Integrated Process Design and Control of Reactive Distillation Processes

Transcription

1 Preprnts of the 9th Internatona Symposum on vance Contro of Chemca Processes The Internatona Feeraton of utomatc Contro WeM4. Integrate Process Desgn an Contro of Reactve Dstaton Processes Seye Sohe Mansour a, Maurco Saes-Cruz b, Jakob Kjøbste Huusom a, John M. Wooey a, Rafqu Gan a,* a CPEC-PROCESS, Department of Chemca an ochemca Engneerng, Technca Unversty of Denmark, Lyngby, Denmark b Departamento e Procesos y Tecnoogía, Unversa utónoma Metropotana-Cuajmapa, Méxco D.F., Mexco (e-mas: seso@kt.tu.k, asaes@correo.cua.uam.mx, jkh@kt.tu.k, jw@kt.tu.k, rag@kt.tu.k) bstract: In ths work, ntegrate process esgn an contro of reactve staton processes s presente. Smpe graphca esgn methos that are smar n concept to non-reactve staton processes are use, such as reactve McCabe-Thee metho an rvng force approach. The methos are base on the eement concept, whch s use to transate a system of compouns nto eements. The operaton of the reactve staton coumn at the hghest rvng force an other canate ponts s anayze through anaytca souton as we as rgorous open-oop an cose-oop smuatons. y appcaton of ths approach, t s shown that esgnng the reactve staton process at the maxmum rvng force resuts n an optma esgn n terms of controabty an operabty. It s verfe that the reactve staton esgn opton s ess senstve to the sturbances n the fee at the hghest rvng force an has the nherent abty to reject sturbances. Keywors: Process esgn, Process contro, Drvng force, Reactve staton, Eement-base metho. INTRODUCTION Tratonay, process esgn an process contro are consere as nepenent probems, that s, a sequenta approach s use where the process s esgne frst, foowe by the contro esgn. The mtatons wth the sequenta approach are reate to ynamc constrant voatons, for exampe, nfeasbe operatng ponts, process overesgn or uner-performance. Therefore, ths approach oes not guarantee robust performance (Sefers an Georgas, 2004). Furthermore, process esgn ecsons can nfuence process contro an operaton. To overcome the mtatons assocate wth the sequenta approach, operabty an controabty are consere smutaneousy wth process esgn, n orer to assure that esgn ecsons gve the optmum operatona an economc performance. In contro esgn, operabty aresses stabty an reabty of the process usng a pror operatona contons an controabty aresses mantanng esre operatng ponts of the process subject to sturbances. number of methoooges an toos have been propose an appe on varous probems to aress the nteractons between process esgn an contro, an they range from optmzaton-base approaches to moe-base methos (Luyben an Fouas, 994; Nkacevc et a., 202). In ths work, ntegrate esgn an contro of reactve staton processes s consere, snce process esgn ecsons w nfuence process operabty an controabty. Numerous esgn agorthms for mutcomponent separaton systems wth reactons have accompane the ncreasng nterest n reactve staton processes. In esgn, the nput an (seecte) output varabes are specfe an the task s to etermne the optma reactve staton process confguraton (for exampe, mnmum number of stages), an the optma esgn parameters (for exampe, optmum refux rato, optma fee ocaton) that acheve the gven prouct specfcaton. It s ntene to acheve the optma esgn n such way that t s aso an operabe process at pre-efne contons uner presence of sturbances. PØrez-Csneros et a. (997) have propose an eement mass baance approach to esgn the reactve staton processes, whch empoys the tratona graphca toos smar n concept to esgn of non-reactve staton coumns, such as McCabe-Thee metho an rvng force approach of ek-peersen an Gan (2004). Moreover, Ham et a. (200) have propose an ntegrate process esgn an controer esgn methooogy. However, ther methooogy covers the aspects reate to esgn an contro of nonreactve bnary staton processes. In ths work, the metho of Ham et a. (200) s extene to aso cover a ternary compoun reactve staton process (usng eement-base approach) an crtera of seectng the optma esgn an the controer structure seecton w be presente. In orer to emonstrate the appcaton of the aforementone approach, proucton of methy-tert-buty-ether (MTE) * Corresponng uthor: rag@kt.tu.k (Rafqu Gan) Copyrght 205 IFC 2

