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Geothermics

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Numerical simulation of the heat extraction in 3D-EGS with thermal-hydraulic-mechanical coupling method based on discrete fractures model

Jun Yaoa,⁎, Xu Zhanga, Zhixue Suna, Zhaoqin Huanga, Junrong Liua, Yang Lib, Ying Xina, Xia Yana,Wenzheng Liua

a School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, ChinabDepartment of Oilfield Exploration & Development, Sinopec, Beijing 100728, China

A R T I C L E I N F O

Keywords:Enhanced geothermal systemDiscrete fracturesTHM couplingNumerical simulationPerformance evaluation

A B S T R A C T

The geothermal heat production from Enhanced Geothermal System (EGS) is influenced by complex thermal-hydraulic-mechanical (THM) coupling process, it is necessary to consider THM coupling effects on utilizationefficiency and production performance of EGS. The geothermal reservoir regarded as a fractured porous mediaconsists of rock matrix blocks and discrete fractures. Based on local thermal non-equilibrium theory, a mathe-matical model and an ideal 3D-EGS numerical model incorporating THM coupling process are established tosimulate the heat production process in EGS, and the distribution regularities of pressure, temperature, stressand deformation in geothermal reservoir are analyzed. The results show that the connecting fractures are themain flow paths and the transmission characteristic of reservoir is altered due to displacement of fracturescaused by the change of pressure and temperature in reservoir. The main parameters controlling the outlettemperature are also studied by sensitivity analysis. An EGS case from Desert Peak geothermal reservoir issimulated with a 3D stochastically generated fracture model to evaluate EGS heat production performance. Theresults indicate that heat production time, thermal output and power generation can meet the commercialstandard with appropriate reservoir and operation parameters, however, energy efficiency and overall heatrecovery remain at low level.

1. Introduction

Energy extraction from geothermal reservoirs involves severalcoupled physical to geo-mechanical processes in the fractured rockmass, including heat transfer, water seepage and solid deformation(Tester et al., 2006; Kohl et al., 1995; Ghassemi and Zhou, 2011; Wanget al., 2016; Zhao et al., 2015). It plays a crucial role to investigate theTHM coupling process in reservoir to reveal the mechanism of heatproduction and predict the state of performance, utilization efficiency,as well as service-life for sustainable utilization period. Till now, manyuseful models have been developed for modeling the performance ofEGS. Zhang et al. (2011) constructed a mathematical model to describethermo-hydraulic coupling in subsurface porous media with a singlefracture and analyzed the heat transfer process between fluids andfracture surface. Chen et al. (2014) and Chen et al. (2013a) came upwith a numerical model incorporating fluid flow and heat transmissionprocess based on discrete fracture network model. Jiang et al. (2013,2014) presented a three-dimensional transient model for EGS subsur-face thermo-hydraulic process by which the geothermal reservoir is

treated as an equivalent porous medium of a single porosity. Xu et al.(2015) proposed a simplified approach to simulate the coupled hydro-thermal system for EGS, capable of providing a detailed prediction offluid flow and heat transfer in geothermal reservoir based on anequivalent pipe network model. Shaik et al. (2011) developed a nu-merical procedure to simulate the heat extraction from naturally frac-tured geothermal systems by coupling fluid flow with heat transferbetween the rock matrix and circulating fluid. It provides a dynamictreatment of the characteristic properties (aperture, length and or-ientation) of individual fractures. However, the effect of fractured rockmass deformation on the coupled hydro-thermal process in EGS isoverlooked in these studies. Lei et al. (2015) and Rutqvist (2011) tookTHM coupling process into consideration with the development ofTOUGH2 code to model the heat production process of EGS, but thecomplex fracture network is simplified. For a better understanding ofthe performance of EGS, Bahrami et al. (2015) studied several self-propped single fracture THM models based on the poro-elastic theory.Zhao et al. (2015) established a 3D THM coupling model of fracturedmedia to simulate the extraction of HDR geothermal energy, by which

https://doi.org/10.1016/j.geothermics.2017.12.005Received 10 September 2017; Received in revised form 23 November 2017; Accepted 8 December 2017

⁎ Corresponding author.E-mail address: yaojunhdpu@126.com (J. Yao).

