CC BY
96
DOI: 10.24143/2072-9502-2018-2-34-42 UDC 681.5
A. M. Dzhambekov, O. V. Fyodorova
OPTIMAL CONTROL OF THE PROCESS OF CATALYTIC REFORMING
OF PETROL FRACTIONS
Abstract. The current task is to develop an optimal control system for the catalytic reforming process, which ensures the achievement of optimal ratios of the octane number of gasoline and production costs. The formulation of the problem of optimal control of the catalytic reforming process is performed, which is distinguished by using the generalized optimality criterion as the target functional. A hybrid mathematical model of the catalytic reforming process has been developed, which takes into account the influence of parameters characterizing production costs and the octane number of gasoline on the efficiency of the process and makes it possible to calculate the values of the generalized optimality criterion depending on the values of the input variables of the process. Based on LP-35-11/1000 model for installation, there have been obtained the maximum annual costs of 4.05 billion RUB and the minimum octane number of gasoline 92.83. A multicriterial choice of the temperature control system at the exit from the furnace is fulfilled. The algorithm for determining the settings of the temperature regulator at the exit from the furnace in various modes of the catalytic reforming process is synthesized. The method of optimal control of the catalytic reforming process is developed, which is characterized by the consideration of expert information in the formalization of fuzzy goals and constraints in process control and allows to calculate optimal control actions, according to the Bellman-Zade scheme depending on the values of the input variables of the process. Based on this technique, a vector of controls corresponding to the minimum of the generalized optimality criterion I = 0.964 is determined. The search of Pareto-optimal solutions for controlling the catalytic reforming process was carried out. Positive effects were obtained using the developed system of optimal control of the catalytic reforming process: decrease in average costs by 0.33 million RUB; increase in the average octane number by 0.53; decrease in the average value of the generalized optimality criterion by 0.025.
Key words: catalytic reforming, generalized criterion of optimality, Pareto optimal solution, hybrid model, classical PID controller, fuzzy PID controller, optimal control system.
Introduction
Catalytic reforming (CR) is the most important technological process of modern oil refining and petrochemistry. The CR process is used to produce high-octane gasoline, aromatic hydrocarbons and hydrogen. The increasing urgency of improving the process of CR is determined by the growing demand for high-octane motor fuel. As of 2016 the share of reforming processes in the total number of petroleum refining processes in Eastern Europe was 13.4% [1].
At present, the process capacity of CR in Russia is 9.3% from the total capacity of primary oil refining. As the component composition of gasoline contains 54.1% of reformate, the process of CR takes a leading place at the domestic refineries [2].
In existing studies on the management and modeling of the process of CR, the task of improving the efficiency of this process is solved by developing automatic control systems of technological parameters, as well as optimal control systems by basic technical and economic indicators (income, octane number, etc.) [3].
Since the efficiency of gasoline production depends not only on increasing the octane number of produced fuel, but also on reducing its cost [3], it is necessary to build a system for managing the process of CR ensuring the achievement of optimal ratios of the octane number of gasoline and production costs.
In the present study, as the target functional for the optimal control of the process of CR, it was proposed to use the generalized optimality criterion (GOC), which includes indicators characterizing the octane number of gasoline and production costs. A great opportunity for taking into account the influence of these indicators on the efficiency of the process of CR is the construction of a hybrid mathematical model (MM) of this process [4]. It is necessary to develop a system of optimal control of the process of CR using a hybrid MM. In order to determine the optimal ratios of particular control
criteria of the process of CR, such as the octane number of gasoline and production costs, this paper suggests the use of the well-known search method of Pareto-optimal solutions [5].
Thus, the development of the system of optimal control of the process of CR, ensuring the achievement of Pareto-optimal ratios of the octane number of gasoline and production costs, is an actual scientific and practical task.
Formulation of the problem
The aim of the study is to increase the effectiveness of the management of the process of CR by developing a system of the optimal management of this process, ensuring the achievement of Pareto-optimal ratios of the octane number of gasoline and production costs.
