Modeling of Catalyst Deactivation in Bioethanol Dehydration Reactor

Subscriber access provided by UNIV OF NEW ENGLAND ARMIDALE

Kinetics, Catalysis, and Reaction Engineering

Modeling of Catalyst Deactivation in Bioethanol Dehydration Reactor Rafael Brandão Demuner, Jeiveison Gobério Soares Santos Maia, Argimiro Resende Secchi, Príamo Albuquerque Melo, Roberto Werneck do Carmo, and Gabriel S Gusmao Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05699 • Publication Date (Web): 05 Feb 2019 Downloaded from http://pubs.acs.org on February 11, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

Modeling of Catalyst Deactivation in Bioethanol Dehydration Reactor Rafael Brandão Demuner,† Jeiveison Gobério Soares Santos Maia,† Argimiro Resende Secchi,∗,† Príamo Albuquerque Melo,† Roberto Werneck do Carmo,‡ and Gabriel Sabença Gusmão‡ †Chemical Engineering Program, Universidade Federal do Rio de Janeiro, P.O. box 68502, Zip code 21941-972 - Rio de Janeiro, RJ, Brazil ‡Braskem, Renewable Chemicals Research Center, 13086-530 - Campinas, SP, Brazil E-mail: [email protected]

Abstract Catalytic ethanol dehydration route is a reality for the production of polyethylene from renewable sources. Ethanol dehydration process is carried out in the presence of acid catalysts, under temperatures ranging from 500 to 800K, obtaining ethylene selectivity ranging from 95 to 99% and ethanol conversion greater than 98%. Despite the favorable values of conversion and selectivity, catalyst deactivation by coking is a well-known phenomenon that occurs in this process.

This phenomenon leads to

catalyst regeneration cycles, being the catalyst’s life cycle dependent on process operating conditions. Thus, obtaining a mathematical model to optimize the ethanol dehydration process is of great interest to industry, allowing process optimization and optimal design of reactors.

This work presents a phenomenological model of an

ethanol dehydration fixed-bed reactor considering the catalyst deactivation and several chemical species. The developed mathematical model for catalyst deactivation

1

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 34

considers species present in the reaction system as coke precursors. The predictive ability of the model, which has been validated with industrial plant data, are shown in the results, presenting deviations of the reactor temperature profile below 5%.

1

Introduction

There is a growing demand for ethylene, mainly for the plastic production. This monomer is produced worldwide mainly through steam cracker process, which uses naphtha and natural gas fractions (e.g., ethane, propane and butane) as feedstock. This process is energy intensive and has yields around 55% and high emissions of CO2 1 . Alternative routes for petrochemical feedstock production have been studied in order to seek more energy efficient and sustainable routes, with greater selectivity to ethylene and, especially, with lower greenhouse gas emissions. The ethane oxidative dehydrogenation is an alternative route for ethylene production, which operates at lower temperature when compared to steam cracker process, but leads to the formation of many byproducts. The ethanol selective oxidation is another option for ethylene production 2 .

However, the

vanadium-based catalyst used in this process is rapidly deactivated, increasing operating costs for catalyst regeneration or replacement 1 . Residual biomass utilization is a possibility to obtain plastics, especially those derived from ethylene, reducing emissions of greenhouse gases, as well as being a way to meet the growing demand for plastic 3 . The ethylene production by ethanol catalytic dehydration appears to be an important alternative route, since ethanol can be obtained from renewable sources such as biomass, which is a reality, particularly in Brazil, which is leading in ethanol production from sugarcane and is in second place as world’s largest producer 4 . The ethanol dehydration generally occurs under acid catalysis, typically alumina or silicaalumina, at temperatures ranging from 500K to 800K, pressures from 1 to 10 atm, and ethanol feed mass fraction around 0.95. Typical ethylene selectivity are in the range of 95 to 99% (mol basis), with ethanol conversion over 98% 5 . Other catalysts have been proposed 2


Page 3 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


for this reaction to achieve different combinations of selectivity and conversion, for instance heteropolyacids 6 . An intrinsic phenomenon of the process is the deactivation of the catalyst, which occurs essentially due to the formation of coke. Consequently, to restore the process performance, the regeneration of the catalyst in certain periods of time is demanded, whose frequency and intensity are dependent on the operating conditions in which the process was submitted throughout the campaign. Therefore, the campaign time of the catalyst present in the industrial reactor is a function of the kinetics of deactivation. The main challenge is to find the operating conditions that optimize the production of ethylene while attenuating the catalytic deactivation phenomenon. Despite this importance for industrial reactors, the deactivation is not frequently studied in the area of process modeling and simulation. Gayubo et al. 7 studied the ethanol dehydration on HZSM-5 catalyst, considering two main deactivation routes: coke deposition and catalyst dealumination due to water presence, this last one more likely for zeolite catalysts. Besides this negative effect, the water content contributes for reducing coke formation by inhibiting coke growing reactions 8 . The model developed by Gayubo et al. 7 considered that ethylene was the main coke precursor, besides gasoline and olefin lumps presented in reaction medium. Gayubo et al. 8 also studied ethanol dehydration on HZSM-5 doped with 1 wt% Ni. On the same way, it was found that ethylene in the reaction medium was the coking precursor, mainly due to coke formation by ethylene oligomerization towards compounds that remain trapped in HZSM-5 zeolite channels. Other processes for obtaining olefins using alcohols as feedstock also lead to the catalyst deactivation, for instance, Methanol to Olefin (MTO). The MTO process is performed with SAPO-34 catalyst, although it was originally studied using HZSM-5 zeolites. Among the similarities, it is important to highlight: the temperature in the MTO process is around 650K and water is co-fed in both processes. However, the main objective of the MTO process is to obtain propene and butene, but not ethylene 9,10 .

