Reduce Distillation Column Cost by Hybrid Particle Swarm and Ant


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1 From the SelectedWorks of Dr. Sandp Kumar Lahr Summer July 20, 2016 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm and Ant Dr. Sandp k lahr chnmaya lenka Avalable at:
2 Journal of Chemcal Engneerng Research Updates, 2016, 3, Reduce Dstllaton Column Cost by Hybrd Partcle Swarm and Ant Colony Optmzaton Technque Sandp Kumar Lahr 2 and Chnmaya Prasad Lenka 1,* 1 Improvement Engneer, Sadara Chemcal Company, Saud Araba 2 Manager, Scentfc Desgn, USA Abstract: A novel method for optmum desgn of plate type dstllaton column ntegratng the equlbrum, hydraulc and economc calculatons s presented n the present paper. The present study explores the use of nontradtonal optmzaton technque: called hybrd Partcle swarm optmzaton (PSO) and Ant colony optmzaton (ACO), for desgn optmzaton of plate type dstllaton column from economc pont of vew. The optmzaton procedure nvolves the selecton of the major plate geometrc parameters such as hole dameters, rato of downcomer area to tower area, wer heght, fractonal hole area n tray, tray spacng, tower dameter etc. and mnmzaton of total annual cost s consdered as desgn target subjected to operatonal constrants lke floodng, weepng entranment, qualty specfcatons etc. The soluton space of such type of problem s very complex due to presence of varous nonlnear constrants and multple mnma. Hybrd Partcle swarm optmzaton and Ant colony optmzaton (PSACO) technque s appled to deal wth such complexty. The partcle swarm optmzaton apples for global optmzaton and ant colony approach s employed to update postons of partcles to attan rapdly the feasble soluton space. Ant colony optmzaton works as a local search, wheren, ants apply pheromoneguded mechansm to update the postons found by the partcles n the earler stage. The presented hybrd Partcle swarm optmzaton and Ant colony optmzaton (PSACO) technque s smple n concept, few n parameters and easy for mplementatons. Furthermore, the PSACO algorthm explores the good qualty solutons quckly, gvng the desgner more degrees of freedom n the fnal choce wth respect to tradtonal methods. One case study s presented to demonstrate the effectveness and accuracy of proposed algorthm. The PSACO approach s able to reduce the total cost of dstllaton column as compare to cost obtaned by commercal smulator. Keywords: Partcle swarm optmzaton, ant colony optmzaton, hybrd partcle swarm and ant colony optmzaton, dstllaton column desgn, plate type dstllaton column. 1. INTRODUCTION Cut throat global competton and shrnkng proft margn forced the chemcal process ndustres (CPI) to ntrospect the tradtonal desgn methodology of process equpments and compel the desgner to take cost (both ntal captal cost and future energy cost) as mportant desgn crtera durng desgn phase. Plate type dstllaton columns (PTDC) are not only contrbuted a major porton of captal nvestment n new projects but also the major consumers of energy n CPI. Because of ther sheer large numbers n any CPI, small mprovement n plate type dstllaton column desgn strateges offer bg savng opportuntes. Computer software marketed by companes such as Aspen plus, Hysys and PROII are used extensvely n the desgn and ratng of plate type dstllaton column. The classcal approach to plate type dstllaton column (PTDC) desgn n these smulators nvolves a sgnfcant amount of tralanderror because an acceptable desgn needs to satsfy a number of constrants (e.g. product purty specfcatons, floodng, entranment, downcomer velocty, utltes constrants, weepng and allowable pressure drops etc.) (Kster 1992) [1]. Varous desgn optons for the dstllaton *Address correspondence to ths author at the Improvement Engneer, Sadara Chemcal Company, Saud Araba; Tel: ; Fax: ; Emal: EISSN: X/16 column ncludng the varatons n the hole dameter, tray spacng, rato of downcomer area to column area, fractonal hole area based on actve area etc. are ncorporated n these software as an user nput. Typcally, for hydraulc calculatons, a desgner chooses varous geometrcal parameters mentoned above based on experence or heurstc to arrve at a possble desgn. The fnal desgn should satsfy a number of hydraulc constrants such as percentage jet floodng, maxmum downcomer velocty, mnmum downcomer back up, maxmum lqud flow rate per unt length of wer, actual mnmum vapor velocty to avod weepng etc. (Kster 1992) [1]. Ths wll ensure that the dstllaton unt wll perform well n actual plant. If the desgn does not satsfy the constrants, a new set of geometrcal parameters must be chosen to check f there s any possblty of reducng the dstllaton column cost whle satsfyng the constrants. Although well proven, ths knd of approach s tme consumng and may not lead to cost effectve desgn as no cost crtera are explctly accounted for. Snce several dscrete combnatons of the desgn confguratons are possble, the desgner needs an effcent strategy to quckly locate the desgn confguraton havng the mnmum column cost. Thus the optmal desgn of plate type dstllaton column (PTDC) can be posed as a large scale, dscrete, combnatoral optmzaton problem Avant Publshers
3 2 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka In lterature, attempts to automate and optmze the PTDC desgn process have been proposed for a long tme and subject s stll evolvng. Snnot (1989) [2] suggested the hydraulc calculatons of dstllaton column and contnuously modfy the szng parameters lke column dameter, downcomer area, tray spacng etc. to meet varous constrants to avod floodng, entranment, weepng etc. Kster (1992) [1] has provded a detaled hydraulc desgn methods based on emprcal equatons provded by varous researchers over the decades. Detaled desgn companes across the world use ther own correlatons and own heurstc to arrve at a functonally acceptable desgn. Agan, desgners have to contnuously evolve the desgn parameters to meet varous constrants. To mprove and optmze such desgn, Luyben (2006) [3] has ncorporated a cost functon to evaluate the fnal desgn. Man am s to evaluate the total number of trays, reflux rato, tray dameter and feed tray locaton of the column usng Aspen plus smulator, whch corresponds to a mnmum total annual cost. Detal of hydraulc calculatons and evaluaton of tray and hydraulc parameters are not ncluded n hs desgn. As seen from lteratures, the detal tray hydraulc calculatons wth cost as desgn crtera s an unexplored area of research. The lmted avalable publshed lteratures to evaluate optmum reflux rato and number of trays normally used tradtonal optmzaton technque (Luyben 2006) [3]. Most of the tradtonal optmzaton technques based on gradent methods have the possblty of gettng trapped at local optmum dependng upon the degree of nonlnearty and ntal guess. Typcal propertes of such problems are the exstence of dscontnutes, the lack of analytcal representaton of the objectve functon, complex cost functon, multple mnma and nose dssemnaton. Hence, these tradtonal optmzaton technques do not ensure global optmum and also have lmted applcatons. In these crcumstances, the applcablty and effcency of classcal optmzaton algorthms are questonable, gvng rse to the need for the development of dfferent optmzaton methods. Partcle swarm optmzaton (PSO) was developed (Kennedy and Eberhart 1995) [4] as a stochastc optmzaton algorthm based on socal smulaton models. Snce ts development, PSO has ganed wde recognton due to ts ablty to provde solutons effcently, requrng only mnmal mplementaton effort. Ths s reflected by ncreasng number of journal papers wth the term partcle swarm n ther ttles publshed by three major publshers, namely Elsever, Sprnger, and IEEE, durng the years Also, the potental of