firth

Studies on the biased slurry subdivision (also referred to uneven slurry splitting) have been reported in the past several decades. Two notable work on slurry flow splitting were published by Nasr-E1-Din and his coworkers [Nasr-E1-Din and Shook, 1986; Nasr-EI-Din et al., 1988]. A detailed literature review on the topic can be found elsewhere [Hu and Firth, 1997]. However, these published papers have considered only simple slurry flow splitters or subdividers, such as T-junction or its variant [e.g. Nasr-E1-Din et al., 1988; Burger et al., 1988]. The recent work of Hu and Firth [1998] appears the first to investigate the biased slurry subdivision in multi-port distributors. They carried out a pilot-plant scale experimental investigation to identify factors causing the biased slurry subdivision in multi-port distributors. The results have indicated that biased subdivision is mainly due to non-uniform solids segregation induced by low line velocity, which reduced the suspension forces on particles and increase the residence time of particles in the distributor. The bias can be reduced or eliminated by using a 'slim' distributor with a diameter as small as that for the feed inlet pipe. However, the distributor diameter in many practical applications has to be larger in order to have enough side face area for the attachment of a number of outlets from the distributor. For a given density and size distribution of the particles in a slurry feed and flowrate, there is a maximum distributor diameter with which no significant particle segregation occurs. To aid the improved engineering design of multi-port distributors, a quantitative model for determining the extent of particle settling needs to be developed. The physics describing particles settling in a flowing liquid is complex due to the interaction between the particles and liquid and between the particles. Detailed modeling has to be based on a fundamental approach involving the solution of velocity and phase distributions for both the liquid and particle phases (Hu and Firth, 1996a &b). But fundamental models tend to contain a number of parameters which are difficult to determine accurately in practice. Also, the model equations have to be solved using numerical methods which are very time consuming and not readily applicable for routine design. A simple model with reasonable capability for the prediction of particle segregation is more useful for engineering design purposes. The objective of this work is to develop a simple quantitative model which permits the degree of particle settling to be determined in a given multi-port distributor with typical combinations of feed flowrate, solids concentration, and particle size and densities. The output from this model will be evaluated as a performance index for predicting the bias to be expected from distributors in a number of case studies. MODEL DEVELOPMENT

To simplify the formulation of the model, a distributor configuration will have a geometry in which the inlet feed enters the distributor in a vertically upward direction into the distributor and the outlet pipes are horizontally orientated will be considered. The applicability of the model to other configurations will be discussed. The degree of particle settling depends upon the settling velocity and the time that the particles spend in the effective f l o w zone in the distributor. The concept of an effective f l o w zone is based on the assumption that some parts of the distributor volume have little involvement in the direct flow pathways of the subdivided feed towards the outlet ports, and are characterised by internal circulation flows. This assumption is supported by the published experimental results [Hu and Firth, 1998], which were obtained for a distributor with the outlets concentrated on one side of the distributor. The majority of the slurry flows through this side of the distributor and the majority of the other half is hydraulically excluded. The mean residence time, T m of particles in the effective flow zone is given by

r:

V

Q

where V e is the volume of the effective flow zone and Q is the volumetric flowrate of the inlet feed. For a multi-port-distributor with symmetrically arranged outlets, V e is equal to the volume of the distributor. For asymmetrically arranged outlets, V e is smaller than the volume of the distributor and given by

