Simultaneous optimal design and operation of a diabatic extractive distillation column based on exergy analysis

7/23/2019 Simultaneous optimal design and operation of a diabatic extractive distillation column based on exergy analysis

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Int. J. Exergy, Vol. 17, No. 3, 2015 287

Copyright 2015 Inderscience Enterprises Ltd.

Simultaneous optimal design and operation of adiabatic extractive distillation column based onexergy analysis

Arley Nova-Rincn*, Manuel A. Ramosand Jorge M. Gmez

Grupo de Diseo de Productos y Procesos,Departamento de Ingeniera Qumica,Universidad de los Andes,Carrera 1 No. 18a-10, Bogot, ColombiaEmail: [email protected]: [email protected]: [email protected]*Corresponding author

Abstract: The concept of diabatic distillation is applied to an extractivedistillation system of ethanol, which uses glycerol as entrainer, to study theinfluence of heat flows in optimal design, operation, and thermodynamicefficiency of such systems via exergy analysis. First, optimal operatingconditions for minimum exergy losses are computed for a diabatic column withfixed feed locations and number of trays. Then, optimal design (feed locations,number of trays, and heat flows along the column) and operation of the systemis calculated as a mixed integer nonlinear programming (MINLP) problem, foran economic and economic-exergetic objective functions for two different

entrainer molar flows. It was found that the entrainer molar flow hasremarkable influence in the reduction of the exergy losses of the system.

Keywords: diabatic extractive distillation design; NLP; nonlinearprogramming) optimisation; MINLP optimisation; exergy minimisation.

Reference to this paper should be made as follows: Nova-Rincn, A.,Ramos, M.A. and Gmez, J.M. (2015) Simultaneous optimal designand operation of a diabatic extractive distillation column based on exergyanalysis,Int. J. Exergy, Vol. 17, No. 3, pp.287312.

Biographical notes: Arley Nova-Rincn is the Programs Coordinator of theChemical Engineering Department at Universidad de los Andes in Bogot,Colombia. He received a BS in Chemical Engineering from UniversidadIndustrial de Santander in Bucaramanga, Colombia, and a MS in ChemicalEngineering from Universidad de los Andes. His research interestsinclude optimisation with integer variables and energy optimisation of processsystems.

Manuel A. Ramos received a BS and MS in Chemical Engineering fromUniversidad de los Andes in Bogot, Colombia. Currently he is a PhD studentat cole Nationale Suprieure des Ingnieurs en Arts Chimiques etTechnologiques (INP-ENSIACET), Toulouse, France. His research interestsinclude dynamic optimisation with integer variables and energy optimisation ofprocess systems.


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288 A. Nova-Rincn et al.

Jorge Mario Gmez is Associate Professor and former head of the Chemical

Engineering Department at Universidad de los Andes in Bogot, Colombia.He received a BS and MS in Chemical Engineering from Universidad Nacionalde Colombia, an MBA from Universidad de los Andes, and a PhD fromUniversit de Pau et des Pays de lAdour, France. Currently, he lectures onoptimisation of chemical processes. His research interests include dynamicoptimisation with integer variables and energy optimisation of process systems.

This paper is a revised and expanded version of a paper entitled Analysis ofthe influence of heat flows in optimal design and operation of multicomponentdistillation columns: extractive distillation case study presented at 2012 AIChEAnnual Meeting, Pittsburgh, PA, USA, 31 October, 2012.

1 Introduction

Conventional design of distillation columns is based on the concept of adiabaticdistillation with two heat exchangers located at the top (condenser) and bottom (reboiler)of the column. Nevertheless, conventional distillation is associated with a very lowthermal efficiency (520% (Schaller, 2007)), a high exergy loss due to irreversibility(Demirel, 2006) and hence a high degradation of energy (De Koeijer et al., 2004;Demirel, 2004; Spasojeviet al., 2010).

Some studies have shown that the implementation of diabatic distillation (on whichheat exchange is carried out along the whole height of the column (De Koeijer et al.,2004; Schaller, 2007)), can significantly reduce the degradation of energy (De Koeijeret al., 2004; Jimenez et al., 2004a, 2004b; Schaller, 2007; Shu et al., 2007; Spasojevi

et al., 2010) because heat exchange in each stage lowers energy degradation along thecolumn and decreases the heat requirements for reboiler and condenser (Schaller, 2007;Schaller et al., 2001). An illustrative comparison between adiabatic and diabaticdistillation columns is shown in Figure 1.

Figure 1 (a) Adiabatic distillation column and (b) diabatic distillation column (see online versionfor colours)


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Simultaneous optimal design and operation of a diabatic extractive distillation 289

Previous works on diabatic distillation columns (Table 1) have studied optimal operation

of binary distillation systems based mainly on entropy production, but none of them havedealt with the problem of the optimal design and operation of diabatic distillationcolumns for multi-component separations. In contrast, in the present work optimaldesign and operating conditions are computed for an extractive distillation system(multi-component separation) via MINLP, taking into account an economic and amulti-objective objective function which includes an economic and an exergetic term.To our knowledge, studies in simultaneous optimal design and operation (MINLP) ofmulti-component distillation systems taking diabatic operation into account have not beenaddressed so far.

