common & basic formulas for mineral processing calculations

common & basic formulas for mineral processing calculations

The control of a milling operation is a problem in imponderables: from the moment that the ore drops into the mill scoop the process becomes continuous, and continuity ceases only when the products finally come to rest at the concentrate bins and on the tailing dams. Material in process often cannot be weighed without a disturbance of continuity; consequently, mill control must depend upon the sampling of material in flux. From these samples the essential information is derived by means of analyses for metal content, particle size distribution, and content of water or other ingredient in the ore pulp.

The following formulas were developed during a long association not only with design and construction, but also with the operation of ore dressing plants. These formulas are herein the hope that they would prove of value to others in the ore dressing industry.

Pulp densities indicate by means of a tabulation the percentages of solids (or liquid-to-solid ratio) in a sample of pulp. This figure is valuable in two waysdirectly, because for each unit process and operation in milling the optimum pulp density must be established and maintained, and indirectly, because certain important tonnage calculations are based on pulp density.

As used in these formulas the specific gravity of the ore is obtained simply by weighing a liter of mill pulp, then drying and weighing the ore. With these two weights formula (2) may be used to obtain K, and then formula (1) to convert to S, the specific gravity. A volumetric flask of one liter capacity provides the necessary accuracy. In laboratory work the ore should be ground wet to make a suitable pulp. This method does not give the true specific gravity of the ore, but an apparent specific gravity which is more suitable for the intended purposes.

A mechanical classifier often receives its feed from a ball mill and produces (1) finished material which overflows to the next operation and (2) sand which returns to the mill for further size-reduction. The term circulating load is defined as the tonnage of sand that returns to the ball mill, and the circulating load ratio is the ratio of circulating load to the tonnage of original feed to the ball mill. Since the feedto the classifier, the overflow of the classifier, and the sand usually are associated with different proportions of water to solid, the calculation of circulating load ratio can be based on a pulp density formula.

Example: A mill in closed circuit with a classifier receives 300 dry tons of crude ore per day, and the percentages of solid are respectively 25, 50, and 84% in the classifier overflow, feed to classifier, and sand, equivalent to L: S ratios of 3.0, 1.0, and 0.190. Then the circulating load ratio equals

A more accurate basis for calculation of tonnage in a grinding circuit is the screen analysis. Samples of the mill discharge, return sand, and the classifier overflow are screen sized, and the cumulative percentages are calculated on several meshes. Let:

The efficiency of a classifier, also determined by means of screen analyses, has been defined as the ratio, expressed as percentage, of the weight of classified material in the overflow to the weight of classifiable material in the feed. Overflow having the same sizing test as the feed is not considered classified material. Let:

When no other method is available an approximation of the tonnage in a pulp stream or in a batch of pulp can be quickly obtained by one of these methods. In the dilution method water is added to astream of pulp at a known rate, or to a batch of pulp in known quantity, and the specific gravity of the pulp ascertained before and after dilution.

In both cases Dx and D2 are dilutions (tons of water per ton of ore) before and after addition of water. These are found from the specific gravities of the pulp, by formulas (4) and (6) or directly by the use of the tabulation on these of Pulp Density Tables.

The Pulp Density Tables were compiled to eliminate the many complicated calculations which were required when using other pulp density tables. The total tank volume required for each twenty-four hour period of treatment is obtained in one computation. The table gives a figure, in cubic feet, which includes the volume of a ton of solids plus the necessary volume of water to make a pulp of the particular specific gravity desired. Multiply this figure by the number of dry tons of feed per twenty-four hours. Then simply adjust this figure to the required treatment time, such as 16, 30, 36, 72 hours.

In the chemical method a strong solution of known concentration of common salt, zinc sulphate, or other easily measured chemical is added to the flowing pulp at a known rate, or to a batch of pulp in known quantity. The degree of dilution of this standard solution by pulp water is ascertained by chemical analysis of solution from a filtered sample, and the tonnage of ore is then calculated from the percentage solid. This method is impractical for most purposes, but occasionally an exceptional circumstance makes its employment advantageous. It has also been suggested as a rapid and accurate method of determining concentrate moistures, but in this application the expense is prohibitive, since ordinary chemicals of reasonable cost are found to react quickly with the concentrate itself.

With the above chart the per cent solids or specific gravity of a pulp can be determined for ores where gravities do not coincide with those in the Pulp Density Tables.This chart can also be used for determining the specific gravity of solids, specific gravity of pulps, orthe per cent solids in pulp if any two of the three are known.

