Optimization of Design & Operation in Reactive Distillation 50

CHAPTER IV D ESIGN OF RO PROCESSES

D ESIGN O F RD PROCESSES

The design methods for reactive distillation processing

developed over the last decades are classified and

described. A fingerprinl of the most representative work in

three categories (graphical, optimization-based and

heuristic-based) is presented and missing opportunities

arc identified. Special attention is paid to the methods'

description , outputs, assumplions, advantages and

limitations. The result of this analysis, presented as a

fingerprint chart, points forward to the development of an

integrated conceptual design approach for reactive

distillation processes.

0pnm17.t11io11 of Design & Opercuwn in Reactive Dl.sUlla!lon 51

4 .0 I MT'RODUCTION The available approaches for the design of RO may be categorized into

three main groups: those based on graphical/topological considerations,

those based on optimization techniques and those derived from

heuristic/evolutionary considerations. In the course of this article,

representauvc methodologies of each category will be discussed focusing in

particular on their description, outputs, assumptions, advantuges and

limitations. A qualitalive analysis of the features that play relevant roles in

RD design result in the definition of an integrated strategy. This approach is

termed multlechelon approach and combines systematically the capabilities

and complementary strengths of available graphical and optimization-based

methods. The design methods can be broadly classified as below

4 .1. GRAPHICAL M &'TKODS

The graphical methods are called so, because the decisions ure made

on the basis of graphical information. This information is often generated

using models. These approaches rely on the behavior of residue curves or

distillation Imes and may be classified mto two well-defined trends:

(~ Methods based on thermodynamic· topological analysis of distillation lines;

(ii) Methods based on composition transformations.

4 .1. l STATIC ANALYSIS The design method based on static analysis in RD

units involves finding the complete SPl of steady stnle modes and the set of

corresponding operating parameters. Since separation is the most costly task,

the prime purpose of static analysis method is the synthesis of RO processes

with reduced separation costs and with improved reaction parameters . For

this purpose, several approaches arc proposed, which are in general terms

based on thermodynamic-topological analysis of distillation diagrams.

Assumptions: (1) the vapor and liquid flow rates in the column are infinitely

large;(i1) the capacity of the reaction part in the column is large enough to

Opttnuzat1on of f)es1gn & Operation in Reactiw Distillation 52

carry out a given conversion rate; (iii) the plant is operated at steady state and

theoretical stages are chosen; and (iu ) one reversible equilibrium reaction is

considered. These assumptions allow one to estimate the liquid composition

on a tray as the composition of vapor one tray below (i.e. xi = yi+ 1) and the

proftles may be estimated by using usual distillation lines.

Advantages

• Answers whether or not a reaction should be performed in a RD column.

• Synthesize flow sheets qualitatively.

• Requires little data.

• Effective tool for the study of strongly nonideal mixtures with multiple

chemical reactions and number of component .Redut:es computational time

dramatically.

• Product compositions, extent of reaction and number of stages need not be

fixed priori.

• Determine the stability of various product regimes

Limitations

• Assumes infinite separation efficiency.

• Matching the operating lines with the assumed product composition can be

sometimes troublesome.

4 . 1.2. RESIDUE C URVE MAPPING

The residue curve mapping (RCM) technique has traditionally been

considered a powerful tool for flow sheet development and preliminary design

of conventional multicom-ponent separation processes. It represents a good

approximation of actual equilibrium behavior and allows one to perform

feasibility analysis of separation processes where nonideal and azeotropic

mixtures are involved.

Furthermore, residue curves have been used to predict the liquid­

composilion trajectories in continuous distillation units. Although for

finite columns those profiles differ slightly compared to the residue curves

under same isobaric conditions, this difference is normally considered

Op<U1UZ11liot1 of lk!ll(Jn & Opt:rotton m Rl'ad11Je Du.nllation 53

negligible al the first stages of design. A feasibility criterion may be derived

from RCM considerations, where feasible composition profiles should be

1:nclosed by the total reflux profiles (i.e. residue curves) and Lhe reversible

profiles (i.e. profiles a t the minimum reflux ratio). Conceptually, residue curve

mapping is a phase equilibrium representation for systems involving

azeotropes and qualitatively studies the behavior of a (non-) reactive mixture

in a heated still.

