ZA200904464B - A method of obtaining data for use in the design of a grinding mill circuit - Google Patents

Description

EE | Page 2 ) BACKGROUND OF THE INVENTION | | | | | I

[0001] This invention relates to the design of a grinding circuit for a grinding - mill and more particularly is concerned with a method of obtaining data for use i in the design process.

[0002] An attractive feature of autogenous and semi-autogenous grinding mills is that they can be fed directly with coarse ROM (run-of-mine) ore with 80 per cent passing sizes often in excess of 150 mm. This obviates the need for complex multi-stage crushing and screening plants prior to milling, although a primary crusher and grizzly are often needed to constrain the feed to a top size that can be easily handled and transported to the mill. Large rocks in the ROM ore serve as grinding media that can self-break and also break ore in intermediate and fine sizes. For some ores, effective grinding can occur without the need for steel grinding balls. Such balls are however often added to prevent the build-up of so-called critical sizes that do not easily self-break and cannot be efficiently broken down by the largest rocks in the mill. The bulk volume of the balls added is typically a few per cent of the internal mill volume, but can be as high as thirty per cent.

[0003] Although semi-autogenous grinding appears to be a very simple way of achieving large size reduction ratios in a single unit, the design of grinding circuits incorporating SAG mills is not a trivial task. One approach is to conduct tests at pilot scale using ROM ore with the same size distribution and composition as the ore likely to be encountered at production scale. Based on : piloting tests conducted over an extended period, it has been found that data

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BE Page 3 ; generated from a SAG mill with an internal diameter of 1.7 m can provide a good indication of the performance of production mills.

[0004] For pilot mills with internal diameters close to 1.7 m, the net specific energy remains essentially invariant to scale-up for a given circuit

ES) configuration and grind size and the design of circuits is relatively straightforward. However, even at pilot scale it ” a costly exercise to explore all grate/liner geometries, operating conditions, and circuit configurations to establish optimal design parameters. Piloting tests can result in the consumption of hundreds of tons of ore. Accordingly, there is considerable incentive to develop test procedures that require far less ore and mathematical models that can be used to accurately extrapolate and interpolate test data using computer simulation techniques.

[0005] Existing test procedures for the design of AG and SAG milling circuits, based on limited sample masses, rely heavily on the application of laboratory : 15 tumbling tests on mono-sized rocks in small mills (nominally 300 mm diameter) to simulate abrasion effects inside a SAG mill, and dropweight tests on individual rocks to simulate impact modes of breakage. These tests hardly reflect the grinding environment in a real AG/SAG mill involving a wide spectrum of particle and rock sizes. Accordingly, strong reliance is placed on the development of empirical correlations linking parameters derived from the tests with the performance of production scale circuits. This calls for a historical database of production information on ores that have previously been tested using the same procedures. If a match cannot be made between

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. the test data and data in the production database, then the design of the circuit for the ore tested becomes a risky exercise. ] [0006] The invention aims to provide a method of obtaining data for use in the design of a grinding circuit which, at least partly, addresses the aforementioned problems.

SUMMARY OF THE INVENTION

[0007] The invention provides a method of obtaining data for use in the design of a grinding circuit for a grinding mill which includes the steps of: a) providing a pilot scale mill with at least one discharge grate; b) charging the mill with ore and steel bails to provide an initial static loading of from 30% to 60% of the mill volume;

Cc) operating the mill to achieve grind-out of the material in which a material particle size is smaller than an aperture size of the discharge grate to provide material discharge through the grate; d) determining the power which is drawn by the mill during this operation; e) monitoring the size distribution and flow rate of the material discharged through the grate; f) crash-stopping the mill when the mill loading is reduced to a predetermined level, and

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. a) using the data obtained at least from steps d, e and f to calculate a cumulative breakage rate function that characterizes breakage kinetics of the material inside the mill and a specific discharge rate function that characterizes - 5 transport behaviour of particles of the material flowing through the discharge grate.

[0008] The pilot scale mill represented in Figure 1 may have a diameter of from 0,6 meters to 1,7 meters.

