Mathematical Model Of Process Research Articles

Ways to increase the efficiency of industrial production of combined feed

This paper aims at finding a solution to the main problem of feed production: increasing the efficiency of the production process while improving the quality of products. The article aims to develop an adequate mathematical model of the technological process of combined feed industrial production. The authors have developed the theoretical background for describing this process on the basis of flow models within the framework of the original “three effects” concept, a stochastic model has been created taking into account the preservation of the exergy balance of the technological system. The main research tool is the apparatus of system analysis and the theory of random processes. An engineering-mathematical calculation of the parameters of the constructed model was performed, verification of the stochastic model of the technological process of preparing compound feeds in laboratory conditions was carried out. As a result of the research, the authors established the possibility of controlling the stochastic feed flow in all subsystems of the production technological system, outlined ways to solve the problem of increasing the efficiency of feed production by reducing energy costs and improving the output product granulometric composition.

Calcium carbide furnace batching system based on integral separation PID control

The precise ratio of raw materials and the uniformity of furnace charge mixing are the premise of calcium carbide quality, energy saving, and consumption reduction, which have a great influence on the operation of calcium carbide furnaces. Based on analyzing the batching equipment and the batching process, the mathematical model of the batching process is established and the model parameters are determined by the method of the soaring curve. According to the characteristics of the batching process, a quantitative feeding control system was designed by using an integral separation PID control algorithm, and PID controller parameters were determined by the empirical trial and error method. The practical application in the production field shows that the quantitative feeding control system designed in this paper can fully meet the precise ratio of raw materials and the uniformity of mixing charge of calcium carbide furnace.

Modeling and simulation of single droplet drying in an acoustic levitator

We present a mathematical model for the full drying process of a single protein formulation droplet taking into account the convective impact arising from its levitation by a standing ultrasound wave. Using the finite element method allows us to compute the evaporation rate directly from the fully resolved heat and mass transfer within and around the levitated droplet. We apply our model to simulate the drying kinetics of pure water and aqueous phosphoglycerate kinase (PGK) droplets under various levitation and drying conditions. Empirical data from the literature are used to validate and discuss our numerical results. The acoustic streaming turns out to accelerate not only the first but also the second drying stage. Moreover, the dehydration of the protein molecules is found to be primarily responsible for their enzymatic inactivation throughout the drying process.

Simulation of asymmetrical rotational flow in the flow part of a well jet pump

In order to improve the mathematical model of the working process of the above-bit ejection system for the conditions of its asymmetric rotation in the well, a method of modeling the circulating injected flow using a hydrodynamic vortex function, the center of which is shifted relative to the axis of the mixing chamber of the jet pump, has been developed. In the process of modeling the rotating asymmetric movement of the injected flow, the concept of circulation of the vector of the translational velocity of the liquid along a closed circuit is used. With the help of the components of the complex potential of the hydrodynamic circulation function, a graphical interpretation of the equipotential lines and flow lines of the spatial vortex with one-sided and two-sided displacement of the coordinate center was obtained. Using analytical relations for the velocity potential and stream function, the components of the circulation velocity are determined and the analyticity of the function of the complex potential with a shifted vortex center is proven. The fulfillment of the Cauchy-Riemann conditions allowed us to present the resulting velocity of the circulating current with the coordinate center shifted along the vertical axis in the form of a partial derivative of the complex potential. In contrast to the complex potential for a symmetric vortex, the ratio for determining the circulation speed in case of misalignment of the working nozzle and the mixing chamber of the jet pump contains an additional component in the form of the displacement of the vortex center.In the process of analyzing the results of using the proposed mathematical model, it was established that the resulting speed of the circulation current and the relative displacement of the spatial vortex center are directly proportional. The conducted studies proved that the ratio of the velocities of the symmetric and asymmetric circulation flow is a function of the displacement of the center of the vortex flow coordinates and varies from 1 to zero. The magnitude of the relative speed of the circulation flow is inversely proportional to the displacement of the coordinate center and the distance to the mixing chamber of the jet pump. The developed mathematical model can be used to predict the influence of the rotation of the ejection system on its pressure characteristic in the case of radial relative displacement of the working nozzle and the mixing chamber of the jet pump.

