- Email: [email protected]
Modelling and optimisation of an industrial batch process for the production of dioctyl phthalate
6¢~IS -u! ~uomd!nbo oqa pu~ sd~:~s ~u!ssoaoad £o~l oq:~ jo uoNd.taasop ~ £q po~olIoJ 'uo!:lanpoad dOG jo £a~s! -moq3 oq:~ jo oUt.Fmo u~ q:~!t~ s:~a~:ls aad~d oq& 'XFI aq~, pu~ u~d~r u! sq~uom I~-~ £aoxO pIoq oaom s~uNoom ~o!xoa I~tUaOd "sMnso~ ptm slopom ' ~ p o~u~qaxo o:~I!~m a!uoaaaoIO~u!sn s!s -~q £[~p ~ uo uot.:ma!unmmoa I~nuNuoa u! ~do~I tu~o~ ORaL '(966I aoqtuoaohI-£a~naqaeI) sqauom uoa jo po!a -od ~ aoAo ulop~ut.~I poa!UFl oqa pu~ tred~ ut. qaoq pos~q ur~o~ u~tsop au!o[ ~ £q ano po!aa~a s ~ 'o~oI -ioD i~!aodtu I pu~ uoi~aodao D i~at.tuoqD !qs!qns~t.p¢ uoot~aq uoN~aoq~IlOa ~ ~UI.A[OAUI.'aao[oad oq,L •suo!:~aodo q a ~ q xoIdmoa o~ pa!idd~ uoqt~ uo!:ms!mNdo ptm uoN~intu!s '~U!ilopom ssoaosd aoj SlOm padolo^O p £I~.UOaOaj.o ssouot, Na~j3o aq~. ssass~ o:~ ~ ~aoFoad oq~ jo ui!~ £a~puoaos V 'suo!~aoI I~a!qd~s~oo~ ~uoaojj!p ~t~ s~u~Id aoj oui~s aq~. £I!a~ssoaou ~ou oa~ £a!iod ~uN~aodo ao/pu~ u~!sop I~mNdo oq~ '£NuanbosuoD "aoq~ou~ o~ uoN -~sodo jo ~a~unoa ouo moaj £Nu~ag!u~!s £a~a uo~jo q3.tqa~ sao:~a~j 3!mouo3o jo aaqtunu ~ uo puodop smoI -qoad osoq~ o~ suoNnIos oq:~ ~q:t po:tou oq plnoqs :~! 'aoaooaoIAI "po~aodo st. :motud!nbo oq:~£FmO!a~o ~oq uo £i:~aoa!p puodop ii!x~ £~Dno i~!d~a £xessoaou oq~ oau!s poldnoa £IOSOIa oxe suo!st.aop ~uN~aado pu~ u~ts -op aq~ 'as'ea aa~:~I oq:~ ut. '£isno!aqo "s~u~id ~au aoj Xa!iod Su!:~aodo pu~ u~!sop asoq oqa £Ipuoaos
~ n ' ~ ' "~${p,~psz~a.~md' • :I!~mo 9099I'6~ I L I l ~ ' + X V d 'possoapp~ oq p l n o q s o a u a p u o d s o a a o a ii ~ m o q t a o:I a o q : m v 4
puv 's:m~id uoNanpoad dO(/ SuNs!xo aoj ,~a!iod ~u! -:~aodo :~soq oq:~ 'asa~I 'out.tuao:~op o:~ ~u!tu!v plojot~:~ aaat~ ~,aa[oad s!q~ jo so~p,aofqo £z~tu!ad oq,L •uo!:~aodo jo ~,!~oadII~aaao aq~. u: os~oaau! o^N~lOa o~a~I ~ o:t puods -oaaoa plnoa uoNanpaa II~mS ~ uo^o OaUlS uoNanpoad jo ~soa ~!un oq~ oanpoa o:~ ~Ioos o~ oaNuoau! ~uoa:~s o:~ asia soxtfl s!q,I, "u!~a'etu :~ffoad II~tus £IOaD~IOa £q post.~o~a~a~qa oa~ uoNanpoad dO(I jo sat.ulouoao oq~ 'puvq aaq~o oq:~ u 0 "iI~tus oq o:1 £Io~tt.I oaojoaoq:~ s! ~uotuaAoadun. aoq~anj aoj ut~a~tu ~m.u.mtuo:t £u v •:~uomoxoadtu! i~:~uatuoaom, q~noaq~ £auota!:l:Iojo ooa~ -op q~!q ~ poqa~aa Xp~oaI~ s~q pu~ sop'eaop I~aOAOS~oJ po:l~aodo uooq s~q ssoaoad aq,l, "(HXg) IOU~XaqIXq~°-8 q~,!~ (Vd) op!apXqu~ a!l~q~qd jo uoN~aff!ao~so oq~ £q poanpoad s! :tI "saom£1od aoq:to ptre DAd o:l aa!:lt.pp~ u~ s~ £s~snpu! u! soNNu~nb l~NU~sqns u! posn st ~q~ aos!aNs~ld qans ouo s! (dO(I) °~I~q~qd I£~,ao!(I "saos!ap,s~Id auoao~!p jo aoqtunu ~ oanpoad oa £IoaNnaosuoa posn ~u!aq lu~id am~s aq~ 'opom qal~q u! po~aado oa~ s~u~id oq,L ' ~ s ~ a~¢I oq~ ut. oaoq~oslo pu~ tmd~ r u! s~u~id jo aoqumu ~ ~up,~aodo £I:moaana 'saos!aN~Id jo saanpoad ao[~uI ~ aa~ (OOlal) sI~a!maqD !qs!qns~!IAI NIOI&O I'I(IOI:LLNII
SIA[O~td fi u! so!:~!i!a~] uo!:~s!tu!:tdo a!ureu£p oq:l Su!sn poAios uaq:~ s! s!q,L -s~u!~a~suoa ~ti~aodtti! ii~ puu 'sa~aurea~d ~tm!~Au!-am!~ aoq~o pu~ sa!~s!ao~a~a~qo u~!sop ~uamdt.nbo aq~ '(,,sioa~uoa,, ) s o i q ~ ! ~ uoisiaop ~uopuodop-ouIN I~agAOS 'uoNaun] 0A!~a0[qo attuouoao Ire ~uN~aodaoau ! moiqmd uoD~s!m!~do a!tu~u£p ~ o~ spuodsoaaoa st.q.L "~u~Id oq~ ao] sop!Iod ~u!~aodo i~tuDdo aa!aop o~ posn uooq s~q Dpom oq~ 'uo!~pII~a ~uDmiioeI "~u~Id I~!a~snpu! ~ui~s!xo u~ jo znoFmqoq a!tu~u£p poAaosqo oq~ £io~anaa~ ~a!po~d o~ olq~ s! iopom aq~ 'suot.~dmnss~ £a~ssaaauun ~u!~u!tu!Io pu~ lt.~op jo aoa~op ~uota!gns ~ut.~aodaoaut. £q '~q~ u~oqs s! ~,I "mo~s£s ~Ut.llOpom ss~aoad SlqO~Id 5 oq~ ~u!sn pa~ana~suoa uooq s~q soanpoaoad Sut.~aodo s~! p ~ '~,u~Id aq~ jo .(a~s!moqa pu~ sat.s£qd oq1 q~oq ~ut.qt.sasop iopom atm~ufp polm~,op V "sao~a~oaq a ~ q u! ~,no po!aa~a oq u~a ssoaoad oq,L ':~s£I~:~a snoouo~omoq ~ ~u!sn (Vd) op!sp£qu~ a!I~q~qd q:~!~ (Hag) IOU~xoqI£qao-g jo uo!:t~ag!ao:tsa oqa ~!a S! uo!:tanpoad s:t! oa oanoa ou 0 'saom£Iod aaq~o pu~ DAd aoj aos!aNs~Id ~ s~ £I!a~tu!ad '£aasnpu! u! so!:~!:tu~nbI~!:tu~:~sqnsu! posn s! (dOG) °:~I~qaqd I£la°!(I - :ta~a:tsqv
