First we must define what is it to optimize?: for a given P80 I think in four factors:

• less energy and ball mill consumption
• less ultrafine content in the product
• less range oversize between P80 and P100 (max. size) 

Recommendations for achieve these goals in ball mill grinding circuit:

• In a plant with hydrocyclones is correct to use higher circulating load (~400%) to diminish residence time in the mill. For instance, versus 300% CL around 5% energy saving is obtained and the product has 5%-10% less -10um fraction (see 4th Grinding and Classification Law)
• But is better to use high frequency screen (like  Derrick) as classification device. In this case the operation goes to lower circulating load (~150%) giving extra capacity to the mill. Because the better efficiency of the screen, less ultrafine are returning to the mill as short circuit compared with cyclones giving 20% less -10um fraction in the product compared with standard circuit. Also the oversize fraction can be controlled with the screen slot. For this application probably a slot screen around 300 um can be used limiting the maximum coarse particles to this size. Savings of 15%-20% in energy have been reported.
• Balance ball charge and better steel ball quality must be use: you must charge two ball size: 33% 2" and 67" 1 1/2" just in case the feed is around P80 1/4". Also high chromium cast steel gives less steel consumption versus forged ball and better grinding efficiency due the shape stability of the balls (less chips), but economic evaluation according ball price must be consider.

Regards

Luis Bernal

PROCESS MINERALS CONSULTING

luis.bernal@processminerals.cl

Have a look at the Functional Performance method of Metcom Technologies (Rob McIvor and his mates).  Have a look on Onemine.org (search for Rob's name or the keyword "functional performance").  The method is a rigorous way of determining how well all three components of the grinding circuit are performing (mill, pump and classifier).

Thanks Alex. I found a paper by McIvor on onemine that allows 1/4 of excerpts. Here is some:

Bond work index analysis takes this method of experimentation several steps further (Bond, 1952; Rowland, 1976). During comparative testwork, variations in the ore grindability, grinding energy input, and feed and product sizing are measured and accounted for through the grinding circuit "model embodied in the work index formulation. For each set of data, both the circuit operating work index and the laboratory test work index of the circuit feed are determined. Relative work index efficiencies with and without the change to the circuit can then be calculated and compared.

Population balance modelling attempts to provide a much more detailed analysis of grinding circuit performance (Austin et al, 1984). Parameters that are used for ball mill modelling include breakage rates and breakage product sizes for each size class of particles, and residence time distribution in the mill. The behavior of each size of particle is also described by the classifier selectivity function. Breakage rate parameters can be compared from plant tests, once again to seek design and operating conditions that provide the best breakage environment. To be used in a predictive manner, all the significant equipment dimensional and performance characteristics, ore and slurry characteristics, and the interactions between them, along with the operating constraints which define boundary conditions, must be identified and mathematically characterized with sufficient accuracy. This is the task of steady state grinding circuit simulation. Regardless of the level of sophistication of the analyses, the basic strategy being applied is similar. The "What if we change this design (or operating) variable?" question is posed. The premise is then tested, either by an actual change in the plant, or by changing one of the inputs of the circuit simulator. Circuit performance with and without the change is then compared to determine whether the net effect was a positive one.

Functional Performance Analysis of Ball Milling

Application of value engineering techniques (Miles, 1972; Wales and Pfeiffer, 1986) to grinding process modelling led to the identification of two basic functions of the ball mill classifier circuit. In terms of a specified circuit product size which is used to differentiate between "coarse" or oversize material and "fines" or undersize material, these basic functions are (a) breakage of the coarse material and (b) removal of the fines. It was proposed that it may be useful to relate circuit design and operating variables to these basic circuit functions, which although related, are conceptually quite distinguishable. If each could be quantified by a suitable parameter, then either or the two together may be correlated to overall circuit efficiency, and hence used to link individual design and operating variables to overall circuit performance.
Ball mill circuit classification system performance is considered here first because it provides the basis for subsequent characterization of ball mill breakage efficiency.