Analytically, RCM are constructed based on physical properties of the

system (i.e. vapor-liquid equilibrium, liquid-liquid equilibrium and solubility

data), wherein the composition of a non-reacting liquid remaining in the

system may be determined by performing overall and component matenal

balances.

Advantages

• Provides a reliable tool to perform feasibility analysis in RD.

• Requires little data.

Limitations

· This techruque is limited by its intrinsic graphical nature.

• Accurate thermodynamic data are required to correctly describe the RD

process.

4 . 1.3 ATTAINABLE REGION TECHNIQUE

The concept of attainable region (AR) has been extensively employed m

Lhe synthesis of reactor structures and successfully extended to processes

combining simultaneous reaction, mixing and separation. In combination

with graphical methods, an activily based reaction-separation vector is

defmed, which satisfies the same geometric properties as Lhe reaction vector

does. Therefore, it allows one to construct the attainable region using the

existing procedure for reaction-mixing systems. In general terms and for a

given system of reactions with given reaction kinetics, the AR may be defined

as the portion of concentration space that can be achieved from a given feed

composition by uny combinauon of reaction and mixing. Thus, this technique

Opi/mizatlon of Oeslg11 & Oµerutlort i11 Meucliue IJisWluliort 54

aims to identify feasible reactor networks -albeit not the optimum- based on

graphical properties of simple models of CSTR and PFR.

Assumptions

(i) Every composition that lies on the segment line clc2 belongs to the AR;

(ii) on the AR boundary the reaction vector point's inward, is tangent or is

zero; and (iii) in the complement of AR no reaction vector intersects the AR.

Advantages

• Points out promising flow sheets.

• Can be easily extended to multiphase systems

Limitations

• Economic considerations are not taken into account to rank the design

alternatives.

4 . 1.4. FrXED POINT ALGORITHM

A sound understanding on ftxed points and the prediction of their

behavior as a function of design parameters have been lately used as a design

tool for RD columns.

Assumptions

This technique is based on several assumptions, which depend on the nature

of the contacting structure.

For Staged columns (Buzad and Doherty, 1994): (1) three component systems

with a chemical reaction given by iAA + iBB _ CCC; (i1) ideal vapor-liquid

equilibrium; (iii) iso-molar reaction; (iu ) negligible heat of reaction; (u)

negligible heat of mixing; (u1) equal latent heats; and (ui1) constant liquid hold­

up on the reactive stages.

For Packed columns (Mahajani und Kolah, 1996): (1) applicability of lhc ftlm

theory of diffusion; (i1) uniform liquid composition in the bulk; (iii) negligible

axial dispersion/diffusion; (iu) CMO; (u) saturated liquid feed; (ut) negligible

heat losses to the walls, heat of reaction and heat of mixing; (ui1) total

condenser; (viii) reboiler modelled as equilibrium stage with reaction; and (ix)

Optimization of Design & Operation in Reactive Distillation 55

constant mass transfer coefficients, interfacial area and liquid hold-up.

Advantages

• Highly flexible in generating alternative designs

• Allows the determination of the column profile only using mass balance and

equilibrium equations

Limitations

• Imposes practical limitations and complicates its extension to systems

where the number of components minus the number of independent

stoichiometric reactions exceeds a value of 3 ..

