A Model of Catalytic Cracking: Product Distribution and Catalyst Deactivation Depending on Saturates, Aromatics and Resins Content in Feed

: The problems of catalyst deactivation and optimization of the mixed feedstock become more relevant when the residues are involved as a catalytic cracking feedstock. Through numerical and experimental studies of catalytic cracking, we optimized the composition of the mixed feedstock in order to minimize the catalyst deactivation by coke. A pure vacuum gasoil increases the yields of the wet gas and the gasoline (56.1 and 24.9 wt%). An increase in the ratio of residues up to 50% reduces the gasoline yield due to the catalyst deactivation by 19.9%. However, this provides a rise in the RON of gasoline and the light gasoil yield by 1.9 units and 1.7 wt% Moreover, the ratio of residue may be less than 50%, since the conversion is limited by the regenerator coke burning ability.


Introduction
Depending on market needs, the catalytic cracking technology can be aimed at increasing the yield of gasoline, light olefins, or light gasoil, the latter being more relevant to Europe with its high amount of diesel cars [1]. Factors affecting the products' yields include interacting operating variables in the reactor and the regenerator, catalyst deactivation, and, especially, change in the hydrocarbon type content in the feedstocks. To improve the oil refining depth, the residual fraction involves catalytic cracking units as a feedstock [2][3][4][5]. When the heavy petroleum fractions are converted, the rising content of coke on the catalyst contributes to its deactivation and an increase in the temperature of the regenerated catalyst [6]. In this case, the amount of heat created in the regenerator should not deactivate the catalyst or disturb the heat balance significantly. Moreover, the conversion of catalytic cracking feedstock is limited by the regenerator coke burning ability. This poses a major challenge when using the existing industrial catalytic cracking units, i.e., how to choose the mixed feedstock in order to increase the production of light gas oil, gasoline, or light olefins when using residual fractions; and how to define the optimal amount of residues in the mixed feedstock to prevent an intensive formation of coke and catalyst deactivation. Since change in the composition of feedstock and non-optimum conditions for the catalyst operation may lead to catalyst deactivation by coke and as a result reduce the cracking efficiency, addressing the above challenge is an essential task. Therefore, the rate of coke formation should be optimized accordingly.
To predict the efficiency of catalytic cracking, scientists have successfully employed both mathematical models and experimental study (Froment, Corella, Gilbert, Ancheyta, Jimeńez-García, Fernandes, Radu, Oliveira, Mujtaba, Al-Khattaf, Barbosa et al.) [7][8][9][10][11][12][13][14][15][16]. Given that the main difficulty when modeling the advanced petroleum processes is to ensure the sensitivity of the model to the saturates, aromatic hydrocarbons, and resins (SAR) composition, most reaction networks have been based on the formation of pseudocomponents according to their wide fractional composition [17][18][19]. However, this approach fails to consider how group characteristics of the feedstock as well as the hydrocarbon reactivity influence the yield of coke and products, which is important when predicting the composition of products considering the catalyst deactivation. Although some models consider the hydrocarbon type content in the feedstock, they may not predict the hydrocarbons groups of the gasoline, which requires forecasting the research octane number (RON) [20,21].
A model for the optimization of the mixed feedstock of the catalytic cracking should be sensitive to changes in the hydrocarbon type content in the feedstock [22], predict the group composition of the gasoline, and take account of not only the cracking temperature, but also the operating variables of the catalyst after the regeneration zone such as temperature, activity, and catalyst consumption. Aggregation of mechanisms of complex chemical reactions using elements of lumping analysis provides an effective and informative approach.
In this article, we apply a complex approach to developing such a mathematical model. We determine the thermodynamic and kinetic patterns of catalytic cracking of high molecular weight hydrocarbons, taking into account catalyst deactivation and the content of the saturates, the aromatics, and the resins in the feedstock. This model allows us to predict the yield and the quality of products, as well as choose the suitable mixed feedstock to increase the yield of gasoline, light olefins, or light gasoil.

