optimal design of three-phase reactive distillation columns using nonequilibrium...
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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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