Table Of ContentCHAPTER 1
Introduction
Accessibility to water and energy in sufficient quantity and quality are essential for human
development. Hence provision of both these commodities accounting for their sustainable use
and the need to mitigate global climate change by reducing greenhouse gas emissions are pri-
marytasksofthe21stcentury.Increasingstressonwaterresources,andtheneedtobetterassess
‘clean’ energy resources such as geothermal energy, require the development and application
ofsophisticated,state-of-thearttoolssuchasnumericalmodeling.Toillustratethispresent-day
worldconcern, wewillstartthisintroductorychapterwithsomeinformation, mostlyfromthe
UNorganizationsontheglobalwaterproblemandfromtheIntergovernmentalPanelonClimate
Changeabouttheprocessofglobalwarmingrelatedtotheenergyissueandcitetheirmostimpor-
tantfindings(sections1.1and1.2).Thesereportshighlighttheimportanceofbetteraddressing
theseissuesguaranteeingthedevelopmentandsurvivalofhumanity.
1.1 THEWATERPROBLEM—THEUNVISION
‘‘Global freshwater consumption rose sixfold between 1900 and 1995—more
thantwicetherateofpopulationgrowth.Aboutonethirdoftheworld’spopula-
tionalreadylivesincountriesconsideredtobe‘waterstressed’—thatis,where
consumptionexceeds10%oftotalsupply.Ifpresenttrendscontinue,twooutof
everythreepeopleonEarthwillliveinthatconditionby2025.’’
∗
KofiAnnan(2000)
Noonecanlivewithoutwater.Waterandairaretheessentialelementsforlifeinthisplanetand
forthedevelopmentandsurvivalofhumanity.Neithernaturenorhumantechnologycangenerate
orcreatemorewater. ThewaterexistingonEarthtransitsthroughthecontinuoushydrological
cycleofevaporation,condensation,infiltration,andflow.Thiswateristhesamefluidthatexisted
formillionsofyears.Thegreatdifferencenowadaysisitsqualityanddistribution.
Ithasrecentlyenteredpublicawarenessthatdrinkingwaterisafragileandrarecommodity.
Theimmensityoftheoceansandtheconstantrenewalofthewatercyclecreatetheillusionthat
water is a simple and eternal fluid. However, recent figures from the UN (UNEP 2009) show
that some 1200 million human beings lack access to drinking water and another 2000 million
receive contaminated water. In other words, serious deficiencies in the supply and quality of
thisvitalliquidcurrentlyaffectalmosthalfofhumanity(February2010:6,912,334,200;source:
http://www.breathingearth.net/).Theecological,social,technical,andpoliticalproblemsrelated
tothesupplyofwaterarenotcausedbyitsamount,butbytheirregulardistributionofwateron
theplanet,aswellasthepollutinginfluenceofhumanactivity.
TheEarthcontainsapproximately1400×106km3ofwaterandtheoceanscontain97.5%of
thistotal(1365×106km3,UNEP2009).Freshwaterresourcesrepresentabout2.5%ofthetotal
volume (35 million km3). Of the total water, 1.7% (24 million km3) is in the form of ice and
perennialsnowcoverinthemountains,theAntarcticandArcticregions.Therefore,only0.8%
∗ Source:KofiAnnanin:WethePeoples,2000.
1
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2 Introductiontothenumericalmodeling
(11millionkm3)oftheEarth’svitalfluidisavailabletohumanityandeventhissmallportionis
subjecttoconstantpollution.(UNEP2009).
Each year the oceans lose some 5 × 105 km3 of water into the atmosphere by evapora-
tion. Only 9% of this amount falls as rain on land. Some 8 million km3 is stored in the form
of groundwater basins, soil moisture and permafrost. This constitutes about 73% of all the
freshwater that is potentially available for human use. Lakes and rivers contain approximately
105,000 km3 (0.3%) of the world’s freshwater (UNEP 2009). Many ecologists, scientists and
international experts believe that water availability will become a critical factor for the sur-
vivalofmankindintheverynearfuture.Waterissueswilldeterminetheveryfutureoflifeon
Earth.
Today,waterisconsideredasafinite,valuableresourceofinequitableandunbalancedworld-
wide distribution in both social and geographical spaces. Industrial wastes, pesticides, natural
arsenic, anddiversechemicalscausecontaminationofdrinkablewater. Thedemandincrement
produced by the demographic augmentation and water wastage creates a dangerous situation.
Population pressures, increasing demands for space and resources, and poor economic perfor-
mances can all undermine the sustainable use of water. Since 1900, water demand has been
multiplied six times (UNEP 2009). Since 1940 the world population has an annual growth of
about2%whilewaterextractionincreasesabout3%peryear(LeónDiez2005).Atthepresent
timepeopleneedanaverageofbetween27and200litersperdaytosatisfytheirneeds(León
Diez 2005). Africa and the Middle East are the two regions of the world where there is less
water. The American continent is the richest in hydraulic resources (León Diez 2005). The
inequity in the consumption of water is evident when comparing figures of the UN (2003):
Brazil, Canada, China, United States, India and Russia have the 40% of rivers and lakes of
the planet. In Canada each inhabitant disposes of 91,640 m3 of water per year; in Australia,
26,032 m3; in Mexico, 4547 m3; in South Africa, 1109 m3 and in Egypt, 29 m3. According
totheUN,(LeónDiez2005)thequantityofwaterthatapersonneedsisabout5000m3/year.
