Mathematical Model Of Process Research Articles

Моделирование процесса вибрационного обезвоживания угольной мелочи в технологических системах гидромеханизированных шахт

Introduction. The article discusses the issues of modeling various variants of flow line tunneling technologies based on an analysis of the structure of the tunneling cycle. Materials and methods. As research methods, the authors used: analysis of the structures of the tunneling cycle of continuous mining technologies, mathematical modeling of processes and operations, and industrial testing of options for implementing the proposed technological tunneling systems. Results. Obtained during the implementation of a mathematical model of a high-frequency, low-amplitude process of vibration dehydration of mineral raw materials of small fractions, using fine coal (sludge) as an example, made it possible to determine the optimal parameters of the kinematics of the working body in accordance with the parameters of the source material. Innovative solutions have been proposed for the design of vibration dewatering devices with mechanical and hydraulic high-frequency flexibly adjustable drives. Conclusion. The article summarizes the results of research in the field of modeling and optimization of fine coal dewatering parameters in technological systems of mining enterprises. Options for implementing innovative technical devices for high-frequency, low-amplitude effects on the source material are proposed to increase the efficiency of dehydration. Resume. An analysis of existing means and methods for dewatering rock mass has shown that in relation to the technology of hydromechanized coal mining with its underground dewatering and recycling of process water, the most promising is the use of high-frequency vibration dewatering devices with a mechanical or hydraulic drive. The study of the kinematics of movement of the dewatered rock mass made it possible to determine the optimal values of vibration parameters

Mathematical model of the hydrocarbon displacement process by water in zonally heterogeneous deformable reservoirs

The problem of displacing hydrocarbon systems injected into the reservoir by water in zonally heterogeneous collectors is considered. In this case, the reservoir of circular shape, developed by a single central well, is assumed to consist of two zones with different reservoir and rheological properties. The solution to the problem is obtained, taking into account the incomplete displacement, compressibility of water, and PVT properties of the hydrocarbon system—phase transformation, mass exchange between phases of the hydrocarbon system. Based on the binary representation of the complex hydrocarbon system, a solution to the considered problem is obtained, and an algorithm for calculating the main indicators of the hydrocarbon displacement process to the well is proposed. This algorithm accounts for the fact that the reservoir has different reservoir and rheological characteristics in the near-wellbore region (internal zone) and the distant part of the reservoir (i.e., in the external zone). Keywords: Displacement; Gas-condensate mixture; Volatile oil; Heterogeneous reservoir; Water flooding; Binary model; Unsteady-state flow.

Mathematical modeling and research of transport flows and processes of transport systems of cities

The problem of mathematical modeling and research of transport flows and processes of transport systems of cities is set and solved. Related works, methods, modeling of traffic flow intensity as a first-order autoregression process, finding estimates of process model parameters with a standard normal random component are considered.

NONLINEAR MATHEMATICAL MODEL OF DEMAND – SUPPLY

Currently, mathematical modeling is more and more persistently invading the economy. The possibility of using mathematical modeling is related to the existence of stable trends that characterize many economic processes. The importance of modeling as a research method is determined by the fact that the model is a conceptual tool focused on the analysis of the researched processes and their forecasting. The need to master mathematical modeling of economic processes as a method of analysis is not limited to purely practical needs: mastering this method contributes to the formation of non-linear thinking. Thus, in addition to solving purely practical problems, the use of this method has a great ideological significance. The paper examines two models of supply and demand: linear and nonlinear. For each model, goals and mathematical formulations of the models are formulated. Methods for analyzing the coefficients of two models are proposed.

