Availableonlineatwww.sciencedirect.com
Journal of Applied Research and Technology
www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology14(2016)93–100
Original
Mathematical modeling and optimization in the design of a maturation pond
Facundo Cortés Martínez
a,∗, Alejandro Trevi˜no Cansino
a, Agustín Sáenz López
a, José Luis González Barrios
b, Francisco Javier de la Cruz Acosta
aaFacultyofEngineering,ScienceandArchitectureoftheJuárezUniversityoftheStateofDurango,Mexico
bNationalInstituteforForestry,AgricultureandLivestockResearch,NationalCenterforDisciplinaryResearchRelationshipWater-Soil-Plant-Atmosphere,Mexico Received30December2014;accepted8March2016
Availableonline4May2016
Abstract
ManylagoonsystemsinMexico,andgenerallyindevelopingcountries,donotmeetthenormforwaterpouringintoreceptorsbodies.Itwas appliedmathematicalmodelingtooptimizethedesignandcostofamaturationpond,consideringthemethodologyadoptedforMexicobythe NationalWaterCommission,takingasvariablesthehydraulicretentiontimeandthenumberofscreens,thentheresultswerecomparedwitha traditionaldesignofamaturationpondwithoutscreens.Bothanalysesfulfillthetreatedwaterqualitystandardsforpouringintoreceptorsbodies.
Theresultsshowareductioninthehydraulicretentiontimeby8.65days,andareductionby48.16percentinlandrequirement.Aboutthecost,it wasobtainedareductionof42.24percentincomparisonwhitthetraditionalmethod.Amajoradvantageofthemathematicalmodelistheobtaining oftheoptimaldesign,whichwouldbeverydifficulttogetwiththetraditionalmethodologybecausetheprocessisiterativeandusesmorethan onevariable,alsocanbeinferredthattheuseofscreensincreasestheefficiency.ThealgorithmusedwastheinteriorpointbyMatlab’sFmincon function,whichdeterminestheoptimalvaluestoaccomplishthewaterqualityconstraintsandobtainsthelowestpossiblecostforconstruction.It isincludedthesensitiveanalysisforthemathematicalmodel.Itisrecommendedtocarryoutthepresentresearchatrealscalewiththefinalityto checktheresultsgivenbytheoptimization.
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Keywords:Mathematicalmodeling;Optimization;Maturationpond;Wastewater
1. Introduction
Thelagoonsystems areprimarilyaimedattheremoval of organic matter, also known as biochemical oxygen demand (BOD)andeliminationoffecalcoliform.Thesetreatmentsys- temsareclassifiedintothreetypes:anaerobic,facultative and maturationor polishing(CNAandIMTA,2007a;Mendonca, 2000).
Themainfunction ofmaturationpondsis toremovefecal coliformbyultravioletraysandtheprocessiscarriedoutaero- bically.AccordingtoMendonca(2000)itisrecommended,for thiskindofponds,depthsof0.5–1.2m.
The construction of these systems is inexpensive, easy to operate and the maintenance is simple. The purpose of the
∗Correspondingauthor.
E-mailaddress:facundo[email protected](F.CortésMartínez).
PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.
stabilization pondsis toretainthewastewaterfor aperiodof time,sothatthewastewateriscleanednaturally(Abbas,Nasr,
&Seif,2006;Mendonca,2000;Naddafietal.,2009;Shilton&
Mara,2005).AccordingtoRojas(2002)andCubillo(1982)the applicationoftraditionaldesignmethodologiesendedinlosses, as thesesystems usuallyhavebeen overstated.Itis alsosug- gestedconsideringinthedesignatleasttwoponds(facultative andmaturation)inotherwordsavoiddesigningthesystemwith asinglelagoon:facultative.Ontheotherhand,whenwastewater isdischargedwithoutcomplyingaboutqualitystandardnorms drivestohealthproblemsinapopulation:typhoid,paratyphoid, hepatitisandleprosy amongothers. Amajordisadvantageof these systems is that they need a considerable area of land, notwithstandingthe foregoing,Naddafietal.(2009),Hamzeh andPonce(2007)recommendedthemfordevelopingcountries withtropicalclimates,sincethetemperatureandintensityofthe sunlightincreasestheefficiencyinremovalofcontaminants.
