Geothermal Reservoirs - A Brief Review
JOURNAL GEOLOGICAL SOCIETY OF INDIAVol.79, June 2012, pp.589-602Geothermal Reservoirs – A Brief ReviewSAYANTAN GANGULY and M. S. MOHAN KUMARDepartment of Civil Engineering, Indian Institute of Science, Bangalore – 560 012Email: sayantan@civil.iisc.ernet.in; msmk@civil.iisc.ernet.inAbstract: A brief discussion and review of the geothermal reservoir systems, geothermal energy and modeling andsimulation of the geothermal reservoirs has been presented here. Different types of geothermal reservoirs and theirgoverning equations have been discussed first. The conceptual and numerical modeling along with the representation offlow though fractured media, some issues related to non isothermal flow through fractured media, the efficiency of thegeothermal reservoir, structure of the numerical models, boundary conditions and calibration procedures have beenillustrated. A brief picture of the Indian scenario and some barriers related with geothermal power are discussed andpresented thereafter. Finally some gaps of the existing knowledge and recent focuses of research are discussed.Keywords: Geothermal reservoirs, Modeling and simulation, Conceptual model, Calibration, Boundary conditions.INTRODUCTIONGeothermal energy is the energy naturally present insidethe earth crust. When a large volume of hot water and steamis trapped in subsurface porous and permeable rock structureand a convective circulating current is set up, it forms ageothermal reservoir. Hochstein (1990) described ageothermal system as ‘convective water in the upper crustof Earth, which, in a confined space, transfers heat from aheat source to a heat sink, usually the free surface’. A geothermal system is made up of three main elements: a heatsource, a reservoir and a fluid, which is the carrier thattransfers the heat (Dickson and Fanelli, 1994). A schematicview of a typical geothermal reservoir system with rDIFFERENT GEOTHERMAL SYSTEMSPower s and production and injection wells installed isshown Fig. 1.As an alternative source of energy geothermal energyhas been under attention of the researchers for quite sometime. The reason behind this is the existence of severalbenefits like clean and renewable source of energy whichhas considerable environmental advantage, with no chemicalpollutants or wastes are generated due to geothermalemissions, and the reliability of the power resource. Henceresearch has been directed in several directions likeexploration of geothermal resources, modeling thecharacteristics of different types of geothermal reservoirsand technologies to extract energy from them. The target ofthese models has been the prediction of the production ofthe hot water and steam and thus the estimation of theelectricity generating potential of a geothermal reservoir infuture years.InjectionWellInjectionWellNatural ConvectionNaturalConvectionHeatSourceHeat SourcFig.1. Schematic representation of a geothermal reservoir systemwith production and injection wells installed.The geothermal systems can broadly be classified intothree systems hydrothermal, geopressured and hot dry rocksystems (Faust and Mercer, 1979). When heat from a nearsurface source is transferred to porous media and the porousfluid within that by conductive and convective processesthe system is called a hydrothermal one. The hydrothermalsystems can be further categorized into liquid dominatedand vapor dominated (or dry steam) systems (White et al.1971) depending upon whether water or vapor is present as0016-7622/2012-79-6-589/ 1.00 GEOL. SOC. INDIA
590SAYANTAN GANGULY AND M. S. MOHAN KUMARthe continuous and pressure controlling phase. In vapordominated systems water and vapor coexist together.Geopressured systems on the other hand is a type of staticsystem in which water gets trapped inside permeablesedimentary rock within low permeable rock strata. Trappedwater is subjected to high pressure and temperature.Finally the hot dry rock system is an artificial reservoirsystem in which boreholes are drilled and water is injectedinto hot igneous rock which is heated by similar process asthe hydrothermal system. The injected water extracts heatfrom the rock body moving through the fractures and thehot water and steam is extracted by another borehole.Geothermal systems are further classified depending onreservoir equilibrium state a static and dynamic systems.Dynamic systems as the name suggests consists of rechargeand discharge of water in a continuous manner. Theconvective or circulating movement of water through thesystem is responsible for the heat transfer. Static systems onthe other hand have minimum or no recharge and heat istransferred in the system mainly by process of conduction.GOVERNING EQUATIONS OF GEOTHERMALRESERVOIRSGeothermal reservoir