CONTROL AND OPTIMIZATION OF A MULTIPLE EFFECT EVAPORATOR

Transcription

1 CONTROL AND OPTIMIZATION OF A MULTIPLE EFFECT EVAPORATOR PD SMITH 1, CLE SWARTZ 2 AND STL HARRISON 2 1 Triagle Limited, P.Bag 801, Triagle, Zimbabwe 2 Departmet of Chemical Egieerig, Uiversity of Cape Tow, Rodebosch Abstract Multiple effect evaporator cotrol is a problem that has bee widely reported i the pulp ad sugar idustries. Evaporators are the largest heat users ad major cotributors to losses i sugar cae factories. These factors make effective evaporator cotrol crucial to overall factory efficiecy. The complexity ad large umber of iteractios make sigle loop PID cotrol (the covetioal proportioal, itegral ad derivative cotrol) difficult ad ofte sub-optimal. A Model Predictive Cotrol (MPC) algorithm is preseted as a differet approach to solvig the multiple iput, multiple output problem. This techique has bee applied successfully i other multiple statio idustries ad is beig applied to a dyamic model of the evaporator statio at Triagle Limited. The first step i the MPC formulatio was to develop a dyamic computer model of the quituple effect evaporator statio at Triagle. The model was the used to obtai a covolutio model (the iteral referece model for the cotroller), which captures the step respose behaviour of the process to key iputs. The two iputs available for cotrol were the juice flowrate ad the steam pressure i the caladria of vessel three. Valve dyamics for these two iputs were first idetified usig real plat data, ad the model was suitably modified so that the cotrol system could assume liearity of these cotrol actios. A objective fuctio was the formulated, combiig tight Brix cotrol with a smooth overall operatio. The proposed cotroller will use the covolutio model to determie the optimal sequece of iput moves. Itroductio Multiple effect evaporators cocetrate juice from the extractio plat to syrup of about 67 o Brix, which is fed to the pa statio (evaporative crystallisers). This ivolves removig the majority of the water from the juice, ad thus is the uit operatio that cosumes the most eergy i the factory. Log residece times ad high temperatures create a potetial loss of betwee 1% ad 2% of icomig sugar by iversio. Therefore evaporatio is a very importat uit operatio ad must be cotrolled smoothly. However, the complexity of the system, ad the large umber of iteractios, make sigle loop PID cotrol difficult. The two most commoly cited objectives for a evaporator cotrol system are tight cotrol of Brix, ad a smooth operatio. These ca be made clearer by usig a ecoomic aalysis. The ecoomic objective is the delivery of the maximum amout of high quality product to the dowstream factory. I the sugar factory, this quality is determied by the syrup cocetratio. The amout of syrup that ca be delivered is costraied by the rate at which juice arrives at the statio, ad there is also a upper limit o the syrup cocetratio i order to avoid spotaeous ucleatio or excessive depositio ad scalig. Smooth operatio meas the eve hadlig of extreme operatig coditios, such as fluctuatios i juice flowrate. Smoothig out process fluctuatios, most otably the clear juice flowrate, greatly icreases the potetial for good evaporator cotrol. At Triagle, two evaporator trais exist i parallel, ad these are cleaed o a rotatioal basis. Thus the performace of the differet trais is seldom idetical ad a higher quality product may be achieved by carefully choosig the proportio of juice that is fed to each trai. Evaporator cotrol Motocchio ad Scott (1985) reported good results usig a variatio o a PID based throughput cotrol scheme, which was istalled at Amatikulu Sugar Mill. By chagig the cofiguratio of the evaporator effects, ad usig good variable pairigs, the evaporator system was made less sesitive to disturbaces. This robustess was depedet o tight juice flow cotrol, ad a well desiged statio, which was early always ru at full throughput. This sceario caot be assured i plats where flow delays due to lack of cae are commo. Hsiao ad Che (1995) also reported promisig results usig a improved PID model. Their algorithm icludes a form of gap actio