PSO for straghtforward parallelzaton, as well as ts plastcty,.e., the ablty to adapt easly ts components and operators to assume a desred form mpled by the problem at hand, has placed PSO n a salent poston among ntellgent optmzaton algorthms. In the early 1990s, ant colony optmzaton (ACO) was ntroduced by M. Dorgo, (1992) [5] as a novel nature nspred metaheurstc for the soluton of hard combnatoral optmzaton (CO) problems. ACO belongs to the class of metaheurstcs, whch are approxmate algorthms used to obtan good enough solutons to hard CO problems n a reasonable amount of computaton tme. The nsprng source of ACO s the foragng behavor of real ants. When searchng for food, ants ntally explore the area surroundng ther nest n a random manner. As soon as an ant fnds a food source, t evaluates the quantty and the qualty of the food and carres some of t back to the nest. Durng the return trp, the ant deposts a chemcal pheromone tral on the ground. The quantty of pheromone deposted, whch may depend on the quantty and qualty of the food, wll gude other ants to the food source. As t has been shown n (Dorgo et al. 1999)[6], ndrect communcaton between the ants va pheromone trals enables them to fnd shortest paths between ther nest and food sources. Ths characterstc of real ant colones s exploted n artfcal ant colones n order to solve CO problems (Shelokar et al. 2007) [7]. It s known that the PSO may perform better than the EAs n the early teratons, but t does not appear compettve when the number of teratons ncreases (Angelne 1998) [8]. To mprove ths character of PSO, one of the methods s hybrdzng PSO wth other approaches such as ACO (Kaveh and Talatahar 2008)[9]. The resulted method, called Partcle Swarm Ant Colony Optmzaton (PSACO), was ntally ntroduced by Shelokar et al. (2007) [7] for solvng the contnuous unconstraned problems and by Mozafar et al. (2006) [10] for reactve power market smulaton. PSACO utlzed PSO as a global search and the dea of ant colony approach worked as a local search and updated the postons of the partcles by appled pheromoneguded mechansm. In vew of the encouragng results found out by the above researchers, an attempt has been made n the present study to apply a new strategy called Partcle
4 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 3 Swarm Ant Colony Optmzaton (PSACO) to the plate type dstllaton column (PTDC) desgn problem. The man objectve of ths study s to explore the effectveness of ths new technque n the desgn optmzaton of PTDC from economc pont of vew. Ablty of the hybrd PSACO based technque s demonstrated usng case study. The paper s organzed as follows: secton 2 descrbes desgn of optmum PTDC; Secton 3 llustrates the case study and varous constrants used n ths study to optmally desgn the PTDC. The bref ntroducton of PSO, ACO and hybrd PSACO s gven n secton 4. Secton 5 llustrates the applcaton of the PSACO algorthm n case study. Sectons 6 summarze the results and advantages of such applcatons n PTDC desgn. Fnally Secton 7 gves a summary of the study. 2. THE OPTIMAL DISTILLATION COLUMN DESIGN PROBLEM Tradtonal desgn approaches (Kster1992, Snnot1989) [1, 2] are based on teratve procedures whch gradually change the desgn and geometrc parameters of tray untl satsfy a gven qualty specfcaton and set of hydraulc and operatonal constrants lke floodng, weepng, entranment etc. As explaned earler, the tradtonal hydraulc method of PTDC desgn (Kster1992) [1] does not take nto account the cost functon durng desgn stage. The proposed new optmzaton procedure nvolves the selecton of the major plate geometrc parameters such as hole dameters, rato of downcomer area to tower area, wer heght, fractonal hole area n tray, tray spacng, tower dameter etc. and mnmzaton of total annual cost s consdered as desgn target subjected to operatonal constrants lke floodng, weepng entranment, qualty specfcatons etc. The procedure for optmal PTDC desgn ncludes the followng step: a. Smulaton of column n any commercal smulators (Aspen plus, Hysys or PROII) for the product purty requred. b. Estmaton of maxmum and mnmum vapor and lqud flow rates for the turndown rato requred. c. Collecton of physcal propertes from the above converged column smulaton. d. Make a tral plate layout: column dameter, down comer area, actve area, hole area, hole sze, wer heght etc. and select a tral plate spacng (values of all the search varables gven n Table 1 s assumed wthn ther specfed lmt). Table 1: Optmzaton Varables wth ther Upper and Lower Lmt Optmzaton Varable Varable Notaton Varable Name Lower and Upper Lmt x 1 d t Tower dameter (m) d mn x 2 tray space Tray spacng (m) x 3 v type valve type (0=seve, 1=round, 2=rectangular) 00 x 4 ϕ Hole area (fracton of bubblng area) x 5 d h Hole dameter (m) x 6 deck t Deck thckness (m) x 7 passcfg Pass confguraton x 8 h w Outlet wer heght (m) x 9 w dct Top downcomer (DC) wdth (m) 0.11(d t)0.20(d t) x 10 w dcb Bottom DC wdth (m) 0.11(12d t)0.20(12d t) x 11 w dcs Bottom DC sump wdth (m, 0=none) 00 x 12 c dc DC clearance (m) x 13 ch w Center outlet wer heght (m) x 14 w cdct Top center DC wdth (m) 0.11(d t)0.20(d t) x 15 w cdcb Bottom center DC wdth (m) 0.25(d t)0.49(d t) x 16 w cdcs Bottom center DC sump wdth (m, 0=none) 00 x 17 c w Center DC clearance (m) x 18 stgno Total number of stage () x 19 feedstg Feed stage number from top () 423
5 4 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka Table 2: Dfferent Constrants and Ther Lmt Optmzaton Varable Varable Notaton Varable Name Lower and Upper Lmt g 1 %Jet flood Fnal percent of jet flood by most approprate method (%) g 2 %Downcomer flood Gltch method percent downcomer flood (%) 050 g 3 %Downcomer Back up Gltsch method DC backup as % of tray spacng (%) 050 g 4 Wer load Wer loadng (gpm/n wer) 213 g 5 u ldc Clear lqud downcomer entrance velocty (m/s) g 6 dp tray pressure drop (Pa) g 7 ar dct Top Downcomer to tower area rato (%) 820 g 8 ar dcb Bottom Downcomer to tower area rato (%) 820 g 9 FPL Flow path length (m) g 10 w frac Weep fracton g 11 e frac Entranment fracton (of vapor rate) e. Estmaton of all the constrants gven n Table 2 such as jet flood percentage, downcomer flood percentage, down comer back up, weep fracton, entranment fracton, pressure drop etc. by usng varous correlatons gven n appendx 1. f. Evaluaton of the captal nvestment, operatng cost and the objectve functon. g. Utlzaton of the optmzaton algorthm to select a new set of values for the desgn varables (gven n Table 1) untl all the constrants (gven n Table 2) are wthn ther specfed lmts. h. Iteratons of the prevous steps untl a mnmum of the objectve functon s found. Fnalze desgn: draw up the plate specfcaton and sketch the layout. 3. CASE STUDY To demonstrate the effectveness of proposed algorthm, a multcomponent dstllaton problem was chosen from Lterature (Flpe Soares Pnto, Roger Zemp, Megan Jobson, Robn Smth, 2011)[11]. Present work has taken nto account the detal hydraulc calculatons and mplement hybrd PSACO algorthm to optmze the cost. Same cost functon was used n present study as n Luyben (2006)[3]. For smplcty 5 component dstllaton column has chosen, however, present algorthm can also be easly appled to complex mult component dstllaton also Dstllaton Problem Descrpton A lowest cost plate type dstllaton column has to be desgned to separate a 5 component mxture of 10 mole% propene, 20 mole% propane, 40 mole% sobutane, 20 mole% nbutane and 10 mole% n pentane. Feed rate s 1000kmol/hr. wth 0.4 vapor fracton and feed temperature and pressure are C and 400kPA respectvely. Fnal product qualty specfcatons are 99.5% top recovery of nbutane and 99.5% bottom recovery of npentane. As a startng, base case dstllaton column has 29 theoretcal stages wth feed stage locaton 11 from top. Number of stages and feed stage locaton can be vared to desgn the lowest cost column. The orgnal problem can be set as; Mnmze Total cost, C tot x Subject to g ( x)! 0 where = 1,2,...,m ( ) where x j L! x j! x j U j = 1,2,..., N Where x s the vector of optmzaton varables as gven n Table 1 wth ther correspondng lower upper lmts L ( x j ) and U ( x j ). Total cost C tot s taken as the objectve functon and detal gven n secton 3.1. The set of constrants g(x) are gven n Table 2 along wth ther lmts. The calculatons of the constrants are summarzed n appendx 1 and the meanng of the constrants summarzed n secton 3.3. These constrants are then converted to nequaltes n same format as stated above wth the help of ther lmts (Table 2). Consderng mnmzaton of PTDC cost as the objectve functon, mproved verson of Partcle swarm optmzaton technque s appled to fnd the
