Mass Transfer Of Impurities Research Articles

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

MODELLING OF MASS TRANSFER IN WASTEWATER FACILITIES

Problem statement. The design of wastewater treatment systems is a complex process and requires the use of special mathematical models. As a rule, empirical models are used at the stage of designing structures of water drainage systems, which allow obtaining only an “integral” characteristic of the efficiency of wastewater treatment. But in a number of cases, it is important to have information about the spatial distribution of the impurity concentration in the structure. To solve this problem, you need to have three-dimensional mathematical models. In the future, there is a shortage of such models, so the creation of three-dimensional multifactorial models for the analysis of the efficiency of drainage system structures is an urgent task. The purpose of the article. Development of a three-dimensional numerical model for the analysis of the mass transfer process to determine the impurity concentration in the clarifier. Methodology. The analysis of impurity concentration fields in the clarifier is carried out by numerical integration of the three-dimensional equation for the velocity potential and the three-dimensional equation of the convective-diffusion transport of the impurity. For the numerical integration of the Laplace equation for the velocity potential, the variable-triangular method and the Liebmann method are used. Finite-difference splitting schemes are used for numerical integration of the three-dimensional equation of convective-diffusion transport of impurities. Scientific novelty. A dynamic multifactorial numerical model was created for the analysis of the process of mass transfer of impurities in a settling tank by conducting a computational experiment. Practical value. The built multifactorial numerical model makes it possible to analyze the efficiency of wastewater treatment in clarifiers that have a complex geometric shape and cannot be calculated on the basis of existing engineering methods. Conclusions. On the basis of the developed three-dimensional numerical model, a computer code was created, which allows you to quickly obtain information about the distribution of the impurity concentration in the settling tank.

Influence of Surface Waves on Liquid-to-Gas Mass Transfer in Molten Silicon

Abstract The paper focuses on the numerical analysis of the mass transfer of impurities from the wavy surface of molten silicon to the gas phase. The mathematical model is described herein, with the modelling of a wavy silicon melt surface being done with the moving mesh technique. The model employs assumptions about the mass transfer process on the surface, namely, that it can be modelled with effective diffusion across the interface. The assumption is verified against limited experimental data for a stationary melt surface, and reasonable agreement is obtained. Thereafter, numerical studies are undertaken for a wavy melt surface. The dependence of impurity removal rate on the wave amplitude, wavelength and frequency is analysed. It is shown that the waves on the surface of the liquid increase the mass transfer rate in a certain parameter range. Finally, results are analysed to find an explanation for this increase and to determine technological factors that impact it. Surface enlargement due to waves and altered flow patterns near the silicon melt are determined as potential reasons for the improved impurity removal rate. A dimensionless criterion for the minimal wave amplitude required to obtain improved impurity removal is found and discussed.

Effect of oxygen blowing on the competitive removal rate of silicon and iron from molten copper

The effect of blown oxygen on the competitive removal of impurities from liquid copper was investigated at 1673 K. Silicon and iron, which are the dominant impurities in molten copper, are clearly separated into the slag by oxygen blowing. Since the area of the reaction site for impurities’ oxidation was found to be one of the most influential aspects, the interfacial area for both cases of top-blowing and bottom blowing was carefully estimated by considering bubbles and cavity formation. The removal rate of the impurities in competitive oxidation regime could be theoretically analyzed. By a comparison of the apparent rate constant obtained from the oxidation experiments with that was theoretically calculated, the present kinetic model based on liquid phase mass transfer of impurities could be verified to be valid for the understanding the competitive removal of the impurities from liquid copper.

High Efficient Impeller for Rotary Gas Injection in Aluminum Melt

In rotary gas injection (RGI), which is widely used in aluminum industry, impurities are removed by reaction with halide-containing chemicals injected into the melt. However, the constantly increasing concern on environmental protection obliges aluminum makers to eliminate or significantly reduce their usage. In this study, aiming at enhancing the efficiency of chlorine gas treatment for impurities removal from the melt, we investigated the effect of impeller design on the impurity mass transfer by performing physical model experiments on CO2 absorption, particle image velocimetry (PIV) measurements and numerical simulation. It is shown that a newly designed impeller intensifies the discharged flow as compared to the conventional impeller case that forces the formed bubbles to move to the fragmentation zone near the impeller blade tip. This results in an enhancement of the mass transfer. From the numerical results, it was found that these phenomena could be explained by the trailing vortex structure near the impeller blades.