Geothermics 74 (2018) 19–34

0375-6505/ © 2017 Elsevier Ltd. All rights reserved.

T

the fracture area was discretely modeled by the Goodman joint element.However, it seems too simplified to be used for modeling heat extrac-tion in rock mass containing dense fracture networks. Sun et al. (2017)investigated the characteristics of heat transfer, fluid seepage and soliddeformation in geothermal reservoir with 2D stochastically generatedfracture model based on an EGS case from Cooper Basin. It can’t re-present the actual fractured porous media due to the simulation isunder 2D.

Although substantial efforts have been made on the numericalmodeling of THM coupling process in fractured rock mass, there is stilla challenge to accurately estimate the heat extraction process in EGSand further theoretical research and numerical simulation are needed.Fractures and fracture networks are the fundamental components ofEGS to determine its technical and economic viability, whereas rela-tively fewer investigations have focused on the simulation of THMcoupling process in dense fracture networks. The deformation andstress variation of rock mass can result in fracture opening and closingwhich may dramatically influence the permeability during extractinggeothermal energy in EGS. The coupled impacts of THM process infractures, especially how mechanical process affects the fluid flow, heatexchange between rock and circulating fluid is essential for under-standing the heat extraction process in EGS, which should be con-sidered in the simulation. Furthermore, the simulation of enhancedgeothermal system on the basis of a realistic THM coupling model, theevaluation of heat production performance of EGS and the optimizationof energy efficiency and heat recovery are crucial to guide economicdevelopment of HDR resources.

Considering the local thermal non-equilibrium, a mathematicalmodel incorporating THM coupling effects is presented in this work forsimulating the fractured EGS reservoir. Deformation, water seepage andheat transfer processes in both of the rock matrix and fractures aretaken into account, as well as their interactions. The coupling model isimplemented in the commercial finite element software, COMSOLMultiphysics. The proposed model and the numerical approach arevalidated by comparing with some analytical solutions. An ideal 3D-EGS model with a geothermal doublet is used to study the character-istics of flow, heat transfer and mechanical behaviors in HDR reservoir.The main parameters controlling the outlet temperature of EGS arestudied by sensitivity analysis. Finally, An EGS case from Desert Peakgeothermal field, is simulated with 3D stochastically generated fracturemodel to evaluate the heat production performance and economicprofit of EGS.

2. Brief description of the THM coupling model

The thermo-poroelastic model for fractured media has been con-structed by Sun et al. (2017). The geothermal reservoir is regarded as afractured porous media consisting of rock matrix blocks and discretefractures. Considering local thermal non-equilibrium between solidmatrix and fluid, the model employs two energy conservation equationsto describe heat transfer in the matrix and the fractures respectively,which can reveal the actual subsurface heat exchange process duringthe development period. The effects of hydraulic loading and heat stressare taken into account of the solid deformation.

The governing equations of THM coupling model in fracturedporous media can be expressed as:

Mass conservation equation in matrix (Liang et al., 2016)

∂∂

+ ∇⋅ − ∇ + ∇ = − ∂∂

+Spt

κη

p ρ g z et

Q( ( ))f (1)

Mass conservation equation in fracture (Liang et al., 2016)

∂∂

+ ∇ ⋅ − ∇ + ∇ = −∂∂

+d Spt

dκη

p ρ g z det

Q( ( ))f f τ ff

τ f τ ff

f(2)

Energy conservation equation in matrix (Xu et al., 2015; Saeid et al.,

2013)

∂∂

= ∇ρC Tt

λ T( )effs

eff s2

(3)

With −λeff ∇ Ts=− qf at the fissure surface, (ρC)eff =(1− ε)ρsCs+ ερfCf, and λeff =(1− ε)λs+ ελf are respectively the ef-fective heat capacity and the effective thermal conductivity obtained byvolume average.

