scholarly journals Mathematical model of the process of ultrafiltration concentration of secondary milk raw materials in tubular membrane devices with filtering elements of BTU 05/2 type

2021 ◽  
Vol 83 (1) ◽  
pp. 36-43
Author(s):  
D. A. Rodionov ◽  
S. I. Lazarev ◽  
D. N. Protasov ◽  
O. A. Abonosimov ◽  
K. K. Polyansky
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Protein Concentration ◽  
Cheese Whey ◽  
Raw Materials ◽  
Experimental Studies ◽  
Transmembrane Pressure ◽  
Specific Output ◽  
Output Flow ◽  
Mathematical Equations

For the qualitative application of ultrafiltration processes for the concentration and purification of food solutions, both experimental studies and a mathematical description of the processes of the membrane separation process of solutions from the standpoint of the development of computational mathematical models are required. In this work, by analytical solution of equations, that is, by the method of finite differences, mathematical equations are solved. To obtain the system, the flow continuity equations, convective diffusion equations, Navier-Stokes equations and flow equations with boundary conditions were solved in order to build a mathematical model of the process of ultrafiltration protein concentration in cheese whey in the production of rennet cheeses. As a result of the analytical solution of the equations, a system of mathematical equations was obtained that allows one to construct a profile of changes in the flow rates of the solution along the cross-section of the intermembrane channel and to determine the protein concentration in cheese whey along the length of the tubular ultrafiltration element BTU 05/2 of industrial type. The obtained mathematical model makes it possible to theoretically describe the process of ultrafiltration protein concentration in cheese whey along the entire length of the membrane channel of the tubular element under laminar and transient regimes of solution flow. The resulting system of mathematical equations makes it possible to find the numerical values of the mass flow rate of cheese whey, make it possible to calculate the specific output flow when the transmembrane pressure changes and to calculate the concentration of solutes in the secondary milk raw materials on the left and right ultrafiltration membrane of the intermembrane channel. The adequacy of the developed mathematical model was carried out by comparing the calculated and experimental data on the specific output flow when the transmembrane pressure in the intermembrane channel changes from 0.1 to 0.25 MPa with ultrafiltration concentration of cheese whey. The deviation of the calculated data found by the mathematical model from experimental studies obtained on a semi-industrial tubular ultrafiltration plant BTU 05/2 using semipermeable membranes, in which the active layer is made of fluoroplastic, hemisulphone and polyethersulfone, did not exceed 10%.

scholarly journals RESEARCH METHOD OF REDUCING POLARIZATION LAYER AT ULTRAFILTRATION OF COTTAGE CHEESE WHEY

2020 ◽  
Vol 4 ◽  
pp. 8-14
Author(s):  
Gregoriy Deynichenko ◽  
Vasyl Guzenko ◽  
Dmytro Dmytrevskyi ◽  
Vitalii Chervonyi ◽  
Aleksandr Omelchenko ◽  
...  
Keyword(s):  
Cheese Whey ◽  
Raw Materials ◽  
Membrane Surface ◽  
Experimental Studies ◽  
Cottage Cheese ◽  
Regression Equations ◽  
Layer Formation ◽  
Research Results ◽  
Skimmed Milk ◽  
Membrane Concentration

The aim of the work is to study the process of membrane concentration of cottage cheese whey, using the bubbling method for decreasing polarization layer formation at the UF-membrane surface. A description of the experimental set and processing method for research results of using the method of fighting against a polarization layer in the process of membrane concentration of protein-carbohydrate milk raw materials are presented. Results of the experimental studies as to using the bubbling method for decreasing polarization layer formation in the process of membrane concentration of cottage cheese whey and its influence on concentration membranes productivity are given. Mathematical models, based on regression equations of factorial experiment with using the method of bubbling separated liquid above the membrane surface for choosing technological parameters of process of membrane concentration of cottage cheese whey, have been constructed. Graphic dependencies of the productivity of ultrafiltration polymer membranes of PAN type depending on initial pressure and temperature parameters of the process of membrane concentration are presented. Rational parameters of membrane concentration of cottage cheese whey using the method of bubbling initial raw materials by gas bubbles, directly close to the concentration membrane surface have been determined. Such parameters are: pressure – 0.4...0.5 МPа, temperature of skimmed milk – 40...50 ºС, skimmed milk bubbling frequency – 0.10...0.15 min-1, bubbling pressure must be 0.56...0.58 МPа. The expedience of using the new-method of gel-layer elimination has been established according to research results

scholarly journals STRUCTURAL CHARACTERISTICS OF MEMBRANES AND KINETIC DEPENDENCES OF ELECTRONANOFILTRATION WASTE WATER TREATMENT OF LATINATING PROCESS

