OPTIMAL CONTROL OF E MULSION COPOLYMERIZATION: APPLICATION TO A PILOT-SCALE REACTOR UNDER A DCS ENVIRONMENT

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1 OTIL CONTOL OF E ULSION COOLYEIZTION: LICTION TO ILOT-SCLE ECTO UNDE DCS ENVIONENT. lhamad,.willis, J.. omagnoli *, V. G. Gomes Laboratory for rocess Systems Engineering (SE) Deartment of Chemical Engineering, The University of Sydney NSW 6, ustralia STCT det ailed model as develoed for the emulsion coolymerization of styrene and to redict the evolution of the article size distribution (SD) and molecular eight distribution (WD) over the entire range of monomer conversion. system exhibiting zero-one kinetics as emloyed. The model as used to otimise the emulsion coolymerization rocess in order to maximize article size olydisersity index (SI) and olecular eight olydisersity index (WI). Five variables ere used as maniulated variables, styrene monomer feed rate, monomer feed rate, surfactant feed rate, initiator feed rate, and the temerature of the reaction by controlling the jacket temerature. The results from otimiz ation ere validated against exerimental and found to sho good agreement. The hole strategy has been develoed ithin a go-excel/oc-dcs environment alloing for direct transfer of the technology to a general industrial alication. Keyords: Otimization, Coolymerization, SI, SD, WI, WD. INTODUCTION Emulsion coolymerisation is idely used in industry to roduce roducts ranging from aints, adhesives through to tyres and et-suits. To imrove the efficiency and safety of the rocess, model develoment becomes necessary to ensure otimized rocesses and roduct quality. Hoever, the modelling of emulsion coolymerisation is a challenging task, since it involves comlex hysicochemical sub-rocesses, some of hich are not ellunderstood. Esecially, the article formation mechanism and inclusion of to or monomers increases the comlexity. oreover, it is a multihase environment consisting of an aqueous hase, surfactants, initiators, buffers, monomer drolets and olymer articles. The reaction mechanisms are yet to be fully elucidated under various reaction conditions. The goal is to develo a ractical tool to redict olymer roduction rate and key roduct attributes for ultimate alication in industry. There is relatively little literature on the control of the full SD, and it is even littler for the coolymerization rocess. In contrast, there is a considerable number of studies reorted in the literature on the control of lumed roerties. (Semino and ay, 995b, Semino and ay, 995a) addressed the very ertinent issue of the controllability of oulation balance systems. They found in their system the controllability of the distributions for the unconstrained case is ensured by emloying the feed concentration of surfactant, initiator and inhibitor as maniulated variables. (Kozub and acgregor, 99) alied the idea of a to-tier control strategy-oen loo feed forard generation of an otimal recie, hich is then recomuted online based on feedback from rocess measurements to a semibatch emulsion olymerization sy stem, for the multivariable control of comosition and average molecular eight. (Saldivar and ay, 997) studied the control of coolymer comosition and averaged molecular

2 eight for semi-continuous emulsion olymerization. (Clarke-ringle and acgregor, 998) resented a batch to batch adjustment strategy for the control of molecular eight distribution (WD) to reotimize the inuts for the next batch based on end-oint measurement of the WD. (Croley et al., ) used a hybrid modelling strategy in batch to batch otimization for SD control. (Croley et al., ) are among the first researchers to address the control of the full article size distribution. (Immanuel and Doyle, ) resented an oen loo otimization study for the control of the full SD in the emulsion coolymerization of vinyl acetate and butyl acrylate. (Zeaiter et al., ) develoed a model for emulsion olymerization of styrene to otimise and control the SD. comrehensive dynamic model for a coolymerization reactor as develoed by (lhamad et al., 3, lhamad et al., 4), hich allos the rediction of key olymer roerties such as: average article size, conversion, SD, WD, n, and. modified zero-one kinetic model is used in the formulation alloing rediction of secondary nucleation under starving monomer conditions. In this ork, based on this comrehensive model, a multi-layer model-based frameork as develoed and imlemented ithin an industrial distributed control system environment, to otimize the article Size olydisersity Index (SI) and olecular Weight olydisersity Index (WI).. EXEIENTL SETU. Data cquisition and Control Environment The