THE KINCALC®FLOTATION KINETICS CALCULATOR … · Figure 8 Flow Diagram of KinCalc® Functions ... The importance of flotation kinetics is that understanding of the flotation process,

© Eurus Mineral Consultants. 2008 Description, Capability and Value of KinCalc™. March 2008.

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Flotation Simulation & Modelling Software

THE KINCALC®FLOTATION

KINETICS CALCULATOR AND ORGANISER

AND THE SUPASIM® FLOTATION SIMULATION MODEL

BRIEF DESCRIPTION, CAPABILITY AND VALUE

Martyn Hay MARCH 2008

(last updated June 2007)


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CONTENTS

1. INTRODUCTION: FLOTATION, KINETICS AND KINCALC®............................................... 3 1.1 KINETICS ...........................................................................................................................................3

2. WHAT KINCALC® DOES .................................................................................................................. 7 2.1 FUNCTIONS........................................................................................................................................7

2.2 LINEAR CORRELATION AND HISTOGRAM FUNCTIONS .............................................................11

3. ACCURACY OF SUPASIM® ............................................................................................................ 13

LIST OF TABLES Table 1 Flotation Kinetics........................................................................................................................... 4 Table 2 Correlation Coefficient Table: Ni Ore 1 ................................................................................... 12 Table 3 Correlation Coefficient Table: Ni Ore 2 ................................................................................... 12

LIST OF FIGURES Figure 1 Flotation Kinetics, Circuit Design and Performance ........................................................... 3 Figure 2 Results from a Flotation Rate Test and Kelsall’s Equation ................................................. 4 Figure 3 Physical Meaning of Kinetics in the Plant ............................................................................. 6 Figure 4 Simulation of Plant from Laboratory Data............................................................................ 6 Figure 5 Flotation “PID” Diagram ......................................................................................................... 9 Figure 6 Factors Affecting Flotation Performance............................................................................... 9 Figure 7 Organisation of KinCalc® Functions ................................................................................... 10 Figure 8 Flow Diagram of KinCalc® Functions................................................................................. 10 Figure 9 Detail of Interconnection of All KinCalc® Functions ........................................................ 11 Figure 10 Histogram ................................................................................................................................ 12 Figure 11 Predicted vs Simulated Plant Recovery............................................................................... 13


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1. INTRODUCTION: FLOTATION, KINETICS AND KINCALC®

In a flotation plant the separation of mineral from waste is only about 85-95% efficient and is

dependant upon a myriad of parameters encompassing the quality and characteristics of the ore,

the operating environment, the reagents and the mechanical effectiveness of the flotation cells.

How much mineral is recovered (and how much revenue is generated) is primarily driven by the

characteristics of the ore which dictate what the operating conditions should be, such as the

fineness of grind, what reagents to use and the pH etc. The efficiency of the equipment (mills and

flotation cells) also has an influence on mineral recovery. How the various economic minerals

occur in the ore – i.e. in what way they are associated with each other and the various components

of the host rock – is determined by the ore’s geology which is measured by a mineralogist. How

these associations affect recovery by flotation is measured as the ore’s flotation kinetics. The

diagram below outlines the pivotal role that flotation kinetics plays in characterising the ore,

understanding why it performs (or behaves) the way it does and what size and configuration of

circuit is best to treat it and to maximise recovery and revenue.

MINERALOGY

FLOTATION KINETICS

CIRCUIT DESIGN

FLOTATION PERFORMANCE

(Grade/Recovery) & REVENUE

Flotation Performance Influence Diagram (Flotation "PID")

Determines

Affects

Defines CONTROLS

Figure 1 Flotation Kinetics, Circuit Design and Performance

1.1 Kinetics

How an ore responds to milling and flotation is determined by laboratory-scale batch milling and

flotation tests. Under chosen conditions a flotation rate test is performed which generates a

recovery, grade and concentrate mass profile over time. A graph showing typical recovery-time

profiles of two “good” ores and one “bad” ore is shown in Figure 2 below. The shape of these

profiles and the relationship between recovery, grade and mass with time is described


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mathematically by Kelsall’s equation where R equals recovery and t equals time. The equation

describes fast and slow floating components which relate to material that is easily and quickly

recovered at the beginning of the process and material that is not (i.e. the slow and difficult to

recover component).