3



Page 4 of 34

Marchi and Froment 9 studied the catalytic methanol conversion to olefins in SAPO-11 and SAPO-34 catalysts. The authors verified that water has an attenuating effect on the coke formation rate, as it competes with the oxygenated compounds and hydrocarbons for active sites. The reduction of silica/alumina ratio also contributes to the reduction of coke formation rate. The authors associated catalyst deactivation with coke formation, which is derived from the adsorption of oligomers and alkenes, to the active sites located in the catalyst pores. Additionally, coke molecules were identified as aromatic structures which block the catalyst pores. Chen et al. 11 studied the deactivation of SAPO-34 in the MTO process. For the purpose of identification of catalyst deactivation precursor, methanol, dimethyl ether and propene were used as reagents. It is important to say that dimethyl ether was tested because it is an important intermediate in the MTO reaction mechanism. Besides, propene was used to evaluate the effect of olefins on catalyst deactivation. The authors verified that coke formation rates for methanol and dimethyl ether are higher when compared to coke formation rate when propene is used as a reagent, showing the low reactivity of the olefins, and that the coke would be originating mainly from the oxygenated compounds in the medium. Chen et al. 12 studied the SAPO-34 catalyst deactivation in a MTO fixed-bed reactor in order to obtain the deactivation mechanism. The spatial time, methanol partial pressure and temperature were utilized as variables in the experimental design. The authors verified that the higher the temperature, the higher the coke deposition. Also, it was verified that coke deposition increases for higher amounts of methanol fed in the reactor per mass of catalyst, which suggests that methanol is the precursor of the deactivation. Schulz 13 studied the deactivation of the HZSM-5 catalyst in a MTO fixed-bed reactor, evidencing differences in the mechanism of deactivation as function of the temperature range.

For temperatures ranging from 540K to 570K, the compounds retained in the

catalyst were identified as ethylbenzene and isopropylbenzene, which are derived from aromatic ring alkylation reactions with ethylene and propene.

4


At temperatures above

Page 5 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


750K, methanol plays a key role, replacing the aromatic ring with methyl radicals. Photographs of the HZSM-5 after tests at low and high temperature were taken. The low-temperature deactivated catalyst had a yellow color that changed to pink when exposed to air, which characterizes highly unsaturated compounds. For high temperature (750K), the catalyst bed had a black zone at the beginning of the bed, an intermediate gray zone and a slightly blue zone in sequence. The authors related different color zones with different coke products. At the beginning of the bed, the black color represents a heavier coke structure, which covers the catalyst. The gray color region is the conversion zone of methanol.

The blue region represents the coke formed from olefins, since the

methanol is almost fully converted in the gray reaction zone, unavailable to react with the coke from the olefins. Bleken et al. 10 performed the comparison of two HZSM-5 catalysts, one commercial and the other desilicated, named DZSM-5. These catalysts were tested in the MTO process in a fixed-bed reactor. After 160h, the catalytic bed was divided into fractions related to sections along the axis, in order to evaluate the characteristics of deposited coke and the coke deposition tendency along the catalyst bed. TGA analyzes showed that the commercial catalyst presented mass loss of 10% in the initial fraction of the bed, while the loss of mass in the lower fractions of the bed was less than 1%. For the DZSM-5 catalyst, the same loss of mass was obtained for all fractions of the bed, being approximately 4.6%. After the 160h catalyst tests, the catalyst fractions were subjected to new tests in order to verify its residual activity. For the commercial catalyst, all the fractions presented conversions values lower than those obtained with fresh catalyst, thus characterizing deactivation along the catalyst bed. However, the initial catalyst bed fractions presented the lowest conversion, being the most deactivated. The same test for the DZSM-5 catalyst showed a conversion profile which decreases as the catalytic bed progresses. Catalyst deactivation is a well-known phenomenon for the ethanol dehydration process 8,14 but there is a lack of works describing the catalyst deactivation for this process in industrial

5



scale. Therefore, the main focus of the present work is the deactivation modeling in the reaction section of the catalytic ethanol dehydration process. The modeling is divided in three main steps, namely: the kinetic model, which contains the kinetic routes and the chemical reactions considered; the reactor model, including mass, energy and momentum conservation equations, and the deactivation model, including the effect of temperature and coke precursor concentration to the catalyst activity loss. The dynamic mathematical model was validated with experimental data from an industrial-scale reactor.

2

Process Modeling

The catalytic ethanol dehydration process studied in the present work is described in Figure 1. A hydrous ethanol feed stream in liquid phase is evaporated and the vapor phase is mixed with a water vapor stream. The gas mixture passes through a furnace, in order to obtain the energetic level sufficient for the reaction occurrence, typically 500-700 K 14 , since the process is globally endothermic. The furnace outlet stream flows through a packed-bed catalytic reactor, where an extensive number of chemical reactions occur, being ethylene and water the major components in the reactor outlet stream, named raw ethylene. This stream is sent to a downstream process, in order to meet the specification for polymer-grade ethylene, which is finally used as raw material for green polyethylene production in polymerization plants. In this section, the mathematical model is described for a dynamic simulation of a fixed-bed reactor, operating adiabatically.

The most relevant simplifying assumptions

adopted for developing the model are the following: one-dimensional, pseudo-homogeneous, negligible mass diffusion and thermal conduction, negligible heat dissipation by viscous effects, porous media resistive force given by Ergun equation, ideal gas behavior, ideal solution, and Newtonian fluid. The same assumptions was also considered in the previous work of Maia et al. 15 , where

6


Page 6 of 34

Page 7 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: Catalytic ethanol dehydration process flowsheet. a steady-state model was proposed to describe an industrial unit for the catalytic ethanol dehydration process, being the model able to predict the axial temperature profile inside the reactor and the outlet composition for different process conditions with errors less than 5%. Additionally, despite the pseudo-homogeneous assumption, in order to deal with mass and heat transfer between solid and fluid phases, correction factors were applied in the source terms of mass and energy conservation equations. These factors were proposed as empirical correlations as functions of dimensionless numbers.

