(198c) Determination of the Kinetic Parameters of the Limestone Size Reduction in a Laboratory Ball Mill; Application to the Design of an Industrial Mill

This work describe the process of the design of a discontinuous industrial tumbling ball mill, starting with the determination of the kinetic parameters of a breakage, the specific rate of breakage S_i and the primary daughter fragment distribution b _i,j, in a laboratory tumbling ball mill for limestone.

The relevance of this work in Powder Technology teaching is that to complete the procedure an experimental work is necessary as well as a bibliographic revision, the application of theoretical knowledge and the use of computer simulation tools.

After the experimental determination of the kinetic parameters, the expressions for the rate of breakage of size iand the cumulative of primary daughter fragment distribution, Bi,j were obtained.

The experiments were performed in a cylindrical laboratory mill using steel balls of 24, 32 and 42 mm. The feed size were 1000-500 micrometers, 500-250 micrometers and 250-125 micrometers being the grinding times 1, 2, 3, 5, 8, 10 minutes. After the grinding time the powder was sieved and the amounts remaining in the different sieves measured. From the equation of the breakage of size i :

or log w_i(t) ? log w_i (0) = -S_i t /2,3 where t is the time of grinding and w_i the weight fraction of material of size i,

plotting w_i versus t, values of Si were obtained for the three initial fractions being 0,48, 0,41 and 0,37 min^-1 for the top, the intermediate and the smaller initial sizes respectively. From these values the parameters of Si a_T = 0,4756and a = 0,1878 were obtained plotting Si values versus x i/x₀ according to equation:

From the experimental values of b _i,j, the cumulative values of the breakage distribution B_j,i were obtained.

From the equation:

plotting these cumulative values versus x _i-1 /x_j the parameters of the expression were obtained being, g = 1,12; f = 0,8 and b = 3,78.

Knowing all the simulation parameters for S_i and for B _j,i both expressions can be introduced in the simulator to predict the size distribution by the equation of batch grinding:

(1)

Figure shows a comparison of computed versus experimental results.

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In the second part of the work the design of an industrial ball mill was performed based on the results of the first part.

The aim of this part was to design a discontinuous ball mill to reduce 8625 Kg/h of limestone from an initial size of 1140-1018 micrometers to a product with 70% less than 180 micrometers.

Value of parameter a_T were modified according to empirical expressions found in bibliography to change mill conditions. Also the value of a was modified maintaining unchanged the rest of the coefficients.

Introducing these coefficients in the simulator the time required for this size reduction was obtained from the equation (1).

With this value and the next scale-up equations found in bibliography:

r₂ = r₁ * (D₂ / D₁) ^0.5

the diameter = 1.83 m and the length = 3.048 m of the industrial mill was obtained.