The equation has four unknowns (collectively known as kinetics), a fast fraction, a fast rate, a slow

fraction and a slow rate. These are estimated from the testwork data in Excel by using the Solver

facility. Accuracy is improved by use of additional algorithms derived from experience.

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

0 2 4 6 8 10 12 14 16 18 20

FLOTATION ROUGHER RATE TIME (min)

LABO

RA

TOR

Y R

ECO

VER

Y

Kelsall's Equation:

R = (100 - Ø) [1 – exp(-kf*t)] + Ø (1 - exp(-ks*t)]

FAST COMPONENT + SLOW COMPONENT

FAST SLOW

Figure 2 Results from a Flotation Rate Test and Kelsall’s Equation

The outcome of using Kelsall’s equation is that the behaviour and response of the ore as in Figure 2

is now described by a set of numbers or kinetics. The various components of the ore that have

been measured by assay (floatable gangue, economic metals and minerals and other gangue or

metal contaminants if desired) each have their own set of kinetics. An example is shown below in

Table 1. If each set of kinetics was put back into Kelsall’s equation then it would recreate the lines

as in Figure 2.

Line IPF kPF kPS IGF kGF kGSPink 0.9011 1.6263 0.1158 0.0496 0.3586 0.0063Red 0.7705 1.8396 0.1493 0.1062 0.2201 0.0021Dark Blue 0.5135 1.1383 0.0554 0.2493 0.5582 0.0043

Table 1 Flotation Kinetics


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Where, I = fraction k = rate P = Platinum Group Metals (PGMs) G = Gangue

Thus, IPF = fast floating fraction of PGMs and kGS = slow floating rate of gangue. The usefulness of flotation kinetics is that the flotation response of both minerals/metals and

gangue can be reduced to a set a numbers. Different ores will have a different set of flotation

kinetics as will the same ore under two different test or operating conditions. This makes

benchmarking of one ore or one condition against another possible and it then becomes easy to

determine which the better is by simply comparing one set of numbers against the other.

Taking this further, each parameter of rate and fraction has a specific physical meaning in terms of

recovery, grade and mass in the laboratory test. Since the laboratory-scale test cell is merely a

scaled-down version of much larger cells in operation in the industry, then the kinetics are also an

accurate description of the ore under full-scale, continuous plant conditions when allowance has been

made for the difference in efficiencies between laboratory-batch and plant-continuous modes. The

difference between batch and continuous systems is described by a set of scale-up factors. An

illustration of the link between each kinetic parameter and operating plant design and

performance is shown in Figure 3).

The importance of flotation kinetics is that understanding of the flotation process, whether in the

laboratory, pilot plant or operating plant, is increased and the process can then be optimised1.

Laboratory flotation kinetics are used by Eurus Mineral Consultants to simulation plant

performance (see Figure 4).

1 Using the SUPASIM™ flotation model to diagnose and understand flotation behaviour from laboratory through to plant. Proceedings 37th Annual Meeting of the Canadian Mineral Processors Conference, Ottawa 2005.


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Laboratory Ro.conc after 25 min

Fast Gangue

Slow Gangue

Fast PGMs

Slow PGMs

% Mass

Grade g/t Rec. %

Fractions 0.0473 0.9527 0.9213 0.0787

Rates 0.0659 0.0028 2.7811 0.0560

Fractions 0.1151 0.8849 0.5422 0.4578

Rates 0.2902 0.0057 0.7215 0.027323.3 16.5 76.9

10.3 47.8 98.1Clean ore

Highly altered ore

0.9213

Recovery

0.1151 0.5422

IPF/IGF: grade, nos of stages of cleaning

Circulating load

0.04730.0028

0.0057 0.0273

kPS/kGS: incremental recovery, residence time, use of scavengers, regrinding?