cotrol whereby the simple PID output is modified i the face of excessive variatios or uusual operatig coditios. The cotrol of syrup Brix was improved by allowig a variable recycle back to the last effect. As with the throughput cotrol used at Amatikulu, this system would limit the capacity of the statio, ad would ot be able to aticipate ad hadle iput costraits. The scheme proposed by Rousset et al. (1989a, b) was based o a series of Feedforward/Feedback cotrollers. The results from this system were very promisig, although a high degree of istrumetatio was required o the plat. Lee ad Newell (1989) proposed Geeric Model Cotrol as a meas of cotrollig a sigle effect recirculatio evaporator. The study was cofied to simulatio studies, ad although the cotrol system gave impressive results, costraits could ot be hadled directly, or aticipated (Harris ad McLella, 1990). Elhaq et al. (1999) have applied a multivariable Geeralised Predictive Cotrol system based o Mohtadi et al. (1987), to a evaporator statio i Morocco. The objective fuctio was based o the total operatig cost. The two outputs chose were syrup Brix ad V2 steam pressure, which was maitaied at a set value despite variatios i vapour draw. Oce agai, this system was ot able to hadle iput costraits directly. Page 274

2 I this paper, Model Predictive Cotrol (MPC) will be itroduced as a ovel cotrol algorithm, which is suitable for evaporator cotrol, as well as other factory areas, i that it ca aticipate ad hadle costraits, ad hadle Multiple Iput, Multiple Output (MIMO) systems i a optimal maer. The problem uder cosideratio ca be split ito three mai areas juice flow cotrol, Brix cotrol ad juice distributio to the three first effects. Juice Flow Cotrol Juice flow cotrol is a useful itroductio to the cocepts of Model Predictive Cotrol, because of the familiarity of this system. At Triagle, maipulatig the mixed juice flowrate cotrols the clear juice tak level, while the clear juice flowrates are cotrolled accordig to operator supplied set poits oly. These clear juice flowrates the idirectly affect the mixed juice tak level. The algorithm preseted below could be applied to both the mixed juice ad clear juice taks. MPC cotroller Campo ad Morari (1989) have used a stadard flow cotrol objective, that is to miimise the Maximum Rate of Chage of Outlet flow (MRCO) of the tak uder cosideratio, with costraits that the level should ot violate upper or lower bouds over some predictio horizo. These authors successfully applied a MPC algorithm to this problem. I this, a simple iteral model predicts the future behaviour of the tak based o the past two level measuremets, ad the previous outlet flow, as outlied i the level equatio (1), below: h predict t ( t + k) = h( t) + k t 1 A ( ( ) ( ) ( ) h t h t 1 + Qo t k = [ Q ( + ) i o t k ] 0 (1) A Where h predict Dt Q o A t k = predicted tak level = time-step used = outlet flowrates = cross sectioal area of tak = time of last measuremet = time steps util predictio Future ilet flowrates are assumed costat ad are iferred by usig measuremets of the outlet flowrate ad the chage i tak levels sice the previous time-step. The future outlet flowrates are chose so as to miimise the MRCO objective, Draught Juice (Diff. & Mill) Mixed Juice Tak Heaters, Clarifiers Clear Juice Tak FIGURE 1. Juice Hadlig at Triagle Limited. Evap. 1A Evap. 1B Evap. 1C f(q o (t+k)), while obeyig costraits o the permissible tak levels ad flowrates. I additio, a fial costrait is added, that the level must retur to set poit by the ed of the predictio horizo (P). The cotrol algorithm was formulated as show below i equatios (2) (6), for ay preset time, t. mi f = max Qo ( t + k) Qo ( t + k 1) Q o ( t k ) (2) + For P ³ k > 0, subject to: Q Q h ( t k ) max + (3) o Q o, ( t k ) mi + (4) o Q o, h( t + k h (5) mi ) ( t p ) hsp max h + = (6) Oly the first computed flowrate is implemeted, ad the optimisatio is repeated at the begiig of the ext time-step. Results This MPC cotroller has bee programmed i the Matlab simulatio laguage, ad applied to the problem of cotrollig the mixed juice tak level, ad the mixed juice flowrate. The followig