A Model for Flotation Processes, AMINPRO, August 2007

Minpro

Amelunxen Mineral Processing Ltd.

Aminpro – Flot Models

A Model for flotation processes

By: Roger Amelunxen

P.O. Box 296 - Garibaldi Ga ribaldi Highlands, BC - Canada, Canada , V0N 1T0 Email : [email protected] - Tel/FAX : (1-604) 898-1111

1

1 Introduction Amelunxen Mineral Processing Ltd has designed two flotation models for its use in project development and plant audits: The Aminpro-Flot Simplex (AFS) and the Aminpro-Flot (AF) size by size model. •

•

The AFS model is based on rougher and cleaner kinetics of minerals derived from standard laboratory testwork. The AF model is similar to the AFS but splits every stream into twenty (20) size classes and models each class on its own. The AF is ideal if screen analysis is required for all streams

Both simulators use standard flotation modeling formulae and have sub-models for: • • • • •

Collection zone recoveries Froth zone recoveries Entrainment Regrind Corrections for differences in lab and plant size distributions

Both Models have the following features: •

•

• • •

Circuit configuration can be changed: o Accepts flowsheet changes o Accepts cell size changes Accepts changes in cell types (columns, mechanical cells, o etc) Will generate grade-recovery curves for any component of the circuit Will allow computation of economically optimum circuit Generates mass balances Examines constraints in carrying capacity, lip length and cell turbulence.

P.O. Box 296 - Garibaldi Highlands, BC - Canada, V0N 1T0 Email : [email protected] - Tel/FAX : (1-604) 898-1111

Minpro


2 Scaling laboratory test to plant performance There are a few key points that make the Aminpro flotation models’ scale-up process successful: •

•

•

The flotation models are based on the flotability of minerals and not elements. The relative speed in flotation between minerals is maintained whether floated in a small laboratory cell or in a plant environment as long as the conditions are the same. The speed of flotation of a mineral is measured by its rate constant. The relative maximum recoveries between minerals in a slurry are maintained whether floated in the lab or in the plant, as long as the chemical conditions are the same. The maximum or ultimate recovery of a mineral is measured in a laboratory test.

The reader should not be a surprised to find that the relative recoveries between minerals floated in a plant is the same as those in the lab. It is the reactor model that differentiates the plant performance (Mixed and continuous flow reactor) from that of a laboratory cell (plug flow reactor).

2.1

Basics of a flotation model

The process of recovering hydrophobic particles by flotation abides by equations of a plug flow reactor when we are dealing with batch laboratory cells and mixed flow reactor when talk about plant conditions. The recovery components of a flotation process are shown in Figure 2-1. This figure shows two distinct zones in the cell: a pulp zone (or collection zone) and a froth zone. Mineral particles in the collection zone can be selectively enhanced with chemicals to render them hydrophobic. These will attach to air bubbles generated in the cells’ impeller area and they will float to the surface of the pulp zone where they form a stable froth bed. Non-sulfide minerals (NSM) remain hydrophilic; they will not attach to air bubbles and will stay in the pulp. The floatable minerals collected in the pulp enter the froth zone and are removed into a pan. Operators can control de depth of the froth zone in order to enhance the grade of the concentrate. Portion of the particles recovered into the froth zone will drop back into the pulp zone as air bubbles collapse; therefore a froth


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recovery component must be applied to all minerals reaching this zone regardless of their size, density or shape. As some water is also recovered into the concentrate, minerals are dragged along and recovered with the water regardless whether they are floatable or nonfloatable species. This event contributes to the overall flotation process and is called entrainment.

Figure 2-1

The Recovery of Minerals in the Lab: Equations

Re

Conc

Rc.Rf

Rf

1

Rc

Feed

1 - Rc Rflot = Rc.Rf / (Rc.Rf + 1-Rc) Rtot = Rflot + (1 – Rflot).Re

Tails


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Minpro 2.1.1


Collection Zone Recoveries

In the laboratory cell (Plug flow reactor), where concentrates are removed from a static pool (i.e. there is no tailings leaving the cell), the collection zone recovery, Rc is defined by a first order rate equation as shown in equation 1, bearing the kinetic rate constant, k, the maximum recovery that occurs at time= (infinity), Rmax, and the flotation time, t. ∞

Rc =

( 1

-

e-kt ) Rmax

Eq 1

In a plant environment (mixed flow reactor), where the concentrate is removed from a cell that continuously receives feed and discharges tails, the collection process is defined by:

Rc = [ ( kt ) / ( 1 + kt ) ] Rmax

Eq 2

In the scale-up process of going from lab test data to plant performance, equations 1 and 2 are the conversion equations governing the models. A graphical representation of the two equations is shown in Figure 2-2. Both lines represent a mineral whose kinetics were determined in the lab. The Rmax is 90% and the rate constant k = 0.7 min -1.