Physical Meaning of Kinetics in the Plant

1st Ro conc to final conc?, air rates

2.78110.0659

Selectivity: 1st Ro to final conc, regrinding?

Degree of alteration/oxidation, pulp density

Liberation

Figure 3 Physical Meaning of Kinetics in the Plant

Measurement to Prediction

NECESSARY INPUTS

SIMULATIONPROGRAM

“SUPASIM™”

SCALE-UP FACTORS +

SGS

Figure 4 Simulation of Plant from Laboratory Data


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2. WHAT KINCALC® DOES

2.1 Functions

KinCalc® calculates flotation kinetics from laboratory float test data in excel format. The program

has the facility to automatically import data (test data and conditions etc) by identifying the cells

or range of cells where the data occurs. This is done by setting-up a format which can be

customised for any arrangement of data in an excel worksheet/spreadsheet including multiple

data sheets per worksheet and multiple worksheets per file. KinCalc® can be set-up to handle the

importation and processing of multiple files in a folder. There is no limit to the number of files

and/or data sheets that can be imported and processed in one batch; however in practice it is best

to restrict importation to about 200 data sheets at one go.

If data exists in hardcopy, software exists (from others) to convert these data into excel format.

Once imported, KinCalc®

1. Calculates flotation kinetics with and without boundary algorithms,

2. Generates five standard graphs,

3. Produces a summary sheet containing test descriptions; kinetics; laboratory test results;

cumulative recovery, grade and mass pull; headgrade and various kinetic ratios,

4. Allows for kinetics to be calculated manually via scroll bars set-up for each kinetic

parameter. This is done in that part of the program called ScrollCalc™,

5. Allows any set of data to be averaged and its kinetics calculated,

6. Allows one button generation of correlation coefficient tables and histograms which are

time consuming to generate each time by manual application of the relevant excel function,

7. Stores all data in Access or SQL where searches can be set up to collate all data according to

requirements such as ore type, reagent type, test date…. Etc. The data can be dumped into

excel for data mining or statistical processing.

Overall, the value of KinCalc® to the client/user is that KinCalc® is an integrated system capable

of handling and organising large amounts of data. With mineralogical Qemsem or MLA data it

also provides a facility to dump both kinetic and mineralogical data into Access in order to

generate correlations as per the diagram below.


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MINERALOGY

FLOTATION KINETICS

CIRCUIT DESIGN


(Grade/Recovery) & REVENUE

Flotation Performance Influence Diagram (Flotation "PID")

Correlate Qemsem/MLA data

with flotation kinetics

Link mineralogical data with circuit design and performance

Determines

Affects

Defines CONTROLS

This “add-on” facility increases KinCalc’s® usefulness as many clients perform a lot of mineralogy

but have not generated the association with kinetics and plant design and performance.

The value of KinCalc® lies in clients/users being able to,

1. Calculate kinetics from float tests they have performed and as a result be able to

benchmark one test, ore type or set of test conditions against another,

2. Automatically import, process and store data,

3. Have a customised graphing facility and one touch generation of r2 correlation tables and

histogram/ cumulative frequency graphs,

4. Use KinCalc® to graph test data and determine r2 correlations without having to use the

kinetics calculation section of the program,

5. Conduct an array of statistical analysis on the data having previously been conveniently

arranged in the KinCalc® summary sheet or in the Access database,

6. Load Qemsem mineralogical data into the Access database and link with the associated

kinetic data for a particular test. This provides the possibility of being able to correlate

Qemsem data with flotation kinetics which are correlated with plant design and

performance,

7. Collate all tests into one database and vehicle for easy access and processing,

8. Generate tables and graphs which are report quality and can be copied and pasted to a

word document.

Figure 5 to Figure 9 shows details of the functions within KinCalc®.


