Dynamic Matrix Control for HDS Reactor

Transcription

1 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong Dynamic Matrix Control for HDS Reactor Priti Cicili, G.P. Reddy and V.Rameh Kumar* Abtract In the preent tudy, the imulation tudie on dynamic and control of a Hydrodeulfurziation (HDS) reactor are carried out in order to get proper inight into ytem behaiour under change in the ariou input parameter namely inlet liquid temperature, liquid flow rate and inlet ulfur concentration. A dynamic model of the reactor i ued for thi purpoe. The performance of a dynamic matrix control(dmc) i ealuated. It i found that DMC cheme gie atifactory reult for et point change in exit ulfur pecification in comparion with a PI controller and important concluion are alo preented. Index Term Hydrodeulfurization, Dynamic, DMC, Control I. INTRODUCTION Studie on dynamic behaiour of hyrotreating reactor are needed for proce deign, optimization and control. Tricklebed reactor are employed for carrying out hydrodeulfurization reaction under adiabatic condition. The publihed literature on dynamic, control and operability characteritic of thee reactor i carce[1]. Mot of the reported theoretical tudie are deoted to the undertanding of hydrodynamic, catalyt wetting etc[34]. Thee theoretical model deal with teadytate performance with little emphai on dynamic analyi[56]. In the preent work imulation tudie are carried out on a laboratorycale adiabatic HDS reactor uing the model propoed by Chao and Chang []. The model ue dipered plug flow decription of the phae and take into account the energy balance. The orthogonal collocation method i ued to obtain the olution of coupled tranient ma and energy balance equation. The goerning equation of the dynamic model and the olution procedure are preented in Appendix. Many control technique uing dynamic matrix hae been deeloped and their indutrial application proed that they are uitable for chemical proce control. In thi imulation tudie hae been carried out on hydrodeulfurization proce to compare the performance of DMC with conentional PI controller. Manucript receied December 6, 008 Priti Cicili i with the Dept. of Chemical Eng., Unierity College of Technology, Omania Unierity,Hyderabad, ,India. G.Prabhaker Reddy i with the Dept. of Chemical Eng., Unirtdity College of Technology,OmaniaUnierity,Hyderabad, ,India. ( gpreddy_ouct@yahoo.com) *V.Rameh Kumar i with the Dept. of Chemical Eng., Unierity College of Technology, Omania Unierity,Hyderabad, ,India. (Phone : Ext. 05; Fax: ramehkumar@omania.ac.in ) V. Rameh Kumar i thankful to UGC and MHRD, Got. of India for the financial upport under TEQIP to preent thi work in ICCA009 in Hong Kong. II. STEADY STATE AND DYNAMIC ANALYSIS Under normal reactor operating condition, change in inlet liquid temperature, liquid flow rate and inlet ulfur concentration can ignificantly affect the bahiour of the proce. The objectie of thi ection i to tudy both the teadytate and tranient effect of ariou input parameter on the behaiour of the reactor, which will ultimately reult in the optimal operation of the reactor ytem. A. SteadyState Behaiour Steadytate olution can be obtained by carrying the dynamic imulation aymptotically to the teadytate or by etting the time deriatie equal to zero in the ordinary differential equation and then oling the reultant nonlinear algebraic equation by trial and error. The conergence of the numerical cheme i trongly dependent on the initial gue alue that are upplied. In the preent tudy, collocation baed GauNewton method i ued for the olution of the equation. The elected method ha the obered merit of leading to conergent olution for fixed initial gue alue of the ariable of = 0.1, = 0.1, θ = 0.1. Steadytate axial concentration and temperature profile are preented in Fig. 1. The concentration profile how reduction in % S along the axi of the catalyt bed. A maximum of 87.1% S remoal i obered. The correponding teadytate temperature profile how a change in temperature (ΔT) from inlet to outlet of 3 K. B. Dynamic Behaiour Figure how the tranient profile along the bed at ariou dimenionle time. From tartup it take approximately 4 τ to reach the teadytate. A maximum of 87.1% deulfurization i obered and a maximum T of 3 K i noticed. Once the ytem reache teadytate (preciely at 40 τ), tep change in inlet temperature, oil federate, ulfur feed concentration are gien indiidually and the dynamic repone of the ytem i tudied. C. Study of Influence of Variou Input Condition Step Change in Inlet Liquid Temperature: The initial reactor temperature i an important factor in influencing the tranient profile of the reactor at the tartup. The reult of exit ulfur concentration and temperature for tep change in inlet temperature are hown in Fig. 3. From thi figure it i obered that increae in inlet temperature lead to a decreae in product ulfur. The temperature profile how inere repone and i due to increaed conerion in the entrance region of the bed. ISBN: IMECS 009