6 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 5 optmum desgn confguraton wth product purty and hydraulc parameters (Table 2) as the constrant Objectve Functon Total cost C tot s taken as the objectve functon, whch ncludes captal nvestment (C cap), energy cost (C e); C tot = C cap Payback perod + C e (1) Captal nvestment ncludes column captal cost, (C col) and reboler and condenser captal cost, (C HE); C cap = C col + C HE (2) Column captal cost depends on column heght and dameter as follows: C col = 17640d t H (3) Where d t dameter and H tower s column heght. H = 1.2( N stage! 2)S tray (4) Where N stage s total number of stages and S tray s tray spacng. Heat exchanger captal cost can be calculated as follows: C HE = 7296( Area condenser + Area Reboler ) 0.65 (5) of ndustral desgn companes are also followed to set the lmts of these varables. For column dameter, a mnmum dameter (d mn s calculated based on 80% jet floodng crtera (Kster 1992) [1]. The pass confguraton feld desgnates one or two pass trays and the specfc orentaton for two pass trays. A value of 1 desgnates a onepass tray and s the default f an entry error s made. A value of 2A desgnates a twopass tray wth lqud flowng from the center to the sde downcomer. A feld value of 2B desgnates a twopass tray wth lqud flowng from the sde to the center downcomer Operatonal and Hydraulc Constrants Though lowest cost column whch obey the product purty specfcatons s the man selecton crtera for PTDC but ths s not the only crtera for commercal plants. The concept of a good desgn nvolves aspects that cannot be easly descrbed n a sngle economc objectve functon e.g. floodng, entranment, weepng, pressure drop, tray geometrc constrants etc. These crtera though emprcal have a profound effect on PTDC performance n commercal plants. Operatng lmt of dstllaton tray s shown n the schematc of Fgure 1.These crtera are sometmes expressed as geometrc, hydraulc and servce constrants. Followng secton brefly descrbe the varous constrants used n the present study. More detal can be found n (Kster 1992, Snnot 1989) [1, 2]. Where; Area condenser = Q condenser U!t = Q condenser 852 ( )( 13.9) (6) Area reboler = Q reboler U! t Q reboler = ( 568) 34.8 ( ) (7) Energy cost s gven by; C E = Q Reboler HC steam (8) Where H s operatng hours and C steam s unt cost of steam Search Optmzaton Varables The varous search optmzaton varables are tabulated n Table 1 along wth ther lower and upper bounds. These upper and lower bounds are taken as per broad gudelnes gven by Kster(1992) & Snnot(1989) [1, 2]. In some nstances, best practces Fgure 1: Operatng lmt of a dstllaton column tray % Of Jet Flood The floodng condton fxes the upper lmt of vapor velocty. Jet flood s caused by massve lqud
7 6 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka entranment to the tray above due to large vapor veloctes. Target for jet flood on seve trays s between 40% and 82% of jet flood. At 82% of jet flood there s roughly a 99% probablty that the tower wll operate wthout jet floodng accordng correlaton (Kster 1992) [1]. At 99% of jet flood there s a 50% probablty that the tower wll not operate due to jet flood. Below 40% of jet flood the predctons are outsde the range of data used to develop the correlaton. Past operatng experence also suggests possble operatonal nstablty below 40% of jet flood % Of Down Comer Flood Down comer flood s caused by not enough down comer open area at the entrance to allow for vapor dsengagement,.e. the entrance velocty s too hgh. Target for % of down comer (DC) flood s to not exceed 50%, although the method used n ths work s the somewhat conservatve Gltsch method (Kster 1992) [1]. Ths method does not consder downcomer backup but rather s lookng at the approach to crtcal downcomer veloctes at whch pont vapors cannot dsengage from the lqud enterng the downcomer % Of Downcomer Backup Downcomer backup occurs when aerated lqud s backed up n the downcomer due to tray pressure drop, lqud heght on the tray and frctonal losses n the downcomer apron. Maxmum desgn downcomer backup s 50% of the tray spacng Wer Load Wer loadng s an ndcaton of the lqud loadng n the tower. Hgh wer loadng can result n jet flood. Wer load s calculated as lqud flow rate dvded by the length of the outlet wer. Wer load s best below 8 gpm per nch of wer and should not exceed 13 gpm/n to prevent premature flood. Wer load can be reduced by ncreasng the number of flow paths. Low wer loadng can result n loss of downcomer seals or spray regme. Below 2 gpm/n wer load, seal pans or nlet wers are requred to mantan downcomer seals Downcomer Entrance Velocty The maxmum velocty of clear lqud n the downcomer needs to be low enough to prevent chockng and to permt rse and satsfactory dsengagement of vapor bubbles from the downcomer lqud. Ths s most restrctve n systems that have a hgh foamng tendency. DC entrance velocty above 0.5 ft/sec s rsk for premature flood. For foamng systems, DC entrance velocty above 0.1 ft/sec s rsk for premature flood Dry Tray Pressure Drop For valves trays, dry tray pressure drop below 0.7 n of H 2 O s rsk for excessve weepng. For seve trays, the weep fracton estmates are more accurate than for valve trays and should be looked at more than dry tray pressure drop Top Downcomer to Tower Area Rato The downcomer from a tray must be adequate to carry the lqud flow plus entraned foam and froth. Ths foamy materal s dsengaged n the downcomer as only clear lqud flows onto the tray below. A mnmum 8% downcomer area s requred to prevent premature floodng Bottom Downcomer to Tower Area Rato A mnmum and maxmum downcomer area to tower area rato s requred to transfer lqud from top to bottom tray smoothly wthout floodng Flow Path Length The flow path length (FPL) s the average dstance travelled by the lqud leavng one downcomer to the wer of the next adjacent downcomer. If the FPL s too short, part of the lqud wll flow nto the downcomer wthout sgnfcant contact wth the vapor, whch wll result n a reducton of tray effcency. Too long FPL can lead to lqud short crcutng and msdstrbutons Weep Fracton The lower lmt of the operatng range occurs when lqud leakage through the plate holes becomes excessve. Ths s known as the weep pont. The vapor velocty at the weep pont s the mnmum value for stable operaton. The hole area must be chosen so that at the lowest operatng rate the vapor flow velocty s stll well above the weep pont. (Snnot1989) [2]. Best practce gudelnes for weep fracton are below Below 0.25, weepng can occur wthout sgnfcant loss n separaton effcency. For seve trays the weep fracton results are reasonably accurate and should be consulted for desgn. For valve trays the weep fracton estmates are more questonable especally for the float valves. As a result, the dry tray pressure drop s better ndcator for turndown desgn.
