J.Obiri - Yeboah and S. Arthur The Use of Statistical ...€¦ · hydrocyclones. The cluster of...

J.Obiri- Yeboah and S. Arthur

The Use of Statistical Analysis for Hydrocyclone

Efficiency

for publication

2

The Use of Statistical Analysis for Hydrocyclone Efficiency Estimation –

A Case Study

J. Obiri Yeboah and S. Arthur

Gold Fields Ghana Limited

P. O. Box 26

Tarkwa

Ghana

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ABSTRACT

In order to optimize gold liberation, an investigation was carried out to determine the particle

classification efficiency with respect to target set (i.e. 80 % - 75 µm) for the cluster of

hydrocyclones. The cluster of hydrocyclones, consist of eight cyclones of which seven are being

operated. A series of wet size analysis was performed over a period of one week, on the

cyclone overflow slurry, under cyclone vortex finder diameter of 10 inches and spigot diameter

of 6 inches.

Results indicate that operating at a cyclone pressure of 110 kPa – 120 kPa with 51 % - 60 %

solids feed density generates an overflow slurry density of 21 % - 31 % solids.

The cyclones had efficiencies between 65.38 % - 90.91 % with percentage passing 75 µm per

percentage solids of cyclone feed density as 0.6538 - 0.9091 respectively. Additionally, the

gradient establishes the extent of classification in relation to the set target and standard unit of

performance as percentage passing per percentage solids of cyclone feed density.

Feed density related linearly to percentage passing 75 µm, even at 1 % critical level of

significance. The prevailing parameters of cyclone pressure, feed rate, circulating load and fixed

parameters of Vortex finder and spigot diameters do not necessarily need to appear in the

formula for calculating or estimating efficiency since their resultant input and output

parameters are used.

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Key words:

hydrocyclones, Vortex finder, spigot diameters, percentage passing, of classification, test for

lineality and critical level

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1 INTRODUCTION

This study was carried out at Yosaj Goldfields Limited, Tarkwa, to optimize leaching in Carbon In

Leach (CIL) tanks of the company’s gold processing plant.

Generally , performance measurement indicates the level of resource usage or/ and a set target

achievement. The level of resource usage to achieve a set target is called efficiency and the

extent of target achievement depicts effectiveness.(Foulks Lynch Ltd, 2002).

Conventionally, the efficiency of a Hydrocyclone can be measured by estimating the probability

of the desired particle size appearing in a classified product (e.g. estimation of cyclone d 50 ). It

relates the weight fraction or percentage of each particle size in the feed which reports at the

apex or underflow to the particle size. The cut point or separation size refers to 50 % of particle

in the feed of d 50 size reporting to the underflow.

However, the Mineral Engineer is usually interested in knowing the fineness of grind reporting

at the overflow and the parameters to control to achieve a set target of fineness than cyclone

d 50 (B.A. Wills 1992). This makes it more important to provide this method of assessment. The

work assesses the use of statistical analysis to measure the level of efficiency of a hydrocyclone

as classification unit of a gold processing plant.

Invariably, at Yosaj Goldfields Limited, the needed grinding size of 80 % passing 75 µm, for the

effective liberation of gold, place important on the efficiency of the classification unit to

enhance leaching. The cluster of hydroclone unit currently in operation, had justification from

the increment in volume of slurry as a result of recent plant upgrade.

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Consequently, this investigation of the performance of hydrocyclones under their operating

conditions is to achieve optimum classification for thickening and leaching. This paper looks at

the relation between cyclone efficiency and cyclone feed density in order to enhance effective

operational control to achieve 80 % - 75 µm grind size, at the cyclone overflow product.

2 THE HYDROCYCLONE

Hydrocyclone is a classifying device that makes use of centrifugal force to increase the settling

rate of particles. It is made up of a cylindrical section connected to a conical shaped vessel with

an opening at the apex. The cylindrical section is closed off at the top with a pipe protruding

into the body of the cyclone. This is called the vortex finder.

The feed is introduced under pressure through the feed inlet, tangential to the cylindrical

section of the cyclone. This produces a spiral motion, which generates a vortex in the cyclone

with a low pressure zone along the vertical axis of the cyclone.

Particles in the pulp stream are subjected to an outward centrifugal force and inward drag force

or centripetal force. The coarsest or Heaviest particles are pulled by centrifugal force to the

inner walls of the cyclone displacing the finer, lighter particle and excess water towards the

center.Thus particles are graded by size and mass from outside to inside of the spinning

mixture. The coarsest or heaviest particles spiral down the walls and discharges through the

apex as underflow.