Results and Discussion
2.1. Experimental 2.1.1. Feedstocks Table 1 contains the SAR compositions and density of VD and R feeds defined experimentally. The results showed that VD was enriched in saturates, with the content of these hydrocarbons 71.8 wt%, which was higher by 13.6 wt% than in the R feedstock (55.8 wt%). Conversely, the latter had a higher content of aromatics (40.1 wt%), which was also confirmed by the value of density (0.9006 and 0.9100 g/cm 3 for VD and R, respectively). Moreover, the content of resins in the R feedstock was 1.8 times higher than for the VD feed, which leads to intensive coke formation and catalyst deactivation and as a result may limit the conversion of the feedstock under certain temperatures. These negative impacts can be reduced if the R feedstock is co-processed with the VD feed. However, this requires finding the optimal R-to-VD ratio in such a mixed feedstock, which will ensure the increase in yield of the desired products. Table 2 presents the change in acid properties of the coked and regenerated catalysts. The results of thermoprogrammed desorption of ammonia showed that the concentration of the acid sites was 224 µmol/g for the regenerated catalyst, which was 1.4 times higher than for the coked catalyst. This confirmed that the catalyst operation in the riser leads to a significant deactivation of the catalyst by coke. The thermogravimetric results (Figure 1a) showed that the coke formed on the catalyst had an amorphous structure since the exothermic peak of coke oxidation was detected at a temperature less than 740 • C.

Catalysts
Catalysts 2021, 11, x FOR PEER REVIEW 3 of 17 than for the coked catalyst. This confirmed that the catalyst operation in the riser leads to a significant deactivation of the catalyst by coke. The thermogravimetric results (Figure 1a) showed that the coke formed on the catalyst had an amorphous structure since the exothermic peak of coke oxidation was detected at a temperature less than 740 °C. The presence of amorphous coke was also confirmed by a thermogram of the spent catalyst with a charge-mass distribution m/z = 44 (mass-to-charge ratio). (Figure 1b). In this case, the ion current peak appeared at a temperature range of 465-650 °C. This indicates the presence of CO2 gas formed during the oxidation of the amorphous coke. The coke content on the catalyst was 0.32-0.5 wt%. Thus, by studying the cracking catalysts, we defined how the coke content on the surface of the catalyst impacts the catalyst deactivation. The patterns of this influence were further taken into account to develop the optimization model (Section 2.2.1).

Equations
The formalized mechanism of cracking reactions simplifies the mathematical description of such a complicated multicomponent process. We developed a 14-lump kinetic model that includes hydrocarbon groups of the feedstock participating in the catalytic cracking. The reaction network is based on quantum-chemical methods and the database of hydrocarbons composition of the feedstock and products obtained at a laboratory of Tomsk Polytechnic University, Tomsk, Russia. Table 3 contains the initial data to develop the model, including the concentration of the hydrocarbons groups of feedstock and products. The presence of amorphous coke was also confirmed by a thermogram of the spent catalyst with a charge-mass distribution m/z = 44 (mass-to-charge ratio). (Figure 1b). In this case, the ion current peak appeared at a temperature range of 465-650 • C. This indicates the presence of CO 2 gas formed during the oxidation of the amorphous coke. The coke content on the catalyst was 0.32-0.5 wt%. Thus, by studying the cracking catalysts, we defined how the coke content on the surface of the catalyst impacts the catalyst deactivation. The patterns of this influence were further taken into account to develop the optimization model (Section 2.2.1).

Equations
The formalized mechanism of cracking reactions simplifies the mathematical description of such a complicated multicomponent process. We developed a 14-lump kinetic model that includes hydrocarbon groups of the feedstock participating in the catalytic cracking. The reaction network is based on quantum-chemical methods and the database of hydrocarbons composition of the feedstock and products obtained at a laboratory of Tomsk Polytechnic University, Tomsk, Russia. Table 3 contains the initial data to develop the model, including the concentration of the hydrocarbons groups of feedstock and products. The predictive ability of the model depends on the set of desired products such as gasoline and fat gas. The developed reaction network ( Figure 2) helps predict the group composition of the gasoline, as well as the content of both the propane-propylene and butane-butylene fractions in wet gas, and coke. In addition, it also takes into account the SAR composition and the reactions leading to coke formation from these hydrocarbons on the catalyst. Therefore, this mechanism allows us to predict the amount of coke and the degree of catalyst deactivation when modeling the process of catalytic cracking. The results of quantum-chemical methods of calculations confirmed the fundamental occurrence of reactions under the study ( Table 4). The probability of their occurrence according to isobaric-isothermal potential (ΔrG°810-848), as well as the reactivity of hydrocarbon groups, were estimated at the equilibrium temperature between the feedstock and the catalyst (Equation (4)). Moreover, the thermal effects of reactions (ΔrH°810-848) defined using DFT are used to solve a heat balance equation of the riser.