simulation needs a correctlyconstructed mathematical model to obtain a propernumerical solution of the system. A mathematical model fora geothermal reservoir needs to have information orunderstanding of 1. Physical and chemical processes operating in thereservoir.2. The initial conditions throughout the system andboundary conditions at the boundaries.3. Hydrogeologic parameters (porosity, permeability etc)with their spatial variations.4. Fluid properties (density, viscosity, enthalpy vaporpressure etc).5. The locations of sinks and sources and their flowrates.The flow of fluid inside a geothermal reservoir is acomplex phenomenon. The flow can be characterized bothas a single phase (water) multi-component (mainly liquidwater and steam, with dissolved carbon-dioxide and NaCl)flow or a multiphase flow consisting of two phases water(liquid phase) and steam (gaseous phase). Governingequations describing the phenomenon are developed in termsof conservation equations or balance laws of massmomentum and energy. Derivations and presentations of themathematical models of geothermal reservoirs have beendone by Mercer et al. (1974), Faust and Mercer (1977a),Brownell et al.(1977), Witherspoon et al. (1975). Theconservation equations should be considered for each phasein geothermal system. Constitutive relations are then usedto simplify and reduce the number of equations. Differentsets of variables can be used in formulating the governingequations of geothermal reservoir. Pressure-temperaturesaturation -pressure enthalpy, density-internal energy canbe cited as examples. The governing equations in the formof partial differential equations are given below.Mass BalanceMass conservation equations are given for two phaseswater (w) the wetting phase and steam (s) the non-wettingphase, normally present in geothermal systems.Steam:(1)Water:(2)Here φ represents the porosity, S is the saturation, ρis the density, q is the source term, ν is the averaged phasevelocity and m represents the mass transfer rate from liquidto vapor.Momentum BalanceMomentum conservation equations are generally givenin form of Newton’s second law. Here Darcy’s Law extendedfor multiphase flow through porous media is used. Itshould be noted that applicability of Darcy law is limitedto a system of fractures. It is not valid to describe flowthrough a single fracture (Arbogast, 1989). In a geothermalreservoir medium, which consists of a system of fracturesDarcy law can be applied as a momentum or dynamicequation for fluid flow analysis. The equations are givenby(3)(4)Where K is the intrinsic permeability tensor, kr is therelative permeability, D is the depth and p is the phasepressure and g is the gravitational constant.Energy BalanceEnergy balance equations are presented in terms ofpressure an enthalpy as primary variables. Assumptions ofJOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012
GEOTHERMAL RESERVOIRS – A BRIEF REVIEWzero capillary pressure and local thermal equilibrium areapplied here.591(12)where pd is the entry pressure or the displacement pressurefor the fracture media,λ is the pore size distribution index,Se is the effective saturation of the wetting fluid and isgiven by(13)(5)where ρ is the density of the total steam-water mixture, givenbyρ Sw ρw Ss ρs(6)with the sum of the individual phase saturation equals to 1.Sw Ss 1(7)hw', hs' and hr' are the enthalpies of water, steam and rockrespectively and h' is the enthalpy of water steam mixtureand is given byS ρ h' Swρwh'wh' s s sρ(8)T represents the temperature and qh is the source/sinkterm.The geothermal reservoir simulation problem is acomplex multiphase multicomponent flow problemconsisting of water in two phases (liquid and steam). Thegoverning equations of multiphase flow are strongly coupledby the relative permeabilities and constraints given by Eqn.7 and 9. The main numerical complexity of the governingequations of geothermal reservoirs arises due to thedependence of the capillary pressure (pc) and relativepermeabilities of the phases (k r) on saturation. Therelationships which define this dependence are calledconstitutive relations which are needed to describe thesystem completely. The capillary pressure can be expressedaspc ps – pw(9)where ps is the non-wetting phase pressure of steam and pwis the wetting phase pressure of water. The most widely usedconstitutive relationships between capillary pressure andsaturation and that between relative permeability andsaturations were parameterized by Brooks and Corey (1964)and van Genutchen (1980). The Brooks and Corey (1964)pc-Sw, kr-Sw relations are given by(10)(11)JOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012where Srw and Srnw are the residual saturations for thewetting (water) and the non wetting(steam) phase. krw