scholarly journals Mathematical modeling and analysis of operation of cylindric pyrolysis reactor with radial heating

Vestnik IGEU ◽  
2021 ◽  
pp. 60-67
Author(s):  
A.V. Mitrofanov ◽  
O.V. Sizova ◽  
N.S. Shpeynova ◽  
V.A. Katyushin
Keyword(s):  
Mathematical Modeling ◽  
Mutual Influence ◽  
Thermal Transformation ◽  
Reaction Model ◽  
Difference Approximation ◽  
Chemical Transformations ◽  
Technological Solution ◽  
Mathematical Basis ◽  
Material Constants ◽  
Pyrolysis Reactor

The vector of development of solid-fuel energy is currently directed towards expanding the range of renewable fuels used. Along with the direct combustion of fuel, the processes of controlled thermal transformation of the raw biomass in an oxygen-free surrounding to obtain a new fuel based on it (liquid, solid, gaseous) are widely spread. A significant part of research in this sphere is related to the study of the formal kinetics of such processes, at the same time, the hardware design of the process is no less important, but less studied. Thus, development of mathematical models of pyrolysis equipment operation is relevant. A decisive difference approximation of these processes in the framework of an axisymmetric formulation of the problem is chosen as a mathematical basis for modeling physical and chemical transformations and transfer processes in the radial direction of a cylindrical pyrolysis reactor. The material constants of the processes are borrowed from the well-known literature references The authors studied the modes of reactor operation not covered by a full-scale experiment, using the previously proposed and verified one-dimensional mathematical model of a cylindrical pyrolysis reactor. The issues of the influence of the dimensionless kinetic function of the process (reaction model) on the thermal transformation of the material in the apparatus are considered. The significant influence of the chosen reaction model on the kinetic nature of the process is pointed out. The mutual influence of drying and pyrolysis the presence of which is due to the energy effects of the processes is considered. A significant spatial heterogeneity of the process is defined and the possibility of the existence of a non-trivial effect of advanced heating of the internal zones of the apparatus in comparison with the peripheral ones is specified. The paper shows that a computational experiment can help to detect non-trivial effects and identify the variability of the process implementation even within the framework of a single design and technological solution of the pyrolysis process. According to the authors, the results of the obtained numerical experiments indicate that mathematical modeling can be the basis of making technological solution. However, further research is also needed to determine reliably the material constants of the process.

Mathematical modeling and simulation of hexane degradation in fungal and bacterial biofilters: effective diffusivity and partition aspectsThis article is one of a selection of papers published in this Special Issue on Biological Air Treatment.

2009 ◽  
Vol 36 (12) ◽  
pp. 1919-1925 ◽  
Author(s):  
Sonia Arriaga ◽  
Sergio Revah
Keyword(s):  
Mathematical Modeling ◽  
Kinetic Constant ◽  
Effective Diffusivity ◽  
Reaction Model ◽  
Small Error ◽  
Bacterial Biofilm ◽  
Order Kinetic ◽  
Biofilm Thickness ◽  
First Order ◽  
Superficial Area

Mathematical modeling in the biofiltration of volatile organic compounds is a valuable tool for performance prediction and in scaling up. Majority of the published models include parameters obtained from fitting experimental data, thus masking their real influence as they are lumped generally. The present work aims to evaluate experimentally some of the most relevant parameters including kinetic constant, partition coefficient in the biofilm, biofilm thickness, superficial area, and effective diffusivity. For the fungal biofilm, all the parameters mentioned above were obtained experimentally; and for the bacterial biofilm, the biofilm thickness and some intrinsic parameters used to obtain the first-order kinetic constant were taken from the literature. These parameters were then incorporated in a mathematical model to describe the steady-state degradation of hexane in bacterial and fungal biofilters operating under continuous mode. Experimentally, the dimensionless partition coefficients (mG) indicated that hexane was 4 and 35 times more soluble in the bacterial (mG = 9.14) and fungal (mG = 0.88) biofilters, respectively, than in water (mG = 30.4). Comparison of model estimates with experimental concentration profiles of the pollutant along the height of the biofilters proves that the first-order limited by reaction model was appropriate to interpret the experimental results with a small error of ∼1%.

scholarly journals Algorithms for Numerical Solution to the Problem of Diffusion in Nanoporous Media

