Flow and Heat Transfer in Geothermal Systems. Basic Equations for Describing and Modelling Geothermal Phenomena and Technologies

380 Pages·2017·18.876 MB·English

by  Aniko Toth, Elemer Bobok

FLOW AND HEAT
TRANSFER IN
GEOTHERMAL
SYSTEMS
Basic Equations for Describing and
Modeling Geothermal Phenomena
and Technologies
A T
NIKO OTH
E B
LEMER OBOK
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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Preface
FlowandHeatTransferinGeothermalSystemsisintendedasasystematic
and analytical exploration of the most important geothermal principles.
Understanding the physical principles of fluid flow and heat transfer, in
both natural and artificial systems, is essential to understanding how
every stage of the geothermal cycle affects geothermal production
wells, injection wells, drilling operations, surface equipment, energy-
conversion systems,and the geothermal reservoir itself.
Although we assume a basic knowledge of mathematics and some
familiarity with the geothermal industry, our book should be accessible
to beginning engineering students and even well-educated laymen who
wish to understand a bit more about this promising alternative to fossil
energy. We expect that Flow and Heat Transfer in Geothermal Systems will
be especially valuable as a handbook for geologists, hydrogeologists,
reservoir engineers, geophysicists, geochemists, drilling engineers, and
productionengineers,allofwhosecollaborativeworkisvitalincreating
and maintaining successful geothermal operations.
Chapter1isanintroductiontothebasicideaofageothermalreservoir
alongwithabriefhistoryofearlygeothermaldevelopment.InChapter2
we explore the basic laws of fluid mechanics and thermodynamics.
Chapter3dealswithtransportprocessesingeothermalreservoirs,based
on the complex continuum model, and introduces the geothermally
useful Darcy’s Law.
Chapter4studiesthedifferentboundaryandinitialconditionswithin
rockmasses,andthevariousmeansofmeasuringhowheatisconducted.
Chapter 5 looks at those important natural processes which obtain in
undisturbed geothermal reservoirs: consolidation, natural convection,
and the development of overpressuredreservoirs.
Chapter6usesanalyticcomplexfunctionstoexplaintwo-dimensional
undergroundflows,includingtheHeleeShawflow.Morespecifically,we
look at geothermal reservoirs and their producing wells, which form a
serially connected synergetic flow system: a radially inward Darcy flow
toward the well in the reservoir, and a turbulent upflow through the
tubing.
TheflowwithinwellsisthesubjectofChapter7,whichalsoexamines
homogeneous waterupflowandtwo-phaseflowsinducedbydissolving
gas and flashing. In this chapter, our examination of the energy transfer
processassumes an unsteady flow ofinviscid fluid.
ix
x
PREFACE
Chapter8dealswiththeuseofsubmersiblepumpstoinduceartificial
lifting, describing the most important types of centrifugal pumps along
with their construction, their operation, their performance curves and
how they affect cavitation. This chapter describes the phenomenon by
which, as production continues, heat transfer causes a gradual rise of
temperature in the surrounding rock, decreasing the temperature
difference andthe heat flux.
Chapter9investigatesboreholeheattransfer,andhowtodeterminethe
temperature distribution of the flowing fluid both in production and
injection wells. In this chapter the flow patterns of two-phase watere
steam mixture flows are analyzed. Temperature distribution along the
pipe axis is also determined. The chapter ends with an examination of
theheattransferprocessaroundaburiedhorizontalhot-watertransport-
ing pipeline.
Chapter 10 looks at how gathering pipelines work in geothermal en-
ergyproductionsystems,introducingthebasicequationsusedtoanalyze
one-dimensional pipe flow for both laminar and turbulent flows. We
demonstrate how to assess the loss of superheated steam, assuming an
isothermal case.
Chapter 11 describes the process of geothermal power generation,
brieflyoutliningthepowergenerationcycle,analyzingthebasicthermo-
dynamic process of wet steam generation and showing how energy is
converted from thermal to mechanical energy in the steam turbines.
Thischapterintroducesseveralofthemostimportanttypesofgeothermal
powerplants: single flash, drysteam, andbinaryplan.
InChapters12,13,and14weinvestigatethefollowingtopics:propa-
gation of the cooled region between injection and production wells in
fracturedreservoirs;flowandheattransferinaboreholeheatexchanger
(both in shallow and in deeper regions); flow and heat transfer during
drilling operations; laminar and turbulent flows of non-Newtonian
fluids through annuli; and temperature distribution in the circulating
drilling mud.
