A Hybrid Methodology to Minimize Freshwater Consumption

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A Hybrid Methodology to Minimize Freshwater Consumption during Shrimp Shell Waste Valorization Combining Multi-Contaminant Pinch Analysis and Superstructure Optimization
Viviana Quintero 1, Arturo Gonzalez-Quiroga 2 and Angel Darío Gonzalez-Delgado 1,*

1 Nanomaterials and Computer Aided Process Engineering Research Group (NIPAC), Chemical Engineering Department, University of Cartagena, Avenida del Consulado St. 30, Cartagena de Indias 130015, Colombia; [email protected]
2 UREMA Research Unit, Mechanical Engineering Department, Universidad del Norte, Barranquilla 25138, Colombia; [email protected]
* Correspondence: [email protected]

Citation: Quintero, V.; Gonzalez-Quiroga, A.; Gonzalez-Delgado, A.D. A Hybrid Methodology to Minimize Freshwater Consumption during Shrimp Shell Waste Valorization Combining Multi-Contaminant Pinch Analysis and Superstructure Optimization. Polymers 2021, 13, 1887. https:// doi.org/10.3390/polym13111887
Academic Editors: Keiko Shirai, Maribel Plascencia-Jatomea and Neith Aracely Pacheco López
Received: 3 May 2021 Accepted: 28 May 2021 Published: 6 June 2021
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Abstract: The conservation and proper management of natural resources constitute one of the main objectives of the 2030 Agenda for Sustainable Development designed by the Member States of the United Nations. In this work, a hybrid strategy based on process integration is proposed to minimize freshwater consumption while reusing wastewater. As a novelty, the strategy included a heuristic approach for identifying the minimum consumption of freshwater with a preliminary design of the water network, considering the concept of reuse and multiple pollutants. Then, mathematical programming techniques were applied to evaluate the possibilities of regeneration of the source streams through the inclusion of intercept units and establish the optimal design of the network. This strategy was used in the shrimp shell waste process to obtain chitosan, where a minimum freshwater consumption of 277 t/h was identified, with a reuse strategy and an optimal value of US $5.5 million for the design of the water network.
Keywords: shrimp exoskeleton; water network; chitosan; pinch analysis multiple contaminants; mathematical program
1. Introduction Global competitiveness policies and environmental regulations have motivated indus-
tries to direct their design strategies towards the valorization of intermediate streams called waste, allowing them to diversify supply and reduce environmental impacts. [1]. In the shrimp industries, around 48% of the shrimp is discarded as waste, which includes the shell and the head [2]. However, the presence of high added value compounds such as pigments, chitin, and lipids in this material has allowed the design of different valorization strategies widely exposed in the literature [3]. One of them is obtaining polymer chitosan composed of β- (1–4) D-glucosamine units with physicochemical properties such as biodegradability, biocompatibility, bioactivity, and low toxicity. For that reason, this compound has been investigated in different fields, for example, antimicrobial activity, wastewater treatment, food industries, nanoparticles, and biopolymers, among others [4,5]. Chitosan is produced by enzymatic or chemical deacetylation of chitin; this last route is characterized by high freshwater consumption and availability of intermediate streams. In this paper, a strategy to minimize the consumption of fresh water and disposal of waste streams is presented [6]. The applied strategy is based on the synthesis methodology that involves two fundamental activities: water network design (WN) and the superstructure model solution. The water network design (WN) is based on the concept of the superstructure, embedding all possible

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process units and all the connections among resources, interceptors, process units, and wastewater treatment [7].
Sources are streams from process units that have water available to be recycled and reused [8]. The stream sources are purified partially by given regeneration units with established performance indexes before. Different technologies used for this purpose are presented with known removal ratios and design parameters in the literature. However, prior identification of the principal pollutants is essential, because this influences the water network’s economic feasibility [9].
On the other hand, sinks are process units that require water but present restrictions in terms of flow and stream composition. An external freshwater source is included to supply the unit sink’s flow rate requirement. Finally, the wastewater treatment units treat the streams not received by the sink [10]. The water network main designs are identified in the literature: water-using networks (WUNs) and total water network (TWN). The WUNs use processes and treatment and/or regeneration units to increase the reuse potential of available water; however, wastewater treatment is considered a discharge unit that is not included in the configuration. In TWN, the water-using units, regeneration units, and treatment units are combined into a single network, with an environmental constriction on the concentration of streams leaving the TWN [10].
The activity related to the superstructure model solution uses pinch methodology and mathematical programming techniques [11].
1.1. Pinch Methodology
The contributions related to the pinch methodology have been directed mainly to the identification of the minimum consumption of fresh water and wastewater disposal, taking into account reuse, recycling, and regeneration strategies, with single or multiple contaminants, through graphical and algebraic approximations and their combinations [12]. Foo [13] presented a review of existing strategies for water network synthesis using the pinch methodology. The techniques were classified into fixed load and fixed flow for flow rate targeting techniques, water reuse networks, and wastewater treatment. He identified the most advanced techniques as limiting compositive curves, material recovery pinch diagrams, and water cascade analyses, which correspond to fixed flow and single contaminant.
Otherwise, Klems [14] shows an analysis of the progress published on the pinch methodology in areas such as heat exchangers, exergy, and water network synthesis. The author included the compilation of existing techniques and guidance for future developments. Regarding the water network synthesis, strategies are identified that include the combination of the pinch of water with the water footprint and sequential methods that involve the objective flow of resources and the synthesis of the network from mathematical methods; however, these strategies are limited to a single pollutant [15].
1.2. Mathematical Programming
From a mathematical programming viewpoint, deterministic methods have been widely used in the water network’s optimal design, addressing it as MINLP problems (mixed integer nonlinear programming) [16] and their combinations of linearization and relaxation, which lead to MILP (mixed integer linear programming) [17], NLP (nonlinear programming), and meta-heuristic algorithms [18]. These methods involve global and component mass balances such as constraints and single or multiobjective functions addressed to maximizer or minimizer criteria [19].
In this context, the single objective provides a global optimal solution directed to a criterion such as total annualized cost, minimum freshwater consumption/wastewater generation, or the minimum number of interconnections [20]. A multi-objective optimization framework is developed to optimize different objectives, especially those in conflict with different functions [21]. These involve several criteria (economic, technical, and environmental), providing a virtually infinite number of equally effective solutions (i.e., the

