SAG III-421 III-422

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1 SAG DEPARTMENT OF MINING ENGINEERING UNIVERSITY OF BRITISH COLUMBIA Vancouver, B. C., Canada III-421 A PROPOSED MECHANISTIC SLURRY DISCHARGE MODEL FOR AG/SAG MILLS Percy Condori, Malcolm S. Powell Mineral Processing Research Unit, University of Cape Town, Rondebosch, 7700, South Africa, percy@chemeng.uct.ac.za. ABSTRACT From a study of slurry transport phenomena and discharge mechanisms in AG/SAG mills it was concluded that the slurry discharge is driven by four major independent factors; flow resistance of the charge; flow through the grate; removal from the discharge chamber (via pulp lifters); and flow-back from the discharge chamber into the mill. No existing models cover all these processes, so independent mechanistic models of such sub process are proposed and these are to be implemented into a single dynamic model. A series of laboratory scale experiments, utilising real ores and slurries, have been designed to simulate each component of the discharge. INTRODUCTION The importance of the slurry transport in grinding devices such as AG/SAG mills is broadly understood as well as its influence in mill throughput capacity. The study of slurry transport along mills using tracers was popular during the late seventies and early eighties as explained largely by Austin et al. (1984) and Abuzeid (2000). To describe the residence time distribution (RTDs) some mathematical models were used, such as the axial dispersion and the tank in series models. No studies on AG/SAG mills were reported elsewhere, although Austin et al. (1987) suggest that the simple concept of RTD loses meaning in AG/SAG mills because the RTD is determined by the rate of breakage of feed material to less than the grate size. III-422 Further, empirical and semi-empirical approaches have been used in order to obtain predictions of mill slurry filling and its relation to flowrate. Some of the investigators are Marchand et al. (1980), who correlate the hold-up in the mill with the flow rate considering other variables to be constant, and Rogers and Austin (1984) who later enhanced the correlation including other variables; such as mill critical speed, slurry density and mill dimensions. One of the most advanced and useful semi-empirical models was developed by Morrell and Stephenson (1996) expanded later by Latchireddi (2002, 2003). They carried out extensive laboratory and pilot scale experiments which together with industrial data was used to correlate slurry hold-up with mill flowrate and mill operating conditions such as: critical velocity, charge filling, diameter, grate open area, radial position of grate apertures and aspect ratio. Slurry rheology and other unknown factors where included in a constant factor. There is limited literature addressing the mechanistic description of hold-up and slurry transport in mills. Hogg (1984) considers two distinct regions for overflow mills; the ball charge and the pool zone; the slurry is continuously interchanged between these zones and flows out of the mill through the pool, ideal settling velocities are considered and the ratio of flow rate to hold-up determines the axial velocity. Moys (1986) used equations similar to the flow of fluids through packed beds and flow through orifices. The incorporation of slurry viscosity and grate discharge parameters are important features in this mechanistic model. Following a similar procedure but considering a dynamic ball charge where the hold-up is related to three zones of ball motion, Shi (1994) developed a mechanistic model describing the hold-up as a function of mill dimensions. Slurry discharge modelling In spite of the importance of the grate discharge and pulp lifter in the removal of slurry from the mill, little published literature has been found on this topic. Mokken et al. (1975) were among the first researchers who studied the grate discharge and pan lifter behaviour. Their study was inspired by slurry pooling issues in the South African style run of mine SAG mills. They developed a theoretical approach to flow patterns as a function of mill critical speed that showed that the only region within which a particle in the pulp chamber could move towards the centre of the mill is where gravitation acceleration exceeds the centrifugal acceleration, and there is only a small portion of the mills revolution where this occurs. The paper reports the use of alternative pan lifters such as curved and spiral designs in order to reduce this problem.