')i'll 'X[Ig LA~S uopuo~l 'out.a!poI~ pu~ ~$oiouqao/L 'oauo!aS jo O$OliOo I~!aodmI ~u!aoou!~u,q smo~s£ S ssoaoa d aoj oa~uoO
,s°p!lo:m~d "O'O pu~ s!aoq!q'q pu~ u~d~f 'glL ~ure£w'IO 'PI!q~an}I '!sopo!qsfl 0I-g ':lu~Id em~.qsnz!lAI 'uoN~zaodaoD I~3!tuoqa !qs!qns:~!lAI so:tooD ~u!soou!~u,q pmz £~OlOUq3~& uot.:lanpoad
!sm,~N"h pu~ ~aml!qs I "j~
o:teIeq qd iAktao!G jo u o D a n p o a d oq: ,lO3 ssoaoad q a , e [ t Ie!a snpuI ue jo uo! es!mDd O p u e U!IlOpOIAI 00o+oo'LI$L 6 / ~ c l - s 6 o o
9-6[~00(L6)~9£I-8600S:Ild
u!m.ul~ mo.tD u! polutM iranzasai s;q~.u IlV prI aaua!oS -ta~AaSlRL66I 0 /.661 'tTi,Z | S-6t;Z I $ 'dd"lddns ' I Z "IOA"guguy -u~aqosaalndvaoD
uom~Baad
S1240
PSE '97-ESCAPE-7Joint Conference
volved in the corresponding industrial process. We then proceed to describe the key features of the dynamic model developed for this process, and its implementation and validation. The main issues involved in determining optimal process designs and operating strategies are then analysed, and our approach to solving this dynamic optimisation problem is presented, together with some of the results obtained. Finally, some more general conclusions on the lessons learned from this work are presented.
2EH Saturat~ with H20
l ........ }
Wa~
R~w~d
PROCESS DESCRIPTION
2~1
PA
Chemistry Dioctyl phthalate (DOP) is formed by the diesterification of phthalic anhydride (PA) and 2ethylhexanol (2EH). The two main reactions taking place are as follows:
2EH
S~gad Steam
Monoester formation This results in the formation of (mono) octyl phthalate (MOP): PA + 2EH -+ MOP
Figure 1: Flowsheet of DOP Reactor (A)
This reaction is irreversible and very fast.
Diester formation MOP + 2EH ~ DOP + H20
(B)
This reversible reaction can proceed via both a catalytic route involving a homogeneous catalyst and a non-catalytic path, and is consequently characterised by rather complex kinetics. In practice, in order to increase the rate of the DOP formation by reaction (B), an excess amount of 2EH is used. The achievable conversion is limited by equilibrium considerations. However, by removing the water formed during the diesterification reaction, it is, in fact, possible to achieve almost complete conversion of the limiting reactant. This idea forms the basis of the industrial process described below.
an evaporation of most of the water formed by the esterification, together with some of the alcohol (i.e., the two most volatile components). This overhead vapour is totally condensed and allowed to separate into two liquid phases in the overhead reflux drum. The aqueous phase is removed from the system while the alcohol rich phase is recycled back to the reactor. A separator unit placed between the reactor and the condenser (see figure 1) is used to improve the effectiveness of 2EH/water separation. Stripping: At the end of the esterification stage, the reactor contains primarily a mixture of DOP with excess 2EH. The latter is removed in the overhead vapour by further heating. In contrast to the step above, the alcohol rich phase recovered in this manner from the reflux drum is not recycled to the reactor but is instead stored in a separate 2EH recovery tank for use in subsequent batches (see Feeding step above).
