10th International Symposium on Process Systems Engineering - PSE2009 Rita Maria de Brito Alves, Claudio Augusto Oller do Nascimento and Evaristo Chalbaud Biscaia Jr. (Editors) © 2009 Elsevier B.V. All rights reserved.

Entropy Production Analysis in Extractive Distillation Using Non-Equilibrium Thermodynamics and a Rate Based Model Diego F. Mendoza, Carlos A. M. Riascos Department of Chemical and Environmental Engineering, National University of Colombia, Cra. 30 No. 45-03 Edif. 453 Of 300, Bogotá, Colombia. Grupo de Ingeniería de Sistemas de Procesos.

Abstract Entropy generation (EG) in an extractive distillation column for ethanol dehydration was determined. The rate based model and non-equilibrium thermodynamics (NET) leads to quantify separately the EG due to interface heat and mass transfer and mixing. Additionally, this model allows estimating the effects of operational conditions such as reflux ratio and feed condition on the EG. The results obtained show that mixing effects at the feeding points (hydrated ethanol and separation agent) and interface mass transfer are the main sources of EG with 55% and 41% of total EG, respectively. The significance of this work is the use of a rate based model and NET theory as a tool for energy use analysis in multicomponent distillation processes. EG analysis is the starting point to define new operational strategies and design characteristics that allow a more efficient energy use. Keywords: extractive distillation, non-equilibrium thermodynamics, entropy production.

1. Introduction Since the industrial revolution, the energy consumption has incremented vigorously, at the beginning; there was not preoccupation for an efficient use of the energy, because of unknowing on energy sources limitation and environmental effects of industrial activities. The global energy crisis, in the late 1970s, and the current energy generation costs have forced the reevaluation of the energy use (Linnhoff and Flower, 1978). Separation by distillation is a major energy demanding operation in chemical process industries. Due to their low energy efficiency several strategies to improve it have been developed, distillation with heat pump and multiple-effect distillation (Seider et al., 2003) are useful techniques for saving energy; however, they can be applied only to mixtures with special characteristics; internally heat-integrated distillation columns has been developed as an alternative, at this configuration the energy consumption can be reduced in about 40% but the controllability of the systems requires special attention (Nakaiwa et al., 2003). Recently, the energetic efficiency analysis has been focused on the loss of energy quality; it may be estimated by exergy analysis (Demirel, 2007) or using non-equilibrium thermodynamics (NET) (Liang et al., 2006). Exergy is defined as the maximum available work, in a source, bringing it to the equilibrium with its surrounding (Demirel, 2007). The exergy loss is proportional to the EG and it is estimated by the difference between exergy going into and out of the system. This

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analysis provides a systematic method to diagnose whether and to what magnitude it is possible to increase the process efficiency. Whereas, the NET approach identifies the mechanism of EG and shows the location and causes of exergy losses (Liang et al. 2006), accordingly, it allows to predict the effect of operational conditions and equipment design on energy efficiency and to define the best conditions for maximizing the energy usage.

2. The Rate Based Model The rate based model (Taylor and Krishna, 1993), considers liquid and vapor phases separated by an interface through heat and mass transport occur. Transport through both phases occurs due to temperature and concentration gradients located in the liquid and vapor films. Vapor and liquid compositions at the interface are related by equilibrium relationships. The equation set that describes the rate based model is presented in Taylor and Krishna, 1993.

Figure 1. A segment in the distillation column (left), fluxes and forces in the system (right).

3. Entropy Production In a distillation column three main sources of EG can be identified, namely, heat and mass transfer and mixing. EG due to transfers is calculated using NET theory in the liquid and vapor films, whereas the EG due to mixing is indirectly calculated as the difference between the global EG and the entropy generation in the films. 3.1. Global Entropy Production The entropy balance (EB) is used to quantify the total EG in a column segment as well as in the boiler and condenser. The EG in the n-th column segment, Figure 1, is:

1 1 1 1p v l v l v l l l

n n n n n n n n n Fn Fn Fn nS V S L S V S L S F S F S+ + − −= + − − − − (1)

Where V, L, F are vapor, liquid and feed flows; S is the molar entropy, subscripts n-1 and n+1, identify the upper and lower segments, superscripts v and l identify vapor and liquid phases. EG in the total condenser and boiler are:

1 1( ) cp l vC C c

QTS V S S= − − Bp v l v

B B B B n n B

QTS V S BS L S= + − − (2), (3)

Where QC, TC , QB and TB are heat and temperature at the condenser and boiler. 3.2. Entropy Production in the Films According to the NET theory the local EG rate per unit of volume, σ, is the sum of the products of fluxes and forces related to heat and mass transfer in the films, Figure 1.