Table 1 Previous research works on diabatic distillation systems

Year Author

Mixture to be

separated Objective System configuration, and analysis

2000 Rivero (2001) Water EthanolMinimumexergy losses

Adiabatic rectification and strippingcolumn, studied separately. Location ofmaximum exergy losses. PonchonSavarit method is used for energybalances. Simulation in Aspen Plus

2001 Schaller (2007)and Schaller et al.(2001)

EquimolarmixtureBenzeneToluene

Entropyminimisation

Distillation column with sequentialheat exchangers. Optimal temperatureprofiles (De Koeijer et al., 2004;Shu et al., 2007), heat exchange areaper stage (De Koeijer et al., 2004),temperature and heat flows of heatexchangers utilities (Jimenez et al.,2004b), have been computed.

Application to multicomponent systemsis mentioned (Spasojeviet al., 2010)

2004 De Koeijer et al.(2004)

2004 Jimenez et al.,(2004b)

2007 Shu et al. (2007)

2010 Spasojeviet al.(2010)

2012Ghazi et al.(2012)

Water Ethanol Exergoeconomic

Adiabatic distillation column ismodelled by MESH equations and theexergy analysis is made. Cost rate ofproduct-ethanol is minimised. Onlycolumn operation is analysed

2014 This research

Multicomponentnon-idealmixture(Ethanol-water-Glycerol)

Economic andthermodynamic(minimumexergy loss)objectives are

studied

Distillation column with anindependent heater/cooler at each stagewhere heat load is required. Analysethe way on which the distillationcolumn achieves the minimum energy

degradation (exergy loss) for optimaldesign and operation

2 Extractive distillation: case study

The study is made for the extractive distillation system for the production of fuel gradeethanol using glycerol as entrainer (due to its energy, availability, being economical, andadvantages against other solvents and distillation techniques), proposed by Garca-Herreros et al. (2011).


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The extractive distillation system is made up of two distillation columns: the first one

for the extractive distillation process and the second for entrainer regeneration. Themixture to be separated and an entrainer are fed into the first column to obtain a distillatewith high ethanol purity. The second column regenerates the entrainer that can be reusedin the extractive distillation column (Lei et al., 2003). The diagram of the process isshown in Figure 2.

The present work is focused on the extractive distillation column that stands for amulti-component separation system. This column operates at atmospheric pressure(101.325 kPa, due to the saturation pressure of the azeotropic mixture fed, the not sopractical chemical degradation of the mixture into the column under this condition, andthe assumption that there is adequate heating media viable to carry the separation (Kister,1992)) and produces, as distillate, ethanol with purity over 99.5 mol %.

The extractive distillation column has 17 equilibrium stages, a total condenser, and a

partial reboiler. The column is fed with 52 kmol/h of glycerol on stage 3 at 305K andwith 100 kmol/h of azeotropic mixture (ethanol: 85% mol) on stage 12 at 351K(saturation temperature), both streams at atmospheric pressure. The aforementioneddescription corresponds to the optimal design for the extractive distillation column for theproduction of fuel grade ethanol, computed by Garca-Herreros et al. (2011).

Figure 2 Extractive distillation of fuel grade ethanol, using glycerol as entrainer (see onlineversion for colours)

3 Model of diabatic extractive distillation

The assumptions taken into account on this work to develop a model for the extractivedistillation column are the following:

stage dimensions are not taken into account.

heat exchange at each separation stage is taken into account

Murphree tray efficiency is assumed constant and equals to 1


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mixing effect at each stage is not taken into account

vapour phase is considered as an ideal gas

the NRTL model represents the behaviour of the liquid phase

residual properties are negligible

there is not pressure drop in the column.

The process is modelled as a series of counter-current separation stages. At each stage (j),entering and leaving liquid (Lj1,Lj) and vapour (Vj+1, Vj) flows get in contact in order toreach thermodynamic equilibrium as shown in Figure 3. The model uses the MESHequations, which refers to (Taylor et al., 2003):

M:material balances

E:equilibrium relations (to model the assumption that the streams leaving the stageare in thermodynamic equilibrium)

S:mole fractionsummation equations

H: enthalpy balances.

To model heat exchange on each stage, it is assumed that a series of band heaters asused to heat liquids flowing through pipes (Chen et al., 2003) can be clamped to thecolumn (one per stage). This assumption is done in order to compute ,

jinQ outjQ and the

side heat exchanger temperature per stage. The calculation of these variables is necessaryto compute exergy losses per stage, as will be seen on the next section.

Figure 3 Scheme of an equilibrium stage, for modelling diabatic extractive distillation column(see online version for colours)


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3.1 The NLP model

Let nc denote the number of components in the system and C= {1, 2, , nc} thecorresponding index in the set of components. Let nt denote the total number of stages inthe column and J= {1, 2, , nt} the corresponding index set of the stages. The subsetsCOND = {1}, REB = {nt} Jdenote the condenser (stage 1) and the reboiler (stage nt),respectively. Additionally, let S= {2, 3, , nt 1} J denote the subset of stagesbetween the condenser and the reboiler. Taking this into account, the proposed MESHequations for stages, condenser and reboiler of the diabatic distillation column are theequality constraints of the model, and are expressed as:

Total mass balances

1 1 0,L

j j j j jV V L L F j S + + + = (1)

1

11 0, COND

j jV L j

RR+

+ =

(2)

1 0, REB.j j jL L V j = (3)

Partial mass balances

1 , 1 , 1 , 1 , 0, ,L

j i j j i j j i j j i j jV y V y L x L x F i C j S + + + + = (4)

1 , 1 ,

11 0, , COND

j i j j i jV y L x i C j

RR+ +

+ =

(5)

1 , 1 , ,

0, , REB.j i j j i j j i j

L x L x V y i C j

= (6)

Equilibrium relationships

sat, sat

,

0, , .i j ij ijij ij ij

i j

y PK K P P i C j J

x P

= = = (7)

Summations

, ,1 1

0, , .nc nc

i j i j

i i

y x i C j J= =

= (8)

Enthalpy balances

Taking into account the proposed heat exchange by stage, for diabatic operation, enthalpybalance can be described as follows:

1 1 1 1 0,V V L L L LF

j j j j j j j j j jV H V H L H L H F H j S + + + + + =

j jin out

Q Q (9)

where jin

Q and ,jout

Q are positive variables which represents the quantity of energysupplied or taken out from thejth stage.

