Jet Za Internet Celotna - Volume 2 - Issue 3 - August 2009

8/3/2019 Jet Za Internet Celotna - Volume 2 - Issue 3 - August 2009

1/104


2/104


3/104

JET

JOURNAL OF ENERGY TECHNOLOGY


4/104

JET

VOLUME 2 / Issue 3

RevijaJournalofEnergyTechnology(JET)jeindeksiranavnaslednjihbazah:INSPEC,CambridgeScientific Abstracts: Abstracts in New Technologies and Engineering (CSA ANTE), ProQuest'sTechnologyResearchDatabase.The JournalofEnergyTechnology (JET) is indexedandabstracted in the followingdatabases:INSPEC

,CambridgeScientificAbstracts:Abstracts inNewTechnologiesandEngineering (CSA

ANTE),andProQuest'sTechnologyResearchDatabase.


5/104

JET

JOURNAL OF ENERGY TECHNOLOGY

Ustanovitelji/FOUNDERSFakultetazaenergetiko,UNIVERZAVMARIBORU/

FACULTYOFENERGYTECHNOLOGY,UNIVERSITYOFMARIBOR

Izdajatelj/PUBLISHER

Fakultetazaenergetiko,UNIVERZAVMARIBORU/

FACULTYOFENERGYTECHNOLOGY,UNIVERSITYOFMARIBOR

Izdajateljskisvet/PUBLISHINGCOUNCIL

Zasl.Prof.dr.DaliONLAGI,

UniverzavMariboru,Slovenija,predsednik/UniversityofMaribor,Slovenia,President

Prof.dr.BrunoCVIKL,

UniverzavMariboru,Slovenija/UniversityofMaribor,Slovenia

Prof.ddr.DenisONLAGI,


Prof.dr.DaniloFERETI,

SveuiliteuZagrebu,Hrvaka/UniversityinZagreb,Croatia

Prof.dr.RomanKLASINC,

TechnischeUniversittGraz,Avstrija/GrazUniversityOfTechnology,Austria

Prof.dr.AlfredLEIPERTZ,

UniversittErlangen,Nemija/UniversityofErlangen,Germany

Prof.dr.MilanMARI,UniverzavMariboru,Slovenija/UniversityofMaribor,Slovenia

Prof.dr.BranimirMATIJAEVI,SveuiliteuZagrebu,Hrvaka/UniversityinZagreb,Croatia

Prof.dr.BorutMAVKO,

IntitutJoefStefan,Slovenija/JozefStefanInstitute,Slovenia

Prof.dr.GregNATERER,

UniversityofOntario,Kanada/UniversityofOntario,Canada

Prof.dr.EnrikoNOBILE,

UniversitdegliStudidiTrieste,Italia/UniversityofTrieste,Italy

Prof.dr.IztokPOTR,UniverzavMariboru,Slovenija/UniversityofMaribor,Slovenia

Prof.dr.AndrejPREDIN,


Profdr.MatjaRAVNIK,IntitutJoefStefan,Slovenija/JozefStefanInstitute,Slovenia

Prof.dr.JoeVORI,UniverzavMariboru,Slovenija/UniversityofMaribor,Slovenia

Prof.dr.KoichiWATANABE,

KEIOUniversity,Japonska/KEIOUniversity,Japan

Odgovorniurednik/EDITORINCHIEF

AndrejPREDIN


6/104

JET

Uredniki/COEDITORS

JurijAVSEC

GorazdHREN

MilanMAR

I

IztokPOTR

JanezUSENIK

JoeVORI

JoePIHLER

Urednikiodbor/EDITORIALBOARD

Prof.dr.JurijAVSEC,


Prof.ddr.DenisONLAGI,

UniverzavMariboru,Slovenija/UniversityofMaribor,SloveniaProf.dr.RomanKLASINC,

TechnischeUniversittGraz,Avstrija/GrazUniversityOfTechnology,Austria

Prof.dr.JurijKROPE,


Prof.dr.AlfredLEIPERTZ,

UniversittErlangen,Nemija/UniversityofErlangen,Germany

Prof.dr.BranimirMATIJAEVI,

SveuiliteuZagrebu,Hrvaka/UniversityofZagreb,Croatia

Prof.dr.MatejMENCINGER,

UniverzavMariboru,

Slovenija

/University

of

Maribor,

Slovenia

Prof.dr.GregNATERER,

UniversityofOntario,Kanada/UniversityofOntario,Canada

Prof.dr.EnrikoNOBILE,

UniversitdegliStudidiTrieste,Italia/UniversityofTrieste,Italy

Prof.dr.IztokPOTR,


Prof.dr.AndrejPREDIN,


Prof.dr.AleksandarSALJNIKOV,

UniverzaBeograd,Srbija/UniversityofBeograd,Serbia

Prof.dr.BraneIROK,

UniverzavLjubljani,Slovenija/UniversityofLjubljana,Slovenia

Prof.ddr.JanezUSENIK,


Prof.dr.JoeVORI,


Doc.dr.TomaAGAR,


Doc.dr.FrancERDIN,


Prof.dr.KoichiWATANABE,KEIOUniversity,Japonska/KEIOUniversity,Japan


7/104

JET

Tehnikapodpora/TECHNICALSUPPORTJankoOMERZU

SonjaNOVAK

Izhajanjerevije/PUBLISHINGRevijaizhajatirikratletnovnakladi300izvodov.lankisodostopninaspletnistranirevije

www.fe.unimb.si/si/ejet/index.php.

Thejournalispublishedfourtimesayear.Articlesareavailableatthejournalshomepage

www.fe.unimb.si/si/ejet/index.php.

Lektoriranje/LanguageEditingTerryT.JACKSON

Produkcija/PRODUCTIONVizualnekomunikacijecomTECd.o.o.

Oblikovanjerevijeinznakarevije/JOURNALANDLOGODESIGNAndrejPREDIN


8/104

JET

Slovenijanapotivnizkoogljinodrubo?

Trajnostni razvoj energetike v Slovenijimora biti oblika razvoja, ki zadoa potrebam poenergiji, ne da bi pri tem ogroal okolje in s tem monosti ivljenja in razvoj prihodnjim

generacijam,da prav tako zadostijo svojim potrebam.V tej smeri (vsajupam tako)je bilspisan tudi dokument Republike Slovenije, sveta vlade RS za konkurennost, StratekidokumentsektorskerazvojneskupineENERGETIKAINTRAJNOSTNIVIRIENERGIJE,zdne10

novembra,2008.Vodseku,kjernavajapremogje zapisano,dapremogdanespredstavlja

pomembenprimarnivirzaproizvodnjoelektrineenergije(vstrukturiproizvodnjepriblinotretjino proizvodnje elektrine energije v RS). Predvideno je, da se bo v prihodnosti

proizvodnjaelektrineenergijeizpremogadoleta2030celopodvojila!?Vduhuzapisanega

stratekegadokumentamebegaodloitev vladeRS, ki sejeodloila za izgradnjonovegablokaTE6,zzastarelotehnologijoseiganjapremogovegaprahupripovianemtlaku(CCT).Tatehnologijasejepojavilav90.letihprejnjegastoletja.(kombiniraniplinskoparniproces

PCCinFBCtehnologiji).eboljerazmislimoinobpoznavanjutrendovrazvoja,bisemoralavlada odloiti vsaj za IGCC (Integrated Gasification Combined Cycle) tehnologijo, ki bi

omogoalaVelenjskiotanjski regijinadaljnji razvojnapodrojuenergetike, tudikobodoizrpanezalogepremogavVelenju.Grezakombiniranplinskoparniprocesspredhodnim

uplinjanjempremoga.Prednosttetehnologijejevmonostiuporabealternativnihgoriv,kotso: lesnabiomasa,odpadnaolja,naftniodpadki, komunalniodpadki.Ob temje zanimiva

monost uporabe zemeljskega plina ob prikljuitvi Slovenije na Juni tok ruskegaplinovoda. V tem primeru je tehnoloki del elektrarne sestavljen iz turbin, ki lahkokoristijo razline vrste plinastih goriv. Ta novozgrajen blok bi v tem primeru deloval v

strukturitrajnostnegaenergetskegarazvojaSlovenije.Strukturnobilahkobilvkljuenvsedo

takrat,kobodotehnologijauporabeobnovljivihvirovenergije(OVE)takorazvita,dabomov

Slovenijilahkopokrilivseenergetskepotrebe.

IsSloveniaonthewaytolowlevelcarbonsociety?

Sustainable energy development in Slovenia should perform as a development to fulfil

today'senergyneedswithoutcompromisingtheenvironmentand,aboveall,giving future

generations the possibilities of quality life and development of their own needs. In this

direction (at least Ihopeso)waswrittentheStrategyPlanofDevelopmentofEnergyand

SustainableEnergySourcesby theCouncilonCompetitivenessof theRepublicofSlovenia

(dated10November,2008).Inthecoalsection, it isstatedthattodaycoal isan importantprimarysourceforelectricityproduction(representingonethirdofelectricityproductionin

Sloveia).Itisenvisagedthatinthefuture,by2030,electricityproductionfromcoalwillhave

doubled. In the spirit of the above strategy document, I am very surprised by the

Government's decision for the implementation of a new TES 6 block, with outdated

technology burning pulverised coal at an elevated pressure. This technology is from the

1990s(combinedgassteamprocessPCCandFBCtechnology).Abetterconsiderationonthe

partofthegovernment,withtheknowledgeoftodaysdevelopmenttrends,wouldbetheIGCC (Integrated Gasification Combined Cycle) technology, allowing the Velenjeotanjregion further development in the energy field, after the coal reserves in Velenje are

exhausted. IGCC is a combined gassteam process with previous coal gasification. Theadvantage of this technology is in its possibility of using alternative fuels such aswood

biomass,wasteoil, andmunicipalwaste. Italsohas theopportunityofusingnatural gas

when Slovenia is connected to the South Stream pipeline from Russia. In this case, the


9/104

JET

technology of the powerplant consists of gas turbines,which can benefit fromdifferenttypes of gaseous fuels. This newly built block could be integrated into the structure ofsustainable energy development, providing much needed energy until the technology ofalternativeenergysourceswillbefullydevelopedtomeetallenergyneedsinSlovenia.