2 Temperature (K) from methano an sobutene usng a reactve staton coumn s consere. 2. RECTIVE DISTILLTION COLUMN DESIGN The computaton of smutaneous chemca an physca equbrum pays an mportant roe n the precton of the mts for converson an separaton of a specfc reactve separaton process, partcuary for the reactve staton systems. Usng the Gbbs free energy mnmsaton approach, PØrez-Csneros et a. (997) propose souton proceures where the mutcomponent chemca an physca equbrum s pose as an eement phase equbrum probem. Ths transformaton s base on the concept of chemca moe as propose by Mchesen (989). Ths concept s erve from chemca moe theory. In chemca moe theory, the equatons of chemca equbrum an any approprate physca moe yeng the chemca potentas are ncorporate nto an eement-base moe (cae the chemca moe). The chemca moe agorthm an those eveope earer, ffer n the use of the chemca moes n a way that reuces the chemca an physca equbrum probem formay entca to the physca equbrum probem for a mxture of eements (representng the system). Further etas can be foun n (PØrez-Csneros, 997; Daza et a., 2003). The reacton for MTE synthess occurs very fast, therefore, chemca equbrum s assume (for other cases a knetc moe may be use) an s gven as foows: C H E C H O Isobutene Methano CH O MT It s cear that the seecton of the eements has an mportant roe n the current formuaton. They are normay chosen as the natura chemca eements present n the reacton mxture. However, one s free to seect any reacton nvarant fragment of the reactants. The eement matrx s constructe base on the rues prove by PØrez-Csneros et a. (997) an t s as foows: Component Eement C 4H 8 () CH 4O (2) C 5H 2O (3) 0 0 Therefore, the ternary system of compouns can be reuce nto a bnary system of eements an an the reacton can be rewrtten as:. The frst component (eement ) an the secon component (eement ) form the thr component (eement ). Havng the ternary system of compouns represente n form of a bnary eement system, smar graphca esgn methos, that are appe to nonreactve bnary staton coumn esgn, such as McCabe- Thee metho can be use. However, n orer to use the McCabe-Thee metho, a reactve equbrum curve s requre. The reactve equbrum curve s constructe through sequenta computaton of reactve bubbe ponts (PØrez-Csneros, 997). In orer to generate the reactve ataset, Wson thermoynamc moe for precton of the qu phase behavour an SRK equaton of state for precton of vapour phase behavour were use. Note that the cacuaton of reactve vapour-qu equbrum (VLE) ata set s n terms of compouns. Therefore, a ternary compoun ata set s obtane. To convert ths ata set to be represente n form of a bnary eement system the foowng expressons are use where moe fractons of eements an are cacuate n the qu phase: x x3 W () x x 2 x W 2 3 x2 x3 x x 2 x 2 3 In the above equatons W an W are the qu moe fractons of eements an, respectvey. For cacuaton of v v the eement moe fractons n vapour phase ( W anw ), the equatons use are the same as () an (2) where nstea of qu moar fracton (x ), the vapour moar fracton (y ) s use. Fg. epcts the temperature (T)-W agram for MTE reactve system. Note that as ong as NC R = 2 (NC s number of compuns an R s number of reactons), any system can be represent by two eements (PØrez-Csneros et a., 997) v W Lqu Vapour Fg.. T-W -W agram for MTE reactve system (P = atm). The esgn task s to separate a bnary eement mxture that s 70 moe percent eement (z Wf = z sobutene = 0.7, z Wf = z methano = 0.3) nto 50 eement moe percent bottoms