[0009] The mass of the run-of-mine ore, charged into the mill in step b, may vary according to requirement and may range from 80kg to 500kg dependent, inter alia, on the size of the pilot scale mill. PQ Drill cores can also be used for the test.

[0010] In step b the static loading of the mill may be of the order of 45% of the mill volume.

[0011] In step f the mill may be crash-stopped when the mill loading is reduced to a charge load which is equivalent to a static volumetric loading of about 35%.

[0012] In a variation of the invention to obtain data which approximates the performance of the grinding circuit with a continuous ore feed, the mill is subjected to a locked-cycle test. In this variation, in step ¢, the mill is operated for a predetermined time period or specific energy and, thereafter: h) the material discharged through the grate is collected,

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] i) the collected material is screened and oversized particulate material is returned to the mill; ); fresh ore according to feed distribution is added to the mill to bring the mass of ore inside the mill to the initial charge mass; and k) steps h andi are repeated to achieve steady state conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The invention is further described by way of examples with reference to the accompanying drawings in which:

Figure 1 schematically represents components of a mill used with a grate discharge,

Figure 2 is a curve of mass fraction in size class versus particle mesh size and illustrates the concept of a cumulative breakage rate function,

Figure 3 is a curve of a cumulative specific breakage rate versus particle mesh size obtained from operation of a pilot mill,

Figure 4 shows specific discharge rates as a function of particle size for a pilot mill,

Figure 5 illustrates a comparison between the cumuiative breakage rates as a function of particle size for a laboratory mill (diameter 0.6m) and pilot mill © (1.7m of diameter) using a UG2 ore in similar conditions, and

Figure 6 shows specific discharge rates as a function of particle size for laboratory and pilot SAG mills.

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. DESCRIPTION OF PREFERRED EMBODIMENT

[0014] The method of the invention is based on conducting tests on a pilot “scale mill to produce data which allows a cumulative breakage rate function and a specific discharge rate function to be determined. As these functions are essentially invariant to scale-up they can be used to model directly the steady state and the dynamic behaviour of a production mill circuit without : undue reliance on a historical database.

[0015] Figure 1 depicts components of a grind mill chamber used for the investigative work referred to herein. The Figure has a side and isometric views of a mill chamber 10, a view in elevation of a grate discharge 12, and a plan view and a side view of structure 14 which forms an opening area 16.

[0016] By way of example only the mill chamber has an internal diameter of 600 mm and an inner length of 485 mm. Fixed internally to the mill chamber are twelve rectangular lifters 18 each of a height of 22 mm and a width of 12 mm.

[0017] For the test work referred to herein the mill was operated semi- continuously. Ore was loaded into the chamber through the opening 16. With the mill running material was discharged from the chamber through the grate discharge 12 which was operable in a controlled manner to vary the grade size, the open area and discharge arrangement.

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} THEORETICAL CONSIDERATIONS

[0018] The specific cumulative breakage rate function, X i" [h]" is defined as } the fractional rate at which particles of a given rock type, k above a given size, x, in the mill break to below that size per unit time. A transformation relationship is used to define an energy-based cumulative breakage rate function, X/, [KWhAT*, which involves the mass of the ore in the mill, M [t] and the net mill power, P[kW] (XK =(M/P)K,,). Consider the fractional rates at which particles above sizes x; and x,,, break to below these sizes, as indicated in Figure 2. Let the total or cumulative masses above these sizes inside the mill be W, and W,,, respectively. If the mill is operated in a simple batch mode the rate of change of mass for particles in size class i and rock type k is given by: accumulation = consumption above size x; — consumption above size x, dw, , P P (1) : — =W, or Kia “Wik 7 Kio it follows that a single function can be used to uniquely quantify breakage kinetics in a SAG mill and to establish a mass balance for material within a given size class.