Figure 2-2

Differences in the shape of Recoveries curves: Plug and Mixed Reactor 100 90 80 70

Plug

60 y r e 50 v o c 40 e R

Mixed

30 20 Rmax = 90% k = 0.7 min-1

10 0 0

5

10

15

20

25

30

35

Flotation time, min


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The difference in the shape of the curve is significant and explains the larger flotation times required in the plant to achieve similar recoveries than those obtained in the lab. It is important to add that in the process of modeling a plant, equation 2 must be applied to each cell in the circuit. This will be explained later. 2.1.2

Froth Zone Recoveries

As indicated earlier, minerals recovered in the pulp zone enter the froth zone where some fall back into the pulp zone and others are recovered over the lip of the cell. The froth recovery, Fr, depicts the fraction of particles recovered in the froth from those that were recovered in the collection zone. The process of recovering minerals from the froth zone can be enhanced in real life by increasing the air rate to the cell or by raising the pulp level. The degree of enhancement is also called the degree of “pull”. By “pulling harder”, the Fr is being raised. The combined action of collection zone recovery plus the froth zone recovery is defined by what we will call the flotation recovery, Rflot, and that is:

Rflot =

( Rc.Rf ) / ( 1 – Rc + Rc.Rf )

Eq 3

Figure 2-3

Differences in the shape of Recoveries curves: Plug and Mixed Reactor - Varying Fr 100 90 80 Plug

70

Fr = 100

60

y r e 50 v o c 40 e R

Fr = 10

30

Fr = 60

Fr = 20 Fr = 40

20

Rmax = 90% k = 0.7 min-1

10 0 0

5

10

15

20

25

30

35

Flotation time, min


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Figure 2-3 shows the effect of applying a froth recovery to equation 3. This figure shows the laboratory test recovery-time curve and a number of “plant” recoverytime curves, starting with a slow “pull” (Fr = 10%) to a very intense “pull” (Fr=100%). As indicated earlier, the plant modeling is done on a cell-by-cell basis. As the flotation times in individual plant flotation cells are commonly below 5 minutes, it becomes apparent that froth recovery has a big influence on the manner in which cells are modeled. In a laboratory cell, the froth recovery is generally 100%, as the froth beds are shallow and operator action is likely pushing the froth recovery to high levels. The Aminpro kinetic tests consider froth recoveries as an important aspect of kinetics determination, because not all lab technicians or plant operators “pull” in the same manner. 2.1.3

Entrainment and Overall Recoveries

As concentrate is recovered over the lip of a cell, it carries with it water, which in turn drags solids along that did not undergo the flotation process. These solids are said to have been recovered by entrainment, Re. The combined effect of Rflot and Re results in a total flotation process recovery that we will call, Rtot, which is defined by:

Rtot = Rflot + ( 1 – Rflot ) Re

Eq 4

In the process of entrainment, material is dragged along with the water in the concentrate regardless whether they are floatable minerals or not. Generally the different sizings and specific gravities of each mineral species result in slight differences in the degree of entrainment 1. Laboratory kinetic test interpretations generally assume that the degree of entrainment is the same for all species. This does not constitute a significant error in the model as the recovery by entrainment is generally a small value.

The Re can be determined from the Degree of Entrainment which is the ratio of solids recovered by entrainment to that of water. The relationship is D.E. = Rs/Rw. This relationship has been studied extensively in industrial plants and databases are readily available to the public domain, and appear in summarized form in Figure 2-4.

