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## SAG Mill Ball Sizing (24 replies)

I don't know that a general rule exists? There are a number of considerations around this:

Are you designing the circuit OR optimizing an existing circuit? This will impact maximum ball and total (rock + ball) charge and available power. As well, it impacts feed size and in turn new ball size. Changes in ore characteristics may change the optimum. Geomet knowledge of orebody will be useful in working to an optimum as ore changes. Is the mill objective well defined - i.e., maximize metal production, maximize recovery, etc.? This I the key to establishing the 'ideal'.

We are optimizing an existing circuit. It is for "Great Dyke" ROM ore. BWI is 16.5kWh/t. The F100 is 250mm with a F80 of 175mm. P80 is 250 micron. The objective of the mill is max throughput, maximum liner life and of course max recovery. They have a total charge of 25% (Ore and balls). Installed power is 5,2MW.

Optimum ball charge in a SAG mill is a function of many factors. Some are discussed below.

For a SAB or SABC circuit

In general, the higher the ball charge the higher the throughput (and fine feed helps as well). Of course, you need a bigger ball mill. But, high ball loads mean higher ball consumption in the circuit. Many ores can be amenable to autogenous milling, but getting it right without piloting can be tricky.

For single stage SAG mills:

Similar story to the above but as the mill is closed with a classifier and targets a fine final product, the key is getting the mill load size distribution correct. Too many big balls will lead to high circulating loads.

As you are speaking about Formula and calculation, we have to refer to Modeling and identification of parameters used in the model. I think it is better also taking a look at selection function (depending to mill characteristics) and breakage function (depending to ore characteristics) to forecast a model being able to evaluate mill performance/throughput. Basically, Ball Size and Ball Charge are special parameters because those depend to both Breakage Function and Selection Function.

I think the philosophy of changing AG to SAG was possibility to decrease the feed size by using steel balls (higher density/lower filling volume) instead. So, the main role of Ball inside SAG is providing enough breaking mass to support Impact, Pressure, Nipping and Abrasion phenomenon which all are effective in rock breakage. If we need for example more impact to break the particles, it is better to optimize liner/shell plates instead of increasing ball charge.

So I suggest having a matrix formula to calculate the ball size and charge by considering all parameters affecting comminution.

An important question one must ask is assuming the ideal ball charge is known "How do you measure the actual ball charge accurately enough?" Remember if you cannot measure you cannot control. The same principle applies here, too. You must also be able to measure accurately the total mill charge (rock + ore). Once these are measured you can control them within their upper and lower control limits. If you have a good quality load cell installed on your mill and it is well calibrated then you have a good idea of what the total charge is. This is the parameter that changes constantly during operation of the mill. And it is mainly due to the change in ore charge. In the short term (day or two) ball charge should not change too much. As for the ball charge once measured accurately, you need to establish a ball accounting / balance system to account for the balls worn / broken and new balls added to the mill. The idea is to keep the ball charge to a set point and add correct amount of balls into your mill. The best and I believe the ideal method, of finding out what your ball charge is to carry out a grind out of the mill charge and get inside the mill afterwards and measure the ball charge. Make sure this is backed up by the mill power measurements. Grind out is easy if you have a VSD on your mill. However even with a fixed speed mill it is very possible. Considering the size of your mill this should be a very easy task to do. You must be careful to do grind out, if you have not done before, not to damage mill liners. To minimize your the risk of liner breakage choose to do it when you are going to do a full mill liner change out. Once you measure the ball charge and measure the total charges then you need to target an appropriate ball to rock ratio for a chosen mill throughput rate. With high aspect ratio SAG mills total charge to ball charge ratio should be greater than 2 (up to 2.5) for a coarse mill feed (say F80 > 110 mm). If the mill feed size is fine, say 50 mm or 30 mm, then you are looking at a total charge to ball charge ratio of about 1.5-1.6. These are guidelines and may fluctuate a bit depending on the specifics of your system. I am also assuming your top up ball size is optimized and you are using balls with correct hardness. Once you know what your parameters are you need to be able to adjust them withchanging conditions, such as ore hardness, and feed size. Assumption here again, is the change in feed size is due to wear in crusher liners, OSS, and what feeders under your stockpile (outside or middle ones) you are using to feed your mill. Finally, you should be able to check the ball charge using any mill shutdown as an opportunity. This time you do not need to do full mill grind out. You can do partial grind out and use an appropriate power model to help you estimate the ball charge. There are very good power models being used by the practitioners in the field.

