Introduction. The present research featured industrial sugar crystallization. The article introduces a generalized mathematical model of specific growth rate of sugar crystals depending on temperature, solids, and the purity of solution, as well as on the concentration and average size of crystals. The model includes the probabilistic component of growth rate of monocrystals and the reduced adjustment of the constrained crystal growth depending on the abovementioned as-pects. Study objects and methods. The research focused on mass crystallization of sucrose, including the growth rate of monocrystals and the number of crystals in the fill mass. The obtained experimental data were processed using nonlinear programming. Results and discussion. 421 experiments made it possible to develop a probabilistic mathematical model of specific mass growth rate of sugar monocrystals and its dependence on the solution temperature, purity, and solids content. Model error: ± 11.3%. The model covers the temperature range, concentration of solids, and purity of the solution. The proximity of crystals was calculated according to the dependence of the growth rate on their concentration and the average size (error: ± 1.3%). The adjustment range: concentration of crystals = 5–60%, average size = 0.25–1.50 mm. Conclusion. The present generalized mathematical model of crystallization considered the temperature, as well as the purity and solids content in the fill mass, the concentration of sucrose crystals and their average size. The research compared the effect of linear size and concentration of sugar monocrystals on the calculated and experimental sizes of specific mass growth rate and the dimensionless adjustment of growth rate. The calculated sizes proved to be close to the ex-perimental data, which showed adequacy to the developed crystallization model. The research results can be used to optimize the process of mass sugar crystallization.
The problem of modeling pyrolysis of naphtha in a modern SR T-VI large-capacity furnace from ABB Lummus Global (USA) was examined. Curves of the yield of basic products as a function of the composition of the feedstock and pyrolysis regime were obtained with the experimental data and physicochemical characteristics of the process. The model is intended for predicting the composition of pyrolysis gas and controlling the pyrolytic process in an active plant.In many domestic ethylene units, obsolete naphtha pyrolysis furnaces are being replaced by modern type SRT-VI furnaces (SRT = Short Residence Time) of high individual capacity: output in feedstock of the order of 300,000 tons/year. The SRT-VI furnace (Fig. 1) differs from the preceding modifications due to the elevated thermal factor (q av » 100 kW/m 2 ) of the radiant part of the coil, high degree of branching of the pyrolysis coal, and shorter feedstock residence time (~0.22 sec) in the reaction zone.With respect to its design, this furnace is much more complicated than the preceding furnaces and can operate in a wide range of variation of the process parameters and feedstock composition. Optimization of the operating conditions in the current market economy is presenting some difficulties for plant personnel. According to ABB Lummus Global data [1], the optimum pyrolysis conditions in the EP-450 ethylene unit will allow increasing profits by 6%.
A method to expand solubility equation for pure sugar solutions to a generalized solubility model has been developed. The proposed approach can be used to calculate the solubility of a substance in an impure solvent with the known equation of its solubility in a pure solvent. A generalized mathematical model of solubility of sucrose in pure and industrial solutions has been obtained. The adequacy of the model was tested on 6 samples of impure solutions, including a water-ethanol-sucrose mixture. The solubility of sucrose in ethanol for a mass concentration from 1.0 to 99.0% of ethanol in the solution is calculated.
In this article, an object of a research is the mechanism of incorporation of mother liquor components in the growing crystals of sucrose and establishment of the dependence allowing to estimate quantitatively inclusion of components of the mother liquor in industrial crystals of granulated sugar. Water and a complex of not sugars are considered as components of sugar solution. To date, experimental estimates of the inclusions of various non-sugars in sugar crystals have been accumulated, and a qualitative and quantitative analysis of impurities in crystals have been made, which showed that the number of inclusions depends on the purity of the crystallized solution, the rate of crystallization, the hydrodynamic situation in the apparatus, temperature and concentration fields, the viscosity of the solution, and other factors. These factors are mainly due to the technological regime of the crystallization process, and understanding the degree of their influence on the inclusion of impurities allows authors to minimize the capture of non-sugars by growing crystals. It is shown that the inclusion of nonsugars occurs mainly during the formation of crystals and their subsequent growth at a high supersaturation coefficient. However, the available data is not sufficient to identify and formalize all the laws of this rather complex phenomenon. At this stage, it is more appropriate to use the mathematical methods of probabilistic interpretation. The purpose of the study was a creation of a mathematical model that could be used to estimate the amount of components of the masterbatch solution (nonsugar and water) passing from solution to crystal, depending on the supersaturation of the solution, its temperature, viscosity, purity, and dry matter content. Based on the probability theory, a mathematical model of the deposition of the mother liquor in industrial crystals of granulated sugar has been developed. The mother liquor includes water in which sucrose and a complex of non-sugars are dissolved. Some of the non-sugars and water can be trapped by the growing crystal. The model allows you to calculate the amount of non-sugars and water that have passed into the sucrose crystal during its growth. The average relative error of the model is 8-10%.
A complete mathematical modeling of the technological process of manufacturing vinyl acetate monomer by vapor-phase method has been implemented. The model is partial differential equations of the material and energy balance and catalyst aging. An algorithm for an integrated equation based on the second-order Gregg-Bulirsh-Shter rectangle symbol has been developed. The error in modeling the process is equal (CH3COOCH=CH2) ± 5.4% rel. for the target matter, and (CO2) ± 6.4% rel. for the secondary substance The kinetic coefficients of differential equations, namely the pre-exponential factors and the activation energy have been refined. The obtained data of the modeling of the vapor-phase manufacturing process of vinyl acetate are shown in the form of tables and graphic three-dimensional dependencies of quality indicators on technological parameters.
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