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Figure 5 Flotation “PID” Diagram

PARAMETERS AFFECTING FLOTATION PERFORMANCE

KINETICS

MINERALOGY

PHYSICAL PARAMETERS

OPERATION/DESIGN

CHEMICAL ENVIRONMENT

HYDRODYNAMIC ENVIRONMENT

Influences on Flotation Performance

Kinetics of metal/mineralKinetics of floatable gangueKinetics of entrained materialWater recoveryMineral/rock association

TextureUni/binary/tertiary componentsGeo-metallurgical considerations

Particle sizeParticle size distribution

Degree of liberationFroth recovery factor

Circuit configurationCell typeCell geometryShort circuitingResidence timeLip length to volumePulp levelFroth depthWhere to add reagents

pHEhAmount of dissolved oxygenWater qualityType of reagentQuantity of reagent

Cell kW/m3Efficency of mixing

Bubble sizeBubble coalescencePulp densityViscosity

Air rate

> 90%What is the effect of each?

Figure 6 Factors Affecting Flotation Performance

WHY ARE FLOTATION KINETICS IMPORTANT?

MINERALOGY

FLOTATIONKINETICS

CIRCUIT DESIGN


(Grade/Recovery) & PROFIT

Dictates

Determines

Affects

CONTROLS

SUITABLE VEHICLE

PERFORMANCE

ASSOCIATIONS

• Increases understanding of flotation…and therefore

• Optimise flotation performance & Recovery + Grade

Flotation “PID”: Flotation Performance Influence D iagram


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Figure 7 Organisation of KinCalc® Functions

KinCalc™ IN DETAIL(Flow diagram linking functions)

Test 1 High r² linear regression All analytes/minerals/gangueTest 2 Equal kF & kS values? All analytes/minerals/gangueTest 3 Very low IMF? All metals/mineralsTest 4 Very high IMF? All metals/mineralsTest 5 High r² & low IMF? All metals/mineralsTest 6 Very high IXF & very low kXS Gangue + contaminantsTest 7 kMF limit? All metals/minerals

Solving Kelsall's equation to determine kinetics sometimes gives values which are mathematically correct but not adequately descriptive of the material's practical response - hence these tests.

kinetics

™ Kinetics

Summary Sheet (per set of data)

Results Page (per test)

Data Sheet (per set of data)

Access Database

Re-import

Re-import

Dump into Excel

Query

ge

Import WizardOpen New

File

Select Existing File

Re-input of Processed

data or Kinetics

Input test data

Input conditions

Input description

Input Page

Choose to:Plot Graphs only

or Calculate Kinetics

ScrollCalc™ KinCalc™

MANUAL CALCULATION

OF KINETICS

AUTOMATIC CALCULATION

OF KINETICSManage/set-up list of Analytes, Minerals

and Other Parameters

Configure Customised Graph Settings

Use 4 standard graphs as visual aid to estimate

kinetics

ScrollCalc™ Kinetics

Choose to use best fit

button, if so go to

KinCalc™

Calculate

KinCalc™

Choose boundary tests

Graphs Page

Choose Graph Type

5 Standard Graphs1. Rec-Time & Grade-Time2. Rec-Grade3. Rec-Mass4. Mas-Time5. Separability

Customised GraphsCompare sets of analytes/minerals. Compare lab, pilot and plant data.

Plot combinations of data

Average PagHistogram & Correlation R² functions

Analyse using standard Excel

functions

Figure 8 Flow Diagram of KinCalc® Functions

WHAT DOES KinCalc® DO?Automatic Import

(single/multiple file) Import Wizard

Boundary test algorithms

Calculate KineticsTest data (Lab, Pilot, Plant)

Results Page (per test)

Summary test data Kinetics

Rec/Time graph Test Details

Sample description Test description Test conditions

Data Sheet (capacity of 4500 tests)

Test information Sample description

Raw data Analytes specified Misc parameters

Graphs Page (5 standard graphs) Rec & Grade/Time

Rec/Grade Mass/Time

Recovery/Mass Separability

Summary Sheet(capacity of 4500 tests)