2.1

Kinetic Model

The set of reactions considered comprises a total of 10 species and 8 chemical routes, and were based on the reaction system presented in the previous work of Maia et al. 15 . To simplify the mathematical notation, the chemical components involved in the reaction rates are described by numbers, as shown in Table 1. It is worthwhile to mention that the isomers of butene and propene have been grouped and treated as a single compound. The chemical

7



Page 8 of 34

reactions considered are described by Equations 1 to 8. Table 1: Components considered in the reaction system. Specie Ethanol Ethylene Water Diethyl ether Acetaldehyde Hydrogen Butenes (1-butene, cis-2-butene, trans-2-butene, isobutane, cyclobutane) Ethane Propanol Propene (propene, cyclopropane)

Formula

Number

C2 H5 OH C 2 H4 H2 O (C2 H5 )2 O C 2 H4 O H2

1 2 3 4 5 6

C4 H8

7

C 2 H6 C3 H7 OH C 3 H6

8 9 10

Ethanol intramolecular dehydration:

C2 H5 OH C2 H4 + H2 O

(1)

Ethanol intermolecular dehydration:

2C2 H5 OH (C2 H5 )2 O + H2 O

(2)

Ethanol dehydrogenation:

C2 H5 OH C2 H4 O + H2

(3)

Diethyl ether intramolecular dehydration:

(C2 H5 )2 O 2C2 H4 + H2 O

(4) 8


Page 9 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ethylene dimerization:

2C2 H4 C4 H8

(5)

Ethylene Hydrogenation:

2C2 H4 + H2 C2 H6

(6)

Propanol intramolecular dehydration:

C3 H7 OH C3 H6 + H2 O

(7)

Butene metathesis:

C4 H8 + C2 H4 2C3 H6

(8)

The reaction rate model for each reaction is based on the previous work of Maia et al. 15 ,16 , which follows the mass action law and consider the reversibility of the reactions. Without loss of generality, the reaction rate expression for a reaction j can be written by the following equation:  RjI = kj,D 

 Y

Ci |νi,j | −

i∈nDj

1 Kj

(C o )∆νj

Y

Ci |νi,j | 

(9)

i∈nRj

In Equation 9, RjI is the ideal reaction rate for each reaction (j = 1, ..., 8), kj,D is the specific rate of the direct reaction j, nDj is the set of reactants in the direct reaction j, nRj is the set of products in the reverse reaction j, Ci is the molar concentration for each species (i = 1, ..., 10), νi,j is the stoichiometric coefficient of species i in reaction j, Kj is the thermodynamic constant of chemical equilibrium, C o is the reference molar concentration

9



Page 10 of 34

for the chemical equilibrium constant (i.e., the concentration of an ideal gas in the reference pressure, P o = 101,325 Pa, and the reference temperature, T o =298.15 K), and ∆νj represents the variation of moles in reaction j, which is the difference between the global order of reverse reaction and the global order of direct reaction. The direct reaction specific rate is defined following the modified Arrhenius equation, as described below 15 :

kj,D = k0j,D T

νj,D

−Eaj,D exp RT

ρcat

1−ε ε

(10)

In Equation 10, ε is the catalytic bed porosity, ρcat is the catalyst density, k0j,D is the preexponential factor, νj,D is the global order of direct reaction, Eaj,D is the activation energy of the direct reaction, R is the universal constant of gases and T is the temperature of the system. Following the same concept introduced by Maia et al. 15 , the reaction rate (RjI ), as defined in Equation 9, describes the ideal reaction rate, which consider a reaction occurring within the catalyst layer without mass and energy transfer limitations, and without catalyst deactivation. In order to represent these phenomena, the following deviations from ideality were considered: 1. Catalyst availability (ef ); 2. Correction factor related to the resistance to mass transfer between the fluid and solid phases (fM T ); 3. Catalyst activity (a). Hence, the rate of chemical reaction j, Rj , considering all the above deviations, is described by:

Rj = ef fM T a RjI

(11)

10


Page 11 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The catalyst availability indicates if, in a given axial position in the reactor, the bed is composed either by a layer of catalyst or by a layer of inert. The basic idea of this definition is to turn on the reaction system when the axial position is within the catalyst layer and turn it off when outside. The catalyst availability function is described as the product of the following hyperbolic tangent function (also known as regularization function) 15 .     z − Li   z − Lf         1 + tanh 250 L  1 − tanh 250 L ef (z) =    2 2         | {z }| {z } eif

(12)

eff

where Li is the length of the inert layer at the reactor beginning, Lf is the end position of the catalytic bed, and L is the total reactor length. The length of the catalyst layer is evaluated as:

Lcat = Lf − Li

(13)

The mass transfer correction factor (fM T ) is related to the mass transfer resistance between fluid and solid phases. It was modeled by an empirical correlation presented on the work of Maia et al. 15 , as described below: " fM T = αM T

2/3

Ref Scf τc,f

# βM T (14)

where the subscript f is related to the value of the property at feed conditions, Ref is the particle Reynolds number, Scf is the Schmidt number, τc,f is the dimensionless combined residence time and αM T and βM T are fitting parameters. More details of the definitions of these terms can be found in the previous work of Maia et al. 15 . The mass transfer correction factor (fM T ) can be interpreted as a correction for the overall mass transfer resistance, which encompasses the external and internal resistances.

