Table of Contents
Hydrocyclones are currently the most commonly used classifiers in wet closed circuit grinding systems. Some recent papers, however, give evidence that high frequency vibrating screens can be a viable alternative to hydrocyclones for a wide variety of grinding applications.
In principle, classifier selection for closed circuit grinding should be based on an evaluation of the advantages provided by each classifier type being considered (e.g., increased circuit capacity, improved water balance, reduction in undesirable fines, etc.) versus costs (capital, installation, operating). Furthermore, the evaluation should be made for those conditions of optimal mill/classifier performance which give the desired product quality. This requires a detailed knowledge of the factors which affect the performance of the classifier types of interest. .
Pilot Plant Study
The feed materials used for the pilot plant study were three different limestones designated here as limestones A, B and C, having Bond Work Indices of 6.4, 7.6 and 11.9 kW-hr/short ton, respectively. All three materials were used for closed circuit demonstration testing; limestone A was the feed material•used for model development and validation.
When constructing models for mills and classifiers it is customary to split the particle size range into geometric intervals according to the √2 sieve series and number the largest size 1, the second largest size 2, etc., down to the smallest (sink) size n. This is done because material in one of these size intervals appears to behave like a homogeneous material, to a sufficient approximation.
Using this basis, models for ball mills are constructed as mass-size balances incorporating the concepts of specific rates of breakage Si, and primary progeny fragment distributions bij. Si is the specific rate of breakage of size i, with units of fraction per minute being convenient for ball mills; bij is the weight fraction of progeny fragments which appear in smaller size i as a result of primary breakage of larger size j. Combining these concepts into a size mass balance for a fully mixed batch mill gives the equation set known as the batch grinding equation:
where wi(t) gives the particle size distribution as a function of grinding time t. Reid showed that the concept of residence time distribution (RTD) could be immediately applied to a steady-state continuous mill to give
where ∅ (t)dt is the fraction of feed which leaves the mill at time t to t+dt after admission, and ∅(t) is thus the RTD (units of fraction per unit time); pi is the fraction of the mill product of size i. The solution of Equations 1 and 2 for known feed size distribution and known ∅(t) can be put as
where fj is the weight fraction of the mill feed of size j and the dij is a matrix of “transfer” parameters. When expressed as Equation 3, the function of the simulation model is to compute dij (which contain the Sj, bij and RTD) for the mill design and operating conditions of interest.
The objective selected for pilot plant simulations was to determine the maximum circuit product rate Q when producing product size distributions with a specified 80% – passing size in the range of 25 to 90 microns. This objective is relatively simple to accomplish since there are no constraints due to specifications on the density of the fine product slurry. Note, however, that simulations performed without regard to specifications on the circuit water balance may not be realistic for many applications.
The reasons for these results are clear upon examination of the corresponding classifier performance data. Figure 8 shows the classifier bypass data corresponding to the results in Figures 5 and 6. Lower bypass tends to give higher Q, by reducing overgrinding of fines and giving a steeper product size distribution as shown in Figure 7. Higher sharpness index has the same effect and as Figure 9 shows the SI is higher for the screen above about 45 microns. The sum effect of bypass and SI is to favor screens for 80% – passing sizes above 40 microns.
Design of a Full Scale Circuit
It was of interest to the authors to evaluate high frequency screens versus hydrocyclones for the wet, closed circuit grinding of a coal in a full-scale ball mill circuit. The coal feed was a crusher product having a top size of 9.5 mm. The specification for the ground coal product was 95 weight percent smaller than 160 ± 10 microns and 80 weight percent smaller than 110 ± 10 microns, with no specification for the solids density of the circuit product.
Use of this hydrocyclone model in effect set the minimum size of mill for the evaluation. That is, since the model is for a particular size of hydrocyclone operated over its normal range of slurry feed rate, which Slechta and Firth report to be 250-500 liters/min at 9 to 35 weight percent solids, the mill required for a single mill/hydrocyclone system had to be large enough to provide, the solid rates necessary for normal operation of the hydrocyclone. For simulation this is necessary in order to establish dimensions for a mill and therefore allow the appropriate Si correcting factors to be calculated. For larger mills than this minimum size, one would use a multiple hydrocyclone arrangement. From the Slechta and Firth report, the maximum hydrocyclone solids feed rate would be about 15 tph of coal. Assuming a reasonable circulation ratio of 2.5, the minimum size of mill appropriate for evaluation was determined to be 1.37 m in diameter for an assumed mill-to-length ratio of 1.5.
Results
Over most of the product size range examined, particularly in the range of interest, 80 weight percent passing 100 to 120 microns, high frequency screening with the DF 88 or DF 105 cloths gives higher Q than when the hydrocyclone is used. That the screen and hydrocyclone results are not so different is due to the relatively low hydrocyclone bypass, a result of feeding the hydrocyclone relatively dilute slurries, to obtain dilute fine products.
It is interesting to examine the costs of high frequency screening versus hydrocyclones for this grinding application. In general these costs are a function of the number of units required and capital cost per unit, installation costs, and operating costs. For high frequency screening, the data presented by Rogers and Brame and substantiated by Derrick show that a Derrick screening machine fitted with DF 88 screen cloths can classify about 500 liters/min of the coal slurry per square meter of screening area.
The results presented in the pilot plant study indicate that high frequency screens can be a viable alternative to hydrocyclones for the wet, closed circuit grinding of fine-slurries.