Krko,August2009

AndrejPREDIN


10/104

10 JET

Table of Contents /

Kazalo

Nuclearrenaissanceasaviablesolutionforreducinggreenhousegasestheenvironmentalimpactofdifferentenergytechnologies/Jedrska energija zmanjuje emisije toplogrednih plinov vplivi razlinih tehnologij za

proizvodnjoelektrineenergijenaokolje

Tomaagar,RobertBergant,SamoFrst................................................................................11

Mathematicalmodelofthepowersupplysystemcontrol/Matematinimodelupravljanjaenergetskegasistema

JanezUsenik...............................................................................................................................29

The calculationof thermodynamicproperties forhydrochloric and copper compounds in ahydrogenproductionprocess/Izraun termodinaminih lastnosti v hidroklorovih in baker klorovih komponentah v procesu

proizvodnjevodika

JurijAvsec,GregF.Naterer,AndrejPredin...............................................................................47

InvestmentsinrenewableenergysourcesandcasesofgoodpracticesoffiscalstimulationinEU/InvesticijevobnovljiveenergetskevireinprimeridobrepraksefiskalnihspodbudvEUMejraFesti.................................................................................................................................65

Cavitationswirlattheentranceofcentrifugalpump/KavitacijskivrtinecnavstopuvradialnorpalkoAndrejPredin,BotjanGregorc,IgnacijoBilu..........................................................................85

Instructionsforauthors..............................................................................................................99


11/104

JET 11

JETVolume2(2009),p.p.1128

Issue3,August2009

http://www.fe.unimb.si/si/ejet/index.php

NUCLEAR RENAISSANCE AS A VIABLE

SOLUTION FOR REDUCING GREENHOUSE

GASES THE ENVIRONMENTAL IMPACTOF DIFFERENT ENERGY TECHNOLOGIES

JEDRSKA ENERGIJA ZMANJUJE EMISIJETOPLOGREDNIH PLINOV - VPLIVI

RAZLINIH TEHNOLOGIJ ZAPROIZVODNJO ELEKTRINE ENERGIJE NA

OKOLJE

Tomaagar,1,RobertBergant2,SamoFrst3

Keywords:emissions,environment,technology,electricityproduction

Abstract

Climate change is happening and represents one of the greatest environmental, social and

economicthreats

facing

the

planet.

The

Intergovernmental

Panel

on

Climate

Change

(IPCC),

an

associationofscientistsfromallovertheworld,cametotheconclusionthatthemainreasonistheenhancedgreenhouseeffect.

Tomaagar,PhD.,GENenergija,d.o.o.,Tel.:+386(7)4910132,Fax:+386(7)4901118,

Emailaddress:[email protected] Tomaagar,PhD.,UniversityofMaribor, FacultyofEnergyTechnology, Tel.:+386 (7)62022102

Robert

Bergant,

PhD.,

GEN

energija,

d.o.o.,

Tel.:

+386

(7)

491

0404,

Fax:

+386

(7)

490

1118,

Emailaddress:[email protected],GENenergija,d.o.o.,Tel.:+386(7)4910136,Fax:+386(7)4901118,

Emailaddress:[email protected]


12/104

12 JET

PhD.Tomaagar,PhD.RobertBergant,SamoFrst JETVol.2(2009) Issue3

The production of electricity is, beside transportation, the most harmful contributor to the

enhancedgreenhouseeffect.Unfortunately,themajorityofelectricityproduction isstillbased

onacombustionoffossilfuels,e.g.coal,oilandgas.Renewablesourcessuchashydro,solaror

wind

are

becoming

increasingly

preferable.

Nuclear

energy

is

also

an

important

low

carbon

energy sourcewith insignificant impacton theenvironment. Itswholecycleemissionsareat

leastaslowastheemissionsofabovementionedrenewablesources.Besidesitsenvironmental

benefits,nuclearenergyhasalsoeconomical, spatial and socialadvantagesover someother

renewablesources.

The purpose of the article is to present integrated environmental impacts for different

technologychainsused forelectricityproduction.Two separateand independent studiesare

shown in this intention.A summaryofdifferent studies,madebyOrganization forEconomic

CooperationandDevelopment (OECD),presents thecomparisonofenvironmental impactsof

differenttechnologychainsfortheelectricityproductionsector,basedondatasuppliedbythe

OECD organizations members. The study of the company GEN energija is focused on thecomparison of environmental impacts of different technology chains that are feasible for

electricity production in Slovenia, i.e. technologies such as nuclear, coal, gas, different

renewablesourcesandamixtureofrenewablesources,whichincludethehydro,biomass,wind

andphotovoltaicproduction.

Theevaluationoftheenvironmentalimpactsfordifferentenergytechnologiesisimplemented

withinradius10kmoftheexistinglocationofNuklearnaelektrarnaKrko(NEK)site,inorderto

evaluateandpresenttheenvironmentalconsequencesofdifferentelectricalpowerproducing

energy technologies.Electricalpowerproduction from fourpotentialnuclear reactordesigns,

imported coalfired power generation, combinedcycle gasfired generation, and renewable

power generation sources, including hydroelectric generation, solar photovoltaic generation,windgeneration,biomasscogeneration,andgeothermalelectricgenerationareconsidered.

Twoassumptionsforelectricalpowerproducingtechnologiesareaninstalledcapacityof1,100

MWeanda90%BaseloadCapacityFactor.Therenewablesourcesareevaluatedasaresource

mix (RESMix)andarenotcapable reaching the required90%BaseloadCapacityFactor. It is

assumedtohaveacombined34%BaseloadCapacityFactoriftheevaluationregionisexpanded

tothewholeofSlovenia.FortheRESMix,32%hydroelectricgeneration,36%windgeneration,

32% biomass cogeneration,


13/104

JET 1

NuclearRenaissanceasViableSolution forreducingGreenhouseGasesEnvironmentalImpactofdifferentEnergyTechnologies

goriv, ki imajonajvejidoprinos kemisijam toplogrednihplinov. Zaradipotrebpo znievanjuspecifinihemisijnapomembnostizopetpridobivatudijedrskaenergija,kisodivnizkoogljinoproizvodnjoenergije.Pravtakosonjeniskupnivplivinaokoljeindrubougodnejialivsajtako

ugodnikotvpliviobnovljivihvirov.

Namen prispevkaje prikaz celostnih vplivov na okolje pri proizvodnji elektrine energije pri

uporabi razlinih tehnologij.V tanamen staprikazanidve loeni inneodvisni tudiji, in sicerpovzetekrazlinihtudijmednarodneorganizacijezagospodarskosodelovanjeinrazvoj(OECD)in tudija podjetja GEN energija. Povzetek tudij organizacije OECD obravnava primerjavovplivov na okolje razlinih tehnolokih verig za pridobivanje elektrine energije na osnovipodatkov, ki jih organizaciji OECD posredujejo njene lanice. tudija GEN energije pa jeosredotoena na primerjavo vplivov na okolje obravnavanih tehnologij, ki so smiselne ter

izvedljive za proizvodnjo elektrine energije v slovenskem prostoru in sicer jedrske,premogovne,plinske,obnovljivihvirov inmeaniceobnovljivihvirov,medkaterespadavodna,biomasna,vetrnainfotovoltainaproizvodnja.

Oje obmoje prikazanih vplivov obsega 10km radij okoli obstojee lokacije NuklearneelektrarneKrko.Cilj tudijejeocenitev katera izmed tehnologijpredstavljanajnijocelostnoobremenitev okolja pri pasovni proizvodnji proizvodni elektrine energije na lokaciji ob

obstojeiNuklearnielektrarniKrko.Zahtevizanovoproizvodnoenotostainstaliranaelektrinamo1100MWeinfaktorrazpololjivostienote90%.Ocenjenoje,dameanicaobnovljivihvirovnemore zadostiti osnovni zahtevi faktorja razpololjivosti 90% pri instalirani elektrinimoi1100MWe.Dosee levrednost34%,ob raziritvipredvidenegaobmojanacelotnoSlovenijo.Deleposameznetehnologijevmeaniciobnovljivihvirovpredstavlja32%vodna,36%vetrna,

32%biomasna,


14/104

1 JET


1 INTRODUCTION

Climatechange

is

aresult

of

increasing

greenhouse

gas

emissions

and

growing

problem

that

requiresinterdisciplinarycooperationacrosstheworld.TheKyotoProtocolAlliancesignatories

havetheobjectiveofa20%greenhouseemissionsreductionin2020,comparedto1986levels.

The instrumentsforachievingthisaredifferentacrosscountries,but ingeneralallsignatories

havetobecomelowcarbonsocietiesinallareas.Anespeciallysensitiveandimportantareain

the transition to a lowcarbon society is the sectorof energyproduction,whichhas a large

contributiontogreenhousegasemissions.Therefore,itisimportantforeachcountrytohavea

detailedplanforthefurtherdevelopmentofthissector;thisalsohasan important impacton

theeconomicperformanceofthecountry.Itisimportanttopursuedevelopmenttowardslow

carbon,economicallyjustifiedandsustainabletechnologies.

2 ELECTRICITY PRODUCTION IN SLOVENIA

Theenergyproduction sectorcombinesheatproductionandelectricityproduction. In recent

years, Slovenias electricityproductionhasbeen insufficient, since annual average electricity

importhasreachedover20%.Suchhighinputlevelshavebeenreducingthecompetitivenessof

the domestic economy; therefore, new investments in the modernization of the electricity

productionaswellasexpansionofcurrentcapacityarenecessary.Amongthemost important

technologies forSlovenianelectricityproductionarenuclear, coal,gas,hydroand renewable

energysources

technologies.

Inaccordancewiththelegalcommitmentsregardingthereductionofgreenhousegasemissions

setby theEU202020objectives,whichcall for20% fewerGHGemissions,20% lower final

energy consumption and a 20% share of renewables in final energy consumption by 2020,

production economy resources aims, greater economic competitiveness and sustainable

developmentobjectives,andallproductiontechnologiesshouldbecomparedunderthesame

principle before the decision for a particular technology in the process of extending the

electricityproductioncapacityshouldbemade.Thecomparisonshouldbebasedonthesame

basicplatformaswellasontheevaluationofindividualtechnologies.

