LA-UR-21-22814 (Accepted Manuscript)

Mathematical Modeling of Liquid-Phase Alkylation of Benzene with

Ethylene Considering the Process Unsteadiness

Khlebnikova, Elena
Ivashkina, Elena
Dolganova, Irena
Dolganov, Igor
Khroyan, Lilit A.

Provided by the author(s) and the Los Alamos National Laboratory (2021-05-18).

To be published in: Industrial & Engineering Chemistry Research

DOI to publisher's version: 10.1021/acs.iecr.0c02660

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 pubs.acs.org/IECR Research Note

Mathematical Modeling of Liquid-Phase Alkylation of Benzene with

Ethylene Considering the Process Unsteadiness
Elena Ivashkina, Elena Khlebnikova, Irena Dolganova,* Igor Dolganov, and Lilit A. Khroyan
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ABSTRACT: Ethylbenzene is a key intermediate in the manufacture of styrene that is an

important industrial monomer. Ethylbenzene is produced by benzene alkylation using either
gas-phase or liquid-phase methods. The liquid-phase alkylation that uses liquid acidic
catalysts needs to be improved. We develop a mathematical model for the liquid-phase
benzene alkylation. The reaction scheme, designed with a due analysis of desired and side
Downloaded via Irena Dolganova on July 28, 2020 at 17:10:46 (UTC).

reactions, and with the analysis of the formation of deactivating agents, reflects, in particular,
the influence of the concentration of heavy hydrocarbons on the catalyst activity. The
account of the catalyst deactivation by heavy alkylaromatics allows predictions of the
temporal changes in the outputs of the alkylation process. In particular, the decrease of the
ethylbenzene concentration by 2−3 wt % and increase of the polyalkylate outlet
concentration by 1.5−2 wt % are the results of the catalyst deactivation. These effects,
however, can be compensated by 1.3-time increase of polyalkylate supply and by the
temperature increase up to 398 K. The calculations also show that it is possible to decrease
the supply of fresh catalyst from 0.498 to 0.472 t/hour without loss in the yield of
ethylbenzene.

1. INTRODUCTION Nevertheless, despite the fact that zeolite-based alkylation

In the chemical industry the alkylation of aromatic hydro- technologies are widespread, many refineries, especially in
carbons with alkenes is usually used for the production of Russia and China, still use the liquid acidic catalysts.16,34 This
different intermediate products1−3 that are required for the process possesses sufficient acidity to catalyze transalkylation
manufacture of textiles, plastics, detergents, etc.4,5 For instance, of diethylbenzenes or diisopropyl benzenes with benzene, and
ethylbenzene is largely used for the production of styrene.6−8 thus increases the selectivity to monoalkyl benzenes. Along
Since the 1930s ethylbenzene production was dominated by with this, the large scientific field on modeling and optimizing
the liquid-phase aluminum chloride (AlCl3) processes.9 Since the AlCl3-catalyzed benzene alkylation process remains
the moment chloroaluminate ionic liquid was found to be a undiscovered. This field includes finding ways to make the
highly active alkylation catalyst that could easily be separated liquid-acid alkylation more friendly to the environment and to
from reactants, it attracted considerable attention, and increase the process selectivity and the product yield. Contrary
numerous research papers and patents were published10−13 to a vast number of studies of the zeolite-based alkylation, the
that, in particular, studied the reaction mechanism in all detail. modeling of the liquid acid-catalyzed units remains rather
Acids such as AlCl3 and solid phosphoric acid were the only limited. In particular, all current mathematical models only
catalysts employed in aromatic alkylation technology units describe steady processes, with no account for the catalyst
until the 1980s. The discovery of medium- and large-pore deactivation. The catalyst activity, however, determines the
zeolites possessing acid sites of strong and medium strength, product yield and the product quality, and thus the inclusion of
bound to the zeolite framework inside the pores, has opened a the changes of the catalytic activity into a model can
new era of technologies for the alkylation of aromatics, and significantly improve its forecasting capabilities. Previously,
reactions of alkyl aromatics in general.14−17 Numerous we studied the feasibility of reconstruction of mixing devices
scientific publications appeared on the ways to improve and with the aim to intensify the mixing of reactants during the
examine various aspects of zeolite-based manufacture of
ethylbenzene,1,18−27 suggesting a novel industrial process for
highly selective ethylbenzene production,25,28 avoiding catalyst Received: May 28, 2020
deactivation,29 and an approach to reduce the energy Revised: July 23, 2020
consumption.30 There are also reports on transalkylation or Accepted: July 26, 2020
disproportion reactions occurring simultaneously with alkyla- Published: July 26, 2020
tion.14,31 There are several mathematical models developed for
the description of the operation of alkylation reactors.31−33

