CC BY
30АМСА-2019
MATHEMATICAL AND NUMERICAL MODELING OF OIL POLLUTION WASTE PROCESSING
G, B, Kalmenova, G, T, Balakaeva
Al-Farabi Kazakh National University, 050040, Almaty
UDC 510.58
DOI: 10.24411/9999-016A-2019-10034
В работе рассмотрена переработка нефтешлама для решения проблем по защите окружающей среды и улучшению экологической обстановки при разработке месторождений и транспортировке нефти. Неблагоприятное воздействие нефтесодержащих отходов на окружающую среду делает вопрос переработки нефтяных остатков весьма актуальным. Один из наиболее эффективный способ очистки нефтешламов — термическая обработка. В настоящей статье рассматривается задача термической переработки нефтешлама. Процессом термической переработки нефтесодержащих отходов необходимо управлять. В связи с этим потребовалось создание математической модели обработки нефтешлама. Математическая модель процесса описывается уравнениями тепломассообмена и включает систему нестационарных уравнений в частных производных второго порядка. Решение проводится по неявной разностной схеме методом переменных направлений до выполнения условия сходимости. В расчетах поставлены достаточные условия корректности и устойчивости прогонки. В этой исследовательской работе использовалось математическое и численное моделирование, и решение проводится с использованием современного языка программирования, такого как С/С Н—Ь, и результат дается с визуализацией Ключевые слова: oil slime, thermal processing, mathematical model, method of alternating directions, environment.
Introduction
The anthropogenic impact on the environment causes its irreparable harm, and one of the major sources of environmental pollution is the oil and oil refining industry. Kazakhstan today is one of the largest countries in the extraction and processing of petroleum and petroleum products. Oil slime is a complex physico-chemical mixture, which consists of petroleum products, mechanical impurities (clay, metal oxides, sand) and water. The ratio of its constituent elements can be very different. The qualitative characteristics of oil slime at enterprises fit within the following limits:
• organic matter from 10 percent to 25 percent of the weight;
• mechanical impurities 5-30 percent of the weight;
•
Shipments are occurring during the technological process of oil refining, and also during the transportation and extraction of oil. These residues, which contain oil, are dangerous for the external environment. In the most general form, all oil slime can be divided into three main groups in accordance with the conditions of their formation: soil, bottom and reservoir type. The first are formed as a result of spills of petroleum products on the soil during manufacturing operations, or in emergency situations. Bottom sludges are formed due to oil spills settling to the bottom of reservoirs, and tank type sludge - during storage and transportation of petroleum products in containers of different designs [1].
By chemical and physical indicators of oil slime are extremely different from each other. The components of water, mechanical impurities and petroleum products in oil lime have an extremely wide range of ratios. The
ISBN 978-5-901548-42-4
Mathematical and numerical of oil pollution waste processing
211
physical properties of oil slime are also far from constant. Density can be either 830 kg / m3 or 1700 kg / m3, and the pour point varies from -3 to +50 degrees Celsius. Such a large range of physico-chemical properties of oil slime are obtained due to completely different environments of their appearance [2]. Recycling of oil products and oil slime is a problem that is relevant for modern Kazakhstan. A rational solution to this problem will have a positive impact on the ecology and the economy of our country.
Every year in our country during the processing or transportation of oil, as a result of natural spills and accidents, about 400 thousand tons of oil waste are generated, and the resources located in earthen barns are estimated at 4.5 million tons. It should be understood that the presence of such barns increases the risk of death of animals, pollution of groundwater and air. Soil pollution with oil, in addition to its direct impact, can lead to excessive accumulation of heavy metals in them - zinc, copper, lead, which adversely affects both the ecology of the region and the quality of life of people. In Kazakhstan, the urgency of this urgent task was highlighted for the first time in the Environmental Code of the Republic of Kazakhstan dated January 9, 2007. The direction of "green"growth and a low-carbon economy as a tool for sustainable development is laid down in the Strategy-2020, in the international initiatives of our country. The head of state constantly emphasizes that the wealth of the subsoil must be used with minimal damage to the environment [3].
At the moment as a result of disposal of slime is already getting a lot of useful products: commercial oil, fuel for heating plants, some building materials. There are also technology and special equipment for processing oil slime with recovery of residual oil and solid waste in materials for road construction. Huge amounts of raw materials provided in the recycling of oil slime, make it possible to produce large quantities of asphaltic concrete - durable road surface friction with improved performance and durability. Total can be divided into 3 main areas of application of slime:
• involvement in the boiler fuel;
• obtaining fuel components and preventive lubricants;
Nowadays, as we know the most common methods of disposal of oil slime can be classified into:
1 Thermal methods
The adverse impact of oil slime on the environment makes the issue of processing oil residue is very important. One of the most effective way to clean oil slime is heat treatment.
