REAL TIME OPTIMIZATION OF a FCC REACTOR USING LSM DYNAMIC IDENTIFIED MODELS IN LLT PREDICTIVE CONTROL ALGORITHM

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1 REAL TIME OTIMIZATION OF a FCC REACTOR USING LSM DYNAMIC IDENTIFIED MODELS IN LLT REDICTIVE CONTROL ALGORITHM Durask, R. G.; Fernandes,. R. B.; Trerweler, J. O. Secch; A. R. federal unversty of Ro Grande do Sul, Abstract: Ths work shows a new way to perform Real-Tme Optmzaton usng two mportant control technology. The frst one s the LLT nonlnear model predctve controller and the second one s the LSM dynamc model dentfcaton method. Ths two concepts assocated consttute a complete technology for Real-Tme Optmzaton usng nonlnear models. The applcaton of ths technology was tested on the FCC (fuel catalytc crackng) reactor whch shows the advantages and dsadvantages of ts applcaton. Keywords: Real Tme Optmzaton,.nonlnear dentfcaton, nonlnear predctve control, Advanced Control. 1. INTRODUCTION The control process has been each tme more developed n dfferent levels due to the desre of havng the best results of a ndustral process. Increasng the level of control of a ndustral process, the concept of Real-Tme Optmzaton becomes very mportant, snce, n ths level, the results are more vsble and t can be easly transformed n proft. The process called Fuel Catalytc Crackng (FCC) represents, n proftable terms, the most mportant ndustral process n a petroleum refnery. Through ths process, all the most valuable products of the petroleum refnery, lke gasolne and Lquefed petroleum gas (LG), are produced, and, for ths reason, t s usual ths process receves a specal attenton n the ndustral envronment, whch make the applcaton of Real-Tme Optmzaton becomes strongly justfed. The man goals of ths optmzaton s to reach the maxmum converson of the feed flow n products, the maxmum producton of valuable products as gasolne and LG, maxmum proft and maxmum producton. In ths work, a frst prncple model was used to smulate the ndustral process behavour, n order to perform an analyss of the applcaton possblty of the two technques (LSM and LLT) n real process. for ths study a mono-layer optmzaton structure was developed on the LLT algorthm whch produce a dynamc optmzaton of the process. THE FUEL CATALITC CRACKING ROCESS (FCC)

2 The FCC process s a mportant perod n petroleum refne, It uses a fracton of the dstllaton called gasol and transforms ths feed flow n gasolne (NC), lquefed petroleum gas (LG), lght crackng ol (LCO), clarfed ol (OCLA), fuel gas (GC) and coke (CK). The gasol s loaded n the converser together wth the catalyst, prevously warm. Ths mxture gets up through the converser generatng the products whch are separated on the top of the converser. In ths separaton, gaseous products are separated from the catalyst and the coke, and sent to dstllaton column. The catalyst covered by coke turns back to the system, beng loaded n the regenerator, where the coke s fred and generates energy to the reacton. Ths energy keeps accumulated on the catalyst whch s ntroduced back to the converser together wth gasol. The model used to represent ths process was developed by (Secch et. al 1) and consst n a frst prncples model wth 65 states, outputs, and 8 nputs. Ths model descrbes de converser as a plug-flow reactor (FR) n whch, the axal varable was dscretzed n twenty stages. 3 THE LOCAL LINEARIZATION ON THE TRAJECTORY (LLT) ALGOTITHM The LLT algorthm (Durask, 1) s a knd of sequental predctve control method whch conssts n a sequence of teratve steps. The frst step n the control acton desgn s to predct the up-to-dated trajectory of the system. Ths trajectory s determned usng the current value of the nputs of the process appled to the nonlnear model. In ths frst trajectory, lnearzed models are obtaned usng a dynamc lnearzaton. The set of models obtaned on each pont of the trajectory s grouped performng one devaton model from the orgnal trajectory, whch s used n the optmzaton step. Ths optmzaton wll generate a set of control actons to the system, whch, not necessarly, wll be the best set of control actons, once that t was obtaned usng a lnearzed devaton model. Therefore, ths set of control actons obtaned are appled to the nonlnear model and a new trajectory s generated. On ths trajectory, a new set of lnearzed models s obtaned and a new optmzaton performed. Ths sequence of steps keep gong on untl the nonlnear predcted trajectory converges to the setpont and no more varatons are observed n the control actons desgned. 3.1 Optmzaton Layer The orgnal LLT algorthm do not allow optmzaton and, therefore, a addtonal mplementaton was necessary to do such work. In predctve control, a closed shape of objectve functon can be obtaned, snce the goals of the control s very well defned. Ths concluson makes that the algorthm use hessan and gradent matrces prevously defned based on the model equatons. When ncludng a optmzaton layer such matrces can not be prevously defned because the expresson of objectve functon can take any shape. Ths fact makes necessary evaluate the hessan and gradent of the objectve functon n each teraton snce the system s solved by a quadratc programmng n each step. The gradent vector n ths mplementaton s been estmated by numercal approach usng conventonal perturbaton of varables. The hessan uses an estmaton suggested by used n BFGS optmzaton method. A lnesearch step was ncluded n ths algorthm to mprove the qualty of the soluton. Ths mplementaton had to be done because the nature of the objectve functon have change consderably. n the orgnal formulaton of the LLT algorthm the objectve functon was completely quadratc whch turns possble the use of successve Q solutons wthout any correcton. usng ths new formulaton of objectve functon, a lnesearch turns necessary snce the new objectve functon can take many nonlnear shapes, and the successve quadratc approach ndcates only the drecton of the search. The orgnal objectve functon of the LLT algorthm was transformed n the followng expresson:

3 ( γ ( y r )) + = M ( λ ( u u 1 ) + = = ( ϕ s ) α ( Lucro ) = J = mn s, δu % conv M β FCG = 1 ηgl µ FCG = 1 η NC ν FCG = 1 η LCO π FCG = 1 M B ( ψ ( δu + u 1) z ) ) + (1) where s the predcton horzon; M s the control horzon; γ s the weght of the error n the controlled varables; y s the value of the controlled varables; r s the value of setponts to the controlled varables; λ s the weght for varaton of the control actons; δu s the varaton of the control actons related to the reference trajectory; u s the absolute value of the control actons; ψ s the weght to the error n the proposed target for manpulated varables; z s the target establshed to the manpulated varables;φ s the weght for volaton of softconstrans set to the controlled varables; s s the volaton of the softconstrans of the controlled varables; α s the weght for the proft n the objectve functon; β s the weght of the converson degree;%conv s the converson degree of the gasol n products; FCG s the gasol feed flow; µ s the mportance of the LG producton; η GL s the mass fracton of LG; ν s the weght of the producton of gasolne; η NC s the mass fracton of gasolne; π s the weght of the mportance of the producton of LCO; η LCO s the mass fracton of LCO n the output; lucro s the expresson of the proft of the process gven by equaton : - fuel gas flow (GC) (product); - lquefed petroleum gas flow (GL) (product); - gasolne flow (NC) (product); - Lght cvcle ol flow(lco) (product); - coke produced (CK) (product); - clarfed ol flow (OCLA) (product); ROD s the prce of the product (postve) or nput (negatve). t tme nterval between two consecutve nstants of the predcton. 4 THE LINEARIZATION ON THE STATIONARY MANIFOLD (LSM) The LSM Algorthm developed by (Fernandes 5) s a dentfcaton method that can descrbe nonlnear models as a approach of multple lnear models by developng a nterpolaton rule to ths models. Ths nterpolaton generates a matrx A of the state space representaton dependent of the nputs of the system. The fnal shape of ths model can be represented n the equaton 3: dx dt ( x SS( )) = A( u) u (3) where A(u) s the nterpolaton of the matrces A of the multple models; SS(u) s the steady states as a functon of nputs, whch are also obtaned by nterpolaton; x s the current state. 5 THE ALICATION OF RTO IN THE FCC REACTOR A sensblty analyss was performed. to decde whch ponts was mportant to perform the dentfcaton of the system. Lucro F prod = 1 + F prod t prod () F ROD s the feed or output é rate of some of the followng product or nputs: - Catalyst (CAT) (nput); - Gasol (CG) (nput); - otênca do soprador (SO) (nput); Fg 1: Sensblty analyss for the temperature on the rser