© XXXX American Chemical Society https://dx.doi.org/10.1021/acs.iecr.0c02660

A Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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AlCl3 alkylation,35 without modeling of the actual alkylation and mass balances, applying the model of ideal blending.
process. Now we focus on improving the performance of the Namely, for the ith component, the equations of material and
alkylation reactor developing a model that takes into account heat balances (for adiabatic mode) read,
the catalyst deactivation,36 as discussed in refs 36−39.
dCi
V = u(Ci ,0 −Ci) + ∑ (±Wi ) (1)
2. METHODOLOGY dt
2.1. Alkylation Reactor. The alkylator is a hollow Cpmix N
dT
columned-type chemical reactor with a sparger (Figure 1). Cpmix = (Tin − T ) + ∑ (−ΔHj)Wj
dt τ j=1 (2)
The change of Gibbs energy was estimated to evaluate the
desired conditions for the chemical reactions. The calculations
were performed with the use of Gaussian 98 software package.
The molecule structures were optimized by the standard PM3
semi-empirical molecular orbital method.40
2.3. Experimental Determination of the Activation
Energies. To determine of the activation energies, the
alkylation of benzene with ethylene was conducted in the
liquid phase using the laboratory rig that is shown in Figure 2.

Figure 1. Alkylation reactor: I, ethylene; II, circulating PABs; III,

benzene-condensate; IV, circulating catalytic complex; V, fresh
catalytic complex; VI, dried benzene; VII, alkylate; VIII, vapors.

Gaseous ethylene is mixed with benzene and catalyst complex

in an external mixing chamber. The alkylation is typically
carried out under the following temperature and pressure:
383−408 K and 0.05−0.3 MPa. The optimal weight ratio for
benzene/ethylene is (8−14)/1. The standard technological
parameters of the alkylation reactor are summarized in Table 1,
and the range of the product flow composition is presented in Figure 2. Laboratory unit for alkylation of benzene with ethylene: 1,
Table 2. cylinder with ethylene; 2, Tishchenko bottle; 3, reactor; 4, heating
furnace; 5, reflux condenser; 6, electromotor; 7, three-way cock; 8,
gasometer; 9, tap; 10, outlet tube with tap.
Table 1. Standard Technological Mode of the Alkylation
Reactor
technological parameters units values
The alkylation process usually involves several stages:
1. dried benzene and polyalkylate flow rate tones/sec 7.0−22.0 • dissolution of aluminum chloride in benzene in the
2. ethylene flow rate tones/sec 0.7−2.2 reactor
3. fresh catalyst flow rate tones/sec 0.3−1.0 • intensive mixing and furnace heating of the liquid raw
4. pressure in the reactor MPa 0.05−0.30 materials to the process temperature
5. benzene to ethylene molar ratio (4−7) ÷1 • feeding ethylene from the cylinder to the reactor
6. reactor bottom temperature K 338−403 The alkylation is typically carried out at a temperature of
333−353 K and under atmospheric pressure. In the measure-
Table 2. Alkylation Product Flow Composition ments, the alkylation of benzene with ethylene was studied at
two temperatures: 346 and 353 K. The amount of supplied
component concentration, wt %
benzene was 80−90 g; the amount of catalyst is 0.1 g per 1 g of
benzene 52.5−62.0 benzene; the ethylene feed rate is 22.4 mol/L, and the
ethylbenzene 26.0−33.6 alkylation time is 1−1.5 h. The product was sampled every 15
diethylbenzene 2.8−5.9 min during 1 h. The selected samples were dried with calcium
branched propylbenzene 0.2−0.3 chloride and examined using gas−liquid chromatography.
ethyltoluene 2.0−2.9 The aim of this part of the work was to understand the
sec-butylbenzene 0.7−1.3 kinetics of the AlCl3-catalyzed benzene alkylation. The
toluene 2.1−3.2 chemical interaction of benzene and ethylene occurs on the
heavy alkylaromatics (resin) ≤2.0 surface of the powdered catalyst that is dispersed in the liquid.
Thus, only a small portion of ethylene that is dissolved in the
2.2. Mathematical Model. The developed mathematical liquid phase takes part in the reaction. The concentration of
model for the alkylation flow reactor is based on the energy ethylene in the solution is determined by the temperature and
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gas pressure. Owing to gas bubbling and intensive mixing of Thus, the deviations of calculated values of thermodynamic
the reactants throughout the reaction volume, it was assumed parameters from their theoretical values are less than 1%,
that the concentration of the dissolved gas remains nearly which means the calculated data are sufficiently reliable, and
constant during the experiment. Consequently, the changes in can be used for development of the reaction scheme of the
the reaction rates during the experiment are assumed to be alkylation process.
solely determined by the variation of the inlet concentrations The generalized reaction network of the alkylation process is
of liquid components. presented in Figure 3.
To simplify the kinetic analysis of the reactions in the
process, it was assumed that the process occurs in two
irreversible stages: conversion of benzene to ethylbenzene and
conversion of ethylbenzene to di-, triethylbenzenes. The
reaction constants for the first and second reactions are
denoted by k1 and k2, respectively.
Consequently, the measurements of the time of benzene half
conversion and of the time of the maximum yield of
ethylbenzene allow us to determine the rate constants of the
first and second reaction stages.
The dependence of the reaction rate on temperature is
described by the Arrhenius equation.41,42 Thus, if the reaction
rate constants are known at least at two process temperatures, Figure 3. Reaction network of the alkylation process
the activation energy of the reaction of alkylation of benzene
with ethylene can be calculated from the following equation: In our kinetic model, we considered all the presented
ij k yz
lnjjj 1 zzz
reactions.