prouct (W, = 0.50) an 99 eement moe percent state (W, = 0.99) prouct. Note that base on the bnary eement reacton matrx, eement an correspon to sobutene an methano, respectvey. The eement fee fow rate s 00 Kgmoe eement/hr at 300K an atm. The operatng pressure of the reactve staton coumn s atm an pressure rop across the coumn s assume to be neggbe. The refux eement rato (RR) s 2. The physca an chemca equbrum curve s constructe usng the ata set presente n Fg.. Theoretca reactve stages are cacuate from the reactve McCabe-Thee metho. parta reboer, tota conenser an chemcay saturate qu refux are set for the coumn. In orer to esgn the escrbe reactve staton coumn for MTE synthess, McCabe-Thee metho s use. Fg. 2 epcts the reactve staton coumn esgn usng reactve McCabe-Thee metho. s t s shown n Fg. 2, the reactve staton coumn has fve reactve stages. (2) Copyrght 205 IFC 22

3 Daza et a. (2003) have extene the rvng force (DF ) metho for non-reactve systems (ek-peersen an Gan, 2004) to ncue reactve systems. Smar n concept to nonreactve systems, the rvng force s efne as the fference n composton between two coexstng phases. The rvngforce esgn metho for reactve as we as non-reactve staton systems s base on the avaabty of ata for the vapour-qu behavour. In the case of reactve systems, the vapour-qu equbrum ata must be base on the eements (see Fg. ). Vapour eement fracton, W v Rectfyng Reactve Operatng Lne Fee Lne W, W,F W, Strppng Reactve Operatng Lne Lqu eement fracton, W Fg. 2. Reactve staton coumn esgn usng reactve McCabe-Thee metho for the MTE reactve system. The rvng-force agram can ony represent bnary nteracton between compouns or eements n two coexstng phases, or two compouns on a sovent-free bass. Note that the eement-base rvng-force agram fuy consers the extent of reacton on an eement bass, an t can be appe n the esgn of reactve staton coumns. Prove the eement vapour-qu behavour ata exst (equbrum or rate-base), or can be compute (whch s the case n ths stuy, see Fg. ), the reactve rvng-force agram can be obtane usng (3) wth respect to eements. W v j DF W W W (3) W j Note that n (3), The reatve separabty α j s a parameter for component wth respect to property (or separaton technque) j (ek-peersen an Gan (2004). The rvng force concept s use to fn the optma esgn target vaues of the process varabes for separaton systems. ase on entfcaton of the argest rvng force (see Fg. 3), efne as the fference n composton of a component between the vapour phase an the qu phase, whch s cause by the fference n the voattes of component an a other components n the system. Fg. 3 shows the rvng force agram for MTE reactve system at atm. s the rvng force ecreases, separaton becomes ffcut an may become nfeasbe when the rvng force approaches zero. On the other han, as the rvng force approaches ts maxmum vaue, the separaton becomes easer. Therefore, from a process esgn pont of vew, a separaton process shou be esgne/seecte at the hghest possbe rvng force, whch w naturay ea to the optma esgn wth respect to the energy consumpton (ek-peersen an Gan (2004)). In ths work, the optma fee ocaton of the reactve staton coumn s etermne usng the rvng force agram. Reactve McCabe-Thee metho has been ony use to etermne the number of stages. The fee an prouct specfcatons are areay known snce they were use n the reactve McCabe-Thee metho. The optma fee ocaton at the maxmum rvng force can be foun usng (4). N N D (4) F x In (4), N s the number of stages whch was obtane from the reactve McCabe-Thee metho (was foun to be 5); D x s the vaue corresponng to the maxmum rvng force on the x-axs (D x = 0.6). The optma fee ocaton s entfe usng the atona rues for rvng force (ek-peersen an Gan, 2004) an therefore t s stage from the top of the coumn. Drvng Force, DF Reactve operatng nes W, W Maxmum DF W, Fg. 3. Reactve rvng force agram for MTE reactve system. 