Cost Minimization Of Recycling Processes At Eti Aluminum Plants. Eti Alüminyum Fabrikalarında Geri Dönüşüm İşlemlerinin Maliyet Minimizasyonu

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1 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 ost Minimiation O Recycing Processes At Eti Aminm Pants Ahmet Şahiner * İkem Trhan Süeyman Demire University Art-Science Facty Department o Mathematics East amps Isparta Dmpınar University Art-Science Facty Department o Mathematics Kütahya *orresponding athor e-mai: ahmetsahiner@sdedtr Received: 8 December 0 Accepted: Febrary 0 Abstract: This paper presents a minimiation mode to redce cost o recycing process o castic in red md in hydrate serving prodct aciity a nit o ETI Amina Pants astic is very important or ETI Amina Pants becase it is so epensive that an optimiation procedre is necessary or the cost minimiation At the same pants there is aso a hydrate serving prodct aciity One shod thereore determine the goba cheapest miing and recycing cost A generic non-inear program ormation or a recycing process is avaiabe in the iteratre which is empoyed in this stdy This program heps to minimie the cost o castic recycing process Key words: ost minimiation recycing chemica processes optimiation Eti Aüminym Fabrikaarında Geri Dönüşüm İşemerinin Maiyet Minimiasyon Öet: B makae bei bir Eti Aüminym Fabrikasındaki kostiğin yeniden kaanımının maiyetini aatmak için bir minimiasyon modei snar Kostik Eti Aüminym Fabrikaarı için çok önemidir Çünkü geri dönüşüm maiyeti çok yüksektir ve b maiyeti düşürmek için bir optimiasyon gerekidir B yüden en c karışım ve geri dönüşüm maiyeti beirenmeidir Literatürde geri dönüşüm prosesi için bir generic non-ineer program ormüasyon mevcttr; b çaışmada b non-ineer programama probeminin ormüasyon kanımıştır B programama kostiğin geri dönüşüm maiyetini minimie eder Anahtar Keimeer: Maiyet minimiasyon geri dönüşüm kimyasa süreçer optimiasyon Introdction Optimiation is to choose the best sotion nder a set o certain conditions There are severa techniqes sed to sove optimiation probems These techniqes are sed to get the best sotion Some o them are inear programming integer programming qadratic programming and noninear programming [] A chemica process comprises a series o processing steps In most chemica processes there are a nmber o streams recyced back to dierent process nits These streams have to meet certain process reqirements sch as ow rate and composition [] As it is mentioned by [] there are sorces and s in a chemica process A sorce is any stream in the process carrying a species o interest A is any nit in the process and handes A resh sorce consists o resh species A process sorce has been 45

2 A Şahiner İ Trhan generated in the process The resh sorces are obtained eternay and composed o either one pre species or a mitre o dierent species Their cost is dependent on the market vae o the pre species present in them Process sorces are composed o more than one species Process sorce cost depends on the manner in which they are created De to the imitations o the process generation there might be pper bonds on the ow rates o the process sorces [] Zebah et a [4] described and sed an ant coony meta-heristic optimiation method to sove the redndancy optimiation probem in pastic recycing indstry This probem is known as tota investment-cost minimiation o series-parae pastic recycing system They reported that the ant coony approach had been sccessy appied to the cassica traveing saesman probem and it showed very good sotions in any appied area The ant coony has aso been adapted sccessy to other combinatoria optimiation probems Yaici et a [5] demonstrate that the consmption o eectriceectronic eqipments eads to the increase o eectronic-wastes (e -wastes) These e- wastes incde high content o metas and precios metas For the recovery o metas rom e-wastes varios treatment options are sed based on conventiona physica hydrometargica biohydrometargica and pyrometargica processes Pons et a [6] worked on a mathematica programming approach to optimie direct recyce-rese networks together with wastewater treatment processes in order to satisy a given set o environmenta regations They deveoped a disjnctive programming ormation to optimie the recyce o process streams to nits and the perormance o wastewater treatment nits They sed the MINLP mode to minimie the tota anna cost o the system which incdes the cost or the resh sorces the piping cost or the process integration and the waste stream treatment cost Appication O The Recycing Probem On Eti Amina Pants Signiicant amont o castic is sed as raw materia in ETI Amina Pants In hydrate prodction aciity a nit o the pant red md is thrown ot o the system as a waste There is signiicant amont o castic in this waste red md which raises prodction cost The pants have a recycing aciity or red md to minimie the ost Penty o Na O and A O compositions in red md need to be recovered via recycing processes The aim is to gain castic with the most concentration at the minimm cost The stream rates need reaching the minimm vae to attain this objective The stream schema o the recycing aciity in the pant is given in Figre 46