graph, Figure 2, shows the results of this system uder a real life situatio o the Triagle plat; i.e. a step icrease i draught juice (DJ) flowrate. The MPC cotroller of Campo ad Morari, (1989), was formulated so that there is o offset after the predictio horizo. This is the tuig parameter i this case, ad it ca be show that for ay give disturbace, there is a critical predictio horizo, i.e. the time at which the tak would overflow, with o cotroller actio. As the predictio horizo is icreased, the MRCO objective is cotiually improved util this critical horizo is reached. Thereafter, the settlig time is oly icreased, with o further beefit to flow filterig. I this example, the predictio horizo was chose as 10 miutes, which resulted i a settlig time of 51 miutes, with a MRCO of 35.7, ad a maximum flowrate of tph. With a smaller predictio horizo, of 5 miutes, the settlig time could be reduced to 26 miutes, at the expese of a higher MRCO, of 78.4 ad a slightly higher maximum flowrate, tph. Flowrate (tph) DJ Flow I MJ Flow Out MJ Tak Level time (mis) FIGURE 2. MPC respose to a step i flowrate Tak Level (%) Page 275

3 Model Predictive Cotrol Model Predictive Cotrol refers to a group of algorithms i which a iteral model is used by the cotroller to predict how past ad preset measuremets will affect the real plat. From this model the optimal sequece of cotrol moves is the computed. The first of these is the implemeted, ad a ew set of measuremets is take at the begiig of the ext time step, providig a feedback mechaism for the cotroller. The future sequece of cotrol moves is calculated by optimisig a objective fuctio, commoly a weighted sum of squares of the setpoit trackig error ad the maipulated variable moves. A commo formulatio of this type is Dyamic Matrix Cotrol, or DMC, which was first developed by Cutler ad Ramaker (1979) at Shell Oil for tacklig the multivariable cotrol problems such as that show i Figure 3 below. I Dyamic Matrix Cotrol, the model of the plat is a covolutio model, i.e., the respose of each output to a step chage i each iput is foud. The values of the respose at discrete samplig times the make up a series of step respose coefficiets (a i ) which may be used to predict the chage i ay output (y) associated with a chage i ay iput (u), as show i the geeral output predictio equatios (7) ad (8), below: 1 i= 1 i ( k i) + a u( k ) y ( k ) = a u + d ( k ) (7) predict Where = the settlig time of the system (umber of itervals) a i = the step respose coefficiets d p (k) = predicted disturbace, which is assumed costat ad is calculated by equatio (8), which calculates the differece betwee the curret measured output, ad the output as predicted by the past cotrol moves: d ( k + j ) d ( k ) p = p 1 i= 1 i ( k i) a u( k ) = y ( k) a u (8) measured The optimisatio problem at each time-step is the to miimise the objective fuctio, f(du), show i equatio (9), below: T T ( y y). Q. ( y y ) + u. R. u mi f = (9) u Where y Iput (u 1 ) Iput (u 2 ) Iput (u 3 ) set set = the vector of predicted outputs, y predict (k) Multivariable Process p Output (y 1 ) Output (y 2 ) Du = the vector of iput moves Du(k) Q ad R are diagoal weightig matrices, ad T is the vector traspose operator. Equatio (9) is a weighted sum of the predicted setpoit trackig errors for both outputs ad the iput variable moves for the iputs, over the predictio horizo. The optimisatio must be solved subject to costraits o the iputs, outputs ad iput moves. This approach has bee used i the Brix cotrol sectio discussed below. I summary, the Model Predictive Cotrol structure ca be cosidered as a observer, ad a optimiser, as show i Figure 4 below. The observer receives measuremets of iputs to the plat (u) ad outputs from the plat (y), ad by usig a iteral model, estimates the preset ad future state of the plat (x). Based o this predictio, the optimiser the determies the sequece of maipulated iputs that would best achieve the desired referece objective. Model Predictive Brix Cotrol The cocept of Model Predictive Cotrol is exteded here to Brix cotrol, where the advatages of this form of cotrol are clearer. Curretly, the syrup Brix leavig the