2 III-423 Later, open end systems (mills without pan lifters) were used and the authors observed a higher slurry flowrate was possible than with conventional discharge mills. Latchireddi (2002, 2003) carried out detailed pilot experiments studying the slurry transport performance of pulp lifters as a function of their design. Here the importance of flow-back which may cause pooling was highlighted and curved pulp lifters were found to perform about 20% better than radial lifters. Recently, in work based on the DEM (discrete element method) Rajamani et al. (2003) attempted to model the flow of particles, especially the motion of pebbles, in the pulp lifter chamber. For slurry the authors claim that the slurry is modelled as discrete spherical particles with properties of fluids, their results show comparison of pebbles discharge as for example it is observed that curved pulp lifters discharge pebbles better than radial lifters. Also, pebbles carry over is observed at high mill speed. Royston (2004, 2006) studied the principal of charge flow mechanisms in pulp lifters, comparing the traditional straight radial and curved types. Using a single particle computer motion tool that tracks a particle along the full flow path, he concludes that the curved pulp lifter is more effective in discharging rocks than the conventional lifter and reduces pulp lifter wear due to reduced backflow. Studies by Powell and co-workers (Powell and Valery, 2006) have highlighted the variability of hold-up with charge composition. For example coarsening the charge in an AG mill or dramatically changing the ball load in a SAG mill can change the slurry volume in a mill by up to 50 %. In summary, there is limited literature related to the mechanistic description of the hold-up and mass transport in grate discharge AG/SAG mills and the slurry discharge mechanism is still not well understood. Despite the importance of the hold-up of the charge and the flow-back occurrence, these have not yet been included in any model in a comprehensive manner. CONCEPTUAL APPROACH A detailed analysis of the slurry flow path throughout the mill, the grate and the pulp chamber as well as the main factors involved in the slurry transport and discharge is required. Figure 1 provides a broad summary of this analysis and can be described as follows: Charge: The charge can be considered to be a porous packed bed through which the slurry must flow. The flow resistance will be a function of the porosity of the charge. III-424 If the voidage is completely filled, then excess slurry will form a pool, with quite a different flow characteristic. Grate: The size of the grate apertures and the pressure of the slurry as it enters the grate slot will control the flowrate out the grate. Flowback: Once the slurry is carried past the profile of the charge, the slurry can flow from the pulp lifter chamber back through the grate holes into the mill. This will be driven by pulp depth above the grate holes and the residence time of the slurry on the pulp lifter. Pulp lifter: As this rotates upwards it carries the slurry with it, and directs its flow towards the central discharge cone. Its pumping capacity will be a function of width, shape and mill speed. Carry-over: It is common for the slurry to still be discharging from the pulp chamber well after it has passed the vertical. This is easily observed in a mill where the discharge cone is visible, and sometimes can form a strong spray if there is inadequate open area at the discharge of the pulp lifters. This slurry will be in a combined state of free fall and flowing down the back of the pulp lifter that was originally ahead of it. If not all the slurry is discharged by the time the pulp lifter passes the horizontal, then the slurry will flow back into the chamber to form a carry-over recycle stream. By-pass: The end side of the pulp lifter connects to the cone discharge of the mill. However, in most mill discharge designs observed by the authors, a gap between the end of the lifter and the cone discharge is found. This gap allows a fraction of slurry to bypass the lifter to the chamber especially at low angular positions. Variables affecting the slurry discharge have been identified and broken down into each component of flow; afterwards, influencing factors that affect each component of flow were identified and listed as shown in Figure 1. Additional factors can be identified during the course of experiments. Figure 2 is a graphical representation of the major slurry transport factors identified in a mill, it can be observed that the aspects involved in the slurry transport process can be modelled independently, with strong feed back from the flow-back process, the carry over recycle and the by-pass in the pulp lifter chamber.