Equipment and Operating Procedures Chemical Additions: Any unreacted MOP and The plant is designed around a kettle reactor, suitcatalyst still left in the reactor are neutralised able for the production of different plasticisers. A and decomposed respectively through the addisimplified schematic of the process is shown in figure tion of further chemicals and hot water. 1. The operation of the plant involves a sequence of Dehydration and V a c u u m Stripping: The DOP product in the reactor is brought up steps. The most important of these are as follows: to the desired final product purity by removFeeding: The preheated fresh 2EH together with ing the remaining water and 2EH by steam the PA and homogeneous liquid catalyst are fed stripping the reactor contents under vacuum. to the reactor. The fresh 2EH may be partially During this period, steam is simultaneously replaced by 2EH recovered from the previous sparged directly into the reactor and fed to the batch cycle (see below) which is also charged to reactor jacket. the reactor via the preheater. Esteriflcation: The contents of the reactor are continuously stirred and heated with steam supplied to the jacket of the reactor. This causes
PSE '97-ESCAPE-7 Joint Conference PROCESS
MODELLING
The key features of the models used for the main units in the process are as follows: R e a c t o r This is modeled as a perfectly mixed jacketed stirred tank reactor that may contain both vapour and liquid phases. The model assumes that all reactions are homogeneous and occur in the liquid phase and that the liquid and vapour phases are in thermodynamic equilibrium. The model also allows phases to appear and disappear, taking into account the three potential operating regimes (all liquid, mixed liquidvapour and all vapour) and the transitions between them. S e p a r a t o r This is modeled as an adiabatic flash drum. As in the case of the reactor, the model allows for phase appearance and disappearance. R e f l u x d r u m This model describes two liquid phases present in equilibrium in the mixing/settling compartment of the reflux drum, taking account of the hydrodynamics of the flow of the organic phase over the weir. The height of the interface between the organic and aqueous phases is maintained between strict limits by a controller regulating the flow of the aqueous phase from the tank.
S 1241
• D i s c o n t i n u o u s p h y s i c s : The DOP system exhibits both continuous and significant discrete aspects. For instance, the overhead separator is initially completely dry, containing only a vapour phase. As the reaction proceeds, the water and some of the excess 2EH are vapourised and then totally condensed and fed to the reflux drum. While the latter is filling up, no actual reflux stream exists. However, once the level of the liquid in the reflux drum exceeds the level of the weir, a 2EH-rich organic liquid phase starts being fed back to the separator. This then leads to the appearance of a liquid phase in the latter. • C o m p l e x o p e r a t i n g p r o c e d u r e : The DOP system is a dynamic system driven by a sequence of external manipulations representing a number of processing steps, some of which were described above. The above process model was implemented in the
gPROMS process modelling tool (Barton and Pantelides, 1994; Oh and Pantelides, 1996) developed at Imperial College. Unlike earlier modelling software which was aimed at primarily continuous processes, gPROMS is specifically designed for the modelling, simulation and optimisation of processes with both discrete and continuous characteristics. This allows the detailed modelling of both the physicochemical behaviour of the system and its operating procedures. The package also provides effective mechanisms for handling complexity in both of these aspects of process modelling.
The overall process model also characterises the flows between the above units in terms of appropriate flow/pressure drop relations. An activity coefficient based model was used for computing the vapour and liquid equilibrium. The PROCESS MODEL VALIDATION AND pure component physical properties (vapour and liqSIMULATION uid enthalpy and density) are computed as correlated functions of temperature. Mixture properties were Typical dynamic simulation results obtained using computed assuming ideal mixture behaviour. the model described above are illustrated in figures 2 The reaction rate model for the formation of and 3*. Figure 2 shows the variation of the mole fracDOP has been derived through laboratory experi- tions of DOP and 2EH in the reactor throughout a ments and describes both the catalytic and the non- single batch cycle. As the reaction proceeds, the mole catalytic routes in this reaction. fraction of DOP increases reaching a limiting value by the end of the esterification stage (around the middle of the figure). At the same time, the 2EH mole MODEL IMPLEMENTATION fraction decreases reaching again a limiting value deThe key characteristics of the model are as follows: termined primarily by the excess amount of 2EH that has been fed to the reactor. During the subsequent • Complexity: The physical and chemical stripping, chemical additions and vacuum stripping mechanisms that govern the time dependent bephases, the molefraction of 2EH is further decreased. haviour of the complete DOP reaction system This generally leads to an increase in the DOP mole are quite complex. The equations describing fraction although a sharp temporary decrease is obthe performance of the system have been deserved over a short period of time due to the addition rived from first principles in terms of the conof other components to the reactor. Eventually, the servation laws, physical constraints and equilibDOP mole fraction reaches the final product purity rium relations which describe the performance specification. of each equipment item, taking account of its Figure 3 shows the corresponding pressure and detailed geometry. The resulting model contemperature profiles in the reactor. It is worth nottains approximately 2000 ordinary differential *The numbering of the axes in these and other results plots and algebraic equations. in this paper has been removed for commercial confidentiality reasons.
PSE '97-ESCAPE-7Joint Conference
S1242
ing the sharp changes in pressure signifying the beE V A L U A T I O N OF D E S I G N ginning of the various processing stages. At the same ALTERNATIVES time, the temperature varies between lower and upper bounds dictated by product quality considera- Having validated the simulation model with the measured plant data, it was then possible to perform a tions. number of operational and design studies using the same gPROMS model and to quantify potential improvements. The studies included a number of operating scenarios (heating profiles, feed policies etc.) as well as design modifications (e.g. improved separator design and introduction of a prereaction unit). However, because of the complexity of the process, it is clear that a more systematic way of searching the rather =~="- large space of possible operating and design decisions is required. This is discussed below.
\
OPTIMAL PROCESS OPERATION AND DESIGN
Figure 2: Reactor compositions 2EH, DOP
The DOP process involves several important degrees of freedom, such as the rates of addition of the main reactants, catalyst and heat to the reactor, as well as the recycle policy for recovered 2EH. It is also subject to several constraints, including:
Physical constraints: These are due to the limited provision of resources (e.g. steam availability) and operational restrictions on the various equipment items (e.g. minimum pressure, maximum reactor capacity etc.).