Automation of the Formation of a Mathematical Formulation of Kinetics for Multistage Chemical Reactions and Numerical Solution to a Direct Problem

Introduction. The basis for research, analysis and mathematical optimization of any chemical process is an adequate mathematical model that takes into account the kinetics of the object. Kinetic analysis is a challenge in chemical technology, since it allows for optimizing synthesis processes and predicting their efficiency. Numerous chemical processes involve several stage reactions. For successful design and optimization, a mathematical model that describes each stage is needed. Creating such a model manually can be time-consuming and costly, since it requires processing a large amount of information. The modern level of automation makes it possible to accelerate the obtaining of a mathematical formulation of the kinetics of multistage reactions. In this case, working with data is greatly simplified, and the probability of making mistakes is reduced. The resulting mathematical model can be applied for further analysis and optimization of the process. The paper considers the industrial reaction of catalytic reforming of gasoline, which occupies an important place in the modern scheme of oil refining, since it is a source of high-octane components of commercial gasolines and individual aromatic hydrocarbons. This process is characterized by the participation of a large number (up to 300) of various hydrocarbons, a change in the number of moles, and non-isothermality in it. Mathematical modeling of such processes involves detailing the stages to the required level. The detailing of up to 173 stages is considered. In this setting, automation of the formation of a mathematical formulation of kinetics for catalytic reforming of gasoline has not been carried out before. Therefore, the presented work aimed at implementing effective numerical methods and algorithms for automating the building of a mathematical model taking into account kinetics, thermodynamics, and changes in the number of moles.Materials and Methods. The mathematical formulation of the kinetics of multistage reactions was developed on the basis of the mass action law. The kinetic parameters values were taken from literary sources. The direct kinetics problem was solved using algorithms: the Gear method, the Runge-Kutta method of the 4th order, and the scipy.odeint() method of the Python language. The automation concept was implemented using the IDEF0 methodology. The software was written in the Python programming language.Results. A new software was created to automate the process of forming a mathematical model, taking into account the kinetics, thermodynamics, and the volume of the reaction mixture. The program results were presented by the example of catalytic reforming of gasoline. The model implemented the possibility of taking into account the intermediate heating of the mixture in the reactor cascade. Numerical values of temperature changes corresponding to industrial data were obtained.Discussion and Conclusion. The results obtained through modeling chemical transformations in the cascade of gasoline catalytic reforming reactors confirmed the exothermic nature of the reaction. The developed software product provides displaying changes in the concentrations of reactants, as well as temperature variations in the reactor, and it can be used in scientific research organizations for the analysis of multistage catalytic processes. The results of the reaction kinetics modeling will be used in the subsequent optimization of the process conditions in production.

Computer 3D Modeling of the Process of Wastewater Treatment in a Settling Tank

Purpose. Settling tanks are widely used in technological schemes of wastewater treatment. As a rule, horizontal settling tanks are used in practice. However, to increase the efficiency of water treatment in a horizontal settling tank, additional elements can be used, which are placed in different places in the structure. When reconstructing such structures or designing them for new facilities, it is necessary to assess the efficiency of the settling tanks under different operating conditions. To solve this problem, mathematical models play an important role, including conducting physical experiments, which requires considerable time to obtain results. In the case of mathematical modeling of the water treatment process in a sedimentation tank, two problems need to be solved: the hydrodynamic problem and the mass transfer problem. The main purpose of this paper is to develop a 3DCFD model for calculating the impurity concentration field in a sedimentation tank. Methodology. A dynamic multifactorial numerical model was developed for computer calculation of the wastewater treatment process in a settling tank. The hydrodynamics of the wastewater flow in the settling tank was calculated on the basis of a three-dimensional equation for the velocity potential (potential motion model). The calculation of the impurity concentration field in the settling tank was determined by numerical integration of the three-dimensional mass transfer equation. This equation takes into account the non-uniformity of the flow velocity field in the settling tank, the diffusion process, and the gravitational deposition of the impurity in the structure. The numerical integration of the modeled equations was carried out by using finite-difference splitting schemes. Findings. The software implementation of the constructed mathematical model was carried out. The results of a computational experiment to study the process of wastewater treatment in a settling tank with visualization of the calculation results are presented. Originality. A multifactorial three-dimensional CFD model has been developed that allows to quickly assess the efficiency of the settling tank. Practical value. The proposed CFD model can be used in calculations in the design of wastewater treatment systems or to determine the efficiency of wastewater treatment under new operating conditions.