ShiltonandHarrison(2003a) suggestconsideringchannels or screensinthe design ofthe lagoonsystems. Accordingto
http://dx.doi.org/10.1016/j.jart.2016.04.004
1665-6423/AllRightsReserved©2016UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccess itemdistributedundertheCreativeCommonsCCLicenseBY-NC-ND4.0.
Nomenclature
DBOi concentration of organic matter in the system input(mg/L)
T loweraverageairtemperature(◦C) Af area(m2)
Qi flowattheentranceofthelagoonsystem(m3/day)
Z depth(m)
V volume(m3)
O averagehydraulicretentiontimeinthepolishing pond(days)
X widthlengthratio
BProm averagewidthofthepond(m) LProm averagelengthofthelagoonin(m) BSup superiorwidth(m)
LSup superiorlength(m) ASup pondsurfacearea(m2)
Qe flowattheoutletofthepond(m3/day) e evaporation(mm/day)
d dimensionlessdispersionfactor Kb bacterialreductioncoefficient(day−1) a dimensionlessconstant
Ni fecalcoliforminthepondoutlet(MPN/100mL) Ne fecalcoliformmodifiedbyevaporationinthesys-
temoutput(MPN/100mL)
Nf/No numberoffecalcoliformintheoutputofthesys- tem(MPN/100mL)
Kf decayconstantatanytemperature(day−1) DBOef BOD5concentrationinthesystemoutput(mg/L) DBOe modifiedBOD5concentrationbyevaporationin
thelagoonsystemoutput(mg/L).
NMamp numberofbafflesinthematurationlagoon
these authorsthe model significantlyimproved the hydraulic conditions: isfavoredthe pistonflow andthedead zonesare eliminated.Alsoincreasestheremovalofpollutants.
Some authors consider screens inthe design: Shilton and Mara(2005),Abbasetal.(2006),MuttamaraandPuetpaiboon (1997) and Banda (2007). These authors carried out labora- torystudieswithdifferentlengthsofbaffles:concludedthatis obtainedimprovedresultswith70percentofthetotallengthof thepond.
Then Bracho, Lloyd, and Aldana (2006) and Winfrey, Strosnider,Nairn,andStrevett(2010)conducted moreexper- imentaltests,alsoconsideringbaffles.Theresultsshowedthat agreater hydraulic efficiency within the pond with agreater numberofbaffles.
In order to minimize the cost of construction Kilani and Ogunrombi(1984)recommendedoptimizingthedesignofthe systemgaps,thenBrachoetal.(2006),Winfreyetal.(2010), OkeandOtun(2001)andOlukanniandDucoste(2011)con- ductedstudieswherewereconsideredlinearmodelstodefine optimumdesign.Itwasdeterminedthatitispossibletoimprove thedesign;i.e,maximizetheremovalofcontaminantsandmin- imizethecostoftreatment systems.ThenSah,Rousseau,and
Hooijmans(2012)recommendedtheneedtoanalyzeanintegral andcalibratedmodelforlagoonsystemssothatitcanbeused asanoptimizationtoolandsupport.
The aim of this paper was to propose and implement a comprehensive mathematicalmodel for theoptimizationof a maturation pond, taking into account the fecal coliform and organicmatterinaccordancewiththeconcentrationlimitsestab- lished. Thepurpose of themodel istominimizeconstruction costsandcomplywithqualitystandardsoftreatedwater.
Twoanalyzeswillbecarriedout:thefirstconsidersthetra- ditional design of the maturationpond excluding screens. In thesecondanalysiswasconstructedamathematicalmodelfor optimizing the design, considering as variablesthe retention timeandthenumberofscreens.Itisintendedtocomparethe economicadvantagesandefficiencyintheeliminationofcon- taminantsbetweenthetwostudies.
Anotherimportantapplication,ofthepresentmathematical model,istocomplementthetreatmentsystemwhenyouhave solelyonepond(facultative)andthequalityofthetreatedwater doesnotmeettherequirementsindicatedbytheregulationsfor dischargingintowaterbodies.AccordingtoBixioetal.(2005) thematurationpondscanbeaddedasasecondarytreatmentfor restrictedandunrestrictedirrigation.
Therewasnotfoundedbibliographyofamathematicalmodel for theminimizationintheconstructioncostfor amaturation pond takinginto account the waterqualityas constraint.The contributionofthepresentpaperistheconstructionofthemodel mentionedabove.
