Modeling Of Mass Transfer Processes Research Articles

One-Dimensional Modeling of Mass Transfer Processes in an Annular Centrifugal Contactor

Due to the importance of process intensification, modeling of Annular Centrifugal Contactors (ACCs) is becoming of increasing interest. By the current state of scientific knowledge, universal modeling without high computing power of these complex apparatuses is not possible to a satisfactory degree. In this article, a one-dimensional model to describe the mass transfer during a physical extraction process in an ACC is presented. The model is based on solely geometrical data and operating conditions of the ACC, as well as physical properties of the components. Regarding the selection of physical properties, only physical properties that are easily accessible were used. With this model, mass transfer calculations are possible and therefore, the output concentrations can be predicted. Simulations of an ACC based on the model were done by creating and running a python code. Validation of the model was conducted by varying and comparing operating conditions in both the simulation and the experiments. Validation was completed successfully for a representative system of components and showed good agreement over a range of rotational frequencies and temperatures.

MODELING OF MASS TRANSFER PROCESS’ KINETICS DURING DYEING AND PRINTING OF TEXTILE FIBERS

MODELING OF MASS TRANSFER PROCESS’ KINETICS DURING DYEING AND PRINTING OF TEXTILE FIBERS

Ефективний чисельний метод длярозв’язання рiвняння Рiчардса-Клюта звiдстеженням зони повного насичення

The article presents modifications for numerical methods for modeling of mass transfer process in porous medium with full saturated zone tracking. The goal of the article is to increase computational efficiency of finding an approximate solution process using division of the area into the two non-intersecting parts: unsaturated zone and zone with full saturation. Numerical methods for solving the one-dimensional Richards-Klute equation with tracking of the full saturated zone have been developed. The cases of monotonic solution and solution with general properties of Richards-Klute equation were considered. A modification of the full saturated zone tracking process using a doubly connected edge list structure have been developed for two-dimensional case. Efficiency increase estimation is proven for one- and two-dimensional cases using probability distibution for a measure of the full saturated zone. A comparative analysis of the proposed modifications was carried out. The results of numerical experiments coincide with the estimates predicted by theory.

MHD Modeling of Mass Transfer Processes in Close Binary Stars

A three-dimensional numerical model has been developed to study the flow structure in close binary systems with a magnetic field. The model uses a system of equations of modified magnetic hydrodynamics, which allows describing all the main dynamic effects associated with the magnetic field. It takes into account the processes of radiation heating and cooling, heating due to current dissipation, as well as magnetic field diffusion. The model allows calculations in a wide range of magnetic field values. Comparison of the calculation results with observational data confirms the reliability and high efficiency of the model. The paper presents the calculation results of the flow structure in a typical intermediate polar. It is shown that an accretion disk is formed in such a binary system, which has the following characteristic features: “hot line”, tidal shock waves, precession density wave, magnetospheric region, and accretion columns. In this case, the magnetic field in the disk is predominantly toroidal. The paper also presents the results of calculations for typical polars. In such systems, instead of an accretion disk, a collimated stream of matter is formed, moving along the magnetic field lines to the magnetic poles of the white dwarf. It is shown that in synchronous polars, variations of the mass transfer rate lead to a change in the spatial configuration of the flow. In asynchronous polars, changes in the flow structure for different phases of the beat period are observed as well as the processes of switching the flow between the magnetic poles of the accretor. Numerical calculations of the asynchronous system are performed under the assumption of the dipole configuration of the magnetic field for different values of the dipole offset relative to the center of the white dwarf. The paper presents a method for estimating this offset from observational light curves.