2 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong For different poitie and negatie large and mall tep change in inlet temperature, the gain alue are calculated. It i obered that though the calculated gain alue remain ame for both poitie and negatie tep change, they differ when the magnitude of tep i changed. So it can be concluded that the ytem exhibit nonlinear behaiour with repect to inlet temperature and one ha to be ery careful in control ytem deign. Table 1 Ealuation of PI Controller etting Step Change in Liquid Velocity: Figure 4 how the repone of exit ulfur concentration and temperature profile to different tep change in liquid elocity. The correponding exit temperature profile how oerhoot. For different tep change in inlet liquid elocity, the gain alue almot remain ame. The ytem can be treated a linear with repect to change in liquid elocity. Step Change in Inlet Sulfur Concentration: Figure 5 how the exit ulfur concentration and temperature profile for different tep change in inlet ulfur content. During initial period after the tep change i introduced, a mall increaing peak i obered and then the concentration fall exponentially. Calculated gain alue are imilar for different poitie and negatie tep change but differ when the magnitude of the tep i changed. Therefore the ytem exhibit nonlinear behaiour with repect to inlet ulfur content. III. CONTROL STUDIES OF THE REACTOR SYSTEM The controller objectie i to keep the exit ulfur concentration at deired et point. The inlet ulfur content i taken a main diturbance to the ytem. The inlet temperature or liquid flow rate can be the manipulated ariable. In thi part of tudy, the main objectie i to compare the performance of a model baed controller (DMC) with a conentional PI controller. In order to ynthei the control algorithm the repone to tep change in initial temperature, liquid flow rate and inlet ulfur content are repreented by firtorder plu time delay (FOPTD) model: τ K e d G( ) = τ p + 1 (1) Where K i the teadytate gain, τ P i the time contant and τ d i the dead time. The alue of K, τ P and τ d are obtained from the proce reaction cure[7]. τ P = 0.67 (t t 1 ) () τ d = 1.3 t t (3) B. Dynamic Matrix Control Dynamic matrix control trategy ue a time domain tep repone model (conolution model) of the proce to calculate the bet alue of the future change in the manipulated ariable uch that a performance index i minimized [9]. A tep change in inlet temperature i gien and the repone in exit ulfur concentration i obtained. From thi openloop repone cure, the tep repone coefficient (b i, i=1, NP) are identified. The predicted alue of the output, at ith tep in the future can be calculated a NP [ ]( ) old mea YOL i Yo + 1, = + bi+ 1 k b1 k Δmk k= 1 (4) old Where the Δm i the old change in the manipulated input. The repone due to thi old input change can alo be called open loop repone The change in final control moe i gien by new T 1 T ( Δm) = ( A A + f I ) A y (5) where A i NP x NC matrix with coefficient aik = b i + 1 K (6) and f i the weighting factor. The cloed loop repone i gien by Y NC new CL, i = YOL, i + aik ( Δmk ) k = 1 (7) The alue of NP, NC and f ued in the imulation are gien in Table where t 1 i time at 35% of the ultimate repone t i time at 85% of the ultimate repone A. Synthei of PI Controller The controller etting are obtained uing ITAE criterion [8] for et point change and gien in Table 1. ISBN: IMECS 009