Quantitative design approach for multi-portdistributors

v : c,v<,

1211

(2)

where C e is an effective volume coefficient depending on the geometric shape of the distributor and Vd is the distributor volume. Particles in a flowing slurry always show a settling tendency and settle at a velocity determined by the balance between the motive force of its weight and the resistive force exerted on it by the liquid in contact with its surface. The resistive force includes drag, shear lifting, turbulent diffusive and other forces induced by gravitational and hydrodynamic effects. The estimation of these resistive forces, except drag force, requires the detailed knowledge of velocity and phase distributions in the flow field. The complexity in obtaining these velocity and phase distributions makes it impractical for the purpose of this model development. However, this model development only requires an estimation of the degree of particle settling at which no significant bias in slurry subdivision occurs. For this particular condition, the average line velocity in the radial direction of the distributor is considerably smaller than the critical velocity [Shook and Roco, 1991] to keep particles suspended. Consequently, shear lifting, turbulent diffusive and other resistive forces are relatively insignificant compared with the drag force. Hence, it will be assumed that the gravity force of a particle in the distributor is balanced only by the drag force produced by the surrounding slurry. The impact of this assumption on the utility of the model will be discussed later. Based on this simplifying assumption, the settling velocity of a particle species with a size of d i and density of pj in a multi-port distributor can be ee~silycalculated as [Shook and Roco, 1991];

IL"4gdi(P./ '~--~L;f)F

1).I'5

(1" C)3

(3)

where C s can take the value of the inlet feed solids concentrations without introducing significant error in most practical cases. The drag coefficient C D is given by

4di3g(pj/p: 1)p 2

CD " a l

I

2

3~tc

I'

(4)

The parameters, a 1 and b I in the above equation are functions of particle shape, size and density, and their values can be found in the literature [page 13, Shook and Roco, 1991]. During the mean rcsidenoe time, Tm that particles spend in the effective f l o w zone in the distributor, a particle with a settling velocity Vii can descend by the distance, :

(5)

This expression implies that particles with a settling velocity of V/j would deposit on the bottom of the distributor within the time of T m if their initial elevations are below Yij" A parameter referred to as the mean distributor height, 1tm is introduced here to represent the effective settling height, which is given by

H,. --

, H,)/2

(6)

where H h is the l~ighest height of the distributor, and H l the lowest height. The percentage of settled particles of those with a settling velocity VU is, therefore, estimated by

•u:

YJ/'/~

The percentage of total settled particles is given by

(7)

1212

St. -

S. Hu and B. Firth

i

(8)

j

i

j

where d i is the particle size of ith fraction and pj is the particle density ofjth fraction. Ply is the percentage of particles with a size of d i and density of pj. Adi is the particle size increment of (i)th to (i+l)th fractions. Apj is the particle density increment of (j)th to (j+l)th fractions. The denominator in above equation is actually the area under the particle size and density distribution curve.

IDENTIFICATION OF A QUANTITATIVE PREDICTOR FOR UNBIASED SUBDIVISION The value of S t is a measure of the degree of particle settling and is clearly dependent upon the geometry of the distributor, the slurry flowrate and size and density distribution of the particles. It is expected that there is a maximum value of S t for which no significant bias occurs in the subdivision of the slurry. Experimental results from another work [Hu and Firth, 1998] will be used to determine this value and then a number of case studies will be used to test the validity of the selection. The biased slurry subdivision results in each substream having different fiowrates, solids concentrations and particle size distributions. It has been found that the difference in the particle size distribution of the substreams provides a reasonable representation of the degree of bias. A parameter, Variation Index (II1) is introduced to characterize the difference of particle size distribution of substreams from a multi-port distributor. The parameter is defined as the maximum value of the areas between any two curves of particle size distribution. There are 10 values for the shade-area in a slurry subdivision system with 5 substreams. The largest value of these areas is defined as the Variation Index (VI), which is mathematically given by VI=

m a x { ~k ]Pli-PljlAdk}

(9)