I hope this helps.

If you go to the mill design specification, you should have the maximum design volumetric loading or the mill supplier can supply you with that information. Typical SAG mill charge contains between 8% and 12% ball charge. Just looking at your F80, the feed is very coarse and I would think of reducing the F80 to increase the amount of material that is easy to grind - i.e. increase material below 50mm.

If you are using magnetic grinding ball, it would be easy also to consider a pebble crusher to improve your capacity and effectively reduce the feed F80.

Something that you might be interested in is the "Mineral Slicer" system. This system was specifically designed to give you an accurate and responsive mill fill level indication. It also shows you where your charge is impacting on the mill shell very accurately. The problem with the conventional loadcell systems is changes in load density.

I commissioned and operated a mill with a 36' SAG. Your ore specs are a little hard, coarse feed and fine discharge which looks like a cyclone overflow discharge size from a ball mill. Do you have a ball mill(s) in line with the SAG?

With what I've seen, ball size is as important as, maybe even more important than charge percent in a case where you are looking for increases in all areas. Mill density, speed and sound can all help you affect wear and throughput properties too.

Just a quick comment on measuring charge:

Very good comment pointing out that "you can't control what you don't measure". This applies particularly to charge volume where very low percentage changes can have a big impact on overall mill performance.

The manual way of measuring charge volume used by practitioners is to go inside the mill and count the number of lifter bars exposed above the charge so as to estimate volume when comparing it to liner assembly plans etc. Other people use a tape measure or disto to measure a few distances to make that same calculation. This can easily introduce an error of several % when compared to the actual charge volume in the mill. There is an alternative to this manual estimation by using the charge volume output of MillMapper (http://is.gd/Az4Z6h) which is derived from high resolution 3D liner surface data collected in 5 minutes by a remotely inserted instrument (no confined space entry).

Measurement of net ball volume in a SAG or ball mill can also be done by completing a grind out and re-measuring the volume with MillMapper. These volumes are accurate to the nearest 1% and account for change in internal mill volume due to liner wear and also account for the volume taken up by the feed and discharge cone which are not accounted for by the manual estimates I mentioned before.

If the 2 charge volume measurements are done (crash stop and grind out), the ore to ball ratio is available. Other related MillMapper output is ball size distribution measurements to identify what the ball wear rates are and control what the ball addition rates should be.

It has never been simple to optimise SAG mill as discussed by other because you need to bring a lot of factors into the problem.

Characterisation of the ore type behaviour in SAG mill is a key to proper design and optimisation of your SAG circuit. If you have done proper test work and assumed your Work index is as you provided above quickly I can estimate that your SAG throughput is around 517 t/h and if the total % of mill charge is 25 % of the total mill volume, then you can assume the following assumption .i.e. mass proportion of grinding body to ore be 15% steel balls and 10 % ore (1.5:1) this means 1ton/h of ore requires 1.5 tons/h steel ball, therefore you need about 1.5*517 ( 776 tons/h of steel balls) with mass flow 517 tons/h of ore in the mill to achieve what you stated from your test work. Otherwise you can use some simulator from different provider like JKSimet.

Note: When conducting any comminution test work select the appropriate test work method (grind ability test or breakage test) in order to get correct information for optimisation or simulate your mill or circuit, otherwise you won’t get correct operating conditions for your circuit. For example for SAG mill you can use SMC,SAG mill test, JK Drop weight test or SAG power index.

It depends on a number of factors but the old 10-12% rule not the optimum in many cases. With less competent ores and fine feed Freeport uses up to 21% balls. Cadia around 16% for more competent rock.

