Simultaneous Optimal Design of an Extractive Column and Ionic

ARTICLE pubs.acs.org/IECR

Simultaneous Optimal Design of an Extractive Column and Ionic Liquid for the Separation of BioethanolWater Mixtures Darinel Valencia-Marquez, Antonio Flores-Tlacuahuac,* and Ruben Vasquez-Medrano Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D.F., 01210 Mexico ABSTRACT: Recently renewed interest in the optimal design of sustainable processing systems has emerged as consequence of pollution issues and global climate changes. The replacement of hazardous industrial solvents widely used for azeotropic separations is clearly a challenging research area for new products design. However, as important as product design is, the design of the optimal processing configuration where the azeotropic separation will take place is also a key issue. As a matter of fact, the strong interaction between product and process design indicates that better optimal processing conditions can be attained by solving both problems simultaneously rather than sequentially. In the present work, we take advantage of this natural interaction for the optimal simultaneous design of both ionic liquids and an extractive distillation column for the high purity separation of the ethanol/water azeotropic mixture for deploying ethanol as a biofuel. The problem is formulated as a steady-state disjunctive mixed-integer nonlinear programming (MINLP) problem. The results indicate that new green solvents constitute a good replacement for hazardous solvents. Because ionic liquids are expensive solvents, it is worth it to explore the deployment of advanced optimization tools for profit maximization of sustainable processing systems. Through the use of the proposed MINLP formulation, improved ethanol/water separation configurations deploying ionic liquids were attained. Because ethanol features high purity, it can be used for biofuel applications.

’ INTRODUCTION The supply of alternative energy sources for various operations such as transport, power generation, and heating is of critical concern in the world today. Due to the forecasted scarcity of fossil fuels and the increase in their cost, as well as concerns about global warming caused by greenhouse gases like CO2, SO2, NOx, etc., growing interest in the deployment of alternative energy sources (such as biofuels, solar, wind, tidal, geothermal) has emerged. Presently, it seems to be clear that none of the alternative energy sources is a full and definitive solution to near future energy demands and that a portfolio of renewable energy sources1 can contribute to a given extent to meeting society’s energy demands. Before a full energy solution can be found, energy demands will probably be met by a clever combination of fossil fuels, alternative energy sources, and nuclear energy depending upon local energy sources, political decisions, and market constraints, among other factors. The transition from an economy completely based on fossil fuel consumption to an economy based on a portfolio of energy sources is a hard issue that each society must handle in the best possible way such that access to clean, sustainable, and relatively cheap energy sources is guaranteed. Ethanol has been proposed as one of the alternative energy sources that can contribute to meeting partial energy demands.26 In fact, ethanol was one of the first fuels deployed for automobile powering.7 However, ethanol was abandoned in favor of fossil fuel gasolines because of economic considerations. However, in countries with a scarce supply of fossil fuels, such as Brazil, for years ethanol has been deployed as an effective and convenient way to meet energy demands, mostly in the transport sector. Anyway, we must highlight that the industrial production of ethanol is not free r 2011 American Chemical Society

of environmental and sustainable concerns. Traditionally, ethanol has been commonly manufactured from corn or sugar cane, and because these two raw materials are deployed for human population consumption, recently there has been a perception that ethanol is one the reasons for the increasing cost of such raw materials.8 Moreover, large land extensions have been cleared for sugar cane production, leading to environmental issues. A way to produce ethanol in a more sustainable way calls for the deployment of cellulosic residues instead of corn and sugar as raw materials. However, before cellulosic ethanol can be widely used as an alternative fuel, some technical issues, such as efficient cellulosic extraction, fermentation, and separation, ought to be solved. In this work, we will address one of the more challenging problems related to ethanol production for the transportation sector. Because of engine constraints, ethanol ought to be delivered at high purities well beyond the normal azeotropic composition present in ethanol/ water mixtures. Traditional ways of separating ethanol/water mixtures beyond azeotropic compositions involve the use of harmful solvents. Presently, there is a growing concern over the large term impact of processing systems on the environment and human health.9 In fact, the design and operation of systems featuring sustainability characteristics is becoming a design objective as important as economic considerations.10

Special Issue: AMIDIQ 2011 Received: August 3, 2011 Accepted: December 5, 2011 Revised: December 5, 2011 Published: December 05, 2011 5866

dx.doi.org/10.1021/ie201726r | Ind. Eng. Chem. Res. 2012, 51, 5866–5880

Industrial & Engineering Chemistry Research In order to find new sustainable ways of addressing the separation of high purity ethanol/water mixtures, in this work, we propose the deployment of ionic liquids in this separation process. A deeper discussion about the use of ionic liquids for azeotropic separations can be found elsewhere.11,12 For the aim of this paper, it is enough to state that ionic liquids can constitute an option for a new kind of sustainable separation system because they can be considered green solvents.1318 However, the main present disadvantage seems to be their high production cost. In a past work, we discussed the optimal molecular design of ionic liquids for high purity ethanol/water separation.11 Moreover, the optimal design of the processing system to carry out the separation task was also discussed.19 We must stress that both works, ionic liquid design and the processing system design, were carried out in a sequential manner. The ionic liquid was designed without considering the processing equipment that eventually would be used to carry out the separation task. Similarly, for the design of the processing system, the structure of the ionic liquid previously designed was fixed. However, there are some strong interactions between both problems that could lead to attaining improved optimal solutions in comparison to solving both problems sequentially. In fact, the interaction between solvent and process design has been exploited by some authors.20 In summary, this work focuses on the idea of using ethanol as a source of alternative and sustainable energy to be obtained from lignocellulosic residues such that the production of ethanol does not compete with the food chain. By exploiting the natural interactions between the chemical structure of the ionic liquid and the separation system design, we hope to find new, economic, and sustainable ways of carrying out the separation task well beyond azeotropic composition. To take advantage of the presence of such natural system interactions, the ionic liquid and processing system design problems are posed as optimization problems to be solved in a simultaneous, rather than in a sequential, way. Since continuous and binary decision variables are involved, the simultaneous optimal ionic liquid and processing system design was approached as a mixed-integer nonlinear programming (MINLP) problem21 whose solution was sought by standard techniques. For the optimal design of the ionic liquid, the same previously proposed methodology was deployed, 11 which consisted of a priori selection of promising cations and anions. Moreover, the optimal column design was based on the methodology described by Yeomans and Grossmann.22

’ PROBLEM FORMULATION The problem to be addressed in this work can be formulated as follows. “Given (1) a set of cations and anions, (2) two feed streams (one containing the ethanol/water mixture to be separated and the other one for the ionic liquid), (3) a set of distillation and bottoms products with desired recoveries, and (4) a maximum number of separation trays, the design objective consists of the simultaneous optimal design of both the ionic liquid chemical structure and the extractive distillation column synthesis (i.e., optimal number of trays, ethanol/water feedtray location, ionic liquid feedtray location, reflux ratio, column diameter, vapor and liquid flow rates, tray temperatures profile, composition of the internal

ARTICLE

vapor and liquid streams, condenser and reboiler heat duties, and heat transfer areas) such that the total annualized cost (TAC) is minimized.” The modeling assumptions made for the ionic liquid design are thoroughly discussed in ref 11. Regarding the extractive column design, we have assumed constant atmospheric pressure, vapor liquid equilibrium, and nonideal liquid phase behavior. Moreover, because physical properties cannot be available for novel ionic liquids, its required physical and thermodynamic properties will be computed by group contribution methods.