jk z
2.303RTT
k 2{
Ea = 1 2 3.2. Kinetic Parameters of the Mathematical Model.
T1 − T2 (3) To describe the mechanism of the alkylation process that
involves more than two reaction stages one needs to solve the
In experiments carried out using gas chromatography−mass system of coupled differential equations of chemical kinetics,
spectrometry analysis, the composition of each of the samples which is solved numerically.
was determined. The Arrhenius plot for the reaction of By the experiment (subsection 2.3), activation energies of
benzene alkylation with ethylene is presented in Figure S1. the reactions were evaluated. Owing to a number of factors, it
The samples analysis was performed according to the is not possible to fully reproduce the settings of the industrial
methods used by analytical laboratories of petrochemical process in the laboratory: for example, there is no circulating
enterprises, and meeting the ASTM standard. catalyst, there is no flow of polyalkylbenzenes, the process
According to the obtained data, the dependences “molar temperature under laboratory conditions is lower than the
composition−reaction time” are obtained. process temperature in the industrial reactor (up to 353 K).
Further, the constants of first and second reactions were Consequently, it was not possible to obtain a similar product
determined. The constant k1 is associated with the half- composition under laboratory conditions, and to estimate the
transformation time of benzene and at a process temperature activation energies of other reactions of the process, the
of 73 °C is equal to k11 = 0.0154 min−1, at temperature of 80 quantum-chemical calculations with the Gaussian method of
°C k12 = 0.0231 min−1. PM3 were fulfilled. Parametric Method 3 (PM3) is a
The rate constants of the product B−ethylbenzene were semiempirical method for the quantum calculation of
determined as follows: several k2 values close to k1 values were molecular electronic structure in computational chemistry. It
chosen and then tmax values were determined by eq 5. is based on the Neglect of Differential Diatomic Overlap
According to obtained data for tmax = 60 min k21 = 0.02675 integral approximation. This method uses a Hamiltonian that is
min−1, and for tmax = 40 min k22 = 0.01880 min−1. very similar to the AM1 Hamiltonian but the parametrization
As a result of found rate constants k1 and k2 reaction stages, strategy is different. Different parametrization, and slightly
the following values of the activation energies were different treatment of nuclear repulsion allow PM3 to treat
determined, Ea1 = 135.5 kJ/mol and Ea2 = 131.9 kJ/mol. hydrogen bonds rather well but it amplifies nonphysical
hydrogen−hydrogen attractions in other cases. The accuracy of
thermochemical predictions with PM3 is slightly better than
3. RESULTS AND DISCUSSION that of AM1. The PM3 model has been widely used for a rapid
3.1. Mathematical Model of Alkylation of Benzene estimation of molecular properties and has been recently
with Ethylene. Results of thermodynamic analysis and extended to include many elements, including some transition
process reaction network metals. For these reasons, the PM3 method was supposed to
Table S1 illustrates the results of the thermodynamic be applicable in the calculations to be performed.
analysis of the alkylation process that are obtained with the As a result of our numerical studies, the thermodynamic and
approach outlined above. kinetic parameters of the process of alkylation of benzene with
The presented results are in good agreement with literature ethylene in the presence of aluminum chloride were
data. For instance, for the reactions of formation of determined. The kinetic parameters (pre-exponential factors
ethylbenzene (no. 1) and diethylbenzene (no. 2), the literature and activation energies) of the process reactions are
values of ΔH are −113 kJ/mol and −112.17 kJ/mol, summarized in Table S2.
respectively. For the transalkylation reaction (no. 3), the The kinetic parameters of the reactions, that were