andkrnw are the relative permeabilities of the wetting andnonwetting phase.CONCEPTUAL MODEL OF A GEORTHERMALRESERVOIR SYSTEM“A good understanding of the important aspects of thestructure of the system and the most significant (physicaland chemical) aspects in it is referred to as its conceptualmodel” (O’Sullivan et al. 2001). Generally it consists offew sketches of several horizontal and vertical sections ofthe system containing information about geological structure,temperature, geochemistry, resistivity and surface activity,important features of a geothermal system like surfacemanifestations (i.e. hot springs, steaming grounds, etc),flow boundaries, main geologic features such as faults andlayers, zones of high and low permeability, iso- therms,location of deep inflows and boiling zones, geophysical data(resistivity boundaries, heat flow contours), etc (O’Sullivanet al. 2001). A huge amount of geological, geophysical,geochemical data is required in setting up a conceptualmodel.Flow through Fractured MediaMost of the geothermal reservoirs all over the world aresituated in fractured rock media where the main flow occursthrough a network of interconnected fractures.Conceptualizing the fluid flow and heat transfer mechanismsthrough a fractured media requires either a grosssimplifications it or detailed description of the aquiferproperties controlling the flow. A fractured media consistsof primary rock porosity along with secondary porositycreated by cracks, fractures, joints and shear zones whichform an interconnected network for flow and transport.Hence analyzing flow and transport through a fracturedmedia requires knowledge of the permeability of the rockmatrix as well as permeability created by the network offractures. The rock matrix although having very low
592SAYANTAN GANGULY AND M. S. MOHAN KUMARpermeability, can contribute to the flow locally. Differentapproaches are followed to simulate the flow throughfractures depending on the physical characteristics of thereservoir (fracture spacing and connectivity, permeabilityof rock matrix etc) (Pruess, 2002).The Effective Continuum Method or ECM is the simplestamong all of the approaches in which the fractured media isrepresented as a single porous media with properties chosenin such a way so as to represent approximately the originalfractured media.Explicit modeling of a fracture may be another approachwhich is applicable to idealized cases of a major fracture orfault zone whereas in real scenarios due to presence ofnumerous fractures in a domain explicit representation isnot viable.A third approach to model flow through fractured mediaand the most widely used one now a days is the doubleporosity method proposed by Barenblatt et al. (1960) andWarren and Root (1963). This approach considers theinterconnected fracture zone permeability and rock matrixpermeability separately. The main advective flow isconsidered to be through the fracture network only due tolow permeability of the rock matrix. The matrix and fracturesinteract locally by exchange of fluid by means of cross flowor interporosity flow which is governed by the localdifference in pressure or temperature between the twomedia. The concept is represented by a cube model offractured reservoir shown in Fig.2. Gerke and Genuchten(1993) proposed a dual porosity mathematical model forone dimensional vertical flow through variably saturatedporous media(14)two regions given by(16)where Γw is the mass transfer rate between fracture andmatrix,θm represents the water content of the matrix, ω isa first order rate coefficient and Sef and S me are effectivefluid saturations of the fracture and matrix zone respectively.Compared to this approach to model the mass transferterm the pressure head based approach (Gerke and vanGenuchten, 1993b) given below which considers Γw tobe proportional to the difference in the pressure headsbetween the fracture and matrix regions is more realisticsince it considers the pressure gradient as the driving force(like Darcy law) for the fracture-matrix mass transfer andhence considers the interface velocity between fracture andmatrix zone(17)where hf and hm are the pressure heads for fracture andmatrix regions αwis a first order rate coefficient given by(18)where β is a dimensionless geometry coefficient, d isthe characteristic half width of the matrix block, K arepresents the effective hydraulic conductivity of the matrixat the fracture matrix interface and γw is a dimensionlessscaling factor. One thing should be noted that here hf andhm are average pressure heads for fracture and matrixrespectively and spatial and temporal variation of them(which is the actual case) are not considered here.Double porosity concept assumes the interporosity flowto be quasi steady and governed