Havinglessthan1700m3/yeariscalledwaterstress;havinglessthan1000m3/yearisconsidered
scarcity.
TheUnitedNationsEnvironmentProgramme(UNEP)compiledanupdatedaveryusefulreport
(VitalWaterGraphics)onthestateoftheworld’swaters.Thisreportfocusesonthecriticalissues
of water quantity, quality and availability—issues that are vital to the quality of life on Earth.
Highlightsfromassessmentactivitiesoverthepasttwodecades,revealthefollowingconclusions
(citedfromUNEP2009):
• Freshwaterresourcesareunevenlydistributed,withmuchofthewaterlocatedfarfromhuman
populations.Manyoftheworld’slargestriverbasinsrunthroughthinlypopulatedregions.
• Groundwaterrepresentsabout90%oftheworld’sreadilyavailablefreshwaterresources,and
some1.5billionpeopledependupongroundwaterfortheirdrinkingwatersupply.Groundwater
is by far the most abundant and readily available source of freshwater, followed by lakes,
reservoirs,riversandwetlands.
• Theamountofgroundwaterwithdrawnannuallyisroughlyestimatedbetween600and700km3,
representingabout20%ofglobalwaterwithdrawals.Acomprehensivepictureofthequantity
ofgroundwaterwithdrawnandconsumedannuallyaroundtheworlddoesnotexist.
• Agriculturalwateruseaccountsforabout75%oftotalglobalconsumption, mainlythrough
cropirrigation,whileindustrialuseaccountsforabout20%,andtheremaining5%isusedfor
domesticpurposes.
• Itisestimatedthattwooutofeverythreepeoplewillliveinwater-stressedareasbytheyear
2025.InAfricaalone,itisestimatedthat25countrieswillbeexperiencingwaterstress(below
1700m3 percapitaperyear)by2025.Today,450millionpeoplein29countriessufferfrom
watershortages.
• Cleanwatersuppliesandsanitationremainmajorproblemsinmanypartsoftheworld,with
20%oftheglobalpopulationlackingaccesstosafedrinkingwater.Water-bornediseasesfrom
faecalpollutionofsurfacewaterscontinuetobeamajorcauseofillnessindevelopingcountries.
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Introduction 3
Pollutedwaterisestimatedtoaffectthehealthof1.2billionpeople,andcontributestothedeath
of15millionchildrenannually.
1.2 THEENERGYPROBLEM—VISIONOFTHEINTERGOVERNMENTAL
PANELOFCLIMATECHANGE
‘‘Modern society continues to rely largely on fossil fuels to preserve economic
growthandtoday’sstandardofliving.However,forthefirsttime,physicallimits
of the Earth are met in our encounter with finite resources of oil and natural
gasanditsimpactofgreenhousegasemissionsontotheglobalclimate. Never
beforehasaccurateaccountingofourenergydependencybeenmorepertinentto
developingpublicpoliciesforasustainabledevelopmentofoursociety,bothin
theindustrialworldandtheemergingeconomies.’’
∗
Minutes,DebateofSenate(EersteKamer),2009(inDutch)
Today(2010)theworldisconsumingabout85millionsbarrelsofoil/day(Mbod).In2008,this
consumptionwas86MbodandwasgrowinginthatperiodbymorethanoneMbodperyear.This
incrementisequivalenttodiscoveranewoilprovincelikeAzerbaijaneachyear.OilpricesinJuly
2008reached145.29USDperbarrel(WTI).Becauseoftheeconomicalcrisis,oilconsumption
reduced0.5Mbodin2008and1.75Mbodin2009,andtheoilpricesdecreasedaswell.However,
thepriceinFebruary2010wasaround80USDperbarrelandthetrendistogrowagain(Oil-
Price.Net2010).Between40and50%ofworldwideoildemandisfortransportation.Inadditionto
thehugeamountofgasolinerequiredbytheindustrializedterritories,thereisanuncontrollable
increase in the appetite for automotive fuel in several countries of Asia, Latin America, and
Africa.Ontheotherhand,theproductioncostsofoilinreservoirslocatedindifferentregionsare
increasinglyhigh(ChevronCorporation2009).ThetotalOPEC’soilsparecapacitywas10Mbod
in1995; thiscapacitydecreasedto2Mbodin2008. Withorwithoutcrisis, thereisnolonger
asafetymargintoensurepricestabilityinthefaceofdemandspikesandsupplyinterruptions.
Therefore,intheverynearfuturewewillhavelimitedoilsupply,increasingdemand,higheroil
prices,increasingpollution,andenvironmentalimpactfromglobalemissionsofgreenhousegases.