’ MINLP FORMULATION Although the MINLP formulations for both the ionic liquid and the extractive distillation column designs have been discussed previously,11,19 in this part they are included for completeness. The meaning of the variables can be found in the Nomenclature section. Objective Function. The optimization of the distillation column is carried out by minimizing a combination of both investment and operating costs. The objective function reads as follows: min TAC ¼ ICC f ðNT, CDÞ þ IACRA u

f ðRAÞ þ IACCA f ðCAÞ þ SUC f ðQ RÞ þ CUC f ðQ CÞ CPetOH f ðDetOH Þ

ð1Þ

where u stands for the set of decision variables. ICC, IACRA, IACCA, SUC, CUC, and CPC2H5OH are coefficients of the cost functions whose values are 0.162844, 0.1782, 0.1782, 4.173 103, 7.48 104, and 1.25 104, respectively. The cost functions read as follows: f ðNT, CDÞ ¼ ðNTÞðCD1:245 Þ

ð2Þ

f ðRAÞ ¼ RA 0:8

ð3Þ

f ðCAÞ ¼ CA 0:8

ð4Þ

f ðQ RÞ ¼ 8000Q R

ð5Þ

f ðQ CÞ ¼ 8000Q C

ð6Þ

f ðDC2 H5 OH Þ ¼ 8000C2 H5 OH

ð7Þ

Continuous Constraints. The continuous constraints include the general column mass balance, the purity and recovery requirements, the calculation of the number of stages, the column diameter, and the reboiler and condenser areas. These constraints are given as follows. General Column Component Mass Balance.

∑n Fni ¼ Di Bi

i ∈ C, n ∈ NFT

ð8Þ

This constraint takes into account all of the streams that are fed to the column and the bottom and top products to set up the component mass balance. 5867

dx.doi.org/10.1021/ie201726r |Ind. Eng. Chem. Res. 2012, 51, 5866–5880

Industrial & Engineering Chemistry Research

ARTICLE

MESH Equations for Feed Tray (Fixed Trays). Fni

þ

Lin þ 1

þ

Vni 1

Lin

Vni

¼0

i ¼ fetOH, H2 Og, n ∈ NFT Fni þ Lin þ 1 Lin ¼ 0 Fni ¼ FTxif

i ¼ fILg, n ∈ NFT

f ¼ fILF, AMFg, n ∈ NFT

Lin ¼ LIQ n xin

hLin

¼

f ðTnL Þ

hV in ¼ f ðTnV Þ hFin

¼

∑i

xin

∑i

yin

f ðTnF Þ ¼1

∑i yin ¼ 1

i ¼ fetOH, H2 Og, n ∈ NCT

ð34Þ

fi,Ln ¼ fi,Vn


fi,Ln ¼ xin Pn0, i γin

ð14Þ

n ∈ NFT

ð15Þ

i ¼ fetOH, H2 Og, n ∈ NFT

ð16Þ

n ∈ NFT

ð17Þ

n ∈ NFT

ð32Þ

ð11Þ

Lin hLin Vni hV in Þ ¼ 0 n ∈ NFT


ð33Þ

ð13Þ

∑i

hDi ¼ f ðTnL Þ



ðFni hFin þ Lin þ 1 hLin þ 1 þ Vni 1 hV in 1

ð31Þ

∑i xin ¼ 1

ð12Þ

¼


ð10Þ

n ∈ NFT

Vni

VAPn yin

ð9Þ

hV in ¼ f ðTnV Þ


ð37Þ

TnL ¼ TnV

n ∈ NCT

ð38Þ

Reboiler MESH Equations (Fixed Tray). Lin þ 1 Vni Bi ¼ 0

Lin þ 1 Bi ¼ 0

ð18Þ

fi,Ln ¼ fi,Vn

i ¼ fetOH, H2 Og, n ∈ NFT i ¼ fetOH, H2 Og, n ∈ NFT



ð19Þ

i ¼ fetOH, H2 Og, n ∈ NRT

ð43Þ

ð21Þ

∑i ðLin þ 1hLin þ 1 Vni hVin Bi hBi Þ ¼ Q R

ð23Þ

n ∈ NRT

Condenser MESH Equations (Fixed Tray). Vni 1 Lin Di ¼ 0

Lin ¼ LIQ n xin Vni

¼

∑i

ðVni 1 hV in 1

VAPn xin

hLin ¼ f ðTnL Þ

ð45Þ

hV in ¼ f ðTnV Þ


ð46Þ

∑i xin ¼ 1

n ∈ NRT

ð48Þ

∑i yin ¼ 1


ð49Þ

ð26Þ

ð28Þ

fi,Ln ¼ fi,Vn

n ∈ NRT



þ D hD Þ ¼ Q C i


n ∈ NRT

ð25Þ



hLin ¼ f ðTnL Þ

hBi ¼ f ðTnL Þ

ð27Þ

i

ð44Þ

ð24Þ


Lin hLin

ð41Þ

Vni ¼ VAPn yin

n ∈ NFT


n ∈ NRT

ð20Þ

TnL ¼ TnV

Rf lux Di ¼ Lin

ð40Þ

ð42Þ

ð22Þ


i ¼ fILg, n ∈ NRT

ð39Þ

n ∈ NRT


Di ¼ DISyin


Lin ¼ LIQ n xin

fi,Vn ¼ yin P


ð36Þ

fi,Vn ¼ yin P

Bi ¼ BOT xin ¼1


ð35Þ

ð29Þ ð30Þ 5868


ð47Þ

ð50Þ ð51Þ

fi,Vn ¼ yin P


ð52Þ

TnL ¼ TnV

n ∈ NRT

ð53Þ



ARTICLE

MESH Equations for the Intermediate Trays in the Rectifying and Stripping Sections. Lin þ 1

þ

Vni 1

Lin

Vni

xiNT g τid

¼0

i ¼ fetOH, H2 Og, n ∈ TM Lin þ 1 Lin ¼ 0

Purity of Component i in Distillate and Bottoms Product.

i ¼ fILg, n ∈ TM

xi1 g τiB

ð54Þ ð55Þ

Lin ¼ LIQ n xin

n ∈ TM

ð56Þ

Vni ¼ VAPn yin

i ¼ fetOH, H2 Og, n ∈ TM

ð57Þ

n ∈ TM

ð59Þ

hV in ¼ f ðTnV Þ


ð60Þ

∑i xin ¼ 1

n ∈ TM

ð61Þ

∑i yin ¼ 1


ð62Þ


¼

yin P

TnL ¼ TnV

ð63Þ


ð64Þ


ð65Þ

n ∈ TM

ð66Þ

Material Balance Envelopes between the Condenser and the Tray n before the Ethanol/Water Feed Tray. Material balance envelopes between the condenser and the tray n before the ethanol/water feed tray include a permanent tray where the IL is fed and between the reboiler and the tray n before the ethanol/water feed tray:

∑i

fFni

þ

Vni 1

Lin

D g ¼ 0 where i

Vn3 1

n > NTF and n ∈ TM

∑i

fLin þ 1

Vni

B g ¼ 0 where i

n < NTF and n ∈ TM

ð72Þ

n ∈ NTC

n ∈ NTC

ð74Þ

RA g

QR ðT S T1L Þ UR

ð75Þ

CA g

QC V ðTNT T CW Þ UC

ð76Þ

IL Boiling Point Temperature. After carrying out the separation of the ethanol/water system, we need to deal with the separation of the resulting water/IL mixture. Because ILs are reported to be expensive liquids,23 we need to maximize IL recovery. To ensure an easy separation of the water/IL system, we formulate a constraint stating that the boiling points of water and the IL must be as far as possible.24 A simple way to state this aim is to formulate a constraint stating that the IL boiling point temperature should be greater than the corresponding water boiling point temperature plus a desired boiling point temperature approach between both. The underlying constraint reads as follows: IL w g Tbp þ ΔTbp Tbp IL ¼ 198:2 þ Tbp

ð77Þ

∑k ðnk ΔTb, k Þ

ð78Þ

IL Melting Point Temperature. To be sure than the water and the IL can be separated and that the IL remains in the liquid phase, the IL melting temperature must be lower than the difference between the system operation temperature and a temperature approach 25 IL L Tmp e TNT ΔTmp

ð79Þ

¼ 0g ð67Þ

Vn3

ð73Þ

Column Diameter, Reboiler, and Condenser Areas.