2. Materialandmethods
2.1. Maturationpond(dispersedflow)
(1) For thehydraulic retention time(O), the methodology isiterativeandthewaytocarriedoutistoproposearetention time,lateraredeterminedthefecalcoliformconcentrationand theBODintheoutputofthepond.Thenormindicatesthatthe pollutants mustbe equalor less than1000MPN/100mLand 75mg/Lrespectively
(a) Fordeterminingthevolumeofthepondwehave:
V =(Qi)(O) (1)
(b) Areaofthepond:
A=V
Z (2)
(c) Width–lengthratioX=3:
BProm=
Af
X (3)
LProm= Af BProm
(4) (d) Fordefiningthesuperiorwidthandlengthwehave:
BSup=BProm+(Z)(slope) (5)
LSup=LProm+(Z)(slope) (6) (e) Areaofthesuperiorwatersurface:
ASup=(BSup)(LSup) (7) (f) Flowintheoutputofthelagoon:
Qe=Qi−0.001ASupe (8)
(g) Fecal coliform decay with screens at 70 percent of the length:
X= (LProm)(0.70)(NMampF+1)
BProm/(NMampF+1) (9)
d= X
−0.26118+0.25392(X)+1.0136(X)2 (10) (h) Bacterialdecaycoefficient:
Kb=0.841(1.075)T−20 (11)
(i) For“a”constantwehave:
a=
1+4KbOd (12)
(j) Numberoffecalcoliformintheoutputofthepond:
Nf
No = 4aexp(1−a)/2d
(1+a)2 Ni (13)
(k) Numberoffecalcoliformcorrectedbyevaporation:
Ne= (Nf/No)(Qi) Qe
(14) (l) Kineticcoefficient:
Kf = Kf35
(1.085)35−T (15)
(m) BODconcentrationofthepond:
DBOef = DBOi
KfO+1 (16)
(n) BODremovalefficiency:
%= (DBOi−DBOe)
DBOi ×100 (17)
(o) BODmodifiedbyevaporation:
DBOe=(DBOi)(Qi)
Qe (18)
Fig.1showstheoperativeroutetoperformtheoptimaldesign ofamaturationpond.
3. Analysisofthemodel
Inordertodesignmaturationpondmustbeconstructedand optimizationmodel,inwhichthevariabletooptimizeisthecost ofconstructionofthepond,thiscostconsidersfourparameters:
land,concretefloorslab,perimeterwallandscreens.Theopti- mizationmodelhastoberestrictedbywaterqualitystandards,
Fig.1.Flowchartfortheoptimaldesignofamaturationpond(Martínezetal., 2014).
inthiscase:BODandfecalcoliform.Thepurposeofthemen- tioned aboveis thatthe modelfinds thelowestcostinwhich the pondaccomplishesthe water qualitystandards. Asimple mathematicalrepresentationisshowninformula(19):
Minimize
Totalcost=Costofland+Costoffloorslab +Costofperimeterwall+Costofscreens Subjectto:
BOD ≤ Max.BODallowedbythestandar Nf/No ≤ Max.Nf/Noallowedbythestandar
(19)
AccordingtothemethodologyindicatedbyCNAandIMTA (2007a),forthedesignisusedadepthof1.0masseeninFig.2.
Thenextstepintheconstructionoftheoptimizationmodel istodeterminehow tolink theconstraintswiththe objective function(totalcost);bothpartsofthemodelmustdependonthe samevariables.Thesevariablesarecalleddecisionvariablesor
1 m
BSup
Fig.2.Transversalviewofamaturationpond.
changingvariables.Forthematurationpondaretakenasdeci- sionvariablestheretentiontime(O)andthenumberofscreens (NMamp).
3.1. Objectivefunction
Thecostoflandwasconsideredtobe$ 750.00persquare meter;perimeterwall:$1200.00permeter;costoffloorslab:
$1200.00persquaremeter;costofscreens:$1200.00permeter.
Withthesedatatheexpression(20)isdetermined.
