Simulation and Control Configuration of Integrated Three-Product (Petlyuk) Distillation Column

Transcription

1 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, Simulation and Control Configuration of Integrated Three-Product (Petluk) Ditillation Column R Solar-Gonzalez #, R Monro-Loperena *, A Velaco-Perez # # Diviión Etudio de Potgrado, Univeridad del Itmo Ciudad Univeritaria, Ba Sta Cruz Tagolaba, Sto Domingo Tehuantepec, Oaxaca, 7070, México * ROMON SA Paeo de lo Pirule 4, México, 0450, México # Departamento de Ingeniería Química, Univeridad Veracruzana Prolongación de oriente No 009 Col Rafael Alvarado, Orizaba, Veracruz, 94340, México Abtract In a Petluk ditillation column, two extra degree of freedom can be ued for optimization purpoe It ha been reported that a tpical energ aving of 30% i achievable with a Petluk ditillation column, compared to conventional ditillation arrangement However, the optimal tead-tate operation point can be difficult to maintain in practice In thi work we propoe and tudied the performance of a parallel control configuration, uing habituating parameter, for the Petluk ditillation column in preence of diturbance The reult how that parallel control configuration can be ued to improve the robutne of operation b extending traditional decentralized product compoition control loop for two and three point b uing the two degree of freedom a manipulated variable in a parallel feedback control loop eword Continuou ditillation, Thermal coupled ditillation, Petluk, compoition control, Parallel control I INTRODUCTION Ditillation i a unit operation widel ued to eparate, multicomponent mixture in pite of it high energ conumption and low thermodnamic A a reult, engineer and reearcher are intereted in developing new configuration capable of reducing and improving the ue of energ It ha been demontrated that thermal linking can reduce energ demand between 30 and 50% depending on the compoition of the mixture to be eparated The three thermall coupled ditillation equence that have been explored in detail are the column that uing a ide rectifier, the column with a ide tripper and the full thermall coupled ditillation equence or Petluk tem[] Becaue of the reduction in the oil reerve of the reduction in the oil reerve and policie of reduction in carbon dioxide emiion [], ignificant reearch ha focued on the deign, optimization and control of the thermall coupled ditillation equence] The Petluk column ha alo been decribed a the mot efficient arrangement for three-component mixture It ha been written [3] that, For mot eparation, the full thermall coupled ditillation column i thermodnamicall more efficient than the conventional arrangement, and a a conequence, ha lower energ requirement The lower energ requirement of the Petluk column configuration lead to maller column diameter and lower overall heat exchanger area in the reboiler and condener The reduced number of reboiler and condener alo reult in a lower capital invetment However, in pite of all thee apparentl attractive feature, the PC configuration ha not found a wide indutrial ue Even for ub ambient temperature ditillation, where energ conumption i of great importance, the Petluk column configuration i et to be ued Thi i rather urpriing becaue the PC configuration ha been known for nearl 50 ear[4-5] The lack of widepread ue of the PC configuration ha been attributed to it difficult deign and control However, coniderable advancement ha been made recentl in both the deign and control apect of the PC configuration The expectance that the dnamic propertie of the PC configuration ma caue more operational problem than conventional equence i one of the factor that have contributed to their lack of indutrial implementation Thi conflict of an energ-efficient tem lead to tight deign, which in turn are more difficult to control A two-column implementation of the PC deign conit of a prefractionator with reflux and boilup from the downtream three-product column, a etup with onl one reboiler and one condener A propoed b Wright [], practical implementation of uch a column can be accomplihed in a ingle hell b inerting a vertical wall through the middle ection of the column, thu eparating the feed and ide product draw Petluk main reaon for thi deign wa to avoid thermodnamic loe from mixing different tream at the feed tra location Repect to the degree of freedom (ee for intance, Dixon [7]), we have that in a conventional given column with fixed tage, feed location, etc Starting with binar ditillation and conidering a tead-tate, where it i aumed that the holdup (condener level, reboiler level, and preure) are alread controlled, we find two independent (manipulated) variable remain, for example reflux rate ( L ) and vapor boilup rate (V ) On the other hand, in a PC we get at teadtate three additional degree of freedom [8-9], one for each of the three additional tream leaving the main column Referring to Figure, thee are the ide-tream S plu the tream SL and SV ent back to the prefractionator Note that in thi anali the prefractionator itelf doe not have an degree of freedom at the tead-tate In a traditional point of 847