3 III-425 MAIN SLURRY TRANSPORT COMPONENTS COMPONENTS OF FLOW FACTORS AFFECTING EACH COMPONENT OF Flow through the charge (pool) Flow through the grate Charge Pool Discharge slots FLOW Charge porosity Slurry viscosity Slot sizes Mill speed Slot position Flow back Flow back (slots) Lifter width Along lifters Lifter shape Lifter spacing Lifter carrying Carry over recycle in pulp chamber Minimum gap Discharge from end of pulp chamber Position of slots along lifter Discharge into trunnion Packing against slots Figure 1: Variables affecting the slurry discharge in AG/SAG mills Mill Pulp lifter Trunnion charge chamber discharge III-426 The volume of slurry in the mill determines the gradient pressure in the charge from the feed end to the discharge end, increasing or reducing the flow transfer. ii. The flow of slurry is controlled by the grate, and is a strong function of grate configuration. Slot size, position, and total open area control the passage of slurry, and the slurry discharge is a function of the viscosity of the slurry. The shape of the charge determines the profile of the slurry that contacts the discharge grate. iii. Rate of slurry removal from the chamber is controlled by the pulp lifter pump capacity The pumping capacity of the pulp discharge chamber determines the limit of the discharge rate and the depth of the pool in the discharge chamber. This pool forms a head (backpressure) against the slurry, which has to discharge through the grate. iv. Flow-back exists due to the grate discharge and pulp lifter configuration As the mill rotates and the slurry passes the shoulder of the charge the grate discharge allows the slurry to flow back into the mill. This adds slurry volume in the mill, increasing the discharge requirement and contributing to the formation of a slurry pool. Transport through The charge Flow back Transport through the grate Carry over recycle Lifter carrying By pass Figure 2: Graphical representation of the slurry transport in a AG/SAG mill In order to build a model and define the laboratory scale experiments, the influence of these main transport components can be hypothesized to be as follows: i. The slurry discharge is controlled by the flow resistance of the mill charge Packing of the charge determines the gradient pressure for a given flowrate which drives the volumetric hold-up. MODELLING APPROACH Based on the conceptual analysis of the mechanisms contributing to slurry flow, the general slurry transport model can be treated as the interaction of four major sub-models as observed in Figure 3. They are: flow through the charge, flow through the grate, pulp lifter transport and flow-back model. The carry over flow in the pulp lifter chamber and the slurry by-pass are consequence of the slurry being transported along the pulp lifter. Therefore, the general slurry discharge model can be expressed as function of the sub models plus an associated error (є). Mill slurry flowrate = f (F charge, F grate, F lifter, F back ) + є [1] It is proposed that the four components can be modelled mechanistically by using known physical transport relationships. The basis of the mechanistically based approach to modelling the slurry transport and discharge is that the equations which constitute the models are not arbitrary mathematical entities, but have a consistent physical basis. However, because of the complexity of the transport process semi empirical models might need to be included in order to address some aspects that are not adequately described by the mathematical relationships.

4 III-427 III-428 F back ( IV ) FLOW BACK MODEL Considering the slurry flow through the charge, the variation in the holdup or the amount of slurry in the mill at any instant of time is: F c in F c out F g in F g out ( I ) FLOW THROUGH THE CHARGE MODEL ( II ) FLOW THROUGH THE GRATE MODEL F lift in ( III ) F lift PULP LIFTER CHAMBER MODEL F c over CARRY OVER F lift out dh dt charge = F c F For a given ore of constant viscosity, charge voidage, pulp density and mill dimensions the rate equation that relates the driving forces and other variables to the slurry flowrate (Ergun equation) is reduced to: in c out [2] SLURRY BY-PASS Figure 3: Models interaction and mass balance F bv pass Model I (Flow through the charge) The mill charge can be considered as a packed bed of solids with a wide range of particle sizes. The slurry created during the grinding action flows through it helped by the gradient pressure inside the mill. In a dynamic situation the slurry hold-up is built up from the bottom of the mill up to the shoulder of the charge according to the mill operating conditions such as feed rate and slurry rheological properties. When the charge reaches its maximum capacity of slurry hold-up, the slurry flows out of the charge forming a pool. The main driving force for the slurry to flow through the charge is the head pressure from inlet to discharge, so it is a direct relationship between differential pressure and the slurry flow. It is proposed that the slurry behaviour in the dead zone (Figure 5) does not contribute to the pressure drop. Although as shown by Latchireddi (2002) the charge fills from the top downwards, discharge through the grate is primarily observed at the base of the charge. The discharge in this upper zone is recirculating in a free-flowing manner with no, or negligible, pressure