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## Effect feed grade on flotation efficiency (16 replies and 2 comments)

I studied the change of kinetic rate with grade. I know various companies that also provide this service.

Now there is clearly a change in kinetic rate with grade of hydrophobic particles, but one of my interests would be a far better model for estimating this.

One of the key factors is how minerals (on the same particles) interact. Therefore if pyrite grade increases chalcopyrite recovery will increase simply as a result of particles having both pyrite and chalcopyrite.

Therefore from a modelling viewpoint, the optimum modelling strategy is a particle-based model rather than a mineral-based model, or an element-based mineral. I would be happy to discuss further, because I am sure there are much ways to model flotation 'efficiency' than is currently available. I was rather hoping this discussion was going to 'take off' and I was going to contribute more.

But I don't want to leave my comments as just for previous. You raised an important question, and there is a related important question in the mineralogy context.

If the grade of ore increases how, do we expect the mineralogy (in terms of liberation) to vary. Now one of the main difficulties with the argument is of course that mineralogy can vary alot, so any generalisation is also subject to this expected variation.

Now from a general viewpoint one can have a model to estimate/predict the change in liberation. The model would predict that liberation would increase as grade increase.

Now I have mentioned this model in a few different groups (Data Reconciliation, VisioBal), hence I thought it appropriate to mention here.

The model is based on information theory, which is a probabilistic approach - I guess I would welcome more detailed discussion in the Group VisioBal; but happy to discuss more here if there is interest.

If the flotation models are based on liberation via a particle-based model, then if the liberation increases the apparent kinetic rate of mineral will also increase.

Hence we can model (via a particle based model) the expected change in grade/recovery of product. And although the model uses advanced methods it isn't difficult to run. I have separately developed plant audit analysis software (but at this stage mainly reconciliation); yet it is extended to a particle-based model (I call 3D).

Now I am hypothesing that VisioBal3D once applied to plant data; (in order to resolve the multimineral particle distributions at all streams) could then be rerun with a new feed grade (fixed). It would effectively assume that recovery of particular particle types at each stream doesn't vary with different ore. The model would end up estimating new distributions at all streams, and could in turn estimate final grade/recovery. Now this would seem dismissive of flotation models, but it isn't. There is no reason that a probabilistic approach/information theory should be in major conflict with a flotation model. However there is definitely a complex question of whether when the flows change (from one ore to the next) how will this affect recovery of particular particle classes. Yes it definitely would; but how important is it?

Now I am more than aware that I may have over-simplified the problem; but on the other hand I may not have. Only validation will prove which way or the other.

The other interesting aspect of this whole approach is that (provided there is no communition) you don't have to estimate recovery at all units and streams. In the end you just need the recovery or the particles from the main feed stream to the main product streams.

The Group VisioBal might be a better forum, so please join if interested in more technical discussion on the modelling issues.

The second note, is that the various subject areas raised: VisioBal, information theory, probability methods, multimineral particles, simulation, flotation modelling, etc. is why I consider mathematics/datahandling/mineralogy etc. to be an integral part of Geomet.

So I think this discussion provides an example for my statements given for the discussion on the Geomet. course.

True to that. Grade alone does not sufficiently predict flotation efficiency recovery. Mineralogy, including grain which influence liberation must be factored into the investigation .

One 'think-tank' endeavours is the back-calculation of mineralogy (using a multivariate approach) I call this psuedo-mineralogy albeit direct mineralogy is prefered. And once you have direct mineralogy or pseudo-mineralogy a particle-based approach can then be used.

This example also provides a forum to discuss/compare the three main frameworks for modelling (flotation):

- Assays independently
- Minerals independently
- Particle types (each particles having a multimineral composition).

Has anyone ever done a comparison of these 3 approaches?

Some comments from a process mineralogist. Our studies indicate that there is certainly some kind of relationship between the grade and flotation recovery (and cyanidation recovery as well in gold and silver extraction), but it is never the same. In some cases, recover changes linearly with grade, and in other cases it does not, depending on the scale of grade change and also depending on the blending quality. From the viewpoint of ore-formation, grade change means the concentration change of target element(s) in the ore-forming fluid, and the latter often accompanies concentration changes of other elements. All these changes, plus the ore-forming condition changes (such as T, P and pH) will result in mineralogy changes (including bulk mineralogical composition, individual mineral chemistry, grain size, grain shape and maybe some other things). Finally, the mineralogical changes will affect the flotation recovery. And don’t forget that flotation is a surface chemistry-based process in which target mineral(s) may react with reagent and cause recovery issues. That is why some plants employ flash flotation circuit to avoid the surface issue (I have a paper on this topic for a Cu-Pb-Zn-Au-Ag ore and can be emailed to whoever wants).