8 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Entranment Fracton As vapor veloctes ncrease, the amount of lqud entraned to the tray above ncreases. In some cases, the fracton of lqud entraned can be farly hgh even though jet flood s not an ssue. Ths creates back mxng and loss of effcency. Maxmum desgn lqud entranment fracton s 0.1% of jet flood s generally a better ndcator of potental tower performance, but f entranment fracton exceeds 0.1 whle stll below 82% of jet flood the engneer should consder the potental mpact of entranment on separaton effcency. However the values of the above constrants are dependent on the detaled desgn and very much problem specfc. In ths work the values of constrants are selected as per general gudelnes gven by Snnot (1989) and Kster (1992) [1, 2] and user s not restrcted to adhere these values. The value of these constrants must be judcously selected as they have a bg mpact on fnal soluton and cost. In case user does not have specfc restrcton on these values, the constrants should be kept as broad as possble. Ths wll facltate the lowest cost dstllaton column. Attempt has been made n ths work to apply PSO optmzaton technque to desgn a lowest cost dstllaton column and satsfy all of the above constrants. 4. HYBRID PARTICLE SWARM AND ANT COLONY OPTIMIZATION: AT A GLANCE 4.1. Partcle Swarm Optmzaton Partcle swarm optmzaton (PSO) was developed by Kennedy and Eberhart (1995) [4] as a stochastc optmzaton algorthm based on socal smulaton models. The algorthm employs a populaton of search ponts that moves stochastcally n the search space (Shelokar et al. 2007) [7]. Concurrently, the best poston ever attaned by each ndvdual, also called ts experence, s retaned n memory. Ths experence s then communcated to part or the whole populaton, basng ts movement towards the most promsng regons detected so far. The communcaton scheme s determned by a fxed or adaptve socal network that plays a crucal role on the convergence propertes of the algorthm. The development of PSO was based on concepts and rules that govern socally organzed populatons n nature, such as brd flocks, fsh schools, and anmal herds. Unlke the ant colony approach, where stgmergy s the man communcaton mechansm among ndvduals through ther envronment, n such systems communcaton s rather drect wthout alterng the envronment PSO Algorthm In PSO, canddate solutons of a populaton, called partcles, coexst and evolve smultaneously based on knowledge sharng wth neghborng partcles. Whle flyng through the problem search space, each partcle generates a soluton usng drected velocty vector. Each partcles modfes ts velocty to fnd a better solutons (poston) by applyng ts own flyng experence (.e. memory havng best poston found n the earler flghts) and experence of neghborng partcles (.e. best found soluton of the populaton). Partcles update ther postons and veloctes as shown below (Shelokar et al. 2007) [7]: v t +1 = w t v t + c 1 r 1 p ( t! x t ) + c 2 r 2 p g t! x t v t +1 = x t + v t+1 ( ) (9) (10) Where x t represents the current poston of partcle n soluton space and subscrpt t ndcates an teraton count p t s the bestfound poston of partcle up to teraton count t and represents the cogntve contrbuton to the search velocty v t. Each component of v t can be clamped to the range [!v max,v max ] to control excessve roamng of partcles outsde the g search space; p t s the global bestfound poston among all partcles n the swarm up to teraton count t and forms the socal contrbuton to the velocty vector r 1 and r 2 are random numbers unformly dstrbuted n the nterval (0, 1), whle c 1 and c 2 are the cogntve and socal scalng parameters, respectvely; w t s the partcle nerta, whch s reduced dynamcally to decrease the search area n a gradual fashon. The varable w t s updated as: ( ) W t = ( W max! W mn )* t max! t mn + W mn (11) t max Where w max and w mn denote the maxmum and mnmum of w t respectvely. t max are a gven number of maxmum teratons. Partcles fly toward a new poston. In ths way, all partcles P of the swarm fnd ther postons and apply these new postons to update ther ndvdual best p t ponts and global best p t g of the swarm. Ths process s repeated untl teraton count t = t max (a user defned stoppng crteron s reached).
9 8 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka 4.3. Ant Colony Optmzaton (ACO) ACO s a multagent approach that smulates the foragng behavor of ants for solvng dffcult combnatoral optmzaton problems, such as, the travellng salesman problem and the quadratc assgnment problem. Ants are socal nsects whose behavor s drected more toward the survval of the colony as a whole than that of a sngle ndvdual of the colony. An mportant and nterestng behavor of an ant colony s ts ndrect cooperatve foragng process. Whle walkng from food sources to the nest and vce versa, ants depost a substance, called pheromone on the ground and form a pheromone tral. Ants can smell pheromone, when choosng ther way, they tend to choose, wth hgh probablty, paths marked by strong pheromone concentratons (shorter paths). Also other ants can use pheromone to fnd the locatons of food sources found by ther nest mates. In fact, ACO smulates the optmzaton of ant foragng behavor (Shelokar et al. 2007) [7]. Recently there are few adaptatons of ACO for soluton of contnuous optmzaton problems. Motvated by Dr. Lahr, Applcatons of Metaheurstcs n Process Engneerng, Sprnger, Swtzerland, (2014) [12] n ths work, a smple pheromoneguded search mechansm of ant colony s mplemented whch acts locally to synchronze postons of the partcles of PSO to quckly attan the feasble doman of objectve functon Hybrd PSO and ACO Algorthm Ths secton descrbes the mplementaton of proposed mprovement n partcle swarm optmzaton usng an ant colony approach. The proposed method (Shelokar et al. 2007) [7], called, hybrd partcle swarm ant colony optmzaton (henceforth referred as PSACO) s based on the common characterstcs of both PSO and ACO algorthm, lke, survval as a swarm (colony) by coexstence and cooperaton, ndvdual contrbuton to food searchng by partcle (an ant) by sharng nformaton locally and globally n the swarm (colony) between partcles (ants), etc. PSACO utlzed PSO as a global search and the dea of ant colony approach worked as a local search and updated the postons of the partcles by appled pheromoneguded mechansm. The hybrdzaton of ths type of evolutonary algorthm are popular, partly due to ts better performance n handlng nose, uncertanty vagueness and mprecson. In general there are two mportant ssue n solvng global and hghly nonconvex optmzaton problem. These are; 1: Premature convergence The problem of premature convergence lead to lack of fath of fnal soluton. 2: Slow convergence Ths means, the soluton qualty does not mprove suffcently quckly. Above two ssues can be attrbuted to the soluton dversty that an algorthm can produce n the searchng process. In nature, the varsty s mantaned by the varety (Qualty) and abundance (quantty) of organsm at a gven place and tme. Smlarly at the begnnng of a search process n PSACO algorthm usually dversty s hgh and t decreases as the populaton move towards the global optmum. Hgh dversty n PSO algorthm may provde better guarantee to fnd the optmal soluton wth better accuracy, but ths wll lead to slow convergence, and thus there are some tradeoffs between convergence and accuracy. On the other hand, low dversty may lead to fast convergence whle sacrfcng the guarantee to fnd global optmalty and wth poor soluton accuracy. Hgh dversty of PSO algorthm encourages exploraton and low dversty does not necessarly mean explotaton because explotaton requres the use of landscape nformaton and the nformaton extracted from the populaton durng the search process. Ths clever explotaton at the rght tme and the rght place s done by ACO. To enable ths hybrdzaton of PSACO algorthm s used to promote dversty and local explotaton along the search for global optmum. The mplementaton of PSACO algorthms conssts of two stages. In the frst stage, t apples PSO whle ACO s mplemented n the second stage. ACO works as a local search, wheren, ants apply pheromoneguded mechansm to refne the postons found by partcles n the PSO stage. In PSACO a smple pheromoneguded mechansm of ACO s proposed to apply as local search (Shelokar et al. 2007) [7]. The proposed ACO algorthm handles P ants equal to the number of partcles n PSO. Each ant generate a soluton z t around p g t the global bestfound poston among all partcles n the swarm up to teraton count as; z t =!( p g t,!" ) (12) In eq. 12 we generate components of soluton vector z t whch satsfy Gaussan dstrbutons wth mean p g t and standard devaton σ, where, ntally at t=1 value of σ=1 and s updated at the end of each