where Adk (tim) is the particle size range for kth fraction; PIi and P~ are the volumetric percentages of particles with a size of dt in ith and jth substreams, respectively. Using Equation (9), I/1 values for those cases presented in a technical report [Hu and Firth, 1998] can be calculated, and the corresponding percentage of total settled particles, St can be also calculated using Equation 8. In processing the data for cases with outlets arranged on one side of the distributor, it has been assumed that the effective volume coefficient, Ce is equal to 0.75, since the other side of the distributor has little involvement in the flow towards outlets. A plot of S t versus VI is presented in Figure 1. It is interesting to note that there appears to be a linear relationship between the percentage of total settled particles, S t and the variation index, VI. This plot clearly indicates that the St can be used as a measurement of the extent of the bias in slurry subdivision. It was observed that for cases with a VI value less than 5 the slurry subdivision is essentially unbiased, and the subdivision is seriously biased if the VI value is larger than 8. The S t values corresponding to VI values of 5 and 8 are 10% and 20%, respectively. Therefore, the maximum value of S t for unbiased slurry subdivision is defined as 10%, and the S t value for very biased subdivision is 20%. Any S t value between 10% to 20% corresponds to minor bias in the slurry subdivision. In the development of this model, a number of assumptions have been made to facilitate the construction of a simple and useful model. Due to the assumption that the effects of shear lifting, turbulent diffusive, and other resistive forces on settling velocity are negligible, the amount of total solids sediment is certainly overpredicted. Therefore, the predicted percentage of total settled solids, S t should be regarded as a quantitative performance index, rather than a real prediction of the total settled particles. The linear

Quantitativedesignapproachfor multi-portdistributors

1213

relationship between ,'it and variation index, W as shown in Figure 1 has verified S t as a performance index over a wide range of conditions. The model was developed for distributors with outlets horizontally orientated, which provided the basis to ignore the effect of slurry flow velocity in the radial direction on the settling velocity in the vertical direction. For cases with both inlet and outlets vertically upward, the settling velocity calculated from Equation 3 should be subtracted by the mean vertical line velocity of the slurry flow, and the model is still valid for the design purpose. For other configurations, some care should be excised in using the model for design,

20 18

Unbiased Zone

16

I [ [

I Minor Biased [ Zone ]

Biased Zone

@

14 12

•

ConventionalDistributor

I • I

8 6 4 2 0

5

10

15

20

25

30

Fig.1 Linear relationship between the percentage of total settled particles, S t and the variation index, V L

SUMMARY OF THE DESIGN APPROACH A model for the estimation of the amount of particle settling has been developed. The predicted S t values using the model are in close relation with the extent of the bias in slurry subdivision. This provides a sound base to use the mo@~.l as a design approach. The detailed procedure is illustrated in Figure 2.

CASE STUDIES A laboratory multi.port distributor To apply the model proposed in the previous section to case studies, a laboratory multi-port distributor, as shown in Figure 3, was constructed. A number of experimental runs on this distributor were carried out using three different solids: pulverised coal, sand and magnetite. Typical results are shown in Figures 4 to 6. Based on known data on particle size distribution of feed, solids concentration, particle density and feed flowrate, the percentage of total settled particles, S~ were calculated for the three cases in Figures 4 to 6, respectively. The c,~a'esponding variation index, V I values for these cases were also calculated from experimental results. The S t and VI values are listed in Table 1.

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S. Hu and B. Firth

Known Data:

feed volumetric flowrate, Q particle size and density distribution, P# ,.J Selecting distributor v I diameter, height and shape

+

IO,ou,a,in0tomonre i nco I time, T,,,using Eqs. 1 and 2

Calculating settling velocity, Vu using Eqs. 3 and 4 Calculating the descending distance, using Eq. 5

+ I Calculating the percentage of settled particles, ~ using Eqs. 6 and 7 A

I Calculating the percentage of total settled particles, St using Eq. 8

,~Yes I Distributor for unbiased slurry subdivision Fig.2

Schematic illustration of the design procedure of unbiased multi-port distributor using the model developed in this project.