These are used to compute the production of concentrate in a mill or in a particular circuit. The formulas are based on assays of samples, and the results of the calculations are generally accurate as accurate as the sampling, assaying, and crude ore (or other) tonnage on which they depend.

The simplest case is that in which two products only, viz., concentrate and tailing, are made from a given feed. If F, C, and T are tonnages of feed r on-centrate, and tailing respectively; f, c, and t are the assays of the important metal; K, the ratio of concentration (tons of feed to make one ton of concentrate); and R, the recovery of the assayed metal; then

When a feed containing, say, metal 1 and metal z, is divided into three products, e.g., a concentrate rich in metal 1, another concentrate rich in metal z, and a tailing reasonably low in both l and z, several formulas in terms of assays of these two metals and tonnage of feed can be used to obtain the ratio of concentration, the weights of the three products, and the recoveries of 1 and z in their concentrates. For simplification in the following notation, we shall consider a lead-zinc ore from whicha lead concentrate and a zinc concentrate are produced:

The advantages of using the three-product formulas (20-25) instead of the two-product formulas (14-19), are four-fold(a) simplicity, (b) fewer samples involved, (c) intermediate tailing does not have to be kept free of circulating material, (d) greater accuracy if application is fully understood.

In further regard to (d) the three-product formulas have certain limitations. Of the three products involved, two must be concentrates of different metals. Consider the following examples (same as foregoing, with silver assays added):

In this example the formula will give reliable results when lead and zinc assays or silver and zinc assays, but not if silver and lead assays, are used, the reason being that there is no concentration of lead or silver in the second concentrate. Nor is the formula dependable in a milling operation, for example, which yields only a table lead concentratecontaining silver, lead, and zinc, and a flotation concentrate only slightly different in grade, for in this case there is no metal which has been rejected in one product and concentrated in a second. This is not to suggest that the formulas will not give reliable results in such cases, but that the results are not dependablein certain cases one or more tonnages may come out with negative sign, or a recovery may exceed 100%.

To estimate the number of cells required for a flotation operation in which: WTons of solids per 24 hours. RRatio by weight: solution/solids. LSpecific gravity, solution. SSpecific gravity, solids. NNumber of cells required. TContact time in minutes. CVolume of each cell in cu. ft.

Original feed may be applied at the ball mill or the classifier. TTons of original feed. XCirculation factor. A% of minus designated size in feed. B% of minus designated size in overflow. C% of minus designated size in sands. Circulating load = XT. Where X = B-A/A-C Classifier efficiency: 100 x B (A-C)/A (B-C)

Original feed may be applied at theball mill or the primary classifier. TTons of original feed. XPrimary circulation factor. YSecondary circulation factor. A% of minus designated size in feed. B% of minus designated size in primary overflow. C% of minus designated size in primary sands. D% of minus designated size in secondary overflow. E% of minus designated size in secondary sands. Primary Circulating Load = XT. Where X = (B-A) (D-E)/(A-C) (B-E) Primary Classifier Efficiency: 100 xB (A C)/A (B C) Secondary Circulating Load = YT. Where Y = (D-B)/(B-E) Secondary Classifier Efficiency: 100 xD (B-E)/B (D E) Total Circulating Load (X + Y) T.

Lbs. per ton = ml per min x sp gr liquid x % strength/31.7 x tons per 24 hrs.(26) Solid reagents: Lbs. per ton = g per min/31.7 x tons per 24 hrs.(27) Example: 400 ton daily rate, 200 ml per min of 5% xanthate solution Lbs. per ton = 200 x 1 x 5/31.7 x 400 = .079

Generally speaking, the purpose of ore concentration is to increase the value of an ore by recovering most of its valuable contents in one or more concentrated products. The simplest case may be represented by a low grade copper ore which in its natural state could not be economically shipped or smelted. The treatment of such an ore by flotation or some other process of concentration has this purpose: to concentrate the copper into as small a bulk as possible without losing too much of the copper in doing so. Thus there are two important factors. (1) the degree of concentration and (2) the recovery ofcopper.

The question arises: Which of these results is the most desirable, disregarding for the moment the difference in cost of obtaining them? With only the information given above the problem is indeterminate. A number of factors must first be taken into consideration, a few of them being the facilities and cost of transportation and smelting, the price of copper, the grade of the crude ore, and the nature of the contract between seller and buyer of the concentrate.

