Process Modeling and Simulation of an Industrial-Scale Plant for

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Process Systems Engineering

Process Modeling and Simulation of an Industrial Scale Plant for Green Ethylene Production Jeiveison Gobério Soares Santos Maia, Rafael Brandão Demuner, Argimiro Resende Secchi, Príamo Albuquerque Melo, Roberto Werneck do Carmo, and Gabriel Sabença Gusmão Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00776 • Publication Date (Web): 22 Apr 2018 Downloaded from http://pubs.acs.org on April 22, 2018

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Industrial & Engineering Chemistry Research

Process Modeling and Simulation of an Industrial Scale Plant for Green Ethylene Production Jeiveison Gobério Soares Santos Maia,

∗,†

Resende Secchi,

Rafael Brandão Demuner,

†

Príamo Albuquerque Melo Junior,

Carmo,

†Chemical

†

‡

†

Argimiro

Roberto Werneck do

and Gabriel Sabença Gusmão

‡

Engineering Program, Universidade Federal do Rio de Janeiro, Brazil

‡Braskem,

Renewable Chemicals Research Center, Campinas, Brazil

* E-mail:

[email protected]

Abstract Catalytic dehydration of ethanol is the key step in the production of polyethylene from renewable raw materials. Obtaining a mathematical model to optimize the ethanol-to-ethylene reactor setup is of great interest to the industry, allowing the optimal design of larger plants and improvements to existing plants. This work presents a phenomenological model of an ethanol dehydration reactor that takes into account eight chemical reactions and ten chemical species, considering non-idealities in the reaction rates and axial catalyst activity prole.

Additionally, the axial

variation of pressure, velocity and thermodynamics properties are considered in the proposed model. Model validation at dierent operating conditions shows that the predicted temperature, and composition proles match the data from an industrial plant with relative deviations below 5%, and from a pilot plant with relative deviation below 0.4%. 1

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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

1

Introduction

The globally prevalent route for the ethylene production is the steam cracking process, which uses as raw material naphtha and natural gas fractions. This process is characterized by high energy consumption, yields of around 55% and large CO2 emissions 1 . Alternatively, the use of bioethanol as raw-material for the production of ethylene is justiable by the today's pursuit of more sustainable chemical routes and by the fact that ethylene accounts for the largest parcel of the plastic market. Currently, about 75% of petrochemical products are produced from ethylene, including acetaldehyde, acetic acid, ethylene oxide, ethylene glycol, ethylbenzene, chloroethanol, vinyl chloride, styrene and vinyl acetate. Ethylene can also be used as a raw material for the production of polymers, such as:

polyethylene, polyvinyl chloride, polystyrene.

Additionally, ethylene production is one of the indicators of the level of development of petrochemicals in countries all around the world 2 . However, inevitably, fossil fuels will continue to face problems related to their reserves increasing scarcity and the end of their conventional extraction is inexorable, besides the problems associated with geopolitical and environmental issues. Consequently, to anticipate eventual scenarios of scarcity, industry and academia have been recently driven eorts towards nding alternative sources of raw-material for such value chains, specically renewable ones. In 1797, that Dutch chemists observed the formation of a gas through the passage of ethanol over alumina. This gaseous substance, when reacting with chlorine, formed an oily product which is today called dichloroethane; however, by that time, it was called olen 3 . The ethylene industrial production process by catalytic ethanol dehydration is known since 1913 4 . Fundamental studies in this area were conducted in the 1960s and 1980s, aiming at, for example, elucidating the mechanism of involved chemical reactions 5 . Commercial production of ethylene from ethanol started before the Frist World War, when ethylene was used as a refrigeration uid, at the Elektrochemischen Werke in Germany 6 .

ICI built an ethanol-to-ethylene plant in England in the 1930s, where it 2


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produced polyethylene, and many other plants followed in dierent countries with dierent uses for ethylene, such as: PVC, SBR, and polystyrene (Winter and Eng, 1976), as well as ethylene oxide and monoethylene glycol (MEG) 7 . The early plants operated with complex reactors because of the need to provide heat to the endothermic reaction. A game changer was the development of an adiabatic process by Petrobras in the 1970s, which increased the conversion and reduced the capital to build the plants 8 . In 2010, Braskem started in Brazil a large-scale, 200,000 ton per year ethanol-to-ethylene plant 9 , using its assets to produce an initial portfolio of 18 dierent grades of polyethylene 10 . The polyethylene via ethanol has received renewable source certicates that attests the nature of the renewable "green" plastic by standardized biobased-content analysis method This property allows the determination of biocarbon (biobased content) of bioplastics using standardized methods 11 , which guarantee that all carbon atoms of ethylene, which end up forming the polyethylene, come from atmospheric CO2 that has been xed by sugar cane during its growth in the eld 6 . The ethanol dehydration generally occurs assisted by acid catalysts, the most common being those based on alumina or silica-alumina, at temperature ranging from 300o C to 500o C, pressure from 1 to 10 atm, and ethanol feed concentration of around 95% (m/m), obtaining ethylene with selectivity in the range of 95 to 99% (mol basis), with high conversion of ethanol, from 98 to 99% 12 . An inherent feature of the process is the catalyst deactivation, which occurs mainly due to coke deposition, leading to the need of catalyst regeneration cycles, that are time dependent on the operating conditions of the process. In fact, the operating conditions of the process are of extreme importance for optimizing the production of ethylene, coupled with the ability to process output and to mitigate the deactivation phenomenon. However, this phenomenon is poorly studied in the framework of processes modeling, while for industrial reactors the planning of the catalytic converter is directly connected to the kinetics of deactivation 13 . Several catalysts for the dehydration of ethanol have been studied and can be arranged in 3