value reported in the literature is −1.64 kJ/mol.41−43 determined with the help of quantum chemistry methods,
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were validated by using the monitoring data collected at an change of the catalyst activity quantitatively. The mathematical
operating industrial installation. The so-obtained pre-exponen- modeling is the only way to consider the heavy alkylaromatics
tial factor in the Arrhenius equation and activation energies for concentration and its influence on the catalyst activity.
all the reactions were used for the solution of the inverse All acid catalysts are active due to their ability to create
kinetic problem. carbon ions from one or more of the reactants under the
To solve the inverse kinetic problem, the experimental reaction conditions. The activity of the catalyst is reduced by
values of the concentrations of all reactants at the inlet and when the catalyst adsorbs organic high-molecular-weight
outlet of the alkylator were used, and the kinetic parameters alkylaromatic compounds. The acid soluble oils (ASOs) are
(Table 3) were matched so to provide the minimal deviation traditionally supposed to reduce the activity of liquid
between calculated and experimental data. catalysts.43,44 It was determined by UV spectroscopy that the
ASOs and their complexes with the catalyst are practically
Table 3. Final Values of the Reaction Rate Constants (393 absent from the hydrocarbon phase.43 The ASOs seem to have
K, 0.1 MPa)
the structure of polycyclic aromatic hydrocarbons with one or
reaction rate more unsaturated hydrocarbon chains.44
constant, k, m3· Under the conditions of petrochemical production, which
no. reaction kmol−1·sec−1
uses a complex compound based on aluminum chloride as a
1 C6H6 + CH2CH2 → C6H5−C2H5 1.6 × 10−3
catalyst, the specific electrical conductivity of a catalyst
2 C6H6 + 2CH2CH2 → C6H4−(C2H5)2 3.3 × 10−4
3 C6H6 + C6H4−(C2H5)2 → 2C6H5−(C2H5) 1.4 × 10−4
characterizes its activity, which depends on the number of
4 2CH2CH2 → CH2CH−CH2−CH3 2.9 × 10−4 AlCl4− ions per unit volume (concentration) of the catalyst,
5 C6H6 + CH2CH−CH2−CH3 → C6H5−CH− 3.6 × 10−3 their movement speed, and the charge transferred by each ion.
(CH3)−CH2−CH3 In this work, the actual values of the electrical conductivity
6 C6H6 + CH2CH−C6H6 + CH2CH−CH3 → 1.8 × 10−1 of the catalyst were normalized to the range from 0 to 1. Thus,
C6H5−CH3−(CH)−CH3CH3 → C6H5−CH3−
(CH)−CH3 the activity of the fresh catalyst varies in the range from 0.27 to
7 CH2CH2 + C6H5−CH3 → C2H5−C6H4−CH3 4.9 × 10−3 1.00, and the activity of the circulating catalyst from 0.02 to
8 2C6H6 + CH2CH2 → 2C6H5−CH3 1.5 × 10−5 0.48.
9 2CH2CH2 + C6H5−CH3 → C6H5−C2H5 + 9.1 × 10−4 Modeling of the catalyst deactivation is based on the
CH2CH−CH3 exponential law that was previously shown to be capable of
10 C6H4−(C2H5)2 + CH2CH2 → C6H3−(C2H5)3 1.2 × 10−3 accurately predicting the changes of the parameters of the
process due to decrease in the catalyst activity.37 Namely, we
set that the catalyst activity to be inversely proportional to the
It was found that the rate of the desired reaction of
concentration of the deactivating agent:
ethylbenzene synthesis (3.72 × 10−2 kmol·m−3·sec−1) at 393 K
and 0.1 MPa at the moment of benzene half conversion
A = A f e−αCASO
prevails over the side reactions: (0.01−2.10) × 10−2 kmol·m−3· (4)
sec−1. The determined values of the kinetic parameters were
used for a mathematical model of the AlCl3-catalyzed benzene Initial conditions: CASO = 0; Af = 1.
with ethylene alkylation. After a large array of industrial data processing it was found
3.3. Development of the Mathematical Model for that the circulating catalyst activity is strongly determined by
Unsteady Processes. In industry, it is frequently observed the flow rate of the fresh catalyst, and the overall result
that catalyst activity varies with time. In the laboratory depends on the circulating catalyst flow rate and both fresh and
measurements, however, it was impossible to estimate the circulating catalyst activities (Figure 4).