Totalcost=750(Landarea)+1200(Perimeterwall)
+1200(Floorslabarea)+1200(Screenslength) (20) Intheexpression(20)issubstitutedthelandareafortheexpres- sions (5) and (6) of the methodology, thenthe perimeters is substitutedfor:2BSup+2LSup.Thefloorslabareaissubstituted bytheformulas(5)and(6);andthescreenlengthcanbyrep- resentedbythemultiplicationofthenumberofscreensandthe length,whichaccordingtothemethodologyisthe70percentof thelagoonlength.Theexpression(21)showsthesubstitutions:
Totalcost=750BSupLSup+1200(2BSup+2LSup)
+1200BSupLSup+1200(0.7)NMampLSup (21) Theexpression(21)canbysimplifiedbyusingthelength:width ratioof3.Theexpression(22)showsthementionedabove:
LSup =3BSup (22)
Inordertodefinethedecisionvariables(OandNMamp);must beclearedthevolumeintheexpression(2)andreplacedbythe formula(1);asseeninformula(23):
O= Afz
Qi (23)
Laterthe expression(23)issubstitutedinformula(3);inthis casetheslopeoftheperimeterwalliscero,soBSupisequalto BPromandisobtained:
BSup=
OQi
3z (24)
Thentheexpression(24)issubstitutedinformula(22),asseen inexpression(25):
LSup=3∗
OQi
3z (25)
Finallytheformula(24)and(25)aresubstitutedintheobjective function(21),andisobtained:
Totalcost=750
OQi
3z
3∗
OQi
3z
+1200
2
OQi 3z
+2
3∗
OQi 3z
+1200
OQi 3z
3∗
OQi 3z
+1200NMamp(0.7)
3∗
OQi
3z
(26) Theformula(26)canbysimplifyasshowninexpression(27):
Totalcost=5850OQi
3z +9600
OQi 3z +2520NMamp
OQi
3z (27)
3.2. Modelconstraint
FollowingthecriterionusedbyMartínez,Cansino,García, Kalashnikov,andRojas(2014),fordeterminingthemodel’scon- straintsofafacultativepondaretakentheformulas(28)and(29):
BODe =
BODi
((Kf35O)/(1.085)35−T)+1
∗
Qi
Qi−0.001BSupLSupe
(28)
Ne=
4Ni(Term 1)exp(Term 2) (Term 3)
[Term 4] (29)
where
Term 1=
1+4KbOF 3(0.7)(NMmp+1)2
−0.26118+0.25392(3(0.7)(NMmp+1)2)+1.0136(3(0.7)(NMmp+1)2)2
(30)
Term 2= 1−
1+4KbOF 3(0.7)(NMmp+1)2
−0.26118+0.25392(3(0.7)(NMmp+1)2)+1.0136(3(0.7)(NMmp+1)2)2 2(3)(0.7)(NMmp+1)2
−0.26118+0.25392(3(0.7)(NMmp+1)2)+1.0136(3(0.7)(NMmp+1)2)2
(31)
Table1
Existentfacultativepond.
Pond Qe(m3/day) Ne(MPN/100mL) BODe(mg/L) WSup(m) LSup(m) ASup(m2)
Facultative 208.93 58,384 43 39.37 112.11 4414.03
Term 3=
⎛
⎝1+
1+4KbOF 3(0.7)(NMmp+1)2
−0.26118+0.25392(3(0.7)(NMmp+1)2)+1.0136(3(0.7)(NMmp+1)2)2
⎞
⎠
2
(32)
Term 4=
Qi
Qi−0.001BSupLSupe
(33)
Thesuperiorwidthandlength(formulas(24)and(25))are substitutedintheexpressions(28)and(33),thatisthewayto link the constraintsto the objective function(27); the model dependsonthedecisionvariables(OandNMamp).Theabove processisshownbelow:
BODe=
BODi
((Kf35OM)/(1.085)35−T)+1
∗
Qi
Qi−0.001(√
(OQi)/3z)(3∗√
(OQi)/3z)e
(34)
Term 4=
Qi
Qi−0.001(√
(OQi)/3z)(3∗√
(OQi)/3z)e
(35)
Finally the optimization model is presented complete (expression(36)),thefecalcoliformandtheBODarerestricted by the norm NOM-001-ECOL-96. Also, it is added a non- negativityconditionforthedecisionvariables(OM,NMamp≥0).