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four categories: phosphoric acid, heteropolyacids, molecular sieves, and oxides 4 . Commercial catalysts include combinations of oxides such as Halcon's Syndol, Al2O3-MgO/SiO2 14 . Since mid-20th century, many researchers have conducted studies on the ethanol dehydration reaction mechanism with dierent catalysts, including activated alumina 15,16 , phosphate 17 , magnesium oxide 18 , molecular sieves 19,20 and heteropolyacids 21,22 among others, but so far, there is still no consensus on which reaction mechanism prevails. One of the rst kinetic models for the dehydration of ethanol to ethylene was proposed in the work of Brey and Krieger 23 , which described a sigmoid model with regard to ethanol partial pressure containing two parameters. Butt et al. 24 proposed reaction rates for four reactions in this process, namely:

intramolecular ethanol dehydration to ethylene,

intermolecular ethanol dehydration to ethoxyethane, decomposition of ethoxyethane into ethanol and ethylene, and dehydration of ethoxyethane to ethylene. These reactions were considered

to

be

irreversible

Langmuir-Hinshelwood-Hougen-Watson

and

following

(LHHW)

type,

a with

mechanism ethanol,

of water

the and

ethoxyethane adsorbing non-dissociatively. Kagyrmanova et al. 25 proposed a kinetic model in which the main products of ethanol dehydration on the surface of alumina-based catalyst were ethylene via intramolecular ethanol dehydration,

ethoxyethane via

intermolecular ethanol dehydration, ethylene via ethoxyethane dehydration, acetaldehyde via ethanol dehydrogenation, and butene via ethylene dimerization.

The reaction rate

equations were described as power-law type models, considering the elementary and irreversible reactions.

Christiansen et al. 26 using Density Functional Theory (DFT)

demonstrated that the most favorable energetic pathway in the γ -Al2 O3 surface is the formation of ethylene via an bimolecular elimination (E2) mechanism (Ea = 117.1 kJ/mol), while the formation of ethoxyethane occurs through a bimolecular nucleophilic substitution (SN2 ) mechanism (Ea = 133.8 kJ/mol). Golay et al. 27 developed a pseudo-homogeneous model for a bench-scale reactor, operating in a non-isothermal and recycled manner. Five reactions and four species were 4


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considered in this model, describing only qualitatively the experimental data. Chen 28 used R to optimize the process in a pilot-scale plant, reducing the heating utility by PRO/II

8.23%, the cooling utility by 5.85%, and the compressor by 24.13%, as compared to the R also to optimize a pilot-scale actual process. Wang and Zhang 29 employed AspenPlus

plant, neglecting the required steam as energy carrier, and generating an energy consumption of 20.2% of that of the initial (non-optimized) process conditions. Kagyrmanova et al. 25 presented a computational work on an ethanol dehydration pilot-scale plant and proposed a non-isothermal heterogeneous xed-bed reactor with two-dimensional mass and thermal dispersion. The relevant simplifying hypotheses were constant axial velocity, constant specic mass of the mixture, constant total pressure, and the use of mean values for thermodynamic and uid properties. More recently, comprehensive reviews related to the dehydration of ethanol to ethylene 3032 emphasized the importance of the development of this renewable process. In the present work, a rst-principles mathematical model for the production of ethylene from ethanol by dehydration in an industrial-scale plant is proposed and implemented in the EMSO simulator 33 , which is presented in Process Modeling Section. Dierently from the literature, varying pressure and velocity were considered in the model. Additionally, the proposed kinetic model considers eight chemical reactions and ten chemical species, with varying thermodynamic and physical properties. The reaction rates include the catalyst activity, described by a non-uniform axial prole inside the bed. Empirical correlations were developed based on dimensionless numbers to describe the mass and heat transfer between the uid and solid phases. In Results and Discussion Section, the proposed model was used to represent an actual industrial-scale plant, and the plant data were used to estimate parameters, validated using statistical criteria, other operating conditions, and data from a pilot-scale plant.

5



2

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Process Modeling

In the ethanol to ethylene unit studied in this work, the ethanol feed stream is vaporized, heated in a furnace and then sent to the reaction section. The reactor euent, consisting mainly of ethylene and water, is sent to the quench tower, where the condensation of water occurs, which is removed as the aqueous euent, along with some condensable species. The crude ethylene that leaves the top of this tower, is sent to a scrubbing tower, for the removal of acids and other water soluble components, and then follows to a drying bed, for residual moisture removal, giving rise to the chemical grade ethylene. The remaining contaminants removal is carried out by a distillation column, which carries out the last polishing to the polymer grade ethylene that is sent, nally, to polymerization units, in order to produce the green plastic 6 . A simplied process owsheet diagram is shown in Figure 1.

VAPOR

LIGHT CONTAMINANTS

FURNACE CRUDE ETHYLENE QUENCH WATER

ETHANOL

NaOH

POLYMER GRADE ETHYLENE

EVAPORATION RAW ETHYLENE

AQUEOUS EFFLUENT REACTOR

QUENCH

CAUSTIC EFFLUENT SCRUBBING

CHEMICAL GRADE ETHYLENE DRYING

HEAVY CONTAMINANTS DISTILLATION

Figure 1: Simplied process owsheet diagram of the ethanol dehydration process 6 . In this section, the mathematical model is described for the steady-state simulation of a xed-bed reactor, operating adiabatically.