2020 ◽  
Vol 63 (7) ◽  
pp. 95-102
Author(s):  
Irina V. Khorokhorina ◽  
Sergey I. Lazarev ◽  
Yuri M. Golovin ◽  
Dmitry S. Lazarev
Keyword(s):  
Packing Density ◽  
Copper Ions ◽  
Structural Characteristics ◽  
Waste Water Treatment ◽  
Retention Factor ◽  
Transmembrane Pressure ◽  
Retention Capacity ◽  
Amorphous Phases ◽  
Specific Output ◽  
Output Flow

The basic structural characteristics of the membrane and kinetic dependences of the electron-filtration separation of wastewater of the brassing process are investigated. The retention factor and the specific output flow for the near-anode and near-cathode membrane were calculated. The dependences of the retention factor and the specific output flow on the transmembrane pressure and current density are analyzed, and it is noted that the anode membrane as a result of the application of a constant electric potential to the membrane-solution system starts to clog and a sludge layer forms on its surface due to the electrochemical process. A comparison is made of the retention capacity of OPMN-P and OPMN-K membranes for a real spent technological solution after the process of brazing and a model solution containing the same concentrations of copper ions (Cu2+) and zinc (Zn2+) as in real runoff. The structural characteristics of nanofiltration membranes of the type OFAM-K and OPMN-P were studied and analyzed. Changes in the crystalline and amorphous phases of the active layer and the membrane substrate are considered. The change in crystalline parameters in crystallites can be explained only by the structural features of macromolecules of polyamide and their orientation during crystallization. Under the action of transmembrane pressure and transport of water molecules, the polymorphism of the packing of the crystal lattice occurs. The packing density of the amorphous phases of the working membrane decreases, which affects the transport and selective properties of the membrane. In fact, the deformation of an amorphous-crystalline polymer leads to a restructuring of the structure not only in the orientation of the macromolecules of the amorphous, but also the crystalline phases of the membranes. It was also noted that the packing density of the amorphous phases of the working membrane decreases, which affects the transport and selective properties of the membrane.

A possibility of using nickel concentrate, obtained as a result of hydrometallurgical enrichment of manganese-containing raw materials, at steel alloying

2020 ◽  
Vol 76 (7) ◽  
pp. 709-715
Author(s):  
O. Yu. Kichigina
Keyword(s):  
Raw Materials ◽  
Experimental Studies ◽  
Selective Extraction ◽  
Technological Parameters ◽  
Nickel Iron ◽  
Nickel Recovery ◽  
Nickel Concentrate ◽  
Steel Alloying ◽  
High Degree ◽  
Comprehensive Processing

At production of stainless steel expensive alloying elements, containing nickel, are used. To decrease the steel cost, substitution of nickel during steel alloying process by its oxides is an actual task. Results of analysis of thermodynamic and experimental studies of nickel reducing from its oxide presented, as well as methods of nickel oxide obtaining at manganese bearing complex raw materials enrichment and practice of its application during steel alloying. Technology of comprehensive processing of complex manganese-containing raw materials considered, including leaching and selective extraction out of the solution valuable components: manganese, nickel, iron, cobalt and copper. Based on theoretical and experiment studies, a possibility of substitution of metal nickel by concentrates, obtained as a result of hydrometallurgical enrichment, was confirmed. Optimal technological parameters, ensuring high degree of nickel recovery out of the initial raw materials were determined. It was established, that for direct steel alloying it is reasonable to add into the charge pellets, consisting of nickel concentrate and coke fines, that enables to reach the through nickel recovery at a level of 90%. The proposed method of alloying steel by nickel gives a possibility to decrease considerably steel cost at the expense of application of nickel concentrate, obtained out of tails of hydrometallurgical enrichment of manganese-bearing raw materials, which is much cheaper comparing with the metal nickel.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

Matrix Acidization with Highly Reactive Acids

1971 ◽  
Vol 11 (04) ◽  
pp. 390-398 ◽  
Author(s):  
J.A. Guin ◽  
R.S. Schechter
Keyword(s):  
Mathematical Model ◽  
Pore Structure ◽  
Pore Size ◽  
Acid Treatment ◽  
Explicit Knowledge ◽  
Experimental Studies ◽  
Design Procedure ◽  
Permeability Change ◽  
Pore Size Distributions ◽  
Matrix Acidization