4.1.5. REACTIVE CASCADE

Chadda et al. (2003) and Gadewar et al. (2003) use the concept of

reactive cascades to screen the feasibility of hybrid RD systems. This

approach has been successfully applied to the preliminary design of single­

feed and double-feed RD columns. The governing expressions for the

stripping (nstrip tstages) and rectifying (nrect t stages) cascades are,

rectifi11g : Y•r' - ¢R1 x J,.1 • 17 <!>R.yx .<,.1 v, ( K~~J ( I ~D ) y {,t 1 )

., / ( trect) •EZ . ,J E 2,n

... (4.1 )

-,,·here oRJ; Vj / Lj-1 is the fraction of feed L vaporized in the jth unit; and D

is a normalized Damk""ohler nu m ber (D; Da I 1 +Da).

Advantages

:\ global feasibility analysis can be performed as a function of the production

~ate, catalyst concentration and liquid hold-up Does not have any restriction

:n the number of components

:..imitations

::>amkohler number is assumed to be invariant on all the reactive stages; the

:O:ffect of structural aspects of the unit is neglected.

OpllmJ7Atto11 of Design & Operlllion in Reactive Dtstillatrnn 56

The energy balances arc left out from the design methodology

4.1.6 THERMODYNAMICS BASED APPROACH

Stichlmair and co-workers studied the RD design from a

thermodynamic-driven point of view. Their approach is based on the existence

of reactive distillation lines and potential reactive azeotropes

Advantages

• Applied to both fast and slow chemical equilibrium reactions.

Feasible product scan be determined within a RD column

Limitations

• Finding the reactive a7.eotropes might be sometimes troublesome

• Detailed knowledge of phase equilibrium, reaction kinetics and residence

time within the column is required

4 .1. 7 CONVENTIONAL GRAPHICAL TECHNIQUES

These techniques allow the distribution of reaction zones within a

column using the McCabe-Thiele and Ponchon-Savarit methods for a given

reaction conversion by adjusting the catalyst hold-up on each stage. Although

the methods are currently limited to binary reactive mixtures, they provide

fundamental insights towards multiple component systems. In general terms,

it is suggested that if the reaction has a heavy reactant and a light product,

the reaction zone should be placed in the rectifying section , whereas if the

reaction has a light reactant and a heavy product, the reaction zone should

be located in the stripping section.

Assumptions:

(1) binary system with a single chemical reaction; (iz) CMO; and (iir)vapor­

liquid equilibrium.

4 .1.7.l P ONCHON-SAVARIT METHOD.

This method is traditionally considered a powerful visualization tool for

the synthesis of distillation columns for binary mixtures. Thus, it allows the

Op!imJzation of Design & ~ration in Reoctuie Dts11/lat1on 57

designer to account graphically for the enthalpy effects that c~use a varyi~g molar overflow when stepping of stages. The main issue of this approach is

the definition of the reactive cascade difference point, which for an exothermic

iMmcriz~tion reaction occurrin~ in the rectifying zone moves towards tht:

reactant and downward as the calculation goes down the column.

4 . 1 .7 .2 M CCABE-THIELE METKOD.

This method is used to assess qualitatively the impo.ct of changing a

design variable. For the RD co.se, two main features are tracked to sketch the

diagram for a binary mixture of reactants undergoing on isomcrization

reaction and under CMO assumption, the intersection point of the operating

line with the y • x hne defines the reactive cascade difference point, which

moves proportionally o.s the ratio molar extent of reaction to product Oowrate

(i.e. xn • xD - an/~; where n denotes the stage number, the heat supplied by

the reaction decreases the slope of the operating line provided that the

location of the reactive cascade difference point is not changed.

Advantages

Allow a transparent visualization of tray-by-tray calculations

Fundamental tools for the conceptual design of RD column visuali:r.e the

impact of the location of the reactive sections and the fet:d location within the

column

Limitations

Exclusively applied to isomerization reactions.