Triagle evaporator statio is cotrolled by maipulatig the flowrate of heatig vapour to the third effect of each trai. I Triagle this vapour is vapour two; the vapour evolved from the secod effect evaporators (V2). The layout of the Triagle evaporator statio is show i Figure 5 below. Although this cotrol system ivolves oly two outputs, syrup Brix ad clear juice flowrate, it is still essetial that this cotrol layer should be able to aticipate ad hadle costraits. At Triagle Ltd. the ITouch Scaig, Cotrol Ad Data Acquisitio (SCADA) system has recetly bee istalled, which provides olie readigs of the most sigificat three disturbaces, i.e. juice flowrate, exhaust steam pressure ad fial effect pressure. The effects of these iputs are more easily icluded i the DMC formulatio, rather tha as a series of trims ad feed forward gais, which would be ecessary for PI cotrol. It is for these reasos that a DMC cotroller has bee selected. Dyamic model A dyamic model first had to be developed which would form the basis for the iteral model of the cotroller. The model was based o the familiar mass ad eergy balaces about each effect. These were solved umerically usig the Ruge Referece Optimiser u Disturbace Plat y Disturbace (u 4 ) Disturbace (u 5 ) Disturbace (u 6 ) Output (y 3 ) x Observer FIGURE 3. Iput-Output process descriptio used i idustrial MPC techology (Qi ad Badgewell, 1997). FIGURE 4. Model Predictive Cotroller. Page 276

4 Clear Juice Tak V1 Bleed V2 Bleed V5 to codeser Exhaust steam 1A 2A 3A 4A 5A Syrup to Factory Exhaust steam 1C V5 to codeser Exhaust steam 1B 2B 3B 4B 5B1, 5B2. Syrup to Factory FIGURE 5. Layout of the Triagle Evaporator Statio. Kutta 4 th order techique. Several other script files cotai code for estimatig physical properties (Peacock, 1995), calculatig vessel parameters, ad covertig steam properties (Perry et al., 1997). The existig model makes the assumptio of costat liquid volume hold-up for the first two effects (without level cotrol) while the levels i the fial three effects are modelled dyamically usig the existig PID cotroller settigs. The iputs to the model are the icomig juice temperature, cocetratio, ad flowrate, the exhaust steam temperature ad pressure, ad the absolute pressure (vacuum) maitaied i the fial effect. These iputs were simulated usig SCADA system data from the plat. The model the outputs all of the states of the system, i.e. the juice temperatures ad cocetratios leavig each of the 12 vessels, alog with the pressures of V1 (first effect vapour) ad V2 vapour for compariso with real plat data. Steady state heat trasfer coefficiets for each vessel i the Triagle statio had bee calculated based o SCADA measuremets ad laboratory aalyses, ad these were geeralised by usig the Dittus - Boelter equatio to take ito accout variatios of flow ad temperature from steady state, as show i equatio (10). U U N Re N Pr N Re,0 N Pr,0 = (10) Where U = Heat Trasfer Coefficiet N Re = Reyolds umber N Pr = Pradtl umber The siusoidal dyamics of the V2 throttlig valve were idetified usig SCADA data, ad icorporated ito the model. Figure 6 shows the results obtaied whe the model was supplied iput data from the SCADA, ad compared with actual data supplied by the Triagle laboratory. Covolutio model ad Dyamic Matrix Cotroller Whe the dyamic model had bee completed, the respose of the system was the measured for 10% steps i each of the iput variables. A samplig time of 1 miute was used, as this is the smallest time iterval possible from the SCADA system, ad it has prove adequate for obtaiig all of the process dyamics from this system. The overall juice residece time i the multiple effect is about 45 miutes, ad thus the settlig time to steady state was set at two hours. The covolutio model is made up of the step respose coefficiets, i.e. the chage i syrup Brix from steady state at each time iterval Syrup Brix (%) time (mis) FIGURE 6. Compariso of dyamic model with plat. Plat Model Page 277