Chapter15isacasestudyofhowmuchenvironmentaldamagecanbe
caused by high-enthalpy geothermal reservoirs. This chapter relates the
history of a serious industrial accident which occurred in Hungary
(cid:1)
when workers, while tapping an overpressured 200 C reservoir,
provokedasteamblowoutfromadepthof4000m.Aspartoftheresult-
ing hydrodynamic/thermodynamic reconstruction, certain inconsistent
phenomena observed during the blowout are explained with the help
of thermodynamical calculations.
Thebook’sfinalchapter,Chapter16,describestwonontrivialformsof
geothermal energy production: the first highlights the substantial
geothermalpotential ofanabandoned copperoremine,wheretheroad-
ways and the shafts were flooded by mine water; the second explores
another unusual application, a deicing system located at the entrance of
a mine tunnel.
Acknowledgments
Over the years the following associations have provided us with an
invaluableforumfortheinvestigationofgeothermaltopics:theStanford
Geothermal Workshop, one of the geothermal world’s longest-running
technical workshops; the Geothermal Research Council (GRC); the
International Geothermal Association (IGA); and the European
Geothermal Energy Council (EGEC). Among the individuals we would
like to thank are Prof. John Lund of the Oregon Geo Heat Center, who
gaveusunstintingadviceandencouragement,andProf.RolandHorneof
StanfordUniversity,whoshowedbyhispersonalexamplethehighlevel
ofacademicrigorneededinthisfield.Inthesamelight,specialthanksare
due to Prof. Burkhard Sanner of the European Geothermal Energy
Council.
WewouldalsoliketothankAndrasDianovszkyandMarkZsemkofor
recreating several important diagrams which had gotten lost in the
shuffle. Last but not least, our special thanks to David Fenerty for his
editing and proofreading suggestions.
Aniko Toth
Miskolc, Hungary
September, 2016
xi
C H A P T E R
1
What Is Geothermal Energy?
O U T L I N E
1.1 Introduction 1
1.2 The Nature andOrigin ofGeothermal Energy 3
1.3 Geothermal Reservoirs 8
References 19
1.1 INTRODUCTION
Geothermal energy is energy contained within the high temperature
mass of the Earth’s crust, mantle, and core. Since the Earth’s interior is
much hotter than its surface, energy flows continuously from the deep,
hotinterioruptothesurface.Thisistheso-calledterrestrialheat-flow.The
temperatureoftheEarth’scrustincreaseswithdepthinaccordancewith
Fourier’s law of heat conduction. Thus the energy content of a unit of
mass also increases with depth.
All of the Earth’s crust contains geothermal energy, but geothermal
energy can only be recovered by means of a suitable energy-bearing
medium. To be practical, the energy-bearing media must be: hot
enough (high-specific energycontent), abundant enough, easily recover-
able, inexpensive, manageable, and safe. Water satisfies these
(cid:1)
requirementsperfectly.Thespecificheatofwateris4.187kJ/kg C.Inthe
steam phase, latent heat is added to it. Hot water and steam can be
recoveredeasilythroughdeep,rotary-drilledwells.Throughtheuseofa
suitabledesignedheatexchanger,heatcanbeefficientlytransferredfrom
FlowandHeatTransferinGeothermalSystems
http://dx.doi.org/10.1016/B978-0-12-800277-3.00001-3 1 Copyright©2017ElsevierInc.Allrightsreserved.
2
1. WHATISGEOTHERMALENERGY?
the water or steam. Steam is an especially suitable working fluid for en-
ergyconversioncycles.
Nowadays,geothermalenergyproductionismainlyachievedfromhot
water and steam production via deep boreholes. Another rapidly-
growing production technology involves exploiting the energy content
of near-surface regions by using shallow borehole heat exchangers and
heat pumps.
It is likely that the natural heat of volcanoes and other geothermal
sourceswerealreadybeingusedintheremotePaleolithicera,butconcrete
evidenceonlydatesfrom8000to10,000yearsago.Wearethereforeforced
to use indirect methods when speculating on mankind’s earliest rela-
tionship with geothermal phenomena andproductsof theEarth’sheat.