The problem of comparing test data is further complicated when the ore in question contains more than one valuable metal, and further still when a separation is also made (production of two or more concentrates entirely different in nature). An example of the last is a lead-copper-zinc ore containing also gold and silver, from which are to be produced. (1) a lead concentrate, (2) a copper concentrate, and (3) a zinc concentrate. It can be readily appreciated that an accurate comparison of several tests on an ore of this nature would involve a large number of factors, and thatmathematical formulas to solve such problems would be unwieldy and useless if they included all of these factors.

The value of the products actually made in the laboratory test or in the mill is calculated simply by liquidating the concentrates according to the smelter schedules which apply, using current metal prices, deduction, freight expense, etc., and reducing these figures to value per ton of crude ore by means of the ratios of concentration.

The value of the ore by perfect concentration iscalculated by setting up perfect concentrates, liquidating these according to the same smelter schedulesand with the same metal prices, and reducing theresults to the value per ton of crude ore. A simple example follows:

The value per ton of crude ore is then $10 for lead concentrate and $8.50 for zinc, or a total of $18.50 per ton of crude ore. By perfect concentration, assuming the lead to be as galena and the zinc as sphalerite:

The perfect grade of concentrate is one which contains 100% desired mineral. By referring to the tables Minerals and Their Characteristics (pages 332-339) it is seen that the perfect grade of a copper concentrate will be 63.3% when the copper is in the form of bornite, 79.8% when in the mineral chalcocite, and 34.6% when in the mineral chalcopyrite.

A common association is that of chalcopyrite and galena. In concentrating an ore containing these minerals it is usually desirable to recover the lead and the copper in one concentrate, the perfect grade of which would be 100% galena plus chalcopyrite. If L is the lead assay of the crude ore, and C the copper assay, it is easily shown that the ratio of concentration of perfect concentration is:

% Pb in perfect concentrate = K perfect x L.(30) % Cu in perfect concentrate = K perfect x C..(31) or, directly by the following formula: % Pb in perfect concentrate = 86.58R/R + 2.5.(32) where R represents the ratio:% Pb in crude ore/% Cu in crude ore Formula (32) is very convenient for milling calculations on ores of this type.

by (29) K perfect = 100/5.775+2.887 = 11.545 and % Pb in perfect concentrate = 11.545 x 5 = 57.7% and % Cu in perfect concentrate = 11.545 x 1 = 11.54% or, directly by (32), % Pb = 86.58 x 5/5 + 2.5 = 57.7%

Occasionally the calculation of the grade of perfect concentrate is unnecessary because the smelter may prefer a certain maximum grade. For example, a perfect copper concentrate for an ore containing copper only as chalcocite would run 79.8% copper, but if the smelter is best equipped to handle a 36% copper concentrate, then for milling purposes 36% copper may be considered the perfect grade.

Similarly, in a zinc ore containing marmatite, in which it is known that the maximum possible grade of zinc concentrate is 54% zinc, there would be no point in calculating economic recovery on the basis of a 67% zinc concentrate (pure sphalerite). For example, the following assays of two zinc concentrates show the first to be predominantly sphalerite, the second marmatite:

The sulphur assays show that in the first case all of the iron is present as pyrite, and consequently the zinc mineral is an exceptionally pure sphalerite. This concentrate is therefore very low grade, from the milling point of view, running only 77.6% of perfect grade.On the other hand, the low sulphur assay of concentrate B shows this to be a marmatite, for 10% iron occurs in the form of FeS and only 2.5% iron as pyrite. The zinc mineral in this case contains 55.8% zinc, 10.7% iron, and 33.5% sulphur, and clearly is an intermediate marmatite. From the milling point of view cencentrate B is high grade, running 93% of perfect grade, equivalent to a 62% zinc concentrate on a pure sphalerite.

henan mining machinery and equipment manufacturer - formula for recirculating load of cyclones and mill

henan mining machinery and equipment manufacturer - formula for recirculating load of cyclones and mill

SBM Machinery is a professional material processing designer and supplier in the world, we have excellent research and development group to provide our clients the ...Circulating Load Formula In Ball Mill, ... load for grinding fundamentals. both the density and flow of the cyclone ... ball mill recirculating load ...