4 Although the other results of sensblty analyss are not shown here, the fgure 1 shows the man behavor of nterest of the process. In ths fgure s shown that the temperature s almost lnear wth gasol feed flow, however t presents a nonlnear behavor wth the ar flow. As the man nonlnearty s ths one produced by the ar flow the lnear models dentfed were dstrbuted n fve ponts of operaton varyng only the ar flow rate. Two of then n the regon of postve gan, two n the regon of negatve gan and one n the regon near by gan zero. The nterpolaton performed n ths case for the A matrx has used a lnear rule whch was the most approprated form, snce the negatve sgnal of the poles have to be kept through all space. The steady state functon follow a quadratc nterpolaton, because t gave to descrbe the nverson of the sgn of the gan of the system. Although the results of the sensblty analyss were not presented here, t s known that, n FCC reactor, the converson of the products are straght related to the temperature of the rser and the behavor of ths varables are equal to the temperature behavor. 6 RESULTS AND DISCUSSION Optmzatons of the FCC reactor were performed usng dfferent weghts for each term of the objectve functon. Ths usage of dfferent weghts looks for show the behavor of the optmzer when goals are changed. The frst smulaton were performed usng a weght 1 for the proft term and for the other ones (except move suppresson whch were kept wth weght equal to 1). Fgure shows the control actons taken by the optmzer when the goal was maxmum proft. n ths fgure s shown that the ar flow rate ncreases untl a value related to the maxmum temperature of the rser. The value reached for the temperature can not be ncreased by the ar flow rate at ths pont and for ths reason the total feed flow has to be decreased to allow that converson n the rser be effectve, as shown n fgure 3, and the most valuable products were produced, reducng the output of gasol from the rser. Fg : Control Actons taken by the optmzer Fg 3: Converson of gas ol n products The same sequence of control actons can be seen when the objectve of the optmzaton s the maxmum converson. Ths goal mples n reducng the feed flow rate to allow the best converson possble snce the lmt of the equpment s reached. Fg 4. Responses of the system optmzaton usng maxmzaton of LG as the goal of the optmzer

5 (Fernandes 5). R. B. Fernandes, Contnuous Nonlnear Identfcaton Usng arameterzed Local Models ; hd. Thess, Unversty of Dortmund; (5) Fg 5. Responses of the system optmzaton usng maxmzaton of LCO as the goal of the optmzer A comparson between other two goals of optmzaton s shown n fgures 4 and 5. Fgure 4 shows the responses of the system optmzaton usng maxmzaton of LG as the goal of the optmzer and fgure 5 shows the responses of the system optmzaton usng maxmzaton of LCO as the goal of the optmzer. Comparng ths two fgures, t s possble to see that the mass fracton of each component changes accordng wth the man objectve of optmzaton. 7 CONCLUSIONS The optmzer used n ths paper shows a good soluton to perform real-tme optmzaton of contnuous dynamc process although, s stll needs some adjusts. As presented n prevous secton, t s possble to see that the optmzer takes the process to a new condton as close as possble of the man goal of optmzaton. t s stll possble to perform so mprovements n ths tool snce some problems were found n ts applcaton on the model of FCC reactor. In some specfc cases oscllatory behavor were captured when the plant reaches the optmum. whch mples n a more detaled analyss of the problem to arse ts possble reasons. 8 REFERENCES (Durask 1) R.. G. Durask.; Controle redtvo Não Lnear Utlzando Lnearzações ao Longo da Trajetóra ; M. Sc. Thess, Unversdade Federal do Ro Grande do Sul, Brazl. (1) (Secch et. al 1) A. R. Secch, M. G. Santos,G. A. Neumann, J. O. Trerweler; A Dynamc Model for FCC UO Stacked Converter Unt; Computer and Chemcal Engneerng; V 5; (1); pp