Product quality constraints: These
it_-
exhibit themselves directly as constraints on the final composition of the material left in the reactor at the end of the batch, and also indirectly as constraints on the operating conditions during the batch. For instance, the reactor temperature must never exceed a certain limit relating purely to the quality of the final product.
Overall, it is clear that the determination of a design and/or optimal operating policy is a non-trivial task, especially in view of the complex interactions between the reaction kinetics and vapour-liquid and liquid-liquid equilibria in the system. Our approach has been to formulate this as a dynamic optimisation Figure 3: Reactor Temperature and Pressure problem incorporating an economic objective funcThe simulation results shown above aimed to re- tion, the time-dependent decision variables and all produce the current operating policy at one existing important constraints. This was then solved using plant. The agreement between model predictions and the dynamic optimisation facilities in gPROMS. actual plant measurements is excellent both qualitaObjective Function tively and quantitatively. In this context, it is worth emphasising that the values of all thermodynamic The objective function to be minimised is the total and kinetic parameters used in the model were de- cost per unit mass of DOP produced. For the design rived from appropriate laboratory experiments. No of new DOP plants, the objective function comprises parameter fitting using the plant data was performed. two main components: 0
1. The operating costs associated with making a batch of DOP, including:
PSE '97-ESCAPE-7 Joint Conference • Costs of raw materials (2EH, PA and catalyst). • Cost of utilities (mainly steam of various qualities). • Cost of chemicals used for MOP neutralisation and catalyst deactivation. 2. The fixed capital costs associated with the plant equipment, including the costs of the reactor shell and its heating coil, and the costs of the condenser and the separator.
S1243
• A constraint on the minimum mean production rate of DOP (defined as the amount of DOP produced per batch divided by the total batch processing time). This is derived from the lower bound on the desired annual production of DOP. • A constraint that ensures that the total amount of recovered 2EH fed into the reactor does not exceed the total amount recovered during a batch.
OPTIMISATION METHODOLOGY Of course, in the case of optimising the operating procedure for an existing plant, the objective function The problem described above involves the optimisaincludes only the operating costs listed above. tion of a complex dynamic system subject to a variety of constraints, and this is to be achieved by manipuDecision Variables lating several time-varying quantities as well as some The solution of the dynamic optimisation problem in- time-invariant ones. The solution of this problem has volves the determination of the total duration r of the been carried out using the dynamic optimisation faoperation and its individual processing steps, as well cilities in gPROMS. as the variation of the following five time-dependent The solution method used by gPROMS for this control variables over the time horizon t E [0, r]: type of problem is based on the control vector parameterisation approach as recently described by Vassil• The rate of addition of PA feed to the reactor. iadis et al. (1994a, 1994b). This involves representing each of the five time-varying control variables in • The rate of addition of fresh 2EH feed to the terms of a finite number of parameters. For instance, reactor. a certain control variable may be varied in a piece• The rate of addition of recovered 2EH feed to wise constant fashion over a given number of intervals spanning the batch processing time. The constant the reactor. value of the control in each interval and the dura• The rate of supply of steam to the reactor heat- tion of the latter form a finite set of parameters to be ing coil. determined by the optimisation. The time-invariant decision variables are also added to this set of param• The pressure profile in the reactor. eters. The current optimisation of the DOP process inIn addition, the optimiser will need to determine corporates a detailed description of the plant operaoptimal values for the following time-invariant pation over the feeding and esterification stages of the rameters: operating procedure, and an aggregate description for • The amount of catalyst to be fed to the reac- the remaining stages. A piecewise constant time varitor t . ation is assumed for all control variables except for the reactor pressure which is defined to be a piecewise lin• The volume of the reactor (design case only). ear and continuous function of time. The time horizon of interest is divided into 4 intervals of variable Constraints duration for the purposes of defining these piecewise Our current optimisation formulation includes the functions. The length of each time interval, as well as that of the total time horizon, is determined as part following constraints: of the solution of the optimisation problem. • Constraints on the minimum and maximum permissible temperatures within the reactor at OPTIMISATION RESULTS all times during the batch cycle. Typical optimisation results are shown in figures 4 to • A constraint on the maximum permissible tem- 5. Figure 4 shows the optimal feed addition policy. perature within the reactor at the end of the The optimal solution starts by feeding the PA simulbatch cycle. taneously with the recovered 2EH; the latter is then • Constraints on the minimum and maximum al- replaced by a fresh 2EH feed. Figure 5 presents the temperature profile resultlowable volume of liquid in the reactor at all ing from the optimal control manipulations. The optimes during the batch cycle. timiser maintains the temperature within the bounds ?The addition of catalyst takes place as a single discrete specified by the product purity constraints at all injection of material rather than as a continuous flow over a times, keeping it close to the upper bound at the period of time. start of the esterification phase.
S1244
PSE '97-ESCAPE-7 Joint Conference
In addition to control profiles of the type illustrated here, the optimisation determines simultaneously the values of the optimal reactor volume, the optimal amount of catalyst to be added to the reactor, and the optimal batch duration.
