Optimization of an Extractive Dividing Wall Column Using Genetic Algorithms

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1 20 th European Symposum on Computer Aded Process Engneerng ESCAPE20 S. Perucc and G. Buzz Ferrars (Edtors) 2010 Elsever B.V. All rghts reserved Optmzaton of an Extractve Dvdng Wall Column Usng Genetc Algorthms Crstofer Bravo-Bravo a, Juan Gabrel Segova-Hernández a, Salvador Hernández a, Clauda Gutérrez-Antono b, Adrán Bonlla-Petrcolet c, Abel Brones-Ramírez d a Unversdad de Guanajuato, Campus Guanajuato, Departamento de Ingenería Químca, Dvsón de Cencas Naturales y Exactas, Nora Alta s/n, , Guanajuato, Mexco. Emal: gsegova@qujote.ugto.mx b CIATEQ, A.C., Av. del Retablo 150, Col. Fovssste, 76150, Querétaro, Querétaro, Méxco. c Insttuto Tecnológco de Aguascalentes, Departamento de Ingenería Químca, Av. Adolfo López Mateos #1801 Ote. Fracc. Bonagens, 20256, Aguascalentes, Aguascalentes, Méxco d Innovacón Integral de Sstemas S.A. de C.V., Calle 2 No. 125 Interor 13 Parque Industral Jurca, 76120, Querétaro, Querétaro, Méxco. Abstract Ths work proposes an extractve dvdng wall dstllaton column, optmal desgns for whch are obtaned through a constraned stochastc multobjectve optmzaton technque. The stochastc procedure allows manpulate 15 varables smultaneously; sx are contnuous and the rest of them are nteger. All resultng optmal desgns are rgorous, snce the optmzaton procedure s coupled to Aspen Plus TM. Several case studes are used to show the feasblty of performng extractve separatons n dvdng wall dstllaton columns. The numercal performance shows that ths method appears to be robust and sutable n the desgn of ntensfed dstllaton systems (wth dvdng wall). Keywords: dvdng wall column, energy savngs, optmzaton, genetc algorthms. 1. Introducton Data from the Unted States Department of Energy ndcate that dstllaton columns n the U.S. consume 5.07 mllon TJ per year; ths s 43% of the total net nstalled capacty of the 439 nuclear power plants n operaton worldwde (Plesu et al., 2008). It s clear that the man dsadvantage of dstllaton columns s ther hgh energy consumptons. Motvated by the large energy requrements of dstllaton, researchers have developed several column arrangements that can brng savngs n both energy and captal cost. Reported studes reveal that the fully thermally coupled dstllaton system (also called the Petlyuk column) provdes the maxmum energy reducton n dstllaton columns. In most cases, ths s mplemented n the form of a dvdng wall column (DWC), n whch both columns are nstalled n a sngle shell. Ths reduces nvestment cost by 25%, operatng cost by 35%, and space requrements by 40%, as compared to the conventonal column system (Schultz et al., 2002). Azeotropc and low-relatve volatlty mxtures are commonly encountered n the fne-chemcal and specalty ndustres, and many chemcal processes depend on effcent and economcal methods for ther separaton. These mxtures can be separated n a dstllaton column by alterng

2 1782 C. Bravo-Bravo et al. relatve volatltes or shftng the azeotropc pont to a more favorable poston. Extractve dstllaton s defned as dstllaton n the presence of a mscble, hghbolng, and relatvely non-volatle component, the solvent, whch forms no azeotrope wth the other components n the mxture. The method of extractve dstllaton uses a separaton solvent, whch s generally nonvolatle, has a hgh bolng pont and s mscble wth the mxture, but does not form an azeotropc mxture. The solvent nteracts dfferently wth the components of the mxture, thereby causng ther relatve volatltes to change. The optmzaton of a complex dstllaton system (as extractve dstllaton) s usually characterzed as beng of large problem sze, snce the tremendous number of strongly nonlnear equatons results n serous dffculty n solvng the model. By consequence, ts solvng wth local optmzaton methods s not relable because they generally converge to local optmums. Durng the last years, the development and applcaton of determnstc and stochastc global optmzaton strateges have ncreased n many areas of Chemcal Engneerng. Partcularly, genetc algorthms optmzaton methods are very attractve