Ore beneficiation equipment, sand making equipment, crushing equipment and powder grinding equipment, which are widely used in various industries such as metallurgy, mine, chemistry, building material, coal, refractory and ceramics.

high recirculating loads in ball mill circuits - grinding & classification circuits - metallurgist & mineral processing engineer

high recirculating loads in ball mill circuits - grinding & classification circuits - metallurgist & mineral processing engineer

A recent grinding bulletin addresses this question from the perspective of Classification System Efficiency (CSE). Simply put, CSE is an emerging efficiency metric that is equal to the percentage of 'coarse' material in the ball mill, and thus also equal to the percentage of useful ball mill power.

I believe this to be the result of the inefficient nature of cyclones. Screens have proved that circulating loads can be reduced to 100%. Unfortunately most cyclones will report high percentages of fines back to the ball mill resulting in high recirculating loads. Applying a more efficient separation technology, circulating loads are not only reduced, but in many cases where multiple mills are installed, are idled.

"With a CLR of 160% the circuit is close to 2.0 times more productive (efficient) than open circuit (0% CLR). Increasing the circulating load to 500% brings that value up to 2.6 times, for a further relative productivity increase of 30% (2.6/2.0 =1.30)."

The reason for keeping the circulating load high is to keep the retention time low. The whole concept of Rob McIvor's method is "separate the fines soon after they are created". Running a low circulating load means you are running a high retention time, and a "fine" particle created at the "front" of the mill must be delivered to the end of the mill, and during the journey it is likely to be overground -- this is the inefficiency David is referring to.

I understand fully the need to run at higher circulating load. I expect the mill capacity to decrease at some point as the circulating load increases. Thus, I wanted to know from the link provided if data represented in Figure 1 are experimental or simulated?

A course at CMP this year showed the same chart as Figure 1, but listed the credit as "Principles of Mineral Dressing", A.M. Gaudin, 1939. I don't have that reference, but hopefully somebody has an old text in their library.

Actually Figure one comes from Gaudins 1939 Principles of Mineral Dressing", where he refers to the work done by E.W. Davis who ran the test in a pilot mill at the Minnesota School of Mines in 1925. Davis manipulated the CLR in his pilot mill to demonstrate that as the circulating load increases the production rate of new fines also increases.

Today, there are grinding circuits operating with low circulating loads due to more efficient classifier closing the circuit. Therefore, benefiting from a higher mill new feed rate and stable operational cautions on downstream process, since overground of the valuable minerals is drastically minimized. Therefore mill operators now have a choice on how they want to maximize the plant operation.

Guys, for you might enjoy using: http://www.911metallurgist.com/blog/circulating_load_calculation_formula and http://www.911metallurgist.com/blog/ball-mill-circulating-load-formula as well as reviewing http://www.911metallurgist.com/blog/ball-mill-circulating-load

Prof. Alban Lynch expressed an opinion on the use of hydrocyclones in closed grinding circuits: "the way they are used now is an absolute nonsense, with circulating loads in some cases of well above 200%. The future is high frequency screens". This has led, unsurprisingly to a few comments on the use of hydrocyclones and screens in milling circuits.

An enigma is defined as a puzzling or inexplicable occurrence. The description fits the present position of wet classifiers well. We need to grind increasing amounts of low grade, harder ores to meet the demand for metals so the expenditure on mills and understanding breakage is high. Classifiers can limit circuit productivity by 10% or more yet there seems to be relatively little expenditure on ensuring that size separation in classifiers is accurate and efficient. Knowing the past is the starting point for doing better so I will briefly review the story of cyclones and size separation.

Cyclone classifiers have been used in dry and wet grinding circuits for decades. The hydro-cyclones used in wet circuits are small, inexpensive, easy to operate, and handle changes in throughput without difficulty. Their disadvantage is that their separation characteristics are poor and they can produce recycling loads up to 400% although the particles which require regrinding may comprise only a small fraction of this. These high loads limit the capacity of mills to grind new feed and reduce the sharpness of the split, both of which may be costly. The problem occurs in both dry and wet processes and the different approaches used in the cement and ore industries to operating centrifugal separators will be discussed.

Surely there is a limit to the particle size one can use high frequency screens for? In dry applications I would guess the limit is around 200-300 microns if you have a dry enough product, but I would be very interested to know what you guys think is the smallest one can practically screen at in dry and wet applications.

At least part of the preference for hydrocyclones lies in the high throughput of modern concentrators. When you are processing 200 ktpd and grinding to a P80 of 200-300 microns with 200-400 % recirculating load in a grinding section, it would require a lot of screen area and there are related wear and maintainability concerns.