[0019] Consider a population balance for a continuously fed mill for particles in size class 1 (whose upper mesh size is equal to or greater than the largest particle in the feed) and rock type k. If there are no particles coarser than size x, the specific breakage rate of particles coarser than this size, KX, is

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. undefined. It follows that the population balance equation with respect to time for size class 1 is given by: . accumulation = in — out — consumption dw, .) P cereeerirrreree nein eee (2) — =F =P Wy 27 Ko where F,, and P,, are the cumulative mass flows of material coarser than size x, in the feed and product streams, respectively. For the first size class

Equation 2 is identical to: accumulation = in — out — consumption — = fix —8isWix “Wik 7 Kas

The first term on the right-hand side of Equation 3 gives the flowrate of size class 1 and rock type k into the mill. The second term expresses the discharge flow rate in terms of the value of the specific discharge function and mass holdup for size class 1 and rock type k. The third term in Equation 3 assumes that breakage rates are proportional to the product of the specific power input and the mass of size class 1 material inside the mill. When expressed in this form, the energy-based specific breakage rate function,

K/, [kWh]! is assumed to be insensitive to scale-up. It should be noted that the power draw of the mill is strongly dependent on the hold-up of rock and pebbles inside the mill, which makes it necessary to solve this equation by numerical methods.

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. The accumulation or rate of change of the holdup of material coarser than x, (i=23---,n—-1) is given by: dW) Po. —= =F,-P,-W, Kl eee (8) where the first term on the right hand size of this equation is the inlet flowrate of rock type k coarser than size x, and the second term is the discharge flowrate of material coarser than size x,. The third term is the rate at which material coarser than size x, breaks to below this size. A similar equation can be applied to material coarser than size x, : dw, ) P a — = Fis - Po, “Wx ALL ee eeeeesreeaeeaeasttatetntinnranns (5)

Subtracting Equation 4 from Equation 5 gives the accumulation of material within size class i: accumulation = in — out + (generation — consumption) aw, P P _. ] een (B) — = fix —8ixWixt fw 7 Ki ~(w, + Wi, )— Ki

The mass balance for particles in size class n (the sink interval with particle sizes between zero and x, ) is given by: dw,,) P —r = Ju — ui Wai + Wok — Ko eee (1)

These equations can be solved numerically to simulate both the dynamic and steady state behaviour of the mill for any circuit configuration.

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. : The total mass of ore inside the mill are functions of the hold-ups of particles of all rock types and all sizes, which makes in necessary to solve Equations 3, 6 and 7 by numerical methods. A model equation which is available in the literature for predicting the power draw, is: n n 0.1

P=106D"LA-1.03)[1-5.)p,/w)J +0.6J,(p; - p, rle1- 5 (8) where J and J, are the static fractional volumetric filling of the mill for the total charge and for the balls, respectively. The effective porosity of the charge is given by &, and w, is the weight of the ore expressed as a fraction of the total mass of ore and water in the mill. The density of the balls and average density of the ore [t/m?] are given by p, and p,, respectively, and ¢, is the mill speed expressed as a fraction of the critical speed.

The cumulative rates model caters for the effects of different aspect ratios (D/L) when scaling up pilot data by treating the production mill as a number of fully mixed reactors in series with back-mixing between adjacent reactors.

It can be shown from Equations 3, 6 and 7 for the population balance for the solids that the cumulative specific breakage rate function can be obtained directly from data generated from a continuously operated mills or from batch grind-out or locked cycle tests. By definition, there are no particles coarser than x,, so Kis undefined. The specific breakage rates for particles coarser than size x, (particles in size class 1 only) can be obtained at steady state by equating the derivative in Equation 3 to zero and rearranging terms:

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KE, IP (0) w, PIM

After equating the derivatives to zero in Equation 6, values for the cumulative breakage rate function can be calculated recursively for i=2,3,...,(n -1): =p. +W, (PIM)KE ke Jum Pu tM, PIDK, 40) (wy WPM

From Equation 7 (for i = n):

Kb ode Pa a) “WPM

All the terms on the right hand side of Equations 9, 10 and 11 are directly measurable.

[0020] Although the equations have been derived for a continuously fed mill they can also be applied to data generated from a locked-cycle or grind-out test. In the case of the grind-out test (where no new feed is added) the terms which involve new feed are equated to zero.