2 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, view of ditillation control, the five degree of freedom for the PC deign ma be ued to pecif (control) the top and bottom compoition and one or two compoition in the ide-tream Thi leave one or two degree of freedom for optimization purpoe We want to report in thi work a two and three point compoition control for the PC configuration, following a habituating approach [0-], due to the PC configuration can be een a a plant with more manipulated input than controlled output, then we reort in the premie that the control obective can be atified more eail b utilizing additional input variable In thi wa, we propoe a imple procedure to expand traditional decentralized compoition control tructure applied to a PC configuration Rigorou nonlinear numerical imulation are ued to illutrate the performance of the propoed control cheme under tpical operating condition in a PC configuration II STATEMENT OF THE CONTROL PROBLEM BY A HABITUATING APPROACH A Let u aume a plant decription of the form () = G() u() where G denote the proce plant model, the meaurement and u the manipulated input If the plant i an input/output linear proce with more manipulated input than controlled output, the underling premie i that the control obective can be atified more eail b utilizing additional input variable For the cae of 4 input/ output we have that, G()=,,,,,,, () = ( ), ( ),3,3,3,3 u() = u ( ), u ( ), u3 ( ), u 4 ( ) where,4,4 e,4,4 i, i the tead-tate gain, i the open-loop time contant, both for output i with input and i the time dela of the propoed proce We propoe to olve the control problem b pairing the variable proceeding along with the following map u, u u 3, u4 then we arrive to a diagonal block tructure, that i, G() =,,,,3,3 e,4,4 The above tructure can be ditinguihed a a Diagonal Parallel Control Structure In thi wa the original problem wa plit into two - input/-output problem, whoe olution can be arrived a follow Let u take the firt problem,,, u u e,, In thi non-quare cae, one ha to pecif a trateg for the additional control input u One alternative i to ue a ort of regularization technique to quare the rectangular control tem We propoe to plit the input/output model b introducing an habituating parameter,, a follow:,, where,,, u,, ( ) u ( ), o that,, Notice that the control output ignal ha been partitioned into two component:, and,, correponding to fraction of the regulated output affected repectivel b the control input u and u Phicall, thi plitting of the controlled output can be een a a ditribution of the control effort between the two control input Propoing the ue of PI control,, then the input can be manipulated a u( ) CPI,( ) u ( ) ( ) C where C PI, C I PI, ( ) 848

3 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, for which well-known control technique (eg, Internal Model Control (IMC)) can be ued for control deign, that i C I C C 075 B introducing the variable z z z3 z 4,,,, a quare 4x4 PI diagonal controller i obtained, that i: C I z z z 3 z4 C I ( ) C 3 I3 C 4 I4 ( ) () The model decription conider onl the material balance of the tem, auming contant molar flow and ideal behavior, a the mixture tudied (benzene, toluene, and o-xlene) i nearl ideal Accordingl, the component have the following relative volatilitie: [0,, 0] The tem conit of a 0-tage prefactionator interlinked with a 3-tage fractionator The latter include a total condener and a partial reboiler The tage location for the feed, product, and interlink are all included in Figure All model equation were imultaneoul olved b mean of an implicit Euler approximation with time-tep equal to 0min At each time-tep, the reulting nonlinear algebraicall equation were olved b mean of a Newton-Raphon method endowed with a pare matrix olver to exploit the parit of the incidence Jacobian matrix Becaue the traectorie of the PC are continuou in time, the Newton- Raphon method wa implemented a a continuation method where the tate of the preceding time tep wa taken a initial gue for the actual tep In thi wa, the Newton-Raphon required or 3 iteration to achieve a relative error lower than % The numerical procedure wa implemented a a FORTRAN program in a Pentium IV computer Note that if i i unit then we recover a traditional x diagonal PI configuration III NUMERICAL SIMULATIONS The cae tud i imilar to cae IV of Weburn and Seader [3] The feed i liquid at it bubble point with a flow rate of 000 mol/min: 00 mol/min of benzene, 400 mol/min of toluene, and 400 mol/min of o-xlene At the bubble point, the temperature and preure of the mixture are 3834 and 033 kpa, repectivel The following general aumption are made: () The reflux divider and all tage, except the condener and reboiler, are conidered to be adiabatic () Heat-tranfer rate for condener and reboiler are never pecified (3) The tem operate at atmopheric preure (033 kpa) with zero preure drop throughout the tem (4) The configuration of the tem, that number of tage and location of feed, ide tream, and interlink, i known (5) All product tream leave the tem a aturated liquid Fig Schematic diagram of the Petluk ditillation column tudied The nominal operating point tudied ha L = 0500 mol/min, V 3 = 00 mol/min, SL = 500 mol/min, SV = 500 mol/min, and SL = 40 mol/min, with x, = 0970, x, = 0948 and x 3, 3 = For a PC configuration one mut at leat adut two product flow rate correctl (eg, L to match the ditillate 849