olymer lab consists of a 5 litre jacketed stirred reactor; a Julabo heating circulator to rovide heat to the reactor through the jacket; 4 solenoid dosing ums for roviding the monomers, surfactant and initiator to the reactor; 3 TDs for monitoring temerature; and 4 recision balances to determine the quantities of the reactants used. The olymer lab is cont rolled by a Honeyell C controller on a Honeyell lantscae DCS. The uloading and configuration of the control schemes to the controller is done using the Control uilder from the Honeyell lantscae r5.. The olymer lab I/O consists of 3 TDs, 3 analogue inuts, 5 analogue oututs, 4 digital oututs and a 4 ort serial to Ethernet converter. The TDs are the jacket inlet temerature, the jacket outlet temerature, and the internal reactor temerature. The analogue inuts are the imeller seed ithin the reactor; the Julabo heating circulator oerating temerature; and the user secified setoint temerature from the Julabo. The analogue oututs are setoint temerature for the Julabo heating circulator, and the dosing frequencies or stroke rates for each of the dosing ums. The digital oututs are used to sto or resume the dosing ums from uming. The 4 ort serial to Ethernet converter is used in conjunction ith softare develoed ithin the SE grou to send florates or differential eight readings from the balances to the controller. ll the maniulated variables rofiles are ut into the Control uilder to be oerated automatically. Data cquisition and control of the olymerization reactor as erformed using Honeyell s lantscae 3 softare residing on a server. This develoed set-u allos the configuration and imlementation of multilayer control scheme for advanced oeration and control of the rocess and a client station is used for oerator maniulations. The loer level control consists of a series of conventional ID controllers to control the monomer feeds, surfactant, and initiator as ell as to control the temerature. The inuts to the ID controllers are the set-oint (uer-layer) rovided from either one of the folloing three sources: ) anual set-oint: this is used hen the key olymerization variables are required to be set at a constant temerature (used during model validation), ) amsoak set-oint: this is a set-oint varying ith time and it changes according to an oerator built-in rofile (used during off-line otimization) and 3) External set-oint: this is used hen an external rogram is used to rovide the set - oint (this is the case in our environment hen imlementing the real-time otimizing control using an C strategy). The model develoed is used ithin the roosed strategy to rovide the otimal set -oints (off-line) in case and to rovide otimal trajectories and as a real-time soft sensor to control SD and WD in case 3. n intelligent control hierarchy is formulated for such distributed arameter system incororating three different levels; offline otimization, on-line DC and regulatory control successively. The novelty of this aroach is the incororation of a validated high order dynamic model as a soft sensor for on-line feedback of the SD and WD. Figure shos the schematic diagram of the overall control hierarchy. onitoring, Diagnosis & Suervision Otimal Trajectories Secondary Set-oints Figure : Overall Control Hierarchy Decision Suort (G) rocess Otimisation ON-LINE EDICTIVE CONTOL (C-DC) EGULTOY CONTOL (ID, Sensors..) lant Inuts/Oututs

3 . Samle rearation and Characterization Styrene (99% urity, inhibited ith 4-tertbutylcatechol) and (99% urity, inhibited ith hydroquinone) monomers ere obtained from Fluka, hile the ater used as urified to a illi-q standard. Surfactant (sodium dodecyl sulfate) and initiator (otassium ersulfate) ere both obtained from Sigma-ldrich. Semi-batch emulsion coolymerisations of styrene and ere carried out at 7, 75, 8 and 85 o C under slight nitrogen ressure. Note that the monomers ere urifed using an inhibitor column, hich is also obtained from Sigma ldrich. onomer conversion as gravimetrically determined off-line by taking samles from the reactor. The WD of the olymer samles as determined off-line by GC, hile most of the SDs ere obtained using the zetasizer and the CHDF. 3. OTIL CONTOL STUDIES 3.. odel Develoment The oulation balance equations (E), based on article formation through both homogeneous and micellar nucleation, rovide estimates for the SD. The Es for the three tyes of articles: those containing no radicals (tye no articles), those containing one monomeric radical (tye n articles), and those containing one olymeric radical (tye n articles), are given by: n ( V, t) ( Kn ) k C n + ρinitn ρn ktrcn t V jcrit + δ V Vo ) C micelle i z i j crit [ k [ I ]] k