Both in foreign and domestic practice, the method of thermal disposal of oil slime is the most common. This
method allows to neutralize the following types of oily waste:
•
conduits or formed over time in barns;
composition and high content of hydrocarbons, as well as used compressor and industrial oils.
212
G. B. Kalmenova, G. T. Balakaeva
Thermal methods of oil slime processing are based on the processes of thermal decomposition of petroleum products. As a result of the complete thermal decomposition of petroleum products, final degradation products are formed — C02 and H20 [4].
The structure of oil slime is a physicochemical system that includes oil products, water and mineral additives (clay, sand, metal oxides, etc.). One of the reasons for the formation of reservoir oil slime is the interaction of oil products with moisture, oxygen, mechanical impurities and the material of the walls of the reservoir. The result of such interactions is the partial oxidation of the feed oil to form resin-like joints and corrosion of the tank walls. Entry into reservoirs with oil products of moisture and mechanical contaminants promotes the formation of water-oil emulsions and mineral dispersions. All oil slime differ in their physic-chemicaO 1 characteristics, which is due to the different composition of the raw materials, the environmental conditions. As a result of various studies, oil slime reservoir type impurities: hydrocarbons are from 5 to 90 percent, water from 1 to 70 percent, solid impurities from 0.8 to 65 percent have a wide range of ratios of oil, water, and mechanical. The method of processing depends directly on the amount of slime that is in oil products. Oil sludges have extremely diverse compositions and represent complex systems consisting of petroleum products, water, and a mineral portion (sand, clay, silt). The ratio of these components fluctuates over a very broad range. The organic materials on the average comprise from 10 to 56 percent; water, 30 to 85 percent; solids, 1-46 percent. Oil wastes can be arbitrarily divided according to the way they form into soil, resid, and tank types and can be divided according to phase state into liquid and solid oil sludges. By liquid sludges, we mean oil wastes in which the crude oil content is greater than 50-90 percent, and accordingly solid oil sludges are oil wastes in which the crude oil content does not exceed 50 percent, i.e., this is oil-contaminated soil [5].
Thermal systems are divided into two categories namely, thermal desorption and incineration. In thermal desorption, the oily wastes are normally heated in an inert atmosphere and the volatilized hydrocarbons and water are recovered and recycled into the main oil/water separation process. By comparison, the hydrocarbons are destroyed by heating to very high temperatures in the presence of air in thermal incineration processes. Thermal treatment processes are being coupled with current methods such as landfill, land farming, and land spreading for final residue disposal. Thermal treatment is the most efficient method for destruction of organics. It also significantly reduces the volume of inorganics such as metals and salts, and reduces their mobility so that the residue can be effectively disposed of. Thermal processes can handle oily drill cuttings, contaminated soils (resulting from spills, reclamation of contaminated waste sites), tank bottoms and other process wastes. In other words, thermal technology is best suited to process oil (preferably brine free) contaminated solids. Another technological method of thermal processing of oil slime is the pyrolysis process, carried out at 500 ° -550 ° C, in which combustible gases and a solid residue are obtained. This process is recommended for processing solid oil sludge with low humidity (no more than 1-3 percent). It is most economically acceptable, as it allows the organic part of the waste not to be converted into toxic products of combustion, but used as an additional fuel for waste incineration.
Pyrolysis is more environmentally friendly than incineration, since it allows the organic part of the waste not to be converted into toxic products of combustion, but used as an additional fuel for incineration of waste or to condense to produce by-products [6].
The goal of High-Temperature Reprocessing is to use heat for recovery of hydrocarbons from influent oily-emulsions and sludges. Temperature influences the physical nature of hydrocarbons and water; hence, temperature affects the separation of oil-in-water emulsions. The fundamental principle of thermally enhanced separation of emulsions is to create conditions where four main benefits of heat are used:
the dispersed-phase droplets;
The method of heat treatment for the purpose of sludge dewatering is becoming more widely used abroad.
2 Mathematical model of the problem
Numerical heat transfer is a broad term denoting the procedures for the solution, on a computer, of a set of algebraic equations that approximate the differential (and, occasionally, integral) equations describing conduction,
Mathematical arid numerical of oil pollution waste processing
213
convection and/or radiation heat transfer. The usual objective in any heat transfer calculation is the determination of the rate of heat transfer to or from some surface or object. In conduction problems, this requires finding the temperature gradient in the material at its surface. In convection problems, the temperature gradient in a fluid flowing over a surface is needed to find the heat flux at that surface. In both cases, the determination of the complete temperature distribution in the region of interest is needed as a first step, and in convection one must also find the velocity distribution.