Looking at mineral processing over the last century once could critically see much of the development in comminution, flotation, solid-liquid separation as being a case where the application as technology (including equipment sizing, flowsheet designs and other developments) has lead science, i.e., the practice of engineering where much depends on people-/team-related work. For us to ignore this aspect re pioneering and application is missing a major component of how mineral processing adds value (both from knowledge and economic perspectives).

Thanks again to Dr. Lynch for the pioneering in this arena and demonstrating industrial operations are important sites for research work & that it is possible to do meaningful work at industrial operations.

I see a combination of screens and cyclones required for optimal performance. The simplicity and high capacity of a cyclone make it ideal for large scale operations, however we must scalp gravel out of the feed to a cyclone to avoid spigot blockages which could have disastrous consequences, placing a screen ahead of the cyclone to scalp out gravel from a cyclone feed is an ideal situation.

But the biggest advantage of a cyclone (if designed correctly) is its ability to reject coarse gangue, thereby increasing throughput and reducing grinding costs. Don't grind what you don't need to grind!

I think you will find that Prof. Lynch was referring to cyclones in closed grinding circuits, where the underflow is fed back into the mill, rather than being used to reject coarse gangue. By rejecting coarse gangue are you confusing hydrocyclones with dense medium cyclones?

1. Worked in pb-zn concentrator with mcnally mills in combination of krebs 15 hydro cyclones, tried with 62.5 mm spigots and varied with vortex finders dia ( 145 to 160 mm) and slurry densities. The results were 14 -17% under cut size material reporting to HC underflow and there upon generating fines and eating up grinding rate of circuit.

2. worked for commissioning of chalcopyrite flotation plant at Mosabani and upon detailing the tailing found that the below 15 micron particle are having copper value three times the average copper value.

Post to these observation want to know the quantum of advantages of inducing a wet screen (may be derrick depends suitability in accordance with cut size) underneath hydrocyclone to divert below cut size material from hydrocyclone underflow to the flotation section. This will have reduced volume also.

There has been much analysis and discussion in the past of the relationship between classification efficiency and grinding circuit performance (e.g., see list of articles by Hukki below). The challenge remains -- finding effective solutions. Some of the alternatives identified and investigated include use of two-stage cyclone classification, use of screens, combining screens and cyclones, etc. Unfortunately, solutions for dealing with the high throughput operations remain. It is great to see the activity in this area & will be even better to see development of solutions which are acceptable from both capital and operating cost and operational considerations.

This article presents a simple arithmetic derivation for the relationship between sharpness of classification and circulating load, as well as world-wide industrial data which are compatible with the derived equation. It is shown that the sharpness of classification decreases with increasing circulating load. Based on the evidence available a comparison is presented between the performance of the present-day hydraulic classifiers.

The purpose of this paper is to present an analysis of the unit operation of grinding and the circulating load, of the unit operation of classification and the circulating load, and of the two superimposed into one operation to clarify the overall trend of events relating the circulating load to the capacity of the closed circuit grinding system, to the specific surface area of the final fine product, and to the energy consumption in the closed circuit grinding process.

In a grinding circuit, to reduce the circulating load, the better idea is to replace the cyclone with higher efficiency. Make sure that your cyclone does not separate lower than required liberation. you may be able to replace that with the one of coarser classification, so circulating load decreases and you need lower pump size, however the pump will be variable speed ones.

You have a high circulating load relative to your specific degree of final product size that you want. It comes to look into your efficiency of mill and classifier. Then the pump has to be bigger to accommodate both your classifier mass flow at same time maintain fresh feed mass flow, which is your production capacity.

The ball mill has higher circulation load, it generates only 30 -35% of actual fines you require to be called as product. If your product size needed is 100% passing 45 micron, then the ball mill total discharge material will contain normally 30% of 45 micron. The rest is oversize which has to be ground again. When this load is passed to classifier you may get only 20-25% product, the bypass of 5-10% (R45) comes back to mill as rejects. Therefore you see 70/30 = 2.09 times of fresh feed. When the fines generated by mill decrease below say 20% then circulation load is 80/20 = 4.0 times the fresh feed. To get the fines you have to size the pump as per this rule.

Interesting article, however it would make sense to publish some simulation when increasing the circulation load vs. the production increase or the increase of Energy, to therefore asses the optimal trend and mill's efficiency limitations BR.

The system handles both the mill inefficiency and the classifier inefficiency, and that is represented in an equation that defines the circulating load. As the efficiency of the classifier is a direct function of % circulating load, this can vary enormously and it will not affect too much the final function of grinding (F80, P80, W), but will only increase the pumping and a bigger influence of the hydraulic system over the performance of the mill itself.