5 followig the step chage. By combiig the resposes to steps i each of these iputs, ad assumig liearity ad time ivariace, a Dyamic Matrix is formed, which predicts the future output of the system based o preset ad past iputs. I the Triagle case there are a total of 5 iputs to the system, which give rise to two outputs, syrup Brix ad actual clear juice flowrate. A clear distictio has bee made betwee geuie adjustable iput variables (A, B), ad disturbace variables (c, d, e), which caot be freely maipulated by the cotrol system: A Clear juice flowrate this ca be directly maipulated via the SCADA system. I a sese, this variable is both a iput ad a output i the MPC formulatio, i that it is available for maipulatio, ad a bias value is also specified as the clear juice flow setpoit. B V2 Valve throttlig positio this ca be directly maipulated via the SCADA system. c Clear juice temperature ay variatio i this parameter must be due to radom process disturbaces. d Exhaust steam pressure this is difficult to vary due to the arragemet with the turbo-geerators, ad was treated as a disturbace. e Fial effect pressure this is also cotrolled about a costat setpoit, ad so ay fluctuatios could be couted as a disturbace. Results The cotroller was the coded ito the Matlab simulatio laguage, Simulik, ad used to cotrol the existig dyamic model of the statio. Figure 7 shows the respose to a icrease i steam pressure at time (t = 20 mis) ad agai at time (t = 60 mis). Figure 7 shows several importat features of dyamic matrix cotrol. Firstly, whe the steam pressure was icreased by 10% at time 20, the V2 throttlig valve started to close, to couteract the effect of this icreased pressure (ad thus temperature) o the syrup Brix. The syrup Brix gradually retured towards a setpoit of 68 o Bx from time 40 to time 60. The, at time 60, the exhaust steam pressure was agai icreased by 10%. This had a similar effect, i that the syrup Brix bega to rise. The V2 throttlig valve was already almost fully closed, ad ow ecoutered a iput costrait. I the overall plat costraits, it is iteded to keep syrup Brix betwee 50 o ad 72 o Bx. Thus whe this Brix costrait was approached, the cotroller icreased the clear juice flowrate, the oly remaiig iput variable move, i order to brig the syrup Brix back uder cotrol. A similar effect was observed for the case where the disturbace caused a decrease i syrup Brix, e.g. a decrease i juice temperature. I this case, the V2 throttlig valve was opeed util it ecoutered a costrait (100% ope) ad the the clear juice flowrate was reduced, to prevet the syrup Brix from fallig below its costrait of 50 o Bx. Steady state optimisatio Optimal Juice Distributio The fial layer of the evaporator cotrol strategy is a distributio cotroller. At Triagle there are three first effect evaporators, ad the total clear juice flowrate must be distributed amogst these so as to achieve the highest possible syrup Brix. Because the evaporators are cleaed o a rotatio basis, they may be operatig at differet efficiecies at ay oe time, ad the aim of a particular flow distributio should be to optimise their curret operatioal coditio. Determiatio of evaporator coditio from codesate flowmeters The distributio cotroller eeds to receive some measure of the coditio of the evaporators before optimisatio ca be doe. This ca be achieved by measurig the flowrate of codesate leavig each evaporator. However, codesate flow measuremet provides particular difficulties because the fluid beig measured is at its saturatio temperature. Love (persoal commuicatio), proposed that a particular desig of liear weir, (Heller, 1980), would effectively address the limitatios of covetioal flow measuremet techiques. The codesate flowmeter, as show i Figure 8, was desiged, built ad tested o the Triagle statio. The flowmeter was desiged so that there is a liear relatioship betwee flowrate ad head maitaied i the outer cyli CJ Flow 100 Exh. Press(kPa) Clear Juice Flow(tph) Syrup Brix V2 Valve Positio Exhaust Steam Pressure V2 Valve Positio Syrup Brix dp time (mis) FIGURE 7. Respose to steps i steam pressure. FIGURE 8. Codesate flowmeter (after Heller, 1980). Page 278