The Mathcad system usage in finding normal equations in the description of food extraction processes

The article describes using electronic computer systems, particularly Mathcad when finding standard equations for building mathematical models of technological processes in the chemical and food industries. Classical mathematical models of the extraction process are usually based on analyzing the differential equation of diffusion under appropriate boundary and initial conditions. Also, when describing mathematical models, Fick's equation, the equation of the adsorption pore model of molecular-statistical studies, models that take into account the physics of the process of substance transfer in a capillary-porous medium, etc., are used. Modeling of mass transfer processes under the influence of the intensifying action of the microwave field is described in the studies for the systems “coffee – water” and “oak wood – water-alcohol solution”, “coffee grounds – alcohol,” “amorant – hexane,” a mechanism of the combined process of mass transfer of extractive substances from a porous structure is proposed into solution The description of mass transfer processes under the influence of microwave field intensification is rather complicated. The mass transfer of extractive substances from porous structures to the solution occurs through the distribution of concentrations at the “solid–solvent” interface. However, it passes from the inner part through the outer part, through the capillaries into the border diffusion layer. Complex mathematical models for mass transfer processes do not have analytical solutions. When using the Mathcad system to solve nonlinear systems of equations, it is recommended to use the built-in find function in the calculated Given block. Also, the universal function genfit is quite adequate, which makes it possible to determine unknown parameters for nonlinear combinations of functions by the method of least squares. This system was used in describing extraction processes in the structure of interaction “oil – containing raw materials – solvent” with the intensifying effect of the microwave field. Such simplified analytical description systems are recommended to be used along with experimental modeling with the classic use of similarity theory and the “dimensional analysis” method. The final result of these directions is the construction of sound engineering methods for the design of extractors for industrial purposes.

MATHEMATICAL MODEL OF TWO-CHAMBER ELECTROLYSER DYNAMICS FOR STUDYING PROPERTIES OF ION EXCHANGE MEMBRANES BASED ON PROTON IONIC LIQUIDS

A mathematical model of mass transfer processes in the electrolysis of one-component solutions of 1,1 symmetric strong electrolytes NaOH and NaCl in a two-chamber electrochemical reactor with mesh electrodes based on platinum titanium is formulated. Experimental modeling of processes is performed was carried out under conditions of continuous precise monitoring of the system (NaOH concentration and volume of solution in the chambers).The electrolysis system was designed to balance the flow of components through the membrane to study its properties and to determine five unknown parameters of mathematical modeling of the process. The mathematical model is a system of equations, which includes the unknown transfer numbers of counterions through the membrane, the electrolyte diffusion coefficient, the electroosmotic flux constant, and the empirical parameters of the approximating expressions.

Automation of the control process of a gas pipeline network with a complex topological structure

The reliability of the gas pipeline network is determined by the perfection of the structures, the precise fullfilament of the conditions of its operation, ensuring the coordination of the flow parameters in the pipe with the parameters of the blowers. Deviation from the established mode of operation in gas pipelines can affect the stability of the system. With a significant deviation from the operating mode, various features arise, both kinematic and dynamic deviations in the flow, which leads to unstable operation of the system. Therefore, it is necessary to automate the control processes of the pipeline gas network during gas transportation, which will be based on the results of mathematical modelling of mass transfer processes in pipes to determine the main flow parameters. It is also known that the main losses and changes in flow parameters in pipelines occur along the entire length of the linear sections of the network. Therefore, to adapt these changes to specific objects, it is necessary to use more accurate mathematical models that allow to adequately control the processes in the network based on automated control systems.

ORGANIZATIONAL AND ECONOMIC MECHANISMS FOR ATTRACTING INVESTMENT IN THE HYDROGEN SULFUR MIXTURE PROCESSING OF THE BLACK SEA

The article is devoted to the hydrogen sulfide mixture usage containing in the depths of the Black Sea as a raw material for processing into hydrogen and obtaining sulfur as a by-product. Some prospects and problems of energy resources utilization under the energy crisis in Ukraine have been considered. Hydrogen sulfide mixture reserves have been established as a result of geological exploration and analytical studies; the procedure for its processing into hydrogen has been proposed. The expediency of application of absorption-electrochemical method of hydrogen purification from sulfur has been considered. It can be used as a by-product for the branches of national economy. It was found that long-term operation leads to partial destruction of the electrochemical reactor elements, so the efficiency of existing treatment equipment is reduced compared to the allowable values. It was established that sanitary protection measures for the processing of raw materials do not comply with the State Sanitary Rules for the Protection of Atmospheric Air of Settlements. The economic and mathematical modeling of mass transfer processes in a gas-liquid system taking into account hydrodynamic processes in absorption-electrochemical installations of air purification from hydrogen sulfide has been proposed from the ecological point of view. The ways to intensify scientific research on this and related issues of its economic efficiency have been identified. The economic, ecological and safety factors influencing the hydrogen sulfide processing have been studied. Some measures to develop the appropriate scientific and technical programs and create a favorable investment climate to attract investment for their implementation have been proposed.

