Flow and Heat Transfer in Geothermal Systems. Basic Equations for Describing and Modelling Geothermal Phenomena and Technologies PDF
Preview Flow and Heat Transfer in Geothermal Systems. Basic Equations for Describing and Modelling Geothermal Phenomena and Technologies
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 Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2017ElsevierInc.Allrightsreserved. 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-800277-3 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/ Publisher:CandiceG.Janco AcquisitionEditor:AmyShapiro EditorialProjectManager:TashaFrank ProductionProjectManager:MohanapriyanRajendran Designer:MariaInesCruz TypesetbyTNQBooksandJournals 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.
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