TheWorkingGroupIoftheIntergovernmentalPanelonClimateChange(IPCC),(Solomon
etal.2007,andIPCChomepagehttp://ipcc-wg1.ucar.edu/wg1/)providedanauthoritativeinter-
nationalassessmentofhowtheactivitiesofthehumanindustryareaffectingtheradiativeenergy
balance in the atmosphere. Their objective is to provide a scientific understanding of climate
change. Concerning the key question: how are temperatures on Earth changing? the Working
GroupIfurnishedthefollowingconclusiveinformation:
‘‘Instrumental observations over the past 157 years show that temperatures at the surface
haverisenglobally, withimportantregionalvariations. ... Anincreasingrateofwarminghas
taken place over the last 25 years, ... Confirmation of global warming comes from warming
oftheoceans,risingsealevels,glaciersmelting,seaiceretreatingintheArcticanddiminished
snowcoverintheNorthernHemisphere,... (and)decreasesinthelengthofriverandlakeice
seasons.... theoceansarewarming;andsealevelisrisingduetothermalexpansionoftheoceans
andmeltingoflandice... Expressedasaglobalaverage,surfacetemperatureshaveincreased
◦
byabout0.74 Coverthepasthundredyears(between1906and2005;Figs.1.1and1.2).’’
Thehumanimpactonclimateduringthiseragreatlyexceedsthatduetoknownchangesin
natural processes, such as solar changes and volcanic eruptions (Solomon et al. 2007) (Fig.
1.2). In the light of the available information, there is an urgent need to replace hydrocarbons
byother, diversified, andcleanprimarysourcesofenergy. Solar, wind, andgeothermalenergy
∗ Source:MinutesofthedebatoftheSenate(EersteKamer)oftheDutchParliament,March31st,2009
http://www.eerstekamer.nl/stenogram/stenogram_254/f=x.pdf.
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4 Introductiontothenumericalmodeling
Figure1.1. Annualglobalmeanobservedtemperatures(blackdots,fromtheHadCRUT3dataset)along
withsimplefitstothedata.Thelefthandaxisshowsanomaliesrelativetothe1961to1990
average and the right hand axis shows the estimated actual temperature. Linear trend fits
tothelast25(yellow), 50(orange), 100(purple)and150years(red)areshown, andcorre-
spondto1981to2005, 1956to2005, 1906to2005, and1856to2005, respectively. From
about1940to1970theincreasingindustrialisationfollowingWorldWarIIincreasedpollution
inthenorthernhemisphere,contributingtocooling,andincreasesincarbondioxideandother
greenhousegasesdominatetheobservedwarmingafterthemid-1970s.(Solomonetal.2007).
g)
k
g/
μ
O ( kg)
N2 g/
g/kg), μCH(4
m
O(2
C
Figure1.2. Summary of the principal components of the radiative forcing of climate change (Solomon
etal.2007).
aresomeofthesesourcesabletoreplaceadvantageouslycoal,oil,gasandnuclear.Particularly,
submarineoffshorehydrothermalenergyisoneofthemostimportantandenormousgeothermal
sourcethathasneverbeenusedonEarth(Suárez-Boscheetal.2005).Supercriticalgeothermal
resources will enable the generation of electricity on an efficient, economical basis through
turbine-generators on the ocean floor that will supply the grid’s demand for electricity. This
approach generates electricity from geothermal energy from a vast, high-temperature resource
never before accessed. Technological improvements will increase efficiency enough to enable
geothermal energy to compete with traditional power plants on cost. This approach will also
accessmuchmoreextensivegeothermalresourcesthanthelandconventionalresourcescurrently
used.
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Introduction 5
1.3 MULTIPHYSICSMODELINGOFISOTHERMALGROUNDWATER
ANDGEOTHERMALSYSTEMS
‘‘Scientificcomputinghasoftenbeencalledthethirdapproachtoscientificdiscov-
ery,emergingasapeertoexperimentationandtheory.Historically,thesynergy
betweentheoryandexperimentationhasbeenwellunderstood.Experimentsgive
insightintopossibletheories,theoriesinspireexperiments,experimentsreinforce
orinvalidatetheories,andsoon.Asscientificcomputinghasevolvedtoincreas-
inglyproducecomputationalresultsthatmeetorexceedthequalityoftheoretical
and experimental results, it has become and indispensable third approach...
Thesynergyoftheory,experimentation,andcomputationisveryrich.’’
∗
MichaelA.Heroux,PadmaRaghavanandHorstD.Simon,2006
Thescientificstudyoftransportprocessesinnaturalporousfracturedsystems,suchasaquifers,
petroleum, gas and geothermal reservoirs, is relatively recent. Over the last 40 years, sev-
eral research methods have been developed based on experimental data and mathematical
approaches. To understand the complicated mechanisms of flow occurring in these scenarios,
variousmathematicalmethodshavebeenemployed:analyticalmethodswereinitiallyused,fol-
lowed by analog models and most recently, numerical models. One of the main problems is
thedifficultyinaccuratelyrepresentingthedimensionsandspatialdistributionoffracturesand
faultscreatedbygeologicandtectonicprocessesofarandomnature. Inhydrothermalsystems
(convection-dominatedgeothermalreservoirs),thetransportofmass,momentumandenergyis
anon-isothermalprocesswithphasechanges,wheredissolvedsalts,non-condensablegasesand
thedistributionofpetrophysicalparametersareofgreatimportance.
