Interesting topic and I'd like to heat up a discussion. We normally get recommendation from flotation cell vendor(s) for the scale-up factor from lab to plant. The following link has a table showing Metso's recommendations.

http://is.gd/r1zrJZ

I compared a couple of them with data we got from another vendor in the last a few years and found they match pretty well. Per my understanding, a pilot plant is something between a lab test and an industrial plant. A factor of 1.5 may be the right one to cover the efficiency loss in a larger system.

Some people consider a pilot test more like a lab test and they simply use the same as lab-to-plant scale-up factor, to stay at the conservative side. It would be interesting if someone has done both lab and pilot plant test for the same ore. That would get a more persuasive scale-up factor.

In terms of metallurgical performance, a mineral separation pilot plant sits somewhere between the bench (locked cycle tests) and a commercial plant.

The 3x retention time for bench to pilot plant scale-up is mostly to compensate for the difference in residence time distribution - the bench cell is plug flow while each flotation cell in the pilot circuit is a perfectly mixed reactor. The 3x factor works well with banks with at least 4 cells per bank for cell to cell flow (i.e. the old Denver Sub-A) and at least 6 cells per bank for open through flow (i.e. the old Denver DR).

One challenge when implementing a pilot plant circuit in a commercial laboratory is that the inventory of equipment available may not be sufficient to allocate the desired number of cells for all stages in the flow sheet. So, choices must be made unless one has access to an unlimited budget to assemble the most ideal pilot plant possible.

There are a number of other equipment selections which can enable or disable flotation selectivity depending on the ore to be processed.

Lab cell only batch flotation and retention will minimum. But for pilot, bench can be used as both. As we know and experienced that retention time scale up will be 1 to 1.2 for lab scale to pilot and pilot to bench almost same. But from lab to plant will be 1.4 or may be 1.5. It all depends on material, type of flotation and type of cell. More important is bubble characteristics and kinetics.

A company in Australia called Gekko systems make and design flotation systems for every type of plant. We manufacture polyurethane and rubber components for them. Give them a try you won't be disappointed.

A company in Denver, Colorado called Quinn Process Equipment Company designs, manufactures, and ships equipment. Please look and navigate through the attractive website: http://is.gd/e4s54K

Despite the fact that scale-up factors is common I don't think an arbitrary scale up factor is a good idea.

It is perfectly reasonable to use the argument of retention time. Similarly above comments about understanding bubble characteristics it’s relevant. Also you need to think about entrainment.

It is basically a matter of working out what you know from the lab. Tests and how this can be used for modeling the actual plant. I would suggest a scientific approach to modeling is always preferable to a one-line arbitrary approach.

So what is exactly the problem you are trying to solve?

It is an interesting question - what scale up factor should be applied to a successful pilot plant bank residence time in order to design a full scale industrial flotation bank.

Three times is a conservative and rather generic scale-up factor for the bench scale to full industrial plant scale; nothing 'incorrect' with it per se - always handy to have more flotation capacity up your sleeve in an operation in case the management wants to push more tonnes through the plant, or there is over grinding or the mineralogy or head grade changes significantly (not that should be a surprise if good geometallurgical practice has been observed during testing).

It is dependent on many things that we do independently understand : mineral type, mineral size range, bubble size range, agitation intensity, flotation rates, bubble-particle collision frequency/success, froth loading/draining, concentrate froth removal rates, etc.; I suspect someone has pulled it altogether and developed a theoretical basis for scale-up for each scale i.e. bench, pilot and industrial - based on the amount of fundamental amount work conducted by the universities around the world over the decades under the auspices of organizations like Amira.

In the meantime, we mustrely on experience, and the Metso document that been provided is a good guide. There are several older publications which show a full scale up factor based on bench scale testing by mineral type.

Anyway, when designing a pilot plant, the full scale up factor is often applied to calculate the required residence times.

Taking the pilot scale residence time data to the full scale design does employ a 'safety factor', typically 1.1, but that depends upon the designer and his experience / 'fear of failure'.

I am curious about scaling up conditioning tank residence times [not that many conditioning tanks are employed these days, particularly in copper porphyry applications]; there doesn't appear to be any guidelines - in theory, it should be straightforward - a simple mixing application with the minimization of short circuiting using downcomers and uprisers.

Mr. James E Quinn Sr. who founded Quinn Process Equipment Company (http://is.gd/e4s54K) worked at Denver Equipment Company before it closed down and has all the specifications on Flotation plans and pilot plants and other equipment. Brochures can be downloaded from our website.

Nice plug - the website does not address the issue of scale-up. Does not inform nor advance the discussion.