The most relevant simplifying assumptions

adopted for developing the model are the following: one-dimensional, pseudo-homogeneous, 6


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negligible axial dispersion and axial thermal conduction, negligible heat dissipation by viscous eects, negligible heat generated by mass diusion, porous media resistive force given by Ergun equation, ideal gas behavior, ideal solution, and Newtonian uid. In the previous work of Maia et al. 9 , a dynamic model was proposed to describe a pilotscale plant for this process, considering axial mass and thermal diusion; however, in the present work, these eects were negligible, which could be justied by considering that the industrial reactors operate at short residence times or high spatial velocities. Moreover, the calculated thermal and mass Péclet number values were 9 × 102 and 9 × 103 , respectively, which indicate that the dispersion ux may be considered negligible when compared to the advective ux. Consequently, the system has rst-order dierential equations with respect to the spatial coordinate, i.e., only the advective transport is considered, and only one boundary conditions must be specied for each dierential equation. Additionally, despite the pseudo-homogeneous assumption, the eectiveness of the mass and heat transfer between the solid and uid phases were taken into account by using correction factors, proposing empirical models as function of dimensionless numbers.

2.1

Kinetic Model

The proposed reaction system is composed of 10 components and 8 reversible reactions, which was based on the reactions considered in the work of Kagyrmanova et al. 25 , containing originally seven species and ve irreversible reactions, listed in Equations 1 to 5, in irreversible form. In the present work, three additional reactions were included, listed in Equations 6 to 8. These additional reactions were included to give the model the ability to predict the ethane and propene compositions in the process outlet stream, since this components are important contaminants to be removed in the distillation column shown in Figure 1. Indeed, accordingly to Mohsenzadeh et al. 30 , the distillation step is performed at cryogenic condition and can be done in two steps. The rst one removes heavy impurities from ethylene such as propylene and ethane. The latter removes light impurities, like hydrogen from ethylene, 7



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being this step a stripper column. At the end, the polymer grade ethylene is obtained with a purity of 99.97 wt%.

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)

Ethoxyethane intramolecular dehydration:

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

(4)

Ethylene dimerization:

2C2 H4 C4 H8

(5)

Ethylene hydrogenation: C2 H4 + H2 C2 H6

(6)

8


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Propanol intramolecular dehydration: C3 H7 OH C3 H6 + H2 O

(7)

Butene metathesis: C4 H8 + C2 H4 2C3 H6

(8)

For the sake of notation, the chemical species involved in the kinetic routes are represented as numbers, as in Table 1. It is important to emphasize that the butene and propene species entail their isomers, which have been lumped into single species. Table 1: Chemical species considered in the ethanol dehydration process. 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 C3 H6

8 9 10

The kinetic modeling of the reactions rates for each reaction (Equations 1 to 8), was done following the Law of Mass Action, considering the reversibility of the reactions, based on the previous work of Maia et al. 9 . In general, the reaction rate for a reaction j can be written by the following expression:

 RjI = kj,D 

 Y

Ci |νi,j | −

i∈nDj

1 Kj

(C o )∆νj

Y

Ci |νi,j | 

i∈nRj

9


(9)


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In Equation 9, RjI is the ideal reaction rate for each reaction (j = 1, ..., 8), kj,D is the specic 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 coecient of species i in reaction j , Kj is the thermodynamic constant of chemical equilibrium, C o is the reference molar concentration 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 dierence between the global order of reverse reaction and the global order of direct reaction, described by the following equation:

∆νj = νj,R − νj,D =

X

νi,j −

i∈nRj

X

|νi,j | =

X

(10)

νi,j

nj

i∈nDj

where nj = nRj ∪ nDj . The specic rate of direct reaction is dened in accordance with the modied Arrhenius equation, as follows:

kj,D = k0j,D T

νj,D

−Eaj,D exp RT

ρcat

1−ε ε

(11)

In Equation 11, 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. The thermodynamic constant of chemical equilibrium is dened by:

∆Hjo − ∆Goj ∆Hjo 1 ln Kj = − − RT o RT RT

Z

T

To

o ∆Cp,j dT

Z

T

+ To

o ∆Cp,j

dT T

(12)

where ∆Hjo is the standard enthalpy change of formation of reaction j , ∆Goj is the standard o Gibbs energy of reaction j and ∆Cp,j is the variation of the specic molar heat capacity of

10


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reaction j . The standard enthalpy of formation of reaction j and the standard Gibbs energy of reaction j were calculated, respectively, by:

∆Hjo =

X

o

(13)

o νi,j ∆G¯i

(14)

¯i νi,j ∆H

nj

∆Goj =

X nj

¯i o is the standard molar enthalpy of formation of each component i and ∆G¯i o is where ∆H the standard molar Gibbs energy of formation of each component i. The variation of the specic molar heat capacity of reaction j was calculated by: o ∆Cp,j =

X

νi,j αi + T

nj

X nj

νi,j βi + T 2

X

νi,j γi + T 3

nj

X

νi,j δi

(15)

nj

where αi , βi , γi and δi are the coecients of the specic molar heat capacity of each component i. The ideal reaction rate (RjI ), as dened in Equation 9, describes a system without inert layer, catalyst with 100% of eectiveness, and without any deactivation. However, for the real system, the following deviations from ideality were considered in the process model: 1. Eectiveness of the xed bed related to the presence of inert layers (ef ); 2. Eectiveness of the catalyst related to the resistance to mass transfer between the uid and solid phases (fM T ); 3. Catalyst activity (a). Therefore, the real rate of chemical reaction j , Rj , combining all the above deviations, is described by: (16)

Rj = ef fM T a RjI 11



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The bed eectiveness indicates if, in a certain position in the reactor, the bed is composed either by a layer of catalyst or by a layer of inert. Therefore, for each reactor, there is a bed eectiveness function, dened as a combination of the following hyperbolic tangent function (also known as regularization function).

    z − Li   z − Lf       1 + tanh 250 L   1 − tanh 250 L  ef (z) =    2 2         | {z }| {z } eif