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with different functions [21]. These involve several criteria (economic, technical, and3 oefn1-3
vironmental), providing a virtually infinite number of equally effective solutions (i.e., the
Pareto front) that are trade-off solutions between objectives. According to his criteria, the
bPeasrtestoolfurtoionnt) athmaotnagrethtreadseet-oofffssoolluuttiioonnssmbeutswt ebeenidoebnjetciftiievdesb.yAtchceoardnianlygstto[2h2is].criteria, the best Tsohleuptiroenseanmt opnagpethr eprsoept oosfessoaluhtiyobnrsidmmusetthboedidoleongtyifi, ewdhbicyhthseeeaknsatloyisnt t[e2g2r]a. te the heuristic Tanhde mpraetsheenmt aptiacpaelrprporgorpaomsemsinaghaypbprridoamchetthhrooduoglhogayp, iwnchhicahnasleyeskiss ftoor minutelgtirpalteeptohlelhuetaunritsstifcolalnowd emdabthyemmaatthiceaml partiocgarlapmromgirnagmamppinrgoascyhntthherosiusg. hIt aalploinwcshaanhaollyisstiiscfdoersmigunltaipnlde opbovlliuatteasntcsofmolplolewxemdabtyhemmaatthiceaml aftoircmaluplarotigornasmfmorinthgesysonltuhteiosins.oIft athlleowprsoapohsoeldistnicetdweosirgkn. Tahnids sotbrvaitaetgeys hcoams bpeleenx dmeastihgenmedatiincaflofuorrmseuqluaetinotniaslfsotrepthse. Fsiorlsut,titohne obfastheescphreompoes’esdmnoedtwelionrgk. aTnhdisssitmrautelagtyiohnaswbeereenddierseicgtnededtoinofobutarinseqspueecnitfiiacl isntefoprsm. Faitrisotn, thaebobuastecsucrhreemnte’asvmaioladbeilliintyg (asnoudrsciem) aunladtiroenstwricetrieondsiroenctesidnktouonbittsai(nfloswpescaifincdicnofonrcmenattriaotnioanbsoouftpcoulrluretannt tasv).aSileacboinlidty, t(hseoucarclceu) laantidonreosftrthicetimoninsiomnusminckounnsuitms (pfltioownsoaf nfrdeschonwcaetnetrriantitohnesporfopceoslsluwtaanstcsa).rrSieedcoonudt, atphpe lcyailncgultahtieomn oetfhtohdeomloingiympurmopcoosnesdubmypCtiohninoeftfraels. h[2w3]a,twerhienrethtehpercoocnecssepwtaosfc“acrorinetdamoui-t naapnptlycainsgcatdheesm” ewthaosddoelvoeglyopperdop. osed by Chin et al. [23], where the concept of “contaminant cascaTdheis”inwdaicsadtesvethloaptetdh.e prioritization of sources and sinks was carried out according to theThcoisnitnadmicinataenstthcoatntcheentprraitoiorintiziantiaosnceonfdsoinugrcoersdaenrd. Tsihnikrds ,wtahsecwararitedr nouetwacocrokrdsuinpgetrostthreuctounrteamcoinastnrtuccotinocnenwtraasticoanrrinieadscoeuntd, icnognosirddeerri.nTghirredu,steheanwdatreergneentewraotrikonsusptreartsetrguiecstutroe acnoanlsytzreucptioosnsibwleasccuarrreinetd ionutetr, accotniosnids earnindg irnetuersceeapnteddreugneitnse’ rvatiaiobnilisttyr.atFeigniaelslyt,oaanmaolydzeel bpaossesdibolenctuhrerebnutiilnt tseurapcetriostnrsucatnudreinitnevrcoelvpetesdgulonbitasl’ mviasbsilbitay.laFnicneasllya,nadmpoodlleultbanastsedinoneatchhe
pbruoicltesus puenristt.rTuhcteuorebjiencvtoivlveefsugnlcotbioanl mmaisnsimbaizlaensctehseatnodtapl onlelutwtaonrtks icnoestachonpsriosctiensgs uonf iftr.eTshe-
wobajteecrt,ivtheefuinvcteiostnmmenintimcoisztesofthteretaotmalennettwunoritks,coasntdcothnesisotpinegraotfinfrgeschowstaftoer, the itnrveaetsmtmeennt,t
tcaoksitngoffrtreesahtwmaetnert ausnaitsr,esatnridcttihoen.oTpheeramtiondgeclowstafsosrotlhvedtrienaGtmaemnst., taking freshwater as a
restriction. The model was solved in Gams.
2. Materials and Methods 2. MTahteeriaaplsparonadchMperthopodossed here is divided into four sequential stages, as is shown in FigurTeh1e: mapopdreoliancghapnrdopsiomseudlahtieorneoisf tdhievpidreodceisnstsocfhoeumres,etqaurgeenttiinagl sotfamgeins,imasuims sfhreoswhwn aintFeirguusraeg1e: (mmoudletil-icnognatnadmsinimanutlamtieotnhoofdtohleogpyro),cbeussilsdcihnegmthe,etawragteetrinngeotwf morikniwmiuthmrefruesseh/wreactye-r culesaagned(mreugletni-ecroantitoanmsintraantetgmieest,haonddoltohgeyw),abtuerilndeintwg othrke wsoalutetrionnetfworomrkawthietmh raetuicsael/orpetciymcliezaantdiorne.generation strategies, and the water network solution for mathematical optimization.