11



Page 12 of 34

The relation presented in Equation 14 is an empirical correlation which is analogous to the Colburn J-factor 17 , commonly used to describe external mass transfer resistance, calculated as a function of Reynolds and Schmidt numbers. Thus, the βM T parameter is also related to this phenomenon. On the other hand, the αM T parameter, besides being related to the external mass transfer, it is also related to internal mass transfer due to its proportionality to the Thiele Modulus, commonly used to describe the relation between reaction and diffusion rates 18 . The catalyst activity is a function of space and intrinsically of time too. This last effect was neglected in Maia et al. 15 due to the steady state assumption. However, Maia et al. 15 developed a non-constant profile for the catalytic activity that represents the initial activity of the same catalyst bed studied in the present work. Therefore, the following equation will be used to represent the initial catalyst activity profile in this work: " 1 + tanh κ a(t0 , z) = a0 (z) =

z/L p

(z/L)2 + 1

−

Li +λ L

!#

2

(15)

where t0 is the initial time considered in this work, a0 is the initial activity profile (at time t0 ) and κ and λ are fitting parameters, already estimated in the work of Maia et al. 15 . Finally, the reaction rate for a component i (ri ) is described by:

ri =

8 X

νi,j Rj

(16)

j=1

2.2

Reactor Modeling

Based on the simplifying assumptions presented above, the mathematical model for the fixed-bed reactor considered in this work is described as follows:

12


Page 13 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Overall mass balance: NC

∂C ∂ (vC) X + = ri ∂t ∂z i=1

(17)

Component mass balance: ∂Ci ∂ (vCi ) + = ri ∂t ∂z

(18)

Energy balance: 8 h i ∂T X ∂T ρCˆp ε + ρs Cˆp,s (1 − ε) + ρCˆp v = −(∆Hj )Rj + ∂t ∂z j=1 ∂P ∂P + +v ∂t ∂z

(19)

Momentum balance:

ρ

∂v ∂P ∂v + ρv =− − FRM + ρg ∂t ∂z ∂z

(20)

Equation of state (algebraic constraint):

P = CRT

(21)

where N C is the number of components, C is the total molar concentration, Cˆp and Cˆp,s is the heat capacity per mass of fluid and solid, respectively, ∆Hj is the heat of reaction j, FRM is the porous media resistive force and g is the gravitational acceleration. It is important to emphasize that the index i refers to the species and the index j is related to the reaction number. An additional hypothesis considered for the reactor model is the quasi steady-state assumption (QSSA) for the global mass balance and for the momentum balance. Thus, the

13



Page 14 of 34

specific mass and the axial velocity have instantaneous responses when the system is subjected to disturbances.

Hence, the time derivatives of those variables will not be

considered in Equations 17 and 20. The dynamic degree of freedom of the partial differential-algebraic equations system is N C + 1 = 10. This means that, in order to solve the system of equations, 11 initial conditions are required. It is important to note that the system has 14 dependent variables (10 concentrations, temperature, pressure, velocity and total concentration), then, three of these variables cannot be specified, being obtained by algebraic constraints. In this case, the initial conditions are written to N C species and temperature, which could be functions of z. t = 0, ∀z : (22)

Ci (t, z) = Ci,0 (z) T (t, z) = T0 (z) The boundary conditions are given by: z = 0, ∀t : Ci (t, 0) = Ci,f (t)

(23)

T (t, 0) = Tf (t) P (t, 0) = Pf (t) vz (t, 0) = vf (t)

where Ci,f is the feed concentration of i-th specie, Tf is the feed temperature, Pf is the feed pressure and vf is the feed velocity. The last one is calculated using the relation between interstitial and superficial velocity:

vf =

4m ˙f uf = 2 εi ρf πDR εi

(24)

14


Page 15 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where uf is the superficial velocity, εi is the inert layer porosity, m ˙ f is the mass feed flow rate, ρf is the feed stream specific weight and DR is the reactor diameter. It is important to emphasize that, analogously to what was done for the development of the reaction rate, a correction factor related to the heat transfer resistance between solid and fluid phases was introduced, since the temperature of these phases may be different. Therefore, the actual heat of reaction is calculated as follows:

∆Hj = fHT ∆HjI

(25)

where ∆HjI is the ideal heat of reaction j, given by the thermodynamic relation: ∆HjI (T )

=

∆Hjo

T

Z +

To

o ∆Cp,j dT

(26)

o where ∆Hjo is the standard enthalpy change of formation of reaction j, and ∆Cp,j is the

variation of the specific molar heat capacity of reaction j. The correction factor fHT was proposed in the work of Maia et al. 15 and it is calculated analogously for the mass transfer correction factor fM T as follows: " fHT = αHT

2/3

Ref P rf τc,f

#βHT (27)

in which αHT and βHT are fitting parameters, P rf is the Prandtl number at the feed condition and τc,f is an dimensionless number that take into account the process conditions and which was proposed by Maia et al. 15 . For more details of these dimensionless numbers calculations, please refer to the work of Maia et al. 15 . Additionally, some constitutive equations are needed to get null degrees of freedom, such as the resistance force of the porous media, the catalytic effectiveness, the heat of reaction, the mixture molar mass, the specific heat of the fluid and the molar fraction. Those equations could also be found in the work of Maia et al. 15 .

15



2.3 2.3.1

Catalyst Deactivation Modeling Experimental Evidence

The proposed catalyst deactivation model was developed based on an industrial fixed-bed reactor, using the information from eight of the internal thermocouples. Figure 2 presents the temporal evolution of the measurements of these thermocouples inserted at different axial positions inside of the reactor, as informed in the figure.

Figure 2: Temporal evolution of the eight thermocouples measurements inside of the reactor at given dimensionless axial length. The catalyst bed starts at position 0.21. When analyzing the dynamic evolution of the measurements on each thermocouple in the reactor campaign period, it is possible to note that the temperature measured by thermocouple 2 (dimensionless length=0.33) increases over time, reaching the value of the temperature measured by the thermocouple 1 (dimensionless length=0.21, located near the catalytic bed entry point). Since the reaction is globally endothermic, it is expected that the temperature inside the reactor must be lower than the feed temperature, due to the 16


Page 16 of 34

Page 17 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


chemical reactions taking place in the catalytic bed.