(17)

eff

where Li is the end location of the inert layer at the beginning of the reactor, Lf is the end location of the catalytic bed, and L is the total length of the reactor, while the length of the catalyst bed is given by: (18)

Lcat = Lf − Li

In Figure 2, the relationship between the bed eectiveness and the dimensionless length of the reactor is illustrated. The catalyst eectiveness, fM T , which is related to the resistance to mass transfer between the uid and solid phases, was modeled by an empirical correlation based on the work of Frössling 34 , and is shown below:

" fM T = αM T

2/3

Ref Scf τc,f

# βM T (19)

in which the subscript f refers to the value of the property at feed conditions, Ref is the Reynolds number of the particle, Scf is the Schmidt number, τc,f is the dimensionless combined residence time and αM T and βM T are tting parameters for each reactor. The denitions of these terms are described below.

12


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Figure 2: Bed eectiveness. Reynolds number of the particle at feed conditions:

Ref =

dp ρf vf µf

(20)

Schmidt number at feed conditions:

Scf =

µf ρ f DM,f

(21)

Dimensionless combined residence time:

τc,f =

τM,f τV,f τH,f 2

(22)

13



Page 14 of 44

Residence time on mass basis:

mcat m ˙f

τM,f =

(23)

Residence time on volumetric basis:

τV,f =

Lcat vf

(24)

Hydraulic residence time:

τH,f =

DR vf

(25)

Mass diusivity at feed conditions 35 :

DM,f =

NC X

(26)

yi,f DM,i

i=1

where DM,i and yi,f are the mass diusivity and molar fraction for each species i in the mixture at feed conditions, given by the Maxwell-Stefan equation:

DM,i =

1 − yi,f yi,f j=1 Di,j

(27)

N PC i6=j

where Di,j is the binary mass diusivity between species i and j at feed condition, calculated by the Chapman-Enskog equation, as follows:

Di,j

Tf 3/2 =b 2 Pf σi,j Ω

1 1 + Mi Mj

1/2

(28)

where σi,j is the average collision diameter, Ω is the collision integral and b is a constant of value 1.72268 × 10−18 kg 3/2 m3 /(s3 K 3/2 mol1/2 ).

14


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Mass of catalyst:

mcat = (1 − ε)ρcat

2 πDR Lcat 4

(29)

In the above equations, DR is the reactor diameter, µf is the feed viscosity, ρf is the feed specic mass of the uid, vf is the feed interstitial average velocity, dp is the equivalent diameter of the catalyst particle and m ˙ f is the feed mass owrate. The catalyst activity is a function of space and inherently of time too. However, the eect of time upon the catalyst activity was neglected in this work, as the model was developed at steady state operation and consider a very slow deactivation process. Hardly a catalytic bed has full activity throughout its length, even at the process startup. Therefore, we proposed a non constant prole for the catalytic activity:

" 1 + tanh κ a(z) =

z/L p

(z/L)2 + 1

−

!# Li +λ L

2

(30)

where κ and λ are tting parameters for each catalytic bed. The expected prole of the initial activity obtained by Equation 30 is a wave-like step function in the domain 0 ≤ a ≤ 1. The

λ parameter has the function of shifting the prole axially, while the κ parameter dictates the growth velocity by modifying the prole slope. In addition, an important result obtained by Equation 30 is the value a(Li ), which indicates the catalyst activity at the entrance of the catalytic bed. In Figure 3, it is shown the catalyst activity prole multiplied by the bed eectiveness with respect to the dimensionless length for a given reactor. Finally, the reaction rate for a component i (ri ) can be obtained by:

ri =

8 X

(31)

νi,j Rj

j=1

15



Page 16 of 44

Figure 3: Catalyst activity prole multiplied by bed eectiveness. 2.2

Fixed-Bed Reactor Modeling

Based on the simplifying assumptions described above, the mathematical model for the xed-bed reactor considered in this work is represented by: Overall mass balance: NC

d(vC) X = ri dz i=1

(32)

Component mass balance:

d(vCi ) = ri dz

(33)

16


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Energy balance: 8

ρCˆp v

X dT dP = (−∆Hj )Rj + v dz dz j=1

(34)

Momentum balance:

ρv

dv dP =− − FRM + ρg dz dz

(35)

Equation of state: (36)

P = CRT

where N C is the number of components, C is the total molar concentration, Cˆp is the specic heat capacity per mass of uid, ∆Hj is the heat of reaction j , FRM is the porous media resistive force and g is the gravitational acceleration. It is noteworthy that the index

i refers to the species and the index j refers to the reaction number. The boundary conditions are given by: Overall mass balance: (37)

C(0) = Cf Component mass balance:

(38)

Ci (0) = Ci,f Energy balance:

(39)

T (0) = Tf

17



Page 18 of 44

Momentum balance: (40)

v(0) = vf The interstitial feed velocity was calculated as follows:

vf =

uf 4m ˙f = 2 εi ρf πDR εi

(41)

being uf the supercial velocity and εi the inert layer porosity on the top of the catalyst bed. Analogously to what was done for the reaction rate, it could be expected that the temperature of the solid and uid phases be dierent, due to heat transfer resistance between phases. Thereby, a correction factor for the heat transfer resistance between the solid and uid phases was introduced (fHT ), so that the actual heat of reaction was calculated as follows: (42)

∆Hj = fHT ∆HjI where ∆HjI is the ideal heat of reaction j , given by the thermodynamic relation:

∆HjI (T )

=

∆Hjo

T

Z +

To

(43)

o ∆Cp,j dT

An empirical correlation for the heat transfer correction factor (fHT ) was developed, in the same structure of the mass transfer correction factor, given by:

" fHT = αHT

2/3

Ref P rf τc,f

#βHT (44)

in which αHT and βHT are tting parameters for each reactor, and P rf is the Prandtl number

18


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at feed condition, described as follows:

P rf =

µf Cˆp,f kH,f

(45)

where kH,f is the thermal conductivity at feed condition 35 , given by:

kH,f =

NC X

yi,f kHi,0

i=1

Tf To

1/2

(46)

where kHi,0 is the thermal conductivity of specie i in the laminar boundary layer at temperature T o . In addition to the aforedescribed dierential-algebraic system, some constitutive equations are needed, as presented below: Mixture specic mass: (47)

ρ=C M

Average mixture molar mass:

M=

NC X

(48)

yi Mi

i=1

where Mi is the molar mass of species i. Dynamic viscosity of the uid:

µf =

NC X

(49)

y i µi

i=1

where µi is the dynamic viscosity of species i. Species i molar fraction:

yi =

Ci C

(50) 19



Page 20 of 44

Specic heat capacity of the uid in mass basis:

Cp Cˆp = M

(51)

Specic heat capacity of uid in molar basis:

Cp =

NC X

y i αi + T

i=1

NC X

y i βi + T

NC X

2

y i γi + T

3

(52)

yi δi

i=1

i=1

i=1

NC X

The porous media resistive force (FRM ) is composed of two parts, one for the inert layer and another one for the catalyst layer. In that way, the total resistive force can be written as follows: i i FRM =fRM FRM

1−

eif (z)

cat cat + fRM FRM ef (z)

Li L

h

+ 1−

i L − L

eff (z)

f

L

+

(53)

Lcat L

i cat where fRM and fRM are tuning parameters for resistive force in the inert layer and catalyst

layer porous media, respectively, for each reactor. The resistive force in each layer can be described by: i FRM

(1 − εi )2 = 150 (εi )2

cat FRM

(1 − ε)2 = 150 ε2

µf v d2p,i

µf v d2p

+

7 (1 − εi ) ρv 2 4 εi dp,i

7 (1 − ε) ρv 2 + 4 ε dp

(54)

(55)

Equations 54 and 55 are written as the Forchheimer quadratic form, being the permeability constants given by Ergun 35,36 .

20


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2.3

Dimensionless form of the mathematical model

In order to rewrite the model in a dimensionless form, the following dimensionless variables were dened: Independent variable:

χ=

z L

(56)

Dependent variables:

Υt =

C Cref

Υi =

Ci Cref

θ=

T Tref

Π=

P Pref

ω=

v vref

(57)

where the subscript ref indicates an arbitrary reference value for the respective variable. Additional variables:

φ=

ρ ρref

∆j =

Γ=

∆Hj ∆Href

Da0j =

Cˆp Cˆp,ref

η=

Daj = ef a fM T Da0j exp [−

1−ε L ν −1 ρcat k0j,D Tref νj,D Crefj,D ε vref

M Mref

σ=

γj νj,D ]θ θ

γj =

µ µref

(58)

(59)

Eaj,D R Tref

(60)

From these denitions, the dimensionless parameters of the model are presented in Table 2. With these denitions, the model equations in the dimensionless form are written as follows:

21



Page 22 of 44

Table 2: Dimensionless model parameters denitions and values. Name

Symbol

Denition

Value

Dimensionless Adiabatic Temperature

B

(−∆Href Cref ) ρref Cˆp,ref Tref

−2.162

Froude Number

Fr

2 vref gL

2.019 × 10−2

Euler Number

Eu

Pref 2 ρref vref

2.028 × 105

Blake-Kozeny Equation

BK

Blake-Plummer Equation

BP

Eckert × Euler numbers

C

150

(1 − ε)2 µref L ε2 ρref vref dp dp 71−ε L 4 ε dp

ρref

Pref ˆ Cp,ref Tref

7.219 × 102

4.237 × 103 4.112 × 10−1

Dimensionless overall mass balance: NC

8

d(ω Υt ) X X = νi,j Daj Ψj dχ i=1 j=1

(61)

Dimensionless component mass balance: 8

d(ω Υi ) X = νi,j Daj Ψj dχ j=1

(62)

Dimensionless energy balance: 8

φΓω

X dθ dΠ =B ∆j Daj Ψj + C ω dχ dχ j=1

22


(63)

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Dimensionless momentum balance:

φω

dω dΠ 1 = −Eu − ΛRM + φ dχ dχ Fr

(64)

Equation of state: (65)

Π = Υt θ

In Equations 61 and 62, Ψj is the dimensionless ideal reaction rate, dened as follows:

Ψj =

Y

Υi

|νi,j |

i∈nDj

1 − Kj

Cref Co

∆νj Y

Υi |νi,j |

(66)

i∈nRj

In Equation 64, ΛRM is the dimensionless porous media resistive force, which can be written as follows: i ΛRM =fRM ΛiRM

1 − eif (z)

cat cat + fRM ΛRM ef (z)

Li L

h i L − L f f + 1 − ef (z) + L

(67)

Lcat L

The resistive force in each layer can be described by: (68)

2 ΛiRM = Λcat RM = BK σ ω + BP φ ω

It is important to note that in Table 2, a single value is presented for BK and BP , which is due to the consideration that the particle diameter and porosity of the inert layers and catalyst are the same. In this way, it is possible to write the equality between the inert and catalyst layers resistive forces, according to Equation 68.