In accordance with the purpose of the research, the formulation of the problem of optimal control of the CR process has completed, which is distinguished by the use of GOC as the objective functional:
1 t
I = kiIi + k212 = - J 1 0
kON 0—1— + k2— Z (t ) 1 0 ON (t) 2 Z0
dt ^ min , (1)
where ON0 - minimum value of octane number ON; Z0 - maximum cost value Z; I1 - a criterion inverse to the criterion of maximization of the average normalized value ON0 of the octane number ON at the time interval [0, T]; I2 - a minimization criterion of the average normalized value Z0 of value of costs Z at the time interval [0, T]; k1, k2 - weight coefficients that regulate the relative importance of the criteria I1, I2 with regard to the adoption of Pareto-optimal solutions, k1 + k2 = 1; 0 < k1 < 1; 0 < k2 < 1; T - the operating time of the installation of the CR, including inter-regeneration and inter-repair intervals.
In a general form, the problem of optimal control of the CR process is formulated. With the given input variables Xin find the control actions U that ensure the minimum of the GOC (1) for superimposed connections in the form of a hybrid MM process of the CR and limitations
ON > ON0; Z < Z0; U eV ; A eW,
where V- set of values of control actions U; W- set of values of variables of the state of the process A.
To achieve this goal, it is necessary to solve the following tasks:
1. Development of a hybrid mathematical model of the process of CR.
2. Multi-criteria selection of automatic control systems for technological parameters of the process.
3. Synthesis of the algorithm for determining the temperature controller settings at the exit from the reforming furnace in various modes.
4. Development of methods for optimal control of the process of CR.
5. Search for Pareto-optimal solutions in the control of the CR process.
6. Development of the optimal management system of the CR process.
Hybrid mathematical model of the catalytic reforming process
A hybrid MM of the CR process was developed [6], which is generally represented
Xout = F(Xm, A, U), (2)
where Xout - a vector of output variables, including the octane number of gasoline ON and production costs Z; F - hybrid connection function between the variables of the hybrid MM of the CR process.
The scientific novelty of the hybrid MM process of the CR is to take into account the influence of the parameters characterizing the production costs and the octane number of gasoline on the efficiency of the process and the calculation of the values of the generalized optimality criterion, depending on the current values of the input variables of the process.
Fig. 1 shows the graphs of the change in the normalized criterion for minimizing the production costs ii(t), the normalized criterion I2(t), the inverse of criterion of minimization of the octane number and GOC I(t) respectively.
0,95
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Тпе :i;::iibcr о:' the month. t
Fig. 1. Change in the normalized criteria for the optimality of the catalytic reforming process
According to (1) the definition of GOC I(t) for a hybrid MM (2) is the finding a weighted sum of normalized partial criteria I1(t), I2(t).
The graphs are made on the basis of a hybrid MM for a typical set of input variables, characterizing the normal operation of the process at the LCH-35-11/1000 CR installation for one month [7].
Verification of the adequacy of the hybrid MM was performed using the Fisher criterion. The maximum error in calculations for the hybrid MM relative to the results of the experiments does not exceed 5%.
Multi-criteria selection of automatic control systems of technological parameters of the catalytic reforming process
Based on the method of fuzzy pair comparisons, mathematical expressions for the multi-criteria choice of automatic control systems (ACS) of the temperature at the exit from the furnace of 5 alternatives according to 7 criteria were developed [8]. A fuzzy solution D on the scheme of Bellman-Zadeh is determined by crossing the particular criteria
7 I min цk (Xj) min цk (X2) min цk (X3) min цk (x4) min цk (x5)'
D = Q k~ = I i=1,7 '=1.7 >=1,7 1=1,7 ' 1=1,7
where (Xj) - the function of belonging (FB) of the element k to the fuzzy set X; «~» - designation of fuzzy dimension.
As a result of calculation by expressions, it was found that ACS with fuzzy controller of PID type MT20-V-E FOTEK + PID Fuzzy, corresponding to the maximum FB of fuzzy solution equal to 0.954, meets all the criteria most fully. The adequacy of these expressions was checked using the Fisher test.
Software has been developed for multi-criteria selection of CR process control tools in the C # language, which allows choosing the best ACS temperature at the furnace outlet from the reformer from 5 alternatives according to 7 criteria. Using the software and the database, ACS temperature was chosen at the furnace output with a fuzzy PID controller of the type MT20-R-E MT-20E FOTEK + PID Fuzzy.
i=i
2
3
4
5
Algorithm for determining the temperature regulator settings at the furnace outlet from the reformer in various modes
The scientific novelty of the algorithm is to take into account the regime parameters in the transfer function of the disturbance quantitatively and in the determination of the temperature regulator settings at the outlet from the reforming furnace, depending on the current regime parameters.