The mathematical model (Equation (1)) represents a system of ordinary differential equations describing the material and heat balances. The riser is modeled as a plug flow reactor, for the gas velocity (≈3.2-9.2 m/s) significantly exceeds the initial fluidizing velocity and the Peclet diffusion number tends to infinity.
Here, i is the number of components; j is the number of reactions; Ci is the concentration of i-the hydrocarbons group, mol/m 3 ; τ is the contact time, s; j is the reaction number; ψ is the deactivation function are the thermal effects of the chemical reactions, kJ/mol; Ti.t. is the temperature of the thermal equilibrium between the feedstock and the catalyst, K; A two-phase flow is required to describe the process with a moving catalyst bed. The passive phase is the gas-liquid flow, the active phase is the flow in pores of solid catalyst particles. The hydrodynamic mode of both phases is close to plug flow. The transfer of matter by moving solid particles of the catalyst is not important if the particles have a small specific surface area that poorly absorbs the reagent [23]. The results of quantum-chemical methods of calculations confirmed the fundamental occurrence of reactions under the study ( Table 4). The probability of their occurrence according to isobaric-isothermal potential (∆rG • 810-848 ), as well as the reactivity of hydrocarbon groups, were estimated at the equilibrium temperature between the feedstock and the catalyst (Equation (4)). Moreover, the thermal effects of reactions (∆rH • 810-848 ) defined using DFT are used to solve a heat balance equation of the riser. The mathematical model (Equation (1)) represents a system of ordinary differential equations describing the material and heat balances. The riser is modeled as a plug flow reactor, for the gas velocity (≈3.2-9.2 m/s) significantly exceeds the initial fluidizing velocity and the Peclet diffusion number tends to infinity.
Initial conditions: Here, i is the number of components; j is the number of reactions; C i is the concentration of i-the hydrocarbons group, mol/m 3 ; τ is the contact time, s; j is the reaction number; ψ is the deactivation function (3); p m , c m are the density and heat capacity of flow, kg/m 3 , kJ/kg · K; T is the temperature; A two-phase flow is required to describe the process with a moving catalyst bed. The passive phase is the gas-liquid flow, the active phase is the flow in pores of solid catalyst particles. The hydrodynamic mode of both phases is close to plug flow. The transfer of matter by moving solid particles of the catalyst is not important if the particles have a small specific surface area that poorly absorbs the reagent [23].
The interdependence between reaction rates (18 reactions) and group concentrations (14 components) is based on the law of mass action according to the reaction network ( Figure 2). Moreover, the reaction rate is multiplied by the catalyst deactivation parameter when the concentration of the components calculates (Equation (2)): The catalyst deactivation parameter ψ is calculated depending on the content of coke on its surface. Using the results TPD, we defined the change in acid properties of the catalyst depending on the concentration of coke (Equation (3)): where A is the current relative catalyst activity (acidity), %; A 0 is regenerated catalyst activity, %; C coke is the coke content on the catalyst, wt%. This approach allows us to implement the relationship among the following parameters: the composition of the feedstock-the content of coke on the catalyst-the change in catalyst activity-the change in the yield and composition of the products.
The model takes into account the interdependence between the operating variables of the riser and the regenerator. The cracking temperature depends largely on the temperature of the thermal equilibrium between the feedstock, the catalyst, and the heat of cracking reactions. The initial temperature of the reactions depends on the consumption of the feedstock and regenerated catalyst, as well as on their temperatures and heat capacities (Equation (4)): where G cat is catalyst consumption, kg/s; G f is the feedstock consumption, kg/s; c f , c cat is the feedstock and the catalyst heat capacity, J/kgK; T cat is the temperature of regenerated catalyst, K; T it is the temperature of the thermal equilibrium between the feedstock and the catalyst, K.