ð58Þ

hLin ¼ f ðTnL Þ

fi,Vn

∑n STGn

NT ¼

Lin hLin Vni hV in Þ ¼ 0


i ¼ fH2 Og

CD g gðTnV , Pn , VAPn Þ

n ∈ TM

ð71Þ

Total Equilibrium Stages as the Active Trays. The total equilibrium stages are the active trays in the final configuration of the column

∑i ðLin þ 1hLin þ 1 þ Vni 1hVin 1

fi,Ln ¼ fi,Vn

i ¼ fetOHg

IL Tmp

¼ 0g ð68Þ

Recovery of Component i in Distillate and Bottoms Product. Di g ξid F i

i ¼ fetOHg

ð69Þ

Bi g ξib F i

i ¼ fH2 Og

ð70Þ

¼

∑k ðNkΔTmp, kÞ þ zH ∑j ΔTmp, j A H þ BH σ þ C H τ þ D H δ

ð80Þ

Thermodynamic Behavior of System Components. Vapor Pressure. Vapor pressure for components etOH and H 2O26 for each permanent tray and each active tray: (n ∈ NT, NFT, NCT, NRT): P0, i ln ni Pc

!

i 1:5

¼ ð1 Xni ÞðVPA Xn þ VPB ðXn Þ i

i

i

þ VPiC ðXni Þ3 þ VPiD ðXni Þ6 Þ

ð81Þ 5869



ARTICLE

where TnL Tci

Xni ¼ 1

i R, i ln γin ¼ ln γC, n þ ln γn

i γC, n

¼

3 ðTnL Þ3 Tref 3 10:38 L Tn B1 i C Tc C λi B B i C T @ bp A 1 i Tc

ð82Þ

Activity Coefficients (UNIFAC)27. Because we assume that the IL is a new compound, for which no experimental physical properties information is available, a group contribution method is used to estimate activity coefficients values. Group contribution methods are aimed at computing some required properties starting from simple functional groups. Along these lines, the UNIFAC method is a reliable technique for activity coefficients estimation27 and is given as follows for each permanent tray and each active tray (n ∈ NT, NFT, NCT, NRT):

ln

1 VnC, i

þ ln

ð83Þ

VnC, i

V C, i V C, i 5qi 1 nC, i þ ln nC, i Fn Fn

!!

þ CPiC 0

CLp, n C0p, n R

ri ¼

¼

∑j

qi j; qj xn

∑k νðiÞk Rk ;

i ln γR, n ¼

¼

VnC, i

qi ¼

∑j

ri j rj xn

ð85Þ

∑k νðiÞk Qk

13

B θmn ψkmn C7 @ A5 θsn ψsnm

θmn

∑m ∑ s

∑i νðiÞm xin Xmn ¼ ∑i ∑k νðiÞk xin

∑s

ψsnm ¼ exp

asm Tn

# ð93Þ

The modified LydersenJobakReid is summarized in the following equations:29 TcIL ¼

ð88Þ

Qm Xmn ¼ ; Qs Xsn

6:3ð1 Tr, n Þ1=3 0:4355 4:2775 þ þ 1 Tr, n Tr, n

C0p, n ¼ ½

ð87Þ 0

∑m

0:49 1 Tr, n

∑k ðnk ACpk 37:93Þ þ ½ ∑k ðnk BCpk 0:210ÞTnL þ ½ ∑ ðnk CCpk 3:91 104 ÞðTnL Þ2 k þ ½ ∑ ðnk DCpk 2:06 107 ÞðTnL Þ3 ð94Þ k

ð86Þ

2 θmn ψmkn Þ

þω

"

IL

¼ 1:586 þ

The ideal gas heat capacity equation is28

∑k νðiÞk ½ln Γkn ln ΓðiÞkn

6 ln Γkn ¼ Qk 41 lnð

ð92Þ

Liquid Phase Enthalpy for Ionic Liquid. To develop the energy balance, it is necessary to calculate the ionic liquid enthalpy. This property can be estimated using the heat capacity. Ge et al.28 predicted the heat capacity of ILs using the principle of corresponding states, and the ideal gas heat capacity is determined using the modified Lydersen JobakReid group contribution method. The critical properties which are used in the principle of corresponding states are predicted using the groups contribution method developed by Valderrama and Rojas.29 The principle of corresponding states equation is28

ð84Þ FnC, i

2 ðTnL Þ2 Tref 2 4 L 4 ðT Þ Tref þ CPiD n 4

hLin ¼ CPiA ðTnL Tref Þ þ CPiB

ð89Þ

PcIL ¼

IL Tbp

A M þ BM

ω

ð90Þ

IL

MW IL þ ∑ðnk ΔPc, k Þ2

½CM "

∑k ðnk ΔTc, k Þ ½∑k ðnk ΔTc, k Þ2

ð95Þ

ð96Þ

k

IL ðTbp 43ÞðTcIL 43Þ

#

PIL ¼ log c IL IL IL Pref ðTc Tbp Þð0:7Tc 43Þ

!

"

# ! ! TcIL 43 PcIL PcIL IL þ log 1 IL log P Tc Tbp Pref ref

Vapor and Liquid Phase Enthalpy for Components etOH and H2O. 26 2 ðTnV Þ2 Tref 2 4 V 4 ðT Þ Tref þ CPiD n 4

ð97Þ

hV in ¼ CPiA ðTnV Tref Þ þ CPiB þ CPiC

3 ðTnV Þ3 Tref 3

26

The enthalpy of the IL reads as follows: ΔHnIL ¼

ð91Þ 5870

Z TL n Tref

CLp, n dT

ð98Þ



ARTICLE

merging the IL enthalpy with the ideal gas heat capacity and the principle of corresponding states equations:

Table 1. UNIFAC Groupsa

hLIL n ¼ (( R

3:15 TcIL ln

6:3 TcIL ln

" # ðTcIL ðTcIL Tref ÞÞ1=3 þ ðTcIL Tref Þ2=3 þ ðTcIL Þ2=3 ðTcIL ðTcIL Tn ÞÞ1=3 þ ðTcIL Tn Þ2=3 þ ðTcIL Þ2=3

" # ðTcIL Tref Þ1=3 ðTcIL Þ1=3

" # T IL Tref þ 0:4355 TcIL ln cIL ! Tc Tn þ ðTcIL Þ1=3 Þ31=3

ðTcIL Tn Þ1=3 ðTcIL Þ1=3 ð2ðTcIL Tref Þ1=3 þ 10:9119 TcIL arctan 3ðTcIL Þ1=3 10:9119 TcIL arctan

ð2ðTcIL Tn Þ1=3 þ ðTcIL Þ1=3 Þ31=3

!