Ways and Tools to Improve the Efficiency of Natural Resources in Ukraine. (Management Mechanisms and Means of Hydrogen Sulfide Mixture Processing into the Black Sea)

The article is devoted to the possibilities of using the hydrogen sulfide mixture contained in the depths of the Black Sea as a raw material for processing into hydrogen and obtaining sulfur as a by-product of processing. Prospects and problems of energy resources use in the conditions of energy crisis in Ukraine are considered. As a result of the conducted geological exploration works and analytical researches the reserves of hydrogen sulfide mixture were established, the mechanisms and means of its processing into hydrogen were proposed. In particular, the expediency of using the absorption – electrochemical method of purification of hydrogen from sulfur, which again can be used as a by – product for the needs of the national economy. It was found that in the process of long-term operation, due to the partial destruction of the elements of the electrochemical reactor, the efficiency of existing treatment plants is reduced compared to acceptable values. It is established that sanitary-protective measures for processing of raw materials do not correspond to the State sanitary rules of protection of atmospheric air of settlements, etc. From the ecological point of view, it is proposed to use economic-mathematical modeling of mass transfer processes in a gas-liquid system taking into account hydrodynamic processes in absorption-electrochemical installations for air purification from hydrogen sulfide, etc. Ways to intensify the process of scientific development on this and related issues of its economic efficiency are identified. Economic, ecological and safety factors influencing the intensification of hydrogen sulfide processing are studied. Mechanisms and means of improving the efficiency of the use of hydrogen sulfide mixture from the Black Sea are described. Ways to organize its processing into hydrogen are proposed. It is proposed to take measures to develop appropriate.

Modeling of mass transfer processes during dehydration of air-dried fish

The study addresses the problems of the Fisheries industry development in the Murmansk region. It has been acknowledged that the percentage of the frozen fish in the output of hydrobionts food products is about 90 %. The focus areas for the Russian Fisheries industry are the increasing share of products with high added value and the development of the domestic consumer market of fishery products. It has been found that the air-dried and dried fish products with defined organoleptic properties is traditionally in strong demand with the population. However, the range of air-dried and dried fish products available for the consumers is rather limited. Moreover, there is a very small part of air-dried and dried fish in the total volume of hydrobionts food products. It is possible to increase the efficiency of air-dried and dried fish production by using the scientific-based process solutions, which allow to reduce the production costs and improve the consumer properties of the finished products. This paper presents the aspects of generalization of the dehydration processes in the production of dried, air-dried and smoked fish. A link between the initial, critical moisture content of fish and the potential conductivity of mass transfer coefficients has been established. A mathematical relation for calculating the duration and modeling the kinetics of drying processes in production of dried and air-dried fish has been determined. The equations for calculating the water diffusion coefficients in the critical points of the kinetics curve have been obtained. The combined use of the received patterns allows to model the dehydration processes when producing the air-dried and dried fish products, calculate the drying time, determine the moisture diffusion coefficients and build dependencies of water distribution in the thickness of the processed object.

A Mathematical Model of Two-Way Heterodiffusion Processes with Cascade Decay of Migrating Particles

We construct a mathematical model of mass transfer processes with regard for the local structure of the medium and cascade decay of foreign particles migrating in two different ways. For a specific scheme of cascade decay, we deduce the mass balance relations for the components of the system and obtain linear equations of state and kinetic relations. The conditions for the intensities of mass production in different components of the system are established. The key systems of the model equations of two-way heterodiffusion with cascade decay of migrating particles are obtained in the case where the decay of substance in the current stage serves as a mass source in the next stage.