Test informationSample description

Test resultsKinetics

Kinetic ratios

Customised Graphing Facility

Analysis and interpretation

Dump to Excel QueryMineralogical Data Access Database

Each set of test data, results and kinetics has a unique identifying code

Report

Report

Report

ReportReport

Input Page

Standard Excel functions Histogram function

Corr. R² function

Report

Average PageAverages

selected test data sets

ScrollCalc™


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KinCalc™ IN DETAIL (functions)

KIN-CALC

GENERATION OF GRAPHS

MANUAL IMPORT OF DATA

SCROLL-CALC

ACCESS DATABASE

AUTOMATIC IMPORT OF DATA

DATA IMPORT FORMAT

INPUT & STORAGE OF TEST CONDITION DATA

DATA OUTPUT

CUSTOMISATION OF PROGRAM FORMATS

TOOL BAR ICONS

OPTIONAL TOOLBAR ICONS

TOOL BAR ICONS

KinCalc™ Kinetics Calculator

Kinetics of metal/mineral

Kinetics of floatable gangue

Kinetics of entrained material

With/without boundary tests

What-if scenarios

Custom FunctionsHistogram

Correlation r2

5 Standard Graphs

Separab ility Curve

Recovery and Grade vs Time

Recovery vs Grade

Recovery vs Mass

Conc Mass vs Time

Customised Graphing Facility

Single data set

Educational facility

What-if scenarios

Kinetics estimation with few data points

Compare lab, pilot and plant profiles

Import of KinCalc, ScrollCalc and Test Description Data

Re-import data for further analysis

Anal ysisData sorting

Correlations

Statistical

Generation of Queries

Single file basis Any number of Data Worksheets

Batch of files in a folder Any number of Files

Any Number of Data Worksheets

Single or multiple data sets per worksheet

Set-up formats

Lab, Pilot or Plant data

Client/Mine

Ore body/type or stream in plant

Date or time

Reagents and additions

Reagent addition Straight or Staged

Conditioning Time

Grind

% Solids

Power (kW) input

Cell Type

Cell rpm

Air Flowrate

Water Type/Quality

Temperature

Eh, pH, Oxygen %

Geographical position

Depth or other position

Sta ndard Graphs

Data Sheet

Test information

Miscellaneous parameters

Analyte names and units

C onc times a nd masses

Analytes selected and category IDs

Feed, Tails and Conc assays

Parameter order indices

Summary Sheet

Test Descriptions

Kineti cs with/w ithout Boundary Tests

Scro llCal c Kinetics

Linear Flag (Mass-Time Curve)

Sum of the squared errors

Kinetic RatiosSlow Floating Ratio

Selectivity

Kinetic Meas ur e of Metal/Mineral and Gangue Floa tabil ity

Test Data SummaryRecoveries

Concentrate Grades

Head Grades

Average PageCalculates average for a set of data

Results PageSing le A4 page

Test Data Summary

Kinetics with/without Boundary Tests

Recovery-Time Graph

Graphs

Font

Type

Markers (12 options)

Lines (12 options)