1

The Degree of Entrainment, DE is the ratio of solids recovered to the water recovery and is a function of particle size, specific gravity and density of the froth. P.O. Box 296 - Garibaldi Highlands, BC - Canada, V0N 1T0 Email : [email protected] - Tel/FAX : (1-604) 898-1111

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Figure 2-4

Relationship between D.E. and P80

0.35 0.3

y = -0.0777Ln(x) + 0.5478 0.25

m n i a r t n 0.2 E f o e 0.15 e r g e D 0.1

Primary Regrind

y = -0.0791Ln(x) + 0.5555 0.05 0 0

50

100

150

200

250

P80

The entrainment model tells us that very fine particles get swept into the concentrate at similar rates water is recovered. However, the coarser particles are less likely to entrain than the finer ones. By knowing this relationship and knowing the size distribution of the material floated, the user can estimate (with the commercial graph above) the overall amount of solids that will be recovered with the water. The model assumes that for solids to float by entrainment, material must have floated by collection. In fact, only the solids remaining in the cell after the collection process has taken place are eligible for recovery by entrainment. The Rs, may be determined by knowing the recovery of water, Rw, and by reading off the degree of entrainment in Figure 2-4.

2.2

The Aminpro-Flot Models’ scale-up procedures

The manners in which collection zone kinetics from a laboratory test are applied to a plant environment follow the steps shown in Figure 2-5. Whereas from the lab test we obtain the total recoveries defined by (Eq.4), we then need to determine the recoveries by entrainment in order to define the collection recoveries


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Figure 2-5

The Basic Procedure of Using Lab data to Define Plant Performance Total Recovery - Entrainment kinetics

Collection Recovery

Collection Recovery + Entrainment Total Recovery C1

C

C

2

3

C4

LAB Feed

Plant

In the plant we do the reverse: we start by estimating the collection zone recoveries (using the lab kinetics) and we then add the entrainment recoveries. Lab entrainment values are markedly different from those encountered in the plant. The difference is because in the plant, cells operate with larger froth beds, which allows the water to drain back into the pulp resulting in lower recoveries by entrainment. This is the main reason why laboratory generated Grade-Recovery curves should never be considered a reflection of a plant operation. The Aminpro-Flot Simplex (AFS) model works on the basis of utilizing the laboratory kinetics ( Rmax and k) determined for each mineral from the lab test. It applies these values to a first order reactor (continuous flow) model shown in Equation 2, again, to each mineral. The plant model is then constructed by applying a Re calculated from well established industrial models and varying the Fr so that it generates a grade-recovery curve.

The froth recovery ( Fr), as explained earlier, is a parameter synonymous to the degree of pull in a flotation cell. It is like raising the air rate to “pull” harder or to raise the pulp level. Extensive research is ongoing relating froth recoveries and degree of entrainment. Modelers vary the froth recovery of a flotation circuit to generate a graderecovery curve. It works as follows: by varying the froth recoveries on a rougher bank, for instance, we obtain a series of performance points. In other words, we obtain a grade-recovery curve for that section. Figure 2-6 shows for a particular ore the Recovery-Time curve for a rougher lab test for gold, a copper mineral and Molybdenite. It also shows the Recovery-Time curve for plant conditions but at P.O. Box 296 - Garibaldi Highlands, BC - Canada, V0N 1T0 Email : [email protected] - Tel/FAX : (1-604) 898-1111

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Minpro


various froth recovery levels using the kinetics (k and Rmax) obtained from the lab test. By estimating the curves for all the remaining minerals, the weights recovered of each mineral (including gangue) can be calculated and the grade of each mineral in the concentrate can be calculated. Figure 2-6 Roughers: Lab Kinetics vs Plant Performance @ P80=150 microns, PHB Ore

100 90

LAB TEST

80 70

% , s e i r e v o c e R

60

Froth Rec

50 40 Plant Performance

30 20

Test-Au Test-Cu Test - Mo

10

Au = 25 Cu = 25 Mo = 25

Au = 35 Cu = 35 Mo = 35

Au = 55 Cu = 55 Mo = 55

Au = 85 Cu = 85 Mo = 85

0 0

5

10

15

20

25

30

35

40

45

50

Flotation Time, min

The plant models the performance of every flotation cell in a row. That is, for each cell, the minerals recovered are calculated. From here the weight of minerals going to tails are determined, which become the feed for the next cell. It is understood that when a mineral has an Rmax of say 90%, that 10% of that mineral is not eligible for recovery through collection but is available to be recovered by entrainment. The model diligently keeps track what is available for flotation and what is not, both in the concentrate and in the tails, cell by cell. In the end, the quantity of concentrate in a row of cells is added up (floatables and non-floatables) and the tailing is determined by the difference.