How can we better predict the recovery using a geomet model? That is not an easy job. Our studies in recent years show that the models that incorporate more mineralogical information certainly works better than those using less mineralogical information. If your flotation recovery is not linearly correlated with grade, you may want to examine the mineralogy of your feed. I don’t think it is the grade that controls the recovery, most likely it is the feed mineralogy

I guess I am concerned you want to know the results that could be obtained from a simulation, without actually doing a simulation. Hence the question isn't a conceptual question but an implementation question. I am also concerned because I know operating conditions (hence recovery at particle streams) are not fixed.

All that being said, a simple recovery equation for the blending of two ores is an equation that is linear.

r(Blend)=(w1 g1 r1 +w2 g2 r2)/(w1 g1+w2 g2)

Here there are two ores '1' and '2', g is grade, r is recovery, and w is component of each ore in the blend.

Now presumable you are saying this equation is not valid (is that correct?) and if so there are numerous reasons, for which the most obvious is the effect of comminution. For example it is sensible to blend if one ore is hard and the other is soft.

This means we have modified the operating condition applied to the particle ore types. That is the energy /tonne applied to ore 1 (if this is the hard ore) has increased, and the energy/tonne applied to ore 2 has decreased. This will of course increase the recovery (which is why we chose to blend) beyond that of the above equation.

But have I missed the point? Or am I on track? If I have missed the point please clarify further. If I am on track we can discuss further.

Not really, I have done some flotation tests, I take one sample from Angoran Lead and Zinc Mine, sample has been gathered before conditioners of flotation cell. I repeat the test in lab using the same setting of mill. then some other samples are made using waste and concentrate of first test, initial sample has been mixed with 5, 10 and 20 percent of concentrate and also 5, 10 and 20 percent of waste (6 new samples with different grades), I've repeated the test using the same setting (same quantity of reagents). The idea was to check the recovery in function of grade variation (+-20%). it does not show a linear behavior.

I'm interested in the similar test and results! the simulation of feed is possible using Mill samples (each 6 h).

OK

I hope someone gives you more feedback. I only did similar work for 'liberation modelling'. i.e. I only measured to the mill product in terms of liberation. There are strong similarities with this approach and yours but also differences. I guess you haven't any mineralogical data.

I would have thought there would be a linear or near-relationship, and without looking at the results further I can't immediately see reasons for significant departures from the equation I presented previously. (Presumably the mill is in batch mode).

Very interesting question as I as mine planner and mine analyst are also interested in finding out about this matter. Let me explain a bit, when we do block modelling we normally interpolate data from drill holes and estimate a geological attribute, let's say metal grade, at an un-sampled location. On the other hand some drill hole data (few of them) is sent for metallurgical tests in order to have information about the processing and recovery and we got a single number, 98%. Then based on these information and some economics we generate the production scheduling using the "estimated" single numbers for grade and recovery and prices, etc. and arrive to a metal production value and Cash low for each production period. Well to make it short, your question is key in this process, i.e., what happens when the ore sent tot the plant does not really have the "estimated" head grade (could be less or more) how the recovery process behave (in a linear fashion as we normally assume?).

A written article titled the effect of grade variability in mine project value where i discuss this problem from a geostatistical-mining-economic/finanancial viewpoint, and would really hear about the processing viewpoint, which would be of great input in this process.

The article discusses the use of estimation and simulation techniques in block modelling and mine project evaluation. Here there is the link to an article about this topic I have written and published in the HighGrade magazine, title 'THE EFFECT OF GRADE VARIABILITY ON MINE PROJECT VALUE' - see the consulting section.

This topic, and the 'Flaw of averages in Mining', will be discussed in the course ROMPEV PTY LTD will run in OCTOBER 10-12 in Brisbane.

Agreed, but we at the mine planning stage (long term production) don't have much information about the recovery process and its reaction to changes in head grade (which is also uncertain). Most of the information we have is a single (average?) number representing the recovery of each ore type, such as 98%. I really believe that there should be more input from processing and metallurgy engineers about this to have a more realistic estimates of future production (here i am talking from the long term production stage). I also believe that Geo-metallurgy is a field that is trying to correct this assumption as it analyze this process with more detail considering recovery process as a non-linear function of several variables (e.g., mineralogy type, alterations and different indexes). The objective is to provide a more realistic recovery process which can vary over time.

Would be more than happy to hear about this and see more realistic examples/applications where recovery is not just a single number but an advanced function that changes over time and considers the inherent geological uncertainty.

Do read the paper by Delgado concerning Escondida concentrate grade modelling. A practical view to spatial and time based concentrate grade prediction including uncertainty in modelling (normative model) and estimation methods.

There some discussions about using recovery in Geostats model in:

Lund reported interesting results around analysis of ores and tracing and analysing their performance in milling for major LKAB.

As for that discussion, it is good practice to aim to convert terms to additive terms.

Recovery is not additive.

'Recovery*Grade' or 'Grade of Recoverable mineral' is additive.