Numerical modeling of mass transfer processes coupling with reaction for the design of the ozone oxidation treatment of wastewater

A computational model for an ozone oxidation column reactor used in dyeing wastewater treatment is proposed to represent, simulate, and predict the ozone bubble process. Considering the hydrodynamics, mass transfer, and ozone oxidation reaction, coupling modeling can more realistically calculate the ozone oxidation bubble process than the splitting methods proposed in previous research. The modeling is validated and shows great consistency with experimental data. The verified model is used to analyze the effect of operating conditions, such as the initial gas velocity and the ozone concentration, and structural conditions, such as multiple gas inlets. The ozone consumption is influenced by the gas velocity and the initial ozone concentration. The ozone’s utilization decreases with the increasing gas velocity while nearly the same at different initial ozone concentrations. Simulation results can be used in guiding the practical operation of dyeing wastewater treatment and in other ozonation systems with known rate constants in wastewater treatment.

Mathematical Model of Mass Transfer Processes in Biological Corrosion of Cement Concretes

Timely protection of underwater concrete and reinforced concrete objects from biofouling will significantly reduce the economic damage from the effects of corrosion damage, improve the reliability of structures operated in high humidity conditions, and reduce the likelihood of accidents. Despite the abundance of ways to protect against fouling, there are still no radical methods of struggle. It is expedient to find a solution to the problem of predicting the durability of concrete and reinforced concrete structures in biologically aggressive liquid media from the point of view of the theory of mass transfer. The model of mass transfer in an unlimited two-layer plate is considered for the first time in the form of a system of partial differential equations of parabolic type with boundary conditions of the second kind at the interface between concrete and liquid and the fourth kind at the interface between concrete and biofilm, which describes diffusion processes in the system of «cement concrete – biofilm – liquid». The proposed physical and mathematical model takes into account the properties of the solid and liquid phases, as well as the kinetics of growth, reproduction and death of microorganisms. The results of calculating dimensionless concentrations of «free» calcium hydroxide over the thickness of the concrete structure and biofilm are presented. The application of the obtained solutions will allow timely monitoring of the biocorrosion destruction of underwater structures and select effective protection methods.

The Influence of Structure Formation Conditions of the Composite on the Mass Transfer Processes

The article describes the phenomenon of moisture transfer in the system “composite non-metallic reinforcement – cement mortar” at the stage of hardening of the composite. The processes of moisture transfer occurring during the structure formation have an impact on the water-cement ratio of the cement mixture. The deformation and operational characteristics of cement concrete, its structural and phase composition, porosity, density and corrosion resistance depend on the water-cement ratio. To obtain a mathematical model of moisture transfer in the formation of the cement matrix, the equations of mathematical physics, the equations of unsteady mass transfer and the differential equations of mass conductivity of parabolic type are used. Mathematical models of mass transfer processes make it possible to predict the change in the characteristics of the composite at the hardening stage and to obtain concretes with specified properties. The presented physical and mathematical model of moisture transfer for the system “cement concrete – composite reinforcement” allows to take into account the change in water-cement ratio at the stage of hardening of the composite and to establish its influence on the structure formation of the composite and its performance characteristics. The formulated physical and mathematical problem can be solved for special cases by the method of microprocesses.

Numerical model of mass transfer processes using fractional derivatives

The article describes the scheme of construction and application of finite element method using Grunwald-Letnikov algorithm. Obtained results make it possible to estimate influence of fractional derivative order in terms of time and space on process of gas filtration in porous medium. Numerical ecperification and analysis performed