Abstract A mathematical model representing the changes in pore structure attending the invasion of a porous material by a reactive fluid tending to dissolve the solid bas previously been tested and found to be valid. This mathematical model is solved by a simulation procedure using Monte Carlo techniques. The results so obtained are indicative of the acidization of sandstone using a last-reacting acid (diffusion limited). A correlation relating the permeability improvement to the change in porosity is presented and found to be applicable to a wide class of initial pore-size distributions. This means that the designer need not have explicit knowledge of the initial pore structure to utilize the correlation. The generality of the correlation stems from the fact that after exposure to fast-acting acids (diffusion-controlled reactions) wormholing tends to occur in all porous matrices, and the acid allows preferentially through these channels. Thus, the process is independent of the fine pore structure since the fine pores receive no acid Wormholing bas been observed in almost all experimental studies of acidization, thus further confirming the validity of the model. Introduction Matrix acidization as practiced in the petroleum industry is a simple operation. Acids treated so as to prevent their corrosive attack on metal parts contacted are pumped down the wellbore and forced into the pore spaces of an oil-bearing rock. The rate of penetration is normally maintained small enough to prevent fracturing of the reservoir The aim of matrix acidization is to enhance the permeability of the region around the wellbore by permeability of the region around the wellbore by dissolving either a portion of the rock or of the foreign impurities that may have been introduced during the drilling operations. The success of this technique of oilwell stimulation is attested to by the fact that a significant fraction of the acids used for stimulation are injected at matrix rates. There were, moreover, in excess of 87 million gal of hydrochloric acid used last year in carbonate formations with many other special purpose acids such as acetic and formic having also been used for stimulation purposes. Despite the fact that acids have long been routinely used as a means of stimulating oil wells to greater production, there is, as yet, no reliable design procedure incorporating all of the essential features into a prediction of the new production that will result from a given acid treatment of a particular well. This lack of a design procedure particular well. This lack of a design procedure has been responsible for the rather minimal efforts expended in obtaining meaningful reaction rate data, for there is very little enthusiasm for obtaining data which cannot be put to practical application. This paper is an extension of some recently reported work on predicting the permeability change resulting from acid treatment of an oil-bearing rock. It has been proposed that the changes in the microstructure owing to acidization in a porous rock can be simulated by considering the effect of acidization of a collection of small, randomly distributed capillaries that are interconnected to the extent that a fluid will be conducted from point to point under the influence of an external pressure gradient. This model, the capillaric model, has been used with varying success in understanding the behavior of porous media. The use of the capillaric model in determining only the results of the evolution of a pore-size distribution, rather than as a vehicle for predicting a number of mare or less independent phenomena, such as capillary pressure curves and dispersion, is, as has been pressure curves and dispersion, is, as has been noted by Schechter and Gidley, a more limited and perhaps attainable goal. Taking the capillaric model to be correct, Guin et al. have shown that an equation relating the porosity change and the permeability change caused by an ideally retarded permeability change caused by an ideally retarded acid can be derived without any assumptions. SPEJ P. 390

Calculation of Technical Characteristics of the Technical Fleet Vessels Involved in Ensuring Safety of the Offshore Facilities of Oil and Gas Complex

2021 ◽  
pp. 7-13
Author(s):  
S.V. Matsenko ◽  
◽  
V.M. Minko ◽  
A.A. Koshelev ◽  
V.Yu. Piven ◽  
...  
Keyword(s):  
Oil And Gas ◽  
Oil Pollution ◽  
Raw Materials ◽  
Experimental Studies ◽  
Industrial Safety ◽  
Theoretical Studies ◽  
Physical Processes ◽  
Oil Spill Response ◽  
Sea Area

Violation of industrial safety rules during the operation of offshore facilities for the production, storage and transportation of the hydrocarbon raw materials leads in the most cases to pollution of the marine environment with oil and its components. The works on localization and elimination of such pollution are carried out with the help of vessels of the technical support fleet and booms. When developing oil spill response plans at such facilities, a calculated determination of the technical characteristics of vessels and booms is required that are sufficient to carry out the planned activities. The basic design principles for determining the towing capacity of the technical fleet vessels involved in the localization and elimination of oil and oil product spills by trawling methods are given in the article. The calculation is based on theoretical studies performed by the authors of the physical processes occurring during the movement of objects of a mobile trawling order in the sea area. The results obtained during the course of theoretical studies were confirmed by the experimental studies carried out by the authors personally using the real pieces of equipment in the actual development of tasks for training spill containment by trawling. As a result, the empirical dependencies were obtained and experimentally confirmed, which can be used to calculate technical characteristics of the ships as part of the mobile orders and anchor systems as part of stationary orders intended for the localization and elimination of oil pollution. These results can be used, among other things, for the calculated substantiation of the technical characteristics of the technical fleet vessels designed to ensure safety of the offshore facilities for production, storage, and transportation of the hydrocarbon raw materials.