6 der. The vet was coected back to the icodesible gas release, to avoid flashig. A Kalma filter was the used i simulatios to idetify heat trasfer coefficiets from flowmeters fitted to each of the first ad secod effects, a total of five vessels (1A, 1B, 1C, 2A ad 2B). The heat trasfer coefficiets were the used i the optimisatio program, where the objective was to maximise the amout of water evaporated from the juice. This is doe by calculatig the weighted Brix of the juice that would leave the secod effects, usig part of the dyamic evaporator model described above. Results Figure 9 shows the optimal juice flowrate through the first vessel of the A set, as the observed heat trasfer coefficiet for either vessel 1A or 2A was varied. I each case, all other heat trasfer coefficiets were kept costat. Figure 9 shows that the heat trasfer coefficiet of the first effect is more importat that that of the secod effect, due to the layout of the Triagle evaporator statio, where there is a additioal first effect vessel, which feeds the two evaporator trais equally. The resposes of each of the first effect vessels were ot idetical. The extra first effect, 1C, was foud to have a slightly differet relatioship betwee its observed heat trasfer coefficiet ad the optimal flow distributio. Coclusio The subject of evaporator cotrol has bee ivestigated ad some recet developmets have bee preseted. Three levels of cotrol are proposed: juice flow cotrol, syrup Brix cotrol, ad the optimal distributio of juice to the three first effects. Good juice flow cotrol is crucial ot oly to improved evaporator cotrol, but also to good clarificatio ad ph cotrol. A ovel algorithm has bee preseted, ad its advatages have bee discussed briefly. Syrup Brix is sigificatly affected by a umber of factors, ad these are efficietly icorporated ito a MPC framework. This type of cotrol also allows iput ad output costraits to be accommodated. Fially, there is a optimal distributio of clear juice to the first effect vessels, which may be determied by their observed heat trasfer coefficiets. Ackowledgemets The authors wish to ackowledge ad thak Triagle Limited for their fiacial support of this project. Thaks are also exteded to Triagle staff for techical assistace ad advice, i particular, Steve Paver, Ash Raa, Clive Wema ad Elisha Mutasa. REFERENCES Campo, PJ ad Morari, M (1989). Model predictive optimal averagig level cotrol. AIChE J, April, Vol 35, No. 4: Cutler, CR ad Ramaker, BL (1979). Dyamic matrix cotrol - a computer cotrol algorithm. AIChE Natioal Mtg, Housto, Texas; also Proc. Joit Aut. Cotrol Cof., Sa Frasisco, Califoria (1980). Elhaq, SL, Giri, F ad Ubehaue, H, (1999). Modellig, idetificatio ad cotrol of sugar evaporatio theoretical desig ad experimetal evaluatio. Cotrol Egieerig Practice, 7: Harris, TJ ad McLella, PJ (1990). Geeric model cotrol - a case study revisited. Ca J Chem Eg, Vol. 68, December: Heller, H (1980). Use weir to measure fluid flow. Chem Eg, November 17. Hsiao, YC ad Che, CH (1995). Evaluatio of cotrol models for multiple-effect evaporator set i a cae sugar mill. Taiwa Sug, Jul- Aug: Lee, PL ad Newell, RB (1989). Geeric model cotrol - a case study. Ca J Chem Eg, Jue, Vol. 67: Mohtadi, C, Shah, SL ad Clarke, DW (1987). Geeralized predictive cotrol of multivariable systems. System ad Cotrol Letters, 9: 285. Motocchio, RG ad Scott, RP (1985). Experieces i evaporator cotrol at Amatikulu. Proc S Afr Sug Techol Ass, Vol. 59: Peacock, S (1995). Predictig physical properties of factory juices ad syrups. It Sug J, Vol 97, No 1162: Perry, RH, Gree, DW ad Maloey, JO (1997). Perry s Chemical Egieer s Hadbook. 7 th editio, McGraw Hill Book Compay, New York, Qi, SJ ad Badgewell, TA (1997). A overview of idustrial model predictive cotrol techology. AIChE Symposium Series, Vol 93, No. 316: Rousset, F, Saicir, Y ad Dacli, M (1989a). Automatic process cotrol of multiple effect evaporatio. Part I: Coditios for static ad dyamic equilibrium. Zuckeridustrie, Vol. 114, No. 4: Rousset, F, Saicir, Y ad Dacli, M (1989b). Automatic process cotrol of multiple effect evaporatio. Part II: Practical realisatio ad results. Zuckeridustrie, Vol. 114, No. 6: Optimal Clear Juice Flowrate, Evap 1A (tph) HTC 1A HTC 2A Heat Trasfer Coefficiet (kw/m 2.K) FIGURE 9. Optimal juice flowrate ito vessel 1A. Page 279