10 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 9 Table 3: Pseudo Code for Hybrd PSO and ACO Algorthm Step 1. Step 1.1. Step 1.2. Step 1.3. Step 1.4. Step 1.5. Step 2. Step 2.1. Step 2.2. Step 2.3. Intalze optmzaton Intalze constants for PSO and ACO algorthm t max, P Intalze randomly all partcles postons x t and veloctes v t ( ) Evaluate objectve functon values as f x t Assgn best postons p t = x t wth f ( p t ) = f ( x t ), = 1,..., P best best 1 P g Fnd f t ( p t ) = mn{ f ( p t ),..., f ( p t ),.., f ( p t )} And ntalze p t Perform optmzaton Whle ( t! t max ) Update partcle postons x t and veloctes v t Evaluate objectve functon value as f ( x t ) Generate P solutons z t usng equaton (6.26) ( ) = p best g best best t and f ( p t ) = f t ( p t ). accordng to equatons (6.24) and (6.25) of all P partcles. Step 2.4. Evaluate objectve functon value as f ( z t ) and f f ( z t ) < f ( x t ) then f ( x t ) = f ( z t ) and x t = z t. Step 2.5. Update partcle best poston f f ( p t ) > f ( x t ) then p t = x t Step 2.6. If f Fnd f t best g best ( p t ) > f p t Step 2.7. End whle best 1 ( p t ) = mn f p t ( )then p t g = p t best and f p t g Increment teraton count t = t+1. P { ( ),..., f ( p t ),.., f ( p t )} ( ) = f best best ( p t ). wth f ( p t ) = f x t Step 3. Report best soluton p g of the swarm wth objectve functon value f(p g ). ( ), = 1,..., P. teraton as σ = σ*d, where, d s a parameter n (0.25, 0.997) and f σ < σ mn then σ = σ mn where σ mn s a parameter n (102, 104 ). Compute objectve functon value f( z t ) usng z t and replace poston x t the current poston of partcle n the swarm f f( z t ) < f( x t ) as x t z t and f( x t ) = f( z t ). Ths smple pheromoneguded mechansm consders, there s hghest densty of trals (sngle pheromone spot) at the global best soluton p t g of the swarm at any teraton t n each stage of ACO mplementaton and all ants P search for better solutons n the neghborhood of the global best soluton. In the begnnng of the search process, ants explore larger search area n the neghborhood of p t g due to the hgh value of standard devaton σ and ntensfy the search around as the algorthm progresses. Thus, ACO helps PSO process not only to effcently perform global exploraton for rapdly attanng the feasble soluton space but also to effectvely reach optmal or near optmal soluton. The pseudocode of PSACO method s gven n Table 3 (Shelokar et al. 2007)[7] where P denotes the number of partcles n the populaton; f( x t ) represents the objectve functon value of partcle at poston x, best best whle f t x t p t g ( ) represents the best functon value n the populaton of solutons P at teraton count t. = The algorthm starts wth ntalzng parameters of both PSO and ACO methods. The frst stage conssts of PSO, whch generates P solutons. Objectve functon values are computed as f( x t ). ACO s appled n the second stage to update the postons of partcles n the swarm. Ths process s repeated untl teraton count t = tmax Handlng the Constrants The orgnal problem can be set as, Mnmze C tot (x) Subject to g (x) 0 where = 1, 2,,m Where x s the vector of optmzaton varables. The set of constrants g(x) corresponds to the nequaltes. For mplementaton of the PSO algorthm, we used a penalty functon n the objectve functon, to provde the followng objectve functon to be mnmzed. (Ponce Ortega et al. 2009)[13]. Obj(x) = C tot (x) + penalty (x) (13) The penalty functon accounts for the volaton of the constrants such that:
11 10 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka " $ penalty(x) = # $ % 0 f x s feasble m 2! r g x =1 ( ) otherwse (14) Where r a varable penalty coeffcent for the th constrant s, r vares accordng to the level of volaton. To provde an effcent algorthm, the value of each, r was ncreased proportonally as a functon of the number of generatons. 5. SIMULATION AND PSACO IMPLEMENTATION 5.1. Process Smulaton Smple process smulaton of dstllaton problem stated above was done n commercal smulators (Aspen plus). As a base case smulaton, total number of stages s fxed at 29 and feed tray locaton s fxed at 11. Reflux rato and reboler heat duty were vared to meet the product purty specfcaton. Same procedure s repeated for total plate number 10 to 35 and some of Table 4: Smulaton Results Stage Feed Stage Lqud Mass Flow Rate Vapor Mass Flow Rate Lqud Densty Vapor Densty Lqud Vscosty Vapor Vscosty Surface Tenson Reboler heat Condenser heat duty duty kg/sec kg/sec kg/m 3 kg/m 3 cp cp dyne/cm MW MW Table 5: Smulaton Results for Dfferent Feed Tray Locaton Stage Feed Stage Lqud Mass Flow Rate Vapor Mass Flow Rate Lqud Densty Vapor Densty Lqud Vscosty Vapor Vscosty Surface Tenson Reboler Heat Condenser Heat Duty Duty kg/sec kg/sec kg/m 3 kg/m 3 cp cp dyne/cm MW MW
12 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No the results are tabulated n Table 4. For the same total number of stages, dfferent feed tray locaton was tested as senstvty analyss and results were partly shown n Table 4 for sake of brevty. The whole results smlar to Table 5 were exported as matrx n Matlab whch was later used by PSACO algorthm durng optmzaton PSACO Implementaton PSACO Code was developed n Matlab envronment. The algorthm begns generatng a set of random ntal populatons, that s, a set of values wthn ther bounds for the nneteen optmzaton varables (refer Table 1) accordng to the populaton szes. Each of these ndvduals (set of desgn or search varables) s then fed to the desgn algorthm for dstllaton column to obtan a set of constrants (usng equatons n Appendx 1) and total annual cost (usng equatons 18 stated above). Based on the randomly selected total number of stages and feed tray locaton, the approprate value for reboler and condenser duty, maxmum vapor and lqud load were selected and used n the hydraulc calculatons and objectve functon evaluatons. The ftness functon.e. total cost (equaton 1) for each ndvdual of the populaton s evaluated dependng upon ther volaton of constrants. From those values, the algorthm (Appendx 2) selects the best ndvduals of the current generatons as the parents to new generatons. The procedure s repeated untl the optmal desgn or lowest total cost detected. The objectve functon s the mnmzaton of PTDC total cost gven n equaton 1 and x s a soluton strng representng a desgn confguraton. The algorthm stopped when no further mprovement n the ftness functon n 30 successve generatons was observed. As an alternatve termnaton step, a maxmum of 300 generatons was mposed. In the present study, the product purty and hydraulc constrants (gven n Table 2) s consdered to be the feasblty constrant. For a gven desgn confguraton, whenever any of the above constrants exceeds the specfed lmt, an nfeasble confguraton s returned through the algorthm so that as a low prorty confguraton t wll be gradually elmnated n the next teraton of the optmzaton routne. 6. RESULTS AND ANALYSIS The effectveness of the present approach usng PSACO algorthm s assessed by analyzng case study. The case study was analyzed usng tradtonal optmzaton approach avalable n commercal smulators (Aspen plus) and taken from lterature (Flpe Soares Pnto, Roger Zemp, Megan Jobson, Robn Smth, 2011) [11]. The orgnal desgn specfcatons, shown n Table 1, are suppled as nputs along wth ther upper and lower bounds to the descrbed PSACO algorthm. These upper and lower bounds are taken as per broad gudelnes gven by Kster (1992) & Snnot (1989) [1, 2]. PSACO algorthm was run for 100 tmes wth dfferent random ntal seeds. If the PSACO s appled n straght forward manner, t s seen that column dameter was chosen randomly and most of the tme selected small dameter cannot handle lqud and vapor load and ended up wth hgh value of jet floodng or downcomer floodng. So, choosng the dameter randomly leads to nfeasble soluton and waste computatonal tme to arrve at feasble soluton. To avod ths trap, a smple methodology s used, where column dameter was back calculated corresponds to 80% floodng for a gven vapor and lqud load. Ths dameter was then set as a mnmum column dameter (d mn) n Table 1. Ths trck mproves the number of feasble soluton and computatonal tme sgnfcantly. Table 6 gves the dfferent solutons found by applyng PSACO along wth correspondng cost. Table 7 gves the correspondng value of the constrants. Followng ponts are noteworthy from the results of Table 6 and Multple Optmum Solutons Instead of a sngle optmum soluton, ths work generates multple optmum solutons. For sake of brevty, 10 such best solutons are tabulated n Table 6 and correspondng constrants are gven n Table 7. From Table 6 and 7, t s clear that multple dstllaton column confguraton s possble wth practcally same cost or wth lttle cost dfference. All these solutons are feasble and user has flexblty to choose any one of them based on hs requrement and engneerng judgment. The lowest total cost s found 0.867M$(corresponds to soluton number 1 n Table 6) and all other solutons are wthn 50% cost of global mnmum cost. From Table 6, t s found that all constrants are well wthn