C [ I ( e, micelle i, aq W j ] crit + V, V V )[ n ( V ) n ( V V ) + n ( V ) n ( V V )] dv ( n V) ( V, V )[ n ( V ) + n ( V )] dv ( n ( V, t) ρ[ n t + n n ] + k n d () + ( V, V V )[ n ( V ) n ( V V ) + n V ) n ( V V )] dv n ( V) ( V, V )[ n ( V ) + n ( V )] dv ( n ( V, t) k tr C n + k ee [ E] n ( k C + k d + ρ) n (3) t Total number articles are given by: n V, t) n ( V, t) + n ( V, t) + n ( V, ) (4) ( t The term Cmicelle is the micelle concentration, hich is determined by the rate of surfactant consumtion. The terms k, k e, k tr, are the kinetic rate coefficients for the roagation, entry and transfer resectively. The transient monomer molar balance for semi-batch reactor oeration is given by: () dn m, Fm, in V V dt (5) here,, and,, are the rate of reactions of reactions of the olymer for monomer and in the article and ater hase, resectively. The rate of constant are defined as follos: ( k k ( r C + C C )) n Ntot (6) k r C + k r C N a ( k k ( r C + C C )) T (7) k r C + k r C here k is the roagation coefficient, N tot is the total number of articles, N a is the vogadro s number, r is the reactivity ratio, T is the total number of radicals, and V is the volumer of the olymer hase. The volume of olymer articles is defined for to searate regimes: hen monomer drolets exit (V) and hen there are no longer any drolets. So the coolymer article volume is calculat ed by to different equations in to stages. The first regime is calculated by: dv, (,, +,, ) +, (,, +,, ) dt d hereas the second regime is calculated by the folloing: dv dt,, (,,,, + d, m,, ) + d + d,,, (,,,, +,, ) dm, d, and are the time-averaged robabilities of finding a free radical ith ultimate unit of tye and, resectively. They are calculated as follos: k C, () k C, + k C, (8) (9) () here C, and C, are the concentrations of monomers and in the article hase. They are obtained by using the artition coefficients (K) beteen the three hases, ater (), monomer (m) and articles (). sat Nm, () C, IN C,, K, m K, m + K, + V here Nm is the number of moles and V is the volume.

4 3. Otimization Strategy Setu s stated reviously, the main objective in this study is to investigate the use of a detailed (validated) mechanistic model (lhamad et al., 3, lhamad et al., 4) to develo an advanced control strategy for the otimal oeration of the reactor. The roosed strategy ill rovide set-oint trajectories for the maniulated variables (for examle, monomer feed rate and reactor temerature) so as to ensure the roduction of a coolymer ith a defined SD and WD in the minimum reaction time. Several objective functions ere studied, in terms of both S and W. For the urose of obtaining the desired broad SD, a olydisersity index as chosen as an objective function to be maximized. For W both WI as ell as simly the molecular eight ere investigated as the objective functions to be otimized. The article concentration densities, article diameter, temerature shift, coolymer comosition and the total amount of monomer to be added to the reactor ere included as constraints along ith the reaction time. The objective functions are otimized by using the five maniulated variables, styrene feed rate, feed rate, surfactant feed rate, and initiator feed rate and temerature. The temerature as used as a maniulated variable for maximizing WI, since the molecular eight is largely affected by the temerature, rather than the SI, hich is not significantly affected by the temerature. The WI as also maximized ithout the temerature as a maniulated variable investigate the actual effect of temerature. olydisersity index indicates the sread of the distribution. The article size olydisersity index (SI) is estimated as follos: < r > SI (3) < r > The number average radius as comuted from r ( r n) n uns (4) The objective functions to be otimized ere defined as: ax [SI(r, tfinal)] and ax[wi(r, m, tfinal]. Where: m is the molecular eight and tfinal is the rocessing time. For oerational reasons, the monomers, surfactant, initiator feed rates and temerature (for molecular eight otimisation) ere secified ithin the folloing uer and loer bounds:.85 g/s F,. g/s (5) m.85 g/s F,. g/s (6) m.85 g/s F. g/s (7) S.85 g/s F I.g/s (8) 343 o C T 358 o C (9) reac The final SD shae as included in this otimisation in the form of end oint inequality constraints formulated in terms of the final molar concentration density of articles n ( final n min n r, t ) () max bove, nmin and nmax denote the loer and uer limits, resectively, and ere secified to match the required distribution. The final coolymer comosition required as 5/5, so a condition as secified as follos:.49 F.5 () Since this is a semibatch rocess ith monomer fed to