by local difference inpressures between fractures and matrix which is applicable(15)Subscripts f and m are used for flow through fractureand matrix respectively, h represents the pressure head,C dθ /dh is the specific water capacity where θ is thewater content, K the hydraulic conductivity, wf is fractionalpore volume w.r.t the total rock volume, z is vertical directiontaken downward positive and Γw represents the mass transferterm between facture and matrix medium.The mass transfer term between the fracture andmatrix here is a critical term to model in all dual porosity/permeability models. In several studies (Philip, 1968;Simu nek et al. 2001) the transfer term is assumed to beproportional to the difference of effective water contents ofFig 2. Idealized cube model of matrix fracture system in DoublePorosity model.JOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012
GEOTHERMAL RESERVOIRS – A BRIEF REVIEWonly for single phase isothermal flows with fluids of smallcompressibility and not for non-isothermal, multiphase flowscenarios like that of geothermal reservoirs. Hence anextension was made to the double porosity model by Pruessand Narasimhan (1982, 1985) named ‘Multiple InteractingContinua’ or MINC. The model treats interporosity flow ina fully transient way and the gradients of pressure,temperature and mass fraction gradients are defined at thefracture matrix interface. Matrix blocks are discretized intovolume elements which subgrids the matrix blocks intoseparate continuums as shown in Fig 3. The interporosityflow is assumed to be one dimensional towards the fracturesor away from it.FractureMatrix593The stochastic continuum approach on the other handconsiders the fractured media can be described on the basisof some spatially variable spatial parameters which varyaccording to some random functions. The domain ofmodeling is discretized to cells and based on the randomfunctions some random values of the properties are assigned.Finite volume or finite difference models are then appliedto calculate the average properties.The Channel network model conceptualizes the flowwithin the fractured media to occur through certain discretechannels which intersect at various intervals. Thecharacteristics of the fractured network are neglected hereand so the amount of data required are lesser than DFNalthough this method considers the discrete nature of thepathways. Consideration of flow through discrete channelsallows the use of one dimensional element to discretize thedomain which reduces the computational difficulty.Fluid flow through a fracture can be fully described bythe Navier-Stokes equation. However as the groundwaterflow velocity and the Reynolds number associated with it issmall, the advective terms can be considered to be negligible.Based on the above assumptions and considering the velocityto be depth averaged over the aperture the fluid flowequations is given as (Muralidhar, 1990)(19)Fig 3. Discretization of matrix and fracture into different volumeelements in MINC method.The mathematical models describing the fluid flow andheat transport through the fractured network are all basedon the continuum theory and correspond to a representativeelementary volume (REV). Mathematical models can bebroadly classified into three categories depending on thevarious scales to analyze the fluid flow and heat transportmechanisms. They are (1) Discrete Fracture Network (DFN)(2) Stochastic Continuum (SC) and (3) Channel Networkmodel (CN) (Dershowitz et al. 1999; Selroos et al. 2002;Gylling et al. 2004).The discrete fracture model as the name suggestsconsiders flow through individual fractures which areconsidered to be interconnected. A statistical description ofthe fracture geometry and hydraulic properties such aslocation, size, orientation, spatial structure is needed to setup a DFN model. The advantage of DFN is that itincorporates the description of the fracture or fracturezones explicitly. The disadvantage on the other hand iscollecting and handling a huge amount of data whichsometimes may be too difficult to collect also.JOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012(20)(21)where ū and v̄ are the depth averaged velocities in x and ydirections respectively, px and py are the depth averagedpressures in x and y directions respectively, t is time, f(z) isthe function describing the variation of u and v over thedepth, Re (umd/v) is the Reynolds number where um is themean velocity in the fracture, d characteristic length of thefracture and v is the kinematic viscosity of the fluid.Assuming the temperature to be uniform over the depththe depth averaged advection-diffusion equation is given as(22)where T is temperature, Pe (umd/α) is Peclet numberwhere α is the thermal diffusivity of the fluid.
