Statistical equations are widely used to describe the laws of various chemical technological processes. The values of constants and parameters included in these equations are determined by various methods. Methods that can determine the values of equation parameters using a limited amount of experimental data are of particular practical interest. In this manuscript, we propose a method to obtain simplex-interval equations. The proposed approach can be effectively used to control the values of technological process parameters. In this paper, we consider examples of chemical kinetics equation transformations and heterogeneous processes of solid particle dissolution. In addition, we describes mathematical model transformations, including equations for functions of the residence time distribution (RTD) of apparatus particles, the distribution of particles by size, etc. Finally, we apply the proposed approach to an example involving modeling of the calcination of coke in a tubular rotary kiln.
The aim was to develop a procedure for obtaining an electrode paste of needle coke in case of thermophysical action in the extruder circuit to produce graphitized carbon electrodes with the required structure and properties for thermal furnaces. To study the properties and composition of electrode pastes and electrodes, X-ray powder diffraction, electron microscopy, infrared spectroscopy, and calorimetry analysis were used. To evaluate the electrode behavior upon its heating in a melt, mathematical and statistical analysis was used. The data were processed using standard MS Office programs. Experiments with graphitized carbon materials were conducted in a calorimetric laboratory at the Scientific Center for Problems of Processing Mineral and Man-Made Resources, Department of Metallurgy, Saint Petersburg Mining University (Russia), using a developed proprietary prototype of the extruder. The conditions and technological parameters for processing electrode pastes were defined and substantiated (rate of extrusion and electrode paste flow, pressure, and heating rate within the defined temperature range to achieve stable structural indicators of electrodes). According to XRD data, the proposed method of thermophysical processing of an electrode paste via a special extruder within 550–620°C and a die pressure of 60–80 MPa provides an evenly directed structure of needle coke with an average needle thickness of 12–20 nm and a length of needle phases of 5–10 mm. The behavior of electrode samples was examined in the furnace melt within 1500–1700°C. The obtained stable levels of the thermal-expansion coefficient (0.3·10-6 °C-1) and specific electrical resistance (4.5–6.0 μmOhm·m) were manifested in reduced electrode sublimation, low losses of overall weight at the electrode end, decreased oxidation, and reduced damage on its side. The proposed electrode structure ensures stable heat and electrical conductivity, as well as high heat capacity, which levels are equivalent to those of imported electrodes and electrode pastes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.