An example has been developed to provide the reader an idea of the calculations involving 3 minerals. For this example, the first cell of a row has been modeled. The reader must understand that the second cell undergoes the same calculations on the tailings of the 1 st cell. The example assumes that the froth recovery is 100%.


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In this example, the laboratory testwork showed the following:

Description

Modeling 3 minerals 100 microns

Grind P80 =

CuFeS2 1.0 0.7 90

Grade k Rmax

Pyrite 4.0 0.4 60

Gangue 95.0 0.08 20

total Weight 100.0

We will assume that the flotation time of the first cell is 5 minutes and that the grind is P80=100 microns. The estimates proceed as follows:

Operation P80 b

Description

Modeling 3 minerals 100 microns 1%

Grind P80 = Water Recovery,Rw = Assuming 100% Froth Recovery

c d e

Grade k Rmax

g

CuFeS2 1.0 0.7 90

Pyrite 4.0 0.4 60

Gangue 95.0 0.08 20

Pyrite 40.0 4.0 2.4 1.6 4.0

5 min Gangue 5.7 95.0 19 76.0 95.0

Flotation time =

h = dg/(1+dg)*e/100 %Recovery a Feed weights j = ce/100 Available for Flotation k = c-j Non Floatable in feed j+k Total in Feed

CuFeS2 70.0 1.0 0.9 0.1 1.0

total Weight 100.0

115.7 100.0 22.3 77.7 100.0

The recovery has been estimated for each mineral, from equation 2 and 3, at a Fr=100%. The calculations are done on the percentages as if they represent weights. Note that from the start the floatable and non-floatable minerals are tracked. The next step is to estimate recoveries by entrainment.


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Minpro


L=hj/100 T1 = a-L T2 = j-L k

TAILS before ENTRAINMENT Recovered by Collection Left in tailing Portion in tails Floatable Portion in tails Non-Flot

f

Degree of entrainment, D.E. =

fb T1 * fb T2 * fb k * fb

Rs = D.E * Rw = Wt Recovered by Entr Portion Floatable Portion Non - Flot

CuFeS2 0.63 0.37 0.27 0.10

Pyrite 0.96 3.04 1.44 1.60 0.19

0.190 0.070 0.051 0.019

Gangue 1.09 93.91 17.91 76.00

total Weight 25.80 97.3 19.6 77.7

from graph at P80=100

0.190 0.578 0.274 0.304

0.190 17.844 3.404 14.440

18.5 3.7 14.8

In order to estimate entrainment recoveries, the program seeks to define the character of tails remaining after collection has taken place. The model then estimates the solids recovered from tails (Rs) by determining the degree of entrainment from Figure 2-4 (which is shown as an oversimplified plot of the industrial models) and using the water recovery into the concentrate. This value can be used from what was found in the lab or can be assumed from industrial experience. The next step is to calculate the concentrate recovered, both by collection and by entrainment. From here, the grades are estimated. Note that the Rmax values for the products may be calculated for use in a subsequent stage. The Aminpro models assume the Rmax values and keep the flotation rate constants as per lab test.

CONCENTRATES C1 = L+ (T1 * fb) Total Wt Recovered C2 = k * fb Tot Non Flot Recovered C3 = C1-C2 Tot Floatables Recovered