Size and Dimension Ratio

General ProgramBackground and foreground colours

Font

Goto Input page

Clear the current Input Data

Manage the List of Analytes

Manage the List of Other Parameters

Manage Stream Names

Add current data to the Summary Sheet

Copy current sheet/page to a new workbook

Import Data Wizard

Import data from KinCalc database

Solve for Kinetics

Goto Results page

Goto Graphs page

Go to the Average sheet

Clear all data off the Average sheet

Delete the highlighted record on the Average sheet

Copy the current average values to the Input sheet

Go to ScrollCalcClear all data off the ScrollCalc page

Copy the active ScrollCalc parameters to the Summary sheet

Customise program settings

Show the Data sheet

Rows to Columns

Columns to Rows

Paste special function maintaing format of worksheet

Create a Correlation Matrix from selected data

Create a Frquency plot from selected data

Transform Layout of Kinetic Data Sets

Rows to Columns

Columns to Rows

Paste special function maintaing format of worksheet

Goto Summary sheet

Highlight Differences between Kinetics with/without Boundary Tests

Sort all data in chosen column in descending order

Sort all data in chosen column in ascending order

Highlight specific row

Delete highlighted row of data

Highlight a Specific Row

Move H ighlighted Row Up

Move H ighlighted Row Down

Copy Hig hli ghted R ow to Input Sheet

Clear Summary Sheet & Input Page

Copy highlighted record to the Average sheet

Copy highlighted row to ScrollCalc

Summary Roll-Up: Hide all details

Post current record to the KinCalc database

Post all summary records to the KinCalc database

Automatic Import, Calculation and Generation of Summary Sheet

Ma nual calculation o f kinetics

Input of anything user wishes to record; examples shown for illustration only

Figure 9 Detail of Interconnection of All KinCalc® Functions

2.2 Linear Correlation and Histogram Functions

Examples of one-touch button generation of linear correlation coefficient tables and a histogram

are shown in Table 2, Table 3 and Figure 10. Associations are identified by an elevated coefficient

between like parameters, for example between fast floating fractions and rates and slow floating

rates of Nickel and Cobalt (INiF vs. ICoF, kNiF vs. kCoF and kNiS vs. kCoS) and fast floating

fractions of Nickel and Gangue (INiF vs. IGF) in Table 2. In Table 3, a more altered Nickel ore has

elevated coefficients between slow floating rates of Nickel and gangue (kNiS vs. kGS) which are

more pronounced for fines than for coarse.


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Correlation MatrixBMS Ore Composite Rougher Rate Tests 1-20: EMC Rates

kGF kGS INiF kNiF kNiS ICuF kCuF kCuS ICoF kCoF kCoSIGF 0.0115 0.0784 0.4357 0.0081 0.7213 0.2184 0.0060 0.1145 0.6038 0.1364 0.5266 0.260kGF 0.1499 0.0065 0.4637 0.0279 0.0044 0.0284 0.0059 0.0001 0.2685 0.0013 0.096kGS 0.0171 0.2385 0.2355 0.0348 0.0005 0.3094 0.0022 0.2353 0.2781 0.150INiF 0.0605 0.2498 0.5368 0.0130 0.1014 0.8786 0.0615 0.1231 0.253kNiF 0.0377 0.0042 0.1436 0.0104 0.0181 0.6508 0.0002 0.124kNiS 0.0800 0.0035 0.1563 0.3435 0.2307 0.5043 0.220ICuF 0.0458 0.2577 0.3902 0.0672 0.0863 0.169kCuF 0.0009 0.0665 0.2120 0.0510 0.083kCuS 0.0637 0.0657 0.3941 0.175ICoF 0.1123 0.1176 0.115kCoF No of Data Points = 20 0.0046 0.005

0.011 0.114 0.153 0.193 0.254 0.146 0.034 0.120 0.263 0.204 0.190

0.142

0.060

0.169

0.199

Table 2 Correlation Coefficient Table: Ni Ore 1

Correlation Matrix

Combined XX Composite + FOT 1-9

kGF kGS INiF kNiF kNiS G & NiIGF 0.1459 0.1573 0.1566 0.0673 0.1694 0.2314kGF 0.1194 0.3309 0.3191 0.0599kGS 0.1299 0.1047 0.7450INiF 0.4224 0.0619kNiF No of Data Points = 26 0.1499

Correlation Matrix

Combined XX Composite + FOT 1-9

kGF kGS INiF kNiF kNiS G & NiIGF 0.0711 0.0510 0.2241 0.0001 0.0790 0.1280kGF 0.1623 0.0006 0.0527 0.0569kGS 0.0013 0.1518 0.5859INiF 0.3411 0.0023kNiF No of Data Points = 32 0.3388