3ðTcIL Þ1=3 )

18:9ðTcIL Þ2=3 ½ðTcIL

1=3

Tref Þ

ðTcIL

Tn Þ

1=3

4:2775ðTref Tn Þ wIL

) # ðTcIL Tref Þ ln 1:586ðTref Tn Þ ðTcIL Tn Þ "

þ 0:49TcIL

aðTref

T 2 Tn2 Tn Þ b ref 2

!

T 3 Tn3 c ref 3

!

T 4 Tn4 d ref 4

4 3 5:15 108 ðTref Tn4 Þ þ 0:00013ðTref Tn3 Þ

principal group

subgroup

1 2 3 4 5 6 7 8 9 10 11 12 13 14

CH2 CH2 OH H2O [mim][DMP] [min][DMP] [mim][CH3SO4] [mim][CH3SO4] [mim][BF4] [mim][BF4] [mim][Cl] [mim][Cl] [mim][CF3SO3] [mim][CF3SO3]

CH3 CH2 OH H2O [mim][DMP] [im][DMP] [mim][CH3SO4] [im][CH3SO4] [mim][BF4] [im][BF4] [mim][Cl] [im][Cl] [mim][CF3SO3] [im][CF3SO3]

a DMP: dimethylphosphate. Cl: chloride. CH3SO4: methyl sulfate. BF4: tetrafluoroborate. CF3SO3: trifluoromethanesulfonate.

This equation guarantees the selection of only one cation of the superstructure to conform to the optimum molecular structure of the ionic liquid. Only One Anion Should Be Selected.

!

Na

∑ αm ¼ 1 m¼1 ð99Þ

2 0:105ðTref Tn2 Þ þ 37:93ðTref Tn Þ where

∑k ðnkΔACpk Þ; b ¼ ∑k ðnk ΔBCpk Þ; c ¼ ∑ ðnk ΔCCpk Þ; d ¼ ∑ ðnk ΔDCpk Þ k k

number

ð104Þ

This equation guarantees the selection of only one anion of the superstructure to conform to the optimum molecular structure of the ionic liquid. To Determine if a Selected Cation Contains the mim (3methylimidazolium) Group in Its Superstructure.

a¼

ð100Þ

Discrete Constraints. IL Selection Constraint. In the pro-

posed formulation, binary variables enter in two kinds of binary constraints: (1) constraints to select anions, cations, and the ionic liquid and (2) constraints to define the type and number of functional groups in the ionic liquid, as well as to determine parameters of the UNIFAC group contribution method. Number of CH3 Groups in the Selected Cation. ns1 ¼

Nc

∑ Gm, 1 σm m¼1

ð101Þ

This equation quantifies the number of CH3 groups present in the cation of the selected ionic liquid. Number of CH2 Groups in the Selected Cation. ns2 ¼

Nc

∑ Gm, 2 σm m¼1

ð102Þ

This equation quantifies the number of CH2 groups present in the cation of selected ionic liquid. Only One Cation Should Be Selected. Nc

∑ σm ¼ 1 m¼1

σ m þ αj λk e 1

m ¼ 1, 2, 3, 5 " j ¼ 1, 2, 3, 4, 5 k ¼ 5, 7, 9, 11, 13

ð105Þ

To Determine if a Selected Cation Contains the im (imidazolium) Group in Its Superstructure. σ m þ αj λk e 1

m¼4 " j ¼ 1, 2, 3, 4, 5 k ¼ 6, 8, 10, 12, 14

ð106Þ

The surface area and volume parameters of the inoic liquids reported in Lei et al27 of the UNIFAC method are represented by a main group and two subgroups. The difference between the subgroups is in the cation structure. The first one is the methylimidazolium (mim), and the second one is only imidazolium (im), while the anion is the same for both subgroups. Each subgroup presented different values of volume (Rk) and surface area (Qk). For this reason, it is relevant to identify the kind of subgroup that is present in the cation of the optimal structure of the ionic liquid. Equation 80 establishes that the selected cation to make the IL contains the mim subgroup. Equation 81 permits identification of whether the selected cation has the im subgroup structure. The different cations in the superstructure only have one of these subgroups. Only an Ionic Pair Should Be Selected. 14

∑ λk ¼ 1 k¼5

ð103Þ 5871

ð107Þ dx.doi.org/10.1021/ie201726r |Ind. Eng. Chem. Res. 2012, 51, 5866–5880


ARTICLE

This equation enforces that only an ionic pair of the family is selected. The ionic pair is used in the method of UNIFAC. The ionic pair has strong electrostatic interaction, and thus it is better to treat the skeletons of the cation and anion as a whole. Number and Type of Ionic Groups in the Final IL. λk nsk ¼ 0 "k ¼ 5, 6, :::, 14 14

nsk ¼ 1 ∑ k¼5

ð108Þ ð109Þ

These equations identify the kind and the number of ionic pairs present in the optimal molecular structure of the ionic liquid. The kinds of ionic pairs considered in this work are shown in Table 1, from 5 to 14 rows. The selection of the ionic liquids was carried out, taking into account the following features: boiling and melting temperatures, chemical stability, and water solubility.11,19 Moreover, the tetrafluoroborate, chloride, dimetilphosphate, and trifluoromethanesulfonate anions and imidazolium compounds have been experimentally tested for the ethanolwater azeotropic separation.16,30 On the other hand, the methyl sulfate anion was chosen because it can be synthesized at low cost when the cation is an imidazolium base.31 Superficial Area of the Final IL. Qks

Qkk λk e 0

3

This equation selects the interaction parameter of the corresponding CH3 and the group of the ionic pair present in the optimal molecular structure of the ionic liquid. Determination of the Interaction Parameter between the CH2 Group and the Ionic Part. ΩkCH2 IL Ω2, k λk ¼ 0, "k ¼ 5, :::, 14 14

∑ ΩkCH IL ¼ ΩOIL 2 k¼5 2

Ω3, k λk ¼ 0, "k ¼ 5, :::, 14 ΩOHIL k 14

ð111Þ

ΩOHIL ¼ ΩOIL ∑ k 3 k¼5

ð114Þ

This equation selects the interaction parameter of the group corresponding to the ionic pair present in the optimal molecular structure of the ionic liquid and the H2O group. Determination of the Interaction Parameter between the CH3 Group and the Ionic Part. ΩkCH3 IL Ω1, k λk ¼ 0, "k ¼ 5, :::, 14

2 OIL Ω4, k λk ¼ 0, "k ¼ 5, :::, 14 ΩH k

14

∑ ΩHk OIL ¼ ΩOIL 4 k¼5 2

ð119Þ

ð115Þ

ð120Þ

ð121Þ

ð122Þ

This equation selects the interaction parameter of the corresponding H2O and the group of the ionic pair present in the optimal molecular structure of the ionic liquid. Determination of Molecular Weight of the Selected IL (MWIL). 5

∑ ðMWamαm þ MWcm σmÞ ¼ MWIL m¼1

ð113Þ

This equation selects the interaction parameter of the group corresponding to the ionic pair present in the optimal molecular structure of the ionic liquid and the OH group. Determination of the Interaction Parameter between the Ionic Part and the H2O Group. 2O ΩILH Ωk, 4 λk ¼ 0, "k ¼ 5, :::, 14 k

ð118Þ

This equation selects the interaction parameter of the corresponding OH and the group of the ionic pair present in the optimal molecular structure of the ionic liquid. Determination of the Interaction Parameter between the H2O Group and the Ionic Part.