You and anyone else are free to navigate the website: http://is.gd/FowAdB and download the brochure on flotation machines that we manufacture here in Denver.

By the way, good to see that you are still making processing equipment in the US!

I will inform you of some historical information on the equipment companies here in Denver. Denver Equipment Company operated for many years here in Denver and was bought by Joy Manufacturing who was bought out by Metso. My uncle worked for Denver Equipment Company then went into a partnership with Wayne Hazen (both went to Colorado School of Mines). The company was called Hazen-Quinn. Then my uncle formed Quinn Process Equipment Company and Hazen became Hazen Research. I hope this helps. Thank you. There is 30 years of experience in equipment here or more. Please come visit anytime you are in Denver. Did you go to the SME Convention that was held in Denver recently? We had a booth at the convention. We work real close on some projects with firms like yours. 

Although I work for the old PAH (based in Denver) now RPM, I am located in Brisbane. I am an SME member and will visit you some time. With that esteemed track record particularly from the earlier days, I am sure that there is lots of great learning, including scale-up that your company can share.

The Metso table referenced typically indicates a scale up factor of 2 from lab cell results which I have often used myself with good outcomes. I have seen very conservative engineers use a factor of 3, especially for large scale projects where the additional cell cost is buried in the overall big capex number for the concentrator. Typically a design allowance is applied to the residence time calculated by applying the scale factor which can be thought of as an additional safety factor.

I have studied various plants from copper, PGM's, zinc, antimony, nickel, phosphate, carbonates, fluorspar etc. and were surprised by the various methods that were utilized to scale-up flotation processes. From power intensity (kW/m^3), Froude number, bubble surface flux and even copying plants with similar geology and mineralogy but nowhere did I find the word "similarity". All these plants that I have analyzed suffer from the same deficiencies and I came to the conclusion that researchers focused on the grinding, particle size, reagent suite and retention time but neglected the "Engineering" side of the scale-up process. The process of creating "Similar" conditions between pilot plant and full scale plant will put you on the correct path of scaling up your process. Characterize the kinetic activity in your pilot plant and then create those conditions in your full scale plant, that are similar to those in the pilot plant which have produced the reference kinetic activity, and you will ensure the same performance.

I suggest that you look at the publications by Martin MC Harris (UCT and others) have published on flotation modeling and simulation.

You use the word 'similarity'.

Like you I appreciate how important a concept this is. Indeed I tried to publish a paper which used this concept 5 years ago, but the reviewer thought the concept was obvious. The concept is obvious, but people don't use it!

In reference to my earlier comments, when it comes to matching plant, pilot plant, lab. Results it is only possible to maximize the analysis of these data if the 'similarity' between the datasets can be identified.

This is why I use a particle-based model (with each particle being multimineral)., Using this framework, when it comes to modeling a plant, I initially assume 'similarity' for unit operations from one plant audit to the next (of the same plant). In information theory (which is an advanced mathematical method) similarity is related to the concept of a prior.

Also, if you use 'similarity' for lab tests, then it provides a method to develop organized comparison. The results now become meaningful and consistent. I am still looking for case studies to validate the power of this approach, although the software had predominantly been written.

If you have access to innovative clients who might be interested in an organized analysis of plant, lab and pilot plant data, I would certainly welcome the opportunity to work together. There are so many ways the analysis methodologies can be advanced.

Chemical Reaction Engineering by Octave Levenspiel is always a good book to consult when interpreting kinetics of processes and scale-up of any batch or continuous operation.

Flotation also has particular phenomenological influences and particle size effects that must be accommodate in the scale-up procedure which are necessarily based on empirical or 'similarity' comparisons, which above contributors have mentioned.

Hence tracer test of both liquids and solids in the pilot plant can be the first step for quantitative design for full-scale plant. But interpretation and judgment based on experience will be required based on reliable knowledge of ore/gangue/mineral response.

Here's my $0.20 worth. Most big recent copper concentrator design has used between 2.3 and 2.6 from lab tests to industrial. Name plate cell volumes are not always the same as the actual cell volumes, so check. Less than 5 cells in a bank will lead to short circuiting and the factor will have to increase. Lip loading and carrying capacities need to be taken into consideration. Air holdup needs to be deducted.

In my opinion, pilot plants are not very good for testing things like retention times. They are pretty imprecise and hard to control. Pilot plants are good for lots of other things, but I would be scaling up from batch cells in a locked cycle test rather than from pilot plant averages.

I'd also like to say, with the exception of the shameless salesmen spamming the thread, that it is a pleasure to see such great discussion on such an important topic online. While these things have been discussed in offices, conferences and bars for years, there's far too little metallurgical discussion online!