3. OPTIML DESIGN-CONTROL SOLUTIONS From a process esgn pont of vew, for specfe nputs, u, an sturbances,, vaues for states, x, an outputs, y, that satsfy a set of esgn specfcatons (process esgn objectves) are etermne. In ths case, x an y aso efne some of the operatona contons for the process. From a controer esgn pont of vew, for any changes n an/or set pont vaues n y, vaues of u that restores the process to ts optma esgne conton are etermne. It shou be note that the souton for x an y s recty nfuence by θ (the consttutve varabes such as reacton rate or equbrum constant). For exampe, the optma souton for x an y can be obtane at the maxmum pont of the reactve rvng force (for reactve systems, see Fg. 3) agrams whch are base on θ. y usng moe anayss, the corresponng ervatve nformaton wth respect to x, y, u, an θ can be obtane (to satsfy controer esgn objectves). For each reactve staton coumn esgn probem, the rvng force agram s rawn an the esgn target s seecte at the hghest rvng force (see Fg. 3). From a process esgn pont of vew, at these targets, the optma esgn objectves can be obtane. From a controer esgn pont of vew, at these esgn targets the controabty an Copyrght 205 IFC 23

4 operabty of the process s best satsfe. The vaue of the ervatve of controe varabes y wth respect to sturbances n the fee,, y/ an manpuate varabes, u, y/u w etermne the process senstvty an nfuence the controer structure seecton. ccorngy, y/ an y/u are efne as (Russe et a., 2002): y y x x y y x u x u The vaues for θ/x can be obtane from the process (ynamc an/or steay state) constrants: x f x, y, u,,, Y, t (7) t an vaues for y/θ, x/ an x/u can be obtane from consttutve (thermoynamc) constrants: 0 g u, x, y (8) 3.. Seecton of Controe Varabes The prmary controe varabe s D x,max, whch s the x-axs vaue corresponng to the maxmum rvng force (DF ). Ths resembes the purty of eement at the maxmum rvng force. The seconary controe varabes are the prouct purtes, whch are the esre prouct composton at the top an bottom of the coumn, W an W. The reason behn ths seecton s that by controng W an W at the maxmum pont of the rvng force w requre ess contro effort n terms of refux rato (RR), an rebo rato (R) n the presence of sturbances n the fee compare to any other canate pont Senstvty of Controe Varabes to Dsturbances Usng the beow key concepts, the senstvty of varabe y wth respect to varabe can be expresse as n (9): The esre eement prouct at the top an the bottom s W (prouct eement composton at the top, state prouct) an W (eement composton at the bottom, bottom prouct). t the maxmum pont of the rvng force agram, W an W (controe varabes) are the east senstve to the mpose sturbances n the fee. The esgn varabes vector s y = [W W ], x = DF, s seecte on the y-axs of the rvng force agram. The sturbances vector s, = [F f z Wf ] (fee fowrate an fee composton of eement ). W W y Ff zwf W W Ff z Wf W DF W W DF W DF W F f DF W z Wf W DF W W DF W DF W F f DF W z W f (9) (5) (6) The reactve eement operatng nes for the rectfyng secton an strppng sectons are gven n (0) an (). RR s the eement refux rato, an R s the eement rebo rato. v RR W W W RR RR (0) v R W W W () R R Substtutng (0) an () n (3) for W v gves the top an bottom eement prouct composton wth respect to the rvng force n (2) an (3) whch s: W DF RR W (2) W W DF R (3) Equatons (2) an (3) are fferentate wth respect to DF an resut n the foowng expressons: W W DF RR RR DF DF W W W DF R R FD DF W The tota eement mass baance s wrtten as foows: f Wf (4) (5) F z W b W b (6) Where, b an b are eement mass fows n top an bottom of the coumn, respectvey. Substtutng (2) an (3), one at the tme, nto (6) for W an W, the tota eement mass baance n terms of rvng force s expresse as: F z DF RR b W b W b (7) or f Wf F z W b W b b F R (8) f Wf D Dfferentatng (7) an (8) wth respect to the F f an z Wf (assumng that the changes n composton, an, top an bottom