2020 ◽  
pp. 44-52
Author(s):  
N.A. Vareniuk ◽  
N.I. Tukalevska
Keyword(s):  
Mathematical Modeling ◽  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Solution ◽  
Heterogeneous Media ◽  
Mutual Influence ◽  
Single Substance ◽  
Nonstationary Diffusion ◽  
Element Method

Introduction. Mathematical modeling of mass transfer in heterogeneous media of microporous structure and construction of solutions to the corresponding problems of mass transfer was considered by many authors [1–9, etc.]. In [6, 7] authors proposed a methodology for modeling mass transfer systems and parameter identification in nanoporous particle media (diffusion, adsorption, competitive diffusion of gases, filtration consolidation), which are described by non-classical boundary and initial-boundary value problems taking into account the mutual influence of micro- and macro-transfer flows, heteroporosity, the structure of microporous particles, multicomponent and other factors. In [8, 9] for a mathematical model of nonstationary diffusion of a single substance in a nanoporous medium described in [2] in the form of a multi-scale differential mathematical problem, the classical problems in the weak formulation were obtained. In this paper, algorithms for solving the above mathematical problems are constructed by using the finite element method. The results of the numerical solution of the test problem are presented. The results confirm the efficiency of the developed algorithms. The purpose is to solve a problem of nonstationary diffusion of single substance in nanoporous medium by constructing discretization algorithms using FEM quadratic basis functions. Results. Algorithms for the numerical solution of the problem of nonstationary diffusion of single substance in a nanoporous medium are proposed. Peculiarities of discretization of the region and construction of the matrix of masses, stiffness, and vector of right-hand sides when solving the problem by using FEM are described. The efficiency of the developed algorithms is confirmed by the results of solving a model example. Keywords: mathematical modeling, numerical methods, nonstationary diffusion, nanoporous medium, finite element method.

NON-ORTHOGONAL MULTIPLE ACCESS BASED ON PARTIAL CODING

2021 ◽  
Author(s):  
Д.К. МАЗУРЕНКО
Keyword(s):  
Mathematical Modeling ◽  
Frequency Spectrum ◽  
Communication Systems ◽  
Multiple Access ◽  
Mutual Influence ◽  
Cellular Communication ◽  
Software Modeling ◽  
Computational Costs ◽  
Physical Level ◽  
Cellular Communication Systems

Рассмотрены вопросы повышения эффективности использования спектра частот при построении систем сотовой связи 5G и 6G, а также проблемы снижения вычислительных затрат при реализации алгоритма последовательного подавления взаимного влияния сигналов. Подробно проанализирована суть нового принципа неортогонального множественного доступа на основе парциального кодирования, а также проведено его сравнение с методом разделения сигналов по мощности Power Division Non-Orthogonal Multiple Access (Рй-NOMA). Результаты получены с помощью программы «Моделирование Telecomm», предназначенной для численного математического моделирования систем связи на физическом уровне. The article considers the increasing the efficiency of using the frequency spectrum when building 5G and 6G cellular communication systems and the problems of reducing computational costs when implementing an algorithm for sequential suppression of the mutual influence of signals. The essence of the new principle of non-orthogonal multiple access based on partial coding is analyzed in detail, and it is compared with the Power Division Non-Orthogonal Multiple Access (PD-NOMA) method. The results are obtained using the software Modeling Telecomm intended for numerical mathematical modeling of communication systems at the physical level.

THE STUDY OF THE PREDICTIVE ABILITY OF NUMERICAL AND ANALYTICAL MODELS (THE CASE OF MUTUAL WELL IMPACT EVALUATION)

2020 ◽  
Vol 6 (3) ◽  
pp. 131-142
Author(s):  
Nikita O. Shevtsov ◽  
Sergei V. Stepanov ◽  
Tatiana A. Pospelova
Keyword(s):  
Mathematical Modeling ◽  
Spatial Distribution ◽  
Mutual Influence ◽  
Predictive Ability ◽  
Test Method ◽  
Analytical Models ◽  
Hydrodynamic Models ◽  
Reservoir Properties ◽  
Oil Deposits ◽  
Synthetic Models