Slovenia

has

a

similar

procedure,

as

the

one

mentioned

above,

in

the

process

of

spatial

planning

called a strategic/comprehensive environmental impact assessment and an environmental

impactassessment.Thesetwoprocessesarenotacomparisonwithothertechnologiesandthe

choiceof theoptimal solution,butonlyevaluationof theenvironmentalacceptabilityof the

individual plans without intervention on site. The Republic of Slovenia therefore has no

legislation for the comparison of technologies thatwould serve foroptimal decisions in the

processofproductioncapacityexpansion.

Similar comparison studiesaremore common abroad.One such stuywas completedby the

OrganizationforEconomicCooperationandDevelopment(OECD),whichhas largestdatabase

for the comparison of technologies based on energy production factors. The analyses

performedby

the

OECD

were

based

on

current

actual

data,

delivered

by

countries

all

around

theworld.Therefore,wewanttopresentthemostimportantresultsofsomeOECDanalysisas

wellasourstudyofenvironmental impactsofdifferentenergy technologyoptions,enhanced

withanalysisanddata,basedonglobalscaleexpertise.


15/104

JET 1


GEN energija is an energy company thatwants to play an active role in the new cycle of

investment in new electricity production capacity in Slovenia. To enhanceGENs technology

decision with substantiated facts, the study of environmental impacts of different energy

technologyoptions

for

electricity

production

in

Slovenia

[1]

was

ordered

from

an

internationally

recognized engineering firm, the Washington Group International (a division of URS

Corporation),whichhasastrongteamofenvironmentalexperts.

3 RESULTS OF OECDs TECHNOLOGY COMPARISONS STUDIES

TheOrganization forEconomicCooperationandDevelopment (OECD)made thecomparison

analysesofdifferenttechnologychains[2].Thesestudieswerebasedon informationsupplied

by the organizations individualmember states, aswell as by countries that are not OECD

members.Thestudies included theenvironmental,socialandeconomicaspectsof theentireenergychainfromthebeggingtotheend(lifecycleassessmentLCA).

Sciencebased, industrial, international lifecycleassessment (LCA)and lifecyclemanagement

(LCM)datafromallovertheworldcanbefoundonhttp://www.ecoinvent.org/.Theecoinvent

Centre is theworld's leading supplierof consistent and transparent life cycle inventory (LCI)

dataofknownquality.TheresultspresentedbelowarebasedonreportsofDonesetal.[46].

Environmental (greenhouse gas emissions, SOX, NOX, nonradioactive waste, land use and

accidentrisks),social(humanhealthimpacts)andeconomicindicators(useofenergyandnon

energeticresources)arepresented.

3.1 Greenhouse gas emissions

Greenhousegasemissionshaveaglobalimpactontheenvironment,withamajorroleinglobal

warming and climate change. Figure1 shows a comparisonof greenhouse gasemissions for

eachelectricityproductiontechnologychain.

Foreachtechnology,theaveragedatavalueispresentedtogethernetmaximumandminimum

values.Themaxandminvaluesarealsolabeledwithcountrycodes,indicatingtheoriginofthe

data.

Emissions are expressed in kgCO2 equivalent per unit of generated energy. Lignite has the

highestemissions

in

the

UCTE

(The

Union

for

the

Co

ordination

of

Transmission

of

Electricity)

average, slightly above 1.2 kgCO2eq./kWh; coal has a slightly lower level, with the UCTE

average of around 1.07 kgCO2eq./kWh. The chain of natural gas has the lowest level of

emissionsoffossilsystemswithUCTEaverageslightlyabove0.6kgCO2eq./kWhandaround0.4

kgCO2eq./kWh for cogeneration.Greenhouse gas emissions from the nuclear chain and the

renewableenergy sources chains are twoordersofmagnitudebelow theemissionsof fossil

fuelschains.TheUCTEaverage fornuclear isabout8gofCO2eq./kWh,5gCO2eq./kWh for

hydro,11gCO2eq./kWhforcostalwindturbines,14gCO2eq./kWhforoffshorewindturbines,

60gCO2eq./kWhforPV(photovoltaics) [7]and100gCO2eq./kWhforwoodcogeneration.


16/104

1 JET


Figure1:CO2equivalentgreenhousegasemissionsforeachelectricityproductiontechnologychains

3.2 Other atmospheric emissions

Whilethegreenhousegasemissionshaveimpactsonglobalwarmingandclimatechange,SOX,

andNOXhavemoreregionalandlocalimpacts.Inaddition,thesepollutantsareimportantalso

fromregularpointofview.ThereareSEVESOEUandnationalregulationsandEnvironmental

protectionActlimitingtheSOXandNOXemissions.

SO2emissionsaredominatedbythedirectemissionsfrompowerplants.Thelevelofemissions

dependsonthesulfurcontentoffuelsandtheemissioncontrolcriteria..AsshowninFigure2

brown

coal

and

oil,

with

a

UCTE

average

of

around

7

g/kWh,

have

the

highest

level

of

SO2

emissions.HardcoalhasaUCTEaverageofabout3g/kWh,whilethechainofnaturalgashasa

UCTEaverageofabout0.2g/kWhemissions,whichistheminimumbetweenthechainsoffossil

fuels.TherateofSO2emissions inthenuclearchainandtherenewableenergysourceschains

aremorethantwoordersofmagnitudebelowtheemissionsoffossilfuelschains.Hydroand

windhavethelowestlevelofSO2emissionsamongrenewableenergysourceschains.


17/104

JET 1


Figure2:SO2emissionsforeachelectricityproductiontechnologychains

Oilhas thehighest levelofNOXemissionsofall theenergy chain,with theUCTE averageat

around2.8

g/kWh

(see

Figure

3).

Levels

of

NOXemissions fromcoalchainsareslightly lower,

with theUCTEaverageofaround2.2g/kWh.Thechainofnaturalgashas the lowest levelof

NOXemissionsamongfossilsystemswithaUCTEaverageofaround0.7g/kWh.ThelevelofNOX

emissionsfornuclear,hydroandwindtechnologyisuptotwoordersofmagnitudelowerthan

therateoffossilfuelsNOXemissions.


18/104

1 JET


Figure3:NOxemissionsforeachelectricityproductiontechnologychains

3.3 Non-radioactive waste

Figure4:Productionofnonradioactivewastefordifferentenergychains


19/104

JET 1


ProductionofnonradioactivewastefordifferentenergychainsisshowninFigure4.Hardcoal

and lignite power chains produce the largest quantities of nonradioactive waste with UCTE

averagesofaround1.18kg/kWh.Withinthelignitechain,amajorcontributionisashproduced

duringpower

plant

operation,

while

within

hard

coal

chains

asubstantial

proportion

of

the

wastecomesfromexcavation.Thenaturalgasandnuclearchainsproduceaminimumquantity

ofnonradioactivewaste.Theamountofnonradioactivewasteinhydroandwindchainsistwo

ordersofmagnitudehigherthanforthenuclearchain.

3.4 Land use

Landuse, shown inFigure5, ismeasured inm2/kWhand refers to areas which are modified

from natural or primary habitat to different habitat states as a result of human intervention

insidethe

whole

energy

chain.

Figure5:LandusefordifferentenergychainsDue to the forestryand logging thatarerequired for theuseofbiomass,woodcogeneration

requires the largest land use, followed by coal and oil energy chains. Exploitation and

productionofoil,aswellastheextractionofhardcoal,requireconsiderablespace.

3.5 Accident risks

The data are derived from a comprehensive severe accidents databases, ENSAD (the Energy

relatedSevere

Accident

Database),

with

an

emphasis

on

the

energy

sector.

Databases

enable

a

comprehensiveanalysisofaccidentsrisks,whicharenotlimitedtoelectricitypowerplantsbut


20/104

20 JET


covertheentireenergychain, includingexploration,extraction,processing,storage,transport

andwastemanagement.

ENSAD currently contains 18,400 accidents, of which approximately 89% occurred between

1969

and

2000.

Human

causes

of

accidents

represent

70%

of

all

accidents,

while

natural

disastersrepresent30%.Allaccidentsrelatedtoenergyrepresenting35%ofallaccidentsand

50%ofhumancausedaccidents.Among theenergyassociatedaccidents, theshareofsevere

accidentsis49%,amongwhich67%accidentsarewithfiveormorefatalities.Accidentsthatare

not related to energy and natural disasters have secondary importance within ENSAD. More

detaileddatacanbeseeninTable1.

Table1:ENSADreportoverviewforaccidentswithatleastfivefatalitiesforperiodfrom1969to2000

Energy OECD EU15 nonOECD

chain

Accidents Fatalities

Accidents Fatalities Accidents Fatalities

Coal 75 2,259 11 234 102

1,044(a)

4,83118,017

(a)

Oil 165 3,789 58 1,141 232 16,494

Naturalgas 80 978 24 229 45 1,000LPG 59 1,905 19 515 46 2,016

Hydro 1 14 0 0 10 29,924(b)

a)Firstlinewithout China,secondlinewithChina

b)BanqiaoandShimantandamfailurestogethercaused26,000fatalities

Figure6:SevereaccidentsindicatorsforOECDandnonOECDcountriesforperiodfrom1969to2000


21/104

JET 21


ChinahasexceptionalaccidentsstatisticforhydroastheresultoftheBanqiaoandShimantan

dam failures,whichoccurred in1975.Bothdamswerebrokenasaresultofconstructionand

engineeringerrors,whichbecamecriticalduringahugefloodin1975.Asaresultofthesetwo

damfailures,

62

dams

were

destroyed

flooding

an

area

of

55

km

by

15

km.

Some

reports

indicatethetotalnumbersoffatalitiesaresomewherebetween90,000and230,000[3].

Figure6representsthefatalitiesnormalizedtotheunitofenergyproducedperGWeyear.The

highestvalueoffatalitieswascausedbyLPGenergychain,duetothedangerofhandlingLPG.

ThesecondhighestvalueiswiththehydroenergychainduetotheabovementionedBanqiao

andShimantandamfailures.Thecoalenergychainisonthirdplaceduetotheminingprocess,

whichisespeciallydangerousinChina,wheresafetyisatlowlevel.ValuesforOECDandEU15

memberstatesarealmostthesamefortheselectedtechnologychainduetothehighersafety

culturelevel.

3.6 Human health impacts from normal operation

Effectsonhumanhealth inrelationtothenormaloperationcanberepresentedbymortality.