4 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, compoition and V 3 to match the bottom compoition), thu at leat two-point control i required However, three product flow rate are preferred to be aduted (eg, L to match the ditillate compoition, L to match the intermediate product compoition and V 3 to match the bottom compoition), to avoid that the compoition of the intermediate product be lowered coniderabl under external diturbance Hereunder thee two cae will be analed The PI parameter for the necear cae were obtained from tep repone with IMC ruler Under thi et of control parameter, the following numerical imulation were carried out In thi cae a LV dual compoitioncontrol configuration i ued (where the reflux flow rate, L, i ued to control the top compoition, x,, and the vapour boilup flow rate, V 3 i ued control the bottom compoition, 3, 3 ) However, it hould be treed that other control configuration can be tudied along the ame line The column wa tarted from the nominal condition and then regulated at the etpoint ( x,, x 3, 3 ) = (095, 099) At t 300 min, the etpoint wa changed to ( x,, x 3, 3 ) = (099, 099), and at t 800 min, the feed compoition wa changed from (0, 04, 04) to (05, 035, 04) Para ue the diagonal PI model, it i necear to mate the original manipulated variable with thoe identified a control degree of freedom that are not ued for control purpoe In our cae we want to pair off the reflux rate, L, with the liquid ide tream flow rate, SL, or the vapour ide-tream flow rate, SV, and either to pair off the vapour boil-up flow rate, V 3, with an of thee two variable Referring to openloop tead-tate gain, we can notice that if we elect to pair off the reflux flow rate, L, with the vapour ide-tream flow V, with the rate, SV, and the vapour boilup flow rate, 3 liquid ide-tream flow rate, SL, then we have the pairing that mot affect over the output variable (ditillate and bottom compoition) Then, the following aignment to the input variable will be ued: u L, u SV, u V u SL, with the 3 3, following output variable aignment: x,, x3, 3 Figure, preent the behaviour of the PI controller for four value of the habituating parameter, i Notice that in principle a we decreae that the habituating parameter a better performance i obtained, thi performance i better that the diagonal LV-PI configuration (that when i 0 ) Alo notice that for the value of 095 and 090 of the habituating parameter the internal flow rate are decreaed, thi implie that lower demand of energ are necear In 4 x turn, thi habituating control operation of the PC will reound in economic aving becaue le refrigerant and heat agent will be ued when the habituating are well elected Fig Dnamic behaviour of the Petluk ditillation column for variou value of the habituating parameter in two point compoition control, when the input variable are elected in accordance with it effect over the output variable To anale the effect of each pairing input variable, we turn off one of the two pairing variable b etting it habituating parameter to unit A a firt cae conider the cae where 0, then the top compoition, x,, will onl be regulated b mean of manipulating the reflux rate, L In the Figure 3, we note a better performance when i decreaed However the energ requirement are larger On the other hand, conider the cae when 0, then the bottom compoition, x 3, 3, will onl be regulated b mean of manipulating the vapour boil-up flow rate, V 3 In the Figure 4 i preented the cae when the etpoint change, note a i decreaed a better performance i obtained until it reach a critical value where thi behaviour i oppoed To avoid exceive control action we atured the SV, to 00 mol/min The ame obervation input ignal, can be made for, when thi parameter i decreaed the proce ha le energ requirement until it reach a critical value, too 850