1 1

11 0, CONDV L

j j j j jV H L H Q j

RR+ +

+ =

(10)


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1 1 0, REB.L L V

j j j j j j jL H L H V H Q j + =

(11)

The main inequality constraint of the model refers to the ethanol purity (molar fraction)on distillate as follows:

0.995, ethanol , COND.ijx i C j = (12)

The validity of the presented NLP model (112) on which the MINLP problem is basedwas already probed and properly represents the behaviour of the extractive distillationcolumn (Nova-Rincn et al, 2012).

For conventional distillation with total condenser, specified operating pressure andfeed conditions, there are two degrees of freedom in the MESH model (Hanson et al.,1962). In order to specify the distillation model, reflux ratio (RR) and reboiler heat duty( )ntQ of the column are considered as operating variables in this research. For diabatic

distillation, it is necessary to add a couple of additional variablesjin

Q and outjQ whichdenote heat exchanged (entering or leaving) at each stage. It represents two additionaldegrees of freedom per stage (S), giving a total of 36 degrees of freedom for the NLPmodel.

3.1.1 Objective functions for NLP problem

The analysis of the influence of heat flows in the operation of multi-componentdistillation is made out from two different criteria: economic and thermodynamic. Thepurpose of this comparative analysis is to determine the differences in the level of thedegradation of the energy (exergy loss).

3.1.1.1 Economic criterion (P1)

The proposed economic object tive function is based on the maximisation of the net profit(P1) for selling distillate product ( )D at distillate cost (CD), taking into account theenergetic cost of boiling (CB) and condensing (CC).

The economic objective function is defined as follows:

1max j jinj

outj

D in B out CQ j J j J

Q

RR

P D C Q C Q C

= +

(13)

with:

CB= 2.2*103

[$/MJ] (Garca-Herreros et al., 2011), using high pressure vapourfor heating

CC= 2.125*104[$/MJ] (Garca-Herreros et al., 2011), using water at 14C

for cooling.

The proposed optimisation problem was carried out for both adiabatic and diabaticdistillation columns. In the case of adiabatic distillation column, the terms

jinjQ and

outjjQ represent only reboiler and condenser heat duties respectively. Terms of capital

cost were not taken into account.


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3.1.1.2 Thermodynamic criterion (E)

As mentioned in Section 1, some researches on diabatic distillation have based theirstudies on the minimisation of entropy production. Nevertheless, computing entropyproduction of the system does not give enough information about how much energy is notbeing effectively used (Arajo et al., 2007; Seader and Henley, 2006; Tsatsaronis, 1993).In this work, an analysis based on the exergy loss of the system is made, considering thatexergy analysis gives information about the supplied heat conversion into separationwork and identifies the energy wastes through exergy loss (Kencse and Mizsey, 2010).

This analysis requires the calculations of the exergy loss on each separation stage andis defined as follows (Soares Pinto et al., 2011):

0streams, streams,out1 ,j jj in

j

TQ Ex Ex j J

T

= +

jloss

Ex (14)

wherej

Q represents the heat load at stagej out( or ),j jinQ Q Tjis the side heat exchanger

temperature (temperature of condenser and reboiler utilities in the case of COND andREB), stream, jinEx

the exergy of the streams entering to stage j1 1

( , , ),j j jV L F

Ex Ex Ex+ +

stream,outjEx is the exergy of the streams leaving to stagej ( , ),

j jV LEx Ex and lossjEx

is theexergy loss of the stage due to irreversibilities of the stage.

The exergy of a stream is given by its enthalpy and entropy as:

,j j o jEx H T S j J= (15)

where To is the reference temperature, set on 298 K.With all the required terms for exergy balance defined, the objective function is

defined as the minimisation of the exergy losses along the length of the column asfollows:

lossmin jinj

outj

Qj J

Q

RR

E Ex

=

(16)

A comparison of the results for the aforementioned optimisations is made to measurethe waste of energy that each column represents and evaluate if distillation efficiencycan be improved by diabatic operation. Besides, the analysis allows measuring the impact(Rosen et al., 2008) and sustainability of the system. We refer to sustainability becauseexergy methods can be used to improve it (Dincer and Rosen, 2007; Stougie and van derKooi, 2011).

The presented objective functions (13) and (16) are analysed independently and each

one of them are subject to the operational constraints (1)(12).

3.2 The MINLP model

In the MINLP problem, the discrete decision variables are related to the calculation ofnumber of stages and feed locations, and the continuous variables are related to theoperating conditions and energy usage involved in the separation.

In the present work, a modification of the MINLP model proposed by Viswanathanand Grossmann (1993) is used to compute the total number of stages, feed locations,


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required heat flows, and operational conditions for the diabatic extractive distillation

column. This model considers binary variables associated with the selection of a tray forthe location of reflux and feed streams.