Modeling of the singularly perturbed process of convection-diffusion heat and mass transfer in multilayer media

A mathematical model of the process of convective-diffusion heat and mass transfer of impurities taking into account mass exchange in a porous multilayer filter has been developed. An algorithm for numerically asymptotic solving of the corresponding singularly perturbed boundary value problem for a layered curvilinear area is constructed. On the basis of the received algorithms software of computer realization for calculation of time-space distributions of concentrations of impurities is created.

EXPRESS MODEL FOR WATER TREATMENT PROCESS CALCULATION

Purpose. The use of a physical experiment to study mass transfer processes in structures used in water supply and sewage systems requires considerable time and is very expensive. The aim of the work is to develop numerical models for a computational experiment to study the mass transfer process in sand traps. Methodology. For mathematical modeling of the mass transfer process in sand traps, the two-dimensional Navier-Stokes equations and the two-dimensional impurity mass transfer equation are used. For numerical integration of equations describing the motion of a viscous incompressible fluid, implicit difference splitting schemes are used. The unknown parameters at each step of the splitting were found by explicit dependencies. For the numerical integration of the two-dimensional mass transfer equation, an alternately triangular difference splitting scheme is used. Findings. To conduct a computational experiment, a specialized code was created on the basis of the constructed numerical model. The results of computational experiments on the study of mass transfer in sand traps with additional elements are presented. It was determined that water purification efficiency changes with installation of additional elements at the bottom of the sand trap. Originality. The constructed numerical models make it possible to quickly analyze and predict the efficiency of sand traps having a complex geometric shape. They also make it possible to take into account the flow hydrodynamics in the treatment plant. Practical value. The proposed numerical models can be used at the design stage of sewage treatment plants.

ATMOSPHERE PROTECTION FROM POLLUTION IN ACCIDENTAL SITUATIONS AT CHEMICALLY HAZARDOUS OBJECTS

Purpose. The work involves the development of numerical models to assess the effectiveness of the air curtain usage near the building in the event of chemical pollution. Methodology. To describe the process of dispersion of a chemically hazardous substance, emitted in emergency situations, the three-dimensional equation of impurity mass transfer in atmospheric air is used. To calculate the air velocity field near the building in the presence of an air curtain, a potential-flow model is used. The modelling equations take into account the velocity field of the wind flow, atmospheric diffusion, and the intensity of the emission of a chemically hazardous substance into the atmosphere. For the numerical integration of the mass transfer equations, implicit difference schemes are used. The complex of programs was created to solve the problem of calculating pollution zones near buildings in the presence of an air curtain. The application of the developed model allows you to quickly calculate this field of concentration of a chemically hazardous substance near the building in the presence of an air curtain. Findings. Numerical models for calculating the aerodynamics of the air flow and the concentration field near the building when using an air curtain were constructed. They can be used to carry out operational calculations of the size, intensity of pollution zones, which are formed in the atmosphere during the emission of chemicals at industrial sites. The developed numerical models can be implemented on computers of low and medium power, which allows it to be widely used for solving problems in developing an emergency response plan (ERP). For practical application of the developed numerical models, standard input information is required. Authors present the results of a laboratory experiment. Originality. Effective three-dimensional numerical models are proposed for estimating the level of atmospheric air pollution when emission of chemically hazardous substances into the atmosphere and using an air curtain near an industrial building. Models allow you to quickly calculate the effectiveness of the air curtain usage. Practical value. The developed numerical models allow solving applied problems arising in the development of ERP for chemically hazardous objects.

Numerical model of rainwater runoff over the catchment surface and transport of contaminant incoming to water stream from soil

This paper deals with development of computational schemes to solve of system equations with lagging argument governing the rainwater runoff along the surface catchment and transport of impurity which permeates into the water flow from soil at the certain areas of this surface. This system consists of two types of equations: the first of them describes the changes of water layer thickness over the slope surface given the precipitation and evaporation, and the second one – the mass transfer of impurity coming into the surface water during its filtration in zone of incomplete saturation of soil. Computational scheme to solve the system of nonlinear differential equations are developed with the finite-difference methods using a priori information about the solution behavior. The numerical model is implemented in the software for computer simulation of the processes with simultaneous graphic visualization of the computing results.