TTwwoo sseeqquueennttiiaall ttaasskksswweerreeddeevveeloloppeedd. .TThheefifrisrtstonoenewwasarserlaeltaedtetdottohethperopcreoscse’sssc’osnccoenp-cteupatlumalomdeoldceolncsotrnusctrtuiocnti,own,hwichhiicnhvionlvvoeslvtehsetshteudstyudobyjeocbtjedcetfidneiftiinointiaonndanitds siutsrrsouurrnoduinndgs-. iRngelse.vRaenltevdaantat,dsautcah, sauscchalacsuclaatlicounlabtiaosne,boapseer,aotpinegractoinngdictoionndsi,tiaonnds,yainelddsy,iewldesre, wcoelrleecctoeld-. lTechteedse.cTohnedsreecfeornsdtoremfeordsetloinmg oadndelisnimg ualnadtiosnim, wulhaetiroent,hwe choenrceetphteuaclomncoedpetluwalams doedseclriwbeads dthesrcoruibgehdmthatrhoeumghatmicaaltheexmpraetsicsaiol nesxparnedsspiorongsraanmdmpirnoggreanmvimroinnmg eenntvsi,roannmd ethnetsp, raonpdosthede pmroopdoeslewdams oredseollvweads. rIetsioslvcoedm.mItoins cinomchmeomnicianl cphreomceiscsaelsptroocuessesessofttowuasree ssoufcthwaasrePsruocIhI, Aspen Plus, and ProSimPlus. In this paper, Aspen Plus version 10.4 was used for mass and energy balance and thermodynamic properties estimation [24].

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as Pro II, Aspen Plus, and ProSimPlus. In this paper, Aspen Plus version 10.4 was 4uosfe1d3 for mass and energy balance and thermodynamic properties estimation [24].
2.2. Targeting of Minimum Freshwater Usage 2.2. Targeting of Minimum Freshwater Usage
The minimum consumption of freshwater was calculated following the methodology propoTsheedmbiyniCmhuinmectoanl.su[2m3]p.tTiohneosfinfrkesphrwocaetessr wunaistscadlcwulearteedfifrostlloidweinntgifitehde,mwehtehroedo𝑑lo𝜖g𝐷y apnrodp𝐷os=ed𝑁by C,hwiniteht tahl.e[2fl3o]w. Trheequsiinrekdpr𝐹ocessaunndittshde mwaerxeimfirusmt idcoenntciefinetdr,awtiohneroefdconDtaamnidnDan=t aNllsoinwk,ewd it𝑍h ,the. flTohwe wreaqtuerirsetdreFaSmKdsaonudrctehtehmatacxainmbuemreccoynccleedntorartrioeunsoefdctoonftualmfiillntahnet sailnlokws e𝑟d𝜖Z𝑅k,s𝑅kd.=T𝑁he watewr sitthreaamvasiloaubrleceftlohwat c𝐹a𝑆n beanrdecythceledpoolrlurteaunstedcotnocfeunltfirlalttihone s𝐶ink, s TrhenR, tRwo=seNqsuoeurncteiawl istthagaevsawilaebrelecaflrorwiedFoSurt,aanpdreth-tearpgoeltliuntganptroccoendcuernetriantwiohnicChk,tshr eTlhimen-, ittwinog sceoqnutaemntiinalansttasgfeosr weaecrhe scianrkriaenddouthte, apposrsei-btalergseetqinugenpcreofcoerdtuhree sionuwrchei’cshutsheewliemreitdinegcontaminants for each sink and the possible sequence for the source’s use were determined, tfeorlmloiwneedd, bfoylltohwe esdinbkys’thloecsaitniokns’alobcoavteioannadbboevleoawndthbeeploinwchthpeopiinntcahnpdotihnet iarncdomthbeiirnacotimonbinineaatciohnreingieoanc’hs srienggiloens’isnski.nTghleessiencko.nTdhsetasgeceowndassstoaguercwe aalsloscoautriocen,awllohcearteiothne, wmhineirme uthme mpoininimt oufmthpeofrinesthowf tahteerfrreesqhuwiraetmerenretqwuairsedmeetenrtmwinasedd.etermined.
22..33.. BBuuiillddiinnggtthheeWWaatteerrNNeettwwoorrkk wwiitthh RReeuussee//RReeccyyccllee aanndd RReeggeenneerraattiioonn SSttrraatteeggiieess TToo ffuurrtthheerrrreedduucceeththeeaammoouunnt ot foffrefrsehswhawtearterreqreuqirueidre, ad,syanstyhnetshisefsoisr ftohre twhaetewranteetrwnoertk-
wisoprrkoipsopsreodp, oassesdh,oaws nshionwFnigiunreFi2g.uDrees2ig. Dn eassisgunmapsstiuomnspatiroenlsisatered lbisetleodwb: elow:

FFiigguurree 22.. GGeenneerraall ssuuppeerrssttrruuccttuurree ddeessiiggnn..

TThhee ssoouurrccee ssttrreeaammsshhaavveea afloflwowFS𝐹r𝑆andanaddeafidneefdinceodncceonntcraentitornatCiokn,sr 𝐶Lik, e sLinikkeusninitks, uthneitys,htahveeyahflaovwe aFSfKlod wand𝐹 maxainmdummaaxlilomwuemd palollolwuteadntpcoolnlucetanntrtactioonnceZnk,tsrkadtTiohne 𝑍fre,shwTatheer fsrtersehamwafltoewr sFtrf reeashmwaflteorwis d𝐹efined fromistdheefpininecdhfaronmalytshisewpiitnhcha zaenraol-ypsoilsluwtaitnht caoznecreon-tpraotlilountoafnpt ocollnuctaennttr. aIttioinncloufdpeosllaustaent to.fItinintecrlcuedpetseda suentiotsf Uinttewrcitehptfiexdedunrietcso𝑈verwieisthCkofuixt e=d rβetckCovkin-, ewriheesre𝐶βtk i=s t𝛽he r𝐶eco, vwerhyeroef c𝛽ontaismtihneanrtekcoinveUrtyMoifxceorsnwtaemreinianncltukdeidn i𝑈n thMe sixuepresrswtreurcetuinrectlouddiesdtriinbuthtee sthuepesrtrsetraumctsutroe etoacdhisotrfitbhueteptrhoecesstrseuanmitsst.otoeaavchoiodf nthoenp-lrinoceeasrsituiensitdsu.teo taovothide nboanla-nlicneeaorfitpiersopdeuretietos athtethbealmanixcienogfpporionptebretifeosreateathceh msinixkinagndpouinntitbienftoerreceepatchprsoincekssa.nAd ufincittitiinotuesrcuenpitt cparlolecdesbs.yApafsisctwitiaosuisnculnuidtecdalwleidthbinypthaessinwtearscienpctlsutdoeddirwecitthtihnetchuerrinentetrscwepitths tporodpireercttietshethcautrarreenntsowt iinthteprcreoppteerdti,ews itthhaetfaferectnivoetnienstseracnedptceods,tweqituhaelftfoeczteivroe.ness and cost e2q.4u.aWl taotezreNroe.twork Solution for Mathematical Optimization
2.4. WTahteerwNaettewrornkeStwolourtkionsofolur tMioanthwemasatcicaarlriOedptiomuitz,attaiokning into account two aspects: the formulation of the mathematical model and its respective solution.
TThheewmaattehrenmeatwticoarlkmsoolduetlioinncwluadsecsatrhreiefdoromuut,latatikoinngofinthtoearcecsotruicnttiotnwsoaansdptehcetso: bthjeecftoivremfuunlcattiioonn. oFf othrethmeastuhpemerasttircuacltmuroedoefl athnedwitsatreerspneecttwivoerkso, ltuhteiorne.strictions consist of mass balanTcheeemquaathtieomnsatfiocrawl matoedr.eTl ihneclcuodnetasmthienafonrtms fuolraetivoenryofutnhiet raersetrpircetisoennsteadndasthfoelloobwjesctainvde faurnecbtiaosne.dFoonr twhhe astuipteprrsotrpuocsteusre[2o5f].thEeacwhasteorunrceetwpororkce, sths ewraesstsreicgtrieognastecodntsoiwstaorfdmdaifsfserbeanl-t ainntceerceeqputaotriso.nEsqfuoartwioante(1r). Tshhoewcsonthtaemgeinnaenratsl bfoarlaenvceeroyfuthneitsaoruerpcereisnetnhteedseapsafroaltloorws.s and