Inthescientificstudyofnatureitisnecessarytomakenumericaloperationsofdiversedegrees
ofcomplexity,fromelementarytohighmathematicalsophistication.Thedevelopmentofmathe-
maticalmodelsisjustifiedbythehelptheybringintheunderstandingandverificationofspecific
mechanismsandbehaviorsofnaturalsystems.Inaddition,theircostisconsiderablylowercom-
pared to any other technique. Furthermore, numerical models can be subjected, without any
risk, tothemostcriticaloperationconditions. Theutilityofmodelingisspecifictothenatural
systems because physical scale models of them cannot be made in the laboratory. The ‘‘pre-
diction’’and‘‘retro-diction’’capacitiesofmathematicalmodelsallowthequantitativeestimation
offuturebehaviorsthatareyettobeobserved,aswellastheestimationofprocessesthatareno
longerobserved,butthatweretheantecedentofthecurrentphenomenon.Numericalsimulation
isirreplaceableasatoolforanalysisandsynthesis,toachieveanongoingcoherentintegration
ofinformationonthereservoir,asitslifespanadvances.Otherresearchtechniquesofferonlya
partialperspectiveontheglobalsystem.Themathematicalmodelanditsassociatednumerical
codecanbeusedtocombineandtoverifyseveralcomplexhypothesesandtotestthemagainst
theobservedfactsanddata.Petroleum,gas,waterandheatreservoirsareexamplesofcomplex
naturalsystems.Tounderstandthemassandenergyflowsinthesesystems,thedevelopmentof
integratedmodelsisrequired.
Inthisbookwedefineaquifersintheclassicalsense:groundwatersystemsoflowtemperature
(<37◦C), which correspond generally to freshwater resources, providing water for drinking,
irrigation and industrial purposes. With very few exceptions, these aquifers can generally be
treatedasisothermalsystems,wheretemperaturevariationsintimeandspacearenotofinterest.
Inaddition,wewillfocusongeothermalsystemsofvariabletemperature(>37◦C),whichareused
asenergyresourceseitherfordirectuseorforelectricpowergeneration.Thesesystems—with
theexceptionofverysimplecases—shouldbetreatedasnon-isothermalreservoirsandinsome
instances, theoccurrenceofboththeliquidandthevaporphaseofwaterhastobeconsidered.
Thepresenceofotherphasessuchasnon-condensablegasesanddissolvedspeciessuchasions,
∗ Source:ParallelProcessingforScientificComputing,SIAM,2006.
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6 Introductiontothenumericalmodeling
furtherincreasethecomplexityofthesystem.Tosimplifythenomenclature,wewilldistinguish
these two groups with regard to their use, by referring to the first group as ‘‘cold aquifers’’
(isothermalgroundwater,freshwateraquifers,etc.)andthesecondgroupas‘‘geothermalsystems’’
(geothermalreservoirs, geothermalresources, geothermalfluid, etc.). Itisworthremembering
thatthephysicallawsandmathematicaldescriptionswhichapplytogeothermalsystemsarealso
validforisothermalaquifersystems.
Numerousinteractingparameters,variablesandfunctionsdrivethemovementofgroundwater
andsteam,andthetransportofheat,solutesandgases.Withtheexceptionofsomeveryspecial
cases,thesetransportprocessesarecoupledthrough(1)theinterstitialporevelocity,(2)thedepen-
denceoffluiddensityonpressure,temperatureandsolute-massfraction,(3)thedependenceof
thefluidviscosityontemperatureandsolute-massfraction,and(4)therockporoelasticity.Asa
consequencetheseprocessescanonlybedescribedusingnumericalmethods.Theinfluencesof
thenumerousvariables,whichmaybefunctionsofspaceandtimeandmayalsobedependenton
temperature,pressure,etc.,governmassandheattransportandtheirinteractions.Allofthesefunc-
tionsshouldbeconsideredatthesametime.Hence,mathematical,computationalandnumerical
modelingbecomevitaltoolsfortheanalysisofisothermalaquifersandgeothermalsystems.
Themostimportantproblemforthegeneralscientificdevelopmentofreservoirengineeringis
thedearthofdatainsomeareasanditsabundanceinothers.Thenatureofthisdisciplinemeans
thatitisalwaysnecessarytoformulateideasbasedonincompleteinformation.Itisalsonotpos-
sibletoconstructphysicalscalemodelswhichfullyrepresentthereservoir.Computernumerical
simulationcanthenachieveanintegraldetaileddescriptionofthereservoirbyreproducingthe
available robust data. Once some approximate reproduction is achieved, extrapolation may be
applied to predict the future behavior of the system as it is subjected to different exploitation
scenarioswithdifferentlevelsofuncertainty.