The split of particles is dependent on the balance between the centrifugal and drag forces and

hence the overall performance of a cyclone depends on the relative values of the radial and

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tangential velocities at all positions. For different solids and liquids, the values of fluid viscosity,

solids and fluids densities and effective values of diameter contribute to the overall cyclone

performance. Fig. 1 shows a sketch diagram of a hydrocyclone (Department of Minerals

Engineering and Extractive Metallurgy, 1988).

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Fig.1 HYDROCYCLONE

Vortex Finder

Feed Inlet

Feed Chamber

Spigot

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3 EXPERIMENTAL CONDITIONS AND SIZE ANALYSIS RESULTS

One liter of overflow samples were taken at a sampling frequency of one hour interval. The

respective overflow densities were measured and their corresponding cyclone feed densities ,

cyclone pressure and mill feed rate were tabulated in table 1 – 7. The samples were taken over

a period of seven days with twelve samples each day.

Each overflow sample was taken through wet sizing analysis using a screen with aperture of 75

µm. The respective +75 µm density was measured by the use of Marcy scale to deduce

corresponding percentage -75 µm from wet sizing log table for percentage passing 75µm of ore

with Specific gravity (SG) of 2.7 shown in fig. 2. Feed density, Mill feed rate and Cyclone

pressure were taken from the scada automatic digital recorded reports.

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Table 1 Test work Results and experimental condition for day 1

Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 60 30 12 671 111 68

900 58 28 7 617 111 75

1000 57 23 5 669 110 78

1100 56 25 5 655 112 80

1200 58 28 8 618 110 71

1300 58 29 6 645 110 79

1400 60 28 9 655 115 68

1500 56 30 6 669 110 80

1600 57 25 7 671 111 72

1700 56 26 7 684 113 73

1800 59 28 5 615 110 82

1900 55 27 8 605 114 70

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Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 60 30 5 498 118 83

900 59 25 6 645 110 76

1000 59 31 12 603 116 61

1100 60 31 10 687 120 68

1200 58 27 8 620 117 70

1300 58 30 6 479 110 80

1400 57 27 4 510 111 85

1500 57 29 4 447 113 86

1600 51 21 6 505 110 76

1700 58 30 6 479 118 80

1800 58 25 5 480 110 80

1900 57 28 4 495 115 86

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Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 54 27 8 587 115 70

900 58 25 6 634 115 76

1000 59 30 9 600 110 70

1100 61 28 9 568 114 68

1200 60 27 8 630 118 70

1300 58 30 8 570 110 73

1400 56 24 6 529 113 75

1500 57 29 7 449 111 76

1600 56 25 6 507 120 76

1700 58 29 8 572 119 72

1800 58 29 9 498 116 69

1900 56 24 6 594 113 75

13


Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 57 23 6 568 117 74

900 59 25 6 643 112 76

1000 58 26 9 602 115 65

1100 56 26 7 597 117 73

1200 58 27 8 595 117 70

1300 58 28 9 496 113 68

1400 57 29 7 573 120 76

1500 56 25 6 498 111 76

1600 53 21 5 572 112 78

1700 56 27 9 490 119 70

1800 57 24 6 585 111 75

1900 58 29 6 590 110 79

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Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 55 27 7 469 110 74

900 55 29 6 654 118 79

1000 57 25 6 604 115 76

1100 55 28 7 597 119 75

1200 57 27 6 623 120 78

1300 56 24 7 507 111 71

1400 57 24 6 582 113 75

1500 56 27 6 508 111 78

1600 57 25 7 512 115 72

1700 56 23 5 572 117 78

1800 55 25 5 459 112 80

1900 56 27 7 595 116 74

15


Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 57 28 9 670 120 68

900 59 25 9 657 110 68

1000 59 26 8 681 118 69

1100 57 30 9 662 117 70

1200 59 27 8 598 115 70

1300 58 29 9 654 112 69

1400 57 30 9 625 114 70

1500 57 25 9 676 113 68

1600 58 25 6 717 110 76

1700 56 28 7 688 112 75

1800 55 23 6 598 114 74

1900 55 27 8 579 112 70

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Time (hrs)

Feed

density

(% solids)

Overflow

density

(% solids)

Overflow

Density of

+75 µm

(% solids)

Mill Feed

Rate (t/hr)

Cyclone

Pressure

(kPa)

Overflow

Percentage

Passing

75 µm (%)

800 56 27 7 611 113 74

900 57 30 8 608 110 73

1000 57 25 7 663 111 72

1100 56 27 8 645 113 70

1200 58 29 9 617 115 69

1300 56 26 8 597 113 69

1400 57 25 9 615 114 68

1500 55 27 8 646 112 70

1600 55 29 8 617 114 72

1700 58 28 9 648 111 68

1800 57 27 8 651 112 70

1900 56 28 7 600 116 75

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4 STATISTICAL ANALYSIS OF TEST VALUES

Table 8 Analysis of day 1 experiment

Sample

No.