CuFeS2 0.70 0.02 0.68

Pyrite 1.54 0.30 1.23

Gangue 18.93 14.44 4.49

C3/C1

Conc Grade Rmax of Concentrate

3.3 97.3

7.3 80.2

89.4 23.7

T5 =a - C1 T6 =k - C2 T7 = j - C3

TAILING Weight Rec to Tails Total non Flotatable Total Flotables

0.30 0.08 0.22

2.46 1.30 1.17

76.07 61.56 14.51

Tail Grade Rmax Tails

0.38 73.0

3.12 47.4

96.50 19.1

T7/T5


total Weight 21.2 14.8 6.4 Calc by weight

78.8 62.9 15.9 Calc by weight

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By applying different froth recoveries, the model provides various concentrate grades and recoveries that can be plotted as a grade-recovery curve. If the concentrates are re-floated in a new stage where no chemical changes and no re-grinding have taken place, the kinetics of those streams is considered unchanged. If a stream is treated with chemicals or becomes affected by a regrind, the kinetics of that stream needs to be re-determined in the laboratory at those operating conditions. Similarly, if we want to deliver a grade-recovery curve for the cleaners, suffice to “pull” or change the froth recoveries in the cleaners as you would in an actual circuit to examine the resulting grade recovery curves. Therefore, it is not necessary to know the exact froth recovery value in a section as it is a flotation control mechanism. In fact, one can define the best operating point on the graderecovery curve by examining the Net Smelter Return per ton of plant feed at various Fr. When two streams join, the new grades and kinetic values may be computed. The calibration of a model takes place when we make a search for D.E. and Fr so that the mass balances for all minerals in the model and actual plant are the same. This is done with the help of the Solver function in Excel spreadsheets. In cases of Greenfield projects, the model is calibrated against locked cycle tests and/or pilot plant runs. The AFS model works because the relative kinetics seen between minerals in the laboratory behaves similarly in a real plant. What makes one model better than another is the manner in which entrainment is applied both to the lab results and the plant model.

2.3

The Aminpro-Flot AF modeling procedures

The modeling procedures for the AF model are the same as those explained for the AFS model. The modeling is simpler in that the many size classes lend themselves better for the estimation of recoveries by entrainment. The model, like the AFS, estimates the recoveries cell by cell keeping track (Figure 2-7) of the tonnages floated or rejected in each size class. P.O. Box 296 - Garibaldi Highlands, BC - Canada, V0N 1T0 Email : [email protected] - Tel/FAX : (1-604) 898-1111

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Figure 2-7

Sampling of tables within the AF model Feed Tonnages Au

Low range 360 275 226 192 167 147 131 117 106 95 86 78 71 65 59 54 49 45 37 1

U. range 642 360 275 226 192 167 147 131 117 106 95 86 78 71 65 59 54 49 45 37

0.46 0.13 0.12 0.11 0.11 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.08 0.08 0.17 1.44

1

T racker2

Spare1

Spare2

Spare3

Spare4

T/h minerals Assays can be determined from the totals

3.71

0.00

0.00

0.00

0.00

0.00

Rmax L end

Mi ds iz e 360 275 226 192 167 147 131 117 106 95 86 78 71 65 59 54 49 45 37 1

501 317 251 209 180 157 139 124 111 100 91 82 75 68 62 57 52 47 41 19

Au

T rac ker2 0.0 0.0 14.8 28.3 38.7 47.2 54.3 60.5 65.9 70.7 75.0 78.7 82.1 85.1 87.7 90.0 92.0 93.7 95.6 93.2

Sp are1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

CuFeS2

S pa re2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

S par e3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Screen Info

S pare4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Cu FeS 2 59.1 71.5 77.0 80.8 83.7 86.0 88.0 89.7 91.2 92.5 93.6 94.6 95.4 96.2 96.9 97.4 97.9 98.2 98.6 96.7

F eS2 1 00.0 100.0 1 00.0 1 00.0 98.8 89.7 81.8 74.9 68.7 63.2 58.1 53.4 49.2 45.2 41.6 38.2 35.1 32.2 28.5 18.4

F e- Ox 12.0 7.6 5.8 4.5 3.6 2.9 2.3 1.8 1.4 1.1 0.8 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.3 2.7

G an ga 11.4 7.6 6.0 4.8 3.9 3.2 2.7 2.2 1.7 1.4 1.1 0.8 0.5 0.3 0.2 0.0 0.0 0.0 0.0 0.7

water t/h Fe-Ox

FeS2

2,433 Ganga

0.03 0.10 0.20 0.30 0.39 0.48 0.56 0.64 0.70 0.76 0.80 0.85 0.88 0.91 0.93 0.95 0.96 0.97 1.95 15.65

0.00 0.00 0.03 0.13 0.32 0.58 0.87 1.17 1.45 1.69 1.87 2.01 2.09 2.13 2.13 2.10 2.04 1.96 3.62 14.41