Measured Breakage Rate and Discharge Functions

[0021] Cumulative specific breakage rate functions and specific discharge functions for SAG were measured using a pilot SAG mill. The mill had instrumentation for monitoring shaft torque and mill speed. These measurements permit the accurate estimation of the mechanical power transmitted to the mill charge. The mill and its drive were mounted on four load cells to allow the accurate measurement of the total mass of the charge

D1:P21662/bjt inside the mill to within an accuracy of about + 2 kg. The mill was fitted with advanced control software to provide accurate control of the charge mass inside the mill and the size distribution of the feed.

[0022] Figure 3 shows four replicate measurements obtained from pilot tests conducted on a gold ore. The mill was operated in closed circuit with a : double-deck screen with mesh sizes of 6.7 mm for the upper deck and 1.18 mm for the bottom deck. The grate was fitted with pebble ports. Ejected pebbles were crushed and recycled back to the mill. The (-6.7 + 1.18) mm and -1.18 mm material served as feed to a secondary ball mill operated in closed circuit. The fitted continuous curve in Figure 3 is given by:

LTC (12)

SETI ayn TR UNTO UURPUPPUROUPT where «,,,k,,,a,,%,,,M, and A, } are parameters that must be estimated by regression. Particle size is usually expressed in terms of the geometric mean size for a given size class, x, [mm]. The first term on the right hand side attempts to account for both attrition breakage at fine sizes and abrasion breakage at intermediate sizes. The second term accounts for the effects of self-fracture, which becomes dominant at coarse rock sizes (typically above 100 mm).

[0023] Figure 4 shows replicate measurements obtained from the same tests for the specific discharge rate function. The fitted continuous curve is given

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. CT Page 14 . by: g.,=d,.. XxX <x,

Zip = do (1+ (1-7, )n(x,) = In(x,)) (n(x, ) = In(x,))) x, <ZX, <x, (13) ; Zip =, (f, (n(x) = In(x;)) /(In(x,) = In(x,))) : X, <X; <x, gp =0 ;%>x,

In this equation, it is assumed that the specific discharge rates for particles up to size x, (about 1mm) are constant with a value d_ [h]". Above this size

SI the specific discharge rate decreases monotonically with increasing particle with a change in slope at the mesh size of the grate apertures, x, [mm], and has a value of zero at the mesh size of the pebble ports, x, [mm]. The parameter f, relates to the relative open areas of the grate apertures and pebble ports.

[0024] Although the measured cumulative breakage rate and specific discharge rate functions follow clear trends, it is evident that it is very difficult to get a high level of precision from a single pilot campaign. This lack of precision is attributed to the difficulty of getting an accurate estimate of the average charge size distribution over the period of the campaign, which is typically an eight-hour shift of steady-state operation. Although it is possible to take composite stream samples over this period, it is impractical to extract composite samples of the mill charge. The charge mass, size distribution and composition are measured only at the end of each campaign. This makes it difficult to establish with a high level of precision the average response of the specific discharge and cumulative breakage rate function to changes in operating conditions, such as feed size, ball load, and rock load.

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: [0025] To establish a better quantitative understanding of how the cumulative breakage rate and discharge functions change. with changes in operating conditions, batch test procedures were developed using laboratory and pilot scale mills with diameters up to 1.7 m. These tests allow the discharge and inlet flows to be directly related to the hold-ups at the same time, which greatly reduces the variance in the estimates of the cumulative breakage rate and discharge rate functions.

[0026] Figures 5 and 6 show values of the specific cumulative breakage rates and discharge rates obtained from dry locked cycle tests in a 0.6 m diameter mill using feed with a top size of 75 mm in comparison to pilot data generated in a 1.7m diameter mill in similar condition. The mill was operated fully autogenously and with a ball charge of 6 per cent of the mill volume. The grate had an aperture size of 13 mm. The total volume of the charge (ore plus balls) was kept at 35 per cent of mill volume. The plot of the cumulative breakage rate function follows a similar trend. Empirical calibration factors are used to extrapolate the result beyond 75mm to predict the performance of pilot and production mills from the laboratory test developed. The plots of specific discharge rate are also similar for size coarser than 1mm. Below 1mm the trend is not similar due to the loss of particles in dust as the laboratory test is conducted dry. Assuming that the discharge rate is constant below 1mm solves the problem. A correction factor can be used to predict the performance of production mills.