Mortalityisdefinedasareductionofexpectationsoflife,expressedintermsofyearsoflifelost

(YOLL). The consequences of diseases could be evaluated, but it is difficult to combine in a

completelyobjectivemanner,becausetheendresult,yearsoflifelost,andpopulationvalues,

providedbymonetaryrelationschangedramaticallydependingon localconditions,densityof

thepopulation,theprospectof lifeexpectancyandthemedicalassistancethat isavailablefor

theaffectedpopulation.Figure7showsanexampleofmortalitythatistheresultofemissions

ofmajorpollutants,specifictothecurrentGermanenergychains,alsotakingintoaccountthe

radioactiveemissions

[8].

The

methodology

for

assessment

of

health

impacts

was

developed

within the European ExternE project and later revised by Friedrich et al. [9] and Bickel and

Friedrich[10].

Figure7:MortalityassociatedwithnormaloperationofGermanenergychainsintheyear2000


22/104

22 JET


Nuclear,windandhydroenergychainshavelowmortalityinrelationtotheirnormaloperation.

Themortality fornatural gas and solar PV chainsare comparable. Fossil systemsother than

natural gas indicate a greater impact than other options.Mortality due to air pollution is

strongly

dependent

on

the

location,

which

determines

the

number

of

people

affected

by

the

emissionsand the technology,whichwilldetermine thequantityofemissions.The figure for

YOLLpertonofSO2releasedinChinaisonaveragealmostseventimeshigherthantheaverage

of the EuropeanUnion,mainly due to drastic differences in population density around the

plants.

3.7 Use of energy resources

Fossilresourceshavebeenselectedasan indicatorofenergyproductuseduetotheir lackof

stock andusefulnesswithinother sectors.Thishas adirect impacton the longtermenergy

sustainability,ifwe

intend

to

preserve

resources

for

chemical

and

other

uses,

and

not

just

for

energy.

Theconsumptionoffossilfuelsforelectricityproductiondifferentchainsaregiven inFigure8

andcoversthememberstatesofUCTEandsomeotherEuropeancountries.

Figure8:RequirementsoffossilresourcesfordifferentenergychainsConsumptionis,ofcourse,muchgreaterinthefossils,coal,gasandoilchains,thaninthecase

ofnuclearandrenewableenergysourceschains.Chainswithcombinedgaspowerplantshave

the lowest consumption of fossil chains, which is expected due to their effectiveness.

Renewableenergysourcesandnuclearchainsindirectlyusefossilfuelsforheatandelectricity

consumptionwithintheirchains.Hydroenergyhasthelowestconsumptionoffossilfuels.


23/104

JET 2


3.8 Use of non-energy resources

Usageofothernonrenewableresourcessuchasfossilfuelsanduraniumisthemeasurementof

electricityproduction

impact

to

the

environment,

and

therefore

is

included

in

economic

indicators.Copperwasselectedasthereferencematerialforthe limitedmetalresources,but

the consumption of othermaterials could also be used. Figure 9 shows the comparison of

copperneedsforvariouselectricitytypesofproduction inUCTEcountries.SolarpanelsorPV

showsthehighestneedforcopper,whichexceededtheneedsoftheotherchainsbyafactorof

five; solar is followed by the wind energy chain. Chains of fossil fuels, nuclear, and wood

cogenerationhavecomparableneedsforcopper,whicharelowerbyafactorof10comparedto

PV.Hydroenergyshowsthelowestrequirementsforcopper.

Figure9:Requirementsofcopperfordifferentenergychains

4 ENVIRONMENTAL IMPACTS OF DIFFERENT ENERGYTECHNOLOGY OPTIONS FOR ELECTRICITY PRODUCTION INSLOVENIA

Sloveniaisinthedecisionmakingprocessforitsfutureenergyproductionsectordevelopment.

Thedecisionforaspecifictechnologymustbebasedonfactsderivedbyenvironmentalimpact

comparisons liketheOECDstudies,as indicatedabove.Therefore,GENenergijahasordereda

widened environmental impact assessment study with comparisons of different technology

optionsforelectricityproductioninSlovenia.

Thisstudy

was

done

by

URSs

team

of

environmental

experts.

The

basic

position

was

the

technology isavailable inSloveniaand, ifpossibletobe locatedwitharangeof10kmaround


24/104


25/104


26/104

2 JET


Table2:Summaryofenergytechnologyimpacts

The summary table (Table3) of the sitespecificdecision factorswas used for assessing and

ranking the relative feasibilityanddesirabilityof the fourprimaryenergy technologyoptions

evaluatedin

the

study.

The summary table decision factors are land requirements per kWh, green house gases per

kWh,energysupplysecurity,baseloadcapacity factor,ability to locate in regionof influence,

cost per kWh, existing infrastructure, uncertainty risk, economictechnology feasibility,

aggregateenvironmentalimpacts.Allthesedecisionfactorswereevaluatedaccordingtoseven

differentrankings:Xexcellent,Ggood,Ffair,Ppoor,Uundesirable,Nnotavailableor

notapplicableandSwherewassourcedepended.

Nuclear technology is evaluated as the most optimal technology for the expansion of

productioncapacities

in

Slovenia.

Renewable energy sources, whose potential in Slovenia is already heavily utilizing, are

estimatedtobe fair toundesirableandcanserveonlyascomplementary technologiestothe

basicscenariofortheexpansionofproductioncapacity.

Nuclear

ImportedCoa

l

NaturalGas

CombinedCycle

Hydroelectric

Solar

(Photovoltaic)

W

ind

Biomass

Cogeneration

Geothermal

ZeroOption

RESMixOption

*

Climate B E D A-B B-C C C C X C

Ai r B D D A A B C B A C

Surface Water and Groundwater C C C B A A C B B C

Noise C B B B B C B B A C

Ground and Agricultural Surfaces B C-D C A A-D C C-D B-D B D

Landscape C C C A A-B C C C B C

Nature and Natural Areas C B-D B C-D B B-D B-D B B D

Waste M anagement System C D A A A A C A A C

Human and Environmental Health Risks C B B A A-B D-E B B B E

Ionizing Radiation C C-D B A-B A A A A-B X B

Inhabi tants and their Environment A-B E C-D A D-E A C-D A D-E A-C

Cumulations with other Regional Projects B D C A A-D B-D B-D C-D A D

Cultural Heritage B C B B B B B B B B

Protected Areas and Zones B C B D B D B B X D

Integrated Ranking C D D C C D D C C D

Features

Impacted

Summary of Energy Technology Impacts

Energy Technologies

A = No Impac t/ positive impact; B = Insubstantial impact; C = In substantial impacts with mitigation ;

D = Substantial impact; E = Destructive impact; X = Establishing impact not possible

* RES Mix is 32% hydro, 36% wind, 32% biomass


27/104

JET 2


Table3:Summaryofdecisionfactorsfortechnologyselection

6 CONCLUSION

Thedecisionmakingprocessforshortand longtermenergyfuturesolutionsshouldbebased

onsolidenvironmentalimpactscomparisons.

GENenergijaordered thepresentedcomparative study to substantiate itsbusinesspurposes

andthe

decisions,

but

the

main

purpose

is

to

convince

all

who

are

involved

in

the

decision

makingprocessesofhow the futuredevelopmentofenergy for Slovenia shouldentitled the

environmental,economicandsustainablepointofview.

Nuclear technology is at the top of the environmental acceptability on the global scale, as

shownbytheOECDstudies,aswell locally,whichhasshownbytheURSGENstudy.Froman

environmental point of view, nuclear energy is one of the optimal technology choices for

Slovenia,whileincombinationwithotherdecisionmakingfactorsitbecomesthemostoptimal.

Itisalsotheonlybaseloadelectricityproducer,whoseinstalledpowercanbeincreasedalmost

without any impact to the environment, as evidencedby the study. In addition to baseload

electricityproduction,newnuclearpowerplantsarealsocapableofoperating in load follow

production.By

increasing

the

share

of

nuclear

energy

in

final

energy

consumption,

Slovenia

could also greatly reduce greenhouse gas emissions and could achieve the EU and national

targetsforreducingsuchemissions.

If Slovenia wants to stay environmentally conscious, if wants to keep or even increase the

competitiveness of the economy and meet the requirements of sustainable development,

nuclearenergyistheoptimalsolutionforthefuture.

References

[1] URS Washington Group: Preliminary Report on Environmental Impacts of Different

EnergyTechnologyOptionsforSlovenia,April2009,URS


28/104

2 JET


[2] OECDNuclearEnergyAgency:NuclearEnergyRisksandBenefits,2007,OECDNEA

[3] http://en.wikipedia.org/wiki/Banqiao_Dam

[4] DonesR.,BauerC.,BolligerR.,BurgerB.,FaistEmmeneggerM.,FrischknechtR.,HeckT.,

JungbluthN.andRderA.,2004a,LifeCycle InventoriesofEnergySystems:Resultsfor

CurrentSystems inSwitzerlandandotherUCTECountries.Final reportecoinvent2000

No.5.PaulScherrerInstitut/Villigen,SwissCentreforLifeCycleInventories/Duebendorf,

Switzerland.

[5] DonesR.,BauerC.,BolligerR.,BurgerB.,FaistEmmeneggerM.,FrischknechtR.,HeckT.,

JungbluthN.andRderA.,2004b,SachbilanzenvonEnergiesystemen:Grundlagen fr

den kologischen Vergleich von Energiesystemen und den Einbezug von

EnergiesystemeninkobilanzenfrdieSchweiz.Finalreportecoinvent2000No.6.Paul

Scherrer Institut/Villigen, Swiss Centre for Life Cycle Inventories/Duebendorf,

Switzerland.

[6] DonesR.,ZhouX.,TianC.,2003,LifeCycleAssessment.In:EliassonB.andLeeY.Y.(Eds):Integrated Assessment of Sustainable Energy Systems in China The China Energy

Technology Program, Book Series: Alliance forGlobal Sustainability Series: Volume 4,

KluwerAcademicPublishers,Dordrecht/Boston/London(2003)319444.(Bookincl.DVD,

Hardbound ISBN 1402011989, Paperback ISBN 1402011997). Available at:

http://www.springeronline.com/sgw/cda/frontpage/0,11855,5403567233707785

0,00.html

[7] http://re.jrc.cec.eu.int/pvgis/pv/imaps/imaps.htm

[8]

HirschbergS.,

Dones

R.,

Heck

T.,

Burgherr

P.,

Schenler

W.

and

Bauer

C.,

2004a,

SustainabilityofElectricitySupplyTechnologiesunderGermanConditions:AComparativeEvaluation,PSIreportNo.0415PaulScherrerInstitut,Villigen,Switzerland.