3 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong Table DMC Parameter compared with conentional PI controller. It i found that DMC cheme gie atifactory reult for et point change in exit ulfur pecification while PI controller gie ocillatory and take longer time to reach et point. APPENDIX IV. RESULTS AND DISCUSSION A. Set Point Change (Inlet Temperature i Manipulated Variable) The cloedloop repone of the exit ulfur concentration (et point) with DMC and conentional PI control cheme are imulated and hown in Fig. 6. The correponding inlet temperature T i manipulation are hown in Fig. 7. It i obered that, DMC cheme perform moothly with no oerhoot and offet. Alo DMC cheme ha mooth manipulated ariation. The repone of PI controller i ocillatory and it take ery long time to reach the deired et point. B. Setpoint Change (Liquid Velocity i Manipulated Variable) Figure 8 and 9 how the cloed loop repone of exit ulfur concentration (et point) obtained with DMC and PI cheme. From the cure it i obered that the PIController fail to reach et point and how ocillatory behaiour. Thi i becaue controller parameter are obtained uing FOPDT model, which ha partially repreented the tep repone data. Howeer, the DMC cheme gie atifactory repone. Looking at the manipulated ariable alo, DMC cheme behae moothly. V. CONCLUSIONS A reported mathematical i ued to timulate the dynamic behaiour of a laboratory adiabatic HDS reactor for tep change in inlet temperature, liquid elocity and inlet ulfur concentration. The tranient profile of temperature and inlet ulfur concentration indicated that the ytem exhibit nonlinear behaiour. The high inlet temperature increae the deulfurization efficiency, but reult in higher bed temperature ditribution along the axi of the catalyt bed. Thi can affect the actiity of the catalyt. The increae in liquid elocity reduce the deulfurization efficiency uddenly but ariation in temperature ditribution along the axi of the catalyt bed i mall. The increae in inlet ulfur concentration howed detrimental reult. Though the increae in inlet ulfur concentration increae the deulfurization efficiency, a maximum rie in bed temperature occurred due to releae of large quantitie of reaction heat, which i a ery harmful operation mode. The performance of dynamic matrix control i imulated and SUMMARY OF AN ADIABATIC HDS REACTOR MODEL EQUATIONS [] Aumption: The main reaction HDS, HDM occur within the porou catalyt particle The reactor operate adiabatically The flow pattern i decribed by the axial dipered plug flow with independently pecified diperion coefficient for ma and heat. The radial diperion effect of ma and heat are negligible. Reitance to tranport of ma and heat between the external fluid phae and particle urface are neglected. The fluid elocity, denity and axial diperion coefficient are taken to be independent of axial ditance and temperature. Ma balance for external fluid phae: ε l 1 ( ) = R ε c t Pem ε l 1 ( ) = ε c t P em R n n e δ (1+ θ ) e δ (1+ θ ) At + 1 z = 0 ω (t )= Pem 1 ω (t )= Pem At z = 1 = 0 = 0 Heat balance for external fluid phae: θ ε c α 1 θ θ = ( R t ( ε l + β + ζ ) PeH z At z = 0 + At z = 1 ω T θ = 1 (t )= P 0 eh θ θ n ( E ( E e f f δ (1+ θ ) ) ) E f h h h ) ISBN: IMECS 009

4 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong REFERENCES [1] T.Y Yan,, Dynamic of a tricklebed hydrocracker with a quenching ytem., Can J Chem Engg., 48, 1980, pp [] Y.C. Chao, and J..S. Chang Dynamic of a reidue hydrodeulfurization tricklebed reactor ytem, Chem Eng Comm., 56, 1987,pp [3] M.H. Aldahan, and M.P. Dudukoic, Catalyt wetting efficiency in tricklebed rector at high preure, Chem Eng Sci, ol 50, 1995, pp [4] W. Garcia and J.M. Pazo Hydrodynamic effect in trickle bed laboratory reactor for hydrodeulfurization and hydrodemetalization of heay feed, Chem Eng Sci, ol 37(10), 198, pp [5] Y.T. Shah and J.A. Parako, Criteria for axial diperion effect in adiabatic tricklebed hydroproceing reactor, Chem Eng Sci., ol 30, 1975, pp [6] W Dohler and M Rupp, Comparion of performance of an Indutrial VGO treater with reactor model prediction, Chem Eng Tech., ol 10, 1987, pp [7] K.R. Sundarean and P.R.Krihnawamy, Etimation of time delay time contant parameter in time, frequency and laplace domain, Can J chem. Engg, ol. 56, 1978,, pp576. [8] C.A. Smith, and A.B. Corripio,, Principle and Practice of Automatic Proce Control, Wiley, NewYork, [9] W.L. Luyben, Proce Modelling Simulation and Control for Chemical Engineer,McGrawHill, New York, Fig. 1 Steady tate ulfur concentration and Temperature profile. Fig. Bed temperature and ulfur concentration Profile from tartup to teady tate Fig. 3 Tranient repone to different tep change the Inlet temperature. in ISBN: IMECS 009

5 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong Fig. 4 Tranient repone to different tep change in the Inlet liquid elocity. Fig. 5 Tranient repone to different tep change in the Inlet ulfur concentration. ISBN: IMECS 009

6 Proceeding of the International MultiConference of Engineer and Computer Scientit 009 Vol II IMECS 009, March 18 0, 009, Hong Kong Fig. 6 Cloed loop repone of the HDS reactor for et point change in exit ulfur concentration wiith DMC and PI control cheme Fig. 8 Cloed loop repone of the HDS reactor for et point change in exit ulfur concentrationwiith DMC and PI control cheme Fig. 7 Inlet temperature manipulation for etpoint change in exit ulfur concentration with correponding DMC and PI control cheme Fig.9 Profile of the liquid elocity manipulation for etpoint change in exit ulfur concentration with correponding DMC and PI control cheme ISBN: IMECS 009