Energy conservation equation in fracture (Chen et al., 2014; Chenet al., 2013a)

∂∂

+ ⋅ ∇ = ∇ ⋅ ∇ + −d ρ CTt

d ρ C u T d λ T h T T( ) ( )f f ff

f f f f τ f τ f f τ f s f (4)

Equilibrium equation (Zhao et al., 2015)

+ + − − ′ + =μu λ μ u α p K α T F( ) 0i jj j ji B i T s i i, , , , (5)

The discrete fracture is approximated by a pair of surfaces betweenwhich normal and shear displacements are permissible. The deforma-tion equation of the rock mass fracture can be written as (Zhao et al.,2015)

= ′ = ′ = ′u σ k u σ k u σ k/ , / , /n n n s s s s s s1 1 2 2 (6)

′ = − ′ = ′ =σ σ α p σ σ σ σ, ,n n B s s s s1 1 2 2 (7)

Where, S is the constrained specific storage of the porous media, p ispressure, t is time, u is the volumetric flow flux, e is the volumetricstrain, k is the intrinsic permeability of porous media, η is the fluiddynamic viscosity, ρf is fluid density, g is the gravitational acceleration,and z is a unit vector in the direction over which the gravity acts. df isthe thickness of fracture, Sf is the specific storage for the fracture, ∇τ

denotes the gradient operator restricted to the fracture’s tangentialplane, kf is the permeability of fracture, ef is the volumetric strain offracture, and Qf is the flow exchange on the fracture surface betweenrock matrix and fracture, = − ∂

∂Qfκη

pn

n , n represents the normal directionon the fracture surface. T is temperature, ρ is density, C is the specificheat capacity, λ is the heat conductivity, ε is the porosity of the rockmatrix, q is the heat loss of matrix to water. The subscripts “s” and “f”mean solid and fluid respectively. h is the convection efficiency. σij,jrepresents the divergence of the transpose of the Cauchy stress tensor,“Fi” is the body force per unit volume in the i-coordinate, and −αBp,idenotes the seepage body force resulting from the pore pressure. ui isthe displacement component; λ and μ are Lame's constants, defined asλ= Eν/[(1+ ν)(1− 2ν)], μ= E/2(1+ ν), in which E and ν are elasticmodulus and Poisson’s ratio respectively；−K′αTTs,i represents thethermal stress term, in which αT is the coefficient of volumetric ex-pansion corresponding to the bulk medium, and K′= E/(1− 2ν) is thebulk modulus of the porous medium. Note that the thermal stress in-duced by temperature change is relative to the reference temperature orinitial temperature. In this regard, the term “temperature in-crement”,Ts,i is used here to distinguish from current temperaturestate.u,σ,σ′ and kdenote the displacement, total stress, effective stressand stiffness, respectively. The subscripts “n” and “s” represent normaland tangential directions to the fracture plane respectively.

In general, under three dimensional stress condition, smooth frac-tures without fillings close or open most readily under normal stressand display weak coupling between shearing and conductivity (Changet al., 2004; Co et al., 2017; Barton et al., 1985). In this work, thepermeability takes the form2 (Rice, 1992; Miller, 2015).

= − ′k k ασexp( )f n0 (8)

Where, kf is the fracture’s permeability, k0 is a baseline permeabilitywhen ′ =σ 0n , α is a normalizing constant, which depends on thefracture's development characteristic, the effective normal stress on thefracture plane is ′ = −σ σ α pn n B , where αB is the Biot’s coefficient. Whenrock mass is fractured to a certain extent void and fracture are con-nected completely, αB=1 (Zhao et al., 2003).

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Thus, the fracture’s permeability is a function of the stress state.Since the rock matrix is assumed to be much more impervious than thefractures and its deformation is relatively smaller, the permeability ofthe rock matrix is assumed to be constant.

Under high pressure and high temperature conditions in the deepunderground reservoir, the density of water, ρf is no longer a constantvalue, this can be expressed as a function of pressure and temperature(Zhao et al., 2015),

= − − − −

− +

−ρ T T p

δ

1/ 3.086 0.899017(647.25 ) 0.39(658.15 ) (

225.5)

f0.147166 1.6

(9)

Where T is the water temperature, p is absolute water pressure, and δ isa function of “p” and “T”; in general, the value of δ does not exceed 6%of 1/ρf. The temperature of water also affects its dynamic visc-osity,η= υρf in which υ is the kinematic viscosity of water. A commonlyused empirical formula for the kinematic viscosity is (Wu, 1983)

=+ +

υT T0.01775

1 0.033 0.000221f f2

(10)

Therefore, the density and viscosity of water are directly relatedwith the temperature, which can dramatically change the couplingprocess of water transport and heat transfer in the reservoir.