Modeling the dynamic semantics of a computer program

In this paper, two approaches are used to construct the dynamic semantics of computer programs: the first is the representation of mathematical models of computational processes generated by a computer program in the form of a discrete transformer; the second is the representation of the mathematical model of a computer program in terms of functional grammars. The study focuses on the computational process generated by a computer program. Application of the discrete transducers concept to describe computational processes allows us to obtain a mathematical model or dynamic semantics of a program, which is a composition of two discrete systems B and C. In this case, component A is a control component (a model of the program block diagram), and component B is a model of the program memory. The decomposition of a program into two components B and B is convenient when studying the process of modelling a computational process. This is due to the fact that the prospects of searching for invariants in critical nodes of a programme for mathematical proof of correctness of a computer programme are opened. The comparative analysis of the two approaches leads to the theorem on the regularity of the representation of a function generated by a programme within the framework of functional grammar.

Modelling and analysis of the biodenitrification process

Massive and excessive use of nitrogen fertilizers and sustained irrigation have been widely practiced in recent years. This strategy leads to a large transfer of nitrates to groundwater, leading to a major environmental problem of nitrate contamination in water, intended for drinking water consumption. One of the most effective solutions is the degradation of nitrites and nitrates, into gaseous nitrogen, using the heterotrophic bacteria during the denitrification process. In this paper, we present and study a mathematical model of the biodenitrification process taking into account the fixed and mobile bacteria. This process is modeled by a system of ordinary differential equations and requires the success of bacteria to colonize the reactor. We study the existence and the asymptotic behaviour of the solution. We show the existence of a value of the injected carbon concentration from which we ensure the success of the biodenitrification process and we propose a heuristic algorithm which serves to control the biodenitrification process over time. Finally, we present some numerical simulations in to support the theoretical results.

Mathematical modeling of oil solid-liquid extraction from mamey sapote (Pouteria sapota) seeds with hexane

Mamey sapote (Pouteria sapota) seeds oil has potential as human consumption oil due to its high content of oleic acid. In order to design a solid-liquid extraction sustainable process, (hexane)-(oil)-(Pouteria sapota seeds) extractive system was modeled for different extraction modes applying novel mathematical relations. One equilibrium stage solid-liquid extractions (SLE) and dynamic SLE with continuous solvent flow through a particles fixed bed were experimentally performed in order to estimate the extractive system thermodynamic properties. The results for thermodynamic distribution constant, specific retained solution and oil diffusivity in underflow (seeds-extract mixture) were 0.24 g/g, 1.58 g/g and 8.68 × 10−11 m2/s (at 30 °C) respectively. These properties, applied in the mathematical models of counter-current equilibrium multistage and dynamic SLE processes, reproduced experimental behavior with 4.53–16.7 average difference %.

ARRA TISHLARIDAN PAXTA TOLASINI YECHIB OLISH JARAYONI PARAMETRLARINI ILMIY ASOSLASH

This paper scrutinizes the process of extracting or separating fiber from seed, which is viewed as one of the milestones in cotton-ginning plants, reviews a series of implemented experiments, presents results, and offers solutions. Increasing demand for cotton produce across the globe leads to large-scale research work to improve the technique and technology of primary cotton processing and to establish their scientific basis in major cotton-growing economies. In this regard, it is becoming important, among other things, to develop mathematical models of processes, boost the productivity of cotton processing machines by means of optimization methods, create efficient working bodies, preserve natural quality indicators of the cotton fiber obtained through improved operational characteristics of machines, and reduce production costs. At the same time, the issues of the development of resource efficient designs of working bodies that won’t negatively affect the quality of products and the justification of the parameters of the sewing machine seem relevant for all cotton-growing economies.