As mentioned above, the principal difficulty in establishing an accurate numerical model is
due to the very limited availability of spatial and chronological field data. This can be readily
appreciatedifweconsider,forexample,theparameterdispersivity.Itisnowwellrecognizedthat
thisparameter,whichisimportantinmodelingsolutetransportinaquifers,isnotmeasurablein
fieldsituationsunlesswehaveaverywell-definedsimpleaquiferfabric, suchasthatfoundat
some experimental test sites. For real problems, dispersivity is merely a fitting parameter that
covers our lack of knowledge of the true flow patterns. It cannot be inexpensively measured
exceptintheimmediatevicinityofawell.Furthermore,itisoftenspatial-scale-dependentand
time-dependent;thus,asingleconstantvaluedoesnotoftenadequatelydescribewhatwemeasure
orwishtopredictinthefield.Suchalackofinputdatamustbeovercomebyindirectestimationof
dataranges,andthemodelhastobeappliedcarefullytoobtainusefulresultsfromthemodeling
analysis. Therefore, a good understanding of the limitations of the data and modeling tools is
vitalfortheintelligentapplicationofmodeling.
1.4 MODELINGNEEDSINTHECONTEXTOFSOCIAL
ANDECONOMICDEVELOPMENT
Theavailabilityoffreshwaterandenergyareintrinsicallylinkedtohumansocialandeconomic
development.Waterandenergyresourcesareincreasinglylimited.Atthesametime,thedemand
fortheseresourcesisincreasingsharplyduetopopulationandeconomicgrowth.Thiseffectis
greatestinthedevelopingworldwiththeirhigherpopulationgrowthrates,theirfast-expanding
emergingeconomiesandrelatedincreaseinlivingstandards.Thiscanbeclearlydemonstrated
usingtheparameter‘‘electricitydemand’’,theworld-averageofwhichispredictedtoincreaseby
afactoroftwofrom2004to2030(EIA2007),withanannualaveragegrowrateof3.5%indevel-
opingcountries(non-affiliatedwithOECD:OrganizationforEconomicCooperationandDevel-
opment),comparedwithagrowthrateof1.3%inindustrializedcountries(OECD)(EIA2007).
Several regions of the planet are experiencing a worsening water shortage. The supply of
freshwaterisacrucialissueinthemanycountriesthathaveverylimitedresources.Forexample,
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Introduction 7
theMediterraneanregionisconsideredtobe‘‘poor’’inwaterbecause180millionpeopleliving
there have less than 1000 m3 per capita per year (LeMonde, 23 December, 2008). Of these,
sixty million are surviving with less than 500 m3/year. This situation is worsening because of
increasingpopulationgrowth,theconsequencesofclimatechangeandpollution,whichrenders
thewaterunsuitableforconsumption. Inmanyregions, riversandaquifersaresharedbetween
differentcountries,whichincreasestheriskofconflict.SomeexamplesaretheGuaraníaquiferin
SouthAmerica,theNubiansandstoneaquifersinnorthernAfrica,theKarooaquifersinsouthern
Africa, the Vechte aquifer in western Europe and the Slovak Karst-Aggtelek aquifer and the
PradedaquiferinCentralEurope.Nationsfacingalackofwaterlookfirsttosecurenewsources
ofsupplybytheexpansionofdrilling, thecreationofdams, andtheconstructionofpipelines.
These policies have their limits due to problems associated with overexploitation of aquifers,
jeopardizingthenaturalgroundwaterrecharge,ordrawingonfossilreserves.
Inconsequence,thesecurityoflong-termfreshwaterandenergysuppliesisaglobalcauseof
concern.Inordertomeetfuturefreshwaterandenergydemands,itwillbenecessarytodevelop
‘‘improvedtools’’forbetterexplorationandexploitationofgroundwaterresources,whichconsti-
tuteover99%oftheworld’sfreshwaterandenergysourcesincludingthegeothermalresources,
whichhaveapotentialforpowergenerationthatismuchgreaterthanthatofallfossilfuelresources
combined. Geothermal resources can be tapped to meet the increasing demand for electric
powerbyapplyingmodernheat-exchangertechnologies,binary-fluids,drilling-technologies,and
submergible-pumps.Thesetechnologiesallowtheexploitationofpreviouslytechnicallyandeco-
nomicallyinaccessiblelow-enthalpy(<150◦C)convection-dominatedgeothermalresourcesand
conduction-dominatedenhancedgeothermalsystems(EGS)(both,high-andlow-enthalpysys-
tems)thatarefoundinpracticallyeverycountryontheEarth(ChandrasekharamandBundschuh
2008).
Althoughnumericalmodelinghasbeenusedinpastdecadesasastandardapplicationindiffer-
entfieldsofmechanical,civilengineeringanddesignitsapplicationtoisothermalgroundwater
systemsandgeothermalsystemshasdevelopedslowlyduringthelastfourdecadesandstilltoday
isnotimplementedtoitsoptimalcapacity. Theimprovementofcomputertechnologiesduring
the last two decades allows actual modeling of complex coupled subsurface processes, which
wasnotpossibleafewyearsago. Thisdevelopmentinhardwaretodaymakesthelimitationof
field-datatheprincipallimitationoftheapplicationofnumericalmodelinginhydrogeologyand
geothermics.