The MINLP model uses the same notation including sets (C, J) and sub-sets(COND, REB, S) presented for the NLP model and requires the inclusion of a new setof feeds (glycerol and azeotropic mixture)K= {g, az}, entering to the distillation column.For the estimation of the total number of stages, it was assumed that the distillationcolumn has a maximum of 55 separation stages (nt= 55), and the model will computewhere the feeds are located and how many of the ntstages really exist.

The formulation for the design of the distillation column considers solvingtwo situations related to discrete decisions. For the first one, the entering locationof the reboil stream is fixed (stage nt1) and the problem is to find the stage on whichreflux stream RF is fed to the column. Therefore all stages above the stage selected for

reflux are non-existing stages where vapour stream is bypassed and no liquid flow goesdownwards through them. The second situation is related to the location of feed streamsalong the distillation column.

Let , ,Rj

f j S denote the amount of reflux ( )RF entering to trayj ( )R Rji S

f F

= and , ,R

jz j S be the binary variable associated with reflux location. In this way, if1,Rjz = all the reflux enters at stage j. On the other hand, let , , ,

k

jf j S k K be the

amount of feed ( , )kF k K entering to tray j ( )k kji S

f F

= and , , ,kjz j S k K be the binary variable associated with the selection of trayjfor the location of feed Fk.In this case when 1,kjz k K= all feed ,

kF k K enters at stage j. A graphic idea ofthe applied methodology for optimal design is shown in Figure 4.

Figure 4 Scheme and notation for optimal design of the diabatic extractive distillation column(see online version for colours)


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The constraints related to the feeds locations are:

, ,k k kj jf F z j S k K= (17)

1, .kj

j S

z k K

= (18)

Constraints related to the reflux location take into account the reflux ratio (RR) anddistillate molar flow rate ( ),D as follows:

R R

jf RR D z= (19)

1.Rj

j S

z

= (20)

One known condition about feeds locations in the column is the fact that for extractivedistillation, the solvent is introduced into the distillation column above the entry point ofthe feed mixture to be separated (Lee, 1990). Therefore for the present case study,glycerol must be fed above the azeotropic mixture. This can be modelled by imposing alogical condition as shown below:

0, .az gj j

j j

z z j S

(21)

These inequalities guarantee that if 1azj

z = for one stage jS, then 1gjj jz = andFg

enters on or above stagej.In the same way, reflux must be fed to the column above the feeds. It is imposed by:

0, .g Rj j

j j

z z j S

(22)

It is not necessary to define the constraint (22) for the azeotropic mixture feed becauseconstraint (21) states that it must be located below the feed of glycerol.

Some changes in the mass and energy balances for the separation stages with respectto the previous NLP model are required in order to define the MINLP model, as follows:

Mass balances for the equilibrium stages equations (1) and (4) become:

1 1 0, ,k R

j j j j j j

K

V V L L F F j S k K + + + + = (23)

1 , 1 , 1 , 1 , 1 ,

0, , ,K R

j i j j i j j i j j i j j i j

k F R F

j i j i

K

V y V y L x L x L x

F x F x j C j S k K

+ + +

+ + =

(24)

where , , COND,R

F

i i jx x j= and

KF

ix are the mole fractions of the reflux and feeds

streams respectively.In the same way, the enthalpy balance equation (9) is defined by:

1 1 1 1*( )

0, ,K R

R V V L L

j j j j j j j j j

j j

k F R F

j j j

K

z V H V H L H L H

F H F H j S k K

+ +

+ +

+ + =

j jin out Q Q

(25)


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where the first term refjj j

z ensures that jinQ and joutQ will only exist in actual stagesbelow the selected one for reflux feeding, and the terms , COND,

RF LjH H j= and

,K

F

jH j S represents the liquid molar enthalpies of the reflux and feeds streamsrespectively.

Due to the formulation of the proposed MINLP problem, where a streamFRis leavingthe condenser and can be divided in nt 2 sub-streams kf instead of a stream Lj,jCOND as was assumed for the NLP problem, the mass and enthalpy balances of thecondenser equations (2), (5) and (10) are formulated in terms of the distillate molarflow ( ),D as follows:

Assumption 1 0L =

1 ( 1) 0, CONDjV D RR j+ + = (26)

1 , 1 ,( 1) 0, , CONDj i j i jV y D RR x i C j+ + + = (27)

1 1 ( 1) 0, COND.V L

j j j jV H D RR H Q i+ + + =

(28)

There are no changes or additional terms that affect the mass and enthalpy balances in thereboiler, then equations that describe reboiler heat transfer keep the same form as in theNLP model.

3.2.1 Model for dry stages, using complementary conditions

Since equilibrium stages are modelled by MESH equations, vapour liquid equilibriummust be accomplished in all stages, even in non-existing where no mass transfer

takes place. This fact tends to cause singularity and numerical difficulties forconvergence because of the absence of liquid flow in the non-existing stages. To dealwith this situation, Gopal and Biegler (1999) developed a NLP formulation based oncomplementary conditions. This approach can model the appearance and disappearanceof phases directly in phase equilibrium problems. It has been tested on benzene-tolueneas a non-ideal (UNIQUAQ) five-component system (Lang and Biegler, 2002).