Analyzing production optimization models across various carbon pricing policies

As the EU and the US successively proposed the carbon border adjustment mechanism (CBAM) and the Clean Competition Act (CCA), importers are now required to declare the carbon emissions of their products. Particularly, wheel companies face increasing time pressure with the gradual development of implementation paths for net-zero emissions and implementing carbon pricing policies in various countries. This research uses the production data of Taiwan wheel companies to establish a mathematical model for the activity-based cost optimisation decision-making process. It explores the impact of different carbon emission costs on a company’s product mix with pricing decisions. Further, the research proposes five mathematical programmes for single-period cost optimisation decision-making under carbon pricing. These models provide some detailed view, such as changes in profits and product mix caused by high carbon taxes or other changes for each resource. Furthermore, the production cost optimal model proposed in this research can be used by enterprises to fulfill their social responsibilities while ensuring profitability and serve as a reference for making net-zero transformation decisions.

MATHEMATICAL MODELS OF CHEMICAL PROCESSES WITH VARIABLE CHARACTERISTICS

The article discusses the construction of mathematical models of complex chemical processes when different factors act on the result of a chemical reaction at different points in time. The method of least squares is used. This material can be used to teach university students in the disciplines of Mathematical Statistics, Numerical Methods, General Technologies of Food Production, Food Chemistry, etc. Applications from the analysis of experimental research models and laboratory testing of innovative technologies for the development of different types of galusa can be supported by incoming students in the chemical engineering program. Examples from the analysis of experimental research models of laboratory tests of new acid components for a carbonate collector can be applied in the training of students in the Chemical Engineering educational program.

Математическое моделирование при управлении системами противопожарной защиты объектов

The problem of reliability of fire protection systems at the production stage and at the design stage is considered. Mathematical modeling of processes aimed at ensuring the safe evacuation of people in case of fire, taking into account the coefficient of compliance of the technical solution used in the methodology for calculating the amount of individual fire risk. The structural constructions of fire protection systems are analyzed with a demonstration of methods for assessing the reliability and structural significance of various structural constructions of fire protection systems on the basis and example of statistical data. To determine the coefficient of compliance of the fire alarm system, in the form of probabilities of effective operation of the fire alarm system, the following parameters are taken into account: the probability of effective operation of the fire alarm system, smoke protection system, and emergency warning system. The performance statistics of the SOUE for the period from 2013 to 2021 are graphically shown. It is shown that the resulting probability of effective operation of the SPS is determined by the structural design, and the corresponding formulas and examples are given. The dependences of the efficiency of the functioning of the SPZ on the efficiency of the SOUE for various structural arrangements have been constructed. Dependencies of the performance of the SDR were constructed based on statistical data. Analytical and graphical dependences of the reliability of the SOUE on the reliability of the SPS for various structural constructions are derived. Depending on the task being solved, the reliability (as well as efficiency) of the fire protection system can be controlled, while the reliability of the fire safety protection system can be determined depending on the required fire risk. Thus, one of the most important measures that minimizes individual risk should be considered to be increasing the efficiency of each of the subsystems included in the SDR, including the SOUE, as well as optimizing the structural design of the SDR.

Mathematical Modeling of Thermal Processing for an Al-Si Alloy

This paper presents the realization of a mathematical model of a heat treatment process of an Al-Si alloy, with the help of which the values of some mechanical properties are preached. The method of elaborating the mathematical model is a statistical method, namely the method of the active experiment.With the help of the MATLAB software and based on the elaborated mathematical model, we created a graphic interface that allows the prediction of the values of three mechanical properties depending on the thermal processing conditions of the studied alloy.

