DIFFERENTIAL ASSIMILATION COEFFICIENTS IN STEEL PRODUCTION CONTROL SYSTEMS - Kharchenko, Аlеxander; Lichkonenko, Natalia (Scientific Journal "Metallurgy", 2021)
Thermodynamic analysis of the «metal-slag» and «metal-slag-gas» systems using the Gibbs chemical potential method has been carried out. The concept of differential assimilation coefficients (DAC) is introduced, which take into account all the cross-effects of the influence of some chemical elements in the metal on the content of others. The definition of DAC as a change in the mass of the i-th element in the metal when adding a unit of mass of the j-th element to the system is given. Analytical expressions for DAC, which are necessary for effective solution of the inverse problem in control systems of melting and alloying processes of liquid steel, are obtained. Specific requirements to the components of the square matrix of DAC concerning its action on the valence vectors of chemical elements in the slag and the composition of the equilibrium metal and slag are formulated. A method for testing the used thermodynamic models of multicomponent solutions in metal and slag by analytical calculation of DAC is proposed. The concept of differential concentration matrix (DCM) as a derivative of DAC is introduced, the elements of which are equal to the change in the con-centration of the i-th element in the metal when adding the unit mass of the j-th element to the system. It is shown that DCM can be used to classify various ma-terials in respect to their effect on the content of oxygen, sulfur, phosphorus and other impurities in steel at the current state of the system «metal-slag-gas». Sys-tems of inequalities with matrices of DAC or DCM for optimization of materials quantities using simplex method on condition of guaranteed compliance in the set chemical composition of an intermediate product or grade structure of steel are derived. An analysis of the possible impact of technological and organizational constraints on the solution of the extended system of inequalities has been made. It is concluded that the use of DAC is a key feature and a necessary element of modern computer control systems for melting and out-of-furnace processing of steel. Examples of practical application of DAC in systems of design and control of steel production are given.