3. Validation of numerical model

The detailed information for validation of the 2D TH and THMcoupling model can be found from the previous work (Sun et al., 2017).An analytical solution of the temperature in the fracture is derived byCheng (Cheng et al., 2001). A single rectangular, vertical fracture ofconstant width 2df separates two 3D-blocks of homogeneous, isotropic,impermeable rock (see Fig. 1).

Basic assumptions:In this work, the following assumptions are made in order to obtain

an analytical solution of the mathematical model:

(1) The rock matrix is impermeable and the fluids can only flow at onedirection along the fracture with stable laminar flow state;

(2) Water in the reservoir doesn’t involve phase change and the phy-sical parameters of rock and water consider to be constant due tothe little change of temperature; the thickness of fracture assumesto be unchangeable.

(3) There is no heat source in the system and the viscous diffusion andradiative heat transfer are neglected, regardless of the variation ofpotential energy and kinetic energy.

(4) The rock matrix and the fracture extend to infinity in the x directionand the rock is assumed to extend in y direction to±∞ value; the

heat convection only exists in fracture along x axis and the heatconduction in rock matrix is along y axis; the temperature of fluidand rock matrix on the fracture are treated to be the same whichthen conform to the continuity conditions;

The temperature distribution equation of the rock matrix:

=−

−= ⎡

⎣⎢

+−

⎤

⎦⎥T

T T x tT T

erfcλ x d u ρ c y

d u ρ cu ρ c

λ u t x( , )

* 2 ( )sDf s f f f f

f f f f

f s s

s f

0

0 (11)

The temperature distribution equation of the fluid:

=−

−= ⎡

⎣⎢ −

⎤

⎦⎥T x t

T T x tT T

erfc λ xd u ρ c

u ρ cλ u t x

( , 0, )( , )

* 2 ( )fDf s

f f f f

f s s

s f

0

0 (12)

A numerical solution is presented to model the three-dimensionalheat extraction problem with a finite domain in100m×100m×100m for the rock matrix. Some computationalparameters used in this model are listed in Table 1. Fig. 2 shows theisothermal distribution in rock matrix with the comparison of the nu-merical and analytical results during 3 years production period. Thetemperature variation in the fracture at different time and the watertemperature evaluation at three different position along the fracture areplotted in Figs. 3 and 4, respectively. It can be seen that the numericalsolution is in good accordance with the analytical one.

4. An ideal 3D-EGS doublet model

4.1. Computational model

The main feature of EGS reservoir rock mass is containing a largenumber of open and connecting fractures, which should be modeled innumerical simulation. Currently, the equivalent treatment is generallyadapted to deal with rock mass containing dense fracture networkswhich is simplified by the mature continuum theory. As for large faultsand primary penetrated cracks, the discrete fracture model is employed

Fig. 1. Illustration of a 3D model with a single fracture.

Table 1Model parameters.

Parameter Unit Value

ρw kg/m3 1000cw J/kg/K 4200ρr kg/m3 2700cr J/kg/K 1000λr W/m/K 3uw m/s 5× 10−3

T0 °C 80T* °C 302df m 0.003

Fig. 2. Isothermal distribution in rock matrix.

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(Zhang and Li, 2012). Some other researches indicate that most of theheat transfer fluid is only circulating through one or several dominatingflow channels from the injection well to production well (Chen et al.,2013b). Adopting this analysis method, an ideal 3D-EGS doublet modelwith a persistent fracture in geothermal heat reservoir is constructed(see Fig. 5). The reservoir is assumed to be located at 1150m below theground surface with a domain of 500m×500m×500m. The injectionwell is placed at a low point along the fracture while the productionwell is drilled higher up (Feng et al., 2012), and the position of these

wells whose wellbore radius is 1 m is shown in Fig. 6. The distancebetween two wells is 300m and well depth is 1075m. The finite ele-ment model used for calculating is illustrated as Fig. 7.

4.2. Computational parameters

The reliability of numerical simulation results depends on the de-termination of calculating parameters’ values. Model parameters usedin this study are listed in Table 2.