.... t.~." It2m
Figure 5: Optimal Temperature Profile
-----:---! .........
l ~tQ4
• 464b • • & ~ O Q
Figure 4: Optimal Feed Addition Policy
CONCLUDING REMARKS The study reported in this paper, carried out jointly by Mitsubishi Chemicals and Imperial College, has led to substantial improvements in the throughput and profitability of the DOP process. It has also opened the way for strategic comparisons among different plant configurations and even geographical locations to be placed on a rational and meaningful basis by comparing the optimal design and operating policies of all such alternatives. The importance of using accurate dynamic models for this study cannot be overemphasised. This is especially true given the tight economics of the process and the tight operating constraints under which it operates. For instance, the difference in the unit DOP production cost achievable by competing optimal designs was often found to be of the order of only a few percentage points, which, nevertheless, represents a large improvement in process profitability. The predictive capability of the model must be within this range of accuracy. The study presented here also provides some evidence of the capability of currently available software tools such as gPROMS to deal with complex industrial batch processes. Of particular note is the increasing ability to solve dynamic optimisation problems involving fairly large models with many interacting decisions and constraints. This significant development over what was practically feasible only a few
years ago is already finding a wide range of application for improved process design and operation. However, it must again be emphasised that the availability of validated process models that can accurately predict the plant behaviour is an essential prerequisite for these benefits to be reaiised. There is little sense in applying a sophisticated mathematical tool to a process that is poorly understood and characterised. REFERENCES P.I. Barton and C.C. Pantelides. Modeling of Combined Discrete/Continuous Processes. AIChEJ., 40:966-979, 1996. M. Oh and C.C Pantelides. A Modelling and Simulation Language for Combined Lumped and Distributed Parameter Systems. Comp. chem. Engng., 20:611-633, 1996. V.S. Vassiliadis, R.W.H. Sargent and C.C. Pantelides. Solution of a Class of Multistage Dynamic Optimisation Problems. 1. Problems without Path Constraints. Ind. Eng. Chem. Res., 33:2111-2122, 1994. V.S. Vassiliadis, R.W.H. Sargent and C.C. Pantelides. Solution of a Class of Multistage Dynamic Optimisation Problems. 2. Problems with Path Constraints. Ind. Eng. Chem. Res., 33:2123-2133, 1994.
~ n ' ~ ' "~${p,~psz~a.~md' • :I!~mo 9099I'6~ I L I l ~ ' + X V d 'possoapp~ oq p l n o q s o a u a p u o d s o a a o a ii ~ m o q t a o:I a o q : m v 4
puv 's:m~id uoNanpoad dO(/ SuNs!xo aoj ,~a!iod ~u! -:~aodo :~soq oq:~ 'asa~I 'out.tuao:~op o:~ ~u!tu!v plojot~:~ aaat~ ~,aa[oad s!q~ jo so~p,aofqo £z~tu!ad oq,L •uo!:~aodo jo ~,!~oadII~aaao aq~. u: os~oaau! o^N~lOa o~a~I ~ o:t puods -oaaoa plnoa uoNanpaa II~mS ~ uo^o OaUlS uoNanpoad jo ~soa ~!un oq~ oanpoa o:~ ~Ioos o~ oaNuoau! ~uoa:~s o:~ asia soxtfl s!q,I, "u!~a'etu :~ffoad II~tus £IOaD~IOa £q post.~o~a~a~qa oa~ uoNanpoad dO(I jo sat.ulouoao oq~ 'puvq aaq~o oq:~ u 0 "iI~tus oq o:1 £Io~tt.I oaojoaoq:~ s! ~uotuaAoadun. aoq~anj aoj ut~a~tu ~m.u.mtuo:t £u v •:~uomoxoadtu! i~:~uatuoaom, q~noaq~ £auota!:l:Iojo ooa~ -op q~!q ~ poqa~aa Xp~oaI~ s~q pu~ sop'eaop I~aOAOS~oJ po:l~aodo uooq s~q ssoaoad aq,l, "(HXg) IOU~XaqIXq~°-8 q~,!~ (Vd) op!apXqu~ a!l~q~qd jo uoN~aff!ao~so oq~ £q poanpoad s! :tI "saom£1od aoq:to ptre DAd o:l aa!:lt.pp~ u~ s~ £s~snpu! u! soNNu~nb l~NU~sqns u! posn st ~q~ aos!aNs~ld qans ouo s! (dO(I) °~I~q~qd I£~,ao!(I "saos!ap,s~Id auoao~!p jo aoqtunu ~ oanpoad oa £IoaNnaosuoa posn ~u!aq lu~id am~s aq~ 'opom qal~q u! po~aado oa~ s~u~id oq,L ' ~ s ~ a~¢I oq~ ut. oaoq~oslo pu~ tmd~ r u! s~u~id jo aoqumu ~ ~up,~aodo £I:moaana 'saos!aN~Id jo saanpoad ao[~uI ~ aa~ (OOlal) sI~a!maqD !qs!qns~!IAI NIOI&O I'I(IOI:LLNII
SIA[O~td fi u! so!:~!i!a~] uo!:~s!tu!:tdo a!ureu£p oq:l Su!sn poAios uaq:~ s! s!q,L -s~u!~a~suoa ~ti~aodtti! ii~ puu 'sa~aurea~d ~tm!~Au!-am!~ aoq~o pu~ sa!~s!ao~a~a~qo u~!sop ~uamdt.nbo aq~ '(,,sioa~uoa,, ) s o i q ~ ! ~ uoisiaop ~uopuodop-ouIN I~agAOS 'uoNaun] 0A!~a0[qo attuouoao Ire ~uN~aodaoau ! moiqmd uoD~s!m!~do a!tu~u£p ~ o~ spuodsoaaoa st.q.L "~u~Id oq~ ao] sop!Iod ~u!~aodo i~tuDdo aa!aop o~ posn uooq s~q Dpom oq~ 'uo!~pII~a ~uDmiioeI "~u~Id I~!a~snpu! ~ui~s!xo u~ jo znoFmqoq a!tu~u£p poAaosqo oq~ £io~anaa~ ~a!po~d o~ olq~ s! iopom aq~ 'suot.~dmnss~ £a~ssaaauun ~u!~u!tu!Io pu~ lt.~op jo aoa~op ~uota!gns ~ut.~aodaoaut. £q '~q~ u~oqs s! ~,I "mo~s£s ~Ut.llOpom ss~aoad SlqO~Id 5 oq~ ~u!sn pa~ana~suoa uooq s~q soanpoaoad Sut.~aodo s~! p ~ '~,u~Id aq~ jo .(a~s!moqa pu~ sat.s£qd oq1 q~oq ~ut.qt.sasop iopom atm~ufp polm~,op V "sao~a~oaq a ~ q u! ~,no po!aa~a oq u~a ssoaoad oq,L ':~s£I~:~a snoouo~omoq ~ ~u!sn (Vd) op!sp£qu~ a!I~q~qd q:~!~ (Hag) IOU~xoqI£qao-g jo uo!:t~ag!ao:tsa oqa ~!a S! uo!:tanpoad s:t! oa oanoa ou 0 'saom£Iod aaq~o pu~ DAd aoj aos!aNs~Id ~ s~ £I!a~tu!ad '£aasnpu! u! so!:~!:tu~nbI~!:tu~:~sqnsu! posn s! (dOG) °:~I~qaqd I£la°!(I - :ta~a:tsqv
')i'll 'X[Ig LA~S uopuo~l 'out.a!poI~ pu~ ~$oiouqao/L 'oauo!aS jo O$OliOo I~!aodmI ~u!aoou!~u,q smo~s£ S ssoaoa d aoj oa~uoO
