The mathematical modeling of mineral processing is a very complex task because of random character of comminuted materials. However, it allows applying of standard laws of mass preservation and mass transport. The basic method of description of comminution processes is determination of particles size distribution curves for products. In the paper, the concept of applying so-called censored distribution functions was presented, what means equations of exponential, Weibull, log-normand logistic distribution functions as the basis of crushers work description (formulas 1, 2, 3 and 4). The censoring of distribution functions is being realized through acceptation of maximum particle size dmax and the shape of them depends on shape and scale parameters. The joining of technical parameters of comminuting devices with parameters of equations describing distribution functions of products allows creating of satisfying models of comminution processes. After application of general forms of separation curves the description of sieving processes is possible (equations 6a and 6b) and then also of comminution systems. The optimization of aggregates production may be based on introduction of goal function determining profit dependably on amount of individual assortments. In case of analysis of comminution systems (formulae 10) in preparation of feed to beneficiation the goal function should be based on levels of useful minerals exposure in individual fractions. The paper shows the possibility of simulation of comminution processes course leading to determination of optimal conditions of systems containing comminution and sieving processes. Furthermore, the necessity of creation of empirical models for grinding processes was shown as they would be the compensation of models being result of heuristic analysis of phenomena. Also, the elementary rules of selection of models forms and their modifications based on justification of relations between distribution function parameters and basic technical parameters of devices as well characteristics of comminuted materials were discussed. The paper is the introduction to further research of general approach to joining grained materials characteristics with comminution effects.

The separation or beneficiation processes are conducted in many devices and concern many various types of minerals and raw materials. The aim of conducting these processes is always to achieve the best possible results allowing as much of the useful component as possible to be obtained by maintaining reasonable costs of the process. Therefore, it is important to have the possibility to monitor the process effects and to have efficient tools to evaluate the course of it. Generally, the ore’s ability to partition into concentrate and tailings is called its efficiency, upgradeability etc. It can be said that there is no unambiguous measure of upgradeability and there are many factors in use which enable to evaluate it qualitatively. Among them are such commonly known parameters as: recovery, losses, yield, upgrading ratio and many others. They are based on three principal parameters that is the average content of the useful component α, the contents of this component in concentrate β and the contents of this component in tailings ϑ. For a given ore (assuming that α = constant), the multi-product separation results can be treated as points of a trajectory located on the surface of factor w in a three dimensional space (β, ϑ, w). The course of the trajectory depends on the ore petrographic and mineralogical properties preparation for the process. For these reasons, searching for optimal (potential) possibilities of the ore is relative, which is presented in the example of Halbich, Fuerstenau and Madej upgrading curves. Such curves are efficient tools to evaluate the course of a separation (beneficiation) process and each of their types allow the effects to be shown in different perspective. Apart from this, they allow also the optimal feed conditions to conduct a certain process with aim of achieving the expected results to be found. Furthermore, the effect of the ore preparation on the flotation results, on the sum of recoveries of the useful component in concentrate and residual recovery in tailings is presented in the paper. The results indicated that any additional contamination of concentrate should be taken into account during the organization of the flotation process. In this way, the results of fractionated flotation have much valuable information to establish the course of the process.