The heating process in the reforming furnace is considered as a control object (CO). The determination of the temperature controller settings at the furnace outlet is carried out under the action of CO disturbances - temperature difference in the furnace AT [9]. To determine the settings of the fuzzy temperature PID controller at the furnace outlet, a mathematical description of CO and perturbations in the form of transfer functions has been performed, and the PID controller settings in the MATLAB system have been determined.
As a result of comparing the quality of transients in the ACS with the classical and fuzzy PID regulators (Fig. 2), positive effects were obtained from using a fuzzy PID controller: the reduction of overshoot by 10.4 times; the decrease of the quadratic integral criterion by 4.3 times.
Based on the algorithm for determining the settings of the temperature regulator at the furnace outlet in different modes of the CR process, implemented in the MATLAB system, the settings of the fuzzy PID controller MT20-R-E MT-20E FOTEK + PID Fuzzy are defined: FB type gaussmf; Mamdani's fuzzy inference system; P = 0.345, I = 0.017, D = 1.725, ensuring the achievement of the best indicators of the quality of the transient: overshoot is 0.005°C and the quadratic integral criterion is 1216.
The method of optimal control of the catalytic reforming process
The solution to the problem of optimizing the CR process using the method of uniform-dimensional search was substantiated. To do this, the dependence of the GOC I on two variables - the temperature of the feed mixture at the entrance to the furnace Tin and the temperature of the feed mixture at the furnace outlet Tout is considered [10].
The optimization algorithm is implemented in the form of software C #. As a result of the calculation by the algorithm, the following optimum values of the parameters of the CR process were obtained: the temperature at the entrance to the furnace Tinopt = 180°C; the temperature at the furnace out-
Based on the algorithm of optimizing the process of the CR, the method for the optimal control of this process has been developed. Scientific novelty of the method of optimal control of the process of the CR is in taking into account the expert information when formalizing fuzzy goals and constraints in the process control and determining the optimal control actions under the scheme of Bellman-Zadeh, depending on the current values of the input variables of the process.
This technique is intended for optimal control of the CR process in the case of an undefined goal
G and fuzzy constraints Q, C2 that are specified by the operator in the form of verbal utterances (formulations) and is an extension (addition) of the algorithm for optimizing the CR process in the case of using verbal formulations in determining the purpose and constraints on management.
0,025
T, °C
400
Fig. 2. Transients in ACS temperature at the outlet of the furnace: 1 - with a classic PID controller; 2 - with fuzzy PID controller
let Toutop '= 210°С; GOC Iopt = 0.964.
A fuzzy decision D in the management of the process of the CR is determined by the Bellman-Zadeh scheme [11] as the intersection of a fuzzy goal G and fuzzy constraints Q, C2:
D = G n C n C2. (3)
On the basis of (3) the alternative x = 212°C is defined, corresponding to the maximum FB of the fuzzy solution. Using the hybrid MM for given input variables, we obtain optimal control actions at x = 212°C for setting the LCH-35-11/1000.
On the basis of the technique, the vector of controls corresponding to the minimum of the GOC I = 0.964 is determined. The vector of U controls that affect production costs is allocated: raw material consumption Gr 1000 t, electricity consumption Ge 82 MJ, fuel gas consumption Gfg 25 m3, catalyst consumption Gc 0.02 kg, reagent consumption Grg 0.001 kg.
The vector of U°" controls influencing the octane number of gasoline is also determined: the productivity of the centrifugal compressor is Qcc 210 000 nm3/h, the volume flow of raw materials is Qr 130 m3/h, the amount of the discharged hydrogen-containing gas is Qhg 90 000 nm3, the volume flow of fuel gas to the first furnace is Qfg1 750 m3/h, the volume flow of fuel gas to the second furnace is Qfg2 850 m3/h, the volume flow of fuel gas to the third furnace is Qfg3 950 m3/h.