[9] FriedrichR.,MarkandyaA.,HuntA.,OrtizR.A.,DesaiguesB.BounmyK.,AmiD.,Masson

S.,RablA.,SantoniL.,SalomonM.A.AlberiniA.,ScarpaR.,KrupnickA.,DeNockerL.,

Vermoote S.,Heck T., Bachmann T.M., Panis L.I., Torfs R., Burgherr P.,Hirschberg S.,

PreissP.,GressmannA.,DrosteFrankeB.,2004,NewElements for theAssessmentof

External Costs from Energy Technologies (NewExt). Final Report to the European

Commission, DG Research, Technological Development and Demonstration (RTD),

September 2004. http://www.ier.uni

stuttgart.de/forschung/projektwebsites/newext/newext_final.pdf

[10] Bickel,P.andFriedrich,R. (Editors),2005,ExternEExternalitiesofEnergyMethodology2005 Update. European Commission, Directorate General for Research, SustainableEnergySystems,EUR21951.


29/104

JET 2


Issue3,August2009


MATHEMATICAL MODEL OF THE POWER

SUPPLY SYSTEM CONTROL

MATEMATINI MODEL UPRAVLJANJAENERGETSKEGA SISTEMA

JanezUSENIK

Keywords:powersupplysystem,control,optimalenergycapacities,Laplacetransform,

fuzzylogic;

Abstract

Inthisarticle,asimplemathematicalmodelofacontinuousstochasticpowersupplysystem isdescribed. Some analytical approaches have been developed to describe the influence of

productionand stock, i.e.additionalcapacitiesonahierarchical spatialpatternanddemand.

UsingtheLaplacetransform, it ispossibletosolvethesystemofdifferentialequations,which

arerepresentedwiththecontinuousmodel.Duetothestochasticnatureofsysteminputs,the

optimality criteria with the Wiener filter are satisfied. The inverse Laplace transform is

calculated with residues in the complex space. Furthermore, an interesting and efficient

approachwithfuzzylogicisused,whichispresentedattheendofthisarticle.

Povzetek

V lankujepredstavljenmatematinimodelupravljanjazveznega stohastinegaenergetskega

sistema.Razvitisonekaterianalitinipristopi,skaterimiopiemomedsebojnivplivproizvodnje

terzalog,v taknihsistemihso tododatnekapacitete,nahiearhinoporazdeljenoprostorsko

dogajanje/porabooziromapovpraevanje.ZuporaboLaplaceovetransformacijereimosistem

diferencialnihenab,kiopisujejodinamikozveznegasistema.Pogojuoptimalnostilahkozaradi

stohastinih vhodov sistema zadostimo z uporabo Wienerjevega filtra. Inverzno Laplaceovo

transformacijoopravimozuporaboresiduov.Vnadaljevanju lankaprikaemoekot izjemno

zanimiv in zlasti zelo uinkovit nain pristopa k reevanju taknega problema tudi monost

uporabemehkelogike.

Corresponding author: Prof. JanezUSENIK, PhD.,University ofMaribor, Faculty of Energy

Technology,tel.+38631751203,Fax:+38676202222,Mailingaddress:Hoevarjevtrg1,8270

Krko,emailaddress:[email protected]


30/104

0 JET

JanezUsenik JETVol.2(2009) Issue3

1 DEFINING THE PROBLEM

Every model of optimal control is determined by a system, input variables and the

optimality

criterion

function.

The

system

represents

a

regulation

circle,

which

generally

consists of a regulator, a control process, a feedback loop, and input and output

information (DiStefano, 1987). In this article, we will only discuss linear dynamic

stationary continuous systems (Usenik et all, 2008). The optimality criterion is the

standardagainstwhichthecontrolqualityisevaluated.The termcontrolqualitymeans

optimalandsynchronizedbalancingofplannedandactualoutputfunctions.

Let us consider aproductionmodel in a linear stationarydynamic system inwhich the

input variables indicate the demand for products manufactured by a company. These

variables, i.e. the demand in this case, can be a onedimensional ormultidimensional

vector functionon the onehandand deterministic, stochasticor fuzzyon the other. In

thisarticle,

stochastic

variables

and

an

outline

of

afuzzy

approach

are

presented.

Let ustakeastationaryrandomprocessXwiththe knownmathematicalexpectationE(X)

and autocorrelationRXX(t) asthe demand inastochasticsituationthatshouldbemet, if

possible,bythe currentproduction.The differencebetweenthe currentproductionand

demand isthe inputfunctionfor the controlprocess,the outputfunctionofwhich isthe

current stock/additional capacities.When the difference ispositive, the surpluswillbe

stockedand when it isnegative,the demandwillalsobecoveredfromstock.Ofcourse,

in the caseofpower supplywedonot have stock in the usual sense (suchas in caror

computeretc.);energycannotbeproducedinadvanceforaknowncustomernorcanstockbe

builtupforunknowncustomers.Thedemandofenergyservicesisneitheruniformintimenor

knownin

advance.

It

varies,

has

its

ups

(peaks)

and

downs

(minima)

and

it

can

only

be

met

by

installingandactivatingadditionalpropertechnologicalcapacities.Becauseofthis,thefunction

of stock in the energy supply process belongs to all the additional technological

potential/capacities, largeenough tomeetperiodsof extrademand. Thedemandofenergy

servicesisnotgivenandpreciselyknowninadvance.Withmarketresearch,wecanonlylearn

about theprobabilityofourspecificexpectationsof intensityofdemand.Thedemand isnot

givenwithexplicitlyexpressedmathematicalfunction;weonlyknowtheshapeandtypeofthe

familyof functions.Demand is,according to these facts,a randomprocess forwhichall the

statisticalindicatorsareknown.

Thesystem inputrepresentsthedemandfortheproducts/services thatagivensubjectoffers.

Let demand be a stationary random process with two known statistical characteristics:

mathematical expectation and autocorrelation function (Usenik, 2001). Any given demand

should be met with current production. The difference between the current capacity of

production/services and demand is the input function for the object of control. The output

function measures the amount of unsatisfied costumers or unsatisfied demand in general.

When thisdifference ispositive, i.e.when thepowersupplycapacityexceeds thedemand,a

surplus of energy will be made. When the difference is negative, i.e. when the demand

surpassesthecapacities,extracapacitieswillhavetobeaddedor,iftheyarenotenough,extra

purchasing fromoutsidewillhave tobedone.Otherwise, therewillbedelays,queuesetc. In

thenewcycle,therewillbeasystemregulator,whichwillcontainallthenecessarydataabout

thetrue

state

and

which

will,

according

to

given

demand,

provide

basic

information

for

the

productionprocess.Inthisway,theregulationcircuitisclosed(Fig.1).Withoptimalcontrolwewill understand the situation in which all costumers are satisfied with the minimum


31/104

JET 1

Mathematicalmodelofthepowersupplysystemcontrol

involvement of additional facilities. On the basis of the described regulation circuit, we can

establishamathematicalmodelofpowersupplycontrol,i.e.asystemofdifferentialequations

forcontinuoussystems(Bogataj,Usenik,2005)inoursituation.

Figure1:Regulationcircuitofthepowersupplysystem

The task istodeterminethe optimumproductionand stock/capacities,sothatthe total

costwillbeaslow aspossible.

2 EQUATIONS OF THE MODEL

Notationsfor 0t areasfollows:

Z t additionalcapacities(stocks)atagiventimet,

u t productionattimet,

d t demandforproductattimet,

leadtime

Let Z t , u t and d t bestationarycontinuousstationaryrandomvariables/functions; theyarecharacteristicsofcontinuousstationaryrandomprocess.

Nowthe

system

will

be

modelled

with

the

known

equations:

Z t v t d t (2.1)

v t u t (2.2)

0

t

u t G Z t d (2.3)

In the equation (03) the function G t is the weight of the regulation that must be

determinedat

optimum

control,

so

that

the

criterion

of

minimum

total

cost

is

satisfied.

The parameter ,namedleadtime, isthe timeperiodneededtoactivatethe additionalcapacities inthe powersupplyprocess.Weusedarealsituation inwhichany goodscan

demand powerstation capacity,potential

production


32/104

2 JET


be sold to the customeronly from the storehouseof finishedgoods,becauseonly in

this case can the information flow of a company be updated and in accordance with

legislation.

Assumingthat

the

input

variable

demand

is

astationary

random

process,

we

can

also

considerproduction and stock/additional capacities tobe stationary randomprocesses

for reasonsofthe linearityofthe system.Let usconsiderthe functions Z t , u t and d t

tobecontinuousstationaryrandomprocesses.

Let us express the total cost, the minimum ofwhichwe are trying to define,with the

mathematicalexpectationofthe squareofrandomvariables Z t and u t :

2 2Z uQ t K E Z t K E u t (2.4)

In(2.4)

ZKand

uK arepositive

constant

factors,

attributing

greater

or

smaller

weight

to

individualcosts.Both factorshavebeendeterminedempirically for the productand are

thereforeinthe separateplant(Usenik,Bogataj,2005).

Equations (2.1)(2.4)representa linearmodelofcontrol inwhichwehave todetermine

the minimumofthe meansquareerror,ifbymeansofaparallelshiftwecausethe ideal

quantitytoequalzero.

Functionsofthesystemare normallytransferred intothe complexareabymeansofthe

Laplace transform. Let be L Laplace operator and Z s , D s , u s , v s Laplacetransforms:

Z s Z t

D s d t

U s u t

V s v( t )

L

L

L

L

Whennow the Laplacetransform isperformedon the functionsofthe system (01)(03),

weobtainthe expressions:

1

Z s v s d s

s

(2.5)

sv s e u s (2.6)

u s G s Z s (2.7)

nthe simplifiedversiontheexpressionsare defined,asfollows

pD s G s d s (2.8)

fV s G s u s (2.9)

f f pG s G s G s (2.10)


33/104

JET


1

f

G sW s

G s G s

(2.11)

wemaydrawthe flowchartinan usualcascadeform(Figure2).