It seems you have woken a few sleeping giants in the flotation industry.

Normal scale up path is Batch Test-Locked cycle test-pilot plant-full scale, the progression attempts to increasingly simulate the dynamics of a full scale plant including, contact stages (probability) air hold up, energy transfer, circulating loads etc.

The old rule of thumb is 2.5 times from Batch to Full scale, but it all depends on what factor you have applied from Batch test to Pilot Plant? If you have used 2.5 and find the PP results replicate batch tests then I wouldn't apply any more factors to the full scale design. Other consideration is the complexity of your circuit (circulating loads) if these are high you might apply a 1.2 to go from PP to full scale.

The ever increasing size of flotation cells may well change the scale up factor, as the number of contact stages is reduced, and residence time distribution changes. Rougher scavenger flotation is pretty forgiving because most of the mineral is recovered in the first few cells so you can't go too far wrong with this, Cleaning is probably more important because this is where circulating loads can bite you.

Whatever you do always leave room in your plant design to install additional cells if you get it wrong, this is always a good idea from an expansion perspective anyway. Good to see some of the heavyweights weighing in on this discussion.

The design and execution of a bench scale test is the single most important factor in the bench scale to plant scale up factor. It is true that the minerals, the flotation conditions, the degree of liberation , the Jg and all the good stuff mentioned here plays a role but the method used at bench scale is going to become important when deciding to use an scale factor of 1.5, 2.0, 2.5, etc. whatever is the factor. You could have a very motivated operator that will remove froth very quickly or a person that uses less air and more frother, etc. Some people like to let the flotation operator decide about collector dosages, air addition rates, etc. Other people want to find the true nature of the ore flotation kinetics and will ask to perform flotation under fixed conditions. There is no agreement about how to perform bench scale tests out there.

I've seen papers indicating that scale up factor from pilot plant to industrial plant has been demonstrated to be close to 1 (CMP, Xstrata Process Support). I've run pilot plants and I've learned that 1 is a good scale up factor. If you want to add some safety factor then 1.1 is a good option. It is recommended that you take a kinetic survey of your pilot plant and compare that to the bench scale kinetic tests. The comparison of mass pull kinetics should provide enough information to make an educated decision. If your pilot plant rougher flotation stage time is at around 20- 30 minutes and you are getting the recoveriesand concentrate grades that you are looking for then you should be safe to use a scale up factor of 1 or 1.1. If you are around 15-20 minutes of flotation time on cleaner stages and you are getting the recoveries and concentrate grades that you are looking for then you should be safe to use a scale up factor of 1 or 1.1

Also, you can involve specialized people that work on designing flotation machines and they will give you the correct answer.

One rule of thumb is that people will always introduce safety factors and will compare residence times for similar ores when trying to make a decision

Thanks for starting this conversation, as you can see most of the people has the same question, Only a few had the experience for specific ores and because every ore is different everyone has different opinions.

Certainly one of the least well defined engineering processes that we have to deal with. In our case at Promet101, we have been fortunate to have managed eight laboratory and pilot plant campaigns in the last 5 years and in one of those are now completing a series of full scale plant audits. Thus giving us a very interesting look into the scale up from each stage, Laboratory -> Pilot plant - > Full scale operation, which was designed based on the analysis of the lab and pilot plant data. This plant commissioned in late 2012 has been running for a year, and we have had an enthusiastic client allow us to obtain down the bank and full float plant samples for both assaying and mineralogical assessment. We have used the same analytical methodology from the same laboratory that did the original work. What can I tell you? Using an arbitrary scale up factor masks a whole lot of issues that can be just as important, such as reagent addition and type, completely different feed mineralogy, specific cell power, flotation feed size distribution changes from laboratory and pilot plant and subsequent impact on recovery versus size. Reality is we in the industry should be pushing for a smaller scale up factor, to reduce power and CAPEX, and finding ways to achieve this instead of being conservative. Our scale up factor of 1 from the pilot plant would be perfect if not for some of the changes mentioned above. From the lab scale a factor of 2-2.5 looks to be sufficient. Anymore and we are just being lazy. Better to put more power into fewer cells to maximize those good kinetics rates we see in the laboratory. I recall Dobby et al developing some form of float cell to better mimic lab scale kinetics, but suffering from the age old agitation vs. flotation conundrum!

Transportation to overflow is related to bubble availability. This in turn bears some relation to pulp recirculation via the impeller zone. Impeller rotational speed contributes to bubble comminution. Similarity in impeller tip speed and air flow rates suggests a factor of 1 to 1.5 otherwise plus 1.5 for safety.