Limited by their inherent graphical nuture

4 .2 . PHENOMENA BASED APPROACH

According lo this method -proposed by Hauan (1998)- three

independent phenomena take place simultaneously in a RD column: mixing,

separation and reaction. These phenomena may be represented by vectors

and allow the description of the total process profile of the system ns a

Advantages Only physical and chemical data arc required to estimate the

~1tm=11on of Design & OperallOn tn R"art11>1! Dtsh1Ja11on 58

phenomena vectors, which arc mdependcnt of the 11tructuraJ design of the

unll Allows designer to assess independently the select of equipment

structure and operating policies on the composition change in RD

Limitations

Although this method is driven by fundamental considerations, Its

applicability requires further studies

4 .2 . l SCALAR/ V ECTORIAL DIPFl:R.ENCE P OINTS TEcHNIQIJE

The concepts of reactive cascade and scalar /Victoria difference points in

reactive cascades have been successfully applied by Hauan et al. (2000a); Lee

et al. (2000a) and Lee and Westerberg (2000) in the design of RD processes.

(For a gluen phase and reaction equilibrium in a stage RD column} .Reactive

cascade difference points are defined as the combined points of stoichiometric

coefficient vectors and product compositions. The procedural steps are (1)for a

liquid phase chemical reaction at the operating pressure p draw the reaction

equilibrium and the bubble point curves (for gas phase chemical reactions,

the dew point curve should be drawn and an equivalent procedure should be

followed. (ii) specify the top and bottom compositions, reboil and reflux ratios,

(iir) step up/ down from the feed stage to the top/bottom stage; (u,, from

graphical considerations (according to expression s 3.25, 3.26 and phase · · I t d extents of reactions for e uilibrium relationship), the accumu a e

q · d· (. ) the liquid composition on stripping/rectifying sections are determine , iv

the tray is calculated; and (v) tray-by-tray calculations are performed

upwards/ downwards until the calculated liquid composition equalizes the

top/ bottom product composition. . Assumptions: (i) known top and bottom compositions; (i1) known reflux ratio;

(ii~ CMO assumption; and (iv) chemical reaction of the type

4 .3. OPTIMIZATION - BASED M ETHODS

Optimizarlon of Design & Operation in Reactillt' Disttlla1ton 59

This second group of design methods is composed of those

methodologies, which are supported by the power of computational

subroutines and talce into account important elements of an overall design

strategy (e.g. types of phase equilibrium, number of components, occurrence

or not of chemical reaction on a given stage.

4 .3.1 M IXED-INTEGE R NONLINEAR PROORAMMLNO(MINLP)

This method is particularly helpful to find fully or partially optimized

soluti<'ns for RD design variables (Malone and Doherty, 2000). The objective

fu.ncti.on for the RD problem is commonly composed of two basic terms:

annual operating cost (e.g. consumption of raw materials, steam and cooling

water) and the annualized investment (i.e. column, internals, reboiler and

condenser). The constraints are formed from the MESH equations on each

tray, material balances at the top and bottom of the column, kinetic and

thermodynamic relationships and logical relationships between process variables and the number of trays.

Assumptions: (I} the vapor and liquid phases are in equilibrium on each tray;

(i1) no reaction takes place in the vapor phase; (iii) the liquid phase is always

homogeneous; (iv) the enthalpy of liquid streams is negligible; (v) the heat of

evaporation is constant; (vz) temperature dependence of the reaction rates can

be expressed in Arrhenius form; and (viz) the cost of separating products

downstream is given by an analytical function.

4.3.2 ORTHOGONAL COLLOCATION ON FINITE ELEMENTS (OCFE)

MINLP has been found to be troublesome for units with large number of

trays and for the simultaneous design of more than one distillation unit due

to the considerable computational time required for attaining the solution

(Seferlis and Grievink, 2001). Furthermore, special attention must be paid in

the MINLP model formulation and initial guesses outside the feasibility

domain may lead into convergence difficulties. OCFE techniques are

suggested by Seferlis and Grievink (2001) for the design and optimizalion of

Optimization of Design & Operation in Reactive Distillation 60

staged RD columns. This approach transforms the discrete number of stages

in the column into a continuous variable and treats the composition and

temperature as functions of the position.