23



3

Results and Discussion

3.1

Parameter Estimation

In order to perform the parameter estimation step, it is necessary to know the following geometrical and physical parameters of the analyzed industrial plant: length of the reactors (L), length of inert and catalyst layers (Li , Lf and Lcat ), diameter of the reactors (DR ), apparent diameter of the catalyst particle (dp ), catalyst density (ρcat ), and porosity of inert and catalytic layers (εi and ε). These data cannot be disclosed due to condentiality reasons; however, the dimensionless form of the model presented in Process Modeling Section and the values of the dimensionless parameters (see Table 2), which encompass those condential parameter values, remove the need to inform the individual values of such parameters 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. 37 , namely, molar mass (Mi ), dynamic viscosity (µi ), specic heat capacity

¯i o ), Gibbs energy of formation coecients (αi , βi , γi and δi ), enthalpy of formation (∆H o

¯i ), average collision diameter (σi,j ), integral collision (Ω) and thermal conductivity (∆G (kHi,0 ), for each of the components i. The estimated kinetic parameters were: pre-exponential factors (k0j,D ) and activation energies (Eaj,D ) for the eight reactions. The estimated dimensionless parameters were: tuning parameters of the activity equation (κ and λ), tuning parameters of the correction factor equation for the mass transfer resistance (αM T and βM T ) and heat transfer resistance (αHT and βHT ), tuning parameters for the resistive force equation in inert layer i cat (fRM ) and in catalyst layer (fRM ).

Therefore, for the entire process model, a total of 16 + 8NR parameters were estimated, where NR is the total number of reactors in the industrial plant. Three periods of industrial data were chosen, named here as periods 1, 2 and 3. The ethanol owrate is distinct in each period, corresponding to the conditions of high, low and moderate owrate, respectively, 24


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when compared to the nominal ow of the process. The plant data for each period consist of measurements of temperature by the thermocouples at dierent positions of the reactor length, for each reactor, and the composition at the outlet of the reaction section, resulting in 10 + 9NR measurements available for each of the three operating conditions, being 10 composition data at the output of the reaction section and the rest of the data are relative to the axial temperature measurements. The objective function was formulated in terms of two contributions: one concerning measurements of the thermocouples and another based on the composition at the outlet of the reaction section, as follows: NR X exp 9 mod X Tk,m − Tk,m Fobj (α) = σT 2k,m m=1 k=1

2

10 X Ckexp − Ckmod + σC 2k k=1

2 (69)

exp mod where Tk,m and Tk,m are the measured and predicted temperatures at the k th thermocouple

in the mth reactor, respectively, σT k,m is the standard deviation of the temperature measured at the k th thermocouple in the mth reactor, Ckexp and Ckmod are the measured and predicted k th component molar concentration at the outlet of the reaction section and σC k is the standard deviation of the molar concentration of the k th component measured concentration at the outlet of the reaction section. It is assumed that the probability distribution of the experimental error is normal. Therefore, the experimental error should not be greater than the lowest possible value of the objective function, in agreement with the hypothesis of the well done experiment. The parameter estimation problem was solved using EMSO process simulator 33 , and the system of dierential-algebraic equations were numerically integrated by DASSLC routine 38 . A non-deterministic optimization algorithm of dierential evolution 39 was used, using 50 generations and 100 particles, providing an initial guess to deterministic algorithms used afterwards. The algorithm of exible polyhedrons 40 with a condence level of 95% was

25



used and the solution was nally rened by Brent's algorithm 41 . The average values of the estimated kinetic parameters in dimensionless form are presented in Table 3. Table 3: Estimated kinetic parameters in dimensionless form. Parameter

Average value

Parameter

Average value

Da01 Da02 Da03 Da04 Da05 Da06 Da07 Da08

2.731 ×1012 8.226 ×108 4.516 ×106 5.330 ×104 5.494 ×107 1.751 ×1011 3.584 ×109 4.685 ×109

γ1 γ2 γ3 γ4 γ5 γ6 γ7 γ8

21.357 21.858 15.258 15.644 17.198 6.485 14.400 16.969

Table 4 displays the estimated dimensionless parameters of the empirical correlations for two of the NR reactors in the reaction section, namely reactor A and B. Table 4: Estimated dimensionless parameters of the empirical correlations. Parameters

Reactor A

Reactor B

λ κ

5.784 ×10−2 105 0.030 -0.528 0.312 -0.052 8.549 1.303

4.072 ×10−2 50 0.074 -0.441 0.891 0.023 2.704 0.293

αM T βM T αHT βHT i fRM cat fRM

In order to verify the condence interval of the parameters and the objective function, statistical tests were carried out after the parameter estimation step. In order to evaluate the objective function, the F-test was performed by comparing the mean prediction variance of the model to the mean experimental variance 42 . The obtained 2 values for the mean prediction variance (σ ˆm ) and the mean experimental variance (σε2 ) were

0.811 and 1.055, respectively. Based on the number of experiments (i.e., three), the degrees

26


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of freedom of the problem (87), and the signicance level of 0.05, the following relation was achieved:

0.306 ≤ Fobj =

2 σ ˆm = 0.769 ≤ 13.947 σε2

(70)

Therefore, the model can represent statistically well the experimental data, with prediction errors not signicantly greater than the experimental errors, and the model provide results not better than the experimental data used in the parameters estimation. Another evaluation of the model t quality was done through the analysis of the coecient of determination (R2 ) which indicates how well the model prediction approximates the experimental data points.

The R2 value found in the parameters

estimation step was 0.938, which represents a good t of the model to the experimental data.