MESH equations are modified by modelling the phase equilibrium as (Biegler, 2010;Gopal and Biegler, 1999; Lang and Biegler, 2002):

, , , 0, ,i j j i j i jy K x i C j J = (29)

1 ,j jj s s j S + = (30)

0j

jV s =

(31)

0jjL s+ = (32)

where j is a corrector for thejth stage, andjs and

js+ are slack (positive) variables forthe jth tray. Their values are relative to the existence of the liquid phase on each stage,according to the following complementary conditions:

If 1 then 0 and 0jj j

s V > > = (33)


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If 1 then 0 and 0.jj j

s L +< > = (34)

For this work, only the absence of liquid flow is modelled because the vapour stream isbypassed by the non-existing stages; therefore constraint (31) is not taken into accountand the term s is removed from constraint (30) giving:

1 , .jj s j S + = (35)

The MINLP problem is to maximise an economic (profit) and a multi-objective(profit-exergy losses) objective functions, subject to a set of model (MESH equations)and an operational (xi,j0.995, i= ethanol C,jCOND) constraints. Degrees offreedom for this problem include the calculation of 165 integer variables( , and )R g az

j j jz z z j S and a couple of additional variables

jinQ and

joutQ per each

existing stage.

3.2.2 Objective functions for the MINLP problem

The analysis of the influence of heat flows in the optimal design and operation of theextractive distillation column is made from two different criteria: economic andeconomic-exergetic. This last criterion is proposed to evaluate the influence of theinclusion of an exergetic term into an economic objective for the optimal design andoperation of the studied system.

3.2.2.1 Economic criterion (P2)

The proposed economic objective function is based on the maximisation of the annual

profit (P) for selling distillate product ( ).D

The objective function is composed by fourelements:

value of products: market value of the ethanol produced in one year of operation(Cp(x))

operating cost: cost of the utilities required for the operation of the column in oneyear (Co(x))

an electric cost was assumed for the design of the intermediate band heaters(2.83[$/MJ] (Mara et al., 2009))

same costs of condenser and reboiler reported in Section 3.1.1.1 were used

capital cost: cost of the column, including cost of stages, condenser and reboiler

(CI(x,y))

annualising factor: factor used to annualise the infrastructure cost in a five-yeardepreciation period (AF).

The economic objective function is defined as follows:

2max ( , ) ( ) ( ) ( , ).kjRj

p o F Iz

z

P x y C x C x A C x y= (36)


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Capital costs were calculated in the same manner as in the supporting information of

Garca-Herreros et al. (2011) and following the guidelines and price correlationsavailable in Turton et al. (2002), Seider et al. (2008), and Doherty and Malone (2001).These infrastructure costs are function of the total number of stages, reboiler, andcondenser heat duties. All of them are variables of the optimisation problem.

3.2.2.2 Economic-exergetic criterion (EE)

In this work, an exergy analysis of the system is made, considering that exergy lossallows determining how much energy is not being transformed into work of separation.

For the optimal operation and design of the diabatic extractive distillation column, itis necessary to modify the exergy balance constraint (14) because there is no exergyloss in non-existing stages. Then, the exergy loss for a stage is defined as follows:

0streams, streams, out

1

1 , .j j

R

j j in

j j j

Tz Q Ex Ex j J

T

= +

jlossEx (37)

The multi-objective economic-exergetic function is defined by:

lossmax ( , ) ( , ) .k jjRj

Exz

j Jz

EE x y P x y w Ex

= (38)

wEx, is a weight factor (104) which ensures economic viability of the system as well as

minimisation of the total exergy losses of the distillation column. This parameter wascalculated iteratively (and offline), according to the following procedure:

arbitrary parameter value was chosen and the optimisation problem was solved

if the solution reports an acceptable value (based on optimisation for economicobjective function) for some variables such as distillate molar flow and profit (andthe problem converged), the parameter value chosen was valid.

Otherwise, the value was adjusted by increasing or decreasing it in an arbitrary wayaccording to the results obtained.

Economic and exergetic terms are combined in order to get a real and profitabledistillation system. If the objective did not include the economic term, the column wouldreach the maximum number of stages (55) with few exergy losses due to the low heatload at stages; nevertheless a low distillation flow rate is attained which represents a non-profitable system.

4 Solution strategy

The NLP is based on the rigorous MESH model, composed by a set of algebraicequations of equality constraints. This set contains equations for computing enthalpiesand entropies, and equalities to determine equilibrium constants which are function ofactivity coefficients computed using the non random two liquids (NRTL) model (Renonand Prausnitz, 1968) leading to a non-convex, NLP problem.

The MINLP problem, which is based on the NLP model, includes decision variablesrelated to number of stages and locations for feeds streams in the distillation column.


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It was modelled using linear relationships between some of the operational variables (i.e.,

reflux ratio, distillate rate, and feeds molar flows) and a set of binary variables-relatedstreams locations.

The NLP and the MINLP problems were modelled in GAMS23.8 on a quad coreIntel i5 2.7 GHz CPU with 8 GB of RAM. To solve the NLP problem, we used IPOPT(interior point optimiser) (Wchter and Biegler, 2005). On the other hand, SBB (simplebranch and bound) was used as MINLP solver and IPOPT as NLP root-solver and sub-solver for the MINLP problem.

IPOPT uses a primal-dual interior-point algorithm with a filter line-search method(Wchter and Biegler, 2005), and is part of the open source COIN-OR (computationalinfrastructure for operations research) project (Biegler, 2010). IPOPT reports advantagesfor the solution of large-scale NLP problems and has shown to converge faster than otherNLP algorithms (Biegler, 2010; Wchter and Biegler, 2005).