Beforewedescribeanaturalreal-worldproblem,suchasanisothermalaquifersystem(fresh-
waterresources),orageothermalsystem(non-isothermalfluids)byapplyingnumericalmodeling,
itshouldbeappreciatedthatthesesystemsaremuchmorecomplexthanmostothermechanical
engineering problems, where numerical modeling has been used as a standard tool for several
decades.Anisothermalaquifersystemisacomplexnaturalundergroundsysteminvolvingcou-
pled mechanisms which control mass, solute, and energy transfer in poroelastic rocks, with
the Earth’s surface acting as a boundary. In the case of geothermal systems, the circulation of
hydrothermal fluids, comprising liquid, steam, and gases, is a fundamental complex coupled
processcontrollingmass, soluteandenergytransferfromtheEarth’smantleandcrustthrough
thesubsurfaceuptothesurface,wheregeothermalfluidsmayemergeashotsprings,fumaroles
orsteamvents.
Inthefollowingpartofthischapterwewilldiscussrecentdevelopmentsintheareaoffreshwater
and energy resources and give some examples of the worldwide importance of increasing the
implementationofnumericalmodelingforimprovedassessmentandsustainableexploitationof
theseresources,andforproblemsolving.
1.4.1 Theroleofgroundwaterfordrinking,irrigation,andotherpurposes
Increasinglimitationsontheavailabilityofsurfacewatercausedbyitsseasonalfluctuationsand
itscontinuouslyqualitydegradationduetoanthropogeniccontamination,makegroundwaterthe
principalwatersourceinmanyareas.Theimportanceofgroundwaterwillundoubtedlyincrease
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8 Introductiontothenumericalmodeling
inthefutureasitisrequiredasdrinkingwaterandforcropirrigationtosustainfoodsuppliesto
anincreasingworldpopulation(Bhattacharyaetal.2008).However,groundwaterresourcesare
under increasing stress, both in terms of quantity and quality. This, together with the growing
importanceofgroundwater, demandsabetterunderstandingofthecriticalprocessesrelatedto
aquifer systems, which necessitates the development and application of improved tools, such
as numerical modeling, to permit the identification and quantification of processes occurring
in the aquifer and allow the prediction of these processes and their effects. This action should
mitigatethenegativeimpactsoftheseprocessesandhelptoidentifyoptimalapproachesforthe
assessment,management,andprotectionofgroundwaterresources,inordertoachievelong-term
sustainability.
Groundwaterflowsimulationcanbeappliedtoinvestigategroundwaterrechargeandrecovery,
wheretheconsequenceofthegroundwaterwithdrawalthroughwells, horizontalwellsoffilter
galleriesonthenaturalgroundwaterflowfield(e.g.decreaseofthegroundwatertableorpressure),
canbesimulatedandusedtodeterminetheoptimaltypeandlocationofawithdrawalinstallation
(a group of wells and the location of single wells in it, horizontal well, filter gallery), and
respectivewithdrawalrate(s). Beyonditsuseforgroundwatermanagementtasks, groundwater
flowsimulationcanalsobeusedforotherapplications,includingthesimulationofwellhydraulics
and the evaluation of pumping and infiltration tests to determine aquifer parameters, and for
numerous tasks in civil engineering, such as designing proper drainage in excavation pits or
determinewaterinfluxintunnelconstructions.Inhydroelectricprojects,theaccuratesimulation
ofwaterpercolationthrough,below,andaroundstoragedams,isimportantforthedesignofproper
measurestoreducetherespectiveflowrates, forexample, bytheuseoflinersorinjections. In
addition, the filling of storage lakes and the impact on the natural groundwater flow field can
alsobesimulated.Inareaswithlimitednaturalaquifers,numericalmodelingisanimportanttool
tooptimizetheaugmentationofwatersupplies,e.g.byartificialrecharge.
Groundwater flow simulation can be coupled with solute transport simulation and may be
applied to model natural or anthropogenic-induced chemical species transport, including pro-
cesses of solute sorption, production and decay. This procedure may be applied to analyze
groundwater contaminant transport problems, and aquifer vulnerability (contamination hazard
andrisk),todefineaquiferremediationmeasuresincasesofcontamination,andtodelimitpro-
tection zones around groundwater capture areas. Numerical transport modeling can be further
applied to the analysis of problems such as those related to subsurface-waste injection, land-
fill leaching, and the evaluation of tracer tests. It is suitable to simulate complex redox- and
pH-dependent chemical and biochemical reactions which occur in the groundwater during its
movement in an aquifer. One example is the occurrence of geogenic contaminants in ground-
water such as arsenic, which is found at toxic levels in many regions of the world, making it
amajorenvironmentalhealthriskforthe21stcentury(seee.g., Bundschuhetal. 2005, 2009,
Bhattacharyaetal.2007a,band2008).Inordertosupplysafedrinkingwatertothetensofmillions
of people affected, an improved understanding of the hydrogeochemical processes responsible
for high levels of arsenic in groundwater is required. Hence, numerical modeling is a reliable
toolwithwhichtoexaminenaturalandanthropogeniccontaminationprocessesofaquifers, by
forecastingcontaminationpropagation,anddefiningoptimalremediationmeasures.
Anotherimportantapplicationisthemodelingofsaltwaterintrusionsintofreshwateraquifers.