Reaction rate constants were defined by solving the inverse kinetic problem, when the kinetic parameters are calculated based on the feedstock and product concentrations. Table 3 contains initial data for solving the inverse kinetic problem. As an initial approximation, we used the kinetic parameters of the reaction of the individual hydrocarbons, which characterized the reaction groups, and lumps, which were defined both experimentally, including quantum-chemicals methods, and using the existent models [24][25][26][27][28][29][30][31][32][33][34][35].
Since the models differ significantly in reaction paths, the number of components, and their characteristics, as well as in catalysts type and operating variables etc., we used the kinetic parameters defined experimentally in several studies, where possible: for unsaturated hydrocarbons cyclization [24], for C 5 -C 12 alkanes and isoalkanes cracking [25], for unsaturated hydrocarbons cracking [26], for aromatics dealkylation [27], for C 13 -C 40 alkanes cracking [28], for diene synthesis [29], for hydrogen transfer [30].
Our kinetic scheme is based on a group approach and includes several reactions when the feedstock converts into gasoline, and often, the products are both components of gas and gasoline. Although the use of the lump approach often involves the formation of a component through pseudo-reactions directly, without considering the specific hydrocarbons, we also take into account the modeling results: for C 5 -C 12 isoalkanes cracking [31], for condensation and coke formation [32,33], for cycloalkanes cracking and dealkylation [34], for cycloalkanes cracking [35].
At the same time, the most important factors are the catalyst nature and the operating variables, when the kinetic parameters are defined; most often, the databases present kinetic parameters of thermal conversion of individual hydrocarbons under a different catalyst.
These factors also lead to the optimization task of the kinetic parameters. To solve this problem, we used a genetic algorithm [36,37]. Finding the solution of the task using a genetic algorithm consists of the application of an iterative procedure, when the original solution improves gradually. At each iteration, several alternative candidate solutions (individuals) are considered immediately, and the genetic algorithm updates the population (the set of individuals used in the iteration) by creating new individuals and eliminating the worst ones.
The generation and mutation of new individuals is based on the modeling of the breeding and mutation processes using the crossing and the mutation operators. The reduction operator ensures the choice of the best ("revivable") individuals among the parents and descendants by eliminating the worst ("poorly adapted") ones. The latter performs according to strictly defined (deterministic) rules; at the same time, the crossing and the mutation occur randomly.
The main selection rule is the evolution law: "the strongest survives", whichimprroves the finding solution. Equation (5) presents the expression for the fitness function: where y i is the value of the i-th parameter (concentration); y icalc is the calculated value of the i-th parameter (concentration); n is the total amount of parameters; k is amount of days under the studied; F is fitness function.
The implementation of these options provides a set of the kinetic parameters of the catalytic cracking reactions in accordance with reaction networks, which has a maximum fitness function. The degree of fitness of the kinetic parameters set is defined as 1/F. Table 4 presents the estimated kinetic and thermodynamic parameters of the reactions involving high molecular weight hydrocarbons that convert into gas, gasoline, diesel fractions, and coke. Thermodynamic values marked with an asterisk were defined by quantum-chemical methods; for low molecular weight hydrocarbons, we used reference data [38].
The defined set of kinetic parameters provides the sensitivity of the developed mathematical model to changes in the SAR composition of the feedstock, as well as in operating variables. In addition to the kinetic parameters, the thermodynamic parameters provide an accuracy of the model in terms of temperature and, consequently, the components concentrations. The mathematical model provides a quantitative account of the influence of the feedstock composition by considering the concentrations of reagents and reaction rate constants.

Verifications
The mathematical model was verified by comparing the calculated data of the product yields and industrial data (Figure 3). A change in the main operating variables of the riser is presented in Table 5. The feedstock composition changed according to Table 6. The defined set of kinetic parameters provides the sensitivity of the developed mathematical model to changes in the SAR composition of the feedstock, as well as in operating variables. In addition to the kinetic parameters, the thermodynamic parameters provide an accuracy of the model in terms of temperature and, consequently, the components concentrations. The mathematical model provides a quantitative account of the influence of the feedstock composition by considering the concentrations of reagents and reaction rate constants.