Mathematical modeling of rainwater runoff over catchment surface and mass transfer of contaminant incoming to water stream from soil

The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the equations for calculating of the water layer thickness over the slope surface given the precipitation and evaporation, and equation of the mass transfer of impurity coming into the surface water during its filtration in zone of incomplete saturation of soil. The model also takes into account a reverse process – adsorption of impurity in soil with its low concentration or in the uncontaminated soil. Water content in the zone of incomplete saturation is determined within the approximate approach based on the model of capillary impregnation. The principal features of nonlinear differential equations are theoretically studied. In particular, it is shown that the equation for water content in this zone can become a differential equation with lagging argument. Keywords: Mathematical Modeling, Runoff, Transport of Contaminant, Catchment, Sorption, Desorption, Incomplete Saturation

Sodium-Bench Testing of a Cold-Trap Model

Experimental data on the precipitation of an impurity (sodium oxide) in sodium coolant in a model of a cold trap of a fast reactor are obtained using a specially developed technique. The working model included the zones of filtration, spontaneous cooling, and cooled settling tank, which were intended for collecting the settling impurities. The working cavity was cooled by sodium-potassium alloy melt outside its housing. It is shown that there are two local maxima in the distribution of the sodium oxide deposits along the height of the model; these peaks correspond to the initial and final sections of the cooling zone. The model constants of impurity mass transfer in the model of a cold trap are refined experimentally. The calculations performed with the refined model of mass transfer for the standard variant of a cold trap built into the reactor tank showed that the model constants are optimal.

Determination of the Heat-Exchange Characteristics of Low-Pressure Heat-Exchangers for Lead and Lead-Bismuth Cooled Loops

Heat removal during transient processes in nuclear power installations and bench loops cooled by lead and lead-bismuth coolant is studied. It is shown that low-pressure heat-exchange equipment is effective. The studies were conducted in a non-isothermal loop with circulating of lead coolant at 450–500°C, average speed in the narrow section of the gap in longitudinal flow over the heat-exchange surface 0.1–1.05 m/sec, Peclet number 300–3300, and the oxygen thermodynamic activity in lead 1–10–3. The processes occurring in a non-isothermal liquid-metal loop with an experimental heat-exchange section model the dependence of the heat-exchange characteristics on impurity mass transfer in the loop.

Experimental Investigations of the Thermohydraulic Characteristics of Transverse Lead-Coolant Flow over the Tubes of a Steam Generator

The results of experimental studies of lead-to-wall heat transfer during transverse flow over a straight-line tube bundle in a steam generator in the circulation loop during monitored and controlled mass-exchange and mass-transfer of oxygen impurities are presented. The investigations were performed in a nonisothermal loop with circulation of lead coolant at temperature 450–550°C, average coolant velocity in a narrow-gap section 0.2–1.5 m/sec, Peclet number 900–3000, and thermodynamic activity of oxygen in lead 1–10–4. The processes occurring in a nonisothermal liquid-metal loop with an experimental cooling section model the dependence of the characteristics of heat exchange on the mass transfer of impurities in the loop.

Calculation of Impurity Mass Transfer in Cold Traps with Sodium Cooling

The design of a cold trap is optimized in order to maximize the capacity in terms of impurities. The main criterion of optimization is uniformity of the distribution of impurity deposits along the length of the trap. The modified OpenFOAM code was used to solve the complex thermohydraulic and mass transfer problem. The problem was modeled in a stationary formulation by solving the Reynolds average Navier–Stokes equations (RANS) by the SIMPLE method. The calculations showed that OpenFOAM makes it possible to calculate the heat exchange and mass transfer of impurities in the trap cavity. The MASKA-LM code was used in the calculations in order to take account of changes in the geometry of the computational region by deposits on solid surfaces. The proposed computational method makes it possible to evaluate the impurity capacity of a cold trap and the time to exhaustion of its service life.

Removal of Vanadium from Molten Aluminum—Part III. Analysis of Industrial Boron Treatment Practice

Transition metal impurities (V, Ti, Zr, and Cr) reduce the electrical conductivity of smelter grade aluminum. These impurities are removed in the form of their borides by reacting with added Al-B master alloys i.e., boron treatment. Although, boron treatment is widely used for the production of high purity aluminum alloys in casthouse the fundamental understanding is lacking and published industrial data are limited. In the current study, industrial trials on the removal of impurities were conducted at one of the high purity aluminum alloys producers in Australasia. Kinetics analysis revealed that the rate of reaction is controlled by the mass transfer of impurities in the bulk melt. The measured mass transfer coefficient (k m) of V and Ti were 1.1 × 10−4 and 2.6 × 10−4 m/s respectively, in the naturally stirred molten aluminum. The rate of V and Ti removal was faster compared to Zr and Cr during the boron treatment of smelter grade aluminum. Mass balance analysis revealed that 70 wt pct of V and Ti combined as borides in the first hour of the total 12 hours of boron treatment process. The calculated amount of un-reacted B was approximately 25.5 wt pct of initial amount added that remained in the final alloy. There was no evidence of boride rings formation, although partially dissolved AlB12 particles were observed under scanning electron microscope. Finally, implications for industrial practice are discussed for the improvement of current boron treatment process that include changing the source of boron, multiple stage addition of boron and better stirring of the molten aluminum.