ð112Þ

This equation selects the interaction parameter of the group corresponding to the ionic pair present in the optimal molecular structure of the ionic liquid and the CH2 group. Determination of the Interaction Parameter between the Ionic Part and the OH Group. Ωk, 3 λk ¼ 0, "k ¼ 5, :::, 14 ΩILOH k

ð117Þ

This equation selects the interaction parameter of the corresponding CH2 and the group of the ionic pair present in the optimal molecular structure of the ionic liquid. Determination of the Interaction Parameter between the OH Group and the Ionic Part.

This equation selects the interaction parameter of the group corresponding to the ionic pair present in the optimal molecular structure of the ionic liquid and the CH3 group. Determination of the Interaction Parameter between the Ionic Part and the CH2 Group. 2 ΩILCH Ωk, 2 λk ¼ 0, "k ¼ 5, :::, 14 k

ð116Þ

ð110Þ

This equation assigns the surface area value of the ionic pair of the optimal molecular structure of the ionic liquid to the Qsk variable, which is employed in the determination of the fraction of the group surface area in the UNIFAC method27 Determination of the Interaction Parameter between the Ionic Part and the CH3 Group. 3 Ωk, 1 λk ¼ 0, "k ¼ 5, :::, 14 ΩILCH k

14

∑ ΩkCH IL ¼ ΩOIL 1 k¼5

ð123Þ

This equation determines the molecular weight of the optimal molecular structure of the ionic liquid from the cation and anion. In the equations of this section, the numbers in the sets of the formulation are functional groups, and the subgroups of the UNIFAC group contribution method are shown in Table 1. Design Column Constraints. These constraints are the ones associated with the discrete choice of enforcing or not vaporliquid equilibrium in a given tray. The Boolean variable Zn takes the value of true when the tray is selected, and hence the equilibrium equations are applied in that tray. In this case, the fugacities of the liquid and vapor streams are calculated, and the temperatures of liquid and vapor streams are set equal. If Zn 5872



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Table 2. Flows and Composition Profiles of the Optimal Synthesized Columna FEED

product 238.3

955.7

44.3 761.7 a

stage

x1

x3

y1

y2

0.6

0.1859

0.5085

0.4915

0.5099

0.0315

0.7726

0.2274

0.2874

0.03

0.9216

0.0784

0.7391

0.1802

0.0807

0.941

0.059

1241.1

0.7764

0.139

0.0846

0.9561

0.0439

1242.7

0.8121

0.1033

0.0846

0.9685

0.0315

525.3

1244.9

0.8419

0.0737

0.0843

0.9782

0.0218

527.5 412.8

1174.5

0.8653 0.9995

0.0507 0.0005

0.084

0.9995

0.0005

liq

vap 1167.5

0.2141

2

1405.8

1240.8

0.4586

3

1479.1

1266.5

0.6826

4

549.1

1241.2

5

523.8

6

523.7

7 8 9

1

x2

Components: 1 = ethanol, 2 = water, 3 = IL. All flow rates are in kmol/h.

Table 3. Big M Values for Disjunctive Constraints description

unit

big M value

liquid flows of component i

kg mol/h

3000

vapor flows of component i

kg mol/h

3000

equilibrium relationship

bar

5

vapor presure

bar

10

composition difference between

mol fraction

0.3

composition difference between vapor streams of adjacent trays

mol fraction

0.3

flow difference between liquid

kg mol/h

600

kg mol/h

600

function value. To avoid this situation, the following set of logic constraints enforces the selected trays to be activated above and below the feed tray:

liquid streams of adjacent trays

streams of adjacent trays flow difference between vapor streams of adjacent trays

takes a value of false, the composition of the inlet liquid stream is set equal to the composition of the outlet liquid stream. The vapor streams are treated similarly, and the temperatures of liquid and vapor streams entering and leaving the tray are set to those of the tray above and below, respectively. Because the equilibrium equations are not used, the values of the fugacity of the liquid and vapor phases are set to zero. The disjunction reads as follows: 2 3 3 ¬Zn 6 7 Zn 6 xi ¼ xi 7 6 n nþ1 7 6 fi,Ln ¼ f ðTnL , Pn , xin Þ i ¼ fetOH, H2 Og 7 7 6 6 i i 6 7 6 yn ¼ yn 1 7 7 6 f V ¼ f ðT V , Pn , yi Þ i ¼ fetOH, H2 Og 7 6 i n n 6 i, n 7 6 Ln ¼ Lin þ 1 7 7 6 f L ¼ f V i ¼ fetOH, H Og 7 6 7 6 i, n 7 6 Vi ¼ Vi 2 i, n 7n ∈ TM 6 L 7 ∨ n n 1 7 6 Tn ¼ TnV 7 6 6 TL ¼ TL 7 6 i 7 n nþ1 7 6 Ln ¼ LIQ n xin 7 6 6 V V 6 7 6 Tn ¼ Tn 1 7 7 6 V i ¼ VAPn yi i ¼ fetOH, H2 Og 7 6 4 n 5 6 STG ¼ 0 7 n 7 n 4 5 STGN ¼ 1 fi,Ln , fi,Vn ¼ 0 2

ð124Þ The big-M formulation is applied for handling the nonlinear disjunctive programming problem, because it yields a tight bound and because it does not require disaggregation of variables.32 Because there exists the possibility of deleting or deactivating different intermediate trays for the same total number of trays, it is possible to obtain multiples solutions with the same objective

Zn w Zn1 ,

n > NFT

ð125Þ

Zn1 w Zn ,

n < NFT

ð126Þ

’ METHODOLOGY FOR SOLVING MINLPS Nonlinear optimization problems featuring both integer and continuous variables are, in general, difficult to solve. They depend upon GOF initial guessed values of the decision variables, and most of the time a specific-case initialization procedure ought to deployed. Even though, there are some general solution strategies than can be raised. The problem tackled in this work is actually composed of two subproblems: the molecular design of the chemical structure of the ionic liquid and the design of the extractive distillation column. Both problems were solved independently in refs 11 and 19, respectively. Also in those refs, general guidelines for solving the corresponding MINLP problems were formulated. Hence, in the present work, we deployed the following methodology for solving the underling MINLP problems: 1. Solve the MINLP problem which provides the optimal chemical structure of the ionic liquid following the MINLP solution procedure suggested in ref 11. 2. Fix the optimal chemical structure of the ionic liquid and solve the MINLP optimal extractive distillation column synthesis problem following the MINLP solution strategy detailed in ref 19. 3. Provide good upper and lower bounds of the decision variables. 4. Using as initial guesses of the decision variables the optimal results of steps 1 and 2, solve the simultaneous chemical structure ionic liquid and extractive distillation column synthesis problem represented by eqs 1126. Following the above approach, we were able to get optimal MINLP solutions of the addressed problems in relatively short CPU times taking into account the number of integer and continuous variables and the nonlinearities embedded in the proposed optimization formulation. We do not claim that the proposed solution procedure will always find an optimal feasible MINLP solution. However, 5873



Figure 1. Optimal MINLP results for the simultaneous design of the ionic liquid and column configuration. (a) Optimal composition profiles in the vapor (y) and liquid (x) phases along the extractive distillation column. Components: 1 = ethanol, 2 = water, 3 = IL. (b) Optimal temperature profile in the extractive distillation column. (c) Liquid and vapor phase molar flow rate profiles along the optimal extractive distillation column.

it worked remarkably well in all of the problems addressed in this work. As previously stated, all of the tackled MINLP problems were solved using the Sbb program available in Gams.33