Ball Mill Circuit Classification System Efficiency

As described above, "fines" may be defined as any material smaller than a specified product size, and "coarse" as any material that is larger. The target 80 percent passing size of the grinding circuit product is a convenient reference point, as it is often used to express the grind size objective. This size is close to the modal value of typical size distributions of ground material (Gaudin, 1939), and also roughly approximates the classifier cut size (Mular and Jull,1980; Arterburn, 1982).

The effectiveness of the fines removal system depends on the transportation of material to the classifier. It also depends on the ability of the classification equipment to remove the fines that are presented to it from the circuit, and to return the coarse material to the mill. Immediate and perfect sorting action would result in a circuit product size distribution dependent only on the material fracture characteristics (Austin et al, 1984), and avail the maximum possible amount of mill volume (and applied power) for the breakage of coarse particles. The fraction of fines in the mill hold-up (the "fines inventory") may therefore be taken as a direct measure of the lack of the system's fines removal effectiveness. Its complement, the "coarse solids inventory" represents the fraction of the mill volume (or power) which is effectively used for the size reduction of coarse particles. Therefore, it also represents the overall classification efficiency of the grinding circuit.

A simple method for estimating the relative coarse solids inventory in the ball mill has been selected. It is the average of the coarse fraction in the ball mill feed and discharge size distributions. In closed circuit grinding, the shift in these size distributions is normally quite small. A more complex relationship between mill contents and measured feed and discharge size distributions no doubt exists. However, the general correlation between the mill (or circuit) production capacity to a given product size and these size distributions is supported by a variety of observations, described as follows.

The circulating load ratio is an excellent subject for study of classification system performance because it has long been recognized as such an important factor in ball milling efficiency. Results from the classical work of Davis (1925) are shown in Figure 2. Note that an increase in circulating load ratio from 150 to 500 percent yielded an increase in production rate from 190 to 230 units, a relative increase of 21 percent. Ball mill feed and discharge size distributions associated with the same circulating load ratios are shown in Figure 3. These were produced by simulation, but are almost identical to reported data from two operating plants (Hawthorn, 1978; Gould, 1976). Based on the circuit product size of 105 microns (150 mesh), the estimated coarse solids inventory increases from 72 to 87 percent, also a relative increase of 21 percent. Because a number of factors and their combined interactions can effect overall circuit output, there is no doubt that these particular data are somewhat coincidental. However, they are presented here as they provided the first clue that led to the discovery that this simple parameter can effectively characterize overall ball mill circuit classification system efficiency.

Coghill and deVaney (1938) also conducted experiments in a pilot plant ball mill closed circuited with a rake classifier over a wide range of circulating load ratios. They noted that, "It held true that the percentage of decrease in mill capacity was almost identical with the percentage of finished material in the composite feed. For example, when forty percent of the finished material was returned it amounted to 19 percent of the composite feed and the reduction in capacity was 21.5 percent." Kelsall et al (1959) were among the earliest to conduct experiments in the perfectly controlled environment provided by a computerized ball mill circuit simulator. They tested the general effect of various circuit design and operating variables, including circulating load ratio. "All product size distributions had the same 80 percent passing size, and fresh feed rate was altered to give a range of circulating loads It was shown that the ratio of the closed to open circuit feedrate, which may be taken as a measure of the increased efficiency of closed circuit operation, was proportional to the fraction of the mill contents which was coarser than the classifier separation size."
Laplante et al (1985) have demonstrated that the cumulative specific breakage rate (i.e., the specific disappearance rate of material of the complete size distribution down to a defined particle size) remains virtually constant over a reasonable range of operating conditions, including variations in the mill feed size distribution itself. This means that the production rate of material finer than a specified size is directly proportional to the percentage of material in the mill feed greater than this specified size, which again is a reflection of the mill coarse solids inventory.
In the more general context of the mineral processing plant, the fines versus coarse solids inventory demonstrates that classification system inefficiency not only means reduced effective grinding energy, but also the direct misapplication of that energy to the overgrinding of fines. This effect and the importance it has on grinding circuit product quality is shown by the simulation results depicted in Figure 4 (Austin et al, 1984).
Further discussion of this parameter for ball mill circuit classification system efficiency has been presented elsewhere (Mclvor, 1988).