0.37 1.05 1.75 2.41 3.04 3.61 4.14 4.63 5.07 5.48 5.85 6.18 6.48 6.75 6.99 7.20 7.38 7.55 15.48 156.22

46.58 26.07 23.62 22.24 21.34 20.70 20.23 19.87 19.60 19.38 19.22 19.09 19.00 18.93 18.89 18.87 18.87 18.89 37.89 491.50

29.01

40.61

257.61

920.77

RATE CONSTANT Au T ra ck er 2 4.43 2.34 1.56 1.10 0.78 0.55 0.38 0.25 0.16 0.09 0.05 0.02 0.00 0.00 0.01 0.03 0.05 0.09 0.15 0.52

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

S p ar e1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

S pa re 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

S pa re 3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Water Balance

Total Stream Tonnage

1248.00

S pa re 4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

C u Fe S2 5.96 1.86 0.73 0.26 0.08 0.08 0.18 0.36 0.59 0.87 1.17 1.49 1.84 2.19 2.55 2.91 3.28 3.64 4.14 5.66

F eS 2

F e- Ox

6.00 1.66 0.55 0.13 0.01 0.06 0.19 0.39 0.63 0.88 1.15 1.42 1.69 1.94 2.17 2.38 2.55 2.69 2.79 0.22

Kinetics

The calculations are done down the bank of cells, facilitating any investigation as to the optimum number of cells one should use. The tracking (Figure 2-8) of information is done on a size-by-size basis.


14

0.32 0.17 0.13 0.11 0.10 0.10 0.10 0.10 0.10 0.11 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.01

G an ga 0.06 0.09 0.08 0.08 0.07 0.06 0.06 0.05 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.00 0.00 0.06

Minpro


Figure 2-8

The Aminpro Flot Tracking of Information – Cell by Cell and Size by Size C uF eS 2

CONC1 FEED 1 C uF eS 2

F eS 2

w at er t /h F e- Ox

2 ,4 33 G an ga

0 .03 0 .10 0 .20 0 .30 0 .39 0 .48 0 .56 0 .64 0 .70 0 .76 0 .80 0 .85 0 .88 0 .91 0 .93 0 .95 0 .96 0 .97 1 .95 1 5. 65

0 .0 0 0 .0 0 0 .0 3 0 .1 3 0 .3 2 0 .5 8 0 .8 7 1 .1 7 1 .4 5 1 .6 9 1 .8 7 2 .0 1 2 .0 9 2 .1 3 2 .1 3 2 .1 0 2 .0 4 1 .9 6 3 .6 2 1 4. 41

0. 37 1. 05 1. 75 2. 41 3. 04 3. 61 4. 14 4. 63 5. 07 5. 48 5. 85 6. 18 6. 48 6. 75 6. 99 7. 20 7. 38 7. 55 1 5. 48 1 56 .2 2

4 6. 58 2 6. 07 2 3. 62 2 2. 24 2 1. 34 2 0. 70 2 0. 23 1 9. 87 1 9. 60 1 9. 38 1 9. 22 1 9. 09 1 9. 00 1 8. 93 1 8. 89 1 8. 87 1 8. 87 1 8. 89 3 7. 89 4 91 .5 0

29.0 1

40.6 1

257.61

920.77 1248.00

F eS 2


3 1. 6 G an ga

0 .0 12 0 .0 42 0 .0 53 0 .0 38 0 .0 19 0 .0 22 0 .0 57 0 .1 17 0 .1 91 0 .2 68 0 .3 43 0 .4 14 0 .4 77 0 .5 34 0 .5 83 0 .6 25 0 .6 60 0 .6 88 1 .4 36 1 2. 15 6

0 .0 00 0 .0 02 0 .0 09 0 .0 12 0 .0 03 0 .0 20 0 .0 87 0 .1 93 0 .3 09 0 .4 14 0 .4 93 0 .5 42 0 .5 63 0 .5 61 0 .5 40 0 .5 06 0 .4 64 0 .4 17 0 .6 92 0 .4 21

