Optimal Design of Three-Phase Reactive Distillation Columns using Nonequilibrium...

AIChE Annual Meeting 16-21 November 2008, Philadelphia PA

Optimal Design of Three-Phase Reactive Distillation Columns using

Nonequilibrium/Collocation Models

Theodoros Damartzis1 and Panos Seferlis1,2

1 Chemical Process Engineering Research Institute (CPERI)Centre for Research and Technology – Hellas (CERTH)

and2 Department of Mechanical Engineering

Aristotle University of Thessaloniki (AUTh)Thessaloniki, Greece

Outline

• Introduction - Motivation

• Overview of three phase distillation modeling and design

• Orthogonal collocation on finite elements model formulation of three phase reactive distillation

• Optimal design framework and solution algorithm

• Case study

• Concluding Remarks

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Introduction - Motivation

• Modeling and design of reactive distillation columns with potential formation of a second liquid phase

• Combined mass and energy transfer

• Thermodynamic phase equilibrium

• Chemical reactions

• System non-ideality

• Potential LLE

• Discrete nature of staged columns

• Approximate packed columns as a sequence of discrete stages

Large sets of nonlinear

differential algebraic equations (DAEs)

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Introduction - Motivation

• Regions with multiple liquid phases within the column are not known a priori

• Optimal design requires the solution of the steady-state process model often a cumbersome task

• Need for an accurate but yet compact model representation that

• can tackle the discrete nature of staged formulation

• allow a detailed description of occurring phenomena

• and further track successfully region boundaries with different number of liquid phases

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Objectives

• The development of an accurate but yet compact model representation that can tackle the discrete nature of staged units and phase boundaries

• The efficient solution of the optimal design problem without reducing the predictive ability of the process model

• Orthogonal collocation on finite element (OCFE) model formulation is an excellent option for three phase distillation modeling, design and optimization

• Additional check of liquid phase stability is introduced for the efficient identification and modeling of the three phase regions

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Overview of three phase distillation design

• Equilibrium models (Shyamsundar and Rangaiah, 2000 - Khalediand Bishnoi, 2005)

• Rate based modeling (Taylor 1994 - Higler et al, 2004 – Eckert and Vanek, 2001 – Repke and Wozny, 2004)

• Reactive distillation (Venimadhavan, Malone and Doherty, 1999 –Steinigeweg and Gmehling, 2002 – Steyer, Qi and Sundmacher, 2002)

• Dynamic simulation (Marquardt, 2004)

• Design optimization – MINLP (Kienle, 2004, 2007)

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Overview of three phase distillation design

• OCFE modeling (Stewart and coworkers 1985)

• Three phase distillation design (Swartz and Stewart, 1987)

• Current work is based on the advances on OCFEdistillation modeling especially its extensions to reactive distillation, rate-based modeling and adaptive element placement (Seferlis and Hrymak, 1994 – Huss and Westerberg, 1994 - Seferlis and Grievink, 2001 - Dalaouti and Seferlis 2004)

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General concept of three phase model

Gas

Liquid I

Liquid II

Gjjji HGy 111, ,, +++

Gjjji HGy ,,,

1,, 1,1Ljjji HLx

11111,1 ,, L

jjji HLx −−−

21121,2 ,, L

jjji HLx −−−

2,, 2,2Ljjji HLx

11 , GLj

GLi QN

22 , GLj

GLi QN

21LLiN

21LLjQ

General case :

Ø 3 interfaces

Ø 6 films

Ø Mass & heat transfer between films (Maxwell –Stefan equations)

Ø Thermodynamic equilibrium only at the 3 interfaces

Ø Reactions occur at film and bulk regions

G-L1 interface

G-L2 interface

L1-L2 interface

Accurate prediction and modeling of third phase formation is needed for optimal column design

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2 phase NEQ model

Gas bulk

Liquid bulk

Interface

Gas Film

Liquid Film

Resistance to mass and heat transfer through gas and liquid films

Described by Maxwell – Stefan equations

Chemical reactions occur in both liquid bulk and liquid film regions

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V – L1 Interface

Gas bulk

Gas Film

Liquid 1

Film

Liquid 1 Liquid 2

bulk bulk

L1 – L2 Interface

3 phase NEQ model - I

An extension of the NEQ two-phase modelTwo thin film model assumption for the diffusion across phase

boundariesStefan – Maxwell equations describe multi-component diffusion

Reactions take place in both the bulk and film regionNo contact between gas and liquid 2 (dispersed) phase