As the catalyst deactivates, the

chemical reactions cease to occur locally, so that the temperature drop between these thermocouples is reduced and tends to zero. Additionally,

this same trend occurs later on thermocouple 3 (dimensionless

length=0.44), but with lower intensity, and one may see that its temperature drop reduction starts when the thermocouple 2 indicates that the bed is completed deactivated up to its position. Although thermocouples 2 and 3 sense the deactivation effect, the temperature values measured by the other thermocouples do not increase, for the analyzed campaign period and operating condition, showing that the deactivation is more pronounced at the beginning of the catalytic bed. In fact, the catalyst deactivation appears to evolve in the axial direction, firstly deactivating the initial layers of the catalytic bed and reaching the other layers over time. The experimental evidence described above, based on the analysis of thermocouples data, can be related to the same effect observed in the works of Haw and Marcus 19 , Schulz 13 and Bleken et al. 10 for the MTO catalyst deactivation system. In all of these works, the authors verified that there is a more intense coke deposition in the early stages of the catalytic bed, which moves slowly with the operating time.

2.3.2

Catalyst Deactivation Proposed Model

The catalyst deactivation experimental evidence presented above is very important to support and motivate the foundation of the proposed catalyst deactivation model. Once the deactivation is most pronounced at the beginning of the bed, it is expected that the alcohol has a fundamental role since, as a reactant, its higher concentration occurs at the beginning of the bed, favoring the formation of coke and consequent deactivation of the catalyst. Thus, a possible model to be used should describe the dependence with the concentration of ethanol, which would be the precursor species for coke formation. Another information that must be added to the model is the influence of water on

17



Page 18 of 34

catalyst deactivation, which, according to Marchi and Froment 9 and Gayubo et al. 8 , has the mitigating effect on coke formation rates. This phenomenon is related to the water chemisorption, which implies that a fairly strong bond is formed between water and the acid catalyst surface, occupying, thereby, an active site, protecting it from deactivation. Additionally, some authors believe that olefins are also precursors of coke formation, as presented in Gayubo et al. 7 . Therefore, it was considered that the deactivation mechanism involving the precursors ethanol and olefins may occur in parallel, which is represented mathematically by the sum of two distinct contributions involving the concentration of each of these precursors. The catalyst deactivation model proposed here is described by a first order decay relationship with the catalyst activity: ∂a = −rd a ∂t

(28)

where a is the catalyst activity and rd is the overall deactivation reaction rate. In Equation 28, it is important to note that the partial derivative notation was used, due to the implied dependence of the variable activity with the spatial position, which is attributed to the dependence with other state variables, such as concentration and temperature. The deactivation rate, as previously described, is composed of two contributions, related to the precursors ethanol and olefins, as shown below:

rd = fM T (Rd,1 + Rd,2 )

(29)

where fM T is the mass transfer correction factor, Rd,1 is the deactivation reaction rate due to ethanol concentration and Rd,2 is the deactivation rate due to olefins contribution.

18


Page 19 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The reaction rates are modeled as:

Rd,1 =

kd,1 y1 1 + Kd,w y3

(30)

Rd,2 =

kd,2 (y2 + y7 + y10 ) 1 + Kd,w y3

(31)

where kd,1 represents the specific deactivation rate due to ethanol, kd,2 represents the specific deactivation rate due to olefins, Kd,w is the constant of water attenuation of the deactivation rate and yj is the molar fraction of species j. The specific deactivation rate and the constant of water attenuation of the deactivation rate are defined by:

kd,j = (1 − ε) ρs k0d,j

−Ead,j T exp RT

Kd,w = (1 − ε) ρs k0d,w

−∆Hd,w exp RT

(32) (33)

where k0d,j is the pre-exponential factor of the deactivation reaction j, Ead,j is the activation energy of deactivation reaction j, k0d,w is the pre-exponential factor of the deactivation attenuation due to water and ∆Hd,w is the heat of adsorption of water onto the catalyst surface. Since the proposed deactivation model is described by a first order decay, it is necessary an initial condition to solve the equation. The catalytic activity is a function of the spatial coordinate, being better represented as a catalytic activity profile. Ideally, in the process startup, the activity could be considered as unitary, since the deactivation has not yet occurred. However, hardly a catalytic bed has full activity in its extension, even in the initial instants of the reaction process. Thus, an empirical model for the initial catalytic activity profile was developed, based on the experimental evidence from industry presented for deactivation phenomenon, mainly the fact that the initial positions of the bed were

19



more deactivated. As presented and described before, the initial activity profile model is described by Equation 15.

3

Results and Discussion

3.1

Parameter Estimation

The following geometrical and physical parameters of the industrial reactor investigated in this work should be precisely known to estimate the parameters of the deactivation model: reactor total length (L), inert and catalyst layers length (Li , Lf and Lcat ), reactor diameter (DR ), catalyst particle apparent diameter (dp ), catalyst density (ρcat ), and inert and catalytic layers porosity (εi and ε). However, these data cannot be disclosed due to confidentiality reasons; in order to deal with this needing, the dimensionless form of the model presented in Maia et al. 15 and the values of the dimensionless parameters were used. These parameters encompass those confidential values and, therefore, remove the need to inform them for all analyses and assessments of the results presented here. Other model parameters, such as thermodynamics data, were obtained from the database of Poling et al. 20 . This information is utilized in some constitutive equations presented in Maia et al. 15 . The pre-exponential factors of the reactions (k0j,D ), the activation energy of each reaction (Ea,j ), the reactor packed-bed porosity (ε), the catalyst initial activity parameters (κ and λ), and the mass and heat resistance correction factors (αmt , βmt , αht and βht ) were previously estimated in a steady-state condition of the process, presented in Maia et al. 15 . In this work, the estimated parameters were the pre-exponential factors of the deactivation reaction (k0d,j - 2 parameters), the deactivation activation energy (Ead,j - 2 parameters), the water attenuation pre-exponential factor (k0d,w - 1 parameter) and the heat of adsorption of water (∆Hd,w - 1 parameter), totalizing 6 parameters. The objective function utilized was the weighted least squares, in which the temperature 20