1

Cq q i ii

J X J Xσ=

= +∑ (4)

790 D.F. Mendoza and C.A.M. Riascos

Where Jq and Ji are the diffusive flux of heat and mass, and Xq and Xi are the thermodynamic forces for heat and mass transfer, given by:

( )1q TrX ∂

∂= − ( ),i T

i TrX μ∂∂

= − (5), (6)

Where T is the absolute temperature and μi,T is the chemical potential of species i, at constant temperature. The Gibbs-Duhem theorem leads to rewrite Equation (4) in terms of mass fluxes in the laboratory frame of reference, Ni, instead of interfacial one:

1C

q q i iiJ X N Xσ=

= +∑ (7)

The EG in the liquid film is:

1lf

Cl l l lq q i iiV

dV J X drdA N X drdAσ=

= +∑∫ ∫ ∫ ∫ ∫ (8)

Where Vlf is the volume of the liquid film, r is the film thickness and A is the liquid-vapor interface area. The entropy in vapor film is estimated analogously. Now, the RHS in later equation (and in the one for vapor film) must be integrated through the film thickness. For terms associated to the mass transfer we have:

, ,I vi T i Tv v v

i i i vfr TN X dr Nμ μ−⎛ ⎞

= − ⎜ ⎟⎝ ⎠

∫ , ,l Ii T i Tl l l

i i i lfr TN X dr Nμ μ−⎛ ⎞

= − ⎜ ⎟⎝ ⎠

∫ (9), (10)

For vapor and liquid phase, chemical potentials differences are:

, ,ˆˆln

I v I Ii T i T i i

vf v vi i

TyRy

μ μ φ

φ

− ⎛ ⎞= ⎜ ⎟

⎝ ⎠ , , ln

l I l li T i T i i

lf I Ii iTxR x

μ μ γ

γ

− ⎛ ⎞= ⎜ ⎟

⎝ ⎠ (11), (12)

The fugacity and activity coefficients, iφ and γi, are calculated at the average vapor and liquid film temperatures, respectively. For terms associated to heat transfer we have:

( )1 1v v vq q q I vr T TJ X dr J= −∫ ( )1 1l l l

q q q l Ir T TJ X dr J= −∫ (13), (14)

Where vqJ and l

qJ are the average heat fluxes in the vapor and liquid films:

( )rvqv v v I

q v

J drJ h T T

δ∫

= = − ( )rlql l I l

q l

J drJ h T T

δ∫

= = − (15), (16)

Here hv, hl are the film heat transfer coefficients at the vapor and liquid sides. Finally, EG rate due to interface heat and mass transfer for a segment (n) of the column, ,p f

nS , is

given by the sum of EG in vapor, ,p vfnS , and liquid, ,p lf

nS , films:

,,1

ˆˆ

1 1 lnvf

I Icp vf v v i in n q i n niI vV v v

i i n

yS dV J R N ayT T

φ

φσ

=

⎛ ⎞⎛ ⎞= = − − ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠∑∫ (17)�

,,1

1 1 lnlf

l lcp lf l l i in n q i n n I Iil IV i i n

xS dV J R N a xT Tγ

σγ=

⎛ ⎞ ⎛ ⎞= = − − ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

∑∫ (18)

4. Simulation The case to be analyzed is a pilot size, extractive distillation column (Table 1) which

Entropy Production Analysis in Extractive Distillation Using Non-Equilibrium Thermodynamics and a Rate Based Model 791

process 50 l/h of an ethanol-water (EtOH-W) mixture, the entrainer used is ethylene glycol (EGly). Column simulations were carried out using the Ratefrac model from Aspen Plus® processes simulator. Table 1. Specifications for simulation Condenser Total (segment 1) Boiler Partial (segment 30) Packing Type Pall, random, metal Size 15.875 mm Total packed height 10 m Column diameter 76.2 mm Number of segments 30 Reflux ratio (molar) 1 Distillate rate 0.651 kmol h-1 Pressure 1 bar Feed 1 (Entrainer) Location Segment 3 State, T & P Liquid; 333.15 K;1 bar Flow rates (kmol h-1) EGly=0.8331; W=0.0509; EtOH=0.0 Feed 2 (W-EtOH) Location Segment 16 State, T & P Liquid, 343.15 K, 1 bar Flow rates (kmol h-1) EGly=0.0; W=0.1149; EtOH=0.7691 Thermodynamic model Liquid phase

Vapor phase NRTL Ideal

Transport properties Mass transfer coefficients Onda correlation Heat transfer coefficients Chilton-Colburn analogy