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Gas bulk

Gas film

Liquid 1

film

Liquid 1

Liquid 2

bulk bulk

Gbs

GbGbsi HGsy ,,,

Gbs

Gbs

Gbsi HGy 111, ,, +++

2,

2,

2, ,,

Lbsi

Lbsi

Lbsi HLx

21,

21,

21, ,,

Lbsi

Lbsi

Lbsi HLx −−−

1,

1,

1, ,,

Lbsi

Lbsi

Lbsi HLx

11,

11,

11, ,,

Lbsi

Lbsi

Lbsi HLx −−−

0|

== Gf

Gfi

Gbi NN

η

0int ||

==== LfGfGf

Lfii

Gfi QQQ

ηδηbLLf

i QQ LfLf1| =

=δη0|

== Gf

Gfi

Gbi QQ

η

0int ||

==== LfGfGf

Lfii

Gfi NNN

ηδη

bLLfi NN LfLf

1| ==δη

V – L1 InterfaceL1 – L2

Interface

GblossQ

2LblossQ

Basic assumptions• one-dimensional mass and heat transport normal to the interface• thermodynamic equilibrium at both interfaces • no axial dispersion• no entrainment of liquid phases from each stage• complete mixing of bulk phases• no contact between gas and dispersed liquid phase

3 phase NEQ model - II

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( ) ( ) ( ) ( ) ( ) ( )( ) NC,...,1j,nc,....,1ihΔAαsNsRsφsL~1sL~tdsdm colint

jbL

ijbL

ijL

ji1ji1j

Li 111

1

==++−−=

Mass balance: Diffusion molar flux

Component molar holdup

Total component reaction rate

( ) ( ) ( ) ( ) ( ) ( )( ) NC,...,1j,nc,....,1ihΔAαsNsRsφsG~1sG~tdsdm colint

jGbij

Gbij

Gjiji

jGi ==−+−+=

Energy balanceloss

Gss

Lss2

Lss1

G1s1s

L1s1s2

L1s1s1

s QHGHLHLHGHLHLdtdU

2121 −−−−++= ++−−−−

( ) ( ) ( ) ( ) ( )( ) NC,...,1j,nc,....,1ihΔAsRsφsL~1sL~tdsdm col

jbL

ijL

ji2ji2j

Li 22

2

==+−−=

Liquid and gas bulk phases

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( ) ( ) ( ) ( ) ( )( )( ) ( )( ) ( )j

GfGfNC

ikk

Gkijj

jGfkj

Gfij

Gfij

Gfk

Gfj

Gfi sδη,NC,...,j,nc,...,i

ÐsT~R/)sP~sNsysNsy

ηsy

≤<==−

−=∂

∂∑

≠=

0111

( ) ( ) ( ) ( ) ( ) ( )( )( ) ( )j

LfLfNC

ik1k

Likjt

jLfkj

Lfij

Lfij

Lfk

Lfj

Lfi

1NC

1kjk,i sδη0,NC,...,1j,nc,...1i

ÐscsNsxsNsx

ηsx

sΓ ≤<==−

−=∂

∂∑∑

≠=

−

=

Continuousliquid phase I

( ) ( ) ( ) ( )jLfLf

jLfiLf

jLfij

Lfi sδηn,...j,NC,...isR

ηsN

tsc

≤<===−∂

∂+

∂

∂0110

Gas phase

Maxwell-Stefan equations for mass transfer at film regions

)s(δη0n,...1jNC,...1i0η

)s(Nt

)s(cj

GfGfGf

jGfij

Gfi ≤<===

∂

∂+

∂

∂

Liquid and gas film equations

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Implementation of OCFE methods in non equilibrium distillation modeling:

Ø provides a compact and easy to solve model

Ø maintains high degree of model resolution in simulation (static and dynamic) and design optimization

Ø collocation points accurately represent overall column behavior

Ø eliminates the need for integer variables in staged columns

OCFE modeling

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OCFE modeling framework I

Bottoms product

Top product

Side productSide feed

Heat duty

Heat removed

Side heat

Collocation points

Element breakpoints

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Top Products

Feed

Bottom Products

Element breakpoints

Collocation pts

Ø Multiple feed stages

Ø Element size is allowed to vary and determines the column sections’ size

Ø Rate-based material and energy balances are valid only at collocation points

Ø Collocation points placed at roots of discrete Hahn polynomials

Ø Material and enthalpy flows are considered as continuous variables of position in the column

Ø Lagrange polynomials approximate material and enthalpy distribution within the elements

Ø Discontinuities due to feed streams treated in distinct stages

Column section

OCFE modeling framework II

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Gas bulk

Liquid bulk

Interface

Gas Film

Liquid Film

2-phase or 3-phase formulation

NEQ/Staged modelNEQ/OCFE model

NEQ/OCFE model

Non-equilibrium model(rate-based balances)

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Phase boundary tracking

• The boundary between column regions with 3 phases and 2 phases is not known a priori• An element breakpoint can be adaptively placed at the liquid phase boundary • LLE equations at the element endpoints determine the element size implicitly

2 liquid phases element

1 liquid phase element

LLE equations

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( )( ) ( )

( ) 0xxxP,T,xKxP,T,xK

xφxφ1x

IIi

Ii

IIi

IIi

Ii

Ii

IIi

Ii

Li

=−=+−=

∑impose |φ|<ε

at top of the element with single liquid phase

Ø Givena set of components and chemical reactionsa flowsheet configurationthe characteristics of the fresh feed streamsa set of product specifications and safety and operating constraintssteady-state process model (NEQ/OCFE formulation)economic data (prices for products and reactants, investment cost)