Eq. (8) is used to describe the permeability evolution of fracturesaffected by hydro-mechanical interaction. For the convenience in ana-lysis, an assumed value of α as −0.2×10−6Pa−1 is employed in thisstudy. When tensile stress appears on the fracture (i.e., the effectivenormal stress is positive), the fracture will open and its permeabilityincreases, otherwise, the compressive stress will be accounted and itspermeability decreases.

4.3. Boundary condition and initial condition

The aforementioned model is adopted to simulate the entire processof heat production in EGS with a total heat extraction period of 80 yearsand each time step of 60d. Initial and boundary conditions are as fol-lows:

(1) Seepage field: The given pressure boundary conditions are used toensure water circulating in the system. The pressure of injectionwell and production well is 21MPa and 5MPa, respectively. For theother external conditions, an impermeable boundary is selected.The initial water pressure in the reservoir is assumed as 12MPabefore water is injected.

(2) Thermal field: The temperature at the injection well is 20 °C. Thetop and bottom boundary and lateral boundary conditions arethermal insulated. The initial temperature in the reservoir is 200 °Cfor both rock and water.

(3) Displacement field: All the external boundaries of the reservoir areconstrained in normal directions. Since engineers are usually moreconcerned with the disturbance to the stress distribution caused byEGS development and heat production, the initial geo-stress in thereservoir is not taken into account. This study focuses on the effectsof pressurized water injection and heat extraction on the stress fieldin fractured rock mass, which may help in understanding theircoupling intersections.

Fig. 3. Temperature variation in the fracture at different time.

Fig. 4. Temperature evolution at three different position along the fracture.

Fig. 5. An ideal 3D-EGS doublet model with a persistent fracture. (unit: m).

Fig. 6. A cutaway view of EGS at y=250m. (unit: m).

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5. Results and analysis

5.1. Results of hydraulic process

Fig. 8 shows the pressure distribution and velocity vectors in thereservoir and fracture at t= 80a. It can be seen that the water pressure

in the fractures increases rapidly which indicates heat transfer fluidprimarily flows through the fracture to the production well when it isinjected from injection well to the reservoir. According to the pressuregradient along the dip of the fracture, it reveals that the fluid flowwould tend to be upslope towards the production well rather thandownwards into deeper rock. The result agrees with the result of Feng(Feng et al., 2012).The penetrated fracture as a main seepage pathwaywill directly influence heat transport efficiency of geothermal heat re-servoir.

5.2. Results of the thermal process

The temperature variation in the reservoir at different time is pre-sented in Fig. 9. At the initial operating stage, heat exchange takes placebetween the rock matrix and the fluid flowing in the fracture due to theinjection of low-temperature water, and then the fluid temperatureincreases immediately. With the effect of heat conduction, the tem-perature of the rock matrix block also decreases gradually forming thelow-temperature zone during the heat extraction period. Meanwhile,the temperature around the production well has no significant change,indicating that the system can maintain a steady heat production for acertain time-span. More heat is extracted from the reservoir as time

Fig. 7. EGS finite element model (tetrahedron elements 391109).

Table 2Computational parameters in EGS modeling.

ρf/(kg/m3) η/(Pa·s) g/(m/s2) Cf/(J/kg/K) λf/(W/m/K) h/(W/m2/K) αB

1000 0.001 9.8 4200 0 3000 1.0

ρs/(kg/m3) κ/(m2) S/(1/Pa) E/(GPa) v Cs/(J/kg/K) λs/(W/m/K)

2700 1.0× 10−15 1.0× 10−8 30 0.25 1000 3

αT/(1/K) ε df/(m) κf/(m2) Sf/(1/Pa) kn/(GPa/m) ks/(GPa/m)

2.0× 10−6 0.01 0.001 1.0× 10−10 1.0× 10−9 1200 400

Fig. 8. Pressure distribution and velocity vectors in the reservoir and fracture at t= 80a.

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Fig. 9. Temperature evolution in the fracture surface and a cutaway view at y= 250m.

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goes by, the low-temperature zone finally expands to the productionwell, which causes the outlet average temperature drops gradually.

The numerical results exhibit strong heterogeneity and anisotropyof the thermal distribution in EGS. It can be observed that the low-temperature area moves more rapid around the fracture channel incomparison to rock matrix. The effect of heat convection is considerablystrong in the fracture due to the high flow velocity. As a result ofanalysis, the heat extraction performance extremely depends on thecirculation of water in the heat reservoir. Thus the optimization of flow-field distribution plays a vital role in improving the efficiency of heatextraction.