Usually, if the coecient of determination is greater than 0.9, the model is

considered satisfactory,

indicating that the values predicted by the model vary

approximately linearly and proportionally to the experimental measurements. Regarding the estimated parameters quality, the parameters correlation matrix was evaluated, and is shown in Figure 4, presenting low correlation among most of the parameters, with only few activation energies having higher correlation with other kinetic parameters, which is a well-known behavior. The mean parametric correlation was equal to 0.207, indicating that the parameters estimation step was ecient, facilitating the identication of their dierent eects on the model outcome 43 . The parameters relative condence intervals at the signicance level of 95% were evaluated from the t-student distribution and the standard deviations of the parameters, and the results are presented in Tables S1 and S2. By analyzing the results in Tables S1 and S2, it is possible to note that the highest value for the relative condence interval of the parameters is 49%, which indicates that all the estimated parameters of the model are statistically signicant.

27



Figure 4: Estimated parameters correlation matrix for the proposed model. For the comparison between the results obtained by the mathematical model and the experimental data, to evaluate the model ability to predict the axial temperature prole and the chemical composition at the output of the reaction section, the three selected operating conditions of the industrial plant were considered. It is worth mentioning that these periods are very close to the plant start-up, such that the catalyst deactivation was moderate. Additionally, these periods exhibits dierent owrates with respect to the total amount of ethanol fed. 28


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Figures 5, 6 and 7 show the temperature proles for each reactor in periods 1, 2 and 3, respectively. As expected, as the global reaction is endothermic, there is a temperature drop within the catalyst layer, mainly because of the ethanol intramolecular dehydration reaction. Furthermore, there is a slight temperature drop within the inert layers due to the gas mixture expansion, which is a result of the pressure drop in this region. It is important to note that this last result could only be obtained due to the pressure terms contained in the right hand side of the energy balance, as presented in Equation 34. Additionally, It is possible to observe that, regardless of the operating condition, the proposed model can describe the temperature proles for each of the reactors, presenting an excellent t to the experimental data. It is important to mention that the operating conditions for periods 1 and 2 are, in fact, extreme conditions for this process, with distinct owrates. A total of 27NR comparison points in terms of temperature prole were used and all the values predicted by the model are within the condence interval of the experimental data.

29



(a) Reactor A

(b) Reactor B

Figure 5: Axial temperature prole for reactors A and B in period 1. 30 ACS Paragon Plus Environment

Page 30 of 44

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(a) Reactor A

(b) Reactor B



(a) Reactor A

(b) Reactor B


Page 32 of 44

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Additionally, Table 5 presents the mean relative absolute error (MRAE) for a given operation period and maximum and minimum relative error for a given reactor considering all the three periods, calculated according to the following equations:

exp 9 mod 1 X Tk,m − Tk,m MRAE = exp 9 k=1 Tk,m

(71)

exp T − T mod k,m k,m Maximum Relative Error = max exp Tk,m exp T − T mod k,m k,m Minimum Relative Error = min exp Tk,m

(72) (73)

for a given period, for reactor m and for k = 1, .., 9 thermocouple. By analyzing the calculated errors presented in Table 5, it is possible to note that the maximum error is 3.34%, obtained in reactor A, which indicates a good agreement between the model predicted values and the industrial data. Moreover, the maximum value for the mean relative absolute error is 2.12%, obtained in Reactor A for the period 3, showing that the model has the ability to predict all thermocouples values with very small deviations. Regarding the model ability to predict the outlet composition, the relative error and the relative condence interval of each component molar fraction for each of the analyzed periods are shown in Table 6. Table 5: Comparison of the axial temperature prole in each reactor for periods 1, 2 and 3. Reactor A

Reactor B

2.01 1.56 2.12 3.34 0.09

0.65 0.83 0.60 1.40 0.07

Mean Relative Absolute Error (%) - Period 1 Mean Relative Absolute Error (%) - Period 2 Mean Relative Absolute Error (%) - Period 3 Maximum Relative Error (%) Minimum Relative Error (%)

By examining Table 6, it is possible to observe that, for period 3, the values of molar fractions predicted by the model were within the condence interval of the experimental data for all species considered in the system. However, the value of the ethoxyethane molar 33



Page 34 of 44

Table 6: Comparison of the composition prediction at the output of the reaction section over periods 1,2 and 3. Period 1 Component Ethanol Ethene Water Ethoxyethane Ethanall Butenes Ethane Propane

Relative Error (%) 10.2 0.5 -0.8 80.3 17.1 33.7 33.2 23.6

Period 2

Relative Condence Interval (%) ± 33.1 ± 8.2 ± 3.8 ± 39.0 ± 26.1 ± 51.9 ± 44.5 ± 45.8

Relative Error (%) 30 -7.3 4.4 35 -21.5 -8.6 1.0 1.2


Period 3 Relative Error (%) -13.4 -1.1 0.7 -4.5 7.2 6.2 12.8 5


fraction is not within the condence interval for period 1, as well as that of ethanal for period 2. It is worth pointing out that, in terms of order of magnitude, the molar fraction of ethoxyethane and ethanal represent small values when compared to the main process component (i.e., ethylene). One may notice that the higher relative error obtained in period 3 is 13.4% for ethanol, which shows that the model presents a good prediction for this variable, with errors less than 2% for ethylene and water, which are the main components. For these components, the largest errors of prediction are obtained in period 2, which is characterized by low owrate. Additionally, the values predicted by the model in any period were very close to the average observed values, thus showing that the model has indeed a very good accuracy. Therefore, with caveats for the minor components, the model is able to properly predict reactors outlet compositions.

3.2

Model Validation

After the parameter estimation step, in order to analyze the model prediction ability at dierent conditions of the data used for estimation, the model was tested at seven new process conditions obtained from the industrial plant studied in this work. Additionally, the model was also tested against pilot plant data from the work of Kagyrmanova et al. 25 for the comparison of axial temperature proles and outlet composition.