The main purpose of any model is to provide an opportunity to study the model object and the processes running in it for obtaining the predictive characteristics, among other reasons. In this connection, it is important to know, which mathematical models can help in analyzing and supporting oil deposit development, in particular, in assessing the mutual influence of production and injection wells. The characteristic features of mathematical modeling of field development include the oil deposits being located in natural formations that cannot be directly observed, as well as the complex filtration processes taking place in the formations due to the formation structure. Therefore, the mathematical modeling of development can be both complex and simple. On the one hand, it may use complex numerical hydrodynamic models, based on the understanding of spatial distribution of reservoir properties, which have an opportunity for detailed description of filtration processes. On the other hand, the modeling may use relatively simple analytical models, which have no need to specify the spatial distribution of properties; yet, the description of filtration processes is significantly simplified in comparison with hydrodynamics. Therefore, the practical value of the modeling result depends on the right approach to modeling. The task of estimating the mutual influence of wells requires the choice of numerical or analytical model to be based on understanding of the predictive ability of the models under consideration. Since such ability depends both on the ability to describe filtration processes in detail and on the need to take into account the spatial distribution of reservoir properties, it is initially impossible to conclude, which model has the best predictive ability. It becomes possible to reveal the level of predictive ability when considering the problem of mutual well impact assessment for synthetic models of oil deposits. This article presents the results of studies in the case of ten synthetic models. Numerical hydrodynamic models and analytical CRM models were set up for “actual” data of well operation. Using the retrospective test method, the authors have shown that the analytical models have a higher predictive power than the numerical models.

scholarly journals MATHEMATICAL MODELING OF STRENGTH-DEFORMED CONDITION OF PIPE CONCRETE CONSTRUCTIONS AT SUSTAINABLE TEMPERATURE

Fire Safety ◽  
2020 ◽  
Vol 35 ◽  
pp. 63-68
Author(s):  
M. Semerak ◽  
N. Ferents ◽  
D. Kharyshyn ◽  
S. Vovk
Keyword(s):  
Mathematical Modeling ◽  
Mutual Influence ◽  
Classical Problem ◽  
Structural Type ◽  
Force Response ◽  
Thermophysical Characteristics ◽  
Tensile Stresses ◽  
Maximum Value ◽  
Layer Structures ◽  
Steel Sleeve

The mathematical modeling of the thermo-stressed state of pipe-concrete structures under conditions of stationary thermal conductivity is carried out. During the study, the most common structural type of TBC was selected and mathematical models of the stress-strain state of TBA under heating conditions were taken into account, taking into account their geometric dimensions and thermophysical characteristics of metal and concrete. The main feature of the TBC study is that the heat exchange in the structure, as well as the corresponding force response, are investigated independently of each other, whereas the problem of fire resistance should be posed as a classical problem of elasticity, taking into account the mutual influence of temperature and mechanical stresses. In two-layer structures (concrete - metal), the largest radial stresses that occur in concrete work in tension. Tensile stresses occur in the thickness of the outer tube. The stresses occurring on the inner surface of the steel sleeve coincide with the stresses in the concrete. When approaching the outer surface, they decrease and on the surface r = R2 equal to zero. In the case where the coefficients of linear extension αt (i = 1, 2) are equal to each other, the maximum tensile stresses are reduced within 0≤r≤R1 .; if νi (i = 1, 2) within 0≤ r≤R2, the stresses will also decrease. Axial stresses work on compression. They reach maximum value in the outer shell. For equal values αt (1) = αt (2), the magnitude of the stresses does not change, and at ν1 = ν2 the stresses in the metal will decrease. Ring stresses in the region 0≤ r≤R1 are tensile stresses and in the region R1≤ r≤R2 are compression stresses, and the compression stresses are greater than the tensile stresses in concrete. For αt (1) = αt (2), the stresses in the concrete decrease and for ν1 = ν2.

scholarly journals PARAMETERS OF COEFFICIENTS OF THE RAIL FOUR-POLE OF THE JOIN THE JOINTLESS RAIL CIRCUI TLESS RAIL CIRCUIT ACCORDING T CCORDING TO LOCOMOTIVE RECEIVER

2019 ◽  
Vol 2019 (2) ◽  
pp. 190-195
Author(s):  
R Aliev ◽  
◽  
E Tokhirov ◽  
M Aliev
Keyword(s):  
Mathematical Modeling ◽  
Mutual Influence ◽  
Supply Voltage ◽  
Normal Operation ◽  
Railway Transportation ◽  
Traffic Light ◽  
Transfer Resistance ◽  
Analytical Expressions