0 .0 08 0 .0 09 0 .0 09 0 .0 08 0 .0 08 0 .0 07 0 .0 06 0 .0 06 0 .0 05 0 .0 05 0 .0 04 0 .0 04 0 .0 03 0 .0 03 0 .0 04 0 .0 05 0 .0 06 0 .0 08 0 .0 24 0 .7 27

0. 230 0. 116 0. 081 0. 057 0. 041 0. 030 0. 021 0. 015 0. 010 0. 007 0. 005 0. 005 0. 005 0. 006 0. 007 0. 010 0. 013 0. 017 0. 048 2 .3 27

18.74

6.25

0.86

3. 05

Aminpro MODEL - 2005 CONC2 C uF eS 2

28.89

FEED2 C uF eS 2

F eS 2

wate r t/h F e- Ox

2401.78 G an ga

0. 01 0. 06 0. 15 0. 26 0. 38 0. 46 0. 51 0. 52 0. 51 0. 49 0. 46 0. 43 0. 40 0. 37 0. 35 0. 32 0. 30 0. 28 0. 51 3 .5 0

0.00 0.00 0.02 0.12 0.32 0.56 0.79 0.98 1.14 1.27 1.38 1.47 1.53 1.57 1.59 1.59 1.57 1.54 2 .9 3 1 3. 99

0.36 1.04 1.74 2.41 3.03 3.61 4.14 4.62 5.07 5.47 5.84 6.17 6.48 6.74 6.98 7.19 7.38 7.54 1 5. 45 1 55 .5 0

46.35 25.96 23.54 22.18 21.29 20.67 20.21 19.86 19.59 19.37 19.21 19.09 18.99 18.93 18.88 18.86 18.86 18.87 3 7. 84 4 89 .1 8

1 0. 2 7

3 4. 37

2 56 .7 5

9 17 .7 2 1 21 9. 11

TAIL1


2 5. 0 G an g a

0.0023 0.0181 0.0350 0.0323 0.0179 0.0213 0.0514 0.0943 0.1350 0.1666 0.1882 0.2011 0.2074 0.2090 0.2073 0.2034 0.1979 0.1916 0.3629 2.4122

0.0000 0.0008 0.0068 0.0107 0.0031 0.0192 0.0773 0.1521 0.2155 0.2553 0.2718 0.2702 0.2565 0.2360 0.2124 0.1882 0.1650 0.1437 0.2331 0.3622

0.0067 0.0079 0.0081 0.0077 0.0072 0.0067 0.0061 0.0055 0.0049 0.0043 0.0037 0.0033 0.0030 0.0030 0.0033 0.0039 0.0050 0.0066 0.0196 0.5866

0.2226 0.1105 0.0770 0.0551 0.0398 0.0288 0.0206 0.0145 0.0101 0.0071 0.0051 0.0041 0.0040 0.0046 0.0059 0.0079 0.0105 0.0136 0.0386 1.8800

4. 96

3.08

0.70

2.56

CONC3 C uF eS 2

11.30

FEED3 C uF eS 2

TAIL2

Aminpro – Flot repeats the calculation if more cells are in a row.

F eS 2

F eS 2

wate r t/h F e- Ox

2376.80 G an ga

0.01 0.04 0.11 0.23 0.36 0.44 0.46 0.42 0.37 0.32 0.27 0.23 0.20 0.17 0.14 0.12 0.10 0.09 0 .1 5 1 .0 8

0.00 0.00 0.02 0.11 0.31 0.54 0.71 0.83 0.93 1.02 1.11 1.20 1.27 1.33 1.38 1.40 1.41 1.40 2 .7 0 1 3. 63

0. 35 1. 03 1. 73 2. 40 3. 02 3. 60 4. 13 4. 62 5. 06 5. 47 5. 84 6. 17 6. 47 6. 74 6. 98 7. 19 7. 37 7. 53 1 5. 43 1 54 .9 1

46.13 25.85 23.46 22.12 21.25 20.64 20.19 19.84 19.58 19.37 19.21 19.08 18.99 18.92 18.88 18.85 18.85 18.86 3 7. 80 4 87 .3 0