Page 20 of 34

Page 21 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


values in the seven axial positions of the thermocouples predicted by the model and the experimental value were compared, in each of the sampling times considered. Thus, the objective function is written as:

Fobj (α) =

NI X NT X

exp mod wT k,j Tk,j − Tk,j

2

(34)

k=1 j=1

where α is the vector of estimated parameters, N I is the number of time intervals, N T is the number of thermocouples in the packed bed, wT k,j is the weight of the {k, j} square exp mod and Tk,j are the experimental and predicted values of the temperature at the error, Tk,j

k-th time interval and each the j-th position. The weights wT k,j were defined following the maximum-likelihood method, corresponding to the reciprocal of the variance for j-th thermocouple measurement within the k-th interval. Despite the objective function was built only using temperature data, if any other experimental data was available (for instance, ethanol conversion, ethylene selectivity or reactor outlet composition), it could also be included.

However, those data were not

available in the experimental unit, being possible only the use of temperature profile. One additional hypothesis is that the probability distribution of the experimental error is normal. Hence, the experimental error should be less than the confidence interval upper limit. This assumption is in agreement with the well-done experiment hypothesis. For solving the parameter estimation problem, the EMSO process simulator 21 was used and DASSLC routine was applied for numerically integrating the system of differential-algebraic equations 22 . The flexible polyhedrons algorithm 23 with a confidence level of 95% for parameter estimation was used and the solution was improved by the Brent’s algorithm 24 . The average values of the estimated catalyst deactivation parameters are presented in Table 2. The relative confidence intervals at the significance level of 95% were evaluated from the t-student distribution and the standard deviations of the parameters, and the results are also presented in Table 2. The reactor model consists of a nonlinear partial differential-algebraic system of

21



Page 22 of 34

Table 2: Average values and relative confidence intervals of the estimated catalyst deactivation parameters. Parameter - [Unit]

Average Value

Relative Confidence Interval (%)

k0d,1 - [m3 / (kg s K)] k0d,2 - [m3 / (kg s K)] k0d,w - [m3 / kg] Ead,1 - [J/mol] Ead,2 - [J/mol] ∆Hd,w - [J/mol]

1.35792 × 10−1 2.29182 × 10−1 1.52779 × 10−1 39504.2 85333.3 −52130.8

±8.920 × 10−8 ±12.961 ±6.084 ±8.501 ±11.108 ±10.800

equations, which needs a discretization method in order to be solved. In this work, the method of lines was applied, using the upwind finite-difference formulas as discretization method with non-uniform mesh. As the process consists of an adiabatic reactor processing a globally endothermic reaction network, the reaction extension occurs mainly in the initial position of the bed. Thus, the mesh with size N was built using a heuristic exponential formula for the distribution of the discretization points, being more refined at the initial region of the bed, as follows: z1 = 0 zk = L p(k−N −1)/N

(35)

k = 2, ..., N

zN +1 = L where zk are the axial position of discretization elements, p > 1 is an parameter to adjust the mesh distribution and L is the reactor bed length. In the present work, p = 100 and N = 25 were chosen, where the number of discretization points (N ) was selected such that the resulting profiles was independent of the mesh size. The reactor model was implemented in EMSO process simulator and, after discretization, the differential-algebraic equations system was solved with the DASSLC solver. In order to study the catalyst deactivation, it is necessary to simulate the reactor operation throughout the reactor campaign period, in which disturbances in the input 22


Page 23 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


variables (operating conditions) occur over time. This period was evenly divided into 24 intervals and the values for the operating conditions and the measured response variables were taken as their average value a mean in each of these intervals. The F-test was applied to verify the objective function confidence interval. The obtained 2 values for the mean prediction variance (ˆ σm ) and the mean experimental variance (σε2 ) were

8.672 and 14.109, respectively. Based on the number of experiments (i.e., 24) and the problem degrees of freedom, the following relation was achieved:

0.603 ≤ Fobj = 0.615 ≤ 1.946

(36)

Thus, the model can represent statistically well the experimental data, with prediction errors not significantly greater than the experimental errors. The coefficient of determination (R2 ) was also calculated to verify model fit quality, which indicates how well the model prediction approximates the experimental data points. The R2 value found in the parameters estimation step was 0.969, which represents a good fit of the model to the experimental data. In order to evaluate the estimated parameters quality, the parameters correlation matrix was evaluated, as shown in Figure 3, which presents low correlation among most of the parameters. Few activation energies have higher correlation with pre-exponential factors, which is a well-known behavior. The average parameter correlation was equal to 0.283, which indicates that the different effects of each parameter were properly identified 25 . It can be observed in Table 2 that the highest relative confidence interval of the parameters is 12.691%, indicating that all estimated parameters are statistically significant. The prediction confidence intervals of the model were also evaluated in order to verify the quality of the predictions. These intervals are used to detect outliers, which cannot be explained and to define the range in which the model prediction and measurement are statistically equivalent, thus defining the region of validity of the model. Assuming a 95%