5 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, Fig 3 Dnamic behavior of the Petluk ditillation column when i fixed to one and variou value of, in a two point compoition control, when the input variable are elected in accordance with it effect over the output variable Regarding then merit of the numerical experimentation preented above, the following comment mut be done: (i) when a candidate of input variable that can be habituated i found, it mut be elected b preference in which have the greater effect over the output variable (ii) The input variable can be habituated mut not provoke a ignal conflict For example, conidering the two point cae the wort behaviour wa obtained when SL, wa paired off with L, to control the ditillate compoition, becaue both are near and began a competition (iii) The value of the habituating parameter ha a direct impact on the performance of the controller Thi obervation ugget the exitence of an optimal value of the habituating parameter (iv) When the pair off the variable and the value of the habituating parameter are appropriate elected thi reound in economic aving, becaue mall internal flow are obtained IV CONCLUSIONS A habituating control approach wa ued to balance the eparation tak provided b the ditillation column and the prefractionator of a Petluk ditillation configuration It wa oberved that an appropriate election of variable to be habituated reound in economic aving, becaue mall internal flow are obtained and then le refrigerant and heat agent will be ued Fig 4 Dnamic behaviour of the Petluk ditillation column for variou value of the habituating parameter in two point compoition control, when the input variable are elected in accordance with it effect over the output variable The main idea wa to include the liquid ide tream, SL, SV, that uuall are not and the vapor ide-tream emploed for control purpoe, in traditional two and three point PI diagonal tructure A a reult, with an appropriate election of the pairing variable, under expected operating condition (that change in the charge compoition to the Petluk column and change in the et point) the reection time can be reduced and even more le energ requirement, can be found, giving a a conequence a better performance with repect to traditional diagonal PI compoition control configuration REFERENCES [] H Ling and W Luben, New control tructure for divided-wall column, In Eng Chem Re, vol 48(3), pp , 009 [] H ence and P Mize, Comprehenive proce invetigation methodolog for energ-integrated ditillation, in Proc Of 7 th European Smpoium on Computer Aided Proce Engineering (ESCAPE), 00, vol4, Elevier, p883 [3] C Triantafllou and R Smith, The deign and optimiation of full thermall coupled ditillation column Tran Int Chem Eng, vol 70, pp8-3, 99 [4] FO Barroo-Muñoz, S Hernández, JG Segovia-Hernández, H Hernández-Ecoto, AF Aguilera-Alvarado, Thermall coupled ditillation tem: tud of an energefficientreactivecae, ChemBiochemEngQ,vol, pp 5-5, 007 [5] pppp [] R O Wright, Fractionation apparatu, US Patent 47 34, Ma 4,

6 R Solar-Gonzalez et al, / (IJCSIT) International Journal of Computer Science and Information Technologie, Vol (), 0, [7] D Ch Dixon, Degree of freedom in dnamic and tatic tem, Ind Eng Chem Fundam, vol (), pp 98-03, 97 [8] E A Wolff and S Skogetad, Operation of integrated three-product (Petluk) ditillation column, Ind Eng Chem Re, vol 34, pp , 995 [9] MA Henon, B A Ogunnaike, and J S Schwaber, Habituating Control Strategie for Proce Control, AIChE J, vol 4, pp 04-8, 995 [0] Muralikrihna, P Madhavan, and S S Shah, Development of dividing wall ditillation column deign pace for a pecified eparation, Tran Int Chem Eng, vol 80, pp 55-, 00 [] J Alvarez-Ramíez, R Monro-Loperena and R Solar, Limitation in the operation and control of continuou middle-veel ditillation column with a draw tream, Ind Eng Chem Re, vol 44, pp 4-49, 005 [] M Barolo and C A Papin Improving dual compoition control in continuou ditillation column, AIChE J, vol 4, pp 4-59, 005 [3] T L Waburn and J D Seader, in Proceeding of the nd International Conference on Foundation of Computer-Aided Proce Deign; CACHE: Ann Arbor, MI, 984; p 75 85