5. Results and Discussion 5.1. Current Operation According to EB equation, Figure 2A, the 48% of total EG is located in the boiler, 51% comes from the packed column and only 1% is generated in the condenser. The high value of the EG in the boiler is due to heat transferred there causes the biggest changes in temperature and composition in the lower column section, Figures 2C and 2D, while in the condenser temperature and composition changes are little, because in it takes place the condensation of high purity EtOH. In the packed column the main irreversibility source is the mixing at the feeding points, with 86% of the total EG in the packed column. Interfacial heat and mass transfer, calculated by NET, Figure 2A, generate only 14% of EG in the column. This behavior departs from works of de Koeijer and Rivero (2003), Tsirling et al. (2006) and Bandyopadhyay (2007) who claim that EG due to mass transfer is the main irreversibility in a distillation column, but agrees with the work of Tarap and Ishida (1996). The work of de Koeijer and Rivero analyzed the EG in ethanol rectification while we analyze EG in ethanol dehydration. In a rectification, the distance between operating and equilibrium lines is bigger than in extractive distillation, therefore driving forces for heat and mass transfer are higher for ethanol rectification than in our process. The relative contribution of heat (12%) and mass (2%) transfer to EG agrees with aforementioned works, where mass transfer effect is the most important irreversibility. 5.2. Feed Ratio The Figure 3A shows that EG is reduced when feed ratio (FR) decrease, and this is due mainly to reduction on mixing effects, and the heat load in the boiler, Figure 3B. However there is minimum FR, near to 1, which makes feasible the operation i.e., to get high purity ethanol (>99%) in the distillate. 5.3. Entrainer Feeding Temperature The influence of the entrainer temperature, Figure 4A, shows that EG is sensitive to this variable, because of the irreversibility in mixing decrease when the difference between

792 D.F. Mendoza and C.A.M. Riascos

entrainer feed and internal flows are reduced, Figure 4B. One important thing to remark is entrainer feeding temperature, at the analyzed values, does not have influence on the distillate composition which is advantageous for the process.

5 10 15 20 25 300

2

4

6

8

SP (

kJ K

-1 h

r-1)

Segment

A

EBNET

5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

SP (

kJ K

-1 h

r-1)

Segment

B

HTMT

5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

Mol

e F

ract

ion

Segment

C

5 10 15 20 25 30350

360

370

380

390Tem

pera

tura

(K

)

Segment

D

LiquidVapor

Figure 2. EG for the current operation: A. Entropy production profile calculated form EB equation and NET. B. EG due to heat (HT) and mass transfer (MT). C. Composition profile: --- EtOH(L), + EtOH(V), ∆ W(L), □ W(V), − EGly(L), ▲ EGly(V). D. Temperature profiles.

0 1 2 3 40

10

20

30

40

50

Sp (kJ

K-1

hr-1

)

FR

A

0 1 2 3 40.88

0.9

0.92

0.94

0.96

0.98

1

XE

tOH

,D

FR

C

5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

Sp (kJ

K-1

hr-1

)

Segment

B

FR=3.96

FR=1.09

FR=0.2

Figure 3. EG related to feed ratio. A. Total EG. B. profile of EG for different feed ratios (FR). C. Mole fraction of ethanol in distillate.

Entropy Production Analysis in Extractive Distillation Using Non-Equilibrium Thermodynamics and a Rate Based Model 793

Other variables were evaluated (feeding temperature for W-EtOH mixture and reflux ratio) but the most important effects on the EG are those related with FR and entrainer feeding temperature.

320 325 330 335 340 345 35010

12

14

16

18

20

22

Sp (

kJ K

-1 h

r-1)

T (K)

A

5 10 15 20 25 300

2

4

6

8

10

12

Sp (

kJ K

-1 h

r-1)

Segment

B

T=321.15 K

T=333.15 KT=345.15 K

Figure 4. EG related to feed streams temperatures. A. Total EG in function of entrainer temperature. B. Profile of EG rate vs. entrainer temperature.

6. Conclusions For Ethanol dehydration, EG take place in reboiler (48%) and column (51%) principally. Mixing effects in feeding segments have the major influence on the column`s EG (86%) followed by mass transfer (12%); heat transfer effects on EG has the least influence (2%). In segments different to feeding points, mass transfer is the major contributor to EG. Among process variables analyzed feed ratio and entrainer temperature showed the major influence on EG. Low feed ratios and high entrainer temperatures diminish the EG due to mixing and heat load in the boiler. EG analysis using EB and NET are valuable and complementary tools for a detailed mapping of the different entropy production sources. This analysis is useful to establishing the main process variables to be considered in the energy optimization of the distillation column.

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794 D.F. Mendoza and C.A.M. Riascos