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: Ch Page 16 ; [0027] A comparison of the specific energy between piloting tests using a mill of 1.7m diameter and the laboratory mill (0.6m of diameter) shows that the precision is within 5% of accuracy. ] [0028] The batch tests offer a higher level of precision than that achievable from conventional pilot tests using continuously fed mills. They are also far less costly to execute and can be conducted on far smaller examples.

Although the grind-out and locked-cycle tests can be conducted wet using a continuous inlet flow of water, it is much more practical to conduct the tests on dry material and to use a calibration factor to provide complete accuracy for wet milling.

[0029] The laboratory test developed information relating to mill product mass and size distribution for a particular grate discharge and mill feed, mill content mass and size distribution at equilibrium, mill circulating load and mill specific energy consumption at equilibrium. This data can be used in different models (not only the cumulative breakage rate function and specific discharge rate function) and simulators available on the market to predict the performance of industrial mills. This is a unique feature of the test.

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Claims (7)

A I 11H | rl CLAIMS | cL

1. A method of obtaining data for use in the design of a grinding circuit for . a grinding mill which includes the steps of - a) providing a pilot scale mill with at least one discharge grate; ~~ b) charging the mill with an ore material and steel balls to provide an initial static loading of from 30% to 60% of the mill volume; c) operating the mill to achieve grind-out of the material in which a material particle size is smaller than an aperture size of the discharge grate to provide material discharge through the grate; d) determining the power which is drawn by the mill during this operation; e) monitoring the size distribution and flow rate of the material discharged through the grate; f) crash-stopping the mill when the mill loading is reduced to a predetermined level, and a) using the data obtained at least from steps d, e and f to calculate a cumulative breakage rate function that characterizes breakage kinetics of the material inside the mill and a specific discharge rate function that characterizes transport behaviour of particles of the material flowing through the mill discharge grate. D1:P21662/bjt

[I B

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2. A method of obtaining data for use in the design of a grinding circuit for a grinding mill according to claim 1 wherein the pilot scale mill has a diameter of from 0,6 meters to 1,7 meters.

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3. A method of obtaining data for use in the design of a grinding circuit for : a grinding mill according to claim 1 or 2 wherein the ore material is run- of-mine ore or-PQ Drill core material. :

4. A method of obtaining data for use in the design of a grinding circuit for a grinding mill according to claim 3 wherein the mass of the run-of-mill ore charged into the mill in step b ranges from 80kg to 500kg.

5. A method of obtaining data for use in the design of a grinding circuit for a grinding mill according to any one of claims 1 to 4 wherein the static loading of the mill is about 45% of the mill volume.

6. A method of obtaining data for use in the design of a grinding circuit for a grinding mill according to any one of claims 1 to 5 wherein the mill is crash-stopped when the mill loading is reduced to a charge load which Is equivalent to a static volumetric loading of about 35%.

7. A method of obtaining data for use in the design of a grinding circuit for a grinding mill which includes the steps of: a) providing a pilot scale mill with at least one discharge grate; b) charging the mill with the ore material and steel balls to provide an initial static loading of from 30% to 60% of the mill volume; D1:P21662/bjt

Cc) operating the mill for a predetermined time period or after a specific amount of energy has been consumed to achieve a material particle size which is smaller than an aperture size of the discharge grate to provide material discharge through the ) 5 grate; d) collecting the material discharged through the grate; e) screening the collected material and returning the oversized particulate material to the mill; f) adding fresh ore material according to feed distribution to the mill to bring the mass of ore inside the mill to the initial charge mass; a) repeating steps d and e to achieve steady state conditions; h) determining the power which is drawn by the mill during this operation; )) monitoring the size distribution and flow rate of the material discharged through the grate; and )] using the data obtained at least from steps h, i and j to calculate a cumulative breakage rate function that characterizes breakage kinetics of the material inside the mill and a specific discharge rate function that characterizes transport behaviour of particles of the material flowing through the mill discharge grate.

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McCALLUM, RADEMEYER & FREIMOND . 5 Patent Agents for the Applicant D1:P21662/bjt