Figure 4. Dependence of circulating catalyst activity on the fresh catalyst flow rate.

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Figure 5. Dependence of activity of the recycled catalyst on the concentration of polyalkylbenzenes and high-molecular alkylaromatics at the outlet
from the reactor (experimental data).

The activity of the circulating catalyst depends on the The Ac parameter in the mathematical model reflects the
amount of polyalkylbenzenes and high molecular alkylaro- changes in the catalyst activity by heavy hydrocarbons. These
matics formed, as presented in Figure 5. changes make the alkylation process time-dependent.
Thus, in order to assess the temporal variations of the To solve the differential equations, the fourth order Runge−
process of industrial alkylation, the relative activity of the Kutta method was used. The kinetic parameters of the
circulating catalyst complex is numerically expressed as follows: reactions were corrected using the available experimental
ij 24.291A f Q yz
Ac = 0.0537 expjjjj cz
zz
data on the reactor output streams using the MATLAB

z
optimization random search method.
k {
Q 3.4. Optimization of the Fresh Catalyst Flow Rate. A
c (5)
combination of the developed model with our earlier
As a result, the mathematical model that takes into account the hydrodynamic study,33 makes it possible to provide a detailed
catalyst deactivation can be written as follows: insight into the process of industrial alkylation, and thus we are

|
o
o
able to suggest the ways to optimize the process.
o
o
o
For instance, the fresh catalyst flow rate varies from 0.498 to
o
o
dC benzene u
o
o
= (C benzene − Cbenzene ,0) + Ac (− W1 − W2 − W3
o
o
0.398 t/hour with benzene/ethylene molar ratio of 5/1 mol/
o
dt V
o
o
mol at a temperature of 121 °C. The questions to be answered
o
o
+ W −3 − W5 + W −5 − W6 − 2W8)
o
o
o
were whether the flow rate of the fresh catalyst to the reactor
o
o
o
o
dCEB u
o
can be decreased, and how to determine the optimal flow rate
o
o
= (C EB − C EB,0) + Ac (W1 + 2W3 + W9 − 2W −3)
o
o
of the fresh catalyst. By the optimal flow rate of the fresh
o
dt V

o
o
o
o
catalyst we define such a flow rate that results in the highest
o
dCdiEB u
o
o
o
= ( C C A
diEB − diEB,0 + c
) (W 2 − W W
3 − 10 + W )
o
−3

o
concentration of desired product, but at the same time the

= (C toluene − C toluene,0) + Ac (− W7 + 2W8 − W9) o

dt V
o
o
o
outlet concentration of polyalkylate should stay below 12 wt %
o
o
dC toluene u
o
o
o
and the concentration of high-molecular aromatics should stay
o
o
o
dt V

= (Cethylene − Cethylene,0) + Ac (− W1 − 2W2 − 2W4 o

below 2.5 wt %. To solve this problem, the developed
o
o
o
o
dCethylene
o
u mathematical model was used to understand the influence of
o
o
o
o
the flow rate of the fresh catalyst on the overall activity of the
o
dt V
o
}
o
+ W7 − W8 − 2W9 − W10) alkylation catalyst and on the yield of reaction products.
o
o
o
Thus, before the optimization, the fresh catalyst flow rate
o
o
o
o
dC propylene
o
u
o
was 0.498 t/hour. The model calculations show that a decrease
o
= (C propylene − C propylene,0) − W6 + W9)
o
o
of the fresh catalyst flow rate up to 0.448 t/hour results in a
o
dt V