5.3. Results of the mechanical process

As for stress field, it focuses more on the effect of the variation of thefracture aperture on its permeability and heat production efficiency inEGS. Fig. 10 illustrates the normal displacement distribution of fracturesurface at 80a. As depicted in Fig. 11, it indicates the variation of theratio of instant permeability to initial permeability, kf/k0. It can beobserved that the distribution regularity of kf/k0 and normal displace-ment remains consistent, the fracture will open with an increment ofpermeability when the normal displacement is positive. Otherwise, thepermeability of fracture will decrease and the fracture will close. Thechange of kf/k0 and normal displacement of fracture also coincides withthe temperature variation in the heat reservoir. The temperature of rockmass around injection well decreases rapidly with rock contractiondeformation, which causes the open of fracture surface.

Fig. 12 displays the evolution of fracture’s kf/k0 along the cuttingline at y= 250m. The low-temperature zone around the injection wellexpands larger with the permeability gradual increasing during the heat

extraction period. The result turns out that the temperature variation ofreservoir leads to rock displacement occurring which results in thechange of fracture flow conductivity. Finally, this process will influencethe heat exchange efficiency between water and rock mass and heatextraction of geothermal heat reservoir. From the above mentionedanalysis, The results show the significance of taking the THM couplingeffects into account when investigating the efficiency and performanceof EGS.

5.4. Sensitivity analysis of heat production in EGS

Many parameters which are interacted with each other are em-ployed in the process of numerical simulation of heat extraction ingeothermal reservoir. Sensitivity analysis with regard to some keymodel parameters are performed, in order to further evaluate their ef-fects on the EGS outlet temperature and its running performance. Theevolution of the average outlet temperature against different fracturepermeability is illustrated in Fig. 13. It can be found that the averageoutlet temperature is sensitive to the permeation properties of thefractures. When the fracture permeability is relatively lower at0.5× 1010 m2, the outlet temperature is observed to be stable during80a. However, the average temperature drops rapidly to 180 °C duringthe 80-year period when the fracture permeability is larger. Fracturesare the main pathways for heat transfer, therefore are crucial in thethermal evolution process.

The thermal conductivity of rocks is typically in the range of 1–3W/m/K (McGuinness et al., 1993). Therefore, different values for rockthermal conductivity are employed to study its effect on the evolutionof the average outlet temperature. As shown in Fig. 14, the average

Fig. 10. The normal displacement distribution of fracture surface at 80a.

Fig. 11. The distribution regularity of kf/k0 of fracture surface at 80a.

Fig. 12. The evolution of fracture’s kf/k0 along the cutting line at y= 250m.

Fig. 13. Evolution of the average outlet temperature with different fracture permeability.

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outlet temperature drops slightly faster when the rock thermal con-ductivity is lower. This observation shows similar trend to Chen et al.’sstudy (Chen et al., 2014), and the rock thermal conductivity seems tohave a relatively limited effect on the average outlet temperature.

The effect of different rock elastic modulus is also investigated. Asdepicted in Fig. 15, the temperature drop varies considerably when therock elastic modulus is changed. It is accredited that the rock de-formation is much more significant with a higher modulus, which canlead to the increase in fracture aperture and its conductive properties.The roles that mechanical process plays in the overall heat production

are strongly associated with the hydraulic process in EGS.Fig. 16 shows the evolution of the average outlet temperature with

extraction time obtained by different inlet temperature (i.e., 10 °C,20 °C and 30 °C). A stable running condition for about 20a with nosignificant difference can be observed for all these three cases. Duringthe period of 20a to 80a, the low-temperature zone expands graduallyto the production well and the heat production of the system decreases.By lowering the inlet temperature, the faster the average outlet tem-perature drops. At the time of t= 80a, the average outlet temperatureis approximately 90%∼ 93% of the reservoir's initial temperature.