5 .3 2

3 1. 29

2 56 .0 5

9 15 .1 6 1 20 7. 81


0 .0 0 00 0 .0 0 03 0 .0 0 49 0 .0 0 98 0 .0 0 31 0 .0 1 86 0 .0 6 84 0 .1 1 94 0 .1 4 91 0 .1 5 64 0 .1 4 87 0 .1 3 35 0 .1 1 58 0 .0 9 85 0 .0 8 29 0 .0 6 96 0 .0 5 85 0 .0 4 95 0 .0 7 90 0 .3 2 05

0 . 00 5 5 0 . 00 7 1 0 . 00 7 4 0 . 00 7 2 0 . 00 6 8 0 . 00 6 3 0 . 00 5 7 0 . 00 5 2 0 . 00 4 6 0 . 00 4 0 0 . 00 3 5 0 . 00 3 1 0 . 00 2 8 0 . 00 2 9 0 . 00 3 2 0 . 00 3 8 0 . 00 4 9 0 . 00 6 5 0 . 01 9 3 0 . 58 4 5

0 .2 1 50 0 .1 0 50 0 .0 7 32 0 .0 5 26 0 .0 3 82 0 .0 2 77 0 .0 1 99 0 .0 1 41 0 .0 0 99 0 .0 0 70 0 .0 0 51 0 .0 0 41 0 .0 0 40 0 .0 0 46 0 .0 0 59 0 .0 0 79 0 .0 1 05 0 .0 1 36 0 .0 3 85 1 .8 6 80

1.60

1.69

0.69

2.52

F eS 2

water t/h F e- Ox

6.51

2352.08 G an ga

0.01 0.04 0.09 0.20 0.34 0.42 0.41 0.35 0.28 0.22 0.17 0.13 0.11 0.08 0.07 0.05 0.04 0.04 0 .06 0 .6 1

0.00 0.00 0.01 0.10 0.31 0.52 0.64 0.71 0.78 0.86 0.96 1.06 1.16 1.24 1.30 1.33 1.35 1.35 2.6 2 1 3. 31

0.35 1.02 1.72 2.39 3.02 3.59 4.12 4.61 5.06 5.46 5.83 6.17 6.47 6.74 6.98 7.19 7.37 7.52 15 .41 1 54 .3 3

45.92 25.74 23.39 22.07 21.22 20.61 20.17 19.83 19.57 19.36 19.20 19.08 18.99 18.92 18.87 18.84 18.84 18.84 3 7. 76 4 85 .4 3

3 .7 2

2 9. 60

2 55 .3 5

9 12 .6 3 1 20 1. 30

3 Users The current Aminpro-Flot models have been developed since 2003, after Minnovex’s FLEET model was created (Of which Aminpro was contracted to oversee the technical aspects). Contrary to FLEET, the kinetic distributions on the AF model are directly related to particle size and are not in an abstract form as FLEET, In addition, both the AFS and AF models will handle variables such as pH, head grade, etc. The AF model has an inherent grind model built in by virtue of tracking 20 size classes. The Aminpro flotation models are being used with more frequency as they become known. A sampling of the users:


2 4. 7 G an ga

0 . 00 0 4 0 . 00 7 7 0 . 02 3 0 0 . 02 7 4 0 . 01 7 1 0 . 02 0 4 0 . 04 5 8 0 . 07 5 3 0 . 09 5 0 0 . 10 2 9 0 . 10 2 3 0 . 09 6 9 0 . 08 9 3 0 . 08 1 0 0 . 07 2 9 0 . 06 5 5 0 . 05 8 7 0 . 05 2 8 0 . 09 0 7 0 . 47 4 4

C uF eS 2

TAIL3

F eS 2

15

Minpro

• • • • • • • • • • • • • •


Codelco -Teniente – Moly Plant (2004-2005) Newmont - Conga (2004) Newmont – Carlin (2005) Northern Orion – Agua Rica Project (2006) Ivanhoe Mines – Oyu Tolgoi (2006-2007) BHP-Nickel – Contact Cell work (March 2007) Newmont-Boddington-Moly (Future) BHP-Tintaya (2003) Pelambres (2003) KCM- Nachanga (2003-2004) KCM-Konkola Copper (2003-2004) Xstrata-El Morro (April) 2007) Ucchu-Chacua Pb/Zn (2003) PD: Bagdad Copper – Contact Cell work (2003)


16

A Model for Flotation Processes, AMINPRO, August 2007

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