Verifications
The mathematical model was verified by comparing the calculated data of the product yields and industrial data (Figure 3). A change in the main operating variables of the riser is presented in Table 5. The feedstock composition changed according to Table 6. Verification of the model shows that the average relative error between the calculated and experimental data is not more than 7.0 wt%. (Figure 3). Figure 3d shows that the alkanes concentration with a step size h = 0.01 and h = 0.001 are close in comparison with h = 0.3-0.5, which ensures the convergence of the results during solving the system of ordinary differential equations.    Figure 4 shows the sensitivity of the model to SAR content in the feedstocks and the major process variable. Model-based calculation shows that the gasoline yield is the highest (55.5-55.7 wt%) when the feedstocks with a high content of saturates are converted (C-1, C-2, and C-6 feed). At the same time, the values of RON of the gasoline are lower (90.48-92.15) relative to other feedstock, which have a high content of aromatics. Although the yields of gas are high values (24.6-24.9 wt%), the amount of light (10.81-11.12 wt%) gas oil is lower relative to other feeds.
The feedstock (F-10) which has a high concentration of aromatics (45.1 wt%) and resins (3.0 wt%), reduces the yield of the gasoline with a high octane number (95.69 units, 53.72 wt%) and gas (22.22 wt%). In addition, this feedstock contributes to the high rate of formation of coke (5.86 wt%), which leads to a decrease in the catalyst activity, as well as the degree of the feedstock conversion, and to an increase in heavy products: light and heavy gas oils (13.3 and 4.9 wt%). Figures 5 and 6 show the effect of the main process variables on the cracking temperature and the latter on the consumption of product components.  Verification of the model shows that the average relative error between the calculated and experimental data is not more than 7.0 wt%. (Figure 3). Figure 3d shows that the alkanes concentration with a step size h = 0.01 and h = 0.001 are close in comparison with h = 0.3-0.5, which ensures the convergence of the results during solving the system of ordinary differential equations. Figure 4 shows the sensitivity of the model to SAR content in the feedstocks and the major process variable. Catalysts 2021, 11, x FOR PEER REVIEW 10 of 17   Model-based calculation shows that the gasoline yield is the highest (55.5-55.7 wt%) when the feedstocks with a high content of saturates are converted (C-1, C-2, and C-6 feed). At the same time, the values of RON of the gasoline are lower (90.48-92.15) relative to other feedstock, which have a high content of aromatics. Although the yields of gas are high values (24.6-24.9 wt%), the amount of light (10.81-11.12 wt%) gas oil is lower relative to other feeds.
The feedstock (F-10) which has a high concentration of aromatics (45.1 wt%) and resins (3.0 wt%), reduces the yield of the gasoline with a high octane number (95.69 units, 53.72 wt%) and gas (22.22 wt%). In addition, this feedstock contributes to the high rate of formation of coke (5.86 wt%), which leads to a decrease in the catalyst activity, as well as the degree of the feedstock conversion, and to an increase in heavy products: light and heavy gas oils (13.3 and 4.9 wt%). Figures 5 and 6 show the effect of the main process variables on the cracking temperature and the latter on the consumption of product components.     Studying the parametric sensitivity showed that the change in the product yields and composition of cracking products is consistent with the theoretical laws about the process. With an increase in temperature, the consumption of feedstock components decreases and consumption of the gas components and the coke increases. The content of gasoline passes through a maximum due to an increase in the rates of cracking reactions with the release of gas components and condensation with further coke formation.
The developed model is intended to predict the yields and composition of products when the SAR composition of feedstock and the catalyst deactivation change. Such a model is to define the suitable ratio of the mixed feedstock for increasing the yield of the desirable product, taking into account the temperature, consumption of regenerated catalyst, as well as its deactivation. Figure 7a shows the effect of the different feedstocks (Table 1) on the yield of the products and the RON of the gasoline when the operating variables were equal (Table 7).  Studying the parametric sensitivity showed that the change in the product yields and composition of cracking products is consistent with the theoretical laws about the process. With an increase in temperature, the consumption of feedstock components decreases and consumption of the gas components and the coke increases. The content of gasoline passes through a maximum due to an increase in the rates of cracking reactions with the release of gas components and condensation with further coke formation.