Minimize
Totalcost=5850OQi 3z +9600
OQi
3z +2520NMamp
OQi 3z Subjectto:
BODe=
BODi
((Kf35O)/(1.085)35−T)+1
∗
Qi
Qi−0.001(3)((OQi)/3z)e
≤75
Ne=
4Ni(Term1)exp(Term2) (Term3)
[Term4]≤1000 O,NMamp≥0
(36)
4. Exampleapplication
Itisneeded toredesignawastewatertreatment plantfora ruralcommunityof1500inhabitantslocatedinthemunicipality ofGómezPalacio,stateofDurango,MX.Thelaststepof the treatmentplantisafacultativepond,butthenumberoffecalcol- iformintheeffluentdoesnotmeetthestandardforpouringinto receptorwaterbodies.Itisproposedtoaddamaturationpond afterthefacultativeone.In Table1areshownthedimensions anddataoutputsoftheexistentpond.
4.1. Resultsanddiscussion
WiththedataoutputsfromTable1isdesignedthematuration pond using the traditional methodology, without considering screens.Table2showstheresults.
Fig.3showsthedimensionsofthepondsystemdetermined withthetraditionalmethodology,asalreadyindicatedtherewere no screensconsidered inthe maturationpond.In accordance withTable 2,were obtained the fecalcoliform andthe BOD withinthemaximumpollutantallowedbynorm.
4.2. Mathematicalmodelapplication
Inordertosolvetheminimizationmodel,itisusedtheinterior pointalgorithm.Themodel(expression(36))mustbewrittenin codeasshownbelow:
Facultative pond Maturation pond
112.11 106.06
35.35 39.37
Fig.3.Treatmentsystemredesignwiththetraditionalmethod.
Table2
Maturationponddesignwiththetraditionalmethodology.
Datainputs
Qi Nf/Noi BODi T
209 58,383.90 43 11.8
Results
Pond O(days) X d Kb a WProm(m) LProm(m) Averagearea(m2)
Maturation 17.95 3 0.3118 0.4648 3.37661 35.35 106.06 3749.53
Pond Qe(m3/day) Ne(MPN/100mL) BODe(mg/L) NMamp WSup(m) LSup(m) ASup(m2) Totalcost
Maturation 190.18 1000 11 0 35.35 106.06 3749.53 $7,650,981.38
function[f]=Objectivefunction(x)
%Firstaredefinedtheinfluentflowanddepthofthepond.
Qi=209;
z=1.0;
%f=TotalCost
%andtheretentiontimeandnumberofscreensarerepresentedbyx(1) andx(2),respectively.
f=5850*(x(1)*Qi/(3*z))+9600*sqrt(x(1)*Qi/(3*z)) +2520*x(2)*sqrt(x(1)*Qi/(3*z));
function[c,ceq]=Constraints(x) Ni=58383.9;
T=11.8;
e=5;
z=1.0;
Qi=209;
DBOi=220;
kb=0.841*(1.075)ˆ(T-20);
%c(1)representstheinequalityconstraintforthefecalcoliform:c(1)=
Ne-1000≤0
c(1)=(4*Ni*sqrt(1+4*kb*x(1)*3*0.7*(x(2)+1)ˆ(2)/(-
0.26118+0.25392*(3*0.7*(x(2)+1)ˆ(2))+1.0136*(3*0.7*(x(2)+1)ˆ(2))ˆ(2)))...
*exp((1-sqrt(1+4*kb*x(1)*3*0.7*(x(2)+1)ˆ(2)/(- 0.26118+0.25392*(3*0.7*(x(2)+1)ˆ(2))
+1.0136*(3*0.7*(x(2)+1)ˆ(2))ˆ(2))))/(2*3*0.7*(x(2)+1)ˆ(2)/(-
0.26118+0.25392*(3*0.7*(x(2)+1)ˆ(2))+1.0136*(3*0.7*(x(2)+1)ˆ(2))ˆ(2)))))... /((1+sqrt(1+4*kb*x(1)*3*0.7*(x(2)+1)ˆ(2)/(-
0.26118+0.25392*(3*0.7*(x(2)+1)ˆ(2)) +1.0136*(3*0.7*(x(2)+1)ˆ(2))ˆ(2))))ˆ(2))...
*(Qi/(Qi-0.001*3*x(1)*Qi/(3*z)*e))-1000;
%c(2)representstheinequalityconstraintfortheBOD:%c(2)=
BODe-75≤0
c(2)=(DBOi/((1.2*x(1)/(1.085)ˆ(35-T))+1))...
*(Qi/(Qi-0.001*3*x(1)*Qi/(3*z)*e))-75;
%ceqrepresenttheequalityconstraints,butasthereisnone.Ceqis equaltocero.
ceq=0;
end
ThemodelwassolvedbyMatlab’sFminconfunction,with theinteriorpointalgorithm.Themodeldeterminesthevariables, inthiscasethetotalcost,retentiontimeandnumberofscreens.
