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ТЕХНИЧЕСКИЕ НАУКИ
MODELING OF AMMONIA SYNTHESIS PROCESS IN THE PARAMETRIC UNCERTAINTY
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Khalilov A.J. , Tursinboeva Z.U., Abdullayeva D.A., Karabekyan S.Kh.4 Email: Khalilov666@scientifictext.ru
1Khalilov Azim Jurakulovich - senior lecturer;
2Tursinboeva Zebo Urunboeva - senior lecturer; 3Abdullayeva Dildora Anvarovna - senior lecturer;
4Karabekyan Svetlana Khamdamova - assistant, DEPARTMENT OF HIGHER MATH AND INFORMATION TECHNOLOGY, NAVOI STATE MINING INSTITUTE, NAVOI, REPUBLIC OF UZBEKISTAN
Abstract: the article deals with the problems of computer simulation of process control systems for ammonia synthesis under parametric uncertainty. These models allow you to solve various problems of system analysis, optimization and control. When developing a mathematical model, modeling programs, MATLAB and Aspen Plus, were used which allow the calculation of closed CTS with high parametric flows and complex modeling of complex objects of chemical technology at various levels. An analysis of approaches to solving problems of constructing models and process control systems of ammonia synthesis under parametric uncertainty is presented.
Keywords: uncertainty, computer model, modeling programs, mathematical model, control system.
МОДЕЛИРОВАНИЕ ПРОЦЕССА СИНТЕЗА АММИАКА В УСЛОВИЯХ ПАРАМЕТРИЧЕСКОЙ НЕОПРЕДЕЛЕННОСТИ Халилов А.Ж.1, Турсинбоева З.У.2, Абдуллаева Д.А.3, Карабекян С.Х.4
1 Халилов Азим Журакулович - старший преподаватель;
2Турсинбоева Зебо Уринбоевна - старший преподаватель;
3Абдуллаева Дилдора Анваровна - старший преподаватель; 4Карабекян Светлана Хамдамовна - ассистент, кафедра высшей математики и информационных технологий, Навоийский государственный горный институт, г. Навои, Республика Узбекистан
Аннотация: в статье рассмотрены проблемы компьютерного моделирования систем управления технологическими процессами синтеза аммиака в условиях параметрической неопределенности. Данные модели позволяют решать различные задачи системного анализа, оптимизации и управления. При разработке математической модели были использованы моделирующие программы, MATLAB и Aspen Plus, позволяющая производить расчет замкнутых ХТС с высокой параметричностью потоков и комплексное моделирование сложных объектов химической технологии различных уровней. Приведен анализ подходов к решению задач построения моделей и систем управления технологическими процессами синтеза аммиака в условиях параметрической неопределенности. Ключевые слова: неопределенность, компьютерная модель, моделирующие программы, математическая модель, система управления.
УДК 517.977.58
In the construction of control systems there are situations when the objects of study can not be described accurately, and the conditions of the problem and the goal can not be sufficiently formalized. Usually fuzzy and uncertainty are considered statistical, random characteristics and are taken into account by methods of probability theory. In real situations, the source of inaccuracy is often not only the presence of random variables, but also the fundamental inability to operate with accurate data due to the complexity of the system, inaccuracy of constraints and goals.
One of the technological stages of ammonia production is the catalytic synthesis of ammonia in the column. The most important adjustable parameter is the temperature in the catalyst zone [1]. Temperature control is quite a difficult task, since the existing mathematical models are difficult to implement due to the complexity of the physicochemical dependencies. In addition, all parameters of the ammonia synthesis column vary over time.
As a research object, this work initially considered a typical chemical-technological system for the ammonia synthesis section. This chemical-technological system (CTS) was considered both separately and together with the section for the release of ammonia from purge gas. The process of producing anhydrous liquefied ammonia consists of the following stages:
- purification of the converted gas from carbon monoxide with liquid nitrogen -production of nitric mixture;
- compression of a mixture of nitric;
- synthesis of ammonia followed by cooling and condensation of ammonia gas to produce liquid ammonia;
- compression of process nitrogen;
- compression of carbon monoxide fraction and ammonia gas.
The technological scheme of the synthesis section is shown in fig. 1.
Fig. 1. Technological scheme of ammonia synthesis section
According to the technological regulations [2], the nitrogen-hydrogen mixture (NGM) necessary for the ammonia synthesis process is obtained by cleaning the converted gas from carbon monoxide, argon, methane with liquid nitrogen.
Compressed gas compressors (pos. 710) up to a pressure of not more than 325 kg f/sm2 (31.88 MPa) and nitrogen-hydrogen mixture is supplied to the units of synthesis of ammonia.
The process of ammonia synthesis from hydrogen and nitrogen takes place in the synthesis columns of units № 7, 8, 9 (pos. 704) on an iron catalyst at a temperature not exceeding 540 0C and a pressure not exceeding 325 kg f/sm2.
In order to achieve the maximum performance of the reaction volume of the synthesis column, it is necessary to condense ammonia (pos. 705) most fully and separate (pos. 703,706) it from the gas mixture. NGM is cooled. In this case, part of the ammonia goes into a liquid state and is removed from the system, the remaining gas returns to the cycle and joins the fresh gas (pos. 707,708). The lower the temperature of NGM, the more ammonia from it condenses, and accordingly less remains in the gas. The residual volume fraction of ammonia in the gas mixture (circulating gas) at a pressure of 300 kgf/cm2, depending on temperature.