I was curious about your calculations therefore decided to follow up with some questions: to reiterate what you are proposing we need to put 1.5 t/h of steel balls for every 1 t/h of ore into the SAG mill. Is this correct? If what you are saying is correct then you have 517 t/h or ore and 776 t/h of steel media on the SAG mill new feed conveyor (for a total of 1,293 t/h, steel media + ore combined). I would love to sell grinding media to this operation, wherever it is. Were these figures meant to be components of mill charge weight for rock and steel media, in which case we should not be using the units of t/h, rather just the unit of tonnes? Another question I have is how did you arrive at component masses from % volumetric filling ratios, unless you can measure the mill charge weight? All contributors so far are referring to % filling by volume not mass. If you have a good quality and well calibrated load cell (or another instrument, which can do the same job) you can measure mill charge mass. But the main question still remains. How do you know what % of charge is rock, what % is steel media even if you are able to measure the total charge. There is more than one possibility. There are ways to measure mill weight on-line & real time, backed-up by off line calibration measurements.

I share the comments of Paul Staples about this case. In case of fine/non-competent ore operations it is difficult to maintain a stable load inside the mill due to high breakage rate of coarse particles. As the larger feed rocks disappear quickly, the apparent charge density approaches values close to just ‘balls plus slurry’ (-5 ton/m3); that is, conventional grinding. In this case is common to use high ball charges to allow to draw the installed power, instead of increasing the mill speed (if you have a VSD) to avoid damaging the liners. In the other hand a BWi of 16,5 not necessarily implies that your ore is hard. DWT Axb parameters or SPI provide more information about ore competency to SAG grinding than BWi.

In your case, given the information provided, I recommend to start with a "benchmark" ball charge level (10-12%) and check for the mill response in terms of load and power drawn. If you want to optimize, then a different package of test work and simulation should be deployed to understand how the ore-mill system will respond.

I meant tonnes and not tonnes/hour otherwise it does not make sense to put every hour 776t of steel ball. The weight of the steel balls used in the calculation is not correct; however the calculation of the % mill filling depends on many factors such as the number of lifters in the mill which is not a case in this discussion. The concept used in the calculation is correct but should be related with the volume of mill charge.

According to you, the % of the mill charge is already exist (25 %). My assumption is , about 60 % of the steel(grinding bodies) and 40 % ore rock are distributed within 25 % of the mil charge (total charge) , which means if you have 1cubic meter ore you need to put 1.5 cubic meter of the steel(grinding bodies) to achieve the specified product size with a given specific comminution energy.

The question how the space between steel ball and ore/rock particle is filled in the mill depends on the size distribution of the feed material and steel ball .For the optimal performance a factor of 10 - 25 times the size of ore can be used to establish the size distribution of the steel ball.

To answer the question directly, there is no such thing as an ideal ball charge as it is ore dependent. For example, in North America iron ore is typically ground in AG mills (ball charge of 0%), some base metals such as lead-zinc have low ball charges (just a few %) and some like copper and gold need a much higher ball charge (up to 20%). However, it is not necessarily mineral dependent. For example, Aitik is a copper mine that uses AG mills. It all depends on the ore characteristics (competency, hardness), feed size distribution (blasting practice, pre-crushing) and the economics.

I agree with you but can we discuss how do we define the hardness of materials? I am aware that work index is one of indices used to define the hardness of material, A and b breakage parameters are also used to define the hardness of the materials.

To me it seems that it is still very difficult to exactly define the hardness materials instead what we normally used to say it is hard is just comparative indices. I give one example suppose you have pumice rock which is very light material but if subjected to breakage process it can be hard to break. How do we define such a phenomenon?

I am also aware that with physics of particle we can measure the strength of materials by measuring the energy absorbed by particle when impacted or compressed by measuring the strain rate and applied forces. The difficult with this is how do we measure the internal energy of the particle precisely?