drop along the length of the mill. So for the purposes of this model it will be assumed that this zone does not contribute to the pressure drop or discharge of slurry from the charge. The slurry flow through the charge can be modelled by using the flow through the bed of solids model (Ergun 1952). The model allows the evaluation of the charge and slurry properties as well as mill geometry (length). Regarding this aspect, it is important to notice that the mill geometry, in spite of its importance, was covered by Tello (2002) only, who incorporated the aspect ratio on the slurry hold-up of Latchireddi s model. However this model was found by the authors to be inaccurate due to the duplication of variables (diameter) in the model. Δ P = a L F + b L F [3] c out 2 c out Where ΔP is the pressure differential, F c out the slurry flowrate leaving the charge, a and b are constants that absorb all variables and conversion factors, L is the mill length and H is the slurry hold-up of the charge at any instant of time (t). From the Equation 3 can be noticed that as the pressure differential increases the flow rate increases. Similarly, at a constant flow, as the length of the mill increases the pressure drop increases in direct proportion up to some limit. The limit is given by the flowrate or the pressure drop. There is a family of length-pressure drop curves that are a function of flowrate, but only one is shown in Figure 4, for a flowrate of 40. Using this, for a flowrate of 40, the pressure drop is 51 and the length with this conditions can not be more than 1. Flow Flow Length Pressure drop Figure 4: Pressure drop as a function of flow and length arbitrary units If the mill charge is saturated and if the slurry flow-back is significant, a pool formation is observed, therefore a transport through the pool zone Length

5 III-429 model is required. It can be modelled conveniently considering the pool as an open channel where the driving force is the pressure drop. The relationship for the pressure drop along the pool is most likely not important, as the flow resistance at the grate will determine the depth of the pool. When a pool is observed, the pulp lifter slurry level increases, producing a back pressure against the pool. This possibility needs to be evaluated experimentally. Model II (Flow through the grate) As observed in Figure 5 the pick up of slurry is considered to be below the dead zone, this assumption facilitates the formulation of a mechanistic model. Only the grate in contact with the charge; except the dead zone; allows the slurry to pass through it and the main driving force is the hydrostatic pressure of the slurry. The continuity equation of the slurry flow through the grate model is expressed as: dhgrate = Fg in Fg out [4] dt Where: F g in = Fc out + Fback ; H grate is the amount of slurry at any instant of time, F gin and F gout are the slurry flow coming in and out of the grate and F back is the slurry flowing back from the pulp lifter chamber into the charge. III-430 discharge coefficient is calibrated from an experimental test, the area available for discharge is determined from the charge shape. The charge shape is a function of mill critical speed and charge filling. No sufficiently realistic description of the full profile of the charge is available in the literature, so this is being pursued in a linked project within the Mineral Processing Research Unit of the University of Cape Town. Model III (Slurry removal from the chamber) The mechanistic modelling of the slurry removal from the pulp lifter chamber is possible by using known fluid transport laws for laminar and turbulent flow of viscous fluid down a channel inclined at an angle. (Bird et al., 1960). The main driving force is now gravity, however as the mill rotates a centrifugal force is developed and a balance of forces must be conducted. As the mill rotates, the angular position of the lifter changes, as a result the slurry is discharged through the outlet trunnion, thus a mathematical integration which covers all angle spectra is required. The slurry depth changes as the lifter slope changes and it is integrated mathematically as a function of angular position. A mass balance around the pulp lifter chamber can be written according to: dhlift = Flift in ( Flift out + Fback ) [5] dt And: F lift out = F F F [6] lift c over by pass Figure 5: Slurry charge profile The slurry flow through the grate can be modelled conveniently by using the well known relationship of flow through orifices (Perry et al., 1999). In order to utilise it, the charge area is divided into blocks, as shown in Figure 5. Then the pressure in each block is estimated. The pressure differential as the main driving force is related to the flow of slurry and a Where: H lift is the slurry hold up in the pulp lifter chamber; F lift in, F lift out are the slurry flow coming in and out of the pulp lifter chamber; F lift is the integrated flow of slurry along the lifters at different angles; F c over is a fraction of slurry which is not being discharged from the lifter; F by pass is the flow of slurry by-passed when the lifter is at a certain angular position. The rate equations which correlate the flow along the lifter (F lift ) to the driving force are based on the mechanistic equation for flow of viscous fluid along a sloping open channel (Bird et al., 1960).