For the case with pulverised coal, the predicted S t of 11.0% suggests a basically unbiased slurry subdivision, while the experimental VI value of 6.5 indicates the presence of a minor bias. But this under-prediction should be reasonable, considering the simplicity of the proposed model. The prediction for the case with sand seems in good correspondence with the experimental measurement. Minor bias is predicted (St=l 3.0% ) for the case with magnetite, although the calculated VI value of 5.3 indicates a small amount of bias as seen in Figure 6. This over-prediction may also due to the simplicity of the model. However, the predictions for the three cases generally reflect the corresponding experimental measurements within an accuracy acceptable for engineering design purpose.

Quantitative design approach for multi-port distributors

1215

¢~340

Igg

i

I I I I I

.o-

Fig.3 Schematic diagram of a laboratory multi-port distributor.

70.0 60.0

o,o 1

50.0

8

0 ~ ' ~

0 2/

40.0

60""'/04 J

30.0

IC2/2 •- I I . . - IC2/4 •"-~;"' IC?./6 "-'--X'---IC2/8 IC2/10

20.0 10.0 0.0

. . . . . . . . . . . 10

bl

.

, .

100

lOOO

Particle diameter (l~m) Fig.4

Particle size distribution of 5 substreams in slurry subdivision using a laboratory multi-port distributor. Particle phase: pulverised coal ; Solids concentration in feed: 12 %; Inlet flowrale to distributor: 18 L/sec(wet sizing data, particle size fraction under 38 pm not included).

TABLE 1 S t and V I values for three case studies Cases Coal (Fig. 4) Sand (Fig. 5) Magnetite (Fi~. 6)

Flowrate (L/see) 18 21 20

Solids in feed (volume % ) 12 8 7

St

(%) 11.0 9.5 13

VI

6.5 3.3 5.3

1216

S. Hu and B. Firth

18

16

III III III ! III III III II II

IIII Id I Ill

I

14 12 10 8 6

,

I J

2

II II II I

0---±J 0.1

1

IJfl ~ fill F '"' IlilJ ~ illlJ all lllll tl J._[[l~ I

IJ 1 il ~ I I1 I1|

mmt A_ 100

10

olo I , °~°2 i

!!!1

60 ~ " ~ 0 4 J

II II II Jl

•- e - - 182,/2 .-11.-182/4

.-~s2~ 182/8 IS2/I0

1000

Particle Size ( ImO

Fig.5

Particle size distribution of 5 substreams in slurry subdivision using a laboratory multi-port distributor. Particle phase: sand; Solids concentration in feed: 8 %; Inlet flowrate to distributor: 21 L/sec.

3O 25

i, o

2O

010

o,

I 60~_..~04 % 15

I'\

10

'

IM1/2 '-i--IM114 !"-k-'lM1/6 ~1M1/8 IMl110

i

5

~J 10

100

1000

pmide D i a m ~ r (~n) Fig.6

Particle size distribution of 5 substreams in slurry subdivision using a laboratory multi-port distributor. Particle phase: magnetite; Sofids concentration in feed: 7%; Inlet flowrate to distributor: 20 L/sec.

Two industrial distributors

CaseA A number of samples were taken from 4 substreams of a slurry distributor at a Queensland Coal Preparation Plant. Particle size distributions of these substreams are shown in Figure 7. The variation index, W, for these curves is 10.4, indicating bias in the subdivision.

Quantitative design approach for multi-port distributors

1217

The distributor has a volumetric capacity of 310 L, and its mean height is 400 ram. Solids concentration of feed is 8% by volt,me and feed flowrate is 212 L/sec. The predicted percentage of total settled particles, St, is 16%, which implies a medium degree of bias in the slurry ,subdivision, and this was in line with the observed experimental results.

40

II 11~11 I

35 30 25 20 15

JJ

III

~'

-e-

--0--- cyc. #2 cyc. #3 -/3--- cyc. #4

10 5

I

0

10

I cyc. #1

I II IIII

100

1000

Particle diameter (gm)

Fig.7

Particle size distribution of 4 substreams in an industrial distributor (wet sizing data, particle size fraction under 38 lan not included).