The uses of natural hot water for balneology and the exploitation of
hydrothermal products for a wide range of practical applications
increasedremarkablyduringthemillenniumprecedingtheChristianera.
This use eventually extended to the boundaries of ancient Rome,
achieving maximum use during the 3rd century A.D., the Roman
Empire’s apex. After Rome’s decline in the 6th century, geothermal
exploitation also declined throughout Southern Europe, a period of
disusewhichlasteduntilthebeginningofthesecondmillennium.There
is evidence that geothermal resources were still being exploited in the
centuriesthatfollowed,inChinaandmanyothercountries,butonavery
limited scaleand only in rudimentary forms.
DeepintheRemontalouRivervalley,atthesouthedgeofAuvergnein
theCentralFrenchmassif,thetownofChaudeseAigueshasan82(cid:1)Chot
spring,oneofthehottestnaturalthermo-mineralspringsinEurope.The
regionhasbeeninhabitedsinceprehistorictimes.Themainspring,called
le par, is one of about 30 gushing springs concentrated in a small area.
Frommid-OctobertotheendofApril,a5-kmnetworkofpipesbringsthe
hotwaterfromfiveofthesespringstoheat150homes.Housesbuiltabove
thespringsusethehotwaterdirectlybelowforheating,andhavedoneso
since the 14th century (Cataldiet al., 1999).
GeothermalwaterwasfirstusedforboricacidproductioninLarderello,
Italy, in 1827. Boric acid production was an Italian monopoly in Europe,
andbecamealarge-scaleindustryinthemiddleofthe19thcentury.
Othercountriesalsobegantodeveloptheirgeothermalresourcesonan
industrial scale. V. Zsigmondy, for example, became a legend in Hun-
garian geothermal history after he drilled Europe’s deepest well (971m)
in Budapest in 1877. Since that date, the resulting geothermal water has
been used for balneology in the famous Szechenyi Spa. In 1892, the first
geothermal district-heating system began operations in Boise, Idaho,
USA. In 1928, Iceland, another pioneer in the utilization of geothermal
energy,alsobeganexploitingitsgeothermalfluids(mainlyhotwaters)for
domestic heating purposes.
3
1.2 THENATUREANDORIGINOFGEOTHERMALENERGY
In 1904, Larderello again became famous as the first place where
electricity was generated from geothermal steam. The scientific and
commercialsuccessofthisexperimentdemonstratedtheindustrialvalue
ofgeothermalenergy,theexploitationofwhichwouldthendevelopmore
significantly. By 1942, Larderello’s installed geothermoelectric capacity
hadreached127,650kW.SeveralcountriessoonfollowedItaly’sexample.
e
In1919,thefirstgeothermalwellsinJapanweredrilledatBeppu.In1921,
geothermalwellsweredrilledattheGeysers,California,USA.
Between the two World Wars, oil prospectors found huge geothermal
waterreservoirsallovertheworld,usuallybyaccident.In1958,basedon
similarexplorationdata,andafterextensivelymappingvariationsinthe
Pannonian Basin’s terrestrial heat-flow 15years earlier, the Hungarian
mining engineer T. Boldizsa´r composed the world’s first regional heat-
flow map of Hungary (Boldizsar, 1964). That same year, a small
geothermal power plant began operating in New Zealand. Another
startedin1959inMexico,andanotherintheUnitedStatesin1960.Many
othercountries would then follow suit in theyears tocome.
As of 2015, 28 nations currently use geothermal energy to generate
electricity(geothermalpower).Therehasbeenasignificantincreasesince
1995.Bythatyear,theworld’sinstalledcapacitywas6833MWe(Bertrani,
2015). By 2005, it was 8934MWe. By 2015, it was 12,635MWe (or
73,549GWh/year).
Asof2015,78countrieshavedirectutilizationofgeothermalenergy,a
significant increase from the 28 reported in 1995, 58 in 2000, and 72 in
2005. For 2015 the reported amount of geothermal energy used is
438,071TJ/year (121,696GWh/year). Approximate geothermal energy
usebycategoryis49.0%forground-sourceheatpumps,24.9%forbathing
andswimming(includingbalneology),14.4%forspaceheating(ofwhich
85% isfordistrict-heating), 5.3% forgreenhousesand uncoveredsurface
heating, 2.7% for industrial process heating, 2.6% for aquaculture pond
andracewayheating,0.4%foragriculturaldrying,0.5%forsnowmelting
and cooling, and 0.2% forother uses.