Feed

Density

(% solids)

X

Overflow

Percentage

Passing

75 µm (%)Y

XY

X 2

Y 2

1 60 68 4 080 3 600 4 624

2 58 75 4 350 3 364 5 625

3 57 78 4 446 3 249 6 084

4 56 80 4 480 3 136 6 400

5 58 71 4 118 3 364 5 041

6 58 79 4 582 3 364 6 241

7 60 68 4 080 3 600 4 624

8 56 80 4 480 3 136 6 400

9 57 72 4 104 3 249 5 184

10 56 73 4 088 3 136 5 329

11 59 82 4 838 3 481 6 724

12 55 70 3 850 3 025 4 900

Sum 690 896 51 496 39 704 67 176

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TEST FOR LINEALITY AT 1% CRITICAL LEVEL

By formula: Sb 2 = Se 2 /SSX …………………………….(1)

Where Sb = standard error of the gradient of regression line on X and Y – axes

Se = standard error of the tested values, b = gradient, n = total number of tested samples and

SSX = X 2 - ( X) 2 /n …………………………………….(2)

Se 2 = {[ (Y 2 ) - ( X 2 )] - [b( XY - X Y/n)]}/n-2 ………………(3)

b = [n( XY) - X Y]/[n X 2 - ( X 2 )] ……………………………(4)

t = (b - B)/Sb …………………………………………………………………………………(5)

n = 12

X = 690, Y = 896, X 2 = 39704, Y 2 = 67176, XY = 51496

From (4)

b = [ 12(51496) – (690)(896)]/[ 12(39704) – (690) 2 ]

b = - 0.82759

From (2)

SSX = 39704 – (690) 2 /12

SSX = 29

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From (3)

Se 2 = {[67176 – (690) 2 /12] – [ -0.82759((51496) – (690)(896)/12]}/12-2

Se 2 = 2498.285

Sb 2 = (2498.285)/(29)

Sb 2 = 86.14777

Sb = 9.281582

Ho:B = 0, implies hypothesis of no gradient or no linear relation.

H 1 :B < 0, implies hypothesis of linear relation

By t-distribution, the following evaluation can be obtained

From (5)

t = (b-B)/Sb

t = (-0.82759-0)/9.281582

t calculated = -0.089165

From t-distribution statistical table at 1% critical level and 11 degree of freedom;

t 01.0 11 = 2.718

Since, -0.08916 < 2.718, Ho is rejected and H 1 is accepted.

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This means that, even at 1 % critical level of significant there is linear relation between Feed

density –X (i.e. % solids) and percentage passing 75 µm – Y (i.e.% solids).(S. Al-Hassan,2004)

Fig. 2 Regression of Percentage passing 75 µm on Cyclone feed density

Subjecting each of the day’s feed densities and overflow percentage passing 75 µm to statistical

linearity analysis as calculated for day 1, table 8 above, shows a linear relation at even 1%

critical level of significance. Also regression of Percentage passing 75 µm on Cyclone feed

density of day 2,3,4,5,6 and 7 experiments as in fig. 3, give graphs with linear equations; y = -

0.6538x + 115.29, y = -0.7699x + 116.83, y = -0.8793x + 123.38, y = -0.875x + 124.83, y = -

0.7079x + 111.11 and y = -0.9091x + 122.2 respectively.

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5 DISCUSSION

Basically, efficiency is given by the ratio of output to input and can be expressed as a

percentage. Hence from table 1-7, output represents percentage 75 µm (i.e. Y on the statistical

table) and input as feed density (i.e. X on the statistical table). This arrangement is in

conformity with the operational principle of hydrocyclone. Interestingly, using parameters

which are not related to input and output may defeat the aim of estimating efficiency.

Consequently, it is imperative to note that, the feed densities (input) and corresponding

percentage passing 75 µm (output) are resultant products of the prevailing parameters of

cyclone pressure, feed rate, circulating load and fix parameters of 10 inches Vortex finder and 6

inches spigot diameters. As in all calculation or estimation of efficiency, these two resultant

products are used to depict level of effect of the prevailing parameter on performance which

may be adjusted for efficiency improvement.