Nice to hear from you! I think the problem with similarity is that various people have various definitions for similarity. I prefer the definition which says: "Two processes may be considered completely similar if they take place in similar geometrical space and if all the dimensionless number, necessary to describe them, have the same numerical values." Once you have generated the dimensionless groups, then the rest of the experiment becomes a delightful treasure hunt. I am also looking for plants where I can apply and expand my models and will certainly let you know when I am successful in convincing certain plants.

First of all; way to go! Wow, it is nice to see that there are customers (companies) that really care about studying these issues. I agree with the term “complacency". It is easy to add safety factors. What this does is to lead us to think that large scales up factors are needed.

In one place we optimized the Cu recovery from 45-50% to reach 75%. That came with Zn recovery gains of 10% (75 up to 85%) and Au and Ag gains of 25% each. How we did; where it was a lot of work! Detailed surveys were performed to characterize circuit’s performance and plant kinetics. One of the main findings was that we had way too much residence time, so a great contributor was to stop some of the flotation banks. Yes, not only flotation cells but the bank. We had way too much residence time and people tried to explain that by re-circulating some loads. And I agree thatbench scale to pilot or to industrial level is where the scale up factor needs to be well defined.

Careful flow sheet development at bench scale level is the key to avoid putting too much residence time in a mill just for the records: we have a plant where the flotation time is only 20 minutes in the rougher circuit. I wish I could see a paper with real data as the one you mention above.

This discussion has attracted a lot of responses and is very interesting. Great to see! I do like the comment about flotation cell power intensity. As background, it is unusual to conduct a pilot plant for an established technology such as copper sulphide flotation, unless it is corporate policy (e.g. a major) or there is a need to produce samples for marketing.

So there is rarely any need to understand this scale-up, noting that it is can be difficult to replicate locked cycle bench scale results in a pilot plant due to issues such as differences in the size distribution in the flotation feed. It is also unusual for the rougher-scavenger flotation residence, particularly porphyry copper sulphide flotation plants, to exceed 28 to 30 minutes.

I would like to add that during flow sheet development there are several steps that are needed in order to get proper data for plant design. It starts with finding the best rougher flotation conditions. There are tools such as DOE or flotation screening but the ultimate solution is the DOE. Experienced people in flotation know that there is no such thing as changing one parameter at a time. As there is lot of chemical interactions involved, when one variable is changed (which means that the concentration of something else in the slurry is changed) then the relative concentration of the remaining variables also change, which in turns produces a condition for a whole new equilibrium. A detailed program will allow finding kinetics curves, grade vs. recovery curves, mass pull vs. recovery, size by size recovery, mineralogical analysis, among other important things.

Once that the rougher stage is understood, one needs to go after the final flowsheet for that ore. Use the rougher results and design the simplest possible flowsheet. Try no regrind, some regrind, one cleaner stage, one cleaner scavenger, etc. Also get flotation kinetic data, mass pull vs. recovery, water recovery, etc. Once you feel satisfied with your flowsheet, perform your first open cycle flowsheet. This obviously means that no streams are re-circulated. Once the assays are back you can simulate a locked cycle test. If you want certainty on the results then run a one locked cycle test (LCT), running at least 8 cycles. If the LCT confirms the OCT then you may not need pilot plant runs.

Remember, the main problem for projects failure is to skip steps. Saving money on metallurgical testing can kill a project. If concentrates samples are needed for marketing purposes, then a pilot plant is needed. Remember, pilot plants can also produce tailings for environmental testing and concentrates and tailings for thickeners and filters design. Almost guaranteed that a company needs this data for their future plant design and for environmental permitting!

Things need to be simple but it is highly recommended that no steps are omitted for met testing. Going fast sometimes leads to disaster. The phrase “the devil is on the details” applies very well to processing plants design.

He did an investigation about projects failure and one of the culprits was “skipping steps”. Some people want to go fast and apply their experience from other places but that is not always the best case scenario. Being humble aboutnew ores met performance is the way to go.

Thank you for starting a very interesting discussion. http://is.gd/FowAdB

I agree with you on view of various studies to made on ore, gangue, mineral response, grinding, practical size, reagent, bubble characteristic, etc in detail .Pilot plant test would give more in puts to tune the operational controls and the upstream and downstream process flow sheets to get the best results .we had used the floatation units from M/s Carpco. Initially we did not get the good results. But by introduction of Derrick screen in the flow sheet to control the particle size the performance has been very good .A good instrumentation all controls on effective froth generation is very vital and gave ultimately the best results.

https://www.911metallurgist.com/methods-of-scale-up/