INVESTIGATION OF METHANE HYDRATE COMBUSTION PROCESS WITH ACCOUNT FOR INCOMPLETE WATER EVAPORATION

In this paper, a mathematical model of the combustion process of a gas hydrate sample taking into account the non-equilibrium of its dissociation process is presented. The system of basic equations is built on the laws of conservation of mass (for the entire system and each of its components), energy and momentum, and is supplemented by conditions at the moving boundary of the phase transition. On the basis of a numerical solution based on the method of large particles, the fields of system temperature and gas mixture components concentrations are constructed. It has been established that with a decrease in the proportion of water turning into steam, there is an increase in temperature at the combustion front, as well as the speed of combustion front movement.

A data-driven optimization framework for industrial demand-side flexibility

Securing profits while offering industrial demand-side flexibility in both energy and reserve markets is critical to ensure the profitability of energy-intensive industrial plants to make available their flexible assets in the electricity markets and hence accelerating the energy transition. Proposing efficient bidding strategies for simultaneous participation in the energy and reserve market is challenging since it requires the integration of different market mechanisms in a single optimization problem (combining energy and reserve markets), as well as an accurate mathematical model of industrial processes from which to obtain energy flexibility. Often, such mathematical models are either not available or are described through complex simulators, making the design of a computationally efficient bidding strategy a complicated task.This paper introduces a novel framework to support energy-intensive industrial plants to offer energy flexibility in the joint energy and reserve market. We use a neural network to model the complex nonlinear dynamics of the industrial flexible process. Then, to reduce the complexity of the resulting optimization process we convert the neural network into linear constraints, formulating the problem of bidding energy flexibility into the electricity market as a mixed-integer linear program. The uncertainties of the process variables are considered using a scenario-based approach.A realistic simulation considering the case of an evaporative cooling tower used in the chemical industry, participating in the Belgian electricity market is carried out to demonstrate the applicability of the proposed scheme.

MODELLING OF THE TOTAL PETROLEUM HYDROCARBON (TPH) DEGRADATION DURING THE BIOREMEDIATION OF CRUDE OIL POLLUTED SOIL USING COW DUNG AND WIRE CROTONS

The contamination of soil due to activities involved in crude oil exploration and production, and oil spillage emanating from pipeline vandalization, sabotage, theft, corrosion of pipeline and the enterprises of artisanal refineries pose health and ecological problems. This is especially as crude oil contains chemical compounds which are grouped into the Total Petroleum Hydrocarbons (TPH), and known to be toxic, mutagenic, and carcinogenic. Bioremediation is currently being explored as a cost effective and environmentally friendly methods of remediating the soil from this contaminant. Thus, the current work is aimed at developing a mathematical model for the bioremediation process. This was carried out while assuming that the process of degradation is a first order reaction, and the principle of the law of conservation of mass was applied. A linear model ( ) was developed relating the instantaneous concentration of TPH, initial concentration of TPH and time duration of the bioremediation. The model fitted well to the experimental data as shown by the result of the statistical analysis where the Analysis of Variance (ANOVA) showed a p-value of 0.004 suggesting that the model is statistically significant. The p-values of the model variables such as time duration of the bioremediation was 0.004, this suggested that the variable is significant. The model can be used as a supporting tool in the management of the biodegradation of TPH to predict the degradation concentration of TPH during the bioremediation process at ambient condition of temperature and pressure using cow dung, wire croton and their combination as a carbon source. KEYWORDS: Bioremediation; cow dung; wire croton; degradation; Mathematical modelling

Preface

International Workshop “Mathematical Modeling and Scientific Computing: Focus on complex processes and systems” (dedicated to the memory of Nikolai Botkin) Munich, October 4-7, 2022 This proceedings volume contains papers presented at the second International Workshop “Mathematical Modeling and Scientific Computing: Focus on complex processes and systems”, MMSC 2022, dedicated to the memory of Nikolai Botkin (22.03.1956–14.09.2019). Nikolai Botkin contributed significantly to mathematical modeling of various physical and biological processes, to the development of numerical methods and algorithms for optimal control of mechanical systems described by ordinary differential equations as well as for complex distributed systems, optimization and nonlinear programming, elasticity theory, hydrodynamics, thermodynamics, and homogenization theory.The first International Workshop MMSC 2020 was held on November 19-20, 2020 at the Technical University of Munich. The proceedings were published with CEUR-WS.org https://ceur-ws.org/Vol-2783/The second workshop MMSC 2022 was held on October 4-7, 2022 at the Technical University of Munich, Germany, in virtual format. Following the scientific interests of Nikolai Botkin, the workshop topics covered mathematical modeling and computer simulation for a wide range of optimal control and trajectory optimization problems, linear and nonlinear programming issues, as well as comprehensive applications in biology, medicine, thermodynamics and aerospace engineering. Recent achievements in machine learning and neural network technologies, challenges in simulation of cerebral blood circulation and bacterial quorum sensing were presented and discussed.In total, 35 invited talks of 77 authors from 12 countries were delivered. Out of 22 papers submitted to Morressier platform, 22 were accepted after peer-review.The editors would like to cordially thank the members of the Program and Organizing Committees, the participants, and the reviewers for actively contributing to the success of MMSC 2022.Editors of the MMSC 2022 ProceedingsVarvara Turova, Andrey Kovtanyuk, Johannes ZimmerList of Program Committee, Organizing Committee are available in this pdf.