Average Between

Fractions :XXX Fines Rougher

Average Between

Fractions :XXX Coarse Rougher

Table 3 Correlation Coefficient Table: Ni Ore 2

Individual and Cumulative Frequency DataNickel Head Jan 00 - Oct 06

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.50

1

0.52

1

0.54

1

0.56

1

0.58

1

0.60

1

0.62

1

0.64

1

0.66

1

0.68

1

0.70

1

0.72

1

0.74

1

0.76

1

0.78

1

0.80

1

0.82

1

0.84

1

0.86

1

0.88

1

0.90

1

0.92

1

Bin Values

% F

requ

ency

Figure 10 Histogram


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3. ACCURACY OF SUPASIM®

To date over 60 case studies (validations) have been done where the flotation performance of

operating plant have been simulated from laboratory batch rate tests. This covers PGM, Base

Metal Sulphide, Phosphate, Pyrite, Graphite and Cassiterite ores and furnace slag and tailings

dams. These include a variety of circuits from MF1, MF2 and MF3 configuration with/without

regrinding of rougher concentrate and cleaner tails.

Figure 11 shows the good agreement between predicted and actual plant recovery where predicted

concentrate grade is at or close to that of the plant. The graph includes secondary metals and

contaminants such as Copper and Nickel in UG2 and Merensky PGM ores and Copper in a Zinc

circuit etc.

ACTUAL vs SIMULATED PLANT RECOVERY PLATINUM, PHOSPHATE & BASE METAL SULPHIDE ORES

Predicted plant recovery = 0.937*(actual recovery) + 5.2638

R2 = 0.977

05

101520253035404550556065707580859095

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

ACTUAL PLANT RECOVERY

SIM

ULA

TED

PLA

NT

REC

OV

ERY

1

7

23 5

4

1 - Foskorite (SA) 2 - Canadian Cu ore 3 - Maranda Cu (SA)4 - Palabora Cu ore (SA)5 - Palabora Cu ore (SA)6 - Gt Dyke Pt ore (Zimbabwe)7 - Northam Merensky ore Pt (SA)8 - Maranda Zn (SA)9 - BMM Pb (SA)10 - BMM Zn (SA)11 - BMM Cu (SA)12 - Gt Dyke PGM ore Oxidised (Zimbabwe)13 - O'Okiep Cu Slag (SA)14 - R/burg PGM UG2 #1 (SA)15 - R/burg PGM UG2 #2 (SA)16 - Palabora Cu Slag (SA)17 - Oxidised PGM Merensky (SA)

PRIMARY STAGE VALUES

6

9810

13

12 1114

17

16

18

2120

1918 - PGM Merensky (SA) 19 - R/burg PGM UG2 #1 (SA) 20 - R/burg PGM UG2 #2 (SA)21 - Silicate PGM (SA)

SECONDARY STAGE (REGRIND) MF2 VALUES

15

22 - Lac des Iles PGM Pd (Canada) 23 - Lac des Iles PGM Pt (Canada) 24 - Lac des Iles PGM Au (Canada) 25 - Lac des Iles PGM Cu (Canada) 26 - Lac des Iles PGM Ni (Canada)

SECONDARY STAGE (REGRIND) MF2 VALUES

25

26

23

2422

Cu in Zn circuit (SA)Pb in Zn circuit (SA)

Cu in Zn circuit (SA)

Ni in Merensky

Zn in Pb circuit (SA)

Zn in Cu circuit (SA)

Cu in Pb circuit (SA)

Ni in UG2

Cu in UG2

Cu in Merensky

27a & b - PGM Furnace Slag 28 - PGM UG2 29 - PGM Merensky30 - Ni & Cu Ore 131 - Ni & Cu Ore 2

27a

27b

28 & 29

3031

Figure 11 Predicted vs. Simulated Plant Recovery

Documents

THE KINCALC®FLOTATION KINETICS CALCULATOR … · Figure 8 Flow Diagram of KinCalc® Functions ... The importance of flotation kinetics is that understanding of the flotation process,