34


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3.2.1

Industrial Plant Data

For the validation of the model, seven operating conditions of the industrial plant at steady state were considered, being this data dierent from that used for estimation and denominated Periods 4, 5, 6, 7, 8, 9 and 10. These periods are also close to the plant start-up, such that catalytic deactivation could be considered time independent. These periods are temporally subsequent, but exhibit a dierent ethanol feed owrates.

In

addition, they are also subsequent to the periods used in the estimation, as can be seen in Figure 8.

Figure 8: Operating conditions for parameter estimation and model validation. Table 7 shows the mean relative error for the operating periods and the maximum and minimum relative error for a given reactor considering all seven validation periods. Analyzing the errors presented in Table 7, it is possible to note that the relative errors are less than 3%, which indicates the excellent agreement between the predicted values and 35



Page 36 of 44

Table 7: Mean Relative Absolute Error of the axial temperature prole prediction for the periods considered for model validation. Reactor A

Reactor B

0.56 0.63 1.65 0.31 0.80 0.66 0.45 2.54 0.00

0.24 0.55 0.78 0.84 0.29 0.47 0.70 2.27 0.02

Period 4 - Mean Relative Absolute Error(%) Period 5 - Mean Relative Absolute Error(%) Period 6 - Mean Relative Absolute Error(%) Period 7 - Mean Relative Absolute Error(%) Period 8 - Mean Relative Absolute Error(%) Period 8 - Mean Relative Absolute Error(%) Period 10 - Mean Relative Absolute Error(%) Maximum Relative Error (%) Minimum Relative Error (%)

industrial data. The relative error for the outlet composition are shown in Table 8 for the seven validation periods of operation for each of the components. Table 8: Relative Error of chemical composition prediction in periods considered for model validation. Component/ Period P4 (%) P5 (%) P6 (%) P7 (%) P8 (%) P9 (%) P10 (%)

Ethanol

Ethylene

Water

Etoxyethane

Ethanal

Butenes

Ethane

Propene

-38.1 39.2 -38.1 -53.3 -3.1 -55.8 -5.0

-3.5 6.3 8.6 -2.3 0.7 0.0 -2.4

1.4 -3.3 -4.3 1.0 -0.4 0.0 0.9

65.5 51.4 46.7 44.8 46.7 42.2 48.6

1.6 -6.2 -2.6 -7.2 -3.3 -6.6 -5.0

9.6 11.1 8.9 10.4 11.8 13.3 5.5

14 9.8 13.3 9.0 12.6 9.6 11.2

16.5 8.4 0.8 4.6 5.5 7.7 -2.3

By examining Table 8, it can be seen that the largest relative error is for the ethoxyethane in Period 4. The highest relative error for ethylene was 8.6% and for ethanol 55.8%. It is observed that the values predicted by the model in any period are close to those from in the industrial plant, showing the good accuracy at conditions extrapolated from those used in the estimation step.

36


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3.2.2

Pilot Plant Data

The experimental data from the work of Kagyrmanova et al. 25 was used to evaluate the prediction ability of the proposed model at dierent scales, since that work refers to a pilot plant for ethanol dehydration to ethylene. Further details on the operating conditions for the plant simulation can be found in Maia et al. 9 , the main one being: T = 438o C ;

P = 1.2 atm and Ff = 1.3 kg/h. This operating condition was initially chosen for the estimation of the empirical correlation parameters that describe the resistance to mass and energy transfer between the uid and solid phases, assuming all other parameters equal to those used in the simulation of the plant at industrial scale. Additionally, it is important to emphasize that the catalyst activity was considered constant and unitary, so that there was no catalyst deactivation. Thus, the estimated parameters for heat and mass transfer empirical correlation were αM T = 0.001, βM T = −0.460, αHT = 0.314, and βHT = −0.024, respectively. The comparison with the experimental data was performed with respect to the axial temperature prole, the ethanol conversion and the ethylene molar fraction on a dry basis. Figure 9 illustrates the comparison of the axial temperature prole between the model proposed in this work, the model proposed by 25 and experimental data from the pilot plant. From Figure 9, it can be seen that the proposed model provides a better t to the experimental data than the model proposed by Kagyrmanova et al. 25 , especially at the end of the reactor. The mean deviation reached by the model proposed in this work was 0.53o C while the maximum deviation for the last thermocouple was −1.83o C , showing an excellent prediction for the temperature prole. The values for ethanol conversion and the ethylene mole fraction on dry basis are shown in Table S3. Table S3 shows that the proposed model presented better adhesion to the experimental data than the model proposed in the work of Kagyrmanova et al. 25 , possibly due to the 37



Figure 9: Comparison of predicted and experimental axial temperature in the pilot plant. dierent simplifying assumptions 9 .

38


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4

Conclusion

In this work, a rst-principles mathematical model for xed bed reactors for the ethanol dehydration process was presented, considering eight chemical reactions and ten species. The model parameters were estimated with data from an industrial plant for dierent operating conditions, over a wide range of throughput/owrate. The model presented good ability to predict the experimental data, with low deviations from plant measurements (axial temperature proles and outlet composition) throughout distinct analyzed operating periods.

The comparison between the observed and predicted values showed relative

deviations below 5% for the main components and temperature at the nominal feed owrate condition. The same model was also capable to predict the experimental results of a pilot plant with relative deviation below 0.4%. The mathematical model presented here can be further used for process optimization.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Contents: Table S1: Relative condence intervals of the estimated kinetic parameters. Table S2: Relative condence intervals of the estimated dimensionless parameters of the empirical correlations. Table S3: Comparison of predicted values and pilot plant data for conversion and ethylene mole fraction.

Acknowledgement The authors are grateful to CNPq Grant 302893/2013-0 for the nancial support.

39



Page 40 of 44

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