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’ RESULTS AND DISCUSSION Generally, waterethanol mixtures obtained from fermentation processes feature a low ethanol concentration (37% ethanol mol fraction). In this work, we have assumed that a previous distillation column has been used such that the main product has a composition slightly smaller than the atmospheric ethanol/water azeotropic composition. In this way, the extractive distillation column and the ionic liquid will be designed only for addressing the difficult separation task, i.e., the separation beyond the azeotropic point, leading to higher ethanol purities as demanded for the use of ethanol as a biofuel. The design specifications of the extractive distillation column are as follows: • top ethanol mol fraction g 0.9995 • bottoms water mol fraction > 0.6 • top ethanol recovery > 0.9 • bottoms water recovery > 0.9Moreover, the column will be operated under atmospheric pressure conditions neglecting drop pressure through all of the column. This column pressure will allow us to use relatively inexpensive water as the cooling fluid to condense ethanol in the condenser. MINLP Results. The MINLP optimization formulation is applied for the simultaneous determination of both the optimal synthesis of the extractive distillation column and the chemical structure of the ionic liquid (IL) as a solvent enabling higher ethanol recoveries well beyond the azeotropic composition. Because the resulting MINLP features nonconvexities and nonlinearities, its efficient solution turns out to be an issue if proper initialization techniques and optimization solvers are not used. Regarding optimization solvers in this work we used the SBB MINLP optimization solver available in the GAMS modeling environment.33 Of course, other available software can also be used.34 The MINLP optimal results indicate that an extractive distillation column featuring nine separation trays should be used. In this column, the main ethanolwater feedstream is located on tray 3, whereas the ionic liquid feedstream is located on tray 8. The separation configuration features a total annualized cost of 851 440.6 DLLS/year. Using [emim][DMP] (1-ethyl-3methylimidazolium dimethylphosphate) as the initial guess of the ionic liquid, the best ionic liquid meeting all of the design requirements turned out to be [dmim][DMP] (1,3-dimethylimidazolium dimethylphosphate). Detailed results of the optimal synthesized separation system are shown in Table 2. Problem statistics are as follows: 64 integer variables, 4502 continuous variables, 4471 constraints, and 178 s of CPU time using a 4 GB RAM, Intel core i7 and 2.67 GHz computer. Although SBB cannot guarantee global optimality, the attained optimal solution has a better economic profit than a previous reported solution where the ionic liquid and the extractive column were designed sequentially19 rather than simultaneously. The set of values for M parameters used for disjunctive constraints is shown in Table 3. Figure 1a shows the composition profiles along the optimal extractive column. In all of the addressed cases, the reboiler is always the first tray of the column, whereas the condenser is tray number 9. The profile of ethanol composition in the liquid phase displays a pronounced slope in the stripping zone and is smoother in the rectifying zone. Between trays 3 and 4, there is a slope change, because of the introduction of the azeotropic mixture. The profile of water composition in the liquid phase quickly decreases along the extractive column in the striping zone and turns out to be smoother in the rectifying zone. The profile of IL composition in the liquid 5874



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Table 4. Sensitivity of the MINLP Solution to Changes in the Ionic Liquid Feed Stream Flow Rate (*Optimal Value of the IL Feed Stream Flow Rate) feed flow IL kmol/h

total anual cost $1000/year

total number of stages

Qreboiler [millions kJ/h]

Qcondenser [millions kJ/h]

reflux ratio

50

877.71

9

51.43

47.37

0.544

44.3 40

849.49 828.31

9 9

50.41 49.65

47.06 46.78

0.542 0.539

35

803.16

9

48.75

46.41

0.533

30

776.24

8

47.83

45.97

0.526

25

747.76

8

46.83

45.42

0.516

20

717.29

8

45.77

44.80

0.504

15

687.01

11

44.64

44.07

0.491

14.4*

665.92

11

43.27

42.72

0.491

11

954.70

12

52.98

52.56

0.789

Table 5. Flows and Composition Profiles of the Optimal Synthesized Column with feed flow rate of the ionic liquid as decision variablea feed

product

stage

238.7

1

955.7

14.4 731.5 a

liquid

vapor

x1

x2

x3

y1

y2

1057.2

0.3404

0.5991

0.0605

0.4572

0.5428

2

1295.8

1096.4

0.4357

0.5531

0.0111

0.7081

0.2919

3

1335.1

1115.6

0.6424

0.3468

0.0108

0.9708

0.0292

4 5

398.6 392.0

1109.0 1109.2

0.8830 0.8960

0.0808 0.0672

0.0362 0.0368

0.9759 0.9803

0.0241 0.0197

6

392.2

1109.7

0.9085

0.0547

0.0368

0.9842

0.0158

7

392.6

1110.1

0.9196

0.0437

0.0368

0.9876

0.0124

8

393.1

1110.5

0.9291

0.0342

0.0367

0.9904

0.0096

9

393.5

1111.0

0.9370

0.0263

0.0367

0.9927

0.0073

10

393.9

1090.8

0.9436

0.0198

0.0366

0.9995

0.0005

11

359.3

0.9995

0.0005

Components: 1 = ethanol, 2 = water, 3 = IL. All flow rates are in kmol/h.

phase decreases between trays 3 and 4 due to the azeotropic mixture feed stream; in most of the remaining trays, it is kept approximately constant, except in tray 9 because there is no IL in the vapor phase since the IL vapor pressure was neglected. On the other hand, the ethanol and water vapor phase composition displays monotonic increasing and decreasing behavior, respectively. The temperature profile (see Figure 1b) along the extractive column displays an increase between trays 3 and 4 due to mixing heats which are originated by the contact between the azeotropic mixture fed in stage 3 and the IL coming down from the stage above. It is clear that the presence of the IL in the reboiler increases the boiling temperature of the water and IL mixture. On the other hand, because the IL is not present in the condenser, since its vapor pressure is negligible, the temperature in this part is the ethanol normal boiling temperature. The profiles of the liquid and vapor phase molar flow rates are depicted in Figure 1c. As noticed, the molar flow rate of the vapor phase displays constant behavior with a light decrease between trays 8 and 9, because the IL feed stream increases the flow rate of the liquid phase and promotes vapor phase condensation. The molar flow rate of the liquid phase shows a significant change between trays 3 and 4 due to the azeotropic mixture feed stream increasing the liquid phase molar flow rate. The results indicate that the molar flow rates are approximately constant in each section of the column. Sensitivity of the MINLP Design to Changes in the IL Flow Rate. Because ionic liquids have low production rates, they

tend to be expensive compounds. Therefore, we are interested in analyzing the optimal system behavior when the flow rate of the ionic liquid is changed. For this purpose, the feed streamflow rate of the IL was varied from 50 to 11 kmol/h, and the optimal extractive column synthesis problem was solved again. In this case, we found a better MINLP solution with lower cost because the column uses less heat duty and the reflux ratio and the amount of IL is lower (see Table 4). In the first four cases, the total number of stages was 9; for next three cases, the total number of stages descended to 8 and later raised to 12 in the last case. The minor heat duty and reflux ratio is due to the high solubility of the entrainer. These results agree with those obtained by Carsten et al.35 and confirm the IL selectivity for the water. On the other hand, the results show savings of around 21.6% in TAC and 67.5% in IL as the entrainer. In all cases, the chemical structure of the ionic liquid turned out to be the same: [dmim][DMP] (1,3-dimethylimidazolium dimethylphosphate). Problem statistics are as follows: 64 integer variables, 4503 continuous variables, 4472 constraints, and 514 s CPU time. Detailed internal liquid and vapor profiles and composition profiles are shown in Table 5, whereas detailed graphical results for each one of the operating points defined in Table 4 for composition profiles, molar flow rates, and temperature profiles are depicted in Figure 2. In all of the analyzed cases, the reboiler is the first tray, whereas the condenser is tray number 12. 5875



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Figure 2. Sensitivity results for different values of the ionic liquid feed stream flow rate. (a) Ethanol liquid phase composition profile. (b) Ionic liquid composition profile. (c) Liquid phase flow rate profiles. (d) Temperature profile.

