energies Article Modeling of a Catalytic Cracking in the Gasoline Production Installation with a Fuzzy Environment Batyr Orazbayev 1 , Dinara Kozhakhmetova 1 , Ryszard Wójtowicz 2,* and Janusz Krawczyk 2 1 Department of Systems Analysis and Control, Faculty of Information Technology, L.N. Gumilyov Eurasian National University, Pushkin Street, 11, Nur-Sultan 010000, Kazakhstan; [email protected] (B.O.); [email protected] (D.K.) 2 Institute of Thermal and Process Engineering, Division of Industrial Equipment and Fluid Mechanics, Cracow University of Technology, Al. Jana Pawła II 37, 31-864 Cracow, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-12-628-3288 Received: 10 August 2020; Accepted: 2 September 2020; Published: 11 September 2020 Abstract: The article offers a systematic approach to the method of developing mathematical models of a chemical-technological system (CTS) in conditions of deficit and fuzziness of initial information using available data of various types. Based on the results of research and processing of the collected quantitative and qualitative information, mathematical models of the reactor are constructed. Formalized and obtained mathematical statements of the control problem for choosing effective modes of operation of technological systems are based on mathematical modeling. Based on the obtained expert information, linguistic variables were described and a database of rules describing the operation of the input parameters of the reactor unit of the catalytic cracking unit was obtained. Keywords: gasoline production installation; catalytic cracking; reactor-regenerative block; mathematical modeling; system analysis; fuzzy logic 1. Introduction Catalytic cracking is the most important process in refining oil to produce gasoline. The catalytic cracking unit is designed for processing vacuum distillate to produce a component of high-octane gasoline. The results of catalytic cracking are generally determined by such indicators as the of conversion raw materials, the yield of target products and their quality. The cracking reaction is mainly represented by a break in the “carbon-carbon” bond, which refers to an endothermic reaction—the higher the temperature, the higher the reaction rate. The cracking reaction is one of the most important types of reactions in the process of catalytic cracking. The higher molecular weight of hydrocarbon in the homological series, the higher the reaction rate. Catalytic cracking is a process whose technological mode depends on the characteristics of raw materials and catalysts, atmospheric air, etc., not all of which can be measured or measured in the laboratory, which requires the experience of experts in control systems. A technological process is subject to strict restrictions on the ranges of temperature, concentration and pressure values in the reactor unit apparatus. One of the ways to use the experience of operational personnel is to use the mathematical apparatus of fuzzy set theory for algorithmization of control problems. For effective research and optimization of processes and units of oil refining, it is necessary to build their mathematical models that take into account the nature and state of the process, the type and other features of objects [1–4]. Ultra-high-silica ZSM-5 zeolites are now most commonly used. An important feature of the zeolite structure is the presence of a three-dimensional anion framework constructed from SiO4 and AlO4 tetrahedra interconnected by strong Si-O-Si and Si-O-Al bridges. This creates a system of Energies 2020, 13, 4736; doi:10.3390/en13184736 www.mdpi.com/journal/energies Energies 2020, 13, 4736 2 of 13 intracrystalline pores and cavities, where occlusion and molecule formation of the appropriate size can easily occur. The presence of pores and cavities in the framework of anhydrous zeolite is associated with important molecular sieve properties of zeolites—the ability to selectively adsorb and desorb molecules of certain sizes. Among the most important properties of zeolites with respect to their use as catalysts is their application as solid acids. The acid-base character of the catalytic surface is due to the presence of Lewis and Brønsted acid sites (Figure1)[5]. Figure 1. Brønsted and Lewis acid sites in zeolites [5]. Zeolites also contain aprotic or Lewis acid centers with electron-acceptor properties (Figure1). These include various coordination-unsaturated atoms or lattice ions that have a vacant p-orbital, as well as exchange cations with a positive charge. When hydrogen forms of zeolites are dehydroxylated, AlO4 tetrahedra are formed, devoid of a proton that compensates for their charge, which have the properties of Lewis bases. ZSM-5 increased the electrophilicity of the metal and therefore