∑ FSUrout =

FSIr,i ∀r ∈


i ∈IU

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The set of streams from the splitter process source unit is sent to mixer 1. The outlet

stream from the mixer unit is directed to the intercept unit. The overall material balance for

the mixer process unit is given by Equation (2), and the mass balance for each contaminant

j by Equation (3).

∑ FIUiinlet =

FSIr,i ∨ i ∈ IU


r ∈SU

∑ FIUiinlet ∗ xIUii,nklet =

FSIr,i ∗ xUSro,ukt ∀ i ∈ IU, ∀ j


r ∈UF

In the unit intercept IU, the inlet FU Iiinlet and outlet FU Iiout stream flows are equal. Equations (4) and (5) show an overall balance and for contaminant k, assumed to be a linear
function in terms Ri,j On the other hand, a fictitious unit is included when the property is not intercepted with effectiveness and cost equal to zero.

FU Iiinlet = FU Iiout ∀i ∈ U I


xU Iio,uj t = βUI i,k ∗ xU Iii,nklet ∀ i ∈ U I, ∀ k



βUI i,k = 1 − Ri,k ∀ i ∈ U I, ∀ k



The streams treated in each interceptor unit IU are sent to the process sink through separator SU Ii Equation (7) shows the overall balance in this unit. The contaminant concentration of every stream treated in each intercept is equal to the contaminant concentration of the segregate stream, as seen in Equation (8).

FIUiout = ∑ FIDi,d + FI Mi ∀i ∈ IU


d ∈UD

xSIUio,uk t = xIUio,uk t ∀ i ∈ U I, ∀ k


The streams from the splitter treatment units are directed to the MD mixer demand unit, and the output stream is directed to the demand unit. The overall material balance for the mixer demand unit is given by Equation (9) and the mass balance for each contaminant j by Equation (10).

∑ ∑ FUDinletd = Ff reshwater +

FIDi,d +

FSDr,d ∀d ∈ UD


i ∈UI

r ∈US

∑ ∑ FUDinletd ∗ xDUdin,k =

FIDi,d ∗ xU Iio,kut +

FSDr,d ∗ xUSro,ukt ∀ d ∈ UD, ∀ k (10)

i ∈UI

r ∈US

In the sink unit, flowrate and composition of specific chemical compounds, such as process constraint xUDdin,j,min ≤ xUDdin,j,max, are included. On the other hand, the freshwater balance is raised through Equations (11) and (12).

Ff w = ∑ Ff w,d



∑ Ff w,d ≤ Pinch



Finally, a final mixer is included that receives the streams from the intercepted units

that do not comply with the sink restrictions. The overall material balance for the final

mixer is given by Equation (13) and the mass balance equation for each contaminant k by

Equation (14).

∑ FMFout = FI Mi



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Finally, a final mixer is included that receives the streams from the intercepted units
that do not comply with thFeMsFinokut r∗esxtkoruitct=ion∑s. TFhIeMoiv∗exraIlUl iom,uk ta,t∀erkial balance for the fin(a1l4)
mixer is given by Equation (13) and the masis∈IbUalance equation for each contaminant k by

EquatioTnhe(1o4b).jective function is formulated to minimize the total network cost consisting

of the cost of freshwater, the cost of investment on treatment units, and the operating

cost for the treatment units (it is co𝐹n𝑀si𝐹dered=as on𝐹e𝐼-𝑀third of the investment), as show(1n3)in

Equation (15) [26].

Min Z =

AR ∗

CIU𝐹𝑀∗ 𝐹(FU I∗ou𝑥t)α +=1∈

𝐹𝐼𝑀 ∗ 𝑥𝐼𝑈 , , ∀ 𝑘
∑ CIU ∗ (FUIout)α + H ∗ Ff w

∗ CUf w (1(41)5)



3 i∈IU


The objective function is formulated to minimize the total network cost consisting of

the cosFtionfalflrye,sthhwe patreorp, othseedcopstiomfizinavtieosntmmeondteol nistarneaNtmLPenttypuen,itsa,kainngditnhtoe aocpceoruantitntghecotystpe

foor fthveartriaebatlmese, ntht euniattsu(riet iosfctohnesirdeestrreidctaiosnosn,ea-nthdirtdheofotbhjecitnivesftumnecntito)n, a. sItsshsoowluntionnEcqauna-be

tiocnar(r1i5e)d[2o6u]t. using computational tools such as LINDO, EMSO, MATLAB, MINOPT, and