TheresultsareshowninTable3.
FollowingthecriteriaofFig.1,thenumberofscreensturned outtobeadecimalnumber,soitisroundedtothenextinteger number,thenNMamp=6.Withthisdataarecalculatedtherestof theresultswiththetraditionalmethodology,asseeninTable4.
According toTables2 and4,the hydraulic retention time wasreducedby8.65days,whichrepresentsthe48.18percent.
According to CNA and IMTA (2007a, 2007b) the above
Table3
Matlaboptimizationresults.
Variables Results
f=Totalcost $4,362,825.34
x(1)=O 9.3024
x(2)=NMamp 5.1224
reduction affects the areaof land required.It is importantto mentionthatunlikethetraditionaldesign,whichisiterative,the interiorpointalgorithmdeterminedtheoptimumretentiontime andnumberofscreens,andthiswouldbeverycomplicatedto achieve withthetraditional method becauseit hasmorethan oneindependentvariable.
With the Matlab software were inferred that 6 screens wouldbethebest,aboutthis,ShiltonandMara(2005),Abbas et al. (2006), Shilton and Harrison (2003a), Muttamara and Puetpaiboon(1997),Brachoetal.(2006),Winfreyetal.(2010), Kilani and Ogunrombi (1984), Muttamara and Puetpaiboon (1996),VonSperling,Chernicharo,Soares,andZerbini(2002), ShiltonandHarrison(2003b)carriedoutstudiesinstabilization pondsweredifferentnumbersofscreenswereconsidered,and Theyconcludedthattheusesofscreensincreasestheelimination ofthepathogens,alsothehydraulicflowgetsimprovedwithin thepond.Thepresentpaperconfirmstheconclusionsmadeby theseauthors.
Tables2and4showsthatthe fecalcoliform andthe BOD arebelowthemaximumcontaminantallowedbynormNOM- 001-ECOL-96 DOF(1996).Theareaintheoptimizeddesign wasreduced by1805.98squaremeters:whichrepresentsthe 48.16percent.Thedifferenceintheareaisanimportantsavingin landrequirement.AccordingtoCNAandIMTA(2007a,2007b), the majordisadvantageofthe pondssystems isthe largearea required.
The cost saving with the optimized lagoon, regard the traditional method, was 42.24 percent which represents
$3,231,865.65.Aboutthis,OlukanniandDucoste(2011)men- tionedthefeasibilitytodiminishtheconstructioncostofapond systemaslongastheconstraintsaredefinedcorrectly;i.e.,when themathematicalmodelisappliedallthepollutantsarewithin thenorm.
Fig.4showsthedimensionsofthematurationpondandthe numberofscreensfortheoptimizationmodel.
Table4
Optimizedresults.
Datainputs
Qi Nf/Noi BODi T
231 10,000,000 220 11.8
Results
Pond O(days) X d Kb a WProm(m) LProm(m) Averagearea(m2)
Maturation 9.30240 102.9 0.0096 0.4648 1.0795 25.45 76.36 1943.55
Pond Qe(m3/day) Ne(MPN/100mL) BODe(mg/L) NMamp WSup(m) LSup(m) ASup(m2) Totalcost
Maturation 199.21 956.02 17 6 25.45 76.36 1943.55 $4,419,115.73
Facultative pond Maturation pond
39.37
112.11
25.45
76.36
Fig.4.Treatmentsystemredesignwiththeoptimizationmodel.
4.3. Sensitivityanalysis
AccordingtoAnderson,Sweeney,andWilliams(1999),sen- sitivity analysis can be done using a tornado diagram. The aforementionedstudyconsists ofmodifying thevaluesof the mainvariablesinordertoobservehowtheoptimumsolutionis affected.
Thetornadodiagramusesbarstodefinesensitivity;i.e.,the widestbarindicatesthemostsensitiveparameteronwhichthe constraintsdependon.Forsensitivityanalysisoffecalcoliform
60%
40%
20%
0%
–20%
–40%
Qi Nmamp Nf/Noi OM
Fecal coliform tornado chart
– 10 % + 10 %
+10%
–10%
Parameter
–2%
2%
Qi
10%
–10%
Nf/Noi
–29%
38%
T
OM 50% –33%
NMamp 4% –3%
T
Fig.5.Sensitivityanalysisoffecalcoliforminthepondsystem.