DEVELOPMENT OF ENERGY-EFFICIENT AIR DEDUSTING

Among the sources of internal pollution one can point to dust, breath products of passengers, various emissions from finishing materials of trains and metro stations, etc. This problem is usually solved in two ways: wet cleaning of tunnels and stations and using powerful tunnel vacuum cleaners. Both of these methods have common disadvantages. Firstly, dust removal can only be carried out at night, when there are no trains on the line. Secondly, the dust removal installations themselves are expensive and are effective only at low speeds of dust movement through the tunnel. All metros in the world have a problem with dust removal. Research methods include analytical and computational studies of air distribution in the metro ventilation network using mathematical modeling methods using graph theory and flow algorithms, as well as experimental studies of air flow parameters in natural conditions of the Almaty metro.This article proposes an innovative method for dust removal of tunnel air based on the use of piston action of trains and labyrinth filters installed in station ventilation joints. The parameters of the calculation model of the metro line are substantiated on the basis of a decomposition approach to the mathematical modeling of aerodynamic processes by moving from a linear model of the metro line to a periodic open-loop model. Computational aerodynamics methods were used to determine the patterns of changes in air speed through the ventilation vent and the available pressure drop depending on the speed and mode of trains passing through the station.

Numerical analysis of temperature effect on CO2 storage capacity and CH4 production capacity during the CO2-ECBM process

Temperature is a key factor affecting the CO2 injection efficiency and CH4 production efficiency, so it is of great significance to clarify the evolution diagram of temperature change during the CO2-ECBM process. In this study, the crushed soft coal seam with low permeability in Huainan coalfield was taken as the research object. Firstly, the fully coupled mathematical models of CO2-ECBM process were constructed, and the influence of temperature field on CO2-ECBM process was emphasized. Secondly, the evolution law of CO2-ECBM process at different time was revealed. Then, the effects of injection temperature and initial temperature on the CO2-ECBM process were analyzed. Finally, the evolution mechanism of reservoir temperature during the CO2-ECBM process was illustrated, and the effect of temperature on temperature field of CO2-ECBM process was further illustrated. The results show that the longer the displacement time, the CH4 concentration gradually decreased, and the CO2 concentration gradually increased. The area where the temperature changes are more concentrated focuses on the vicinity of CO2 injection well, which are mainly determined by the dominant reaction of adsorption and desorption reactions of binary gas. Reservoir temperature and permeability are positively and negatively correlated with injection temperature, respectively. Both CO2 storage capacity and CH4 production capacity increase with the increase of injection temperature, and the sensitivity of CO2 storage capacity to temperature was greater than that of CH4 production capacity. With the increase of displacement time and injection volume, the effective displacement radius increases, but the increment of influencing radius gradually decreases. The lower the initial temperature of coal reservoir, the larger the influencing radius, and which increases with the increase of displacement time. CO2 storage capacity and CH4 production capacity decrease with the increase of initial temperature. Young's modulus and Poisson's ratio can effectively change the reservoir strength. CO2 storage capacity and CH4 production capacity decrease with the increase of Young's modulus, and increase with the increase of Poisson's ratio. This study can support the engineering landing of CO2-ECBM technology in crushed soft coal seam with low permeability, and promote the realization of China's “Dual Carbon” strategic goal.

Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments.

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Evaluation of fatigue life and osseointegration parameters of carbon-carbon composite material for medical applications

The aim of the present work is to study the strength characteristics Carbon fibre-reinforced Carbon (CFRC) material as an osteoimplant under its stepwise loading and to estimate the parameters of osseointegration at the bone-implant interface from the position of histological analysis and mathematical modeling. Fatigue life estimation of materials for implantation and endoprosthesis is based on the study of its "behavior" and determination of the degree of microstructure transformation under different types of cyclic loading using a system for the analysis of acoustic emission under loading. The key parameter in studying the strength of samples from carbon fiber reinforced composite materials under stepwise loading is the determination of the moment of transition of the controlled object into a pre-destructive state. We propose to use the ratio of degree in the equation defining the relationship between the number of acoustic emission events depending on the loading conditions as a key factor in studying the strength of samples made of CFRC under staged loading. When assessing the properties of implant materials, in addition to the study of strength parameters, an important aspect is the determination of the major biomedical characteristics, in particular, the study of bone tissue regeneration processes at the border of the implant-bone block. The osteoinductive activity of materials for plasty of bone tissue defects and endoprosthetics is one of the parameters of the success of reconstructive measures. In this regard, the use of modern methods of histological analysis and mathematical modeling of osseointegration processes of CFRC specimens will allow to predict the effectiveness of their application in clinical practice when replacing bone tissue defects of different localization and in therapy of patients with degenerative-dystrophic diseases requiring endoprosthesis.

