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## Circulating Load Equation (9 replies and 4 comments)

I think you are making this too complicated. The usual definition of a circulating load is the (dry) mass flow returning to the mill from the classifier and is expressed as a percentage of the mass flow of new feed (Wills Min. Proc. Technology, 2016)

So do a material balance around the circuit, figure out the mass flow rate of solids in the cyclone underflow and divide that by the mass flow of solids in the circuit feed. You can then get more complicated if you want, and track the circulating load of some sub-fraction, the water, radioactive tracers or whatever.

Some ideas in here: https://www.911metallurgist.com/blog/ball-mill-circulating-load-formula

I support the explanation of of Alex Doll. That is simple and easiest way to calculate the circulating load. We can use the mass flow rate of solid in the cyclone underflow divide it with the fresh feed coming into the mill.

1230agua, I agree too. However, that is not my concern. You may see the details to my reply to his statement below. Thanks.

Hi Alex,

Thank you for your insights. Yup. there's no question about the definition of circulating load. I think no one will argue that Wills Min Proc Technology Reference is a standard reference. Actually, the two methods I asked in this post were included in his book or Gupta's, if I'm not mistaken.

There's no doubt that it would be easy to determine circulating load given that you know the mass flow rate of solids in the cyclone underflow and circuit feed. For most local plants here though, they only monitor the mass flow rate of solids in feed through weightometer or belt cut, and not mass flowrate of solids in cyclone underflow. Nevertheless, I'm also aware that mass flowrate of underflow can be measured/estimated by using fluid flow equations such as Manning's through experimentation or through basic methods, such as determining the total time it takes to fill a known volume of container. There's no question about these. Despite having these methods for underflow, like what you have said, most plants determine circulating load through material balance of some sub-fraction, the water, radioactive tracers.

Back to my question with a simple case, the circulating load results through sub-fraction do not match with the results using water. It's like 310% vs 700%. In such case, which one is accepted to be more reliable?

By the way, I checked the link https://www.911metallurgist.com/blog/ball-mill-circulating-load-formula, and I must say it is a perfect example because circulating load from sub-fractions doesn't vary significantly. With this, I would like to add another question. If there's a huge variation of circulating load based on sub-fractions, would the arithmetical average circulating load still be accurate?

Please take note that the samples were taken during continuous grinding operation so the differences are expected. However, I'm quite concerned with the enormous difference with the results. Your comments and suggestions are highly appreciated.

If you want to determine the circulating load (CL) using data from particle size distribution (hydrocyclone feed, hydrocyclone overflow, and hydrocyclone underflow) is possible to get different results in the different fraction sizes.

The solution is to consider a reconciliation analysis. The idea is to adjust particle-size data to eliminate the potential effect associated to the sampling process errors.

Thanks Jorge for your idea. I would highly appreciate if you can elaborate more about how to do the reconciliation.

You should review the article written by *Reid and Voller, "Reconciling hydrocyclone particle-size data". Chemical Engineering, June, 1983*. The article explains the reconciliation process.

By any means, do you have a copy of this article? It is not included in our e-library.

It got my intention with its description. "The procedure is to find the recirculating load for which the sum of the squared adjustments is a minimum. The algorithm as presented applies to particle-size data for three hydrocyclone streams." However, since I don't have access on it, I'm still not confident how it's done.

I think I now understand, most of your question is related to conducting mass balances in situations without sophisticated sampling.

I suggest you buy "The Circulating Load" book from the Society for Mining, Metallurgy & Exploration (SME). I expect it talks more to your needs as it is based on non-instrumented plants.

http://smemi.personifycloud.com/PersonifyEbusiness/Store/ProductDetails.aspx?productId=116779

The Circulating Load: Practical Mineral Processing Plant Design

An alternative paper written by Voller is below,

V.R. Voller and P.J. Ryan. Automated Material Balance and Assay Data Adjustment Around a Piece of Mineral Processing Equipment. International Journal of Mineral Processing, 10 (1983) 279--288.

Hi mlticzon,

Welcome to 911Met and thanks for this useful question. This is one of those learn by reading/doing/trying.

Have a good look at https://www.911metallurgist.com/blog/moly-cop-tools-download and all its content.

ARTHUR TAGGART says about** Tonnage of circulating load:** If the actual circulating tonnage is required, the weight of feed or classifier overflow must be known. When the assay formulas are used and screen analyses constitute the assay it is wise to calculate the per cent, circulating load for more than one size and use the average figure; in taking the average, reject all computed circulating loads that are obviously out of line, probably on account of errors in sampling or sieve analysis.

Also see http://www.osti.gov/scitech/servlets/purl/887498-PyO15S/

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What is the most reliable method to determine actual circulating load in grinding circuit? A simple one - ball mill w/ hydrocyclone.

I observed that the most common methods applied are (1) use of water balance - taking samples of cyclone feed, cyclone underflow and cyclone overflow. They will get the %solids, then compute for dilution ratio - then finally, %circulating load. and (2) use of particle size distribution - the samples taken for %solids will be screened for PSD; then circulating load can also be calculated by just using the %weight of samples in sieve fraction.

Which is more preferred when results are not so close? Are there other methods?