The SBB had been developed by ARKI Consulting and Development A/S. It isavailable as a commercial solver within GAMS and implements a branch-and-boundalgorithm using nonlinear relaxations for the bounding step. The NLP relaxations aresolved by one (or several) of the NLP solvers available with GAMS (Bussieck et al.,2010) (i.e., IPOPT). SBB may perform better than other MINLP solvers (i.e., DICOPT)on models that have fewer discrete variables but more difficult nonlinearities, andpossibly on models that are fairly non-convex (GAMS Development Corporation, 2001)as the proposed MINLP model.

A combined strategy for search node was used for the solution of the MINLPproblem, which is made up by depth first search (DFS) and best bound or best first (BB)strategies, and is included into the SBB options (GAMS Development Corporation,2013).

5 Results and analysis

5.1 Results for NLP problem

Economic and thermodynamic optimisations were run for adiabatic and diabaticextractive distillation columns. The optimal distillate flow rate computed for theeconomic optimisation of the adiabatic column (85.427 kmol/h) is assumed as theminimum distillate rate for remaining optimisations (for NLP problem), to study the sameseparation system under different assumptions of operating conditions (adiabatic anddiabatic). Besides, it ensures the economic feasibility of the system because system profitdepends mainly on the distillate flow rate.

Table 2 summarises results for the adiabatic and diabatic distillation columns for theproposed optimisation objectives.From data presented in Table 2 it can be noticed that the assumption of diabatic

operation leads to the biggest profit value (economic optimisation) and the lowest exergylosses (thermodynamic optimisation). Nevertheless the most profitable system alsorepresents the worst system in terms of energy efficiency (exergy loss). It can be alsonoted that when the column operates with minimum exergy loss, the profit of the systemis just 0.001% lower than the maximum achieved for the system.


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Table 3 shows optimal heat loads at stages for the proposed optimisation objectives,

where for the thermodynamic objective, small quantities of heat must be removed at eachstage from stages 2 to 10, and in the same way small heat duties are required from stages11 to 18, which differs from the results of the economic one in which heat exchange wascarried out only in four stages of the column.

Table 2 Operating variables for NLP problem

Variable

Adiabatic column Diabatic column

Initial values[P1] and [E]Optimisation

Initialvalues [P1] Optimisation

[E]Optimisation

RR 0.103 0.885 0.012 0.191 0.237

D [kmol/h] 66.435 85.427 69.569 85.427 85.427

Exergy loss [GJ/h] 2.972 3.902 1.2577 4.05 2.605Profit [$/h] 1982.81 2543.776 1952.54 2548.925 2548.89

ntQ [GJ/h] 4.379 8.048 3.357 5.309 5.573

1Q [GJ/h] 2.85 6.269 2.809 3.960 4.113

Table 3 Stages heat loads, for the diabatic distillation column. NLP problem

Heat load

Diabatic column

Initial values [P1] Optimisation [E] Optimisation

Stage Value Stage Value Stage Value

joutQ [GJ/h]

2 0.001

12 0.604

2 0.001

3 0.006 3 0.006

4 0.002 4 0.002

5 0.003 5 0.003

6 0.005 6 0.005

7 0.005 7 0.005

8 0.005 8 0.005

9 0.004 9 0.004

10 0.002 10 0.002

jinQ [GJ/h]

11 0.003

2 4.271E-04

11 0.003

12 0.230 12 0.230

13 0.025 13 0.02514 0.020

3 0.17214 0.020

15 0.018 15 0.018

16 0.018

4 0.002

16 0.018

17 0.019 17 0.019

18 0.019 18 0.019


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Besides, when total energy consumption Total 1( ( ) ( ))j jnt in out Q Q Q Q Q= + + is calculated,

a value of 1.779 GJ/h is attained for all of them. It means that the system complies withthe first law of thermodynamics. The distillation systems use the same amount of energy,but it is being used in different ways, i.e. different locations along the column.

The main objective of the thermodynamic analysis is to evaluate whether adiabatic ordiabatic distillation system has lower total exergy losses, which represent a more efficientuse of energy in the system. Additionally the analysis estimates how much energy iswasted with the optimal configuration achieved for the economic optimisation in contrastwith the system with the minimum exergy loss. For the mentioned analysis, exergy lossprofiles for adiabatic and diabatic distillation columns for the studied optimisations aredepicted in Figure 5.

Figure 5 Exergy losses profiles for adiabatic and diabatic distillation column, thermodynamic

and economic objectives (see online version for colours)

By inspection of the profiles presented in Figure 5, it can be noticed that the major exergylosses for both distillation systems and optimisations are located at reboiler (stage 19),condenser (stage 1), and at the surroundings of feed stages of the extractive distillationcolumn (stages 3 and 12 to 15).

Until this point and based on results on Table 2, a reduction of 33.24% in the exergylosses of the system has been attached via diabatic operation of the extractive distillationcolumn.

Presented results highlight the importance of measuring the energy efficiency of theseparation systems since it is possible to get the same net profit with a lower energywaste, when an additional exergy-based analysis is made.

Taking this into account, exergy analysis was included for the design of thedistillation column to find out if the results of the NLP problem can be extrapolated to theMINLP problem.