Therefore, the prevailing parameters of cyclone pressure, feed rate, circulating load and fixed

parameters of 10 inches Vortex finder and 6 inches spigot diameters are not necessarily

needed to appear in the formula for calculating or estimating efficiency when their resultant

input and output parameters are used.

From fig 3 - 9 graphs, all the least square regression analysis equations (Y = a + bx) (S. Al-Hassan,

2004), have negative sense (i.e. Negative gradient). This negative gradient which is the

percentage passing 75 µm (grinding grade) per percentage solids of the cyclone feed density

(input), authenticates the fact that lower feed densities favour higher percentage of -75µm

particle size in the overflow product (output). a = the intercept on Y (percentage of -75 µm) axis

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and b = the gradient (Percentage of -75 µm of overflow per percentage solids of feed density).

The gradient is therefore equal to output divided by input which is efficiency by definition.

Therefore, fig 3-9 graphs had equations with gradients (efficiencies) which occurred under the

cyclone feed densities between 51 % to 60 % solids at pressures of 110 kPa to 120 kPa. This is a

quicker and a more convenient method of estimating efficiency as compared to conventional

method. The high linearity between cyclone feed density and percentage of -75 µm, is a proven

justification and accuracy of this statistical method.

When y = o, the x – intercept, shows the limit of percentage solids at which classification would

be practically impossible. That is at this point of feed density, there will not be enough water or

liquid to enhance differential settling among particles. Therefore classification is zero at this

point. Also when x = 0, the y – intercept depict a point where there is no solid flowing through

the cyclone. The zero feed density corresponds to a point on y – axis where virtually, only water

comes as overflow. Practically, that is 100 % - 75 µm. This means that all overflow discharge

may be only water or solid of size -75 µm.

The least square regression method makes use of all variables under consideration, giving it a

higher potential of low deviation as compared to forming composite samples and subsequently

dividing for size analysis. It also gives better account of the end result than using the average

value. That is all values are taken into consideration to overcome the effect of skewness on the

average value (i.e. mean).

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6 CONCLUSION

Using the conventional method of estimation (i.e. by computing the particle size probability of

appearing in a classified product, example estimation of cyclone d 50 ) has higher potential of

deviation. This is due to errors that may occur in numerous sequence of test works involved in

the method. It does not give direct relations for trouble shooting.

On the other hand, statistical methods of estimating hydrocyclone efficiency provides the

means of optimizing the extent of control of the cyclone feed density to achieve expected

target. This is due to the expression of efficiency as percentage of the cut off size per

percentage solid of cyclone feed density.

Additionally, statistical analysis of hydrocyclone efficiency, has higher accuracy due to fewer

sequential test work method as compared to others. The proven linearity between the

parameters used in the method at even 1 % critical level of significance is an indication of the

effectiveness of the method.

Graphically, regression of percentage passing 75 µm on cyclone feed density can be used for

quick estimation with gradient of the regression line, representing the efficiency of the cyclone

during the time of operation.

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REFERENCE

B. A. Wills (1992), Mineral Processing Technology, Cambonne School of Mines and Cornwall,

England, pp. 381-387

Department of Minerals Engineering and Extractive Metallurgy (1988), The Extraction and

Recovery of Gold, Western Australian School of Mines, Australia, pp. 4.1-4.5

Foulks Lynch (2004), Managing People, EPP Books Services, pp. 75&76

S. Al-Hassan (2004), “Lecture Notes on Statistical Models MSc. Modular Programme”, Western

University College, Tarkwa, pp. 11& 4

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James Obiri-Yeboah is a Metallurgical Superintendent at Gold Fields Ghana

Limited, Tarkwa. He has worked as a Metallurgist at Teberebe Gold Fields from

1997 to1999, AngloGold Ashanti from 2000 to 2005. He holds a PhD in

Management from Swiss Management Center University and MSc degree in

Mineral Engineering from the University of Mines and Technology, Tarkwa. He

is researching into the use of engineering and management (Strategic

Opportunity Management) principles to resolve production problems.

Sampson Arthur is a Unit Manager Technical Service at Gold Fields Ghana Limited,

Tarkwa. He has worked as a metallurgist at Teberebe Goldfields from 1994 to

1999, AngloGold Ashanti from 2000 to 2004. He holds an MSc degree in Mineral

Engineering from the University of Mines and Technology, UMaT. His research

area is Assessing the need for Knelson Concentrator in the CIL plant at Goldfields

Ghana Limited.

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