,s°p!lo:m~d "O'O pu~ s!aoq!q'q pu~ u~d~f 'glL ~ure£w'IO 'PI!q~an}I '!sopo!qsfl 0I-g ':lu~Id em~.qsnz!lAI 'uoN~zaodaoD I~3!tuoqa !qs!qns:~!lAI so:tooD ~u!soou!~u,q pmz £~OlOUq3~& uot.:lanpoad
!sm,~N"h pu~ ~aml!qs I "j~
o:teIeq qd iAktao!G jo u o D a n p o a d oq: ,lO3 ssoaoad q a , e [ t Ie!a snpuI ue jo uo! es!mDd O p u e U!IlOpOIAI 00o+oo'LI$L 6 / ~ c l - s 6 o o
9-6[~00(L6)~9£I-8600S:Ild
u!m.ul~ mo.tD u! polutM iranzasai s;q~.u IlV prI aaua!oS -ta~AaSlRL66I 0 /.661 'tTi,Z | S-6t;Z I $ 'dd"lddns ' I Z "IOA"guguy -u~aqosaalndvaoD
uom~Baad
S1240
PSE '97-ESCAPE-7Joint Conference
volved in the corresponding industrial process. We then proceed to describe the key features of the dynamic model developed for this process, and its implementation and validation. The main issues involved in determining optimal process designs and operating strategies are then analysed, and our approach to solving this dynamic optimisation problem is presented, together with some of the results obtained. Finally, some more general conclusions on the lessons learned from this work are presented.
2EH Saturat~ with H20
l ........ }
Wa~
R~w~d
PROCESS DESCRIPTION
2~1
PA
Chemistry Dioctyl phthalate (DOP) is formed by the diesterification of phthalic anhydride (PA) and 2ethylhexanol (2EH). The two main reactions taking place are as follows:
2EH
S~gad Steam
Monoester formation This results in the formation of (mono) octyl phthalate (MOP): PA + 2EH -+ MOP
Figure 1: Flowsheet of DOP Reactor (A)
This reaction is irreversible and very fast.
Diester formation MOP + 2EH ~ DOP + H20
(B)
This reversible reaction can proceed via both a catalytic route involving a homogeneous catalyst and a non-catalytic path, and is consequently characterised by rather complex kinetics. In practice, in order to increase the rate of the DOP formation by reaction (B), an excess amount of 2EH is used. The achievable conversion is limited by equilibrium considerations. However, by removing the water formed during the diesterification reaction, it is, in fact, possible to achieve almost complete conversion of the limiting reactant. This idea forms the basis of the industrial process described below.
an evaporation of most of the water formed by the esterification, together with some of the alcohol (i.e., the two most volatile components). This overhead vapour is totally condensed and allowed to separate into two liquid phases in the overhead reflux drum. The aqueous phase is removed from the system while the alcohol rich phase is recycled back to the reactor. A separator unit placed between the reactor and the condenser (see figure 1) is used to improve the effectiveness of 2EH/water separation. Stripping: At the end of the esterification stage, the reactor contains primarily a mixture of DOP with excess 2EH. The latter is removed in the overhead vapour by further heating. In contrast to the step above, the alcohol rich phase recovered in this manner from the reflux drum is not recycled to the reactor but is instead stored in a separate 2EH recovery tank for use in subsequent batches (see Feeding step above).
Equipment and Operating Procedures Chemical Additions: Any unreacted MOP and The plant is designed around a kettle reactor, suitcatalyst still left in the reactor are neutralised able for the production of different plasticisers. A and decomposed respectively through the addisimplified schematic of the process is shown in figure tion of further chemicals and hot water. 1. The operation of the plant involves a sequence of Dehydration and V a c u u m Stripping: The DOP product in the reactor is brought up steps. The most important of these are as follows: to the desired final product purity by removFeeding: The preheated fresh 2EH together with ing the remaining water and 2EH by steam the PA and homogeneous liquid catalyst are fed stripping the reactor contents under vacuum. to the reactor. The fresh 2EH may be partially During this period, steam is simultaneously replaced by 2EH recovered from the previous sparged directly into the reactor and fed to the batch cycle (see below) which is also charged to reactor jacket. the reactor via the preheater. Esteriflcation: The contents of the reactor are continuously stirred and heated with steam supplied to the jacket of the reactor. This causes
PSE '97-ESCAPE-7 Joint Conference PROCESS
MODELLING
The key features of the models used for the main units in the process are as follows: R e a c t o r This is modeled as a perfectly mixed jacketed stirred tank reactor that may contain both vapour and liquid phases. The model assumes that all reactions are homogeneous and occur in the liquid phase and that the liquid and vapour phases are in thermodynamic equilibrium. The model also allows phases to appear and disappear, taking into account the three potential operating regimes (all liquid, mixed liquidvapour and all vapour) and the transitions between them. S e p a r a t o r This is modeled as an adiabatic flash drum. As in the case of the reactor, the model allows for phase appearance and disappearance. R e f l u x d r u m This model describes two liquid phases present in equilibrium in the mixing/settling compartment of the reflux drum, taking account of the hydrodynamics of the flow of the organic phase over the weir. The height of the interface between the organic and aqueous phases is maintained between strict limits by a controller regulating the flow of the aqueous phase from the tank.