Figure2:The cascadeflowchart

The function (2.4), the minimum of which we are trying to determine, is written in

accordancewiththedefinition ofthe autocorrelationinthe followingform:

0 0 Z ZZ u uuQ K R K R

or,divided

by

0ZK

2

2

0 0 ZZ uu

Z

u

Z

P R A R

QP

K

KA

K

(2.12)

FromFigure2wecansee:

u s W s D s (2.13)

1fZ s W s G s D s (2.14)

Spectraldensitiesfrom ZZR t and uuR t are asfollows:

0

1 1st

ZZ ZZ ZZ f f DDs R t R t e dt W s G s W s G s s

L (2.15)

0

st

uu uu uu DDs R t R t e dt W s W s s

L (2.16)


34/104

JET


Bothequations(2.15)(2.16)are transformedinthe realtimespaceand insertedintothe

equation(2.12):

2

1 1 2 1 2 2

1 1 2 2 3 3 4 1 2 3 4 4

2

1 1 2 1 2 2

0 0

0 2

ZZ uu

DD f DD

f f DD

DD

P R A R

R W t dt G t R t t dt

W t dt G t dt W t dt G t R t t t t dt

A W t dt W t R t t dt

(2.17)

Weare looking for the minimumof the equation (2.17).Thisoptimum isobtainedwith

thevariation

calculus:

optW t W t W t (2.18)

In(2.18),thefunction W t isavariationofthe function W t , representsavariation

parameterand optW t isthe optimalsolutionof(2.18).Function 0W t for 0t .From

(2.17)and(2.18),theWienerHopfequationisderived

2

3 3 2 2 4 1 2 3 4 4 1 3

2 1 2 2 10 for 0

opt f f DD DD

f DD

W t dt G t dt G t R t t t t dt A R t t

G t R t t dt t

(2.19)

The second variation 2

2

d P

d

is obviously positive for every 1 0t and the solution

optW t ofthe equation(2.19)istheminimum.

3 SOLUTION OF THE WIENER-HOPF EQUATION

The WienerHopf equation (2.19) is solved by the spectral factorisation method

(Schneeweiss,1971).From (2.19) theWienerHopfequation isobtained inthe following

form:

0 for ,optW t d t t

(3.1)

Thisequation isanordinary integralequationof the firstorder,whichcan besolvedby

theFourier/Laplace

transform:

0optW s s s


35/104

JET


andfinally

opt

sW s

s

(3.2)

The function s has its zeros(i.e.polesof(3.2))onlyonthe leftsideofthecomplex

plane (s1,s2, s3 inFigure3).Similarly,the function s has itszeroson the rightsideofthecomplexplane(s4,s5, s6inFigure3).

Figure3:Polesofthefunction(21)

Alsothefunction s has itspolesonly inthe lefthalfcomplexplane,whereas s onlyintherighthalfcomplexplane.

The optimalsolution for the cascadeoperator isobtained in formaldesignby (3.2).The

functionsinthe formula(3.2)are definedwithexpressionsinthe Laplaceform:

2 f DD

f f

G s ss

G s G s A

2 f f DDs G s G s A s

4 THE INVERSE LAPLACE TRANSFORM AND RESIDUES

The Laplace transform method solves differential equations and corresponding initial and

boundary value problems. The solution of the subsidiary equation in the complex plane is

transformedback to realplane to obtain the solutionof the given problem. In theend,we

determinethe

inverse

transform -1 f t F sL , i.e. the solution of the problem. This is

generally themostdifficultstep,and in itwemayuse the tableofLaplace transformsor the

residues(Kreyszig,1999).


36/104

JET


The purpose of the residue integrationmethod is the evaluation of integrals C

f s ds ,

takenaroundasimpleclosedpathC.Iff(s)isanalyticeverywhereonCand insideC, such

an integralequalszero: 0C

f s ds .Iff(s) has a singularity at the point

0s s inside C, but is otherwise analytic on C and

insideC,the function f(s)assumestheLaurentseries:

0

0 10

2 3 31 2

0 1 0 2 0 3 0 2 3

0 0 0

k k

k kk k

b f s a s s

s s

bb ba a s s a s s a s s

s s s s s s

(4.1)

thatconvergesinall pointsnear0

s s (exceptats=s0itself), insomedomainofthe form

0, 0s s R R .The coefficient 1b ofthe firstnegativepowerofthisseriesisobtainedby

theformula

11

2 Cb f s ds

i

(4.2)

Wecanuse the formula(4.2)toevaluatethe integral:

12C

f s ds ib Herewe integratecounterclockwisearound the simple closedpath containing

0s s in

its interior, but noothersingularpointsoff(s)onorinsideC.

The coefficientb1iscalledthe residueoff(s)at 0s s andisdenotedby

0

1Re

2s s

C

s f s f s ds

i

(4.3)

Residue integrationcanbeextended from thecaseofasinglesingularity to the caseof

severalsingularitieswithinthe contourC.Thisisthepurposeofthe residuetheorem:Let

f(s)beanalytic insideasimpleclosedpathCand onC,except for finitelymanysingular

points s1, s2,, sn insideC (Figure4). Then the integralof f(s) taken counterclockwise

aroundCequals2itimesthe sum ofthe residuesoff(s)ats1,s2,,sn.

1

2 Rej

n

s sjC

f s ds i s f s

(4.4)


37/104

JET


Figure4:The residuetheorem

The formulafor theresidueatapoleofany orderisgivenby(Kreyszig,1999):

1

11Re lim 1,2,3,1 ! kk

N

NkNs ss s

ds f s s s f s k N ds

(4.5)

Inthisformula,f(s)has apoleofNthorderat ks s ,and nisthenumberofall poles.Inparticular,for asimplepoleat 0s s theformulais:

00

0Re lim

s ss ss f s s s f s

(4.6)

The residueswillbeusedtocomputethe inverseLaplacetransform:

1 lim2

c i st

c i

f t F s F s e dsi

L-1

(4.7)

In(4.7),wehaveto integrateoverthe lineRe(s)=c.Thislineisbasedonthe assumption

thatall the singularities(poles)ofthe functionF(s)are onthe leftsideofthe line(Fig.5).

Figure5:Integrationoverthe lineRe(s)=c

Ifwe

are

to

apply

the

residue

theorem,

we

have

to

integrate

over

the

counter

clockwise

closed path d . An integral taken over the line Re s c is given as follows. We can


38/104

JET


describeacirclewiththecentreinthe point0and withsucha largeradiusdthatallthe

singularitiesofthe functionf(s)are insidethiscircle(Figure6)

Figure6:Path d andthe insidesingularitiesofthe function f s

Following the residuetheorem, weshallnow write

1 Re2 k

st st

s skd

F s e ds s F s ei

(4.8)

The integraloverthepath d ispossiblydividedintwoparts:the integraloverthe line

AB andthe integral overthe restofthe circle BCDEA .

st st st d AB BCDEA

F s e ds F s e ds F s e ds

(4.9)

Becausethe secondintegral in(4.9)equalszero,weget the followingequationfrom(4.8)

and(4.9):

Rek

st st

s skd

F s e ds s F s e

(4.10)

andthe integral(28)equalsthe sum ofthe residuesof stF s e at 1 2 3, , , , ks s s s toleftofthelineRe(s)=c:

1

lim Re2 k

c ist st

s skc i

f t F s F s e ds s F s ei

L

-1

(4.11)


39/104

JET


5 AN EXAMPLE

For the problem (2.1)(2.4), let the autocorrelation function of demand be known, for

example:

ddR e

(5.1)

Comparing(2.5)(2.7)with(2.8)(2.10)wecanwrite:

1

p

s

f

f f

s

p

G ss

G s e

G s G s

eG s

s

(5.2)

The spectraldensityofthegivenautocorrelationfunctionis,asfollows:

2

2

1dd dd s R t

s

L (5.3)

From

p

d sD s G s d s

s weget

2 2

2

1DD

ss s

andinthe righthalfplane

1

1DD s

s s

Due to

2 1f fG s G s A As

and 2 1

f fG s G s A A

s

wecanobtaintheoptimalcascadeoperator

1

1opt

s CsW s

As

(5.4)

where

1

1

A eC

A

Nowwecanobtainthe operatorofthe optimumregulation


40/104

0 JET


1

1 1 1

opt

s

opt f

W s s CsG s

W s G s As e Cs

inorder

to

get:

a) theoptimalproduction:

1

1 1opt opt p

Csu s W s G s d s

As s

(5.5)

b) theoptimalstock/additionalcapacities:

1

11

s

opt f opt

CsZ s G s u s D s e D s

As

(5.6)

Withthe inverseLaplacetransformweobtainthesefunctionsinthe timearea.

a)the optimalproduction:Informula (5.5),thereare two singlepoles

1

1s A

and2

1s and consequentlytwo

residues:

1

11 1Re lim

1 11

t

st A

sA

Cs e A C es s s

A A A A A s sA

1

1 1Re 1 lim 1

1 11

st t

s

Cs e C es s s

A A s s

A

Consequently,the functioninthe realtimespaceis, asfollows:

2

1

1Re

1 1k

t tAst

opts s

k

A C e C eu t s F s e

A A A

and finally

1

11

t

tAopt

C Au t e C e

A A

(5.7)

Similarlyit

is

possible

to

obtain:

b)the productionwhichreachesthe storehousewiththe delayoftimeunits:


41/104

JET 1


1

1 1

t

tAA C C

v t u t e eA A

(5.8)

c)the

total

demand

in

agiven

time

interval

with

avariable

upper

limit:

1 t D t D s e L-1 (5.9)

d)the totaloptimalstock/additionalcapacities:

t

tAopt

Z t M e Ke

(5.10)

whereKand Mare constants:

1

1

CK e

A

and 1

C AM

A

6 FUZZY CONDITIONS

6.1 Fuzzy logic

Fuzzy logic isan innovative formof logicthatallowsadescriptionofthe desiredsystem

behaviourusing spoken language.Many successfulapplicationshavebeenachievednot

with conventional mathematical modelling but with fuzzy logic. As a theoreticalmathematical discipline, fuzzy logic is designed to react to continuously changing

variables and to challenge traditional logic by not being restricted to the conventional

binaryvaluesof0and 1.Fuzzy logicallowsthe interpretationthatsomething isnot only

trueorfalse,but isalsoapplicabletopartialormultivaluedtruths.Thisdiscipline is

especially useful with problems that cannot be simply represented by classical

mathematicalmodelling for reasons of incomplete data or an overly complex process.