AUTOMATED OPERATIONAL SCHEDULING SYSTEM FOR MULTI-STAGE PRODUCTION: MATHEMATICAL MODEL AND SOFTWARE IMPLEMENTATION

2021 ◽  
Vol 3 (102) ◽  
pp. 18-37
Author(s):  
OXANA S. LOGUNOVA ◽  
MIKHAIL B. ARKULIS
Keyword(s):  
Mathematical Model ◽  
Raw Materials ◽  
Software Implementation ◽  
Scheduling System ◽  
Operation Conditions ◽  
Multi Stage ◽  
Complete Set ◽  
Wip Inventory ◽  
Production Areas ◽  
Strip Production

The purpose of the study is to improve the efficiency of production areas of multi-stage production with the possibility of rational use of equipment capacity and stocks of WIP inventory in the operation conditions of the automated operational scheduling system. Features of the considered problem regarding operative calendar planning are: necessity of processing raw materials at several stages according to the flow chart; an array of the equipment which demands division of work into three periods for each party; availability of planned and unscheduled equipment downtime; necessity to complete set of orders from several suborders; availability of incomplete production in a warehouse; restrictions in order and timing of orders. In the work, the authors construct a mathematical model with the use of multidimensional matroids with structured elements in the construction of free time scale for equipment loading. The research was carried out for a metallurgical plant at the cold strip production site...

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

STUDY OF EXTERNAL MASS TRANSFER DURING DRYING OF BERRY RAW MATERIALS TAKING INTO THE SHRINKAGE PHENOMENON

2019 ◽  
Author(s):  
А.В. АКУЛИЧ ◽  
Л.А. ГОСТИНЩИКОВА
Keyword(s):  
Mass Transfer ◽  
Energy Supply ◽  
Raw Materials ◽  
Mass Transfer Rate ◽  
Experimental Studies ◽  
Volume Shrinkage ◽  
External Mass Transfer ◽  
Transfer Coefficients ◽  
Ir Radiation ◽  
Criterial Equations

Исследованы закономерности внешнего массообмена при сушке ягодного сырья для различных способов энергоподвода. Установлено, что ягоды при сушке подвержены значительной объемной (72–81%) и линейной (35–43%) усадке, которую необходимо учитывать при расчете коэффициентов массоотдачи. Объекты исследования – ягоды черники, красной и черной смородины. Проведены экспериментальные исследования по сушке ягодного сырья при конвективном и конвективном с ИК-излучением способах энергоподвода. Исследования проведены при скорости сушильного агента хса1,2 м/с и температуре tса 70°С. Получены критериальные уравнения внешнего массоообмена при сушке ягод для периода постоянной скорости, учитывающие объемную усадку. Определено, что при сушке с конвективным энергоподводом объемная усадка при одном и том же значении критерия Рейнольдса оказывает на 12–20% большее влияние на интенсивность массоообмена для красной смородины по сравнению с черникой и черной смородиной. При сушке с конвективным энергоподводом, ИК-излучением и предварительным прокалыванием объемная усадка наиболее существенно влияет на массообмен для черной смородины, протекающий в 1,5–1,8 раза интенсивнее по сравнению с черникой и красной смородиной. Полученные критериальные уравнения могут быть использованы при расчете и проектировании установок для сушки ягодного сырья. The laws of external mass transfer during drying of berry raw materials for various methods of energy supply are investigated. It is established that the berries during drying are subject to significant volumetric (72–81%) and surface (35–43%) shrinkage, which must be taken into account when calculating the mass transfer coefficients. The objects of the study were various berries: blueberries, red and black currants. Experimental studies have been carried out on the drying of selected berries both in the case of convective and convective methods with IR radiation. Investigations were carried out at a drying agent velocity хса1,2 m/s and its temperature tca70°С. The criterion equations of external mass transfer during drying of berries for a period of constant speed, taking into account the volume shrinkage, are obtained. It was determined that during drying with convective energy supply, volume shrinkage with the same value of the Reynolds criterion on 12–20% has a greater effect on the mass transfer rate for red currants. When drying with convective energy supply, IR radiation and preliminary piercing, the volume shrinkage most significantly affects the mass transfer for black currants, which is 1,5–1,8 times more intense than blueberries and red currants. The obtained criterial equations can be used in the calculation and design of berries dryers.

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