The program implementation of the optimal control methodology for the process of the CR in the C # language is made, which allows determining the vector of controls corresponding to the minimum of the GOC. For the obtained control vector, the efficiency indicators of the process of the CR were determined: production costs are Z = 0.825 billion rubles; octane number of gasoline is ON = 92.83; GOC is I = 0.964.
Search for Pareto-optimal solutions for controlling the catalytic reforming process
The use of normalized values of the criteria is associated with the possibility of combining them on one criteria plane and searching for Pareto-optimal solutions (Fig. 3).
0,96 0,965 0,97 0,975 0,98 0,985 0,99 0,995 1
Criterion for minimizing costs Ii
Fig. 3. Search for the optimal solution on the Pareto set
The values of the partial criteria and GOC are determined using the hybrid MM process of the CR [6].
The optimization algorithm is implemented in the form of software C #. As a result of the calculation by the algorithm, the following optimum values of the parameters of the CR process were obtained: the temperature at the entrance to the furnace Tinopt = 180°C; the temperature at the furnace outlet Toutopt = 210°C; GOC Iopt = 0.964.
The Pareto set (Fig. 3) is constructed on the basis of the method of optimal control of the CR process for a typical set of input variables characterizing the normal operation of the process at the LCH-35-11/1000 installation for one month [7].
Based on Fig. 3, the best solution corresponding to the minimum of GOC is determined:
{/!,12}:I ^min, (4)
where {Ij!, I!} - the values of the partial criteria for the 1st (best) solution.
The optimal solution (4) corresponds to the values of the criteria: I! = 0.959; I2 = 0.967; I = 0.964 at weighting factors k! = k2 = 0.5.
Development of the system for optimal control of the catalytic reforming process
The system of optimal control of the process of the CR is developed, the structure of which is presented in Fig. 4.
ON,Z
The optimajjsdntrol system
<1>
h -п
о Ell С О ii>
■■w Ш
с С = Sä, Q. О о
a> en
Q
Selection of ACS
Determining the settings of the ACS regulators
10
11
Operator
Hybrid model of the process
8
7
2
5
6
Fig. 4. Structure of the optimal control system for the catalytic reforming process
The control object (CO) - 1 is the CR process, which receives the input variables XIN and control actions U. At the output of CO the values of the octane number of gasoline ON and production costs Z are obtained.
The optimal control system - 2 serves to control the CR process with a fuzzy goal G and the fuzzy constraints Cl, C2 specified by operator - 3 when implementing the optimal control technique -4. To determine GOC - 5, the operator - 3 sets the values of the fuzzy input variables X*IN (catalyst activity, state of the reforming furnace, etc.) to the input of the hybrid MM process - 6. On the basis of the algorithm for optimizing the process - 7, with the given explicit constraints, the alternative "x" is determined - the temperature at the exit from the furnace, at which GOC I(x) is minimal.
Based on the method of optimal control process - 4 using the Bellman-Zadeh scheme, an alternative to "x'" is defined, different from "x", at which the minimum of GOC I(x) is reached.
For the obtained alternative "x'" and for alternatives from the range, when all components are equal the GOC is minimal with respect to two other local minima, using the search procedure for the Pareto optimal solution - 8 and the hybrid MM - 6, the control vector U - 9 corresponding to the minimum GOC is determined.
Based on the multi-criteria selection of ACS - 10 and the algorithm for determining the settings of the CR process controllers in various modes - 11 the best model of ACS is determined and regulator settings for the three parameters of the CR process are the temperature at the outlet from the reforming
furnace (ACSi); pressure in the reforming reactor (ACS2); level in the re-forming separator (ACS3). To determine the initial information in the selection of ACS, the database of tools for managing the CR process was developed.
Positive effects were obtained using the developed system of optimal control of the CR process: a decrease in average costs by 0.33 million rubles; an increase in the average octane number by 0.53; decrease in the mean value of the GOC by 0.025.
Conclusion
1. The problem of optimal control of the CR process has been formulated.
2. The hybrid MM of the CR process has been developed, based on which the maximum annual costs of 4.05 billion rubles and the minimum octane number of gasoline is 92.83 were obtained for the LCH-35-11/1000 CR installation.