13 12 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka Table 6: Optmal Column Geometry Usng Improved PSACO Methods Varable Notaton d t tray space vtype ! d h deck t passcfg h w w dct w dcb w dcs c dc ch w w cdct w cdcb w cdcs c w stgno feedstg C E C cap C tot ther upper and lower lmts and thus represent a feasble soluton. If someone looks n detal nto the varous solutons of Table 5, he wll be amazed the varety of solutons wth dfferent heght, dameter of column and dfferent feed stage locatons. Now, users have the flexblty to choose any of these solutons based on hs engneerng judgment. Note that, n actual shop floor, lowest cost desgn may not be always the best desgn Analyss of Mnmum Cost Desgn Correspondng to mnmum cost desgn, column dameter s 2.26Meter, plates are 2B pass confguraton, total number of stage s 18 wth feed stage 15(refer Table 6). Energy and captal cost are and M$ respectvely. As seen from Table 7 none of the constrants hts ther lmt. However, jet flood% s 78.53% aganst 80% maxmum lmt. The Table 7: Value of Constrants Correspondng to Optmum Soluton Constrants %Jet flood %Downcomer flood %Downcomer Back up wer load u ldc dp ar dct FPL w frac e frac
14 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Fgure 2: Column dameter at dfferent number of stages (Commercal smulator vs. present work). Fgure 3: Column heght at dfferent number of stages (Commercal smulator vs. present work). followng desgn varables hts ther lmt: Outlet wer heght hts t mnmum value of m, Hole area (fracton of bubblng area) hts at maxmum value of 0.15, Downcomer clearance hts at maxmum value of (refer Table 6) whch ndrectly ndcates that relaxng any of ther lmt may reduce total cost further. User need to nvestgate that whether he has the scope/flexblty to relax ther lmts of the above varable further. The jet flood 78.53% and downcomer backup 16.42% are well wthn ther lmt. From energy and captal cost value of 10 solutons tabulated n Table 6, t s concluded that energy cost s the domnant factor (corresponds to 66% of total cost) as compared to captal nvestment n the optmum solutons. Note that a payback perod of 3 years was taken to calculate the total cost as per equaton Comparsons of Results wth Commercal Smulators The resultng optmal columns archtectures obtaned by PSACO are compared wth the results obtaned from commercal smulators and shown n Fgure 24. Aspen plus smulaton model s used to compare the result. As stated earler, for each total number of stages, senstvty analyss was carred out n commercal smulator by varyng feed stage locaton. The feed stage whch corresponds to mnmum total
15 14 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka Fgure 4: Total cost at dfferent number of stages (Commercal smulator vs. present work). cost of the column s taken as reference feed stage to draw the plot of Fgure 24. Dfferent hydraulc parameter nput n aspen smulaton model lke tray spacng, hole dameter etc are kept at default value due to absence of gudelnes for ths partcular problem. As seen from these fgures, column dameter, column heght and overall total cost are less n the present work as compared to results obtaned from commercal smulators. The red color canddate n Fgure 24 corresponds to global best soluton as ndcated n frst column of Table 6. Ths s possble due to optmum selecton of varous tray geometrc parameters lke fractonal hole area, hole dameter, downcomer wdth, tray spacng wer heght etc. Optmum values of these parameters (refer Table 6) helps to reduce the captal and total cost of the column. On the contrary, n commercal smulators, most of the tme these parameters are treated as user nput and desgner gves these parameters as default value or based on hs experence. Ths proves a genune advantage of applyng PSACO n PTDC desgn Advantages of PSACO over Standard PSO As seen from lterature standard PSO has been appled manly for unconstraned contnuous optmzaton problems. The applcaton of standard PSO n the feld of constraned optmzaton problem s very few. When standard PSO (wthout ACO) wth penalty functon method s appled at current PTDC desgn problem, t was found that most of the tme the algorthm unable to fnd a feasble soluton. Ths s due to very complex nonlnear relatonshp of constrants (lke floodng, downcomer floodng, weepng, entranment, pressure drop etc.) wth the search optmzaton varables (lke column dameter, tray spacng, downcomer wdth etc.). After large number of trals wth extensve computatonal effort, such algorthm sometmes able to fnd out feasble solutons but the fnal soluton are much nferor as compared to solutons of PSACO. On the contrary, when PSACO was appled n current case study, the executon tme to arrve at lowest cost feasble soluton ncrease dramatcally. The soluton space of PTDC cost s very nosy and complex and havng lot of mnma. Consderng the feasblty based rule tends to cause hgh pressure of feasblty on the partcles, hybrd algorthm combnng PSO and ACO helps to overcome the premature convergence. In partcular, the property of ACO s employed to the best of the swarm to help PSO escape from local optma. Ths s evdent from the fact that, n present case study, out of 100 fresh starts, most of the tme algorthm converges to global mnma. Also each tme t s able to converge to feasble soluton. The qualty of fnal soluton s better than standard PSO and number of functon evaluatons and executon tme s much less than standard PSO. In a standard pentum4 processor executon tme s 1.4hrs and 0.5hrs. Respectvely for PSO and PSACO algorthm. Based on the smulaton results and comparsons, t can be concluded that the present algorthm s of superor searchng qualty and robustness for constraned engneerng desgn problems. Other dstnct advantages of present approach over tradtonal approach of PTDC desgn are explaned below:
16 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Integrated Approach to Determne the Number of Equlbrum Stage and Column Dameter In ths work, number of equlbrum stage and dameter of column s determned by the method of overall total cost mnmzaton. In tradtonal technque of chemcal engneerng, most of the tme they are determned by equlbrum calculaton and hydraulc calculaton separately. As reflux rato has great nfluence on both of them, these two calculatons are ntermngled and cannot be separated. In present technque, ts nfluence on total cost s analyzed smultaneously and number of equlbrum stage and dameter of column s determned by the method of overall total cost mnmzaton technque. 