In article questions of a conclusion of the coefficients of the equations of a rail four-polar of a jointless rail circuit are considered, taking into account uncertainty of borders where the travelling receiver which is applied now on a railway transportation is used. Mathematical modeling of four-pole coefficients by locomotive receiver is given. Analytical expressions and coefficients for calculation of the locomotive current flowing under the receiving coils and transfer resistance are derived. The scheme of a jointless rail circuit in the presence of moving units and mutual influence on each other is given. The influence of the carrier information from the traffic light in front, where it is necessary to take into account the factor of the signal level from the outgoing train, so that the information of the neighboring rail circuit would not be perceived, since there are no insulating joints. A scheme with five four poles has been developed and coefficients of these four poles have been obtained to calculate the current of the locomotive flowing under the receiving coils. Analytical expressions are obtained for determining the current for receiving by the receiving coils of a locomotive, the minimum supply voltage of an unbroken rail circuit and the transmission resistance of a rail circuit in normal operation for a locomotive receiver.

scholarly journals Evaluation of reserve economic development of production potential of the enterprise of the hotel and restaurant industry in Dnipropetrovsk region

2019 ◽  
pp. 58-68
Author(s):  
Оlena I. Judina
Keyword(s):  
Mathematical Modeling ◽  
Economic Growth ◽  
Economic Development ◽  
Multiple Regression ◽  
Mutual Influence ◽  
Restaurant Industry ◽  
Mathematical Statistics ◽  
Production Potential ◽  
Production Activity ◽  
Factors Of Production

The purpose of the research. The purpose of this work is economic and mathematical modeling of features of interaction of production resources at the hotel and restaurant business and assessment of reserve development of their potential on the basis of coefficients that reveal the possibility of increasing the economic efficiency of the resource consumption process. Methodology. The methodology of the research is based on fundamental principles of enterprise economics, econometrics, mathematical statistics, as well as publications of domestic and foreign scientists on the problems of economic development of enterprises. To analyze and evaluate the reserve economic development of the productive potential of the hotel and restaurant business based on the coefficients and indicators of economic development of factors of production used general scientific and special research methods, including grouping, statistical, stochastic, correlation-regression analysis, methods of economic and mathematical modeling, mathematical statistics. Tabular technique was used to clearly present the results of the study. Results. In the work by means of economic and mathematical modeling, models of multiple regression of production activity, variable costs and production efficiency are constructed. On the basis of the mathematical equations obtained, the regularities of the mutual influence of factors of production are explained, the estimated coefficients and indicators of the reserve economic development of the production potential of the hotel and restaurant enterprise are determined. With the help of the calculated estimation parameters, the power of indirect and direct action of a particular factor on the efficiency of the business entity's performance, the contribution of the factor to the cumulative influence of all factors, the possibility of revenue growth due to the development of resource potentials have been established. By interpreting certain estimated coefficients, a mathematical formula is proposed to calculate the indicators of a reserve economic development of an enterprise, which allow establishing reserves of growth of a productive indicator due to the development of a certain resource, taking into account the share of its contribution to the integrated effect of factors. On the basis of the models of multiple regression of production activity of the enterprises of the hotel and restaurant industry the regularity of mutual influence of the studied economic indicators is established, the coefficients and indicators of economic growth and reserve development are calculated, as well as their quantitative parameters by which the differentiated and integrated influence of the elements of the investigated elements is determined, an assessment of the reserve economic development of production potential. Practical meaning. The proposed methods of analysis and evaluation of indicators were used in the formation of the organizational structure of the system of management of economic growth and development of the enterprise. The prospects for further research are to create a model for managing the sustainable economic development of hotel and restaurant businesses.

scholarly journals Mathematical modeling of agglomerates evolution

2019 ◽  
Author(s):  
V.A. Babuk ◽  
N.L. Budnyi ◽  
A.A. Nizyaev
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Solid Propellant ◽  
Combustion Products ◽  
Chemical Transformations ◽  
One Dimensional ◽  
Oxide Particles ◽  
Burning Propellant ◽  
Physical And Chemical

The model of evolution of the condensed products as a part of a flow of combustion products of solid propellant is developed. The model includes the description of physical and chemical transformations for two basic fractions of the condensed products: agglomerates and smoke oxide particles (SOPs). Model testing is carried out using experimental data about evolution of the condensed products for two compositions in the conditions of a one-dimensional flow. These compositions differ considerably in properties of combustion products at a surface of burning propellant. The results of testing give the grounds to draw a conclusion about high enough quality of modeling.

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