the reactor, the maximization of SI and WI must also be subjected to additional constraints to account for the total amount of monomer in the recie (Nm,T), and the total reaction time. These constraints are defined as follos: N 8 mol and tmin t tmax () m, T The solution to this constrained otimal control roblem as obtained via an interface to the got dynamic otimization code. Five bounded time intervals (of initially equal duration) ere secified for the maniulated variables, Fm,, Fm,, FS, FI and Treac, such that it remained constant over a certain time interval, before moving discretely to the value for the next interval. violation over. o C is ut for the temerature, so that the temerature hen juming from one temerature to the other, the temerature rises gradually. 3.3 esults and Discussions s discussed, the otimal control strategy involved the comutation of a monomer feed trajectory hich ould drive the rocess to give a SD ith a secified broad distribution. The required SD as generated by fixing the reactor temerature at 75 o C, and alloing a 5 min (batch) re-eriod to allo for initial article nucleation, before any further addition. Imlementation of the otimal control strategy for the reminder of the run as fully automatically achieved through the control and dat a acquisition strategy develoed, using the amsoak set-oint

5 otion from oerator built-in rofiles. The final shae of the exerimental SD, WI and W as in good agreement ith the simulation results. Figure shos the results obtained to maximize SI. Figure 3 shos the results obtained in order to maximize WI using only the florates, that is, temerature as not used as a maniulated variable. Figure 4as used to maximize WI using the additional variable, hich is the temerature. The WD, average article size, SD and conversion ere used as a validation to the otimization rocess. It can be Florate (g/s) Fm, Left xis Fm, Left xis FI, ight xis Fs, ight xis? Volume fraction seen that on maximizing SI, a bimodal distribution as roduced, since the requirement as to have a very broad distribution. nother observation regarding the molecular eight is that the molecular eight roduced ith the temerature as a variable as much larger, and that shos the great effect that temerature has on molecular eight. It has also been observed that maximizing the WI ould result in the maximizing of the n article Size (nm) Exerimental (CHDF) Florate (g/s) Conversion d/dlog(w) T 75 C all times (controlled) Fm Fm Fs FI Fm: Styrene feed rate Fs: Surfactant feed rate Exerimental Time(s) Fm: feed rate FI, g/s at all times log(w) Exerimental n d/dlog(w) article Diameter (nm) Exerimental log(w) Figure. Validation of otimal trajectories to maximize.(a) maniulated variables otimal rofile; (b) SD; (c) Conversion; (d) WD Exerimental Exerimental Figure 3: Validation of otimal trajectories to maximize WI. (a) maniulated variables otimal rofile; (b) article diameter; (c) WD; (d) n

6 Florate (g/s) Fm Fm Treac Temerature K article Diameter (nm) Exerimental. 5 d/dlog(w) Exerimental n 5 Exerimental log(w) Figure 4: Validation of otimal trajectories to maximize n. (a) maniulated variables otimal rofile; (b) article Diameter; (c) WD (d) n CONCLUSIONS model-based frameork to otimally control key coolymerization variables has been develoed and imlemented ithin a ilot -scale environment under DCS. Validation results sho very good agreement beteen model rediction and exerimental runs. Work is currently underay to imlement a simultaneous WD/SD control strategy in an online environment ithin a model redictive control scheme. EFEENCES lhamad,., omagnoli, J.. and Gomes, V. G. (3) In 3st ustralasian Chemical Engineering Conference CHEEC, delaide, South ustralia,. 38. lhamad,., Willis,., omagnoli, J.. and Gomes, V. G. (4) In ESCE- 4,Lisbon. Clarke-ringle, T. L. and acgregor, J. F. (998) Industrial & Engineering Chemistry esearch, 37, Croley, T. J., Harrison, C.. and Doyle III, F. J. () In merican Control Conference, Jun 5-7, Vol. Institute of Electrical and Electronics Engineers Inc., rlington, V, Croley, T. J., eados, E. S., Kostoulas, E. and Doyle, F. J. I. () Journal of rocess Control 4th IFC World Congress, Jul 5- Jul 9 999,, Immanuel, C. D. and Doyle, F. J. I. () Chemical Engineering Science, 57, Kozub, D. and acgregor, J. F. (99) Chemical Engineering Science, 47, Saldivar, E. and ay, W. H. (997) iche Journal, 43, -33. Semino, D. and ay, W. H. (995a) Chemical Engineering Science, 5, Semino, D. and ay, W. H. (995b) Chemical Engineering Science, 5, Zeaiter, J., omagnoli, J.., arton, G. W., Gomes, V. G., Hakett,. S. and Gilbert,. G. () In Chemical Engineering Science, Vol. 57 Elsevier Science Ltd,