7. STRATEGY TO SELECT TRAY GEOMETRIC PARAMETERS Ths method provdes a strategy to ntellgently determne the value of varous tray geometrc parameters lke tray spacng, downcomer wdth, seve hole dameter, wer heght etc. Tradtonally these parameters are determned by experence or by some heurstc gudelnes. Most of the tme, these parameters were not changed e.g. tray spacng was tradtonally kept 24 nch n most of the column desgn. These parameters had very mportant mpact on column desgn and had mmense nfluence on column cost. As for example, low tray spacng reduces the captal cost by reducng column heght, whereas ncrease the cost by ncrease the column dameter. Hence ther approprate value should be judcously selected by optmzng the column overall cost. Ths methodology gves a platform to select these tray geometrc parameters by mnmzng column cost whle obeyng all the hydraulc constrants lke floodng, entranment, pressure drop etc. However, f for any specal case, desgner want to fx the value of any of these parameters based on hs specal consderaton/ experences, he can freely able to do so by puttng same upper and lower lmt n Table 4. Ths algorthm wll not change the value of that partcular parameter n course of optmzaton Detal Hydraulc Calculaton Commercal smulators lke aspen plus, ProII does not perform detal tray hydraulc calculaton as mplemented n ths work. Most of the cases, tray vendors lke Koch gltch, Sulzer had ther propretary software to perform detal hydraulc calculatons. These softwares are avalable as executable fles and cannot perform the teratve calculatons. The detal engneerng desgner, usually perform the equlbrum calculatons n commercal smulators (lke aspen plus, Hysys, ProII etc.) to determne number of stages and then export the tray loadng varables to tray vendor software (lke Sulzer software) to perform the hydraulc calculatons to determne the column dameter. Most of the cases, total cost s gnored n ths type of functonal desgn stages. Also, once through calculatons do not necessarly leads to most cost effectve desgn. Ths work, gves a platform to optmze all the parameters by performng an teratve detal hydraulc calculatons and optmze them smultaneously Optmze Feed Tray Locaton Ths work gves a methodology to select feed stage locaton. Strategy adopted here s smple: feed stage should be located n such a tray where overall cost should be mnmum. Ths s qute dfferent from the tradtonal feed stage locaton procedure where feed was ntroduced to a tray where lqud / vapor compostons matches wth feed composton. Actually, locaton of feed tray greatly nfluences the reboler/condenser duty, lqud and vapor traffc n the column. In other words, feed tray locaton has a bg mpact on column workng captal (energy cost) and ntal nvestment cost. So where cost mnmzaton s the man desgn objectve, the best strategy s to locate the feed tray n such poston whch corresponds to overall total mnmum cost Choosng Best Desgn Confguratons from Varous Alternatves of Columns The soluton space of cost objectve functon wth multple constrants s very much complcated wth multple local mnma. Cost wse these local mnma may be very near to each other but geometrcally represent complete dfferent sets of columns. To assess these multple local mnma, the PSACO program was run 100 tmes wth new startng guess every tme. Most of the tmes PSACO converged to global mnma but sometmes t were found that t got stuck to local mnma dependng upon the complexty of soluton space. All these feasble solutons were collected and soluton wthn 50% of global mnmum cost s presented n Table 6 for case study. From ths table, t s clear that multple dstllaton column confguraton s possble wth practcally same cost or wth lttle cost dfference. All these solutons are feasble and user has flexblty to choose any one of them based on hs requrement and engneerng
17 16 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka judgment. As for example, some user has very less space avalable n hs company, so he may choose lowest dameter column. Selectng the best dstllaton desgn from Table 6 s a combnaton of scence and arts. Decson of best column selecton for a partcular servce and ndustry s based on multple crtera ncludng costs. Crtera lke mantanablty, ease of cleanng, flow nduced vbratons; less floor space requrement, compactness of desgn etc sometmes nfluence the best selecton decson much more than the smple lowest cost crtera. The lowest cost column s not always performng best n actual shop floor. These crtera though very nfluental for fnal selecton of column are often qualtatve and dffcult to express quanttatvely. Snnot (1989) [2] gves some broad gudelnes regardng varous crtera nfluence the fnal choce. It requres desgner experence, engneerng judgment, customer requrements and normally very problem specfc. By default, the frst soluton n Table 6 s consdered as the best column as ths represents the lowest cost column whch satsfes all the constrants. Then users have to compare the frst soluton wth the other solutons n Table 6 one by one and based on hs specfc requrements, the best column to be found out. All the solutons n Table 6 are wthn 50% range of lowest cost column (.e. ther costs are comparable) and users can select the best for hs servce from varety of solutons. The fnal decson s dedcated to the user. CONCLUSION Plate type dstllaton column desgn can be a complex task and advanced optmzaton tools are useful to dentfy the best and cheapest column for a specfc separaton. The present study has demonstrated successful applcaton of PSACO technque for the optmal desgn of PTDC from economc pont of vew. Ths paper has appled hybrd partcle swarm Ant colony optmzaton, whch provdes an effectve alternatve for solvng constraned optmzaton problems to overcome the weakness of penalty functon methods. The presented PSACO technque s smple n concept, few n parameters and easy for mplementatons. These features boost the applcablty of the PSACO partcularly n separaton system desgn, where the problems are usually complex and have a large number of varables and complex nonlnear constrants n the objectve functon. Furthermore, the PSACO algorthm allows for rapd feasble solutons of the desgn problems and enables to examne a number of alternatve solutons of good qualty, gvng the desgner more degrees of freedom n the fnal choce wth respect to tradtonal methods. Ths paper evolve a strategy to optmze varous tray geometrc parameters lke tray dameter, hole dameter, fractonal whole area, down comer wdth etc and also decde on optmum feed tray locaton based on overall cost mnmzaton concept. The solutons to case studes taken from lterature show how commercal smulator desgns can be mproved through the use of the approach presented n ths work. NOMENCLATURE C tot = Total cost (10 6 $). C cap = Captal nvestment (10 6 $). C e = Energy cost (10 6 $). C col = Column captal cost (10 6 $). C HE = Reboler and condenser captal cost (10 6 $). N stage = Total number of stages (). S tray = Tray spacng (m). Area Reboler = Reboler Area (m 2 ). Area condenser = Condenser Area (m 2 ). C steam Q condenser U t Q Reboler d mn = Unt cost of steam ($/MT). = Condenser heat duty (MW). = Total heat Coeffcent (W/m 2 K). = Delta Temperature. = Reboler heat duty (MW). = Mnmum dameter (m). r 1 and r 2 = Random numbers between 0 and 1. c 1 and c 2 w t t max K ε u dfc σ = Cogntve and socal scalng parameters. = Partcle nerta. = Gven number of maxmum teratons. = Boltzmann constant. = Step sze. = Crtcal froth velocty (m/s). = Surface tenson, dynes/cm.
18 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No ρ L = Lqud densty, kg/m 3. ρ V = Vapor densty, kg/m 3. µ L = Lqud vscosty, cap. M L q w q ldc q L = Lqud mass flow rate, kg/sec. = Weep rate (gpm). = Lqud rate to downcomer (gpm). = Lqud rate down tower (gpm). a t = Superfcal tower area (m 2 ). r d t l w w dct = Tower radus (m). = Tower dameter (m). = Outlet wer length (m). = Top downcomer (DC) wdth (m). a dct = Area downcomer at top (m 2 ). l dcb w dcb = Bottom downcomer chord length (m). = Bottom downcomer (DC) wdth (m). a dcb = Area downcomer at bottom (m 2 ). l dcs = Bottom downcomer sump chord length (m). h w ch w u bdcvt u bdcvw u bdcv u b M V q ls F r h cl η α t h f C d h cl = Outlet wer heght (m). = Centre outlet wer heght (m). = Ub at downcomer crtcal velocty at downcomer entrance (m/s). = Ub at downcomer crtcal velocty wthn downcomer (m/s). = Bubblng area vapor velocty at dc crtcal velocty (m/s). = Vapor velocty based on bubblng area (m/s). = Vapor mass flow rate, kg/sec. = Scaled lqud rate down tower for constant l/v (gpm). = Froude number based on bubblng area. = Lqud head on tray (m lqud). = Volumetrc rato of vapor/lqud on tray. = Average lqud volume fracton on tray. = Froth heght on tray (m lqud). = Lqud head coeffcent. = Lqud head on tray (m lqud). w dcs = Downcomer (DC) sump wdth (m). P = Total tray pressure drop (m lqud). a dcs = Area of bottom downcomer sump (m 2 ). a dc = Average downcomer area (m 2 ).! = Hole area (fracton of bubblng area). a h = Hole area (m 2 ). l cdct = Top centre downcomer chord length (m). a b = Bubblng area (m 2 ). w cdct = Top centre downcomer (DC) wdth (m). weep df = Weepng drvng force. a cdct = Area of centre downcomer at top (m 2 ). u BWP = Weep pont (m/s). l cdcb w cdcb l cdcs w cdcs = Bottom centre downcomer chord length (m). = Bottom centre downcomer (DC) wdth (m). = Sde centre downcomer chord length (m). = Sde centre downcomer (DC) wdth (m). a b = Bubblng area (m 2 ). deck t = Deck thckness, m. d h = Hole dameter, m. q w q ldc = Weep rate (gpm). = Lqud rate to downcomer (gpm). a f = Free area (m 2 ). c b = Capacty factor based on bubblng area (m/s).