New horizons for hydrography

Compared to the complexity required to measure other physical quantities, the continuous monitoring globally of water levels, current directions, and velocities, as well as the measurement of underwater topography, do not appear ambitious tasks for modern technologies. The challenges lie in the sheer size of the area to be measured, which makes up about 70% of the Earth’s total surface, in its constant variability due to natural processes, the inaccessibility of the seabed, and the still inadequate mathematical modelling of global geophysical processes at the oceanic scale. Since most of the world’s population lives on, from and with the oceans, a demand-oriented provision of hydrographic information is of fundamental importance. Hydrography is called upon to serve this need for information in support of informed decision-making. Starting from the present status and the discernible trends in technical development, this article aims to provide a glimpse into the expected future development up to the end of the current decade.

Enhancing uranium in-situ leaching efficiency through the well reverse technique: A study of the effects of reversal time on production efficiency and cost

In this study, the application of the Well Reversal Technique (WRT) and the impact of reversal time on the efficiency of uranium mining via In-Situ Leaching (ISL) were investigated. A prevalent issue in ISL mineral extraction is the formation of stagnant zones caused by limited access of the lixiviant, which leads to increased operating expenditures. The WRT, which involves altering the function of some wells from injection to production or vice versa, is a potential solution to this problem. The efficiency of WRT is heavily dependent on the well pattern and reversal time. Two commonly used well patterns in ISL are the 9-spot (row arrangement) and 7-spot (hexagonal arrangement). The objective of this study was to determine the optimal reversal time for a 9-spot well pattern through mathematical modeling of hydrodynamic and physico-chemical processes and subsequent economic assessment. A mathematical model of uranium extraction processes was developed using the principles of mass conservation, Darcy's, and mass action laws. The results obtained for a 9-spot well pattern without reversal, with two reversal options, and a 7-spot scheme were analyzed comparatively. The 7-spot scheme without reversal was found to be the most effective of the options examined. The application of WRT on a 9-spot well pattern allows to enhance production efficiency to a level comparable to that of a 7-spot well pattern. Additionally, the effect of reversal time on recovery was studied based on two well reversal options. The results from calculation revealed that the optimal scenario was when the well reversal is conducted immediately after the time point at which the average concentration of the pregnant solution in the production wells reaches its peak value. The overall efficiency of WRT application was determined through economic calculations of capital (CAPEX) and operating (OPEX) expenditures. Based on economic calculations, it was determined that the utilization of WRT results in a 3–18% increase in mineral production efficiency for a 9-point scheme, depending on the chosen reversal method.

МОДЕЛЮВАННЯ ДИНАМІКИ ТЕМПЕРАТУРИ СУБСТРАТУ ТА ПОВІТРЯ УГРИБНИЦІ

Economic efficiency of greenhouse vegetable growing depends quite significantly on the cost of energy carriers, which is why the introduction of energy-saving technologies in greenhouse vegetable growing is an urgent issue. One of the ways to save energy resources can be the use of a closed ventilation system of the "plant greenhouse - mushroom greenhouse" type, which is based on the opposite type of respiration of plants and mushrooms. A closed ventilation system includes air exchange between the greenhouse with growing plants and the cultivation room for growing mushrooms. The closed ventilation system allows you to save energy by reducing the heating of the incoming air, as well as increasing the yield of vegetable products due to the increased concentrations of carbon dioxide in the air that flows from the cultivation room for mushrooms to the greenhouse and mushrooms due to the increased concentrations of oxygen in the air that flows into the cultivation room for mushrooms from the greenhouse. Mathematical modeling of the process of heat transfer between greenhouses makes it possible to simulate transitional processes between rooms in order to assess the quality and accuracy of regulation, as well as to evaluate the parameters of the object in transitional modes. Mathematical modeling of dynamic processes is the basis for the formulation of transfer functions for the automatic control system. As a result of the study, mathematical models of the temperature dynamics of the substrate of mushrooms and greenhouse vegetables were obtained due to the analytical solution of the system of differential equations. The adequacy of the solution was verified by the Runge-Kutta method and compared with experimental data. The difference between the theoretical and experimental values is not significant and amounted to -3 % for the substrate temperature and -3.2 % for the air temperature.