GAMS, among others. 1

𝑀𝑖𝑛 𝑍 = 𝐴𝑅 ∗


3. Resu∈lts

) +3

𝐶𝐼𝑈 ∗ (𝐹𝑈𝐼 ) + 𝐻 ∗ 𝐹 ∗ 𝐶𝑈


FinAasllay,cathse spturodpyo, sthede sohprtiimmpizsahtieolnl wmaosdteesl pisroacnesNsiLnPg stychpem, teakwinags cihnotoseanccfour nthtethpero-

tydpue cotfiovnaroifabchleisto, tshaen nfraotmurethoef stherimrepstreixcotisoknesl,eatonnd. the objective function. Its solution can

be carried out using computational tools such as LINDO, EMSO, MATLAB, MINOPT, an3d.1G. PArMocSes,saMmoodneglinogthaenrds.Simulation

The flow diagram was constructed from information reported in the literature,

3. 6R6e0s0ukltgs/h of shell wastes was taken as the basis of calculation according to the avail-

abiAlitsyaocfatsheestruadwy,mthateesrhiarli;mthpesshcehllewmaeswteasspsriomceuslsaitnegdswchiethmtehwe ahselcphoosfetnhefoAr sthpeenprPol-us duscimtiounlaotforchinitoassatnabfrleomstatthee, csohnrismidpereixnogsk3emleatoinn.functional blocks, which are explained be-
low. The thermodynamic model for property estimations was the electrolyte non-random

3.1tw. Por-olicqesusidM(oedNelRinTgLa).nd Simulation The first stage is pretreatment (see Figure 3). The raw material composition (SSHRIMP)
waTs hmeofdloewleddicaognrasmidewriansgcaomnsitnruocateciddfsr,ofmattiynfaocrimdsa,ticoanrbroenpaotretse,dainndthpeiglimteernattuarcec,o6r6d0i0ng kgt/ohwofhasht ewllaws raespteosrtwedasbtyakGeónmaeszt-hReíobsaesitsaol.f[c2a7l]c.uTlahtiisosntaagcecoirndcilnugdetos pthheysaivcaaillaobpielirtaytioofns thseurcahwams awtearsihailn; tghetoscrhememoevewiams psiumriutilaesteudswinigthathweahteerlp/roafwthme Aatsepreianl Pralutisosoimf u10la/t1o,r sinize a srteadbulectsitoanteu, pcotnos5idmermingto3hmomaiongfeunniczteiotnhaelsbalmocpklse, uwshinicghaacrreuesxhpelraiwneitdh baeclouwt o. fTfhseiztehreart-io moofd6y,naanmdicexmtroadcetilofnorofpororgpaenrtiyc ceostmimpaotuionndss w(aasstatxhaenethleicnt)roulsyitnegneotnh-arnaonld–owmattewr o85-l%iquwi/dw. (eNThReTCLH). SDRY stream is directed to the demineralization stage, where minerals like calcium
carTbhoenaftiersatresrtaegmeovisedpbryetraedadtminegnat s(osleuetioFnigoufrede3-h).ydTrhoechrlaowric macaidter5i%al wc/owm;proesaicttioionns (SSEHquRaItMioPn)s w(1a6s)–m(1o9d) ewleedrecmonosdideleerdintghraomuignhoaaccoidnsv,efrastitoynarceiadcst,ocra(rRbSotnoaicte).s, and pigment according to what was reported by Gómez-Ríos et al. [27]. This stage includes physical

operations such as washingCatoCrOe3m+ov2eHiCmLpu→ritiCeasCuls2in+gHa 2wOa+terC/rOaw2 material ratio of 10/(11,6) size reduction up to 5 mm to homogenize the sample using a crusher with a cut off size

ratio of 6, and extractionNofa2oCrgOa3n+ic2cHomCLpo→und2Ns (aaCslta+xaHn2tOhin+) CuOsin2 g ethanol–water 85(%17)

w/w. The CHSDRY streamMigsCdOir3ec+te2dHtCoLth→e dMemgiCnle2r+aliHza2tOio+n sCtaOg2e, where minerals lik(1e8) calcium carbonate are removed by adding a solution of de-hydrochloric acid 5% w/w; re-

actions Equations (16)–(19C)aw3(ePreOm4)o2d+el6eHdCthLro→ugh3CaacColn2v+er2sHio3nPrOe4actor (RStoic).


Figure 3. Shell waste pretreatment. Adapted from Meramo-Hurtado et al. [28]. Figure 3. Shell waste pretreatment. Adapted from Meramo-Hurtado et al. [28].

Polymers 2021, 13, 1887

𝑁𝑎 𝐶𝑂 + 2𝐻𝐶𝐿 → 2𝑁𝑎𝐶𝑙 + 𝐻 𝑂 + 𝐶𝑂


𝑀𝑔𝐶𝑂 + 2𝐻𝐶𝐿 → 𝑀𝑔𝐶𝑙 + 𝐻 𝑂 + 𝐶𝑂


𝐶𝑎 (𝑃𝑂 ) + 6𝐻𝐶𝐿 → 3𝐶𝑎𝐶𝑙 + 2𝐻 𝑃𝑂

7 o(f1193)

Next, the CHD1 stream was subjected to deproteinization using a sodium hydroxide

2% w/w solution; reactions Equations (20)–(24) were simulated in a conversion reactor at

71 °CN,eoxbtt,atihneinCgHthDe1cshtriteianmaswtahsesmubaijencpterdodtoucdte. proteinization using a sodium hydroxide

2% w/w solution; reactio𝐶ns𝐻Eq𝑁ua𝑂tion+s2(𝑁20𝑎)𝑂–(𝐻24→) w2e𝐶re𝐻sim𝑁𝑁ul𝑎a𝑂ted+in𝐻a𝑂conversion reactor(2a0t)

71 ◦C, obtaining the chitin as the main product.