for engneerng applcatons due to ts relablty and smplcty n numercal mplementaton. Moreover, n 2008 Hernández studed the separaton of a typcal mxture of ethanol and water from a fermentaton process. The results show that the extractve dvdng wall column can produce energy savngs of ca. 30% n comparson to a conventonal extractve dstllaton column. Then, studes must be done on the complex extractve dstllaton systems relatng to optmal desgn and optmzaton. In ths study we analyze the feasblty of separatng dfferent mxtures usng an extractve dvdng wall column, EDWC, Fgure 1. The desgn and optmzaton were carred out usng, as a desgn tool, a mult-objectve genetc algorthm wth restrctons coupled wth the process smulator Aspen PlusTM, for the evaluaton of the objectve functon, ensurng that all results obtaned are rgorous. To the best of our knowledge, multobjectve stochastc methods have not been reported for process desgn of extractve dvdng wall columns. The numercal performance shows that ths method appears to be robust and sutable n the desgn of extractve dvdng wall columns. Fgure 1. Extractve dvdng wall dstllaton column (EDWC). 2. Optmzaton methodology The objectves of the optmzaton problem for the desgn of extractve dvng wall columns nclude mnmzaton of total number of stages on both sdes of the shell (man

3 Optmzaton of an Extractve Dvdng Wall Column Usng Genetc Algorthms 1783 column and postfractonator accordng to Fgure 1, the extractng agent flow, and the heat duty of the sequence, but constraned by the desred purtes and recoveres,.e.: Mn ( Q, N, F ) = f ( R, N, N, F, F, N, F, ) subject to y x m m EA F, EA k k PS o (1) where R s the reflux rato, N F, s the number of the feed stage and N s the number of stages of column of the sequence, F EA s the extractng agent flow, F k and N k are the value and locaton of the nterconnecton flow k. Also, the product stream flows, F PS,o, are manpulated, due to ths also beng requred to manage the recoveres of the components along wth ther purtes; and are the vectors of obtaned and requred purtes and recoveres for the m components, respectvely. In the extractve dvdng wall dstllaton column there are four objectves to mnmze: the number of stages n each sde of the shell, the extractng agent flow, and the heat duty of the sequence. For these sequences the objectves are n competton, so they have to be optmzed smultaneously. The manpulated varables nclude reflux rato, total number of stages, the stage number and value of lqud and vapor nterconnecton flows, product streams flows, and extractng agent flow. The multobjectve genetc algorthm works as follows: For each run, a feasble ntal desgn of the EDWC s gven as ntal soluton to the algorthm; from ths ntal soluton the algorthm generates N ndvduals to make up the ntal populaton. The manpulated varables of each of the N ndvduals are sent to Aspen Plus to perform the smulaton; then, the algorthm retreves, from Aspen Plus, the values of objectve functons and constrants for each ndvdual. Wth the retreved nformaton the populaton s dvded n subpopulatons accordng to the number of satsfed constrants; at ths tme, the best ndvduals are those that satsfy the c constrants, followed by those ndvduals that reach c-1 constrants, and so on. At the end, a set of non-domnated optmal desgns of the extractve dvdng wall dstllaton columns are obtaned. More detals of the method can be found n Gutérrez-Antono and Brones-Ramírez (2009). 3. Case of study Optmal desgns of the extractve dvdng wall dstllaton columns were obtaned for four bnary mxtures wth dfferent extractng agents (Table 1). For the extractve dvdng wall dstllaton sequences we used 2500 ndvduals and 40 generatons as parameters of the genetc algorthm, wth 0.80 and 0.05 of crossover and mutaton fracton. Phase equlbrum of these mxtures s calculated wth the soluton model UNIQUAC for all mxtures. For all mxtures studed, the purtes and recoveres were fxed at 99% for the compostons of the products and the extractng agent. Table 1. Mxtures analyzed. Mxture Feed components Extractng agent Feed Flow, (kgmol/h) Feed composton (Mol fracton) M1 n-heptane/toluene Anlne /0.5 M2 Tetrahydrofuran/Water 1,2-Propanedol /0.1 M3 Isopropyl alcohol/water Dmethyl sulfoxde /0.5 M4 Acetone/Water Octanoc acd /0.5