Statements using subjective categories have a major role in the decision making

processes of the humans. The contents of these statements may be quantitative,

uncertain, imprecise or ambiguous, but people can use them successfully for complex

evaluations.

A mathematical model is required to implement the human logic into engineering

solutions. Fuzzy logic makes the representation of the human decision and evaluation

processespossibleinalgorithmicform.Fuzzylogicoperateswithtermssuchasfuzzyset,

fuzzy variable, fuzzynumber, fuzzy relation, fuzzy reasoning etc.A classicalBooleanor

binary logic isbasedon two crisp extremes: yesnow. Yesornow is an answerbeyond

doubt.The set in thiscase isdefinedbycrispboundaries,whereanelement iseithera

memberof some crisp setor it isnot,or its membership can be representedwith the

special functionwhose values are 0 or 1. Fuzzy logic, however, has unclear threshold.

Fuzzy set is not defined by crisp boundaries, some elements are members with

membership1,

some

elements

are

members

with

membership

0,

but

certain

elements

canalsobemoreor lessmembersof this set an theirmembershipcanbebetween0

and 1. Membership mapping the objects onto the unit interval [0, 1]. The degree of


42/104

2 JET


membership inafuzzyset,for examplenamedA, isexpressedbyacontinuousfunction,

calledthemembershipfunction A x .The combinationofimpreciselogicrulesinasinglecontrolstrategyiscalledapproximate

orfuzzy

reasoning.

Thus,

the

fuzzy

inference

is

the

process

of

mapping

from

agiven

input

to an output, using fuzzy logic. Generally, there are five parts of the fuzzy inference

process: fuzzificationof the inputvariable,applicationof the fuzzyoperator (and/or) in

the antecedent, implication from the antecedent to the consequent,aggregationof the

consequentsacrossthe rules,andfinally,defuzzification(Ross,2007).

In fuzzy logic, different values of a given linguistic variable represent concepts, not

numbers.LinguisticvaluesortermsassociatedwiththelinguisticvariablePRICEcanbe

obtainedby specific fuzzy sets like LOW, MEDIUM, HIGH etc.A technicalquantity

PRICE ismeasuredwithnumbers(crispvalue),for example1,000EUR. Incontrast,the

fuzzy approach uses terms, not numbers. Each fuzzy set like LOW or MEDIUM or

HIGHis

formed

by

its

membership

function.

This

function

represents

acertain

degree

to

whichacrispvaluebelongstoagivenfuzzyset.Fromexperience,weknowthatapriceof

10EURor20EUR isLOW,apriceof1,000EURor5,000EUR isHIGH,but 10EUR is

less than 20 EUR, so the degree of membership of the fuzzy set LOW for the crisp

number10isgreaterthanfor the crispnumber20. Theprocedureoftransformationcrisp

numbersintofuzzytermsiscalledfuzzification.Asinglefuzzyruleassumesthe form:

if x isSET_A,thenyisSET_B,where SET_A and SET_B are linguistic values defined by fuzzy sets in the universes of

discourseXandY,respectively.The ifpartofthe ruleiscalledthe antecedentorpremise,while

the

then

part

is

called

the

consequent

or

conclusion.

The

variables x

and

y

are

definedonthe setsXandY.The output of the fuzzy process can be the logical union of two or more fuzzy

membership functions defined in the universe of discourse of the output variable.

Defuzzification is the conversionofagiven fuzzyquantity toaprecisecrispquantity. In

literature, at least seven methods (Ross, 2007) are common for defuzzifying: max

membership principle, centroid method, weighted average method, meanmax

membership,centreofsums,centreofthe largestarea,first(last)ofmaxima.6.2 Fuzzy reasoning

Inprincipleeverysystemcanbemodeled,analyzedandsolvedbymeansof fuzzy logic.

Due to the complexityof the givenproblemand the subjectivedecisionsof customers,

which are better described with fuzzy reasoning, it is advisable to introduce a fuzzy

approach. Some basic solutions of the control problems using fuzzy reasoning were

presented inthe paper (Usenik,Bogataj,2005).For someproblemsaboutthe controlof

the powersupplysystem,weproposefuzzyreasoning.Itisobviousthatdecisionmakers,

whensolvingeverydayproblems incontrolofsystems,operatewithfuzzy logic(Terano,

1992).

Our proposed fuzzymodelwillbebasedon these assumptions,whereby the usual five

stepshave

to

be

taken:

fuzzification

of

the

input

and

output

variables,

application

of

the

fuzzy operator in the antecedent, implication from the antecedent to the consequent,

aggregationofthe consequentsacrossthe rules,and defuzzification.


43/104

JET


6.3 Fuzzification

In the fuzzification phase we have to define fuzzy sets for all fuzzy variables (input and

output)and definetheirmembershipfunctions.

Let us assume for example that the demand id at the location jz depends on a) the

market area, b) the density of the area, c) price, d) season and d) uncertainty. The

demand is in fact the basic variable, on which the behaviour of all retailers depends

(Figure7).

Figure7:Outputfuzzyvariabledemanddependson5inputfuzzyvariables

We assume that all expressions are fuzzy variables, market area, density of the area,

price, season and uncertainty are input fuzzy variable, and demand is an output fuzzy

variable.Everyfuzzyvariableispresentedbymoreterms,for example:

a) inp utfuzzyvariableMARKETAREAisrepresentedby: SMALL,BIG,

b) inp ut fuzzy variable DENSITY OF THE AREA is represented by: WEAK, MEDIUM,

STRONG,

c) inputfuzzyvariablePRICEisrepresentedby: LOW,MEDIUM,HIGH,

d) inp utfuzzyvariableSEASONisrepresentedby: LOW,HIGH,

e) inp ut

fuzzy

variable

UNCERTAINTY

is

represented

by:

SMALL,

MEDIUM,

BIG,

VERY_BIG,

f) output fuzzy variable DEMAND is represented by: VERY_LOW, LOW, MEDIUM,

HIGH,EXTREMELY_HIGH.

For everyfuzzysetand for everyfuzzyvariable, wehavetocreatemembership functions.

For the fuzzy variable DEMAND they could be as shown in Figure 8. On the xaxis, we

measurethevariableDEMANDgiveninunitslikekWh,MWh and soon, dependingonour

data. On the yaxis, we measure membership for every possible demand and for every

fuzzyset VERY_LOW,LOW,MEDIUM,HIGH,EXTREMELY_HIGH.


44/104

JET


Figure8:MembershipsfunctionsoffuzzysetsforfuzzyvariablePRICE

6.4 Fuzzy model

Inourcasewecandefinenphasemodelwithatleastnruleblocksandnsetsofinput/output

fuzzyvariables(Fig.9),(Usenik,2009).

Figure9:Thestructureofthefuzzysystem

These fuzzy variables can solve the problem in general and can introduce quite a good

startingpointfor furtheractionsand stepstobetakeninthe processofdecisionmaking.

Due to the simplicity of this process, all membership functions will be of a simple

triangular and trapezoidal shape. Of course, in further iterations and studies of market

behaviour relevant for the customers demands and requests, we shall state more

sophisticatedconditionstofindanswerstoquestionsinrealworldsituations.6.5 Fuzzy rules inference

The computationof fuzzy rules iscalled fuzzy inferenceandconsistsof threesteps: the

application of the fuzzy operator (and/or) in the antecedent, the implication from the

antecedent to the consequentand the aggregationof the consequentsacross the rules.

The firststepdeterminesthe degreetowhichthe completeIFpartofthe ruleissatisfied.

In thisstep,weusuallyuse theoperatorOR for the minimumand the operatorAND for

the maximum.The secondstepmakesuse ofthe supportofthepreconditiontocalculate

thesupport

of

the

consequence.

Finally,

the

aggregation

step

determines

the

maximum

degreeofsupportfor eachconsequence.


45/104

JET


In our work, we applied FuzzyTech software (FuzzyTech, 2000). In accordance of this

softwaretool,the ruleswereautomaticallycreated.

6.6 Defuzzification

The resultfromthe evaluationoffuzzyrules isfuzzy.Defuzzification isthe conversionof

a given fuzzyquantity to aprecise crispquantity. The most frequentlymethodused in

praxis isCoMdefuzzification (theCenterofMaximum).Asmore than one output term

can beacceptedasvalid, the defuzzificationmethod shouldbea compromisebetween

differentresults.The CoM methoddoesthisbycomputingthe crispoutputasaweighted

averageofthe termmembershipmaxima,weightedbythe inferenceresults(Ross,2007).

CoM is a kindof compromise between the aggregated resultsofdifferent termsjof a

linguisticoutputvariableandisbasedonthemaximumYjofeachtermj.

7 CONCLUSION

Inthisarticle,the modelofthe controlofthe powersupplysystemhas beenpresented,

provided that the input functions (and for reason of linearity and stationarity, also an

outputfunction)weregivenasstochasticorfuzzyprocesses.Onthe basisofthe specific

items of the systems, the mathematical model of a system for the possibility of

input/outputfunctionsbeingrandomprocesseswas createdandsolved. Incaseoffuzzy

conditions, demand and other functionswere represented as fuzzy sets. In the future,

researchwill

have

to

be

done

in

order

to

create

amathematical

model

of

the

power

supplysystemfor fuzzyconditionsingeneral,showninFig.8.Oneofthe veryinteresting

and highly realisticpossibilities is the creationof the fuzzymodel forsolvingor,better,

predicting optimal energy capacities and technologies for permanent and reliable

electricitysupply,consideringriskcontrol(Fabijan,Predin,2009).Thisresearchispartof

the realizationofthat.

References

[1]

DiStefano,

J.J.,

Stubberud,

A.R.,

Williams,

I.,J.:

Theoryand

Problems

of

Feedback

and

ControlSystems,McgrawHillBookCompany,1987.