6 III-431 III-432 To estimate the flowrate of the slurry by-pass (F by pass ) a relationship between flowrate and lifter angle is proposed and it is similar to the classification function. Thus, if the lifter angle is at 90 0 no by-pass occurs. As the pulp lifter rotates towards the horizontal and the volumetric flow rate and the stream velocity decrease, there is an increasing likelihood of the slurry not reaching the discharge cone, and instead bypassing directly back in to the chamber. The carry-over flow can be estimated as a difference of the remaining flows in Equation [6]. A laboratory scale experiment has been designed in order to determine the mathematical relationship of slurry depth on a lifter as a function of lifter angle. It consists of an individual static lifter who s angle can be varied. Slurry is fed at a constant flow at each angular position and the slurry depth at points along the lifter is measured. The same rig is used in order to test the by-pass factor. Model IV (Slurry Flow-back) The slurry flow-back is a function of grate discharge aperture and hole positions. If the grate aperture increases the gross slurry flow out of the grate discharge gradually increases. However, increasing the aperture has an effect on the maximum flow discharge due to the slurry flow-back occurrence. The flow back reduces the gross flow rate out of the grate discharge and the net flow from the mill will be lower as seen in Figure 6(a). A maximum flow-back is observed if the grate holes are closer to the inner centre, as the slurry collection zone is located close to the outer edge and the holes close to the centre give more chance to the slurry to flow back (Figure 6 (b)). Figure 6 (c) shows the holes position relative to the lifter and its effect in the flow-back. At a given mill flow rate the flowback decreases if the holes position (height) increases, the same trend is observed at different mill flow rates. Although the evaluation of flow back is complicated due to the slurry flow nature along the lifter and the grate holes presence, an approach based on the momentum principle for lateral flow (Chadwick and Morffet 1993) is proposed. Considering a rectangular channel where a slurry profile at different angular positions is formed, the flow out of each individual hole can be estimated. The models obtained are then combined in a single slurry discharge model, however as observed, each model can be treated individually and the wide range of factors are used separately. Figure 6: Flow-back responses from laboratory experiments As observed, some of the models presented do not include all the factors shown in Figure 1, therefore, some semi-empirical relationships will need to be included in order to refine and/or modify the models proposed. These aspects are not covered in this paper. EXPERIMENTAL DESIGN In order to address the proposed hypothesis and to test and manipulate the mathematical models, laboratory scale experiments using real ore were designed. These experiments are divided into three main groups. The first group has been designed to evaluate the flow through the charge and flow though the grate. It consists of a laboratory scale rig (Figure 7, next page), that simulates the internal conditions of a mill in terms of charge composition. In addition, an impeller simulates the rotating motion of the charge. A range of slurry flow is driven by a pump simulating the head pressure through the mill, afterwards the head pressure is correlated to the slurry flowrate. The rig has interchangeable grate discharge panels with different configurations to evaluate the flow through orifices model. The second group was designed to evaluate the flow on the pulp lifter and the slurry flow-back. An individual static lifter who s angle can be varied is used to evaluate the slurry depth on the lifter as a function of lifter angle; the slurry flow-back is measured in each individual hole as illustrated in Figure 8 (see next page).

