Abstract
The object of research is the process of oxide reduction in a reaction system of mass m due to the reaction on a contact surface with an area of S.
 An adaptive technology is proposed that allows one to construct the kinetic equation of the process in which the oxide is reduced from the initial product under conditions of a priori uncertainty. A priori uncertainty regarding the behavior of a physicochemical system is understood as the fact that the following information is not available to the researcher:
 – about the change in the mass of the reaction system and the area of the contact surface;
 – about the rate of accumulation of the finished product;
 – about the time of withdrawal of the finished product from the system.
 The proposed adaptive technology includes five sequential stages to eliminate a priori uncertainty. This is ensured through the use of an adaptive algorithm, which allows obtaining the maximum accuracy in estimating the output variable by selecting the optimal parameter of the adaptive algorithm, and the subsequent canonical transformation. The introduced concept "canonical transformation of the kinetic equation" has the following meaning: having received some adequate description of the kinetic equation in a Cartesian coordinate system, a transformation is carried out that allow representing the equation in a new Cartesian coordinate system in such a way that its structure corresponds to the canonical form. The basic postulate of chemical kinetics can be such a canonical type.
Highlights
Formal kinetics methods are still a reliable and relatively simple tool for studying physicochemical processes
Obtaining mathematical models of the processes under study makes it possible to identify the mechanisms of these processes and, as a consequence, find ways to control them. This is evidenced by the publication of research results by methods of formal kinetics of proces ses that differ significantly in nature: combustion [1], flue gas cleaning [2], processes occurring during the processing of polymers [3] and the production of explosive components [4], structural transformations in alloys [5], interactions between viral proteins and specific antibodies [6]
The essence of the adaptive technology for constructing the kinetic equation: theoretical justification The parameters k and η are unknown in equation (2), but under the conditions of a priori uncertainty, the parameters S, m are unknown
Summary
Formal kinetics methods are still a reliable and relatively simple tool for studying physicochemical processes. Obtaining mathematical models of the processes under study makes it possible to identify the mechanisms of these processes and, as a consequence, find ways to control them. This is evidenced by the publication of research results by methods of formal kinetics of proces ses that differ significantly in nature: combustion [1], flue gas cleaning [2], processes occurring during the processing of polymers (polyethylene processing) [3] and the production of explosive components [4], structural transformations in alloys [5], interactions between viral proteins and specific antibodies [6]. It is natural to formalize such systems taking into account the internal chemical kinetics and mass transfer, which open up new possibilities in creating a wide range of chemical engineering products: catalysts [7], enriched (2021), «EUREKA: Physics and Engineering» Number 4 minerals [8], coatings on materials [9], or obtaining new theoretical concepts on the processes for their subsequent implementation in the energy sector [10]
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