S 1241
• D i s c o n t i n u o u s p h y s i c s : The DOP system exhibits both continuous and significant discrete aspects. For instance, the overhead separator is initially completely dry, containing only a vapour phase. As the reaction proceeds, the water and some of the excess 2EH are vapourised and then totally condensed and fed to the reflux drum. While the latter is filling up, no actual reflux stream exists. However, once the level of the liquid in the reflux drum exceeds the level of the weir, a 2EH-rich organic liquid phase starts being fed back to the separator. This then leads to the appearance of a liquid phase in the latter. • C o m p l e x o p e r a t i n g p r o c e d u r e : The DOP system is a dynamic system driven by a sequence of external manipulations representing a number of processing steps, some of which were described above. The above process model was implemented in the
gPROMS process modelling tool (Barton and Pantelides, 1994; Oh and Pantelides, 1996) developed at Imperial College. Unlike earlier modelling software which was aimed at primarily continuous processes, gPROMS is specifically designed for the modelling, simulation and optimisation of processes with both discrete and continuous characteristics. This allows the detailed modelling of both the physicochemical behaviour of the system and its operating procedures. The package also provides effective mechanisms for handling complexity in both of these aspects of process modelling.
The overall process model also characterises the flows between the above units in terms of appropriate flow/pressure drop relations. An activity coefficient based model was used for computing the vapour and liquid equilibrium. The PROCESS MODEL VALIDATION AND pure component physical properties (vapour and liqSIMULATION uid enthalpy and density) are computed as correlated functions of temperature. Mixture properties were Typical dynamic simulation results obtained using computed assuming ideal mixture behaviour. the model described above are illustrated in figures 2 The reaction rate model for the formation of and 3*. Figure 2 shows the variation of the mole fracDOP has been derived through laboratory experi- tions of DOP and 2EH in the reactor throughout a ments and describes both the catalytic and the non- single batch cycle. As the reaction proceeds, the mole catalytic routes in this reaction. fraction of DOP increases reaching a limiting value by the end of the esterification stage (around the middle of the figure). At the same time, the 2EH mole MODEL IMPLEMENTATION fraction decreases reaching again a limiting value deThe key characteristics of the model are as follows: termined primarily by the excess amount of 2EH that has been fed to the reactor. During the subsequent • Complexity: The physical and chemical stripping, chemical additions and vacuum stripping mechanisms that govern the time dependent bephases, the molefraction of 2EH is further decreased. haviour of the complete DOP reaction system This generally leads to an increase in the DOP mole are quite complex. The equations describing fraction although a sharp temporary decrease is obthe performance of the system have been deserved over a short period of time due to the addition rived from first principles in terms of the conof other components to the reactor. Eventually, the servation laws, physical constraints and equilibDOP mole fraction reaches the final product purity rium relations which describe the performance specification. of each equipment item, taking account of its Figure 3 shows the corresponding pressure and detailed geometry. The resulting model contemperature profiles in the reactor. It is worth nottains approximately 2000 ordinary differential *The numbering of the axes in these and other results plots and algebraic equations. in this paper has been removed for commercial confidentiality reasons.
PSE '97-ESCAPE-7Joint Conference
S1242
ing the sharp changes in pressure signifying the beE V A L U A T I O N OF D E S I G N ginning of the various processing stages. At the same ALTERNATIVES time, the temperature varies between lower and upper bounds dictated by product quality considera- Having validated the simulation model with the measured plant data, it was then possible to perform a tions. number of operational and design studies using the same gPROMS model and to quantify potential improvements. The studies included a number of operating scenarios (heating profiles, feed policies etc.) as well as design modifications (e.g. improved separator design and introduction of a prereaction unit). However, because of the complexity of the process, it is clear that a more systematic way of searching the rather =~="- large space of possible operating and design decisions is required. This is discussed below.
\
OPTIMAL PROCESS OPERATION AND DESIGN
Figure 2: Reactor compositions 2EH, DOP
The DOP process involves several important degrees of freedom, such as the rates of addition of the main reactants, catalyst and heat to the reactor, as well as the recycle policy for recovered 2EH. It is also subject to several constraints, including:
Physical constraints: These are due to the limited provision of resources (e.g. steam availability) and operational restrictions on the various equipment items (e.g. minimum pressure, maximum reactor capacity etc.).
Product quality constraints: These
it_-
exhibit themselves directly as constraints on the final composition of the material left in the reactor at the end of the batch, and also indirectly as constraints on the operating conditions during the batch. For instance, the reactor temperature must never exceed a certain limit relating purely to the quality of the final product.
Overall, it is clear that the determination of a design and/or optimal operating policy is a non-trivial task, especially in view of the complex interactions between the reaction kinetics and vapour-liquid and liquid-liquid equilibria in the system. Our approach has been to formulate this as a dynamic optimisation Figure 3: Reactor Temperature and Pressure problem incorporating an economic objective funcThe simulation results shown above aimed to re- tion, the time-dependent decision variables and all produce the current operating policy at one existing important constraints. This was then solved using plant. The agreement between model predictions and the dynamic optimisation facilities in gPROMS. actual plant measurements is excellent both qualitaObjective Function tively and quantitatively. In this context, it is worth emphasising that the values of all thermodynamic The objective function to be minimised is the total and kinetic parameters used in the model were de- cost per unit mass of DOP produced. For the design rived from appropriate laboratory experiments. No of new DOP plants, the objective function comprises parameter fitting using the plant data was performed. two main components: 0
1. The operating costs associated with making a batch of DOP, including:
PSE '97-ESCAPE-7 Joint Conference • Costs of raw materials (2EH, PA and catalyst). • Cost of utilities (mainly steam of various qualities). • Cost of chemicals used for MOP neutralisation and catalyst deactivation. 2. The fixed capital costs associated with the plant equipment, including the costs of the reactor shell and its heating coil, and the costs of the condenser and the separator.