3. The algorithm for determining the settings of the temperature regulator at the outlet from the furnace in different modes of the CR process has been synthesized. Based on the algorithm for the given mode of the CR process, the parameters of the fuzzy PID controller MT20-R-E MT-20E FOTEK + PID Fuzzy have been determined, which ensure the achievement of the best parameters of the transient: overshoot 0.005°C and integral quality index 1216.
4. A method for optimal control of the CR process has been developed, on the basis of which a control vector corresponding to the minimum of the GOC I = 0.964 has been determined.
5. A set of Pareto-optimal solutions has been constructed for a typical set of input variables characterizing the normal operation of the process at the LCH-35-11/1000 CR installation for one month. On the Pareto set, the best solution corresponding to the values of the criteria I1 = 0.959; I2 = 0.967; I = 0.964 is defined at weighting factors k1 = k2 = 0.5.
6. The structure of the system of optimal control of the CR process has been developed.
7. The assessment of improving the management effectiveness of the CD process has been made. Positive effects have been determined while using the developed system of optimal control of the CR process: the decrease in average costs by 0.33 million rubles; the increase in the average octane number by 0.53 points; the decrease in the mean value of the GOC by 0.025.
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The article submitted to the editors 16.01.2018
INFORMATION ABOUT THE AUTHORS
Dzhambekov Azamat Matifulaevich - Russia, 414056, Astrakhan; Astrakhan State Technical University; Postgraduate Student of the Department of Automation and Control; [email protected].
Fedorova Olesya Victorovna — Russia, 414056, Astrakhan; Astrakhan State Technical University; Candidate of Pedagogical Sciences, Assistant Professor; Assistant Professor of Department of Foreign Languages; [email protected].
А. М. Джамбеков, О. В. Федорова
ОПТИМАЛЬНОЕ УПРАВЛЕНИЕ ПРОЦЕССОМ КАТАЛИТИЧЕСКОГО РИФОРМИНГА БЕНЗИНОВЫХ ФРАКЦИЙ
Рассматривается актуальная задача разработки системы оптимального управления процессом каталитического риформинга, обеспечивающей достижение оптимальных соотношений октанового числа бензина и производственных затрат. Выполнена постановка задачи оптимального управления процессом каталитического риформинга, отличающаяся использованием обобщенного критерия оптимальности в качестве целевого функционала. Разработана гибридная математическая модель процесса каталитического риформинга, которая учитывает влияние параметров, характеризующих производственные затраты и октановое число бензина, на эффективность процесса и позволяет вычислять значения обобщенного критерия оптимальности в зависимости от значений входных переменных процесса. На основе модели для установки ЛЧ-35-11/1000 выполен расчет максимальных годовых затрат (4,05 млрд руб.) и минимального октанового числа бензина 92,83. Выполнен многокритериальный выбор системы регулирования температуры на выходе из печи. Синтезирован алгоритм определения настроек регулятора температуры на выходе из печи в различных режимах процесса каталитического риформинга. Разработана методика оптимального управления процессом каталитического риформинга, учитывающая экспертную информацию при формализации нечетких целей и ограничений при управлении процессом и позволяющая рассчитывать оптимальные управляющие воздействия по схеме Беллмана-Заде в зависимости от значений входных переменных процесса. На основе данной методики определен вектор управлений, соответствующий минимуму обобщенного критерия оптимальности (I = 0,964). Выполнен поиск Парето-оптимальных решений при управлении процессом каталитического риформинга. Получены положительные эффекты при использовании разработанной системы оптимального управления процессом каталитического риформинга: снижение средних затрат на 0,33 млн руб.; повышение среднего октанового числа на 0,53; снижение среднего значения обобщенного критерия оптимальности на 0,025.
Ключевые слова: каталитический риформинг, обобщенный критерий оптимальности, Парето-оптимальное решение, гибридная модель, классический ПИД-регулятор, нечеткий ПИД-регулятор, система оптимального управления.
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Джамбеков Азамат Матифулаевич — Россия, 414056, Астрахань; Астраханский государственный технический университет; аспирант кафедры автоматики и управления; [email protected].
Федорова Олеся Викторовна — Россия, 414056, Астрахань; Астраханский государственный университет; канд. пед. наук, доцент; доцент кафедры иностранных языков; [email protected].
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Статья поступила в редакцию 16.01.2018
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