The specific diffusion behaviour in paper and migration modelling from recycled board into dry foodstuffs

Recycled board plays an important role in food packaging, but the great variety of organic impurities must be considered as potential food contaminants. The diffusion behaviour of the impurities is significantly different from that in plastic materials. The two-layer concept for paper and board introduced recently is now treated in more detail. In the rate-determining surface region the diffusion coefficients of the n-alkanes in the homologous series with 15–35 carbon atoms decrease proportionally as their vapour pressures. This leads to a different equation of the diffusion coefficients in comparison with that for the core layer. Different polarities of the migrants have additional influences on the diffusion due to their interactions with the fibre matrix. A new analytical method for the quantification of aromatic impurities has previously been developed. Based on this method and on the described diffusion behaviour, a migration model for specific and global mass transfer of impurities from recycled board into dry food and food simulants is given.

Numerical simulation of impurity mass transfer in the cold traps in fast reactors

Numerical simulation of impurity mass transfer in the cold traps in fast reactors

Effects of a Forced Solution Flow on the Step Advancement on {110} Faces of Tetragonal Lysozyme Crystals: Direct Visualization of Individual Steps under a Forced Solution Flow

To grow protein crystals of better quality, there still exists an open question whether a solution flow should be suppressed or intentionally introduced. To obtain a comprehensive understanding of the effects of a solution flow, we directly measured the velocities of individual elementary steps (on {110} faces of tetragonal lysozyme crystals) under a forced solution flow, for the first time, by laser confocal microscopy combined with differential interference contrast microscopy. When we used crystals grown by a two-dimensional (2D) nucleation growth mechanism in a solution of commercial lysozyme (98.5% purity, from Seikagaku Co.), while increasing the solution flow rate, the step velocity decreased monotonically. We confirmed that this decrease in the step velocity with flow rate was due to the enhancement of the mass transfer of impurity (mainly covalently bonded dimer), by the observation using a lysozyme further purified (dimer was removed). In contrast, when we used crystals grown by a spiral growth mechanism in a commercial lysozyme solution, with increasing the flow rate, the step velocity increased and had the maximum at the flow rate of 10 μm/s, and then decreased monotonically. Also, the step velocity was 2–4 times higher than in the case of the 2D nucleation growth. These results demonstrate that the growth of spiral steps is less affected by impurities because the density of spiral steps is much higher than that of 2D island ones.

Studies validating a sodium purification system for fast reactors

The sources of impurities entering the sodium in fast reactors were investigated. The analysis showed that oxygen and hydrogen can be removed from the sodium by using cold traps in all operating regimes of a nuclear power plant as well as hot traps. An operating regime preventing hydrogen accumulation in the first-loop cold trap is proposed for a system purifying the first two loops. A computer code for calculating the impurity mass transfer is perfected. Test calculations showed that the procedure developed and the code are both serviceable. The deviation of the computational results from the experimental data is about 30% on average. For a built-in purification system, it is essential to develop a cold trap with a large impurity capacity. It is shown on the basis of experiments that such cold traps can in principle be developed. Thermohydraulic and mass-transfer codes must be developed in order to realize this possibility.

Fundamental Researches on the High-speed and High-efficiency Steelmaking Reaction

AbstractTraditionally, steelmaking reactions have been analyzed by thermodynamics. Recently, software packages that can be used to calculate the equilibrium conditions have improved greatly. In some cases, information obtained in this software is useful for analyzing the steelmaking reaction. On the other hand, in industrial operation, steelmaking reactions, i.e., decarburization, dephosphorization, desulfurization or nitrogen removal, do not reach the equilibrium condition. Therefore, the kinetic model is very important for gaining a theoretical understanding of the steelmaking reaction. In this paper, the following recent research activities were shown; 1) mass transfer of impurities between solid oxide and liquid slag, 2) simulation model of hot metal dephosphorization by multiphase slag, 3) evaluation of reaction rate at bath surface in gas-liquid reaction system and 4) condition for forming of metal emulsion by bottom bubbling.