15%
10%
5%
0%
–5%
–10%
–15%
BODi
BODe tornado chart
–10 % +10 % T
OM
+10%
–10%
Parameter
10%
–6%
–10%
BODi
6%
T
–5%
6%
OM
Fig.6.BODsensitivityanalysisinthepondsystem.
andBOD,weestablishedthecellsonwhichtheydepend,and thentheirvaluesarechanged±10percent(Muramatsu,2011).
Fig. 5 shows the sensitivity analysis for fecal coliform.
The widebar isthe hydraulic retentiontime, it isinterpreted that the concentration of fecal coliform increaseswhen there islowerretention time.The second parameterthatinfluences thefecalcoliformremovalistemperature:lowertemperatures meanhigherconcentration oftheindicatororganism,inorder ofimportancethetornadochartcontinues withthenumberof partitions.
Regarding sensitivity analysis for biochemical oxygen demand(Fig.6),BODconcentrationintheinfluentrepresents themostsensitiveparameter.Next,inorderofimportance,the temperature:thelowerthetemperature, thepollutantremoval efficiencydecreasesandincreasestheconcentrationoforganic matter inthe effluent. Finally,the hydraulic retention timeis interpretedthatashorterretentiontimeincreasestheconcentra- tionoforganicmatterintheeffluent.
5. Conclusions
Amathematicalmodelwasconstructedtooptimizethedesign andcostof amaturationpond.Theresultsshow asignificant
decreaseinhydraulicretentiontimeandcostcomparedtothe results of thetraditional system. The decisionvariables were consideredopen,i.e.,theoptimalvariablesweredeterminedby Matlab,takingintoaccountthewaterqualityconstraints.
Theoptimizationresultsinthematurationpondindicatemore efficientremoval of fecal coliform with baffles.The climatic conditionsinGómezPalacio,locatedinDurango,Mexico,were consideredinthisstudy.
Itiswisetomentionthattheproposedmathematicalmodel canbeadjustedandappliedtodifferentdesignconditions,but itisnecessarytochangethedatatotheenvironmentalcondi- tionsprevailingintheregionunderstudy(e.g.:temperatureand evaporation).Otherimportantdataaretheinfluentflow,costof concretewalls,costofthelandandcostofscreens.
AsseeninTable4,theconsiderationsandmathematicalrea- soningwereverifiedusingthedecisionvariablesdefinedinthe optimizationofthetraditionaldesignmethodology.Itisrecom- mendedtoconductthisstudyinalaboratoryinordertoverify theresultsofthemathematicalmodel.
Conflictofinterest
Theauthorshavenoconflictsofinteresttodeclare.
References
Abbas,H.,Nasr,R.,&Seif,H.(2006).Studyofwastestabilizationpondgeom- etryforthewastewatertreatmentefficiency.EcologicalEngineering,28(1), 25–34.
Anderson,D.R.,Sweeney,D.J.,&Williams,T.A.(1999).Métodoscuantita- tivosparalosnegocios.pp.746–760.InternationalThomsonEditores.
Banda,C.G.(2007).Computationalfluiddynamicsmodelingofbaffledwaste stabilizationponds(Ph.D.thesis).Leeds,UK:SchoolofCivilEngineering, UniversityofLeeds.
Bixio,D.,Cikurel,H.,Muston,M.,Miska,V.,Joksimovic,D.,Schäfer,A.I., etal.(2005).Municipalwastewaterreclamation:Wheredowestand?An overviewoftreatmenttechnologyandmanagementpractice.WaterScience andTechnology:WaterSupply,5(1),77–85.
Bracho,N.,Lloyd,B.,&Aldana,G.(2006).Optimisationofhydraulicper- formancetomaximisefaecalcoliformremovalinmaturationponds.Water Research,40(8),1677–1685.
CNA,&IMTA.(2007a).ManualdeDise˜nodeAguaPotable,Alcantarillado ySaneamientoPaquetesTecnológicosparaelTratamientodeExcretasy AguasResidualesenComunidadesRurales. Jiutepec,México:Mexican InstituteofWaterTechnology.
CNA,&IMTA.(2007b).ManualdeDise˜nodeAguaPotable,Alcantarillado ySaneamiento,Manualdedise˜nodelagunasdeestabilización.Jiutepec, México:MexicanInstituteofWaterTechnology.