Worldwide,coastalaquifersareincreasinglyaffectedbysalinizationduetoseawaterintrusions
causedbyexcessivegroundwaterexploitationincoastalareas.Here,numericalmodelingcom-
binedwithextensivegroundwatermonitoring,canoptimizefreshwaterexploitationandavoidor
reducesalinizationofaquifers.
In special cases, heat transport has to be considered, e.g. in relation to applications such as
seasonalheatstorageunderground, thestorageofradioactivewasteandothersituationswhere
temperaturechangesinaquifersareofimportance.Heattransportmayalsobeofinterestifwe
wishtodescribethemixingofwatersofdifferenttemperatures,asoccursduringgroundwater-
surfacewaterinteractions.Inthiscase,heatmaybeusedasatracertoidentifyandquantifymixing
processes,suchasinfiltrationofriverwaterintoanaquifer,orgroundwaterrechargeprocessesdue
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Introduction 9
toprecipitation,whichcanfurtherbeusedforassessingthegroundwatercontaminationpotential
from contaminated surfaces or rivers. In addition, heat transport is of interest, e.g. if we want
tomodelprocessesresultingintemperaturevariationsinspringwaterorshallowgroundwater,
whicharerelatedtotemperaturechangesattheEarth’ssurface(Bundschuh1992,1993a,b,1995).
1.4.2 Geothermalresources
Thegeothermaloptionforelectricitygenerationhasrecentlybeenrecognizedastheoptimal—
economicallyandenvironmentallysound—choicetomeetmuchofthefutureelectricitydemand
andguaranteeenergysecurityandenergyindependenceofbothdevelopinganddevelopedcoun-
tries(ChandrasekharamandBundschuh2002,2008,AaheimandBundschuh2002,Bundschuh
etal.2002,2007,BundschuhandCoviello2002;furtherinformationcanbefoundonthehome-
pages of the International Geothermal Association (IGA2009a, b) the Geothermal Resources
Council(GRC2009)andtheGeothermalEducationOffice(GEO2009)).
Recentinnovationsintheformofbinaryfluids,heatexchangers,anddrillingtechnologieshave
madethecommercialexploitationoflow-enthalpyconvectivegeothermalresources(<150◦C)and
conductiveenhancedgeothermalsystems(low-andhigh-enthalpy)possible(Chandrasekharam
andBundschuh2008).
Convection-dominated high-enthalpy geothermal systems (vapor- or liquid-dominated;
>150◦C)arerelatedtovolcanicand/ortectonicactiveareas,andthereforeareonlyfoundalong
activeplateboundariesinboththecontinentsandtheoceans.Attheselocations,uprisingmagma
or deep-seated intrusives are the main source of heat for low- and high-enthalpy convective
geothermal systems, whose main source of thermal fluid is meteoric water. Convective low-
enthalpyresourceshaveconsiderablygreatergeothermalpotentialthanhigh-enthalpysystems,
andmuchlargerregionaldistributionsincetheyarenotlimitedtoactivetectonicplateboundaries.
Despite these benefits, low-enthalpy systems are practically unutilized for electricity genera-
tioninbothdevelopedanddevelopingcountries(ChandrasekharamandBundschuh2002,2008,
Bundschuh and Chandrasekharam 2002, Bundschuh et al. 2002, 2007), even though geother-
◦
malwaterwithtemperaturesaslowas80 Ccanbeusedforeconomicalcommercialelectricity
generationwithcurrentlyavailabletechnologies.
Enhancedgeothermalsystems(EGS),whicharenotlimitedtovolcanicand/ortectonicactive
areassuchasconvectivehigh-enthalpygeothermalsystems,haveevengreaterpotential.Inthese
systems,heatisprovidedbythenaturalradioactivityofelementslikeU,Th,andK,andthecon-
ductionofheatfromthemantletoshallowerlevelsalongdeepcontinentalcrust(Chandrasekharam
andBundschuh2008).EGS,whichareavailableinpracticallyeverycountry,havereceivedgreater
attentioninrecentyears.AccordingtotheMITreport(MIT2006),theUSAalonehasanEGS
potentialofabout13,000,000ExaJoules(EJ=1018Joules)(depth3–10km),ofwhich200,000
EJcanbeextractedforutilization, whichcorrespondstoabout2000timestheannualprimary
energy consumption of the country in 2005. By 2050 the USA could economically generate
about100,000MW withmodestR&Dinvestment(MIT2006).Recentincreasesinthecostand
e
uncertainty surrounding conventional energy supplies make these EGS resources increasingly
attractive.ThesedevelopmentsintheUSAarefollowingtheinternationalprogressinthedevel-
opmentofEGSandrelatedtechnologies,whichhasobtainedconsiderableinterestinEuropeand
Australiaoverthelastfewyears.Itisespeciallyimportantthatdevelopingcountries,whichcanall
accesslow-enthalpyconvectiveandconductiveEGSsourcesforelectricitygeneration,areaware
oftheseresources.Formanyofthesecountries,theexploitationoflow-enthalpyresourcesisnot
newsincetheyhavebeenusedoverthepastcenturiesforbathing,andfordirectapplicationsthe
lastfewdecades(ChandrasekharamandBundschuh2008).Lundetal.(2010)reporteddirectuse
productiondatafromthesesystemsin78countriesintheyear2010(72intheyear2005).