Model Application
The developed model is intended to predict the yields and composition of products when the SAR composition of feedstock and the catalyst deactivation change. Such a model is to define the suitable ratio of the mixed feedstock for increasing the yield of the desirable product, taking into account the temperature, consumption of regenerated catalyst, as well as its deactivation. Figure 7a shows the effect of the different feedstocks (Table 1) on the yield of the products and the RON of the gasoline when the operating variables were equal (Table 7). Model-based calculations showed that the cracking of VD provides a high yield of gasoline and C3-C4 gases (56.1 and 24.9 wt%) due to the high content of the saturates in its composition. The RON of the gasoline is 91 units and the coke yield was 4.8 wt%. This amount of coke leads to decrease in the catalyst deactivation by 12.6% relative to the activity of regenerated catalyst.

Model Application
When R feed was converted, the yield of coke was 6.7 wt%. This stems from a high content of resins (4.1 wt%), which condense intensively to form the coke and crack so weakly under the catalytic cracking conditions. The conversion of such feedstock leads to a significant deactivation of the catalyst by coke and exceeds the regenerator coke burning ability for the unit under the study. The composition of R ensures an increase the degree of the catalyst deactivation by 26.0% relative to the initial value for regenerated catalyst. This reduced the yield of the gasoline and the wet gas by 3.0 and 3.9 wt% as well as increased the RON of gasoline by 3.5 units. In this case, the decrease of the slops consumption to the riser by 20 m 3 /h may improve activity loss negligibly by 4.6%.
Although R feed is inappropriate to convert in the catalytic cracking unit due to intensive formation of the coke on the catalyst, the co-processing of R and VD feeds is suitable to increase the yield light gasoil and the RON. Figure 7b compares the yields of products when the ratio of R:VD changes at the equal process variables. The ratio of R in the mixed feed may be less than 50% to decrease in coke yield (5.8 wt%) and prevent a significant catalyst deactivation. This feedstock leads to a rise in the yield of light gasoil by 1.7% and the RON of gasoline by 1.9 units in comparison with the VD feed. Given that the catalytic cracking gasoline is a part of the commercial petrol, the optimization of mixed  Model-based calculations showed that the cracking of VD provides a high yield of gasoline and C3-C4 gases (56.1 and 24.9 wt%) due to the high content of the saturates in its composition. The RON of the gasoline is 91 units and the coke yield was 4.8 wt%. This amount of coke leads to decrease in the catalyst deactivation by 12.6% relative to the activity of regenerated catalyst.
When R feed was converted, the yield of coke was 6.7 wt%. This stems from a high content of resins (4.1 wt%), which condense intensively to form the coke and crack so weakly under the catalytic cracking conditions. The conversion of such feedstock leads to a significant deactivation of the catalyst by coke and exceeds the regenerator coke burning ability for the unit under the study. The composition of R ensures an increase the degree of the catalyst deactivation by 26.0% relative to the initial value for regenerated catalyst. This reduced the yield of the gasoline and the wet gas by 3.0 and 3.9 wt% as well as increased the RON of gasoline by 3.5 units. In this case, the decrease of the slops consumption to the riser by 20 m 3 /h may improve activity loss negligibly by 4.6%.
Although R feed is inappropriate to convert in the catalytic cracking unit due to intensive formation of the coke on the catalyst, the co-processing of R and VD feeds is suitable to increase the yield light gasoil and the RON. Figure 7b compares the yields of products when the ratio of R:VD changes at the equal process variables. The ratio of R in the mixed feed may be less than 50% to decrease in coke yield (5.8 wt%) and prevent a significant catalyst deactivation. This feedstock leads to a rise in the yield of light gasoil by 1.7% and the RON of gasoline by 1.9 units in comparison with the VD feed. Given that the catalytic cracking gasoline is a part of the commercial petrol, the optimization of mixed feedstocks to increase the yield and RON of gasoline should correspond to the consumptions and properties of the other flows (riformates, isomerizates, etc.) [39].

Methods
In our research, we studied a typical vacuum gasoil catalytic cracking unit that consists of two interconnected units performing the continuous "reaction-regeneration" cycle for the circulated catalyst. The microspherical catalyst used in the unit contains Y-zeolite. The bulk density of the catalyst equals 872-877 kg/m 3 ; the pore volume is 0.419-0.423 sm 3 /g; and the catalyst activity is not less than 72-76%.