7 Slurry feed Grate III-433 Slurry overflow Impeller Walls cut away to show interior III-434 Finally the model will be tested on a data base of industrial mills that has been collected by the author and co-workers, as for example Powell and Valery (2006). CONCLUSIONS The slurry discharge mechanism in AG/SAG mills is still not well understood and a review of the literature shows a knowledge gap. In order to close the gap a hypothesis has been proposed which will lead to the development of a new mechanistic slurry transport and discharge model. Mechanistic based models with minimum semi empirical relationships have been considered. The range is by no means exhaustive. However, the principles which have been applied will be capable of adaptation to the slurry discharge and transport issues for new and novel applications. Figure 7: Experimental rig for the evaluation of slurry flow through the charge and the grate Slurry feed To confirm, manipulate and rebuild the models if needed, an experimental plan has been designed; they are divided into three main groups which cover most of the factors to be studied. In all cases real samples are available to be used. These samples were collected from a large number of sites covering a wide spectrum of ore types. It is hoped that a mechanistic model of this form will have good predictive capabilities to assist in mill discharge grate and pulp lifter design. Figure 8: Experimental rig for the evaluation of lifter carrying and flow-back The third group is dedicated to evaluate others aspects which are not covered by the previous group as for example the analysis of lifter carrying capacity under dynamic conditions, the effect of number of lifters on the slurry carryover, the procedure for the determination of slurry apparent viscosity and the analysis of the charge shape. Pilot tests will be conducted to validate the model and possibly calibrate some of the model parameters. REFERENCES Abouzeid, A.-Z.M., 2000, Material transport in mineral processing system. Proceedings, Mineral processing on the verge of the 21st century, Balkema, Rotterdam., pp Austin, L.G., Menacho, J.M. and Pearcy, F., 1987, A general model for semi-autogenous and autogenous milling, APCOM 87. Proceeding of the 21st International Symposium on the application of computers and mathematics in the mineral industries. Volume 2: Metallurgy. Johannesburg, SAIMM, pp Austin, L.G., Klimple, K.R., and Luckie, P.T., 1984, Process engineering of size reduction, AIME. Bird, R.B., Steward, W.E., Lightfoot, E.N., 1960, Transport phenomena, Wiley International Edition. Chadwick, A. and Morffet, J., 1993, Hydraulic in civil and environmental engineering, Third edition published by E & FN Spon.

8 III-435 Ergun, S., 1952, Fluid flow through packed columns, Chemical Engineering Progress, Vol. 48, No 2, pp Hogg, R., 1984, Mass transport models for tumbling ball mills, International symposium on Automatic control in mineral processing and process metallurgy, Control 84. SME, AIMM, New York, pp Latchireddi, S.R., 2002, Modelling the performance of grates and pulp lifters in autogenous and Semiautogenous mills PhD. Thesis, University of Queensland, Australia. Latchireddi, S.R. and Morrell, S., 2003, Slurry flow in mills: grate-pulp lifter discharge systems (Part 2). Mineral Engineering, 16, pp Marchand, J.C., Hodouin, D. and Everell, M.D., 1980, Residence time distribution and mass transport characteristics of large industrial grinding mills, Proceeding, Third IFAC Symposium, J. O shea and M. Polis, eds., Pergammon Press, pp Mokken, A., Blendulf, G., Young, G., 1975, A study of the arrangements for pulp discharge on pebble mills and their influence on mill performance, J. S.A. Inst. Min. Metal., May., pp Morrell, S., Sthepenson, I., 1996, Slurry discharge capacity of autogenous and semiautogenous and the effect of grate design, Int. J. Miner. Process., Vol. 46 (1-2), pp Moys, M.H., 1986, The effect of grate design on the behaviour of gratedischarge grinding mills, Int. J. Miner. Process., Vol. 18, pp Perry, H.R., Green, D.W. and Maloney, J.O., Eds., 1999, Perry s Chemical Engineers Handbook, 7th Edition. McGraw-Hill. Powell, M.S. and Valery, W., 2006, Slurry pooling and transport issues in SAG mills, Proceeding, SAG 06 Conference, September, Vancouver, Canada. Rajamani, R.K., Latchireddi, S. and Mishra, B.K., 2003, Discrete Element simulation of ball and rock charge and slurry flow through grate and pulp lifters, SME Annual meeting, February. Cincinnati, Ohio. Preprint Rogers, R.S.C. and Austin, L.G., Residence time distribution in balls mills, Particle Science and Technology, Vol 2, pp Royston, D., 2004, Charge flow in pulp lifters, Proceeding, Metallurgical plant design and operating strategies. AusIMM, Perth WA, Australia, pp Royston, D., 2006, Developments in SAG mill liner design. Advances in Comminution, SME, S.K., Kawantra ed., pp Shi, F., 1994, Slurry rheology and its effects on grinding, PhD thesis, University of Queensland, Australia. Tello, S., 2002, Modelling the influence of aspect ratio on slurry holdup, 6 th Progress Report, P9M AMIRA Project, AMIRA,Melbourne.