The accelerated growth of interest in geothermal systems requires further development of
sophisticatedsoftwareandthecreationofnumericalmodelstofacilitategeothermalexploration
andexploitation,andtosustainlong-termproductivity.Tounderstandbothconvectiveandcon-
ductivegeothermalsystems, thegeologicalandtectonicfeaturesthatcontrolthemneedstobe
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10 Introductiontothenumericalmodeling
thoroughlyunderstood. Simplenumericalmodelsofgeothermalreservoirs(includingscenario
modeling)canassistinunderstandingthesesystemsduringpre-drillingstages,andasmoredata
becomeavailable,moresophisticatedmodels,e.g.thosethatincludethermoporoelasticprocesses,
canbedeveloped.Thedevelopmentofthesetoolscanbeongoingduringdrillingandexploita-
tion,tohelpensurethatconvection-dominatedgeothermalreservoirsareutilizedoptimallyina
sustainableway.InthecaseofEGS,theheatexchangebetweenrockandtheartificiallycirculated
fluidsalongthereservoirfracturescanbemodeledtoassistmanagersduringtheexplorationphase
(e.g.indecisionsaboutartificialfracturingusedtoincreasethevolumeofthefluidspace),and
toensureoptimalexploitationofthesystem.Thisinvolvesmodelinghydraulicfracturingusing
highfluidpressureonareservoirtoenhancetheexistingpermeabilityandestablishconnectivity
betweenadjacentfracturesbyopeningsealedjointsorbycreatingnewfracturestoallowgeofluids
tomovemorefreelythroughtherockformation.Thisisaninterestingapplicationthatisusedto
assistinthedesignandtooptimizetheoutcomeofthefracturingprocess.
1.5 THENEEDTOACCELERATETHEUSEOFNUMERICALMODELING
OFISOTHERMALAQUIFERSANDGEOTHERMALSYSTEMS
Compared to the aforementioned advances in computer technologies, numerical methods, and
the identification of application possibilities, the use of numerical modeling in hydrogeology,
particularlyitsapplicationtogeothermalsystems,isstillrare.Themainreasonforthisisthegap
betweenthepeopleinvolvedinthisissueandtheirrespectiveknowledge.Theprincipalgroups
ononesideincludesoftwaredevelopers,engineers,andappliedmathematicians,whomayhave
insufficient knowledge about the geological, hydrogeological or geothermal background and
hence of the application possibilities of numerical models and the respective software needs,
so that the design of the software is not optimal. An insufficient understanding of subsurface
processesoccurringingroundwaterandgeothermalsystemsmakesthedevelopersunawareof
thenumericalneedstooptimizemodelcalibrationsubprogramsandtoolsthathandletheproblem
ofirreguarlyavailabledataintimeandspace.Ontheotherside,therearethehydrogeologistsand
othergroundwaterprofessionalsorgeothermists, whomayhavelittleknowledgeofnumerical
methods,applicationpossibilities,orthecorrectapplicationofmodels.Inparticularthesegroups
lack expertise in (1) the elaboration of an accurate conceptual model, (2) the selection of the
appropriatemodelcodesuitablefortheelaboratedconceptualmodel(orinafewcasestheproper
elaborationofanumericalprogramcode),(3)thediscretizationofthemodelareainspaceand
timetoestablishthenumericalmodel,(4)thecorrectcalibrationandvalidationofthemodelby
selectingtheappropriatecalibrationandvalidationparameters,and(5)thecorrectevaluationof
thesimulationresultsandreliabilityconsideringthemodeluncertainties,thatarerelatedtothe
uncertaintyofthedatausedtotesttheselectedconceptualmodel.
This book aims to bridge these knowledge gaps and to provide integrated information on
numericalmodelinginhydrogeologyandgeothermicsforallthoseinvolved. Wehopetoshow
thatnumericalmodelingisareliabletool,whichshouldbeimplementedfortheimprovedintegral
management of groundwater and geothermal resources. However, users must always approach
numericalmodelsandtheirsimulationresultswithacriticaleye.Itshouldberememberedthat
numericalmodelsaretoolsandthatthequalityofthesimulationresultsdependsontheprepa-
rationoftheconceptualmodel,knowledgeofthegeologicalsituation,thehydrogeologicaland
hydrogeochemicalparametersandthedata,particularlytheinitialandboundaryvalues.
Thebasisofthisbookistheideathatspecificmathematicalmodelscanbegeneratedandsolved:
models that are useful in underground hydrology and in geothermal systems with transport of
mass,heatandsolutes.Thefundamentallawsandconceptsoffluid,energyandsolutetransport
inporoelasticrocks,aswellastheirmathematicalrepresentation,areintroducedanddiscussedin
detail.Therebythemassandheattransportprocessesandmodelshavebeenexpressedingeneral
form, valid for all types of aquifers: isothermal aquifers, where heat transport is normally not
ofinterest,andconvectivegeothermalsystems,whereheattransportandthepresenceofliquid
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