The maximum possible decrease in the temperature of the gas mixture and the improvement of the liquid ammonia separation conditions allows reducing the ammonia content at the synthesis column inlet and increasing the productivity of the column. The amount of ammonia formed corresponds to the difference of its content in the gas leaving the column and entering the column [3].
As a research tool, the simulation programs MATLAB and Aspen Plus were used. A linearized model was used in the work as a predictive model for predicting the behavior of the control object in industrial implementations:
x = /(x0, u0, v0, d0) + Vx/(x0, u0, v0, d0) (x - x0) + Vu/(x0, u0, v0, d0)(u - u0)
+Vvf(x0.u0,v0,d0)(v - v0) + Vd/(x0, u0,v0, d0)(d - d0) y = h(x0, u0, v0, d0) + Vxh(x0,u0,v0,d0)(x — x0) + Vuh(x0,u0,v0,d0)(u - u0)
+Vvh(x0, u0, v0, d0)O - v0) + Vdh(x0 , u0, v0, d0)(d - d0) (1) Assuming that the estimates of the state vectors , are available at time , the action of the predictor controller can be obtained by solving the minimization problem for the quadratic quality functional:
I 2
+
mm
Vu(fc|fc) Vu(m-l+k\k)
{^(i^ii Ни Ык+'++глк+1+d)!2
UjQc + i\k))\2 + Z^lwZjiujQc + i\k) - Uht{k + 0)|2) + pEe2}
(2)
Obviously, when solving the problem of optimal control, a more detailed model is required that would allow controlling the temperature regime of the reactor and, as a result, take into account the peculiarities of the catalytic process of ammonia synthesis on promoted iron catalysts. In order to analyze the influence of parametric uncertainty in the equations of the mathematical description of a synthesis column, a mathematical model was proposed based on known patterns.
Based on the results of the analysis of the number of degrees of freedom of the stationary mode model of the synthesis section, the selection of control variables was carried out when solving the problem of optimal control. When choosing control variables, one should take into account a number of operational limitations imposed by the technical regulation of the process on the regime parameters of flows. It is also allowed to fix some variables in their optimal value, found from the results of optimization.
The choice of optimization criterion for the problem of optimal control should be made taking into account the specificity of the studied CTS. In particular, within the framework of this work, it was shown that the optimal control found for the reactor site without taking into account other apparatus and processes of the synthesis cycle is not always optimal for the CTS as a whole.
It is obvious that the parameters in the equations of the mathematical description of the CTS model can have a different effect on the objective function. Accounting for a large number of uncertain parameters increases the computational complexity of the problem. On the other hand, not including some parameters in the number of uncertain ones can lead to
the fact that the found mode of functioning of the CTS will be either not optimal or unattainable [4].
In this work, it is proposed to exclude from the set of uncertain parameters that have a negligible effect on the objective function. The estimation of the influence of parametric uncertainty in the equations of mathematical description on the objective function was performed using the method of estimating the sensitivity of the CTS. As indefinite parameters, parameters were selected that have the greatest impact on the objective function according to the results of the correlation analysis. As a selection criterion, it was proposed to use the coefficient of partial correlation.
In order to obtain a sample for the correlation analysis, a computational experiment was conducted using various second-order non-compositional plans. The work contains a list of parameters that were considered as undefined.
To solve the problem of optimal control in the conditions of parametric uncertainty, a multiple nonlinear regression model of the objective function was obtained using the Brandon method. Also, solving the problem of conditional optimization, the author suggests using regression models of state variables on which inequality constraints are imposed. The resulting functions are:
f (и, в ) = /п Г=! Xi (и д n;=e! f j (в j) (3)
In order to account for operational constraints, it is proposed to obtain approximations of state variables on which inequality constraints are imposed. These approximations have the form:
xfc (и, в ) = xk п ^ p i, fc (и i) tfi! Ф j , k (в j) ,к = 1.....n *, (4)
where: n* is the number of inequalities in the system of constraints. In this work, the resulting regression model (3) was chosen as a function of the optimization goal. When solving the optimal control problem for the minimax strategy, the conjugate gradient method was used in conjunction with the Monte Carlo method. The optimization procedure developed in this work also be used for modeling of processes of ammonia synthesis in the conditions of parametric uncertainty [5].
References / Список литературы
1. Ali D., Kayvan Kh., Mehdi A., MadjidK. Modeling and simulation of ammonia synthesis reactor. Petroleum and Coal. 48(2). P. 15-23. [Electronic resource]. URL: https://www.researchgate.net/publication/229034628_Modeling_and_simulation_of_am monia_synthesis_reactor./ (date of access: 23.06.2019).
2. Permanent technological regulations № 24 of the complex 325 "A" of the third stage ammonia production (gas purification with liquid nitrogen, compression, synthesis). For educational and scientific purposes. - Navoi: OJSC "NAVOIYAZOT", 2012. P. 14-32.
3. Demidenko I.M. and others. Ammonia: technology issues: production and practical publication / total. ed. Yankovsky N.A. Gorlovka: Concern Stirol OJSC, 2001. P. 108-120.
4. Akhnazarova S.L., Kafarov V.V. Methods of experiment optimization in chemical technology. M.: Higher School, 1985. p. 205.
5. Mukhitdinov D.P., Khalilov A.J. The program of modeling and optimization of the technological process of ammonia synthesis. // State Patent Office. Certificate of official registration of computer programs. № DGU 05783, 21.11.2018.