C H N O + 2NaOH → 2C H NNaO + H O




C1C0HH16NN2OO7 +S 2+Na2ONHaO→H →2C25CHH8NNNaNOaO4 +S H+2OH O


C18HC 20HN2ON3 O+ 2+N2aNOaHOH→→2C2C9HH10NNNNaOaO4 ++HH2OO




Finally, chitinCw12aHs r2e6Nac4tOed3 w+i2thN5a0O%Hw→/w2sCo6dHiu1m3Nh2NydarOo2xi+deHa2tOhigh temperatur(e2,4a)s
shown in reaction 2C5,8aHn1d5NchOit6o+saNn awOaHs o→btaCin6eHd1,3qNuOan5 t+ifyCin2Hg 31N40a0Ok2g of chitosan/660(225k)g of processed shrimp shell wastes.
FTinhaeldlye,scchriibtiendwscahs ermeaectperdeswenitths 5a0h%igwh/frwesshowdiautmer rheyqduriorxemideenatt(hwig1–hwte7m) qpuearanttuifriee,daisn s3h8o7wLn/king roefacchtiiotons2a5n,.aWndatcehritaovsaainlawbialistyobthtarionuegdh, qtuhaenwtiafysitnegst1r4e0a0mksgwoafschoibtosesravne/d6,6w02hkicgh ojuf sptrioficeesstsheedasphprilmicaptisohnelolfwthaestienst.egration strategy mass.
The described scheme presents a high freshwater requirement (w1–w7) quantified in
338.27.LT/akrggetoifncghoiftoMsainni.mWalaFterersahvwaaitlearbUilistaygtehrough the waste streams was observed, which justifies the application of the integration strategy mass.
The minimum amount determination of freshwater was carried out following the
3m.2e. tThaordgeotlionggyofinMfinviemsaelqFuresnhtwiaaltsetraUgessagaes described below:
TInhethmeifnirimstusmtagaem, tohuensttrdeeatmersmnianmateiodnsoouf rfcrees(hrw) watiethr wthaesircraersrpieedctoivuet ffloolwlowanindgcothmempoetshitoiodnolwogeyreinidfienvteifsieeqdu. AenctcioalrdstianggetsoaFsigduesrcersi3b–e5d, btheeloswel:ected source streams were RW1, RW3I,nRtWhe4fi, rasntdstRaWge5, ,thwehsitcrheaamresantaemnveidrosnomurecnet(arl)cwonitdhitthioenirs raensdpehcatviveewflaotweraanvdaicloabmilpitoy-. sTithioensiwnker(edi)duenntitifis eadre. Aidcecnotridfiiendg: tWo AFiSgHur1e, sN3E–U5,1t,hWe sAeSleHct2e,dNsEoUur2c,eWstAreSaHm3s, wNeErUe 3R,Wan1d, RWWA3S, HRW4,4c, oannsdidReWrin5g, wthheicrheqaureiraetdefnlovwiro. nInmtehnistaclacsoen, dthiteionnesuatrnadlizhaatvioenwuanteitrsawvaeirleabtailkiteyn. Tinhethseinakna(dly)suisnaitssaasrienigdleensitnifike.dT:hWe cAoSmHp1o,uNnEdUs c1a,lWledApSHol2lu, tNanEtUs k2,wWeAreSsHel3e,cNteEdUw3i,thanthde WsiAnkSHan4d, csoonusricdeeriinnfgortmheartieoqnu,irwedhiflchowp.rIensetnhtisrceasstrei,ctthioennseiuntrtaelrimzastioonf cuonmitps owseitrieontakfoerntihne tshienkan. aFloyrsisthaissapsrioncgelsessidnika.gTrahme c,otmheposuelnedctsecdalpleodllpuotallnuttsanwtsekrewoerrgeasneilceccteodmwpoituhntdhes s(ilnikke aansdtasxoaunrtcheinin, fmoremthaytilonp,awlmhiitcahtep,raensednterthesatnrioclt)ioannsdinsateltrsmrseosuf cltoinmgpofrsoitmionnfeourtrthaleizsaintiko.nF,oars tshhisowprnocinesTsadbilaeg1r.am, the selected pollutants were organic compounds (like astaxanthin,
methyl palmitate, and ethanol) and salts resulting from neutralization, as shown in Table 1.

Polymers 2021, 13, x FOR PEER REVIEW

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FFiigguurree44. .DDeemmininerearlaizliaztaiotinonanadndedperoptreointeizinaitzioantiorenacrteiaocntsi.oAnsd.aApdteadpftreodmfrMomeraMmeor-aHmuort-aHduoretat dalo. [e2t8]a.l. [28].


Table 1. Date case study.
Source r1 r2 r3

Flow Rate kg/h 58,621 265,115 489,905






𝐶 (𝑝𝑝𝑚) 10 200 270

Polymers 2021, 13, 1887

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Table 1. Date case study.
r1 r2 r3 r4
d1 d2 d3 d4

Flow Rate kg/h
58,621 265,115 489,905 197,886
Flowrate kg/h
235,107 64,029 96,132 142,072

Corganic (ppm)
300 470 600 1100
Zorganic (ppm)
50 20 40 25

CNaCl (ppm)
10 200 270 350
ZNaCl (ppm)
20 10 15 10

The second stage corresponds to identifying the limiting pollutant for each sink and determining the most likely source prioritization sequence for each sink. For this, the relationship proposed in Equation (16) was used, using the maximum concentration of each pollutant in the source (Corganic = 1100 ppm and CNaCl = 350 ppm).

Z∗k,skj = ZK,rj − CkFW (26) C∗k,sr_max Ck,rmax − CkFW
Table 2 shows the results obtained where lower ratios <1 were evidenced, indicating a limitation of the sink by pollutants. In this case, the pollutant with the lowest ratio for each sink was chosen, being the cascade pollutant organic d1 and d3 and NaCl contaminant cascade for d2 and d4.

Table 2. Source prioritization sequence/contaminant cascade of each sink.



Minimum Ratio









0.057 0.017 0.043 0.017

0.045 0.017 0.037 0.017

Organic NaCl
Organic NaCl

The total flows of the sinks were accounted for. In other words, for the case study, if the total flow d1 + d3 (331,239 kg /h) is higher than the total flow d2 + d4 (206,101 kg/h), then the pinch analysis will start on the organic cascade pollutant. Additionally, the source order was identified to fill the sinks according to the pollutant concentration. In this case, it was r1–r2–r3–r4 for the two pollutants.
At this stage, the pollutant sequence can also be defined for pinch analysis, taking into account the total flows of the sinks. In other words, for the case study, if the total flow d1 + d3 (331,239 kg /h) is higher than the total flow d2 + d4 (206,101 kg/h), then the pinch analysis will start on the organic cascade pollutant. Additionally, the source order was identified to fill the sinks according to the pollutant concentration. In this case, it was r1–r2–r3–r4 for the two pollutants. Finally, the required freshwater flow calculation was performed for each pollutant, applying the material recovery pinch diagram technique, where the compound curves (CC) for the source and sink are drawn in a plot with axes impurity load vs. cumulative flow rate. Then, the Source CC was shifted until it was on the right side of the Sink CC [25].
As indicated, the calculation begins for the organic pollutant cascade, since it is the one that requires the highest flow. In Figure 6, the freshwater target can be identified as 230 t/h.