23



Figure 3: Estimated parameters correlation matrix for the proposed model. confidence level, the mean of the relative prediction confidence interval for the temperature profile was 1.3%. Figure 4 shows the time evolution of the measured and observed temperature in each of the thermocouples distributed axially in the catalytic bed, for all 24 time intervals in the campaign. It is possible to observe that the results predicted by the model show good agreement with the experimental data, being able to predict the dynamic evolution of the thermocouples in different operating conditions. As a consequence of the catalyst deactivation, it is found that the temperature values of the thermocouples located closer to the beginning of the catalytic bed show a tendency

24


Page 24 of 34

Page 25 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: Temporal evolution, in terms of percentage of total campaign period, of the thermocouple measurements inside of reactor (—: model; •: experimental data). of increase, so that a complete deactivation occurs in certain axial positions of the bed, since the measured temperature value reaches the feed temperature value. This complete deactivation occurs for the thermocouple 2 and starts to occur for the thermocouple 3. The thermocouples in the end positions have practically not been affected by the deactivation. Figure 5 shows the axial profile of the catalytic activity for different times (in terms of percentage of total campaign period). The observed axial displacement of the activity profile, typically described as a "deactivation wave", shows a deactivation of the first 20% of the catalytic bed. It is also noted that the effect of the catalyst deactivation on the final portions of the bed is insignificant during the considered time period, with activity reaching values close to 0.97 at the exit of the bed. This result confirm that ethanol is considered as a precursor of coke formation, since its concentration is higher at the beginning of the bed. Furthermore, since the temperature is higher at the beginning of the bed, this effect also contributes to a greater deactivation in this region. Figure 6 shows the time evolution of 25



Figure 5: Temporal evolution of the catalyst activity inside of reactor. the axial temperature profile, where the initial portions of the bed reach the unit value, which corresponds to the value of the feed temperature. In fact, the temperature profile, for different times, moves parallel to the initial profile, as a function of the deposition of coke in the catalyst.

26


Page 26 of 34

Page 27 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: Temporal evolution of the temperature profile inside of reactor. As presented in Equation 29, the deactivation rate has to contributions, one related to reagent ethanol and other related to olefin products (ethylene, butene and propene). Therefore, it is expected that the rate related to the products will have a greater effect on the end positions of the bed, while the rate related to the ethanol will be reduced. This result can be observed from the ratio between deactivation rates (Equations 30 and 31) presented in Figure 7. The deactivation rate related to ethanol (Rd,1 ) has magnitude greater than the deactivation rate related to the olefins (Rd,2 ) throughout the bed length, as shown in Figure 7, having order of magnitude 24 times higher in the initial positions and 2.8 in the final positions of the bed. Additionally, the ratio of reaction rates increases over time. This effect is related to temperature raise due to the catalyst deactivation, increasing the rate Rd,1 , which has lower activation energy. Another contribution to increase this ratio is due to the increase in ethanol concentration that occurs by the decrease in conversion. 27



Page 28 of 34

Figure 7: Temporal evolution of the deactivation rates ratio inside of reactor. Table 3 presents the mean relative absolute error (MRAE) of the 8 thermocouples for a given time interval considering all the 24 intervals, calculated according to the following equation: exp 8 mod 1 X Tk,m − Tk,m × 100 MRAE = exp 8 k=1 Tk,m

(37)

where k is the axial thermocouple position and m is a given time period. It can be seen in Table 3 that the maximum value for the mean relative absolute error is 0.97%, corresponding to Period 4. This result indicates a good agreement between the model predicted values and experimental data. Furthermore, the maximum error at a given position k and time period m are calculated

28


Page 29 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3: Mean relative absolute error (%) for temperature axial profile in each period. Interval

MRAE

Interval

MRAE

Interval

MRAE

Interval

MRAE

1 2 3 4 5 6

0.309465 0.238982 0.342803 0.976239 0.425613 0.711047

7 8 9 10 11 12

0.950825 0.390308 0.799058 0.618138 0.353821 0.202615

13 14 15 16 17 18

0.175559 0.436429 0.467215 0.415141 0.220305 0.283696

19 20 21 22 23 24

0.437316 0.377358 0.276684 0.218241 0.524943 0.353079

as follows: exp T − T mod k,m k,m Maximum Relative Error = max exp Tk,m

(38)

Based on the definitions above, the maximum calculated error is equal to 1.70%, which is also a small deviation and corroborates to the model prediction ability. This error occurs at the last thermocouple (k = 8) at Period 4. Indeed, based on the calculated errors shown in Table 3, the deviations for the thermocouples are shown to be higher at Period 4. It is verified that, at this period, the mass feed flowrate of ethanol reached the minimum value, indicating that the parameters estimated for the model present limitation of extrapolation for this operating condition, assigning such responsibility to the correction factors of external resistance to mass and heat transfers. Figure 8 shows the relationship of these factors with dimensionless numbers at the feed condition. Different values for dimensionless numbers results from the influence of the input variables. For instance, as ethanol feed stream flowrate changes, the reactor inlet velocity also changes and, consequently, the Reynolds number.

Also, if inlet temperature and

pressure change, physical and transport properties vary, affecting the Schmidt and Prandtl numbers.

29



Figure 8: Heat and mass transfer correction factors in each time interval as a function of dimensionless numbers at the feed condition.

4

Conclusion

In this work, a dynamic phenomenological mathematical model for catalytic ethanol dehydration fixed-bed reactor has been presented, considering eight chemical reactions and ten species. A catalyst deactivation model was developed which considers ethanol and olefins as coke precursors, while water has an attenuating effect. The catalyst deactivation model parameters were estimated based on the time evolution of axial temperature profile data from an industrial plant for different operating conditions, over a wide range of throughput/flowrate. The model predicted temperature profile was in agreement with experimental data, presenting low deviations and a mean relative absolute error below 1% throughout different operating periods analyzed.

In this way, it is possible to use the proposed model for

process monitoring, as well as the determination of the catalyst campaign time, that is, a dynamic optimization problem.