3 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 AUTOLAVE PULP TODEOMPOSER THIKENERS SEDIMENT SINK V Tota ow rate=598 t/h REDMUD ' ' Figre The stream schema o the recycing aciity in the pant (The schema is taken rom ETI Amina Pants) One can deine the probem in accordance with [] as oows The system consists o one process sorce caed as red md another one in process caed as the sediment and two other resh sorces consisting o species Na O and A O Let s deine those resh sorces as sorce and sorce respectivey and deine process sorce as sorce In sch a case the oowing qantities as variabes and parameters are necessary or the optimiation process : Unit cost o sorce (TL/ton) : Unit cost o sorce (TL/ton) : Unit cost o sorce (TL/ton) L : Tota ow rate o sorce (ton/hrs) L : Tota ow rate o sorce (ton/hrs) L : Tota ow rate o sorce (ton/hrs) L : Tota inet ow rate o detrits (ton/hrs) : Individa ow rate rom sorce to the sediment (ton/hrs) : Individa ow rate rom sorce to the sediment (ton/hrs) : Individa ow rate rom sorce to the sediment (ton/hrs) N : Nmber o iterations or tota inet ow rate o the sediment N : Nmber o iterations or composition o Na O in the sediment N : Nmber o iterations or composition o A O in the sediment N : Nmber o iterations or ow rate o sorce N : Nmber o iterations or ow rate o sorce N : Nmber o iterations or ow rate o sorce N 4 : Nmber o iterations or composition o Na O species o sorce N 4 : Nmber o iterations or composition o A O species o sorce 47

4 A Şahiner İ Trhan N arge : Arbitrariy seected arge nmber : Tota nmber o s N N N sorce species : Tota nmber o sorces : Tota nmber o species t : Iteration inde corresponding to tota inet ow rate o the sediment : Iteration inde corresponding to composition o Na O species in the sediment : Iteration inde corresponding to composition o A O species in the sediment v : Iteration inde corresponding to ow rate o sorce v : Iteration inde corresponding to ow rate o sorce v : Iteration inde corresponding to ow rate o sorce w : Iteration inde corresponding to composition o Na O species o sorce w : Iteration inde corresponding to composition o O : omposition o Na O species in sorce : omposition o A O species in sorce : Inet composition o Na O species or the sediment : Inet composition o A O species or the sediment : Known pper bond on ow rate o sorce : Known inet ow rate o the sediment : Known inet mass oad o Na O species to the sediment : Known inet mass oad o O A species to the sediment The probem deinition wi have the oowing steps Objective nction: A species o sorce Since the aim is to minimie the cost one shod redce stream rates whie minimiing the cost de to the more stream rate occrences and the more compositions in the sorces that participate in the process ths the more amont o materia can be redced Sorce materia baance: min L L L For process sorces there is no pper bond on ow rate Ths it is written as an eqation constraint However the pper bond on ow rate is known or the process sorces and represented throgh the oowing conditions and restriction 48

5 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 L L Sink materia baance: L Sink inet composition baance: Sorce imits: ower pper ower pper ower pper ower pper L L L ower pper Sink inet imits: j N and k N j k ower j k j k pper species L L L j N and k N j pper j j pper species Ater the genera deinition o the probem as above a sotion strategy is adapted rom [] Accordingy one can write the oowing eqations; L pper L ower L () N pper ower N pper ower N () 49

6 A Şahiner İ Trhan L pper L ower L () N pper ower N 4 pper ower N 4 (4) Frthermore eqations () () () and (4) can aso be written as oows L L t L pper pper pper L L v L pper w pper w pper In mitre probems a compositions shod be eqa to 0 [7] So one can write the eqations (5) and (6) as (5) (6) In the probem sotion a oop is necessary that takes into consideration the increasing vaes o t v w and w Each o iteration in the oop is appied nti the oowing conditions are satisied t N v w w N N N N4 N4 50