Fully agreed on the latter geostats comment. If the geostats guys are concerned about using the recoverable grade (as it is so close to the head grade), then converting the data to a non-recoverable fraction (or residue grade) is a work-around that most will be comfortable with.

Aside - I saw your comments on additivity within a comminution context (you were totally correct). It is really worthwhile putting a paper out there to assist mets with these concepts. 2013 Geomet may be a good place to present this?

In regard to comminution, you were the only one who noticed! LOL

This is why I tried to emphasise the importance of mathematics in the discussion on a geomet. course. Again not one comment of support. Given that maths is so intrinsic: Geostats, sampling, optimisation, mine planning, simulation, it is all very disappointing.

I suspect the issue with lack of comment stems from the "discipline silo's" we built (1990s to 2000s) in the industry where only a few have taken the time to understand the greater process of mine development / mine modelling.

Geomet is supposed to magically remove these barriers, however, if we all dont take the time to understand what our peers in geology, resource geology, mining, met and our mathematical whizkids have to do in the process then we will not be able to better guide / influence the process of mine optimisation / planning.

The basic math understanding has been a real eye opener to me. Will attempt to contribute to your geostatistics post.

OK. I suspect your problem relates to the relative flotation rates of floatable mineral and waste. Complicated by a little entrainment.

Do try this approach.

- Recovery (ultimate or maximum) in Roughers is additive by Helena's calculationn.
- Kinetics (take the natural log, for each component, of the recoverable mineral content x exp (kinetics))... OR k mixture = -ln [(assay_Pb_1 x Rec_Pb_1 x exp (kinetics_Pb_1) + assay_Pb_2 x Rec_Pb_2 x exp (kinetics_Pb_2)) / (assay_Pb_1 x Rec_Pb_1 + assay_Pb_2 x Rec_Pb_2).
- Do the same for the gangue mixtures.
- Now you have recoverable fractions per component for the mixture.
- Apply any std CSTR model (or Savassi Equivalent) to simulate... or cheat and look at the relative ratio's of kinetics and use this to drive the Grade Recovery relationship based on the blend.

Note: dilution of the concentrate was your original problem with mixing. By taking both recoverable mineral content and component kinetics into account you should be able to solve the problem.

Aside - 2. only works for first order kinetics. I have not complicated this with entrainment for that I recommend a good simulator.

It is good to see geometallurgy focusing on financial forecasting, mine planning and economic evaluation. At SGS Geometallugy we specialise in addressing these issues.

I will discuss recovery at target grade because metal mass flow is most important for economic evaluation. Metal mass flow is additive and can populate the geostatistical block model. As James notes, the flotation kinetics need to be transformed if we aim to populate those onto the block model although typically this is not necessary.

The main issues around the relationship between feed grade and recovery are flotation kinetics and mass flows around the circuit. At the low grade end, we generally see recovery dropping off because the valuables are less floatable - eg. smaller crystals and more intergrowth with gangue. At the high grade end we can see mass / volume flow constraints dominating recovery - eg. recirculating loads in the cleaners, froth loading and pumping constraints. However, high feed grade samples can show low recovery and vice versa. That is the purpose of testing the kinetics.

The kinetic effects can be estimated in a batch test with timed concentrates, but mass constraints are only seen on plant. A process model can capture these constraints and explain the recovery variation with feed grade. The IGS simulator we have developed is specifically designed for geometallurgical forecasting to support mine planning and economic evaluation.

We can estimate the concentrate mass flow including quantitative uncertainty for millions of blocks and / or develop proxy relationships to populate the block model. The specific approach we take is tailored to the amount of detail from the mine plan but we recommend using a weighted average of the ore types in the feed per production period to estimate recovery at target grade. We are presenting this approach to forecasting at CMP 2013.

A change in grade is especially noticeable in poly-metallics where the mass going to the galena or sphalerite cleaner circuit can change over a wide range, but we have also seen strong recirculating load effects in large copper operations.

A process model requires a few plant surveys and flotation kinetic testing or we can estimate circuit performance based on our database of existing benchmarks for greenfields forecasting.

When a parameter is not additive it's behavior is not linear, and I'm interested in the form of this function. It could be very useful for a SA in economical evaluation of project.

I would like know if anybody has studied the relationship of flotation efficiency in function of feed grade of ore, normally system set for a defined grade, what happen if the grade varies? About efficiency for me, flotation RECOVERY is important. My question is if recovery change linearly with grade in a fixed setting of operation or not? I will try to explain my problem more clear using the following example:

eg. in a Pb flotation cell sat for 12% Pb feed (operational conditions are optimized for the best recovery), we consider normally average garde of feed so wished or estimate Pb is feed tonnage*recovery.

But the grade of feed varies depending on blending quality, the relationship between grade and recovery is not linear so the recovered Pb differ from estimate Pb. to model that I need know the form of this relationship. Thank you.