Ø Calculatetotal number of stages/packing height for every column sectionlocation of the feed stagesliquid holdup or catalyst load per stage for every column sectionoperating conditions for the column

Ø that Minimizeannualized investment costsannual operating costs

Optimal design problem definition

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G a s b u lk

L iq u id b u lk

I n t e r f a c e

G a s F ilm

L iq u id F ilm

Ø Step 1 - The column is modeled and optimized as a 2-phase reactive distillation column

Ø Step 2 - Optimal solution is checked for regions with possible liquid-liquid split à formation of second liquid phase

Ø Step 3 - Corresponding elements with 2 liquid phases are modeled as 3-phase elements

Ø Adaptive element breakpoint placement to mark the phase boundary

Ø The 3-phase column is optimized

LLE check for 3-phase regions

Optimal design algorithm

LLE check for phase transition regions

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Bottom Product

Aqueous Phase

ButanolButyl acetateWater

Organic Phase

101.3 kPa

Ø The column is divided into two sections separated by the feed stage

Ø Condenser (total), reboiler and decanter are modeled as EQ stages

Ø Butyl acetate recovery > 99.5%

Ø Butanol recovery > 97%

Distillation – Phase boundary tracking

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Ø objective function: Total annualized costs

Ø equilibrium stage model

Ø OCFE model formulation – 4 elements – total 8 co pts

Ø MINOS 5.5 for steady-state optimization

Ø Optimal column design

Ø 15 stages

Ø Feed stage – 6

Ø Three phase region extends in stripping section

Ø Element breakpoint in stripping section placed to separate the two regions

Distillation – Phase boundary tracking

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0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Column position

BuA

C c

ompo

sitio

n

Feed stage

One liquid phaseregion

Two liquid phaseregion

Bottom Product

Aqueous PhaseButanol

Acetic Acid

Organic Phase

101.3 kPa

Ø The column is divided into two sections separated by the feed stage

Ø Condenser, reboilerand decanter are modeled as EQ stages

Ø Bottom product purity = 98%

Ø Top section has two liquid phases (organic and aqueous)

Ø UNIQUAC for VLE-LLE calculations

Reactive distillation - Case Study

−

= RT56670

41 e*10*108.6k

−

= RT67660

42 e*10*842.9k

Butanol + Acetic Acid Butyl Acetate + H2Ok1

k2

(esterification)

(hydrolysis)

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Bottom Product

Aqueous PhaseButanol

Acetic Acid

Organic Phase

101.3 kPa

Ø Reactive sections are possible in both sections

Ø OCFE column model formulation:

5 elements – 2 co pts/elem

Number of variables

3 phase – 6117

2 phase - 5967

Reactive distillation - Case Study

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Ø objective function: Total annualized costs

Ø solution in gPROMS® modeling environment utilizing its steady-state optimization capabilities

Case study- Liquid phase profiles

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

Column Trays

Liqu

id M

ole

Frac

tion

Butanol (Org. Phase)BUAC (Org. Phase)H2O (Org. Phase)H20 (Aq. Phase)

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0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

Column Trays

Vapo

r Mol

e Fr

actio

n ButanolBUACH2O

Case study- Vapor phase profiles

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0

30

60

90

120

150

0 10 20 30

Column Trays

Flow

rate

(mol

/hr)

Organic PhaseAqueous Phase

Aqueous phase

disappears at feed stage

Case study- Liquid flow rates

Element boundary adaptively

placed at point of phase transition

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350

360

370

380

390

0 10 20 30

Column Trays

Tem

pera

ture

(K)

2-Phase3-Phase

Case study- Temperature profiles

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Case study – Model comparison

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

Column Trays

BU

AC

Liq

uid

Mol

e Fr

actio

n

2-Phase

3-Phase (Continuous Liquid)

Butyl-acetate molar fraction at bottoms product 98%Aristotle University of Thessaloniki CPERI

1103.61002.2Total Cost (k$/yr)

2/4028/1800.988

2/2715/2640.989

StagesStage holdup (lt)

Feed BuOH/ACOOH

0.9794.24

0.9215.63

Reboiler Duty (MW)Boilup ratio

1.01 10-30.994 10-3ACOOH in distillate

0.980.98BuAC purity in bottoms product

3-Phase model2-Phase model

Design Optimization Results

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Case study – Extent of reaction

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0

10

20

30

40

0 10 20 30 40

Column Stages

Rea

ctio

n R

ate

(mol

/hr/m

3 )

3-Phase Organic Phase3-Phase Aqueous Phase2-Phase

Concluding remarks

• A NEQ/OCFE model has been developed for three phase reactive distillation units

• OCFE model formulation allows the development of a compact in size but yet very accurate process model for reactive three phase distillation columns

• The compact size allows the incorporation of a more detailed process model (rate-based equations)

• Explicit tracking of phase boundaries is achieved with the adaptive placement of element breakpoints

• Design optimization reveals significant differences between 3-phase and 2-phase models in butyl acetate production

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Acknowledgement

• The financial support of European Commission (contract no INCO-CT-2005-013359) is gratefully appreciated

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