increased the oxidation stage in the catalytic cycle during the CPOM reaction, increasing the reaction rate accordingly [6]. When developing mathematical models in order to solve problems related to control of operating modes of actual chemical/technological systems (CTS), fuzziness problems associated with lack and fuzziness of initial information often occur. The most effective way to solve such fuzziness problems is to use systematic approach based on availability of various information [7,8]. Methods of system analysis play a significant role in designing and improvement of complex systems and process control [9]. However, these methods can not be applied if uncertainty is combined with fuzziness of initial information and this is often the case in the real working conditions. In these conditions statistical information is either not available or insufficient under such conditions and probability theory axioms (statistical stability of researched object, repeatability of experiments under identical conditions) are not performed. Available information is sometimes uncertain that is person’s (person making decisions—PMD, expert) knowledge (experience, intuition, judgment). Effective formalization of uncertain information representing knowledge of experts on CES may be obtained based on methods for expert evaluations and fuzzy set theory (FST) [10–13]. If PMDs, experts are competent and there is proper organization for their questioning, collecting and processing of uncertain information, models can be built that include all complex interrelations with various parameters and variable complex CES. Such models can be more informative than those developed via traditional methods plus they may accurately describe real CESs and problems. This paper is aimed to develop a method for constructing mathematical models of reactor block of catalytic cracking based on fuzzy models and expert knowledge with membership functions for values of linguistic variables under conditions with fuzzy information. Energies 2020, 13, 4736 3 of 13 2. Experimental Unit One of the main upgrades of Atyrau Oil Refinery is construction of a complex for deep oil refining that will significantly increase production of high-quality light petroleum products. The presented two-stage regeneration system (R2R) processes mixed raw materials from atmospheric residue, vacuum gas oil, heavy coking gas oil, heavy gas oil (heavy recycled gas oil of atmospheric distillation), heavy raffinate, polymer kerosene. Deep oil refining complex will be integrated with existing refineries. The capacity of the catalytic cracking unit is 2,388,540 tons/year. The complex consists of the following units (Figure2): reactor block, block for fine cleaning and recuperation of flue gases, rectification block and block for stabilization of gasoline and gas fractionation. The unit is designed to convert the residue of atmospheric distillation (AR, fuel oil), heavy gas oil, vacuum gas oil, heavy gas oil from (from coking unit), heavy raffinate (from plant for production of aromatics and heavy aromatic compounds) into more valuable products, such as liquefied petroleum gas, gasoline and light gas from catalytic cracking. Figure 2. General flow diagram of the catalytic cracking unit (R2R): R0101—riser, R0102—reactor-separator; R0103—stage one regenerator; R0104—stage two regenerator, R0105—section for blow off catalyst from smoke gases; C0201—distillation column; 1, 2, 3, 4, 5—pumps; 3, 9—coils; 4, 10—air cooling devices; 5—container; I—raw; II—coked catalyst; III—reaction product; IV—regenerated catalyst; V—gas; VI—acidic water; VII—petrol; VIII—light gas oil; IX—remainder of the above 343 ◦C, X—flue gases. The catalytic cracking unit consists of two main parts: the reactor R0101, R0102 and the regenerator R0103, R0104 (Figure2). The central part of the catalytic cracking unit is the R0101, R0102 reactor, which functions as follows: the raw material passes through the heater, mixes with the catalyst and enters a vertical pipe (riser) leading to the lower part of the large vessel (settling part of the reactor). The main task of the reactor is to separate hydrocarbons from the catalyst. This occurs in the settling zone of the reactor. The steam phase rises up and passes through the cyclones and is sent to the distillation column for further cleaning and processing. The solid phase (coked catalyst) due to the difference in the static pressure of the catalyst in the reactor and the regenerator flows by gravity along an inclined transport line to the regenerator R0103. Some of the hydrocarbons that are converted to coke during cracking are deposited on the catalyst. When the surface of the catalyst is covered with deposits, the catalyst becomes inactive (spent). To remove these