Case B Another industrial distributor in a NSW Coal Preparation Plant has a volumetric capacity of 318 L, and the mean height is 485mm. Solids concentration of feed is 11% by volume and feed flowmte is 160 L/sec. The calculated percentage of total settled particles, S t , is 17%, which is good correspondence to the bias observed from plant sampling data on the bank of hydrocyclones, particularly with regard to the efficiencies of the hydrocyclone performance as shown in Figure 8.

Cyclone Bank Performance 1.2 1

i t

III

Lit

III

0.8

III

IIIh]Ll II

,

c~s

•~ C ' ) , c

6

-.-X--C~c 7

0.6

C~9 --e--eye tO

0.4 0.2

II

fill

I Cy¢12 C'y¢l

_~~IJL~_

0 0.1

1

10

100

1000

ST~, (MICRONS)

Fig.8 Partition curves of a bank of hydrocyclones (Cyc. 2, 5, 8 & 11 not in operation).

1218

S. Hu and B. Firth

CONCLUSIONS To aid the improved engineering design of multi-port distributors, a simple quantitative model has been developed to predict the percentage of total settled particles in a given distributor with typical combinations of feed flowrate, solids concentration, and particle size and density distribution. It has been verified from experimental results that the prediction from this model is in linear relationship with the Variation Index, a quantitative measurement of the degree of bias in slurry subdivision. The maximum value of the predicted percentage of total settled particles has been determined for which no significant bias occurs in the subdivision of the slurry. A design procedure based on the model has been established to determine the maximum diameter of a multi-port distributor with which no bias in slurry subdivision occurs for given feed conditions. The validity of the model is also confirmed in a few case studies. The quantitative model for predicting the percentage of total settled particles was validated mainly using laboratory results obtained on two different distributors. Further validation on different distributors, particularly from industrial sampling data are needed to improve the confidence level for using the model for design purpose. It is also considered that investigations into the application of the model to larger particle sizes should be carried out. ACKNOWLEDGEMENTS This work has been carried out with the support of the Australian Coal Association Research Program (ACARP Project C5052). REFERENCES

Burger, A.J., Van Deventer, J.S.J. & Cloete, F.L.D., Segregation of particles during flow-splitting of slurry, Minerals Engineering, 1, 255-259 (1988), Hu, S. and Firth, B., Numerical studies of phase redistribution phenomena in slurry flow splitting, in Computational Techniques and Applications: CTAC95, pp 395-402, World Scientific Publishing Corp: Singapore (1996a). Hu, S. and Firth, B., Application of Multiphase Flow CFD to the Analysis of Slurry Flow Subdivision Devices, Australian Engineering Mathematics Conference: AEMC' 96, Sydney (1996b). Hu, S. and Firth, B., Reducing the biased slurry feed subdivision in vertical pipe T-junctions using partition wall and stratifier, Minerals Engineering, 10, 163-174 (1997), Hu, S and Firth, B., Slurry subdivision under pressure, Report of Australian Coal Association Research Program (ACARP)-Project C5052, CSIRO/CET/IR 19, Jan.,1998. Nasr-EI-Din, H., Shook, C.A. and Esmall, M.N., Wall sampling in slurry systems, Can. J. Chem. Engng., 63, 746-753 (1985). Nasr-E1-Din, H. and Shook, C.A., Particle segregation in slurry flow through vertical tees, Int. J. Multiphase Flows, I2, 427 ~.A.3 (1986). Nasr-EI-Din, H., Afacan, A. and Masliyah, J.H., Solids segregation in slurry flow through a T-junction with horizontal approach, Int. J. Multiphase Flows, 15, 659-671(1988). Segev, A. and Kern, K.C., Solid-liquid separation in a slurry manifold, ASME Winter Mtg; Synfuels and Coal Energy Symp., Dallas,Tex (1985). Shook, C.A. and Roco, M.C., Slurry Flow: Principles and practice, Butterworth-Heinemann, Stoneham, USA (1991).

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