1.2 THE NATURE AND ORIGIN OF GEOTHERMAL
ENERGY
There was a time, not so long ago, when the high temperature of the
Earth’s interior was not known. Kelvin solved first the differential
equation of the heat conduction in a spherical coordinate system. The
sphericalsymmetryofEarth’sshapesuggestedtheideaofthespherically
symmetricaltemperaturedistributionaroundtheworld.Thetemperature
distribution along the depth is monotonically increasing. In accordance
the Fourier’s law of heat conduction, a radial outward heat flux occurs.
4
1. WHATISGEOTHERMALENERGY?
This is the so-called terrestrial heat-flow. The terrestrial heat-flow is
mainly conduction but can be convection also. Kelvin collected surface
heat-flowdatafromRussia,Australia,SouthAfrica,DeccanPlateau,and
Labrador. Unfortunately, these places are geothermally similar with a
relatively low heat-flow. Kelvin’s measurements confirmed the idea of
spherically symmetrical temperature distribution obtaining an average
heat-flowvalueof0.0556W/m2.ThisthermostaticmodeloftheEarthwas
proven false on the basis of Boldizsa´r’s (1943) terrestrial heat-flow
measurements, especially after the discovery of the regional geothermal
anomalyintheCarpathianBasin.Boldizsar’sheat-flowmapofHungary
was the first in the world in 1944. It was proven by the convincing
evidence of the regionally varying heat-flow distribution. He got the
name“Fatherofgeothermal.”Boldizsar’searlyresultswereconfirmedby
extended investigations of Bullard (1954), exploring the extremely high
heat-flow distribution along themid-oceanic ridges (Fig. 1.1).
As a result of international scientific cooperation, large-scale conti-
nental heat-flow maps demonstrate the varying heat-flow intensity
belonging to certain tectonic structures. Along the displacing mid-ocean
ridges the terrestrial heat-flow attains the value of 0.2W/m2. The
average heat-flow in the Carpathian Basin is 0.1W/m2 (Toth, 2010). On
the continental shields or the oceanic crust, heat-flow density hardly at-
tains thevalueof0.02W/m2.Alltheseareconnectedastheresultofthe
plate tectonics, the movement of thelithosphereplates.
The generally accepted model of the Earth’s structureposits an outer,
sphericalshell, known asthecrust.Itstwo parts canbedistinguished as
thecontinentalcrust,withanaveragethicknessof35km,andtheoceanic
crust, with a thickness of about 8km. Beneath the crust lies a boundary
FIGURE1.1 Terrestrialheat-flowmapinHungary.
5
1.2 THENATUREANDORIGINOFGEOTHERMALENERGY
knownastheMohorovicicdiscontinuity,wherethespeedofpropagation
of seismic waves suddenly increases from 7km/s to 8.1km/s. The
Mohorovicicdiscontinuitycanbefoundbeneaththecrustandabovethe
mantle.Themantleextendstoadepthof2900km,wherethereitchanges
intothemuchdenserliquidcore.Thecoreiscomposedlargelyofmolten
iron.Withinthisliquidcoreisasolidifiedironinnercorewitharadiusof
about 1350km. On a large scale, these are the main components of the
Earth’s structure,as shown in Fig. 1.2.
Fromthegeothermalpointofview,onlythecrustandtheuppermantle
areof importance. Directinformation about the mantleis available from
deep boreholes only. The three deepest are in Sakhalin, Qatar, and the
KolaPeninsula.Theyhaveabottomholedepthofabout12km.Allother
data derive from indirect gravimetric, seismic, dipole-resistivity, and
othergeophysical information.
The crust is not a homogeneous spherical shell. The continental crust
beneaththecontinentsandtheenclosedseasismainlygranitecomposite,
rich in silica with a density of 2670kg/m3. The oceanic crust is mainly
basaltic.Itispoorinsilicawithadensity2950kg/m3.Thethicknessofthe
continentalcrustisvariable.Beneaththehighrangesitcanbe70e75km
thick, but beneath the sinking sedimentary basins its thickness is only
20e25km.
Beneath the crust, the upper mantle is rigid. This is the so-called lith-
osphere. Its thickness is approximately 80e100km. Under the litho-
sphere, the propagation speed of the seismic waves decreases in a
FIGURE1.2 StructureofEarth’sinterior.