4 1784 C. Bravo-Bravo et al. 4. Results In ths secton we analyze the resultng Pareto fronts of the extractve dvdng wall dstllaton columns for the dfferent mxtures studed. We begn wth a detaled analyss of mxture M1. For M1 we calculate the Pareto front usng, as desgn tool, the multobjectve aforementoned genetc algorthm. Fgure 2 shows the Pareto front for mxture 1, whch ncludes the objectves to mnmze: heat duty of the sequence, extractng agent flow, and the number of stages on both sdes of the shell. The frst observaton s that a dvdng wall dstllaton column can perform an extractve separaton, proof of ths are the 25 optmal desgns that made up the Pareto front. These optmal desgns satsfy the specfed purtes and recoveres wth dfferent structures and solvent flows, but always wth the lowest energy possble. Thus, the engneer can choose the best desgn for hs partcular needs. Fgure 2. Pareto front of extractve dvdng wall dstllaton columns for mxture M1. Each desgn n the Pareto front s an optmal desgn, and ths set ncludes desgns from mnmum number of stages to mnmum reflux rato, along wth all desgns between these extremes. Also, from ths fgure we can observe a good dversty n the desgns that made up the Pareto front; solvent flows, number of stages and heat dutes cover a wde range of values. Now, wth respect to the structure of the man column of all optmal desgns of the Pareto front, we can easly observe that the proportons between the dfferent stages are kept when the number of stages of the man column s ncreased. From ths fgure, we can easly observe lnear relatonshps between the dfferent feed and product flows. Also, we notce that, n spte of the sze of the postfractonator varyng consderably, the locaton of the sde stream stage s kept nearly constant. Thus, the sze of the postfractonator vares, but the separaton performed s the same for all cases. In the man column, (frst sde of the shell) the total number of stages vares around 53, wth 51 and 57 as the lowest and hghest values, respectvely. On the other hand, n the postfractonator (second sde of the shell), the number of stages vares consderably, from 12 to 28; n other words, ths means that the sze of man column remans almost constant, whle the Pareto front s made up of wth the varatons n the structure of the postfractonator. Moreover, the rato of flows extractng agent/feed vares from 1.55 to 2.95, wth 1.88 beng the average rato, whch means that, n spte of all the nterconnecton flows, the rato value does not ncrease consderably; therefore, compettve operatng costs can be expected. Also, t appears that the nterconnecton

5 Optmzaton of an Extractve Dvdng Wall Column Usng Genetc Algorthms 1785 flows of optmal desgns present a lnear relatonshp between one another. Fnally, t was found that the optmum energy consumpton desgn can be related to the mnmum total annual operatng cost (calculated usng the method of Guthre), mnmum greenhouse gas emssons, and hgher thermodynamc effcences. We clearly observe wth the ncrease n solvent flow and total number of stages, the total annual cost also ncreases. From all desgns of the Pareto front, we have selected the optmal desgn of lowest total annual cost and the one of lowest CO2 emssons. In Table 2, we can observe that, for ths mxture, the optmal desgn represents the lowest annual cost and the lowest greenhouse gas emssons. The thermodynamc effcency of ths sequence s 23.70%, whch s slghtly hgher than the effcency of a conventonal extractve sequence, 21.42%; ths value was obtaned from an optmzaton of a conventonal sequence only for comparatve purposes. It s therefore mportant to remark that the thermodynamc effcency of the extractve coupled system s slghtly hgher than the conventonal one. Table 2. Optmal desgn of the extractve dvdng wall column wth lowest total annual cost and lowest greenhouse gas emssons, M1. Desgn varable Value Operatng pressure (atm) 1.0 Reflux rato n column B Number of stages of column B1 56 Number of stages of column B2 19 Feed