High circulating load is common in both reverse and direct ball mill grinding circuits. Why? Because the ball mill closed circuit is the last stage before separation. Cyclone overflow should be clean of coarse particles. About the big pump, its one of the most important equipment when you are going to increase your capacity. Its always a limitation unless you have thought of it at the beginning of plant designing.

What is "high" in terms of a re-circulating load? In my experience, from 200-350% re-circulating is "normal" for a closed circuit ball mill (reverse or direct). The selection of the hydro-cyclones, pumps and piping sizes all go hand in hand with mill sizing selection.Perhaps the most critical thing is selecting the hydro-cyclone vortex finder to ensure the cyclone overflow is clean.

Pump static head and therefore mill elevation and plant layout are absolutely critical, and should be done at the very first design phase. Pump size is largely determined by this and the required throughput (volumetric slurry flow).

Actually with the re-circulating load of about 250-300%, your operations are fine on the ball mills. You only experience high re-circulating loads if there is a change in the material being treated meaning the Bond work index tends to be higher for the new material. If the new material has a high bond work index then you have to revisit your design criteria as well as the throughput. There is no point to push more then you fail to get your required P80=75um etc.

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vrm and ball mill circulating load - page 1 of 1

vrm and ball mill circulating load - page 1 of 1

Mainly in USA , the term circulating load is more often used than the circulation factor.Circulating load is percentage of coarse return in relation to fines & it can be calculated by : Coarse return TPH X 100/ Mill output TPH.Normal range of cirulating load in a conventional close circuitball mill is around 100-200%.Vertical mill normally be operated with a circulating factor through the separator installed of about 3.Furthermore a preseparation does take place between the grinding section and the,mainly over and above the nozzle ring.A very high circulation of material does take place here.Often the circulation factor over the nozzle ring area will be in the range of 15-25, i.e. 1400% - 2400% circulating load

Mainly in USA , the term circulating load is more often used than the circulation factor.Circulating load is percentage of coarse return in relation to fines & it can be calculated by : Coarse return TPH X 100/ Mill output TPH.Normal range of cirulating load in a conventional close circuitball mill is around 100-200%.

Vertical mill normally be operated with a circulating factor through the separator installed of about 3.Furthermore a preseparation does take place between the grinding section and the,mainly over and above the nozzle ring.A very high circulation of material does take place here.Often the circulation factor over the nozzle ring area will be in the range of 15-25, i.e. 1400% - 2400% circulating load

I guess this could be measured as usually based on the particle size distribution (PSD)of the separator feed, product and rejects. Based on these three PSD curves, the circulating factor (load) might be evaluated as well as the separation curve. See this reference for the full details:http://www.mapei.it/dam/Pdf/DAMCatalogue.pdfOn page 34 you will see the Koulen formula that evaluates the circulating load.I have no idea if the samples needed for these measurements can be obtained in practice or not.

I guess this could be measured as usually based on the particle size distribution (PSD)of the separator feed, product and rejects. Based on these three PSD curves, the circulating factor (load) might be evaluated as well as the separation curve. See this reference for the full details:

metcom expertise

metcom expertise

What is the circulating load ratio in your ball milling circuit? There is a rapid and easy way to calculate it from any set of circuit size distribution data for the standard circuit arrangement shown in Figure 1, as follows.

Let's first clearly define "circulating load ratio" as the ratio of the amount of solids going through the ball mill divided by the amount of solids going through the circuit. As it turns out, a valid "mass-balance" formula can be derived from the following two questions:

Example: A ball mill circuit product (cyclone overflow) contains 80% passing 75 um (200 mesh). The circuit feed (from the previous stage of size reduction) contains 20% passing 75 um. Therefore, the circuit is producing 60% (percentage points) of new minus 75 um material (i.e. 'A', above, equals 60). At the same time it was determined that the ball mill feed (cyclone underflow) contains 25% passing 75 um, and the mill discharge contains 45% passing 75 um. Therefore, during each pass through the mill 20% (percentage points) of new minus 75 um material is generated ('B', above, equals 20). The circulating load ratio is then 60 divided by 20, thus equal to 3.0, or 300%.

Try this out with any good set of data from the standard circuit arrangement shown above. It works with any screen size you choose to do the calculations. What is sometimes regarded as a perplexing question is readily answered from a set of size distribution data, both quickly and accurately.

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