MATHEMATICAL DESCRIPTION OF A BLEACH IMPREGNATION RESERVOIR

This article discusses the issues of constructing a mathematical model of the technological process of bleaching textile materials in an impregnating reservoir using the heat balance equation, on the basis of which a qualitative analysis of the dynamic properties of an object has been carried out in order to create highly efficient control systems with the use of energy-saving technologies. While constructing a mathematical model characterizing the established and non-established modes of the control object (impregnating reservoir) used changes in heat flow and mass velocity of the incoming tissue. An algorithm for constructing a mathematical model of the process of bleaching cotton fabrics has been proposed. The results of solving a practical problem show the adequacy of the developed model.

Design of cell expansion processes for adherent-growing cells with mDoE-workflow.

Adherent cells, mammalian or human, are ubiquitous for production of viral vaccines, in gene therapy and in immuno-oncology. The development of a cell-expansion process with adherent cells is challenging as scale-up requires the expansion of the cell culture surface. Microcarrier (MC)-based cultures are still predominate. However, the development of MC processes from scratch possesses particular challenges due to their complexity. A novel approach for the reduction of development times and costs of cell propagation processes is the combination of mathematical process models with statistical optimization methods, called model-assisted Design of Experiments (mDoE). In this study, an mDoE workflow was evaluated successfully for the design of a MC-based expansion process of adherent L929 cells at a very early stage of development with limited prior knowledge. At the start, the analytical methods and the screening of appropriate MCs were evaluated. Then, cause-effect relationships (e.g., cell growth related to medium conditions) were worked out, and a mathematical process model was set-up and adapted to experimental data for modeling purposes. The model was subsequently used in mDoE to identify optimized process conditions, which were proven experimentally. An eight-fold increase in cell yield was achieved basically by reducing the initial MC concentration.

Study of linear and angular oscillations of the moving platform of the ground robotic complex

Background Modern ground robotic complexes have a significant speed, which leads to the occurrence of vibrations of the platform and the manipulator. The problem is to develop highly efficient vehicles that take into account dynamic processes, and their impact is minimized by constructive solutions and dampers. Objective The purpose of the work is to study the dynamics of the moving platform of the robotic complex and establish its dynamic parameters. At the same time, it is necessary to determine the characteristics of oscillatory processes, in particular, linear and cross-angular movements of the platform. Methods A dynamic model of the platform has been developed. It has three degrees of freedom and takes into account the working processes of caterpillars and rollers. The calculation scheme has six points of support on the surface. The method is based on finding the position of the rollers determined by the profile of the road surface. The elastic-dissipative properties of the track and the surface are taken into account in the model. A research of the platform during its movement on a surface with a complex profile was carried out. Polyharmonic dependencies with random parameters are used to describe it. Results The developed model determine the dynamic characteristics of the robotic platform during its interaction with irregularities of arbitrary shape. Based on the found equations of spherical motion, mathematical modeling of work processes was carried out, angular coordinates and angular speeds of platform rotation were determined. Conclusions The results of modeling the spherical movement of the platform correspond to the physical essence of work processes. These data are necessary for studying the dynamics of the manipulator of the mobile robotic complex. Minimization of platform oscillations improves the characteristics of ground robotic complexes moving at a high speed.

ANALYSIS OF PROCESSES IN CONVERTER WITH TWENTY-ZONE VOLTAGE REGULATION ANDACTIVE-INDUCTIVE LOAD

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for fifteen zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

SIMULATION OF VARIABLE INDIVIDUAL GRAPHS OF THE ELECTRICAL LOAD OF THE INDUSTRIAL ELECTRIC DRIVE

In the process of developing and creating means of controlling the energy efficiency of technological processes based on electric drives, a task arises related to the modeling of individual electric load schedules of the electric drive. In the analytical study of electricity consumption, the substantiation of the mathematical model of the random process is important. This model, on the one hand, should most adequately reflect the properties of the real process of electricity consumption, and on the other hand, it should allow research of this process using known theoretical methods. A way out should be sought on the basis of compromise solutions regarding the choice of the simplest, but sufficiently accurate models, which will solve the tasks in the most rational way.
 