The equations describing heat transfer are complex, having some or all of the following characteristics: they are nonlinear: they comprise algebraic, partial differential and /'or integral equations: they constitute a coupled system: the properties of the substances involved are usually functions of temperature and may be functions of pressure: the solution region is usually not a simple square, circle or box: and it may (in problems involving solidification, melting, etc.) change in size and shape in a manner not known in advance. Thus numerical methods, leading to exact, closed form solutions, are almost always not available [8].
When we develop a mathematical model of thermal processing of oil slime, consider the heating of the sludge layer. We consider a non-stationary, two-dimensional problem with constant flow rates in a rectangular area. The mathematical model of the process is described by heat and mass transfer equations and includes a system of nonstationary second-order partial differential equations. The solution is carried out according to an implicit difference scheme using the alternating directions method until the convergence condition is satisfied. In the calculations, sufficient conditions for the correctness and stability of the sweep were set. such as the condition of the diagonal dominance of the matrix and the condition in which the modulus of the average driving coefficient is greater than the sum of the modules of the other driving coefficients.
There are various methods for solving boundary value problems for the heat equation, including the variable direction method. In the scheme of the method of alternating directions (MAD), as in all splitting methods, the time step is divided into the number of independent spatial variables (in the two-dimensional case, into two). At each fractional time layer, one of the spatial differential operators is approximated implicitly (scalar sweeps are performed in the corresponding coordinate direction), and the others explicitly. At the next fractional step, the next in order differential operator is approximated implicitly, and the others explicitly, etc [9.10].
The implicit scheme of variable directions (longitudinal-transverse scheme) expresses quite clearly this algorithmic idea. This scheme is often called the scheme of the Pisnian Reckford (by the name of the authors who first proposed it) [11]. In the picture 1 can be shown that in the two-dimensional case the MAD scheme is absolutely stable. The advantages of the method of variable directions include high accuracy, since the method has the second order of accuracy in time. The disadvantages include conditional stability when the number of spatial variables is more than two. In addition, the MAD is conditionally stable in problems with mixed derivatives already in the two-dimensional case.
Graphical result of this task shown in below picture:
Conclusion
The amount of waste from the refining industry is increasing every year. The harmful effects of sludge waste affects environmental factors that pose a threat to human life and health, or a threat to the life or health of future generations. Therefore, the main objective of the task was the development of heat treatment of oil slime
Pue. 1: Pattern diagrams of the method of alternating directions
214
G. В. Kalmenova. G. Т. Balakaeva
Рис. 2: The graphical result
by numerical methods to protect the environment. The goals were achieved. The resulting mathematical model of thermal processing of oil slime characterizes the temperature change in the stream over time and makes it possible to manage.
Список литературы
fl] A.F. Ahmetov. A.R. Gaysina. I.A. Mustafin. Metody utilizacii nefteshlamov razlichnogo proishojdenii// Prikladnye i academicheskiye issledovanye. 2011. 9. 3. 98 101
[2] https://vtorothody.ru/utilizatsiya/ricftcshlamov.html
[3] S. Temirgalyev. Prevrawaya othody v dohod // Ivazakhstanskaya Pravda 2015. 30 Jan. lop
[4] https://neftok.ru/pererabotka/utilizatsiya-nefteproduktov.html
[5] P. R. Khaidarov and S. K. Ivudratova. Molodoi Uchenyi. No. 11. 125-127 (2014). I. R. Khairudinov. Crude Oil Waste and Sludge Treatment Methods. Khimiya. Moscow (1989). 425 pp.
[6] http://ru-ecology.info/term/48585/
[7] Naghi Jadidi . Behrooz Roozbehani . Akrani Saadat. The Most Recent Researches in Oily Sludge Remediation Process // American Journal of Oil and Chemical Technologies: Volume 2. Issue 10. Octoober 2014
[8] http://www.thermopedia.com/content/991/
[9] Samarskii A.A.. Gulin A.V. Chislermye metody matematicheskoi fiziki. 2 e izd. -M.: Nauchnyi riiir. 2003. 316 p.
[10] Shan Zhao. A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces// Journal of Scientific Computing. April.2015. Volume 63 Issue 1 pp 118-137
[11] Samarskii A.A. The Theory of Difference Schemes USA. Marcel Dekker. Inc. 2001 788p
Balakayeva Gulnar Tultaevna, doctor of phys.- mathematical sciences, professor
of the Department of Computer Science, Faculty of Information Technology, Al-Farabi Kazakh National University ;
e-mail: gulnardtsa Qgmail. com; Kalmenova Gaukhar Bolatbekovna, Phd student of the Department of Computer Science, Faculty of Information Technology, Al-Farabi Kazakh National University ;
e-mail: kalmenova.g.bQgmail.com; Received June 1, 2019