Cubillo,A.(1982).Criteriosparaeldimensionamientodelagunasdeestabi- lización.pp.86.Mérida:ICA-CIAT.
DOF.(1996).NormaOficialMexicanaNOM-001-ECOL-1996.Queestablece loslímitesmáximospermisiblesdecontaminantesenlasdescargasdeaguas residualesalossistemasenaguasybienesnacionales.DiarioOficialdela Federación(DOF)SEMARNAT-SecretariadeGobernación.
Hamzeh,R.,&Ponce,V.M.(2007).Designandperformanceofwastestabi- lizationponds..http://www.ponce.sdsu.edu
Kilani,J.S.,&Ogunrombi,J.A.(1984).Effectsofbafflesontheperformance ofmodelwastestabilizationponds.WaterResearch,18(8),941–944.
Martínez,F.C.,Cansino,A.T.,García,M.A.A.,Kalashnikov,V.,&Rojas, R.L.(2014).Mathematicalanalysisfortheoptimization ofa designin afacultativepond:Indicatororganismandorganicmatter.Mathematical ProblemsinEngineering.
Mendonca,S.R.(2000).SistemasdeLagunasdeEstabilización.ComoUtilizar AguasResidualesTratadasenSistemasdeRegadío.Bogotá,Colombia:OPS andOMS,McGraw-Hill.
Muramatsu,M.(2011).Risksolver.Versión11.5.InclineVillage,Nevada,EUA:
FrontlinesystemsInc.
Muttamara,S.,&Puetpaiboon,U.(1996).Nitrogenremovalinbaffledwaste stabilizationponds.WaterScienceandTechnology,33(7),173–181.
Muttamara,S.,&Puetpaiboon,U.(1997).Rolesofbafflesinwastestabilization ponds.WaterScienceandTechnology,35(8),275–284.
Naddafi,K.,Hassanvand,M.S.,Dehghanifard,E.,Razi,D.F.,Mostofi,S., Kasaee,N.,etal.(2009).Performanceevaluationofwastewaterstabilization pondsinArak-Iran.IranianJournalofEnvironmentalHealthScience&
Engineering,6(1),41–46.
Oke,I.A.,&Otun,J.A.(2001).Mathematicalanalysisofeconomicsizingof stabilizationponds.NigerianJournalofEngineering,9(1),13–21.
Olukanni,D.O.,&Ducoste,J.J.(2011).Optimizationofwastestabilization ponddesignfordevelopingnationsusingcomputationalfluiddynamics.
EcologicalEngineering,37(11),1878–1888.
Rojas,R.(2002).CursoInternacional:Gestiónintegraldetratamientodeaguas residuales,Conferencia:Determinacióndelaconstantecinéticaenlagunas deestabilización,MétodosExperimentales.CEPIS/OPS-OMS.pp.9.
Sah,L.,Rousseau,D.P.,&Hooijmans,C.M.(2012).Numericalmodellingof wastestabilizationponds:Wheredowestand?Water,Air&SoilPollution, 223(6),3155–3171.
Shilton,A.,Harrison,J.,&InternationalWaterAssociation.(2003).Guidelines forthehydraulicdesignofwastestabilizationponds.pp.1–64.IWA.
Shilton,A.,&Harrison,J.(2003).IntegrationofcoliformdecaywithinaCFD (computationalfluiddynamic)modelofawastestabilisationpond.Water ScienceandTechnology,48(2),205–210.
Shilton,A.N.,&Mara,D.D.(2005).CFD(computationalfluiddynamics) modellingofbafflesforoptimizingtropicalwastestabilizationpondsystems.
WaterScienceandTechnology,51(12),103–106.
Von Sperling,M.,Chernicharo,C.A.L., Soares,A.M.E., &Zerbini,A.
M.(2002).Coliform andhelmintheggsremovalin acombined UASB reactor–baffledpondsysteminBrazil:Performanceevaluationandmath- ematicalmodelling.WaterScienceandTechnology,45(10),237–242.
Winfrey,B.K.,Strosnider,W.H.,Nairn,R.W.,&Strevett,K.A.(2010).Highly effectivereductionoffecalindicatorbacteriacountsinanecologicallyengi- neeredmunicipalwastewaterandacidminedrainagepassiveco-treatment system.EcologicalEngineering,36(12),1620–1626.