The way I would describe it is that there are two components to a particle: the matrix and the "grains". The matrix can be softer than the grains, the usual case, so it is easier to crush than it is to grind (as we get closer to grain size the particles are harder). If the matrix is very soft then we say the ore is not competent (crumbles easily down to grain size). The opposite where the matrix is harder than the grains does occur but is less common. In this case crushing is harder than grinding. So, when we characterize the ore we need to measure both the matrix and grain strength. This is what we do when we use the drop test and ball mill work index (some also use the crushing work index, rod mill work index and ball mill work index). There is no single index that can give the entire picture.

The selection of equipment and operation e.g. ball load depends on those indices and economics. For example, an ore can be amenable to both AG and SAG milling but the equipment dimensions for the same throughput would be different. The choice should then be based on the total cost of ownership (capital plus operating costs).

I agree with the breakage theory. However, I think only breakage kinetics are necessary for determining the liberation of material. As initial data, capacity, BWI and PSD (F80, feed top size, and P80-desired size) of material are enough for successfully determining.

In addition, very important question, whether is about of crushing or grinding. If it is about grinding, more characteristics of material are important. I will further determine the grinding charge/media, ball top size (if we speaking about ball mill) etc. On my opinion, any measurement of internal energy isn't important in practice.

The word 'hardness' is a source of confusion, and needs to be avoided. I prefer propensity to break, breakage resistance etc. A PhD student, George Leigh, I advised wrote a number of pages (about 20) on clear definitions and discussion of terms. I regard this is the best description I am aware of.

Failure to understand the difference between hardness and breakage resistance is why some incorrectly use hardness tests (indent tests) to assess propensity to break. The unimaginative descriptors: A and B, are parameters used for breakage tests and are fundamentally empirical measures determined from actually breaking particles (now primarily using a drop weight test). This is reasonable.

The validity of this approach to fines is questionable. Therefore more detailed analysis requires further experimentation for fines particles. As explained there are other breakage tests available, and many are based on actual breakage. I do not think there has been any serious review of all the current methods with a view to strength/weaknesses.

Could you clarify your comment:

However, I think only breakage kinetics are necessary for determining the liberation of material.

Under "breakage kinetics" is being implied size reduction of particles to desired coarseness that is suitable for further beneficiation.

This involves crushing and grinding kinetics where we can perceive how much energy is needed for size reduction of particles to the final coarseness (the final coarseness is determined according to process treatment such as: flotation, hydrometallurgy, physical treatment etc.)

So I tried to explain that everything is about power consumption, because the comminution process that is alpha and omega of each process requires the maximum power consumption beside other consumption of spare parts. According to above stated, I think any measurement of internal energy of particles is not necessary.

Measurement of internal energy is more practical when it comes to understanding the strength of materials which is so important for rock mechanics and civil works.

All the recent discussions are fine in the context of ore hardness, breakage & grinding kinetics, etc. But the key question we are discussing in this discussion is that a system has been given to us. Which means that a plant has been built, the mill is operating, and operators come to work daily, busy with their best efforts to meet their production targets? They need to be given best targets to run a specific mill(s) to achieve optimum production targets. These targets may be grind size, throughput rate, recovery, etc One of the target parameter(s) to run a mill is the ball charge. How and at what level(s) do you set it? Do you need to change it as the feed ore parameters change? If so how? I do not believe we have answered this key question.

There is no doubting that there is no ideal ball charge for all systems. However there has got to be one for a given system (even) for a given time period. The plant has been built, equipment is installed and even the type and size of grinding media is fixed (even for a short period). On the other hand feed ore parameters (size, texture, hardness, etc) may change more frequently as compared to equipment parameters. A plant metallurgist’s job is to match these on a daily/weekly/ monthly basis (among other issues to attend). How can we assist the plant met in this respect?

One important issue: "Work Index is not Hardness", but is the energy we need to reduce from F80 to P80. Also I was reading about the ball recharge policy...for this is very important to know the Abrasion Index of the material, the F80,pH and Diam of the mill so at this way we can determine how much steel we have to add to maintain the same level of steel into the mill. SAG is a very complex system and more difficult is to determine the real level of charge and rocks, usually we perform crush stop to measure total level and grind-out to try to measure the grinding media level.

Is there a general rule or a formula to calculate the ideal %ball charge in a SAG mill?