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5.2 Results for MINLP model

Taking into account the original feed molar flows (100 kmol/h of azeotropic mixture and52 kmol/h of glycerol; simplified as [52G] for further reading), the design of the diabaticdistillation column is computed for the objective functions described in Section 3.2.2.Furthermore, the MINLP problem with the two objectives was used to determine theoptimal design and operation for the molar feed flows for the optimal control of theextractive distillation column for the production of fuel grade ethanol presented byRamos et al. (2013) (100 kmol/h of azeotropic mixture and 35 kmol/h of glycerol are fed;simplified as [35G] for further reading). This is made to analyse the influence of theentrainer molar flow in the column design as well as in the exergy losses of the systemwhich are related to its impact and sustainability (Stougie and van der Kooi, 2011; Rosenet al., 2008). Molar feed flow of glycerol is not considered as continuous variable

because cost of glycerol must be included in the objective function, changing theproposed objectives in Section 3.2.2.Initialisation is an essential part of the successful algorithms for distillation columns

design (Barttfeld et al., 2003; Grossmann et al., 2005) due to the limitations of discreteformulations related with its dependency on proper initialisation and bounding of theproblem (Neves et al., 2005). Therefore, initial values for both cases (52G and 35G) werefeasible solutions for the proposed MINLP cases.

Regardless of the molar feed flow of glycerol (52 or 35 kmol/h), neither the initialvalue for this stream location nor the two proposed optimisation objectives, this feedstream is located in the second stage in all of the achieved optimal designs, as shown inTable 4.

Table 4 Design variables for economic and economic-exergetic optimisation

Design variable

52G 35G

Initialvalues

[P2]Optimisation

[EE]Optimisation

Initialvalues

[P2]Optimisation

[EE]Optimisation

Number of stages 27 18 20 25 29 26

Location for feed g 3 2 2 3 2 2

Location for feed az 20 12 10 18 19 17

Comparing profit and exergy losses values for the proposed optimisations in Table 5, thesystems with the best profit also presents the greatest exergy losses. Besides, the systemwith minimum exergy losses (35G for economic-exergetic objective) presents a reductionof only 0.45% on its profit with respect to the most profitable (52G for economic

objective), but the reduction in exergy losses is 45.09%. It means that in order to get asmall extra-profit, great quantities of energy are being wasted (1.526GJ/h). Furthermore,the selection of an appropriated entrainer molar flow has a significant influence in theexergy losses of the system. Similarity in the profit value for both economic andeconomicexergetic optimisations confirms the validity of the proposed exergetic-economic objective function and the proper selection of the wExparameter value.

From Tables 4 and 5 results, it can be observed that for a 52 kmol/h feed flow ofglycerol, achieved optimal designs present shorter columns with a very small reflux ratio,when compared with the results for 35 kmol/h feed flow of glycerol for the proposed


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optimisations. Nevertheless, similar values of the system profit were computed. To

understand the differences in columns length for the studied cases, liquid and vapourmolar flows and temperature profiles are analysed.

Profiles presented in Figures 68, shows that optimisations for the 35G feed presentlower liquid flows per stage with a lower temperature variation from the last equilibriumstage to the reboiler than optimisations for 52G case. Furthermore, the 35G case presentshigher vapour flows per stage at a lower temperature than the 52G case, due to lesspresence of glycerol in the column. Described conditions might be the cause of lowerexergy losses for the 35G designs because more liquid is being condensed (resulting inlower total energy consumption) and the energy introduced in the reboiler is used to boila lighter entrainer-water mixture. For 35G cases, more energy is being transformed intowork of separation.

Table 5 Operating variables for economic and economic-exergetic optimisations

Variable

52G 35G

Initialvalues

[P2]Optimisation

[EE]Optimisation

Initialvalues

[P2]Optimisation

[EE]Optimisation

RR 0.150 0.007 0.005 0.263 0.211 0.223

D [kmol/h] 85.427 85.411 85.426 85.414 85.425 85.423

Exergy loss [GJ/h] 3.538 3.384 2.581 2.902 2.874 1.858

Profit [$/year] 14,932,445 14,970,476 14,920,755 14,935,738 14,938,756 14,902,631

ntQ [GJ/h] 5.661 5.314 5.321 5.318 5.231 5.271

1Q [GJ/h] 3.824 3.477 3.471 4.199 4.112 4.150

Figure 6 Liquid molar flow profiles for economic and economic-exergetic optimisations(see online version for colours)


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Figure 7 Vapour molar flow profiles for economic and economic-exergetic optimisations

(see online version for colours)

Figure 8 Temperature profiles for economic and economic-exergetic optimisations (see onlineversion for colours)

For heat loads at stages, results for the NLP problem reported that additional heat flowsare required in the surrounding of both feed streams for the economic optimisation of thediabatic extractive distillation column; nevertheless, when the optimal distribution of heatloads is computed by a simultaneous strategy for operation and design, the additional heatflows are only necessary at the neighbouring of the azeotropic mixture feed stage, asshown in Table 6.

Figure 9 compares exergy loss profiles for economic-exergetic objective functionfor the studied systems in the NLP problem and the profile achieved for a minimumexergy loss system achieved for the NLP problem (base case).


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Table 6 Heat loads for economic and economic-exergetic designs

Heat load

52G 35G

Initialvalues

[P]Optimisation

[EE]Optimisation

Initialvalues

[P]Optimisation

[EE]Optimisation

Stage Value Stage Value Stage Value Stage Value Stage Value Stage Value

jinQ [GJ/h]

18 0.00611 0 .061 9 0.052 17 0.026 18 0 .031 16 0.028

19 0.061

joutQ [GJ/h] 20 0.125 12 0.127 10 0.124 18 0.083 17 0.086 17 0.084

Figure 9 Comparison of systems with minimum exergy loss (see online version for colours)

From exergy loss profiles in Figure 9, it can be noticed that regardless of the number ofstages and location of feeds, the major exergy losses are located at the glycerol feed stageand the reboiler for the analysed cases. Detailed values are shown in Table 7.