Table 6. Sensitivity of the MINLP Solution to Changes in the Feed Stream Ethanol mol Fraction ethanol flow [% mol fraction]

IL flow [kmol/h]

TAC [$/year]

total stage number

Qreboiler [millions kJ/h]

Qcondenser [millions kJ/h]

reflux ratio

85

14.43

665.93

11

43.2701

42.7263

0.4913

80

14.93

603.09

11

39.9535

39.5776

0.4640

75

15.70

567.03

11

37.5015

37.0952

0.4593

70

20.91

471.99

15

34.4691

33.9152

0.3167

65

24.76

453.57

14

32.4336

31.6575

0.3230

60

26.28

454.76

10

30.6539

29.8734

0.3919

55

28.79

439.84

11

28.4360

27.5280

0.4290

50 45

33.18 38.41

429.72 430.96

13 14

26.6750 25.4401

25.4499 23.7882

0.4595 0.5098

40

43.64

434.64

14

24.3126

22.1967

0.5801

35

48.87

418.34

15

22.5577

19.9196

0.6136

30

54.10

409.96

15

21.0741

17.8853

0.6840

25

59.32

392.05

16

19.2902

15.5042

0.7443

Sensitivity of the MINLP Design to Changes in the Ethanol mol Fraction. We have previously stated the fact that, before

using ILs for azeotrope breaking, a purification step is deployed such that the resulting ethanol/water mixture is attained near its azeotropic composition. We did so because we suspected that the amount of IL is a function of the composition of the ethanol/water mixture. This means that

as the ethanol mol fraction decreases, the amount of IL needed to carry out the separation would increase. Therefore, this fact would justify the deployment of ILs for azeotropic separations mainly for feed streams featuring close to azeotropic composition. Hence, in Table 6, the amount of IL as a function of the ethanol feed stream composition is shown. In all of the cases, the optimal 5876



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Figure 3. Sensitivity results as a function of the ethanol feed stream composition. (a) Ethanol liquid phase composition profile. (b) Ionic liquid composition profile. (c) Liquid phase flow rate profiles. (d) Temperature profile.

designed IL was always the same ([dmim][DMP], where dmin is the 1,3-dimethylimidazolium group). As noticed, by decreasing the amount of ethanol in the feed stream, the cost of the tower also decreases, but the flow of IL necessary for the separation increases. Because the amount of purified ethanol decreases as its feed stream mol fraction decreases, the thermal duty also diminishes, leading to a cheaper separation scheme. However, as mentioned above, the amount of purified ethanol would make these optimal separation task designs not so attractive from a productivity point of view. In Figure 3, detailed graphical results about the sensitivity of the MINLP solution to changes in the feed stream ethanol mol fraction are depicted. In general terms, wide variations in the addressed profiles are observed, which agrees with the large variations of the ethanol mol fraction.

’ CONCLUSIONS AND FUTURE WORK There is a growing world concern about the replacement of hazardous industrial solvents by friendly, green solvents to carry out certain separation tasks such as the separation of azeotropic mixtures.36,37 Ionic liquids constitute one of the promising new kinds of green solvents. In fact, ionic liquids can be considered as designer-made solvents because they can be properly designed to feature some target properties such as low toxicity levels, viscosity, vapor pressure, etc. However, their high production cost seems to be a major issue against their wide use. As a matter

of fact, few industrial operations which deploy ionic liquids have ben reported until now.38 Anyway, it is clear that new, sustainable and economically attractive ways of performing traditional separation operations are needed. As new sustainable operations become economically competitive, we will witness more examples of green engineering technology applications. In this paper, we have addressed the simultaneous molecular design of ionic liquids and the separation structure to carry out the high purity separation of ethanol/water azeotropic mixtures. We demand high purity ethanol, assuming that ethanol will be used as a biofuel. Normally, one of the ways of approaching the separation of azeotropic mixtures requires the use of hazardous solvents, which are difficult to recover and easily enter into the atmosphere. Therefore, in previous works, we have addressed first the molecular design of ionic liquids11 and later the separation task configuration19 to perform the high purity ethanol/water azeotropic separation. Those results clearly indicate the feasibility of the proposed design approach since high purity ethanol for use as a biofuel was attained. We must highlight that the work reported in refs 11 and 19 was done in two separate steps. First the ionic liquid was optimally designed, and second, fixing the chemical structure of the ionic liquid, the separation configuration was also optimally designed. However, because both tasks are related, there was the feeling that better optimal designs can be attained by exploiting the natural interaction arising from solving both problems in a simultaneous manner. This was the proposal from which this work originates and that was confirmed through the results presented in the present work. As a matter of fact, 5877


Industrial & Engineering Chemistry Research important interesting economic savings were attained, confirming that better optimal results can be obtained by exploiting the interactions between the optimal design of ionic liquids and the separation configuration deployed to carry out the target separation. Of course, the work is prone to improvements such as the deployment of more reliable physical properties estimation.39 As future work, we will consider the design of ionic liquids for CO2 capture,40 for the treatment of lignocelullosic biomass for biofuel or biorefinery applications,41 for fuel cells,42 and in nanotechnology applications.43

’ AUTHOR INFORMATION Corresponding Author

*E-mail: antonio.fl[email protected].

’ NOMENCLATURE i = components {etOH, H2O, IL (ionic liquid)} j, k, m, s = functional groups for UNIFAC{CH3, CH2, OH, H2O, [mim][DMP], [im][DMP], [mim][CH3SO4], [im] [CH3SO4], [mim][BF4], [im][BF4], [mim][Cl], [im] [Cl], [mim][CF3SO3], [im][CF3SO3]} n = trays of the column, numbered from bottom to top, so that the reboiler is tray 1 and the condenser tray is number NT, n = 1, 2, ..., NT f = type of feed, such as ionic liquid feed (ILF), azeotropic mixture feed (AMF) Sets

C = set of components present in the feeds, C = {|i = etOH, H2O, IL} NTC = set of number of trays in column, NTC={n | n = NFT, NCT, NRT, TM} NFT = the feed trays (two): one of them is fed with ionic liquid, and the second is fed with an ethanol/water mixture, NFT, n ∈ NTC NCT = the condenser tray of the column, NCT, n ∈ NT NRT = the reboiler tray of the column, NRT, n ∈ NTC TM = subset of trays, which are conditional in the rectification and stripping sections of the column, TM, n ∈ NTC u = set of decision variables Variables

asm = UNIFAC group interaction parameter between group s and m (K) ACpk, BCpk, CCpk, DCpk = group contribution parameters for ideal gasheat capacity of the IL AH, BH, CH, DH = coefficient in the model equation for the melting temperature AM, BM = coefficient in the model equation for the critical temperature Bi = molar flow of component i in the bottom product (kmol/h) BOT = total molar flow of bottoms (kmol/h) CA = condenser area (m2) CD = column diameter (m) CM = coefficient in the model equation for the critical pressure CPetOH = cost of ethanol product (1.25 104 103 dollars/ kmol) CPiA, CPiB, CPiC, CPiD = constants for ideal gas heat capacity of component i C0p,n = ideal gas heat capacity in tray n (kJ/kmol K) CLp,n = liquid heat capacity in tray n (kJ/kmol K) CUC = cooling utility cost (7.48 104 103 dollars/106 kJ)