594SAYANTAN GANGULY AND M. S. MOHAN KUMARSome Issues Regarding Non Isothermal Flow throughFractured MediaSince the fractured media is originally a fully coupledmedium, coupled interaction exists between the matrix andfracture in terms of fluid diffusion, heat transfer and rockdeformation. Considering the fracture to be a vertical planeof uniform width (Fig. 4) the heat balance equations(Ghassemi et al. 2008) for a fracture segment and matrixare given respectively by(23)and(24)here T is temperature, v is the velocity of fluid in the fracture,D L represents the thermal dispersion coefficient, K rrepresents the rock thermal conductivity, e is the fractureaperture, cf and cr are the specific heat of the fluid and rockrespectively and ρf and ρr is the density of the fluid androck respectively.The geothermal reservoir being a deformable porousfractured medium due to the extraction of the geothermalfluid it undergoes deformation due to the thermal stressproduced. The apertures of the fractures undergo changesand hence the fracture permeability is also evolutesaccordingly. Ghassemi and Suresh Kumar (2007) derivedan analytical solution which is given below for the changein aperture fracture with time resulting from thermoelasticdeformation assuming the thermally induced stress is onedimensional and rock deformation occurs only by normalstrain.(25)where υ is the Poisson’s Ratio, αT represents thelinear thermal expansion coefficient, ρm represents thedensity of the matrix, λm represents the thermal conductivityof the matrix, C m represents the rock specific heat,ΔT T (x,y,t) -T , where T is the temperature at infinity,A1 x λm ρ mCmQ ρ m Cw tandA2 ρ m Cm2 λmtwhere Q is the volumetric injection rate.Results of the research work showed that the thermalstresses consequences in the reduction of the aperture alongthe length of fracture which is maximum near the tureExtractionwellExtractionwelxFig.4. Top view of an idealized vertical fracture extending frominjection to production/extraction well.well. The fracture permeability (Kf) calculated from the‘cubic law’ K f e 2/12, reduces accordingly and thevolume of flow and pressure distribution undergo significantchange due to small change of the aperture induced bythermal stress generating from heat extraction.Modeling of reactive transport under non-isothermalconditions as in the case of a geothermal reservoir has beenan important aspect since the solute transport results inchanging the fracture aperture which in turn affects fracturepermeability. Phenomenon like quartz dissolution orprecipitation, nonlinear sorption of the solutes thus has acontribution in maintaining the reservoir efficiency. SureshKumar and Ghassemi (2005) have presented a numericalmodel to simulate combined effect of the thermal andreactive solute transport in a coupled fracture-matrix systemusing dual porosity concept. Results from their model showthat higher the initial temperature of the rock higher is thequartz dissolution near the injection well which increasesthe fracture aperture. It is also inferred that higher initialvelocity of flow in the fracture, higher initial fractureaperture, lower reservoir porosity, lower effective matrixdiffusion coefficient and lower reservoir thermalconductivity results in higher dissolution of quartz and thusreducing the resistance of flow between the injection andproduction well.Non linear sorption on the other hand is anotherphenomenon to retard the solute movement in the fractureaffecting the extent of solute spreading in the fracture.Natarajan and Suresh Kumar (2010) studied the effect ofnon linear sorption on solute transport in a coupled sinusoidalfacture-matrix system. Results suggest that as sorptionintensity reduces sorption becomes more favorable and theconcentration of solutes along the fracture reduces. Sorptionintensity has also negligible effect with respect to the changeof fracture aperture.The flow rate the within the fracture is dependent on alot of factors. Fluid flow within a fracture is essentially acoupled process between fluid flow and rock deformation(Wu and Pruess, 2000) since geothermal reservoir mediumis a deformable fractured medium. Fluid density, porosityand permeability are all functions of the pressure which isJOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012
GEOTHERMAL RESERVOIRS – A BRIEF REVIEWresponsible in controlling the flow rate. Pressure changesinduced by the deformation of the fracture walls results indensity change of the reservoir fluid which in turn influencesthe flow rate. According to Indraratna et al. (2003) flowrates of the phases of a two phase flow (air and water) maydecrease by 80% when the confining pressure exceeds 5MPa. Temperature changes as in the case of non isothermalflows also plays vital role. Other effects like thermo andporoelasticity, reactive transport of solutes (precipitation/dissolution, non-linear sorption) also results in change offracture aperture controlling the fracture permeabilitywhich governs the flow rate. Hence a constant flow thoughthe fractures is essentially a simplified assumption andpractically not feasible to maintain.Another issue regarding the non-isothermal flow throughthe fractured reservoir is the variation of pressure in thereservoir due to injection and production. The method ofinjecting fluid into the geothermal reservoir is necessary tomaintain the pressure inside the reservoir. Additionally itreduces amount of non-condensable gases (NCG) andbenefits the energy extraction. The injected water isheated up by heat transfer from the rocks and starts