19 18 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka c bfl u lv = Capacty factor based on bubblng area at constant lqud rate jet flood (m/s). = Vertcal lqud velocty based on tower area (m/s). FPL = Flow path length (m). gmpjf = Gltsch method percent jet flood (%). FID = Flow nto the downcomer (gpm/ft 2 ). c s = Capacty factor based on tower area (m/s). HLUDC = Gltsch method head loss under downcomer (m lqud). c sp = System lmt parameter. Wer load = Wer loadng (gpm/n wer). c ss p vsl v load = Capacty factor at system lmt based on tower area (m/s). = Percent of vapor system lmt at constant l/v (%). = Gltch method Vload term (m 3 /s). DCBU = Gltsch method DC backup (m lqud). %Jet flood = Fnal percent of jet flood by most approprate method. %Downcomer flood = Gltsch method percent downcomer flood (%). T k = Temperature at generaton k, C. APPENDIX1 %Downcomer backup = Gltch method DC backup % of tray spacng (%). Ths secton descrbes step by step procedure for calculatng varous constrants gven n Table 2. The equatons are taken from varous lteratures namely Kster 1992 [1], Snnot 1989 [2], Lahr SK [12], Luyben [3] etc. As most of the correlatons, plots, monographs and equatons found n lterature are n FPS unt, the whole calculatons (equaton 15 to 108) are done n FPS unt and approprate converson was made at ntal nput and fnal results to convert t to SI unt. Step 1: Crtcal froth velocty (ft. /s), (Refer equaton 15 n Table 8) Step 2: Calculate q ldc lqud rate to downcomer (gpm) (Refer equaton 16 to 18 n Table 8) Step 3: Calculate a dc average downcomer area (ft2) (Refer equaton 19 to 32 n Table 8) For pass = 2A (Refer equaton 33 to 37 n Table 8) For pass = 2B (Refer equaton 38 to 45 n Table 8) For pass = 1 (Refer equaton 46 to 47 n Table 8) Step 4: Calculate u bdcv bubblng area vapor velocty at downcomer crtcal velocty (Refer equaton 48 to 50 n Table 8) Assume ntal hcl = 0.75 nch. Flag = True Do whle flag = True and teraton<1000 Step 5: Scale q l for constant l/v (Refer equaton 51 to 52 n Table 8) Step 6: Calculate Froude number (Refer equaton 53 n Table 8) Step 7: Calculate! vapor/lqud volume rato on tray (Refer equaton 54 n Table 8)
20 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Step 8: Calculate! t lqud volume fracton on tray (Refer equaton 55n Table 8) Step 9: Calculate h f froth heght on tray (Refer equaton 56 n Table 8) Step 10: Calculate C d lqud head coeffcent (Refer equaton 57 n Table 8) Step 11: Calculate h cl lq head on tray (m lqud) (Refer equaton 58 n Table 8) Step 12: Calculate P pressure drop n lqud (Refer equaton 59 n Table 8) Step 13: Calculate u l  horzontal lqud velocty (ft/s) (Refer equaton 60 to 62 n Table 8) Step 14: Calculate weep df weepng drvng force (Refer equaton 63 n Table 8) Step 15: Calculate q w.weep rate (gpm) (Refer equaton 64 to 69 n Table 8) Step 16: Calculate u bdcv bubblng area vap velocty at down comer crtcal velocty (Refer equaton 70 to 73 n Table 8) If (abs (u bdcv1 u bdcv2 )<control Or ter maxter T hen (Refer equaton 74 n Table 8) Flag = false Else, Calculate from equaton 75 and 76 n Table 8. Iter = ter+1 Endf loop Step 17: Calculate % jet flood by FRI method (Refer equaton 77 to 84 n Table 8) Step 18: Calculate % jet flood, %DC flood and %DC backup by Gltsch method (Refer equaton 85 to 97 n Table 8) Step 19: Calculate fnal constrants values (Refer equaton 98 to 103 n Table 8) Step 20: Calculate entranment fracton (Refer equaton 104 to 108 n Table 8). Table 8: Equatons to Calculate Varous Constrants of Dstllaton Column Equaton No. Equaton Eq. 15 Eq. 16 Eq. 17 Eq. 18 Eq. 19 q L = 481M L 60! L q ldc = q L! q w a t = 3.14d t 2 4
21 20 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka Eq. 20 Eq. 21 r = 12d t 2 l w = 2 " 2 # 2w dct r! w dct $ % 0.5 Eq. 22 Eq. 23 Eq. 24 Eq. 25 l dcs = 2 " 2 # 2w dcs r! w dcs $ % 0.5 Eq. 26 Eq. 27 Eq. 28 a cdct = a t! 2 (" sn!1 l cdct % *# $ 2r & '  ), r2! / r! r! w cdct / 2 0 ( ( )) l cdct Eq. 29 ( " l cdcb = 2 2 r! w cdcb % # $ 2 & ' r! r! w 2 " cdcb % + * # $ 2 & '  )*, 0.5 Eq. 30 Eq. 31 Eq. 32 Eq. 33 Eq. 34 Eq. 35 Eq. 36 Eq. 37 Eq. 38 Eq. 39 Eq. 40 Eq. 41 Eq. 42 Eq. 43 Eq. 44 Eq. 45 Eq. 46
22 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Eq. 47 Eq. 48 Eq. 49 Eq. 50 Eq. 51 Eq. 52 Eq. 53 Eq. 54 Eq. 55 Eq. 56 Eq. 57 Eq. 58 Eq. 59 Eq. 60 Eq. 61 Eq. 62 Eq. 63 Eq. 64 Eq. 65 Eq. 66 Eq. 67
23 22 Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No. 1 Lahr and Lenka Eq. 68 Eq. 69 Eq. 70 Eq. 71 Eq. 72 Eq. 73 Eq. 74 Eq. 75 Eq. 76 Eq. 77 Eq. 78 Eq. 79 Eq. 80 Eq. 81 Eq. 82 Eq. 83 Eq. 84 Eq. 85 Eq. 86 Eq. 87
24 Reduce Dstllaton Column Cost by Hybrd Partcle Swarm Journal of Chemcal Engneerng Research Updates, 2016, Vol. 3, No Eq. 88 Eq. 89 Eq. 90 Eq. 91 Eq. 92 Eq. 93 Eq. 94 Eq. 95 Eq. 96 Eq. 97 Eq. 98 Eq. 99 Eq. 100 Eq. 101 Eq. 102 Eq. 103 Eq. 104 Eq. 105 Eq. 106
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