eement fowrates (b an b ) wth respect to the fee fowrate s neggbe), the expressons for W F, W z are obtane. Havng these ervatves, the souton Wf to (9) s expresse by (9). Note that n (9), a,.., a 8 are constants. Vaues of FD /W are cacuate an shown n Fg. 4. Note that n Fg. 4, two other ponts (ponts II an III) whch are not at the maxmum are entfe as canate aternatve esgns for a staton coumn, whch w be use for verfcaton purposes. Note that operaton at the maxmum rvng force oes not restrct achevabe esgn performance (for exampe, component purtes). It must be note that the expressons for W DF DF W an W DF DF W n f Copyrght 205 IFC 24

5 Drvng Force, DF (9) are equa to at pont (I) n Fg. 4 (maxmum rvng force) an greater than n any other pont. DF/W W II II I I III III Fg. 4. Drvng force agram for W W separaton (reactve zone ony top fgure) an ts corresponng ervatve of FD wth respect to W (bottom fgure). DF DF a RR W W DF W DF a2 a 3 W DF W W Ff DF DF R a4 W W W DF W DF a5 a 6 Ff W DF W W z Wf DF DF a7 RR W W W DF W DF 2 3 z a a Wf W DF W DF DF a8 R W W DF W DF a5 a 6 W DF W W (9) Furthermore, at pont the vaue of FD /W s equa to zero. Therefore, equaton (9) at Pont (maxmum rvng force) can be expresse as: W W a a y Ff Ff a3 a6 0 0 W 0 0 W a 7 a zw z 3 6 f W a a f (20) Equaton (20) reveas that the senstvty of controe varabes to sturbances n the fee s mnmum at the maxmum rvng force Seecton of the Controer Structure The controe varabes are efne as top an bottom eement composton W an W. In ths case, the potenta manpuate varabes are refux rato (RR) an rebo rato (R). (2) an (3) gve the top an bottom prouct compostons wth respect to the rvng force. Hence, they are fferentate wth respect to RR an R. Therefore, (6) can now be expresse as: W W y RR R u W W RR R DF W W DF D W W DF RR RR W RR RR W R R W DF W W R DF RR W RR R (2) From Fg. 4, t s known that DF W at the maxmum rvng force s equa to zero. Furthermore, assumng that W RR W R 0, (22) s obtane. The best controer structure can easy be etermne by ookng at the vaue of y/u. It can be note from (22) that snce the vaues of W RR an W R are bgger, controng W by manpuatng RR an controng W by manpuatng R w requre ess contro acton. W W y RR R DF 0 (22) u W 0 W DF RR R Ths s because ony sma changes n RR an R are requre to move W an W n a bgger recton. Ths parng between controe-manpuate varabes s aso further verfe by obtanng the transfer functons between the pars usng a reactve staton ynamc moe base on eements (PØrez-Csneros, 997). Note that most of the moeng of ynamc reactve staton operatons has been one by ntroucng a rate of reacton expresson n the component mass baances. However, when the chemca reactons occurrng are fast enough to reach the equbrum (for MTE reactve system) chemca equbrum conton s mpcty ncorporate nto the eement mass baances through the functonaty of the phase compostons on the eement chemca potentas (PØrez-Csneros, 997). The next natura step to verfy the parng n (22) s cacuatng the reatve gan array (RG) for the esgn at the optma fee ocaton (Desgn (I), N F = ) an two other aternatve esgns (Desgn (II), N F = 2; an Desgn (III), N F = 3). Note that n cacuatng RG, R s represente by heat aton to the reboer uty nstea of rebo rato; an, MTE top an bottom compostons represent W an W, respectvey. The transfer functons have the form as equaton (23) wth one zero an two poes. zs Gs K (23) s s p p Usng the transfer functons, RG matrx for esgn (I) (at the maxmum rvng force) an esgns (II) an (III) s cacuate an they are as foows: RG,, I RG RG II III s t can be seen the parng at the maxmum rvng force (esgn (I), fee ocaton ) has the cosest vaues on the agona to unty. Therefore, t has the east nteracton between the oops. Furthermore, the suggeste parng by RG for esgn (I) matches the parng that was obtane from the rvng force. Furthermore, snguar vaue anayss Copyrght 205 IFC 25

