The use of waste paper as a fibrous semi-finished product in the production of paper and paperboard products makes it possible to somewhat reduce the consumption of cellulose. However, waste paper contains a number of water-polluting components of mineral and organic nature, which were introduced into its composition at the stage of production. One of the issues that may arise in the design of technological systems for the production of a given type of paper or cardboard or in the reconstruction of existing production to reduce losses of fibrous semi-finished products and ensure their optimal use or reduce fresh water consumption is to calculate the pollution and also to determine the impact of cardboard and paper production tanks and treatment plants on the dynamics and level of watercourse pollution.
To study and analyze the paper and cardboard production processes, which belong to the class of complex technological systems, a methodology was developed that, using computer technology, allows assessing the state of a technological system until its implementation in action. However, from a practical point of view, methods still should be developed that will allow the designer to find solutions to problems that may arise at the design stage of the technological system for production of a given type of paper or cardboard or in the reconstruction of existing production. These problems are related to the calculation of the pollution level and the determination of impact from cardboard and paper production tanks and treatment facilities. The purpose of this article is to conduct research and forecast calculations based on mathematical models to determine the patterns of influence exerted by tanks on the dynamics and level of watercourse pollution in the production of paper and cardboard. The generalized technological system of cardboard production, which is presented in the form of a material flow graph, is taken as an object for research. Water-soluble contaminants of mineral and organic nature enter the production system together with fibrous raw materials, partly with fresh water, and with chemical additives used to impart certain qualities to the product at the stage of its production and at the stage of mechano-chemical water purification. In order to study their impact, it is necessary to conduct at least two stages of calculations on a personal computer using pre-designed models for the dynamics and level of watercourse pollution.
At the first stage, the dynamic characteristics of each element of the technological system were equated to elements that do not have a dynamic delay and for which the passage of all watercourses is subject to the speed at which the cardboard web is cast on the mesh. The number of cycles before equilibrium is 99. In the second stage of calculations, it was taken into account that the four tanks in the technological system of production are characterized by a moment of delay and, therefore, the values of delay factors were chosen based on water reserves that accumulate in these basins. The number of cycles before equilibrium in the second stage increased to 264. The main conclusion from the analysis of two options: the technological system in both cases goes to equilibrium at equal values for all components of water-soluble mineral and organic components.
However, there are often situations when, in the process of developing (designing) a complex technological system for the production of paper or cardboard, developers are interested in the weighted average concentration of water-soluble mineral components that most affect the state of water flows, and then the technological system can be simplified and presented as a single container linked to the environment.
Analysis of the calculation formula of the time for the technological system to reach equilibrium shows that the time value is largely determined by the ratio of the water capacity (W) of the process system to the amount of water (BS) removed from the system. The greater the water capacity of the technological system and the smaller the BS, the longer the time the technological system reaches equilibrium. The next step of the study is to verify the results obtained on the basis of adequate mathematical models in actual production conditions.
Stability analysis and controller synthesis for hybrid dynamical systems