S1243
• A constraint on the minimum mean production rate of DOP (defined as the amount of DOP produced per batch divided by the total batch processing time). This is derived from the lower bound on the desired annual production of DOP. • A constraint that ensures that the total amount of recovered 2EH fed into the reactor does not exceed the total amount recovered during a batch.
OPTIMISATION METHODOLOGY Of course, in the case of optimising the operating procedure for an existing plant, the objective function The problem described above involves the optimisaincludes only the operating costs listed above. tion of a complex dynamic system subject to a variety of constraints, and this is to be achieved by manipuDecision Variables lating several time-varying quantities as well as some The solution of the dynamic optimisation problem in- time-invariant ones. The solution of this problem has volves the determination of the total duration r of the been carried out using the dynamic optimisation faoperation and its individual processing steps, as well cilities in gPROMS. as the variation of the following five time-dependent The solution method used by gPROMS for this control variables over the time horizon t E [0, r]: type of problem is based on the control vector parameterisation approach as recently described by Vassil• The rate of addition of PA feed to the reactor. iadis et al. (1994a, 1994b). This involves representing each of the five time-varying control variables in • The rate of addition of fresh 2EH feed to the terms of a finite number of parameters. For instance, reactor. a certain control variable may be varied in a piece• The rate of addition of recovered 2EH feed to wise constant fashion over a given number of intervals spanning the batch processing time. The constant the reactor. value of the control in each interval and the dura• The rate of supply of steam to the reactor heat- tion of the latter form a finite set of parameters to be ing coil. determined by the optimisation. The time-invariant decision variables are also added to this set of param• The pressure profile in the reactor. eters. The current optimisation of the DOP process inIn addition, the optimiser will need to determine corporates a detailed description of the plant operaoptimal values for the following time-invariant pation over the feeding and esterification stages of the rameters: operating procedure, and an aggregate description for • The amount of catalyst to be fed to the reac- the remaining stages. A piecewise constant time varitor t . ation is assumed for all control variables except for the reactor pressure which is defined to be a piecewise lin• The volume of the reactor (design case only). ear and continuous function of time. The time horizon of interest is divided into 4 intervals of variable Constraints duration for the purposes of defining these piecewise Our current optimisation formulation includes the functions. The length of each time interval, as well as that of the total time horizon, is determined as part following constraints: of the solution of the optimisation problem. • Constraints on the minimum and maximum permissible temperatures within the reactor at OPTIMISATION RESULTS all times during the batch cycle. Typical optimisation results are shown in figures 4 to • A constraint on the maximum permissible tem- 5. Figure 4 shows the optimal feed addition policy. perature within the reactor at the end of the The optimal solution starts by feeding the PA simulbatch cycle. taneously with the recovered 2EH; the latter is then • Constraints on the minimum and maximum al- replaced by a fresh 2EH feed. Figure 5 presents the temperature profile resultlowable volume of liquid in the reactor at all ing from the optimal control manipulations. The optimes during the batch cycle. timiser maintains the temperature within the bounds ?The addition of catalyst takes place as a single discrete specified by the product purity constraints at all injection of material rather than as a continuous flow over a times, keeping it close to the upper bound at the period of time. start of the esterification phase.
S1244
PSE '97-ESCAPE-7 Joint Conference
In addition to control profiles of the type illustrated here, the optimisation determines simultaneously the values of the optimal reactor volume, the optimal amount of catalyst to be added to the reactor, and the optimal batch duration.
.... t.~." It2m
Figure 5: Optimal Temperature Profile
-----:---! .........
l ~tQ4
• 464b • • & ~ O Q
Figure 4: Optimal Feed Addition Policy
CONCLUDING REMARKS The study reported in this paper, carried out jointly by Mitsubishi Chemicals and Imperial College, has led to substantial improvements in the throughput and profitability of the DOP process. It has also opened the way for strategic comparisons among different plant configurations and even geographical locations to be placed on a rational and meaningful basis by comparing the optimal design and operating policies of all such alternatives. The importance of using accurate dynamic models for this study cannot be overemphasised. This is especially true given the tight economics of the process and the tight operating constraints under which it operates. For instance, the difference in the unit DOP production cost achievable by competing optimal designs was often found to be of the order of only a few percentage points, which, nevertheless, represents a large improvement in process profitability. The predictive capability of the model must be within this range of accuracy. The study presented here also provides some evidence of the capability of currently available software tools such as gPROMS to deal with complex industrial batch processes. Of particular note is the increasing ability to solve dynamic optimisation problems involving fairly large models with many interacting decisions and constraints. This significant development over what was practically feasible only a few
years ago is already finding a wide range of application for improved process design and operation. However, it must again be emphasised that the availability of validated process models that can accurately predict the plant behaviour is an essential prerequisite for these benefits to be reaiised. There is little sense in applying a sophisticated mathematical tool to a process that is poorly understood and characterised. REFERENCES P.I. Barton and C.C. Pantelides. Modeling of Combined Discrete/Continuous Processes. AIChEJ., 40:966-979, 1996. M. Oh and C.C Pantelides. A Modelling and Simulation Language for Combined Lumped and Distributed Parameter Systems. Comp. chem. Engng., 20:611-633, 1996. V.S. Vassiliadis, R.W.H. Sargent and C.C. Pantelides. Solution of a Class of Multistage Dynamic Optimisation Problems. 1. Problems without Path Constraints. Ind. Eng. Chem. Res., 33:2111-2122, 1994. V.S. Vassiliadis, R.W.H. Sargent and C.C. Pantelides. Solution of a Class of Multistage Dynamic Optimisation Problems. 2. Problems with Path Constraints. Ind. Eng. Chem. Res., 33:2123-2133, 1994.