6 MTE ottom Composton [moe%] MTE Top Composton [moe%] MTE Top Composton [moe%] MTE ottom Composton [moe%] Refux Rato Heat ton [kj/h] (SV) was performe. However, very arge conton numbers (CN) were obtane wth no specfc tren. Thus, no partcuar concuson can be mae base on them. The openoop an cose-oop performance of the system has been teste wth the Proportona-Integra (PI) controer n a screte-tme manner. The rgours ynamc reactve staton moe (PØrez-Csneros, 997) was use. The controer mpementaton s vsuaze n Fg. 5. Note, however, any other contro strategy can be appe to perform cose-oop smuatons. (t) u(k) D/ u(t) Rgorous Dynamc Moe /Physca Process (Pant) Contro gorthms y(t) /D y(k) y(k) Fg. 5. Dscrete-tme controer structure mpementaton. Fg. 6 an Fg. 7 show the open-oop an cose-oop performance of the system at maxmum rvng force (Desgn (I)), respectvey. The sturbance scenaro s that after 5 sampes, the fee fowrate of eement (sobutene) s ncrease from 70 kg-moe to 85 kg-moe (~2% step change n composton of sobutene) % 0.033% 0.03% 0.029% 0.027% 0.025% % 90% 86% Tme (Sampes) MTE Top Composton Set-pont 82% Tme (Sampes) MTE ottom Composton Set-pont Fg. 6. Open-oop performance of Desgn (I) to a sturbance n the fee. Ths sturbance resuts n a change n tota fee fowrate by +5% an aso a change n the fee composton. s t can be seen n Fg. 6, as a resut of an ncrease sobutene fowrate, ts recovery n the top has ncrease whch resuts n a ower MTE composton n the top. Furthermore, because of excess sobutene n the system an thereby shftng the reacton equbrum, MTE composton has ncrease n the bottom. It can be seen n Fg. 7 that sturbance has been rejecte wth east nteracton between the oops an both top an bottom compostons are we controe usng the seecte parng obtane from the rvng force. Note that the contro of the MTE top composton s acheve wth very sma changes n RR % 0.033% 0.03% 0.029% 0.027% 0.025% Tme (Sampes) Set-pont Tme (Sampes) % 90% 86% 82% Tme (Sampes) Set-pont Tme (Sampes) Fg. 7. Cose-oop performance of the contro structure for Desgn (I) to a sturbance n the fee. 4. CONCLUSIONS Integrate process esgn an contro of a ternary compoun reactve staton process was nvestgate n ths work. The optma esgn-contro soutons were obtane anaytcay an verfe through rgorous ynamc smuatons. It s verfe that the reactve staton esgn opton s ess senstve to the sturbances n the fee at the hghest rvng force an has the nherent abty to reject sturbances. Furthermore, t s avantageous to empoy the eement-base metho for esgnng mut-component an compex reactng systems. REFERENCES ek-peersen, E., Gan, R. (2004). Desgn an synthess of staton systems usng a rvng-force-base approach, Chem. Eng. Process., 43, Daza, O.S., PØrez-Csneros, E.S., Gan, R. (2003). Graphca an stage-to-stage methos for reactve staton coumn esgn, IChE J., 49, Ham, M. K.., Sn, G., an Gan, R. (200). Integraton of process esgn an controer esgn for chemca processes usng moe-base methooogy. Comput. Chem. Eng., 34, Luyben, M. L., Fouas, C.. (994). nayzng the nteracton of esgn an contro 2. Reactor-Separator- Recyce system, Comput. Chem. Eng., 8, Mchesen, M.L. (989). Cacuaton of Mutphase Iea Souton Chemca Equbrum, Fu Phase Equb., 53, Nkacevca, N.M., Huesman,.E.M., Van en Hof, P.M.J., Stankewcz,.I. (202). Opportuntes an chaenges for process contro n process ntensfcaton, Chem. Eng. Process., 52, -5. PØrez-Csneros, E.S., Gan, R., Mchesen, M.L. (997). Reactve separaton systems I. Computaton of physca an chemca equbrum, Chem. Eng. Sc., 52, PØrez-Csneros, E.S. (997). Moeng, esgn an anayss of reactve separaton processes, Ph.D. Thess, Technca Unversty of Denmark, Lyngby. Russe,. M., Henrksen, J. P., Jłrgensen, S.., Gan, R. (2002). Integraton of esgn an contro through moe anayss. Comput. Chem. Eng., 26, Sefers, P., Georgas, M. C. (2004). The ntegraton of process esgn an contro, Esever. V., msteram. Copyrght 205 IFC 26