30


Page 30 of 34

Page 31 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Acknowledgement This work was supported in part by the National Council for Scientific and Technological Development (CNPq) grant numbers 302893/2013-0 and in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

References (1) Matachowski, L.; Zimowska, M.; Mucha, D.; Machej, T. Ecofriendly production of ethylene by dehydration of ethanol over Ag3 PW12 O40 salt in nitrogen and air atmospheres. Applied Catalysis B: Environmental 2012, 123-124, 448–456. (2) Gucbilmez, Y.; Dogu, T.; Balci, S. Ethylene and Acetaldehyde Production by Selective Oxidation of Ethanol Using Mesoporous V-MCM-41 Catalysts. Industrial & Engineering Chemistry Research 2006, 45, 3496–3502. (3) Haro, P.; Ollero, P.; Trippe, F. Technoeconomic assessment of potential processes for bio-ethylene production. Fuel Processing Technology 2013, 114, 35–48. (4) Hira, A.; de Oliveira, L. G. No substitute for oil? How Brazil developed its ethanol industry. Energy Policy 2009, 37, 2450 – 2456, China Energy Efficiency. (5) Zhang, X.; Wang, R.; Yang, X.; Zhang, F. Comparison of four catalysts in the catalytic dehydration of ethanol to ethylene. Microporous and Mesoporous Materials 2008, 116, 210–215. (6) Bailey, C.; Bolton, L. W.; Gracey, B. P.; Lee, M. K.; Partington, S. R. Process for producing ethylene. Patent US426664B2, 2005; US426664B2. (7) Gayubo, A. G.; Aguayo, A. T.; Tarrio, A. M.; Olazar, M.; Bilbao, J. Kinetic Modelling for Deactivation by Coke Deposition of a HZSM-5 Zeolite Catalyst in the

31



Transformation of Aqueous Ethanol into Hydrocarbons. Catalyst Deactivation. 2001; pp 455–462. (8) Gayubo, A. G.; Alonso, A.; Valle, B.; Aguayo, A. T.; Olazar, M.; Bilbao, J. Kinetic modelling for the transformation of bioethanol into olefins on a hydrothermally stable Ni–HZSM-5 catalyst considering the deactivation by coke. Chemical Engineering Journal 2011, 167, 262 – 277. (9) Marchi, A.; Froment, G. Catalytic conversion of methanol to light alkenes on {SAPO} molecular sieves. Applied Catalysis 1991, 71, 139 – 152. (10) Bleken, F. L.; Barbera, K.; Bonino, F.; Olsbye, U.; Lillerud, K. P.; Bordiga, S.; Beato, P.; Janssens, T. V.; Svelle, S. Catalyst deactivation by coke formation in microporous and desilicated zeolite H-ZSM-5 during the conversion of methanol to hydrocarbons. Journal of Catalysis 2013, 307, 62 – 73. (11) Chen, D.; Rebo, H. P.; Moljord, K.; Holmen, A. In Catalyst DeactivationProceedings of the 7th International Symposium; Bartholomew, C., Fuentes, G., Eds.; Studies in Surface Science and Catalysis; Elsevier, 1997; Vol. 111; pp 159 – 166. (12) Chen, D.; Rebo, H.; Grønvold, A.; Moljord, K.; Holmen, A. Methanol conversion to light olefins over SAPO-34: kinetic modeling of coke formation. Microporous and Mesoporous Materials 2000, 35–36, 121 – 135. (13) Schulz, H. “Coking” of zeolites during methanol conversion: Basic reactions of the MTO-, MTP- and {MTG} processes. Catalysis Today 2010, 154, 183 – 194, Eleventh International Symposium on Catalyst Deactivation , Delft(The Netherlands,) October 25-28, 2009. (14) Morschbacker, A. Bio-Ethanol Based Ethylene. Polymer Reviews 2009, 49, 79–84.

32


Page 32 of 34

Page 33 of 34 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(15) Maia, J. G. S. S.; Demuner, R. B.; Secchi, A. R. Process Modeling and Simulation of an Industrial Scale for Green Ethylene Production. Industrial and Engineering Chemistry Research 2018, 33, 479 – 490. (16) Maia, J. G. S. S.; Demuner, R. B.; Secchi, A. R.; Jr, E. C. B. Modeling and Simulation of the Process of Dehydration of Bioethanol to Ethylene. Brazilian Journal of Chemical Engineering 2016, 33, 479 – 490. (17) Frössling, N. The evaporation of falling drops (in German). Gerlands Beiträge zur Geophysik 1938, 52, 170–216. (18) Froment, G.; Bischoff, K.; De Wilde, J. Chemical Reactor Analysis and Design, 3rd Edition; John Wiley & Sons, Incorporated, 2010. (19) Haw, J.; Marcus, D. Well-defined (supra)molecular structures in zeolite methanol-toolefin catalysis. Topics in Catalysis 2005, 34, 41–48. (20) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2000. (21) Soares, R. P.; Secchi, A. R. EMSO: A New Environment for Modelling, Simulation and Optimisation. European Symposium on Computer Aided Process Engineering 2003, 13, 947–952. (22) Secchi, A. R. Differential-Algebraic System Solver in C. 2007; http://www.enq.ufrgs. br/enqlib/numeric/. (23) Nelder, J.; Mead, R. A simplex method for function minimization. Computer Journal 1965, 7, 308–313. (24) Gegenfurtner, K. R. PRAXIS: Brent’s algorithm for function minimization. Behavior Research Methods 1992, 24 .

33



(25) Schwaab, M.; Pinto, J. C. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: Problems involving one kinetic constant. Chemical Engineering Science 2007, 62, 2750 – 2764.

For Table of Contents Only.

34


Page 34 of 34

Modeling of Catalyst Deactivation in Bioethanol Dehydration Reactor

Recommend Documents