Ball Mill Breakage Efficiency

Consider a ball mill circuit processing material of a given feed size and at a given throughput rate to a target product size, the latter which once again distinguishes the "fines" from the "coarse" material. The production rate of fines or new product size material can be calculated from the circuit feed and product size distributions and the throughput rate of the circuit. Based on the energy expended in the ball mill, the production rate of new product size material (tonnes/h) equals the amount produced per unit of energy applied (tonnes/kwh) times the rate at which energy is applied (kwh/h). The rate at which energy is applied is the power draw of the ball mill. If we then define the production per unit, of energy applied as the "energy specific production rate" of the circuit, then we can write the following equation:

....get the original paper and more at OneMine.org

Discussion

These examples highlight some of the important characteristics of functional performance analysis as an innovative approach to evaluating and improving the performance of ball milling circuits. At Selbaie, influx of both fines and additional water from the crushing plant were seen to offset one another, yielding little change in classification, breakage, or overall circuit efficiency. At Dome, high water usage was seen to contribute directly to high circuit efficiency through its positive impact on classification efficiency. At Kidd Creek, percent solids in the ball mill was found to be an important factor in circuit efficiency because of its effect on the breakage environment. Thusly, functional performance characteristics were used in each case to relate specific design or operating variables to overall circuit performance.
This approach provides an important extension to Bond work index analysis. The only material size data utilized by the Bond method are single point values of the circuit feed and product. One of the most serious shortcomings of the Bond approach is that in its simplicity some important circuit variables are neglected, among them classification. Functional performance analysis uses all the circuit size data and recognizes classification as one of the two basic functions of the ball mill circuit.

It may be noted that classification system efficiency as defined here is independant of the ore type. It can be studied separately from the ball mill breakage efficiency, which determinations require laboratory tests of ore grindability. This is convenient because a practical sequence for a general milling circuit upgrading program may be, initially, to consider the classification system, which when modified, will affect the material size distribution inside the mill.

While providing a significantly higher level of sophistication than work index analysis, functional performance characterization offers a useful simplifying algorithm upon which a more complex model may be structured. Conceptually, the functional performance equation clearly exposes to the researcher and plant metallurgist alike those four factors upon which net circuit output is dependent.
In many investigations, it may be difficult or even impossible to assess the net effect of a given variable on overall circuit efficiency. For example, in studies of rheological factors in ball milling, batch laboratory tests were used to successfully predict rheological effects in continuous open circuit mills. However, the addition of a classifier to the circuit introduced complexities which made such predictions unreliable (Klimpel, 1982-83). The decoupling of ball mill circuit classification and breakage performance through functional performance characterization provides an important simplification for developing an understanding of the complicated effects that such factors have on overall circuit performance.

Most importantly, compared to either the Bond or population balance methods, functional perfor-mance analysis is more fundamentally analytical than trial and error in its application. Using the Bond approach, a change to the circuit which actually improves breakage but which simultaneously causes an offsetting loss in classification efficiency would lead to the incorrect conclusion that the change had no effect. For example, a reduction in water addition rate at the feed end of the ball mill may provide a more favourable breakage environment, but result in poorer classification performance due to a net reduction in classifier feed water. Although population balance modelling may reveal a change in breakage rates, it would provide no specific conclusion as to why no increase in overall circuit output was achieved. Circuit functional performance characteristics would reveal the improvement in breakage, and permit further gains through identification and correction of the classification system deficiency, in this case by making up for the change in classifier feed water at the pump box.

Finally, it has been shown that ball mill circuit functional performance parameters can be related directly to work index efficiency measurements. Because energy and steel consumption are also directly related to one another and together dominate ball milling costs, the Bond approach provides a useful link to grinding circuit economics. The methods can therefore be combined to develop cost-benefit information for economic justification of process improvements which require capital expenditures (Mclvor, 1989). This is one of the essential elements of a process analysis system if potential improvements are to become industrial realities.

Also see http://www.metcomconsulting.com/ball_milling.php

Determining the Bond Efficiency of industrial grinding circuits

I went to a Derrick screen like Liberal and all of my classification problems went away.

https://www.scribd.com/user/161408287/Cristian-Dosque-Munoz