ASSESSMENT OF THE POSSIBILITY OF USING POLYMERS IN THE BODIES OF PROMISING LAUNCH VEHICLES BASED ON THE HEAT RESISTANCE FACTOR

One of the possible ways to solve the problem of quick and low-cost payloads to low Earth orbits is the creation of ultralight rockets that use new construction materials, in particular, synthetic polymers. A promising approach to creating a launch vehicle of this type is the concept of a burnt rocket, the body of which is made of thermoplastic polymer materials. At the same time, the practical implementa- tion of such a launch vehicle requires additional research, in particular, the possible process of premature destruction of the structure due to aerodynamic heating. In this work, the heat resistance of polymer bodies of a new type of ultralight launch vehicles during flight in the atmospheric part of the trajectory was evaluated. For mathematical modeling of heating processes, we used the results of experimental studies of the thermodynamics of polyethylene and polypropylene during heating. These results allowed us to propose a mathematical model for calculating the process of heating polymer shells. The dynamics of the temperature fields during movement along the given trajectory of the launch vehicle in the atmospheric stage have been determined. It was established that under the given trajectories, both considered materials satisfy the conditions of heat resistance. The influence of temperature on the reduction of the strength characteristics of polymer bodies is shown, and the necessary thicknesses of the walls of the body shells, which should prevent deformation of the structure during aerodynamic heating, are determined. So, for the first time, the possibility of making rocket bodies from thermoplastic polymer materials has been theoretically substantiated.

Simulation and Experimental Study of Solid-Liquid Extraction of Coal Tar Residue Based on Different Extractants.

Coal tar residue (CTR) is recognized as a hazardous industrial waste with a high carbon content and coal tar consisting mainly of toxic polycyclic aromatic hydrocarbons (PAHs). The coal tar in CTR can be deeply processed into high-value-added fuels and chemicals. Effective separation of coal tar and residue in CTR is a high-value-added utilization method for it. In this paper, ethyl acetate, ethanol, and n-hexane were chosen as extractants to study the extraction process of coal tar from CTR, considering the mass transfer in the liquid phase outside the CTR particles and the diffusion inside the CTR particles, and a mathematical model of the solid-liquid extraction process of CTR was established based on Fick's second law. First, the mass-transfer coefficients (kf) and effective diffusion coefficients (De) of ethyl acetate, ethanol, and n-hexane in solid-liquid extraction at 35 °C were determined to be 1.54 × 10-5 and 4.99 × 10-10 m2·s-1, 1.14 × 10-5 and 3.57 × 10-10 m2·s-1, and 1.01 × 10-5 and 3.48 × 10-10 m2·s-1, respectively. Furthermore, the simulated values obtained by the model also maintained a high degree of agreement with the experimental results, which indicates the high accuracy prediction of the model. Finally, the model was used to investigate the effects of the solvent-solid ratio, temperature, and stirring speed on the extraction rates with the three extractants. According to the analysis with gas chromatography-mass spectrometry (GC-MS), among the three solvents, n-hexane extracted the highest content of aliphatic hydrocarbons (ALHs), ethyl acetate extracted the highest content of oxygenated compounds (OCs), and ethanol extracted the highest content of aromatic hydrocarbons (ARHs). The model and experimental data can be used to provide accurate predictions for industrial utilization of CTR.