The system which reported major reduction in exergy losses is the distillation column

designed for a 35 kmol/h flow of glycerol. The system 35G leads to reductions of 34.1%and 26.82% in exergy losses with respect to the base case for the glycerol feed stage andthe reboiler respectively.

Table 8 summarises the reduction of the exergy losses of the extractive distillationcolumn for the production of fuel grade ethanol from the adiabatic distillation systemachieved by Garca-Herreros et al. (2011) (adiabatic case), then by the inclusion ofdiabatic operation made in the NLP problem (base case), and ending with the optimaldesign, taking into account the analysed molar feed flows of entrainer of the MINLPproblem.


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The overall reduction of the exergy losses from the adiabatic case to the optimal

diabatic design for 35G reports a value of 52.38%, showing that the implementation ofdiabatic operation into the design of a distillation system (extractive distillation for thepresent study) leads to a remarkable improvement of the thermodynamic efficiency ofmulti-component separation systems (De Koeijer et al., 2004; Jimenez et al., 2004b;Rivero, 1993, 2001; Schaller et al., 2001; Shu et al., 2007).

The fact that the change of the molar flow of entrainer leads to the minimum exergylosses for the studied system supports the statement of the significance of the selection ofa proper molar flow of entrainer to get a better performance of the extractive distillationcolumn in terms of thermodynamic efficiency (less exergy losses). It can be achieved byincluding the molar feed flow of entrainer as a variable of the optimisation problem.

Table 7 Major exergy loss for analysed cases

Main exergy loss reductions [GJ/h]

Stage Base case 52G 35G

Glycerol feed stage 0.793 0.852 0.522

Reboiler 1.078 1.041 0.789

Table 8 Evolution of exergy loss for the extractive distillation column

Total exergy losses

Adiabatic case Base case 52G 35G

3.902 2.604 2.589 1.858

6 Conclusions

This work presents a new complete formulation and solution for the optimal design andoperation for a diabatic distillation system taking into account a multi-component mixture(Glycerol, and ethanol-water azeotropic mixture), using an MINLP model. The proposedmodel includes binary variables related to reflux and feeds locations, and an MPCCformulation to model the vapour-liquid equilibrium in the separation stages.

For the proposed objectives and arrangements of feed flows, it was found that heatloads along the length of the column are only necessary in the surroundings of theazeotropic mixture feed stage. Aforementioned results differ significantly from thecomputed for optimal operation achieved using a consecutive strategy.

The designs achieved for proposed economic-exergetic objective function shows thatthe assumption of heat exchange into the equilibrium stages of the column can lead to amore sustainable process ensuring also the high profit of the system.

Although the implementation of a diabatic distillation system with minimum exergylosses as proposed in the MINLP problem has several technical limitations (band heatersalong the column), the presented study gives a first approach to the design of moresustainable distillation columns.

In terms of process intensification, although the results for the studied system showsan increase in the size of the column (19 to 26 separation stages) it leads to a majorreduction in exergy losses which means a more sustainable separation process.


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7 Perspectives

The studied economic-exergetic criterion can also be applied to the design of otherenergy-transforming systems associated to low thermodynamic efficiencies, taking intoaccount alternative strategies related to the energy usage of the system (like diabaticdistillation in the case of distillation columns).

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Nomenclature

Subscripts

B Boiler

D Distillatei Component index

j Stage number index

Superscripts

az Azeotropic mixture.

g Glycerol

k Feed species index

L Liquid

R Reflux

V Vapour

Latin symbols

AF Annualising factor

CB Cost of boling, $/MJ

CD Cost of distillate, $/kmol

Cpx Value of products, $/kmol

CI Capital cost, $

Cox Operating cost, $

D Distillate, kmol/h


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lossjEx

Exergy loss on stagej, GJ/h

streams,in jEx Exergy of a stream entering to stagej, GJ/h

streams,out jEx Exergy of a stream leaving stagej, GJ/h

kF Feed of species k

k

jf Amount of feedKentering to trayj, kmol/h

L

jF Liquid feed molar flow rate on stagej, kmol/h

RF Reflux, kmol/h

R

jf Amount of reflux (FR) entering to trayj, kmol/h

LjH Molar liquid enthalpy for stagej, GJ/kmol

LF

jH Molar liquid enthalpy for feedFon stagej, GJ/kmol

V

jH Molar vapour enthalpy for stagej, GJ/kmol

Kij Equilibrium constant for component i on stage j

jL Liquid Molar Flow on stagej, kmol/h

nc Total number of components

nt Total number of separation stages

P Total pressure of the system, set to 1 atmsat

ijP Saturation pressure for component ion stagej, kPa

jQ Duty of stagej, GJ/h

jinQ Energy supplied to stagej, GJ/h

joutQ Energy taken out from stagej

RR Condenser molar reflux ratiojs+ Slack variable for trayj, related to the existence of liquid phase

js Slack variable for trayj, related to the existence of vapour phase

Tj Side heat exchanger temperature, K

To Reference temperature, 298 K

jV Vapour molar flow on stagej, kmol/h

wEx Weight factor for economic-exergetic criterion

xi,j Liquid molar composition for component ion stagej

yi,j Vapour molar composition for component ion stagejR

jz Binary variable associated with reflux location

k

jz Binary allocation associated with feedFklocation


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Greek symbols

ij Activity coefficient for specie ion stagej

j Corrector for stagej, for equilibrium modification

Documents

Simultaneous optimal design and operation of a diabatic extractive distillation column based on exergy analysis