Polymers 2021, 13, 1887

impurity load vs. cumulative flow rate. Then, the Source CC was shifted until it was on itmhepruigrihtyt sliodaedovfst.hceuSminuklaCtiCve[2f5lo].w rate. Then, the Source CC was shifted until it was on the riAghs tinsiddiecaotfedth,ethSeinckalCcuCla[2ti5o]n. begins for the organic pollutant cascade, since it is the one tAhastinredqiucairteeds ,ththeehciaglhceusltatfiloonwb. IengiFnisguforre t6h,ethoergfarensihc wpoaltleurttaanrtgceatsccaandeb,esiidnecnetiitfiiesdthaes o23n0e tt/hha.t requires the highest flow. In Figure 6, the freshwater target can be identifie9dofa1s3 230 t/h.

Figure 6. Composite curve for organic cascade. FFiigguurree66..CCoommppoossiitteeccuurrvveeffoorroorrggaanniiccccaassccaaddee..
WWWiiittthhh rrreeessspppeeecccttt tttoooNNNaaaCCClll(s((sseeeeeeFFFigiigguuurerree7)77,))a,, afareffrsreehsswhhawwteaartteerrreqrrueeqqiruueiimrreeemmnteeonnftt aoopffpaarppoppxrirmooxxaiitmmelaayttee9ll0yyt/9900h ttc//hahnccaabnne bbideeeiinddteeinnfitteiidffii.eeddI.n. IInnthttihhsiiwss wwayaa,yy3,,23302200t/tth//hhcccaaannnbbbeeeeeessstttaaabbbllliiissshhheeeddd aaasss ttthhheee mmmiiinnniiimmmuuummm fffrrreeessshhhwwwaaattteeerrr cccooonnnsssuuummmppptttiiiooonnntttaaarrrgggeeettt,,,aaaccchhhiiieeevvviiinnnggg aaa rrreeeddduuuccctttiiiooonnn ooofff 444000%%% wwwiiittthhh rrreeessspppeeecccttt tttooo ttthhheee iiinnniiitttiiiaaalll rrreeeqqquuuiiirrreeemmmeeennnttt...

FFiigguurree77..CCoommppoossiitteeccuurrvveeffoorrNNaaCCll.. Figure 7. Composite curve for NaCl.

IInn oorrddeerr ttoo bbuuiilldd tthhee wwaatteerr nneettwwoorrkk wwiitthh rreeuussee//rreeccyycclleeaanndd rreeggeenneerraattiioonnssttrraatteeggiieess,,

tthhee wwInaatteoerrdnneeerttwwtooorbrkkudidldeesstiighgnen iwissapptreroorppnooessteewddouurkssiinwnggittthhheeremmuasaetthh/reeemmcyaacttilicecaaallnppdrroorggergraaemmnemmraiinntiggonaappspptrrraootaaeccghhiettsoo,

ttthaakekeeweeavvteenrnnmmeotowrreeoarakddvvdaaennstitagagngeeisoofpf trthohepeoffllsooewwd uaavsviaaniilglaabtbhllee iminnatththheeesmsooauutrricceealuupnnriiottssg[r[22a99m]]..mIIttiniissgbbaaapsspeedrdooaoncnhtthhtoee

tooappktteiimmeviizzeaanttiimoonnorooeff aadssvuuappneetrrassgttrreuuocctftuutrhreee,, pfplroreewsseeannvtteaedidlaiinbnlFeFiigignuurtrehee22.s.FoFouorrrcthetheuecncaiastssee[s2st9utu]d.dyIy,t r,iesrvebevaresresdeosoomnsmothsoie-s


sssieeslleiesccttpeedrdoapasossppeoodllllauusttaannrttessg[[e11n88e,,33r0a0]t].i.oTTnhhueeniinintvvdeeusstetmmtoeenntthteccoorsestmt((CoCvOOaIlI))effofoerrctthhiveeetntrreeesaasttmmofeentnhtteuucnnoiimtt ((prreoevvueenrrdssese

sooesslmmecootsesidiss))aiissspsshhoololwuwtnnaniinntsEE[qq1u8ua,a3tt0iio]o.nnT((h115e5)).i.nTTvhheeestllmaattettenerrtwwcoaasssttt(aaCkkOeennI)aafccoccroortrdhdieinntggrettoaotwmwhehnaatt wwunaasistrr(eerppeovorerttreesdde

obbsyymAAohhsmims)eetitsoovsvhiićc´oewettnaalli..n[[22E66q]]uaaanntddiouunpp(dd1a5at)te.edTdhwweiitltahhttttehhreewiinnaddseetxxakccoeonssttattcooc2o200r1d199in.. g to what was reported

by Ahmetović et al. [26] and updated with the index cost to 2019.

COI = 3311.13 m (t/h)


where m represents mass flowrate. The unit costs for the freshwater were taken from 1 dollar/m3, considering the Colombian regulations for water consumption in industry.

3.3. Synthesis of the Water Network
The superstructure shown in Figure 3 was solved with the help of GAMS, taking into account Equations (1)–(15) that represent the mathematical model. The solution was found

Polymers 2021, 13, 1887

COI = 3311.13 m (t/h)


where m represents mass flowrate. The unit costs for the freshwater were taken from 1 dollar/m3, considering the Colombian regulations for water consumption in industry.

3.3. Synthesis of the water network

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The superstructure shown in Figure 3 was solved with the help of GAMS, taking into account Equations (1)–(15) that represent the mathematical model. The solution was faoftuenrd91a5ftietrer9a1t5iointesraattinoondsea9t1n5o,dweit9h15a,nwexitehcuantioenxeticmuteioonf 7ti.m3 se, ofbt7a.3insin, ogbatadiinsitnrigbuatdioinstroifbthuetisotnreoafmthaes ssthroeawmn ains sFhigouwrne 8in. Figure 8.