The target products produced by catalytic cracking are gasoline and fat gas. The gasoline after the stabilization represents a high-octane component of commercial gasoline (about 30 ÷ 40 wt%), while the fat gas becomes a feedstock for the gas fractionation unit and contains a high content of propane-propylene (PPF) and butane-butylene (BBF) fractions. The propane-propylene fraction is further used as a feedstock for propylene concentration, from which petrochemical products are obtained. The butane-butylene fraction performs as a feedstock for producing MTBE and alkylation units and is also a component of household gas and commercial gasoline. Depending on the market needs, the hydrocarbons composition of the feedstock and the operating variables for raising the yield of gasoline, light olefins, or light gas oil differ considerably.
To optimize the composition of the mixed feedstock taking into account the catalyst deactivation, we applied the strategy of system analysis and the method of mathematical modeling. This approach also included numerical studies and a group of physicochemical methods, such as liquid and gas chromatography, mass spectrometry, structural group analysis, etc. The results of gas chromatography, mass spectrometry, and structural group analysis can be found in [36,40].
The SAR content in the catalytic cracking feedstock, including the vacuum distillate (VD) and residues (R), was determined by the methods of liquid adsorption using ASKG silica gel (grain size of 0.2-0.5 mm) as a fixed phase. During the liquid adsorption chromatography, the sorbent in the column was treated with n-C 6 H 14 to remove the heat of wetting. The saturates and aromatics were eluted by n-C 6 H 14 and a mixture of C 6 H 6 and C 7 H 8 in the ratio of 6:1 for vacuum distillate and heavy gasoil, and 3:1 for light gasoil. The alcohol-benzene resins were isolated by a mixture of C 2 H 5 OH and C 6 H 6 in the ratio of 1:1. During the chromatographic separation, we measured the refractive index and carried out the formalin reaction, which allowed us to verify the absence of arenes in the saturated part of the feedstock.
After that, we conducted the experimental study of the spent and the regenerated catalysts, which facilitated the development of a model that also takes into consideration the effect of the catalyst deactivation on process efficiency. The acid properties of both catalysts were studied by the method of temperature-programmed desorption of ammonia (TPD) using the thermal desorption unit with programmed heating. Ammonia was adsorbed at 100 • C on a pre-trained sample and further desorbed from the zeolite surface in a linear heating mode at a rate of 10 K/min. The strength of the catalyst acid sites was estimated by the temperature maxima on the thermal desorption curve. The concentration of the acid sites was expressed in µmol per 1 g of the catalyst and determined by the amount of ammonia desorbed when fixing the desorption peaks. The quantity and structure of the coke on the spent and regenerated catalysts were determined experimentally by the TG-DSC method (thermogravimetric analysis and differential-scanning calorimetry) using NETZSCH STA 449 F3. This equipment captured the gravimetric analysis and registered mass changes and thermal effects that occurred with changing the temperature and time of heating. The catalysts were heated from 50 to 1000 • C at a rate of 10 deg/min in corundum crucibles in the air.
The above complex of experimental studies was further combined with the methods of quantum chemical modeling (DFT (B3LYP, basis 3-21G)) and methods of solving the inverse kinetic problem. DFT results allow evaluating the fundamental occurrence of reactions using Gibbs energy and take into account the heat effects of the reactions when the model has been developed. This approach allowed us to determine the thermodynamic and kinetic parameters of reactions accounting for the catalyst deactivation by coke. These parameters form the basis of the kinetic model. Figure 8 illustrates the major operating variables that we took into account during developing the model. inverse kinetic problem. DFT results allow evaluating the fundamental occurrence of reactions using Gibbs energy and take into account the heat effects of the reactions when the model has been developed. This approach allowed us to determine the thermodynamic and kinetic parameters of reactions accounting for the catalyst deactivation by coke. These parameters form the basis of the kinetic model. Figure 8 illustrates the major operating variables that we took into account during developing the model. Using the mathematical model, we predict how the SAR content in the VD feedstock and R feedstock influences the yield of products and the RON of the gasoline. Given that the conversion of feedstock is limited by the regenerator coke burning ability and degree of the catalyst deactivation, we were also able to optimize the composition of the mixed feedstock in order to increase the yield of gasoline, light olefins or light gasoil when VD and R were co-processed in a different ratio.