tovaporize. Due to the vaporization the volume of thefluid expands and pressure increases which propagateaway from the injection plume. Pruess (2008) found thatdue to the injection, the pressure is highest near the injectionwell (where temperature is minimum due to cold waterinjection) and then there is a sharp gradient of pressurefollowed by gradual decrement towards the productionwell. With continuous injection the pressure near theinjection well also increases with time. But with passage oftime the pressure away from the injection well decreasesdue to the overall heat transfer from the rock to the injectedwater.GEOTHERMAL RESERVOIR EFFICIENCYA big concern regarding the geothermal reservoir is tomaintain its efficiency. The lifetime efficiency of ageothermal reservoir can be defined as the ratio of the heatproduced over its lifetime to the total available heat contentof the reservoir (Brown et al. 1999). The efficiency of thegeothermal reservoir system is dependent greatly on thefracture aperture thickness. The production or extractionfrom the reservoir depends directly on the permeability ofthe fractured media of the reservoir. The permeability inturn is dependent on the square of the fracture aperturethickness as calculated from the ‘cubic law’. Hence changesin fracture aperture would affect the reservoir efficiency alot.JOUR.GEOL.SOC.INDIA, VOL.79, JUNE 2012595Thermo and poroelasticity plays vital role in determiningthe reservoir efficiency as these two effects are hugelyresponsible for changing the aperture of the fractured media.In general the geothermal reservoir is a fully coupled thermoporoelastic medium. Ghassemi et al. (2008) have shown thatthese two effects play an opposite role to change the fractureaperture. Thermally induced stresses tend to increase thefracture aperture whereas poroelastic effects are responsiblefor closure of fracture opening along the length of fracture,both the effects being maximum at near the injection pointand gradually reducing towards the outlet. The thermoelasticeffects being predominant the combined effect of the twowith fluid losses from the fracture increases the fractureopening with time which reduces the pressure in thefracture with time due to increase of fracture aperture andhence less injection pressure would be needed at theinlet.Efficiency also depends on some other factors like thedepth of the production and injection wells as evidently atmore depth the wells will be exposed to more temperatureleading to more heat extraction. Spacing of the injectionand production wells also plays vital role in reservoirefficiency. Injection of water is essential in addition to fluidextraction from the reservoir in order to maintain thereservoir pressure and to stimulate the flow from injectionto production wells. Close spacing of the injection andproduction wells helps in maintaining the reservoir pressure.But since the injected fluid is much colder than the reservoirfluid it results in reduction of the temperature near theinjection well. As this temperature front of colder fluid growswith time and reaches at the production well, the temperaturethere remains no longer constant and the reservoir efficiencymay be affected (Stopa and Wojnarowski, 2006) Hencesufficient spacing of the injection and production wells isnecessary to maintain constant temperature at the productionwell. The reservoir efficiency is therefore dependent ontwo contrasting situation of increase in reservoir pressureby decreasing distance between the wells and increasing thedistance concerning the reservoir temperature reduction(Kocabas, 2005).To maintain the efficiency of a geothermal reservoir theconnectivity between the injection between the injection andthe production wells has to be ensured. Hydraulic stimulationhas been a mean of ensuring that. Higher injection pressureis applied in this method which results in higher meanpressure of the reservoir which causes access of the reservoirfluid to more rock volume and reduction of flow impedancebetween injection and production wells in enhancedgeothermal systems (EGS) (Brown et al. 1999). Howeverincrease of injection pressure has resulted in few cases in
596SAYANTAN GANGULY AND M. S. MOHAN KUMARshort circuiting of flow paths and water losses from thereservoir e.g. in Hijiori reservoir, Japan (Tenma et al. 1997)and Rosemanowes reservoir, United Kingdom (Richards etal. 1994). Another problem regarding hydraulic stimulationis that the injection of excessive cold water may reduce thetemperature of the surrounding hot rock and the method offracturing may cause microscale earthquakes too. Hence thefeasibility of the hydraulic stimulation has been limited bythese issues.MODELING AND SIMULATIONLike other fields of modeling and simulation geothermalsystems can also be modeled in deterministic as well asstochastic way. Models of geothermal reservoir systems canbe broadly classified into (1) natural state models or freeconvection models which are the models of the systemswithout exploitation or prior it and (2) models to study theeffects of exploitations from a geothermal reservoir.Geothermal reservoir models can be further classified intolumped parameter mode
Abstract: A brief discussion and review of the geothermal reservoir systems, geothermal energy and modeling and simulation of the geothermal reservoirs has been presented here. Different types of geothermal reservoirs and their governing equations have been discussed first. The conceptual and numerical modeling along with the representation of
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