 The probabilistic approach to load estimation allows the most probable description of the process of changing the electrical load over time, given the random nature of this change. The application of this approach should be based on reliable statistical data, which allows to ensure high accuracy of the obtained models. The task consists in simulating random processes of electricity consumption by the main consumer of electrical energy - the electric drive.

Non-destructive testing of an aluminum alloy welded joint based on a mathematical model of the thermal welding process and computer microtomography

Strength control of welded joints is used in many industries. X-ray microtomography as a method of non-destructive testing allows not only to detect the presence of defects, but also to classify them and assess the size of cracks and non-crack-like defects (pores). This article discusses the non-destructive testing of welded joints of aluminum alloy 6061 T6 using computer micrototomography and a mathematical model of the thermal welding process implemented in ANSYS Workbench. Experimental results of the X-ray microtomograph are presented, and the size of defects in this sample is estimated. The mathematical model allowed us to obtain the thermal histories at which the faults were formed.

Mathematical Model Desublimation Conditions

The developed and software-implemented simplified three-dimensional mathematical model of the unsteady-state process of HFS desublimation is described. The study of regularities in the HFS desublimation process is performed by numerical modeling.

NEW INFORMATION OPERATORS IN PROBLEMS OF NUMERICAL INTEGRATION OF FUNCTIONS OF THREE VARIABLES

The rapid development and implementation of the latest information technologies in many fields of science and technology contribute to the rise of new methods in mathematical modeling of systems and processes. In particular, new mathematical theories have appeared that can be effectively used for building and improvement of existing mathematical models of various phenomena and objects. One of these theories is the theory of new information operators, authored by the Laureate of the State Prize of Ukraine in Science and Technology, doctor of physical and mathematical sciences, professor (думаю, это излишняя информация в аннотации) O. M. Lytvyn. New information operators have found their application in the digital processing of signals and images, namely in the numerical integration of rapidly oscillating functions of many variables. Cubature formulas were built that are optimal in the order of accuracy and use the value of the non-oscillating factor of the integrand function not only at points, but also on planes or lines. The article demonstrates the application of new information operators to the numerical integration of functions of many variables, namely, the issue of approximate calculation of the integral from functions of three variables is considered in the case when the information about the function is given by its traces on the lines. The cubature formula uses an interlineation operator built on the basis of an interflatation operator with auxiliary functions in the form of piecewise constant splines. An estimate of the approximation error of the proposed cubature formula on the class of differentiable functions was obtained. The results of the calculation experiment in the computer mathematics system Mathcad are presented. Numerical calculations confirm the theoretical statements of the study.

COMPUTER STUDY OF THE MATHEMATICAL MODEL OF THE ARTILLERY SHOT PROCESS

The article deals with the issue of computer research of the mathematical model of the artillery fire process. Russia’s war against Ukraine showed that the success of the Armed Forces of Ukraine (AFU) largely depends on artillery units. The effectiveness of the actions of the artillery units depends on the normal functioning of artillery weapons. 
 The phenomenon of the shot is characterized by short duration, high pressure and high temperature. The duration of the shot phenomenon is determined by tenths and even hundredths of a second. A pressure of up to 400 MPa and a temperature of more than 2000 С develop in the bore of the weapon.
 It should be noted that the processes of gunpowder combustion are very complex. They depend on the manufactures, namely, on the type of gunpowder, chemical composition, its type (geometry) and pressure. So, the process of gunpowder combustion is described by equations that were obtained experimentally. Such experiments were carried out a long time ago, so most of the constants currently used in the calculation of the combustion process are expressed in the old ICGSS system of units. Therefore, it should be taken into account in the calculations when determining, for example, the pressure in MPA.
 The mathematical model of the artillery shot process takes into account all the factors that affect the processes occurring in the barrel. The mathematical model of an artillery shot consists mainly of the gunpowder combustion equation, the energy conversion equation, the projectile motion equation, the initial and boundary conditions. The numerical solution of the given systems of equations was carried out by numerical methods and the differential equations were solved by the Runge-Kutta method. The obtained values of the maximum pressures of powder gases and their comparison with the experimental ones showed that the error does not exceed 3 % which confirms the adequacy of the mathematical model of the artillery shot. Thus, the proposed mathematical model of an artillery shot and the method of its solution can be used to study the influence of various parameters (gunpowder parameters, design parameter of the guns, mass of the projectile and others) on the processes occurring during a shot.