stage n column B1 33 Feed stage of the extractve agent 15 Stage of the nterconnecton flow 22 FV1 Stage of the nterconnecton flow 44 FV2 Thermodynamc effcency (%) CO2 emssons (kg/h) 2, Total annual cost ($/year) 2,477, Wth respect to the structure of the dvdng wall columns, n the case of mxtures M2- M4, we found tendences n the locaton of nterconnecton and feed streams. For all mxtures, we observe that the extng streams are always located at the extremes of the columns, wth all the feeds between them. After the FL1 nterconnecton flow, the frst stream leavng the column, the solvent flow s present. Locatons of FL2, FV1 and feed are always between the solvent flow stage and FV2 nterconnecton flow. The dstrbuton of the nterconnecton and feed flows obeys the basc prncple of ncreasng the nteracton between the mxture and the solvent as long as possble; ths s the reason why the ext flows are located at the ends of the column. In the postfractonator, the locaton of the sde stream wth respect to the number of stages s the same for all optmal Pareto front desgns; the sze of the postfractonator vares, but snce the specfcatons of the separaton are the same, the rato of number of stages remans unchanged. The range for the mnmum-maxmum rato of the solvent/feed flows oscllates around [ ], [ ] and [ ] for mxtures M2, M3, and M4. These ratos show that the presence of four nterconnecton flows does not necessarly ncrease the solvent flow; therefore, compettve operatng costs can be expected. Moreover, for all mxtures we found lnear relatonshps between the nterconnecton vapor and lqud

6 1786 C. Bravo-Bravo et al. flows. The rato between FV2 and FV1 oscllates around 1.5 for mxtures M1, M2, and M3, but for mxture M4 ths value s around 3.2. The value of ths rato depends on the modfed nature of the mxture, after the addton of the extractng agent. 5. Conclusons In ths study, a multobjectve stochastc procedure s presented to obtan optmal desgns of extractve dvdng wall dstllaton columns. The stochastc procedure allows manpulaton of 15 varables smultaneously; sx beng contnuous and the rest beng nteger. All resultng optmal desgns are rgorous, snce the optmzaton procedure s coupled to Aspen Plus. The results show that dvdng wall dstllaton columns are a feasble opton to separate extractve mxtures, despte ther hghly non-deal nature. The Pareto fronts obtaned for extractve dvdng wall dstllaton columns present good dversty, n terms of the dfferent structures of the columns, and also wth respect to energy consumpton. Moreover, t was found that the optmum energy consumpton desgn can be related to the mnmum total annual operatng cost, mnmum greenhouse gas emssons, and hgher thermodynamc effcences. The Pareto front s obtaned from keepng constant the structure of the man column, and varyng the sze of the postfractonator; ths behavor s because the hard separaton s preferably performed n the man column. The desgn of the man column remans almost constant; however, the postfractonator structure vares consderably. In general, the rato of solvent flows wth respect to feed s around 1.6, nsde the range recommended by the heurstc rule for conventonal extractve sequences. For all cases, there are lnear relatonshps between the nterconnecton flows of the dvdng wall dstllaton columns. 6. Acknowledgements The fnancal support of ths work provded by Unversdad de Guanajuato, Insttuto Tecnológco de Aguascalentes, CONCyTEG and CONACyT (Mexco) s gratefully acknowledged. References C. Gutérrez-Antono, A. Brones-Ramírez, 2009, A. Pareto front of Ideal Petlyuk sequences usng a multobjectve genetc algorthm wth constrants, Comput. Chem. Eng., 33, 454. S. Hernández, 2008, Analyss of Energy-Effcent Complex Dstllaton Optons to Purfy Boethanol, Chem. Eng. Technol., 31, 597. A.E. Plesu, J. Bonet, V. Plesu, G. Bozga, M.I. Galan, M.I. 2008, Resdue Curves Map Analyss for Tert-Amyl Methyl Ether Synthess by Reactve Dstllaton n Knetcally Controlled Condtons wth Energy-Savng Evaluaton, Energy, 33, M.A. Schultz, D.G. Stewart, J.M. Harrs, S.P. Rosenblum, M.S. Shakur, D.E. O Bren, 2002, Reduce Costs wth Dvdng-Wall Columns, CEP Magazne, 64.