[2] Usenik, J., Vidiek, M., Vidiek M., Usenik, J.: Control of the logistics system using

Laplacetransformsandfuzzylogic.Logisticsandsustainabletransport,2008,vol.1,issue1,pp.119.

[3] Usenik,J.:ControlofTrafficSystem inConditionsofRandomorFuzzy InputProcesses,

PrometTrafficTraffico,2001,Vol.13No.1,p.18.

[4] Bogataj,M.,Usenik,J.:Fuzzyapproachtothespatialgamesinthetotalmarketarea.Int.j.prod.econ.[Printed.],2005,vol.9394,pp.493503.

[5] Usenik, J., Bogataj, M.:A fuzzy set approach for a locationinventorymodel. Transp.plann.technol.,2005,vol.28,no.6,pp.447464.


46/104

JET


[6] Schneeweiss, C.: Regelungstechnische stochastische Optimierung Verfahren inUnternehmensforschungundWirtschsaftstheorie,SpringerVerlag,Berlin,1971.

[7] Kreyszig, E.:Advanced Engineering Mathematics, JohnWiley& Sons, Inc.,New York,1999.

[8] Ross,J.,T.:FuzzyLogicwithEngineeringApplications,2nded.,JohnWileySonsLtd,TheAtrium,SouthernGate,Chichester,England,2004,reprinted2005,2007.

[9] Terano, T., Asai, K., Sugeno, M.:FuzzySystemsTheoryand itsAplicactions,AcademicPress,Inc.,SanDiego,London,1992.

[10] Usenik,J.:Fuzzyapproach inprocessofmultipleattributedecisionmaking,JETJournalofEnergytechnology,Volume1(2009),p.p.4358.

[11] FuzzyTech,UsersManual,2000,INFORMGmbH,InformSoftwareCorporation.

[12]

Fabijan,D.,Predin,A.:Optimalenergycapacitiesand technologies forpermanentandreliable electricity supply, considering risk control, JET Journal of Energy technology,

Volume2(2009),p.p.6984.


47/104

JET


Issue3,August2009


THE CALCULATION OF THERMODYNAMIC

PROPERTIES FOR HYDROCHLORIC AND

COPPER COMPOUNDS IN A HYDROGEN

PRODUCTION PROCESS

IZRAUN TERMODINAMINIH LASTNOSTIV HIDROKLOROVIH IN BAKER KLOROVIH

KOMPONENTAH V PROCESU

PROIZVODNJE VODIKA

JurijAvsec1,GregF.Naterer2,AndrejPredin11UniversityofMaribor,FacultyofEnergyTechnology,

Hoevarjevtrg1,8270Krko,SLOVENIA

2UniversityofOntarioInstituteofTechnology,Oshawa,Ontario,Canada

Keywords:Hydrogenproduction,CuClcycle,thermophysicalproperties,statistical

thermodynamics

Abstract

Efficientand sustainablemethodsofclean fuelproductionareneeded inallcountriesof the

world in the faceofdepletingoil reservesand theneed to reducecarbondioxideemissions.

With commitments for a hydrogen village, a hydrogen airport and a hydrogen corridor, the

CanadianprovinceofOntariohasalreadybeguntomovetowardahydrogenfueledeconomy.

However,akeymissingelement isa largescalemethodofhydrogenproduction.Asacarbon

based technology, the predominant existing process (steammethane reforming (SMR)) is

unsuitable.

Correspondingauthor:Assoc.Prof.JurijAvsec,,Tel.:+38676202217,Fax:+38626202222,

Mailingaddress:Hoevarjevtrg1,8270Krko,SLOVENIA

Emailaddress:[email protected]


48/104

JET

J.Avsec,G.F.Naterer,A.Predin JETVol.2(2009) Issue3

This paper focuses on a copperchlorine (CuCl) cycle, and the models of calculating

thermodynamic properties. It discusses the mathematical model for computing the

thermodynamicpropertiesforpuresubstancessuchasH2,CuClandHCl,whichareimportantin

hydrogenproduction

in

their

fluid

phase,

with

the

aid

of

statistical

chain

theory.

The

constants

requiredmakethiscomputation,suchasthecharacteristictemperaturesofrotation,electronic

stateetc.,andthemomentsof inertiaareobtainedanalytically,byapplyingtheknowledgeof

theatomicstructureofthemolecule.Theproceduresforcalculatingessentialthermodynamic

propertiessuchaspressure,speedofsound,thespecificheat,volumetricexpansioncoefficient,

enthalpyandentropyarepresented.Tocalculate the thermodynamicpropertiesofLennard

Joneschains,wehaveusedtheLiuLiLuandTangLumodels.Thethermodynamicpropertiesof

theLennardJonesmixturesareobtainedusingtheonefluidtheory.

Inrecentyears,thermodynamictheoriesbasedonstatisticalthermodynamicshavebeenrapidly

developed.Fluidswithchainbondingandassociationhavealsoreceivedmuchattention.The

interestin

these

fluids

isdue

to

the

fact

that

they

cover

much

wider

range

of

real

fluids

than

sphericalones.Agood theory for these fluidswillbeverybeneficial forchemicalengineering

applications, by reducing the number of parameters, and making them more physically

meaningfulandmorepredictable.

Intechnicalpractice,energyprocessesareofvitalimportance.Inordertodesigndevicesinthis

field of activity, it is necessary to be familiar with the equilibrium and nonequilibrium

thermodynamicpropertiesofstateinaoneandtwophaseenvironmentforpurerefrigerants

andtheirmixtures.Tocalculatethethermodynamicpropertiesofreal fluid,theLiuLiLu(LLL)

(revisited Cotterman) equation of state, based on simple perturbation theory and SAFTVR

equationofstateforLJchainfluidwasapplied.Wedevelopedthemathematicalmodelforthe

calculationof

all

equilibrium

thermodynamic

functions

of

state

for

pure

hydrocarbons

and

their

mixtures.

Inthispaper,wehavedevelopedananalyticalmodelbasedonthestatisticalthermodynamics

andchaintheoryforpurecomponentssuchasH2,CuClandHClinthefluidregion.

PovzetekToplogredni plini, ki nastajajo pri zgorevanju fosilnih goriv, predstavljajo veliko potencialno

nevarnost za prihodnost obstoja loveka. Zaradi zmanjevanja emisije ogljikovega dioksida v

ozraju inzaradizmanjevanjazalog fosilnihgorivv svetujepotrebnopreitivprihodnostina

novetehnologijepridobivanjagoriv.Kanadajezrazvojemvodikovihvasi,vodikovihletalie

priela z aplikacijo vodikovih tehnologij. V principu manjka za primer irokomasovneproizvodnjelemetodazapridobivanjevodikavvelikihkoliinah.

lanekopisujebakerklorovprocesintermodinaminelastnostivomenjenemprocesu.Vlanku

jeprikazanmodel,kako izraunati termodinamine lastnostikomponentkotsovodik,CuCl in

HCl.Omenjene komponente so zelopomembne vproizvodnemprocesupridobivanja vodika.

Omenjenametodajepovsemanalitina inzadoloevanjetermodinaminih lastnostiuporablja

statistinomehanikoinmolekularnostrukturomaterialov.

Talanekopisujemodelizraunatermodinaminihlastnosti,kotsonaprimertlak,hitrostzvoka,

specifinetoplote,volumetriniekspanzijskikoeficientinentropija.Vtanamensmozaizraun

LennardJonesovih

verig

uporabili

Liu

LiLu

jev

model.

Termodinami

ne

lastnosti

zmesi

so

izraunanenaosnovienofluidneteorije.Predstavljenmodelpredstavljaprvitovrstenposkusv

svetovni literaturi za izraun termodinaminih veliin, ki se uporabljajo v bakerklorovem

procesu.


49/104

JET

Thecalculationofthermodynamicpropertiesforhydrochloricandcoppercompoundsinahydrogenproductionprocess

1 INTRODUCTION

Currently, the world consumes about 85 million barrels of oil and 104 trillion cubic feet of

natural

gas

per

day,

releasing

greenhouse

gases

that

lead

to

global

warming.

In

contrast,

hydrogenisacleanenergycarrier.Somehavequestionedwhetherthehydrogeneconomyis

feasible inthenearfutureorremainsadistant ideal.However,theglobalhydrogenmarket is

alreadyvaluedatover$282billion/year,growingat10%/year,risingto40%/yearby2020,and

reaching several trillions of dollars by 2020. In Alberta, Canada, the oil sands need large

amounts of hydrogen to convert bitumen to synthetic crude and remove impurities. A key

challengefacingthehydrogeneconomyisamoreefficient,sustainableandlowercostmethod

of hydrogen production. As a carbonbased technology, the predominant existing process

(steammethanereforming(SMR)isunsustainable.

Ratherthanderivinghydrogenfromfossilfuels,apromisingalternative isthethermochemical

decompositionofwater.Electrolysis isaproven,commercial technologythatseparateswaterinto hydrogen and oxygen using electricity. Net electrolysis efficiencies (including both

electricity and hydrogen generation) are typically about 24%. In contrast, thermochemical

cycles to produce hydrogen promise heattohydrogen efficiencies up to approximately 50%.

This article examines the thermophysical properties of a specific cycle called the copper

chlorine (CuCl) cycle, with particular relevance to nuclearproduced hydrogen. A conceptual

schematicoftheCuClcycleisshowninFig.1.

IntheCuClcycle,waterisdecomposedintohydrogenandoxygenthroughintermediateCuCl

compounds [4,5]. Nuclearbased water splitting requires an intermediate heat exchanger

betweenthe

nuclear

reactor

and

hydrogen

plant,

which

transfers

heat

from

the

reactor

coolant

to the thermochemical cycle. An intermediate loop prevents exposure to radiation from the

reactorcoolant in thehydrogenplant,aswellascorrosive fluids inthethermochemicalcycle

enteringthenuclearplant.

This paper develops new models for calculating the thermodynamic properties of copper

chlorinecompoundsintheCuClcycle.Statisticalassociatingfluidtheoryisusedtocalculatethe

thermodynamicproperties,basedontheCottermanequationofstate[13],aswellastheTang

Lu model [3] from the OrnsteinZernike equation of state and perturbation chain theory.

Predictive mod

Documents

Jet Za Internet Celotna - Volume 2 - Issue 3 - August 2009