ARTICLE

DetOH = ethanol distillate product (kmol/h) f(DetOH) = 8000DetOH (kmol/year) FC,i n = auxiliary property of component i (surface fraction/mol fraction) in tray n (dimensionless) f(CA) = CA0.8, gives inversion annual cost (103 dollars/year) fLi,n = fugacity of component i in the liquid phase in the tray n fVi,n = fugacity of component i in the vapor phase in the tray n Fin = molar feed flow of component i in tray n (kmol/h) f(NT,CD) = NT CD1.245, gives inversion annual cost (103 dollars/year) f(QC) = 8000QC (106 kJ/year) f(QR) = 8000QR (106 kJ/year) f(RA) = RA0.8, gives inversion annual cost (103 dollars/year) FT = total molar feed flow feed (kmol/h) Gm,s = variable that considered the number of the groups CH3 and CH2 (n = 1, 2) in the cation structure (m = 1, 2, ..., 5) hBi = liquid molar enthalpy of component i in the bottoms (106 kJ/h) hDi = liquid molar enthalpy of component i in the distillate (103 kJ/h) i hFn = liquid molar enthalpy of component i in the feed to tray n (106 kJ/h) hLin = liquid molar enthalpy of component i out of the tray n (106 kJ/h) i hVn = vapor molar enthalpy of component i out of the tray n (106 kJ/h) IACCA = condenser cost coefficient, 0.1782 IACRA = reboiler cost coefficient, 0.1782 ICC = column cost coefficient, 0.162844 LIQn = total molar flow of liquid out of tray n (kmol/h) Lin = molar liquid flow of component i out of tray n (kmol/h) MWi = molecular weight of component i MWam = molecular weight of the anion m MWcm = molecular weight of the cation m nsm, nIL m = vector that contains the type and the number of groups m of the IL selected nk = number of times that a group of type k appears in the IL molecule NT = number of real trays Pic = critical pressure of component i (bar) PIL c = critical pressure of component IL (bar) P0,i n = vapor pressure of component i in tray n (bar) Pn = pressure in tray n (bar) Pref = reference pressure (1.01325 bar) QC = heat load of condenser (106 kJ/h) qi = parameter relative to molecular Vander Waals surface areas of pure component i (UNIFAC) Qk, Qm, Qs = group surface area parameter in the UNIFAC model QR = heat load of reboiler (106 kJ/h) R = the universal gas constant (8.314 kJ/kmol K) RA = reboiler area, m2 Rflux = reflux ratio (dimensionless) ri = parameter relative to molecular Vander Waals volumes of pure component i (UNIFAC) Rk = group volume parameter in the UNIFAC model STGn = counter for the existence of a tray SUC = steam utility cost (4.17 103 103 dollars/106 kJ) TAC = economic function (103 dollars/year) Tibp = normal boiling temperature of component i (K) Tic = critical temperature of component i (K) TIL c = critical temperature of IL (K) TCW = temperature of heating utility (K) 5878


Industrial & Engineering Chemistry Research Tr,n = reduced temperature in tray n, TLn /Tc Tref = reference temperature(K) TIL mp = melting temperature of selected IL (K) Tfn = feed stream temperature to tray n (K) TLn = temperature of liquid out of tray n (K) TVn = temperature of vapor out of tray n (K) TS = temperature of cooling utility(K) UC, UR = overall heat-transfer coefficient for condenser (C) and reboiler (R) (kJ/h m2 K) VAPn = total molar flow of vapor out of tray n (kmol/h) VCn ,i = auxiliary property of component i (volume fraction/mol fraction) in tray n (dimensionless) Vin = molar vapor flow of component i out of tray n (kmol/h) VPiA, VPiB, VPiC, VPiD = constants for vapor pressure equation of component i xif = liquid mole fraction of component i in type of feed f Xmn, Xsn = fraction of group m or s in the mixture of the liquid phase in tray n(dimensionless) xin = liquid mole fraction of component i out of tray n xjn = the same as xin yin = vapor mole fraction of component i out of tray n Zn = logic variable, which can be true or false ZH = coefficient in the model equation for the melting temperature Greek Variables

αm = binary variable representing each anion m considered in the superstructure (m = 1, 2, ..., 5) γin = activity coefficient of the component i in tray n (dimensionless) γC,i n = combinatorial contribution to the activity coefficient of component i in tray n (dimensionless) γR,i n = residual contribution to the activity coefficient of component i in tray n (dimensionless) ξid = recovery of component i; it represents de minimum recovery fraction of component i in the distillate (mol) ξib = recovery of component i, it represents de minimum recovery fraction of component i in the bottoms (mol) Γk,n = residual activity coefficient of group k in tray n (dimensionless) Γ(i) k,n = residual activity coefficient of group k in a reference solution containing only molecules of type i in tray n (dimensionless) δ = number of C substitutional groups in the molecule ΔHIL n = change of IL’s enthalpy with respect to one reference temperature ΔTbp = temperature approach between the normal boiling temperature of water and the normal boiling temperature of the selected IL ΔTmp = temperature approach between the temperature of the equilibrium stage and the melting temperature of the selected IL ΔPc,k = group contribution parameter for group type k relative to the critical pressure ΔTb,k = group contribution parameter for group type k relative to the normal boiling temperature ΔTc,k = group contribution parameter for group type k relative to the critical temperature ΔTmp,k, ΔTmp,j = group contribution parameter for group type k relative to the melting temperature θmn, θsn = the group fraction of group m or s in the mixture of liquid phase in tray n (dimensionless)

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λi = heat vaporization of component i (kJ/kmol) λk = binary variable representing the combination k between cations and anions in the superstructure (k = 5, 6, ..., 14) σ = number of same groups which connect to >NH and dN (ringofimidazolium) σm = binary variable representing each anion m considered in the superstructure (m = 1, 2, ..., 5) τ = number of ring groups in the molecule τid = purity of component i; it represents the minimum purity of component i in the distillate (mole fraction) τib = purity of component i; it represents the minimum purity of component i in the bottoms (mole fraction) ψsmn, ψmkn, ψkmn = the group interaction parameter in tray n (dimensionless) ωIL = acentric factor of IL (dimensionless) Ωk,s = group interaction parameters ΩOIL m = interaction parameters between the groups (m = 1, 2, 3, 4) and the molecular design of the IL 3 = interaction parameters between the IL ionic part (j = 5, ΩILCH j 6,..., 14) and the group CH3 2 ΩICLH = interaction parameters between the IL ionic part (j = 5, j 6, ..., 14) and the group CH2 ΩICOH = interaction parameters between the IL ionic part (j = 5, 6, ..., j 14) and the group OH 2O = interaction parameters between the IL ionic part (j = 5, 6, ΩICH j ...,14) and the group H2O 3IL = interaction parameters between group CH3 and the IL ΩCH j ionic part (j = 5, 6, ..., 14) 2IL = interaction parameters between group CH2 and the IL ΩCH j ionic part (j = 5, 6, ..., 14) = interaction parameters between group OH and the IL ionic ΩOHIL j part (j = 5, 6, ..., 14) 2OIL = interaction parameters between group H2O and the IL ΩH j ionic part (j = 5, 6, ..., 14)

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