Distribution Factors

In a circuit of various separations the factors of distribution of the first separator are nominated with SF1 and those of the second separator SF2 and thus progressively. When it to be related with some of the constituents one will have to add the initials to the constituent for its identification, for example:

• Ws F1       : Factor of distribution of the first separator related to the weight of the material or mineral.
• Au SF2     : Factor of distribution of the second separator related to the content of the gold.
• Ag SF3     : Factor of distribution of the third separator related with the content of the silver.

Applying this symbology and the concepts of the union and separation to a circuit of flotation, this can be solved algebraically, the equasions are as follows:

• F3 = F1 + F2                                 (1)
• F4 = F3 (SF1)                                (2)
• F5 = F3 (1 – SF1)                          (3)
• F2 = F5 (SF2)                                (4)
• F6 = F5 (1 - SF2)                           (5)

Equalling the fluxes F4 and F5 one obtains:

• F2 = F3 (1 – SF1) (SF2)                (6)

Replacing the equasion                  (1)

• F3 = f1 + f3 (1 – SF1) (F2)

Simplifying it, one has the value of F3

Which is an expression with known data such as F1 which is the flux of original feeding, and the factors of distribution SF1 and SF2 obtained of the metallurgical tests.

With this known expression we can simplify the other equasions of flux as follows: 

• F4 (SF1)                                           (8)
• F5 = F3 (1 – SF1)                             (9)
• F2 = F3 (1 – SF1) (SF2)                   (10)
• F6 = F3 (1 – SF1)  (1 – SF2)            (11)

This group of equasions is used in first place to calculate the distribution of the weights and after that of the rest of the components in base that F1 takes the value of 100 and the factors of distribution have been specified for each case. The laws of the chemical elements in each flux are calculated in base of the known law of the mineral of feeding and the corresponding distributions.

As is observed, the formulation of equasions and the resolution through conventional techniques is feasible. Nevertheless, the come to be highly tedious and complex when they are worked in various sizes of fractions, higher number of stages and higher number of chemical elements. For this reason, and with the purpose of bettering the efficiency, one recurs to the help of a computer system in which one uses the interactive calculus in base of the algebraic equasions described; the prepared program has been run in a programmable calculator called Texas Instruments 59.