Figure 8. Optimal design for the water network.
FFiigguurree 88 sshhoowwss tthhaatt tthhee ooppttiimmaall ddeessiiggnn ooff tthhee wwaatteerr nneettwwoorrkk pprrooppoosseess aa mmaaxxiimmuumm tthheeoorreettiiccaall rreedduuccttiioonn iinn ffrreesshhwwaatteerr ccoonnssuummppttiioonn ooff 4488%%,, iinntteeggrraattiinngg rreevveerrssee oossmmoossiiss aass aann iinntteerrcceepptt uunniittwwitihthreremmoovvalalpeprecrecnetnatgaegseosfo9f09%0%forfothrethcoemcopmoupnodusniddsenidtiefinetdifaiesdpaoslluptoalnluts-. Ttahnetsf.rTeshhewfraetsehrwsuatpepr lsyupispdlyisitsridbiusttreidbuintedalilnthaell sthineksiunnkiutsn, idtsi,redcitriencgtinagboaubtou49t %49%totsoinsiknk1 1anadnd222%2%totosisninkk4;4t;hthisisisisdduueetotoitistsflfolowwrreeqquuiirreemmeennttssaannddrreessttrriiccttiioonnssrreeggaarrddiinngg oorrggaanniicc ccoommppoonneennttss aanndd NNaaCCll.. OOnn tthhee ootthheerr hhaanndd,, hhiigghh wwaatteerr aavvaaiillaabbiilliittyy iiss oobbsseerrvveedd iinn tthhee fifinnaall mmiixxeerr,, wwhhiicchh ccoouulldd bbee uusseedd iinn ootthheerr aaccttiivviittiieess wwiitthhiinn tthheeccaasseessttuuddyyiinndduussttrryy..
OOnn tthheeootthheerrhhaanndd, ,thtehemmatahtehmemataictaiclaml omdoedl eulseudsefdorftohretmheasms ainssteignrtaetgiornatoiofnthoefptrheepsernestecnatsceassteusdtyudsyhoshwoswastaottaoltaalnannunaulaclocsotsot fofUUSS$$55.5.5mmililliloionn..TThhee aapppplliieedd mmeetthhooddoollooggyy tthhaatt iinnvvoollvveessppininchchanaanlaylsyissiasnadnmd amthaetmheamticaatilcparlopgrroamgrmaminmg ignigvegsicvoems pcoarmabplaerraebslueltrseswuiltths wwoitrhkswroerpkosrtreedpoinrttehde ilnitetrhaetulirtee.rBataullrae.etBaall.la[3e1t] aaln.a[l3y1z]eatnhaelysuzegatrhme saunguafarcmtuarninugfapcrtoucreinssg, pursoincgestsh,eutseinchgntihqeuteecfrhonmiqwueatferormcaswcaatdeer acnasaclaydsies a(pnianlychsisan(pailnycshis)a,nsahloywsisin),gshaodwecinregaasediencfrreesahswe iantefrrecsohnwsuamterpctioonnsoufm4p3t%io,nanodf 4637%%, ianndw6a7st%ewinatwerasdtieswchaatregred.iLsceheaertgael..L[2e3e]edt eavl.e[l2o3p] daemvealtohpema amtiactahlemmoatdiceal lamppoldieedl atpopalinedextoisatinngexwisatitnegr nweattweronrketiwnoarkpiunlpa apnudlppaanpderpampielrl mfoirlldfiroerctdriereucste/reruecsye/crleincygcslitnragtesgtireasteagniedsreagnednereragteinoenrasctihoenmsecshuemsinesg umsoinngo-manondom- uanltdimobujeltcit-iovbejeocptitvime iozpattiiomniztoatmioinnitmo imzeinfrimesihzwe aftreershcownastuemr cpotniosnumanpdtiroenasaonndabrleeapsoanyabbalcek.payb4.acCko. nclusions
4. CoTnhcelumsieotnhsodology proposed in this paper allows identifying the minimum freshwater consumption through the pinch approach, taking into account the limitation in the sink for mTuhletimpleetphooldluoltoagnytsp. rItopwoassedalisnotphoissspiabpleertoalolobwtasinidaenptriifoyriintigztahtieomn isntrimatuegmyffroershsowuartceer caonndssuimnkp, ttiaoknintghrionutogahctchoeunptinthcehcaopnpcreopatcohf,rteauksien.gNienxtot, aucscinogunmtatthheemlimatiitcaatliopnroignrathmemsiinngk ftoecrhmniuqlutiepsl,eitpwoallsuptaonsstsib. lIet twoaesstaalbsloisphoasnsiobpletimtoaol dbteasiingnafoprritohreitwizaatteironnesttwraotrekg,ymfionrimsoizuirncge athnedtositnakl ,antankuinagliziendtocoacstcoouf ntht ethneetcwonocrekp. tFoorf trheuescea.sNe setxut,duy,siitnwg amsapthoessmibalteictaol ipdreongtrifaymamcoinnsgumtecphtinoinqureesd,uitctwioansopfo4s0s%iblue stiongesotanblylisrheuasne ostprtaitmegailedseasnigdnoffo4r8t%heuwsiantgerrenuestewaonrkd, mregineinmeirzaitniognthsteratotetaglieasn,nwuhailcizhepdrcoovsitdoefs tahme noeretwhoorlkis.tFicovritshioencafoser sdteucdisyi,oint wmaaskpinogs.sible to identify a consumption reduction of 40% using only reuse strategies and of 48% using
Author Contributions: Conceptualization and methodology, V.Q.; formal analysis and investigation, A.D.G.-D. and V.Q.; resources, A.G.-Q.; writing—original draft preparation, A.D.G.-D., A.G.-Q., and V.Q. All authors have read and agreed to the published version of the manuscript.
Funding: This work was financially supported by the Project “Diseño y aplicacion de estrategias de integracion de proceso a las biorefinerias de exoesqueleto de camaron y racimo de palma en el departamento de Bolivar”, funded by the call 848-2019. Postdoctoral stays of the Ministry of Science and Technology MINCIENCIAS–Colombia Technical; facilities and human resource support from Universidad de Cartagena and Universidad del Norte.

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A Hybrid Methodology to Minimize Freshwater Consumption