Conclusions
Currently, the study of the mechanism and the kinetic patterns of catalytic reactions in industrial conditions using the methods of the mathematical modeling represents both the major direction of fundamental research in the field of catalytic processes as well as an important scientific and practical task.
The problems of catalyst deactivation and optimization of the mixed feedstock become more relevant when vacuum distillate and residues are co-processed as catalytic cracking feedstocks in a various ratio. Given that the degree of the catalyst deactivation depends significantly on the operating variables and the SAR content in the feedstock, the latter should be optimized when the residues are involved in the catalytic cracking. This ensures both minimization of the catalyst deactivation by coke and the production of the required coke amount, since the feedstock conversion is limited by regenerator coke burning ability.
We developed the kinetic model of the catalytic cracking, which ensures its sensitivity to SAR content in the feedstock and predicts how the mixed feedstock composition influences the yield and composition of the product, the RON of the gasoline, and the coke content on the catalyst surface. The obtained experimental and numerical results of the catalytic cracking, including the feedstock, as well as the spent and the regenerated catalysts allow us to consider the catalyst deactivation by coke using the TPD results.
To improve the yields of desired products, we chose the suitable feedstock composition by changing the ratio of vacuum gasoil and residuals in the mixed feed. The vacuum gasoil should be converted to increase in the yields of the wet gas and the gasoline (56.1 Using the mathematical model, we predict how the SAR content in the VD feedstock and R feedstock influences the yield of products and the RON of the gasoline. Given that the conversion of feedstock is limited by the regenerator coke burning ability and degree of the catalyst deactivation, we were also able to optimize the composition of the mixed feedstock in order to increase the yield of gasoline, light olefins or light gasoil when VD and R were co-processed in a different ratio.

Conclusions
Currently, the study of the mechanism and the kinetic patterns of catalytic reactions in industrial conditions using the methods of the mathematical modeling represents both the major direction of fundamental research in the field of catalytic processes as well as an important scientific and practical task.
The problems of catalyst deactivation and optimization of the mixed feedstock become more relevant when vacuum distillate and residues are co-processed as catalytic cracking feedstocks in a various ratio. Given that the degree of the catalyst deactivation depends significantly on the operating variables and the SAR content in the feedstock, the latter should be optimized when the residues are involved in the catalytic cracking. This ensures both minimization of the catalyst deactivation by coke and the production of the required coke amount, since the feedstock conversion is limited by regenerator coke burning ability.
We developed the kinetic model of the catalytic cracking, which ensures its sensitivity to SAR content in the feedstock and predicts how the mixed feedstock composition influences the yield and composition of the product, the RON of the gasoline, and the coke content on the catalyst surface. The obtained experimental and numerical results of the catalytic cracking, including the feedstock, as well as the spent and the regenerated catalysts allow us to consider the catalyst deactivation by coke using the TPD results.
To improve the yields of desired products, we chose the suitable feedstock composition by changing the ratio of vacuum gasoil and residuals in the mixed feed. The vacuum gasoil should be converted to increase in the yields of the wet gas and the gasoline (56.1 and 24.9 wt%). The rise of the ratio of residues up to 50% leads to reducing the gasoline yield; however, this provides an increase in the amount of the RON of gasoline and the light gasoil by 1.9 units and 1.7 wt%. This stems from the high content of aromatics in the mixed feedstock. Although the residual feed, which contains of 40.1 and 4.1 wt% of aromatics and resins, increases the amount of light gasoil by 3.2%, this feedstock tends to produce more coke on the catalyst surface. Therefore, the catalyst is progressively deactivated by 26.0% relative to the activity of the regenerated catalyst. This leads to a reduction in the yield of gasoline and gas.
Since the conversion and capacity of the unit are limited by the regenerator coke burning ability, the ratio of the residue may be less than 50%. This prevents the catalyst decay and increases the yield of the target products. The feed, which contains about 30% of residuals, tends to the high yield and the RON of gasoline on the level of 55.2 and 92 units.
The use of the developed model allows us to increase the resource efficiency of the industrial catalytic cracking units by prediction and optimization of the mixed feedstock depending on the desired products. In addition, the model has a high predictive ability of the operating variables such as the temperature and consumption of the feedstock and re-generated catalyst, as well as its activity. The developed model at TPU has a high adaptability to various technological challenges of oil refineries.