Assumptions: (z) complete mixing of each phase a t each stage; (iz) constant

liquid hold-up and no vapor hold-up at each stage; (iiz) no liquid entrainment

from stage to stage; (iv) adiabatic stages; and (v) thermal equilibrium between

the liquid and vapor streams leaving each stage.

4.3.3 MIXED INTEGER OPTIMIZATION (MIDO)

In general a chemical process that shows poor ability of meeting control

objectives gives rise to missing opportunities with respect to economic

performance and satisfaction of product specifications. This fact may imply

the existence of a trade-of between those processes designed with respect to

control performance considerations and those driven by economic issues. In

order to circumvent this duality, relevant improvements are recently done

towards the integration and simultaneous optimization of the design and

control tasks. The general design and control problem involves finding

parameters (continuous and/or integers) that define the RD column and

control tuning parameters at the minimum economic cost and with an

accep table dynamic performance in the presence of disturbances. The

continuous parameters include column diameter, reboiler and condenser

areas and tuning parameters, while integer variables· --y- involve the

existence or not of catalyst on a given stage. According to Georgiadis et al.

(2002), the simultaneous a pproach takes advantage of the interactions

between design and control and provides a fully opera tional process design

that is cheaper and more controllable th an that generated by the sequ ential

approach.

Advantages

• Applicable for multiple reactions and where reactive equilibrium or thermal

neu trality cannot be assured.

• Generation of optimum designs with respect to economics and

controllability

Limitations

0prunaa11on of Design & Operation on Reactive Di.s1olla11on 61

• The optimization problem might be difficult to solve.

• Huge computational time can be required

• Difficult to perform sensitivity analysis of the optimum solution

4 .3.4 EVOLUTIONARY / HEURJBTIC METHODS

A third trend of conceptual design approaches may be identified from

the evolution of RD as a derivation from conventional distillation processes.

As proposed by Subawalla and Fair (1999), residue curve map techniques

and fixed-paint algorithms have been traditionally very useful tools for

preliminary screening and design of RD systems. However, they cannot be

used for detailed design, since they rely on several limiting assumptions and

do not account for the special nature of reactive column internals. Those

authors propase a post-design algorithm to estimate parameters such as

column pressure, reactive zone location, catalytic mass, reactant feed

location, reflux ratio, column diameter, number of equilibrium stages and

packed height. Moreover, the feasibility of up-st.ream are addressed

(Subawalla and Fair, 1999),

Advantages • Estimates easily several equipment and/ or operal.lonal variables.

Limitations • Basically a post-design algorithm and as such it requires an already defined

process structure.

4 .4. CONCLUDING REMARKS

Both the graphical and optimization-based design methods have

already proven their potential in RD process design but have also shown

some signifiCllnt limitations. Graphical methods ore fairly flexible in

generating alternative designs at various design parameters. Furthermore, the

graphical nature of the methods clarifies the undererstanding of those

Opanuzabon of Deslgn & 0pttot1011 on Rroctwe Dlslll/a11on 62

fundamental is:sucis in RD, which might be disguised by other approaches

(e.g. reactive azcotropcs). On the other hand, graphical methods are strongly

limited by their graphical nature (i.e. (nc - nrx) • 3). Optimization-based

methods overcome the last limitation and have successfully solved design

problems, where multicomponent mixtures, multiple chemical reactions and

multiple units are involved. However, additional caution 1s required in the

problem formulation and inappropnate initial guesses or the optimization

variables may lead into convergence difficulties.

Based on their assumptions, Limitations and outputs a Qualitative

fingerprint chart or the design methods used in reactive distillation is

prnduccd for the methods descrlucd above.