Mathematical modelling of mass transfer processes under water ultrafiltration

Mathematical modelling of mass transfer processes under water ultrafiltration

К РЕШЕНИЮ ЗАДАЧ НЕСТАЦИОНАРНОЙ ДИФФУЗИИ В СЛОИСТЫХ СРЕДАХ

The issues of nonstationary diffusion in layered structures are considered. When designing the devices for implementing mass transfer processes, it is necessary to take into account the properties of the substance and the nature of the processes. Design time reduces significantly and the efficiency of the devices is higher if a good physical model is built and a mathematical analysis with kinetics of the processes is applied. The difficulties of theoretical analysis and calculation of mass transfer are determined by the complexity of the transfer mechanism to and from the phase boundary. Therefore, simplified models of mass transfer processes are used in which the mass transfer mechanism is characterized by a combination of molecular and convective mass transfer. Many important practical problems involve the calculation of nonstationary diffusion (Fick's second law of diffusion) for a certain volume of substance (substances). For qualitative evaluation of processes, in the case of symmetry, volumetric issues can be considered as one-dimensional tasks, i.e. dependent on one coordinate. The general solution of the non-stationary diffusion equation for layered environments is proposed. The case of non-stationary boundary conditions of the third kind on the external surface and boundary conditions of the fourth kind conjugation for contiguous layers has been considered. The solution is obtained by separating the Fourier variables by the eigenfunctions of the problem using the Duhamel integral. The proposed solution is explicit and due to the recurrent form of the basic relations can be useful in numerical calculations

Nonequilibrium poroelectroelastic theory for polymer electrolytes under conditions of water electrolysis

The paper deals with the nonequilibrium poroelectroelastic theory (PEET) for polymer electrolytes (PE) under the conditions of water electrolysis with a view of further use in the theoretical description of mass transfer processes in layers of a membrane–electrode assembly. Moreover, this paper presents a review and analysis of the models of electrochemical and mass-transfer processes in electrolyzers, and analyzes problems associated with their physicochemical description. The authors came to the conclusion that it was necessary to use models of water sorption and PE swelling. It was further concluded that the existing PEET may be most suitable to be modified for use under nonequilibrium conditions during electrolysis. The fundamental equation for pressure balance of the classical equilibrium PEET for PE was considered. A modification of the PEET was carried out in order to use it under nonequilibrium conditions of water electrolysis for the purpose of further modeling of mass transfer processes. Based on experimental data available in open sources, the authors studied properties and features of the elastic forces in PEs, and then refined the dependencies of the elastic forces in PE on swelling and temperature. Taking into account the existing experimental data on the permeability of gases in a PE and the swelling property of a PE when in a contact with liquid water, parameters of the nonequilibrium PEET were obtained for the conditions of water electrolysis.

Model of mass transfer processes in a mixture of continua, consisting of one deformable and two liquid components

Model of mass transfer processes in a mixture of continua, consisting of one deformable and two liquid components

Имитационный подход при прогнозировании радиационной обстановки в случае лесных пожаров в зонах радиоактивного загрязнения

Purpose: The accident at the Chernobyl NPP caused radioactive contamination of large areas, including forestry. For the last decades forest fires in the RF tend to increase and, more alarmingly, their burnt-out area significantly expands. So, the risk of large-scale forest fires in the area of radioactive contamination increases. Effectiveness of the measures for radiation protection of population and personnel involved in fire response is directly related to existence of valid methods of radiation situation prognostication. The work is aimed to develop a method of prognostication of radiation situation at forest fire in the area of radioactive contamination, taking into account random nature of atmospheric turbulence and a convective column over the body of fire, and to estimate validity of this method. 
 Material and methods: Methods of simulation modeling of mass transfer processes in the atmosphere (method of Bird) based on the molecular-kinetic theory and gas-dynamic theory were used when developing the prognostication method. 
 Results: The simulation model of formation, spreading and fall-out of radioactive cloud taking into account random nature of atmospheric turbulence and presence of a convective column over the body of fire has been developed; the method of prognostication of radiation situation at forest fire in the area of radioactive contamination has been developed and verified based on data of European experiment E1. The relative error of received values in the control points of radiation situation parameters based on data of experiment E1 did not exceed 0.25. 
 Conclusion: Use of modified method of Bird allowed developing 3D dynamic model of spreading of radioactive impurity into atmosphere at convective rising by heated air flow from underlying surface. This model takes into account random nature of atmospheric turbulence and presence of a convective column over the body of fire which significantly increases accuracy of the method of radiation situation prognostication.