7 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 Minimm cost can be ond according to arbitrary nmbers o iteration by an aready mentioned agorithm de to [] This sotion can change according to increasing nmbers o iterations and it may not give the tre sotions every time This matter can be overcome by the deveoped stream schema given in Figre This schema can be sed whie soving the probem by sing the Mape program Figre A stream schema or two resh sorces and one process sorces This stream schema is or minimiation o cost o recycing by sing the simpe method The reationa cost parameter ( ) is irst cacated according to ( ) ( ) I is positive then the cheapest option is to se and as t t t ( t) On the other hand i is negative then there are two possibiities [] ase t 5

8 A Şahiner İ Trhan t ( t ) ( ) 0 t ( t) ( ) ase t 0 t ( t) t t I the cacated vae eceeds cheapest sotion one has to se a three sorces to get the t t t ( t) ( ) Findings Let s deine the symbos given above and write the known vaes as oows : Unit cost o sorce (TL/ton) : Unit cost o sorce (TL/ton) : Unit cost o sorce (TL/ton) : omposition o sorce t : Tota composition o sediment the : Known pper bond on ow rate o sorce t : Tota inet ow rate o sediment (ton/hrs) : Tota ow rate o sorce (ton/hrs) 5

9 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 : Tota ow rate o sorce (ton/hrs) : Tota ow rate o sorce (ton/hrs) The known vaes are given in Tabe Tabe The vaes taken rom ETI ALUMINA PLANTS =47 TL/ton =767 TL/ton =0 TL/ton =598 ton/hrs t =0445 =50 ton/hrs One can sove this probem by sing the oowing Mape codes restart; : 50 : : 088 : c : 47 : c : 767 : c : 0 : t : 598 : t : 0445 apha : ( c c) ( c c); : i apha 0 then : t t; : t ( t); cost : c c; ei apha 0 and t then : t ( t ) /( ); : 0; : t ( t) /( ); ese : 0; : t ( t) / ; : t t / ;cost : c c c; end i ; 5

10 A Şahiner İ Trhan i then : t t ; : t ( t) ( ) ; : ; cost : c c c; end i ; 4 oncsion The rests o this stdy can be smmaried as oows =9990 ton/h =500 ton/h =50 ton/h Minimm recycing cost is 49 8 TL/ton which means that the system shod work with that ow rate to achieve the minimm cost I one compares the sotion with the cost o the recycing processes in ETI Amina Pants then he/she can see that it is mch cheaper than the cost spent The we-known basic simpe method invoves choosing n points where n is the nmber o variabes The main re or the simpe evotion is to eiminate the worst point and to repace it by its symmetrica with respect to the centroid o the hyperace ormed by the remaining simpe points One cod sove the present probem by sing the simpe method too However it is more compe and takes mch time to sove By sing this agorithm one can reach the rests more speediy Reerences [] Kmar DN 009 assica and Advanced Techniqes or Optimiation Optimiation Methods [] Parthasathy G 00 Minimiation o cost o recycing in chemica processes hemica Engineering Jorna (8) : 7-5 [] Parthasathy G 000 Mass integration o mticomponent non-idea systems with phase change Dissertation Thesis [4] Zebah A hateet E Samrot M Hajeri S 008 Investment ost Optimiation o Pastic Recycing System Under Reiabiity onstraints Leonardo Jorna o Sciences () : [5] Yaici YE; Deveci H (009): E-Atıkardan Metaerin Geri Kaanımı Madenciik 48 () : -48 [6] Ponce JM Hort A E Hawagi M Gtierre AJ 009 A Property-Based Optimiation o Direct Recyce Networks and Wastewater Treatment Processes Ahe Jorna 55 (9): 9-44 [7] Otrk A 009 Yöneyem Araştırması Ekin Yayınevi Brsa p86 [8] Bhaskar V Gpta SK Ray AK 000 Appications o Mtiobjective Optimiation in hemica Engineering Reviews in hemica Engineering 6 ():

11 SDU Jorna o Science (E-Jorna) 0 7 ():45-55 [9] Grossmann Amanah M Morari M Maotti M Morbidei M 008 Optimiing contro o simated moving bed separations o mitres sbject to the generaied Langmir isotherm Springer Science+Bsiness Media 4: 4-4 [0] Hemker T Fower KR Farthing MW Stryk OV 008 A mied-integer simation-based optimiation approach with srrogate nctions in water resorces management Optimiation and Engineering 9 (4): 4-60 [] Kamon A Jairi M haaboni M 009 The se o the simpe method and its derivatives to the on-ine optimiation o the parameters o an injection moding process hemometrics and Inteigent Laboratory Systems 96 : 7- İkem Trhan e-mai: ikemtrhan@maidmpinaredtr 55