From this qualitative plot the following conclusions can be drawn:

{•) Most of the graphical methods provide fundamen tal insights on the

feasibility of the RD process and define the initial process structure;

(ii) Economic consideration s are taken into account exclusively by

optimization-based methods;

(iir) The availability of the process has not been included as design output

by any method, since this temporal feature is normally dealt at the next level

of engineering design;

(iu) The heuristic-based methodology is based on an already designed

process and is therefore a post-design tool;

(u) Most of the design methods have been developed for steady state

operation;

The initial effort required for optimization-based methods is far more

significant than that for graphical approaches, but the output generated by

the programming-based design is more comprehensive.

Due lO the size and conceptual/computational complexity of the RD design

problem, a single comprehensive design strategy might not be available for

years to come. The integrated design approach -termed multiechelon design

approach proposed by Almeida-Rivera and Grievink (2001); Almeida-Rivera et al. (2004a) allows the designer to combine in a systematic way the es1pabilities

Optmuzatoon of Desrgro & Opc:rt111on in Reuetwe Dts1illat1on 63

and complementary strengths of the available graphical and optimization­

based methods. Moreover, it constitutes the framework of a highly aggregated

design methodology, which focuses on the RD design problem from a life­

span perspective

Input phase equilibrium model chemical reaction equilibrium chemical reaction kinetics fees compositions compositions of product streams reboiVreflux ratios initial spatial superstructure type pac~ing/hydrodynamic features temporal disturbance scenario

Knowledgw required Model assumptions phase equilibrium negligible heat effects equilibrium controlled regine kinetically controlled regine steady stae operation multicomponent systems(~ 3) single reaction constant molor overflow constant liquid holdup isomolar stolchioenelty negligible axial dispersion constant volatilies infinite vapor/liquid flows f~eory validity constant mass transfer coefficiet Rules connectivity. units' selection operating conditions

Output feasibility of the RD process definition process superstructure

operating conditions (reftux, reboil) number of (non-) reactive stages location feed stages location (non-) reactive azeotropes delenminalion MSS Life-span perspective economic considerations exergy efficiecy considerations controllability considerations

Nature of Output structure perform2nce (economics) physical behavior (operability} physical behavior (availability)

Effort model complexity implementation time tool's complexity

Optimization of Design & Operation in Reactive Distillation 64

G G, G. G, G, G. G, G. Go M, Mo M, H,

•• •••••••• • • • •••••••••• • •• •••••••••• • • • •••••••••• • •• D ••••••••• • •• DD D DDDD D • D D D • D D DDDDDDD • • •• O O OOODODD • • •• DDDDDDDODD 0 • D

.............. • • 0 •• 0 ....... 0 •• DD •• D ••• o •• DD • D D ••••• D •• DD DD • DDD •••• o •• DD •• o ... DD • D • DD OD 000 ... D •• D • o • oD • DD -'. DD • D • D D D D DOD .t.• D • DDD • DD 000 .t. DD • D • DDDD 000 .t. DDDDDD • DD DDDDD • DDDDDDD

C • D D~ 0 0 0 0 D D 0 D D ODO DDDO D DDDD 000 • 00000 00 00

O DDDDDDDDD 0 O • ooooonDooo 0 o •

•••••••• DD OD O ••••• DODOO o • o ooD • DD •• o • • •• ooD • DD • D •• • •• o • D • Do • o •• • •• o • o • DD • DDOO • o • D • D DOODDDD DD

DDDODODDD • • • o OOODODDDOD 0 DD DDDDOODOOD • • D

•••••••••• • •• ODOODDDOD • • • D •••• D DDDDDD • O OODDDDDDDDD DD

ODOO D ODDOO • • D D O OOODDDD •• • D DD OOODDDD •• • D

G,-Static Analysis G,-RCM G,-Attainable region G,-Fixed Points

G.-Reactive Cascade G.-Thenno Based G7 -Graphical G. -Phenomena G.-Difference points M,-MINLP M,-OCFE M,-MIDO H,-Heuristics -Applicable -Nonapplicable -Original assumption relaxed by later c ontributions