= (C butylene − C butylene,0) + W4 − W5 + W −5) o o

o
o
o
dC butylene decrease of the desired product concentration (from 29.3 to
o
u
o
o
o
o
26.5 wt %) and increase of the polyalkylate outlet
o
o
dt V
o
o
concentration (from 6.9 to 8.8 wt %). However, owing to
o
o
o
dC IPB u
o
o
acceleration of the transalkylation reaction, these effects can be
o
= (C IPB − C IPB,0) + Ac W6
o
o
o
dt V
o
compensated by increasing the polyalkylate supply to the
o
o
o
o
dCsec BB reactor (by 1.3 times) and by increasing the process
o
u

o
o
= (Csec BB − Csec BB,0) + Ac (W5 − W −5)
o
o
temperature up to 398 K. These measures make it possible
o
dt V
o
o
o
to maintain the ethylbenzene concentration of 29.8 wt % with
o
o
dCethyltoluene
o
u
o
the fresh catalyst flow rate of 0.472 tones/hour.
o
o
= (Cethyltoluene − Cethyltoluene,0) + Ac W7
o
o
o
dt V

o
o
o
~
dC TEB u 4. CONCLUSIONS
= (C TEB − C TEB,0) + Ac W10
dt V
In this study, the mathematical model of AlCl3-catalyzed
(6)
alkylation of benzene with ethylene was developed. The major
This set of differential equations needs to be supplemented by advantage of the developed model is that it considers the
the initial conditions: t = 0, Ci(0) = Ci,0, where i denotes the catalyst deactivation by heavy alkylaromatics, so the model is
corresponding hydrocarbon. capable of describing the temporal changes in the alkylation
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■
pubs.acs.org/IECR Research Note

process. This, in particular, allows using the model for NOMENCLATURE

understanding how the concentration of the deactivating
agents influences the catalyst activity. This finding is used to Abbreviations
recommend the optimal regimes with the lowest flow rates of ASO = acid soluble oils
the fresh catalyst. EB = ethylbenzene
The problem of decreasing the flow rate of the fresh catalyst diEB = diethylbenzene
without decreasing the concentration of ethylbenzene was also IPB = isopropylbenzene
solved. It turned out to be possible to maintain the highest secBB = secondary buthylbenzene
concentration of ethylbenzene at the level of 29.8 wt % with PAB = polyalkylbenzene
the fresh catalyst flow rate of 0.472 t/hour (in contrast to TEB = triethylbenzenes
initial value of 0.498 tones/hour). The expected decrease in Variables
the desired product yield is compensated by the polyalkylate A = catalyst activity
increasing at the reactor (by 1.3 times) and the process Ac = relative activity of the circulating catalyst
temperature increasing up to 398 K as this mode favors Af = relative activity of the fresh catalyst
transalkylation. Ci = outlet concentration of the ith component (mol m−3)
It is necessary to highlight that the problem of catalyst Ci.0 = inlet concentration of the ith component (mol m−3)
deactivation is equally important for both liquid and zeolite Cpmix = molar heat capacity of the reaction mixture (J mol−1
catalysts. The developed mathematical model gives an initial K−1)
approach to understand and to improve all types of alkylation E = activation energy (kJ mol−1)
reactors. In future research, the mathematical model will be k0 = preexponential coefficient
applied for more specific recommendations for optimization of k1 = reaction rate constants for the first reaction (m3 kmol−1
technological modes of the alkylation process. s−1)

■
*
ASSOCIATED CONTENT
sı Supporting Information
k2 = reaction rate constants for the second reaction (m3
kmol−1 s−1)
ki′ = reaction rate constant of the first order (sec−1)
The Supporting Information is available free of charge at Qc = experimental flow rate of the circulating catalyst (tones
https://pubs.acs.org/doi/10.1021/acs.iecr.0c02660. sec−1)
Qf = experimental flow rate of fresh catalyst (tones sec−1)
Arrhenius plot for reaction of benzene alkylation with T = process temperature (K)
ethylene (Figure S1); Thermodynamic characteristics of Tin = inlet reactor temperature (K)
benzene alkylation process (393 K, 0.1 MPa) (Table t1/2 = time of benzene half conversion (sec)
S1); Kinetic parameters of the alkylation process (393 K, tmax = time of maximum yield of ethylbenzene (sec)
0.1 MPa) (Table S2) (PDF) u = volumetric flow rate through the reactor (m3 s−1)

■
V = the apparatus volume (m3)
Wi = reaction rate (sec−1)
AUTHOR INFORMATION
ΔHj = heat effect of the jth reaction (J mol−1)
Corresponding Author ΔGj = change of the Gibbs energy in the jth reaction (J
Irena Dolganova − Division for Chemical Engineering, National mol−1)
Research Tomsk Polytechnic University, Tomsk 634050, τ = residence time (sec)

■
Russia; orcid.org/0000-0002-8536-0501;
Email: dolganovaio@tpu.ru REFERENCES
Authors (1) Corma, A.; Martínez-Soria, V.; Schnoeveld, E. Alkylation of
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