The evolution of the average outlet temperature, obtained by dif-ferent well distance between injection well and production well (i.e.,240m, 300m and 360m), is shown in Fig. 17. The production tem-perature differs apparently in the case of different well distance. Forwell distance larger than 360m, the system can maintain a stable run-ning condition for about 80 years. However, the average outlet tem-perature drops sharply faster and the stable running period gets shorterwhen the well distance becomes smaller. Considering that the welldistance may influence the residence time as well as heat exchangeamount between hot rock and injected fluid, an appropriate well dis-tance is crucial to the performance and service-life of EGS.

6. An EGS case study

The Desert Peak EGS project was launched in 2002, and it is locatedon the eastern edge of the Desert Peak geothermal field about 130 kmENE of Reno, Nevada. The ultimate goal of this project is to develop2–5MW of EGS-derived power from a stand-alone binary power plantsupplied by a doublet or triplet well2 (Robertson-Tait et al., 2005;Carlson et al., 2004). In the first stage of the project, well DP23-1 wasthe main research object. Its production capacity, hydrological condi-tion and stimulation method were investigated in detail. Because theEGS resource potential around well DP23-1 had been systematicallyevaluated in 2002–2005 and much geological data had been obtained2(Robertson-Tait et al., 2005; Carlson et al., 2004), well DP23-1 data isadopted to perform the numerical research.

According to exploration, Fig. 18 shows wells and fracture zonedistribution at Desert Peak field, in which the grey area1610m×2606m was the resource development zone. Target forma-tion is buried at a depth from 1219m to 2743m, and the temperature isbetween 207 °C and 216 °C, with an average value of 210 °C. Fracturesin the natural joints and the graben settings models are three-dimen-sional and reticular, so internal flow paths are also three-dimensionaland reticular. The actual fracture structure is highly complex due tocomplex geological conditions, so one of key problems in EGS reservoirsimulation is to properly characterize the fracture2 (Tester et al., 2006;Hayashi et al., 1999). The porosity is about 2% over a 439m

Fig. 14. Evolution of the average outlet temperature with different rock thermal con-ductivity.

Fig. 15. Evolution of the average outlet temperature with different rock elastic modulus.

Fig. 16. Evolution of the average outlet temperature with different inlet temperature.

Fig. 17. Evolution of the average outlet temperature with different well distance.

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investigation radius around well DP23-1, and the permeability is about0.01 mD (Sanyal and Butler, 2005). Based on the data of well spacingand reservoir thickness from the EGS field test (Tester et al., 2006), thegeothermal energy is buried in a reservoir at a depth from 1219mto1619m, corresponding lithostatic pressure of this interval from9.65MPa to 13.10MPa, and the pressure gradient is approximately8.63MPa/km (Robertson-Tait et al., 2005). To simplify the analysis, thechanges of lithology in the target formation is neglected and with anassumption that the whole target formation is homogenous porousgranodiorite, and its density is evenly distributed and constant.

6.1. Computational model

For the sake of computational efficiency and accuracy, a 3D

stochastically fracture network is modeled based on the above men-tioned reservoir geology condition to represent the geothermal re-servoir and is used to predict the performance of EGS heat extraction.Fig. 19 shows the 3D computational model for EGS reservoir (in500m×500m×500m). The stochastically generated fracture networkmodel shows a strong anisotropy, which can represent the fracturedrock mass in the statistical sense and thus reflects the main features ofTHM coupling process in EGS (Chen et al., 2014).

According to the actual injection well-reservoir-production wellsystem, the location of injection well and production well is depicted asFig. 20. The length of perforation interval is 20m, with the intermediatedepth −1540m and −1380m of injection well and production well,respectively. The horizontal distance between two wells is 400m andwellbore radius is 1 m. The injection interval of the injection well andthe production interval of the production well with limited length are

Fig. 18. Desert Peak well location and fault map. The EGS area is shaded gray (Robertson-Tait et al., 2005).

Fig. 19. Geometry of the EGS considered.

Fig. 20. A cutaway view of the EGS at y= 0m.

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located at different depths, making the system more realistic ratherthan theoretical (Zeng et al., 2013). The finite element model utilizedfor numerical simulation is shown as Fig. 21.

6.2. Computational conditions and parameters

The entire process of heat production in EGS is simulated with theaforementioned model. It is best to stop the heat extraction when theproduction temperature has declined by 10% (Baria et al., 1999), so theultimate temperature of production well adopted in this study is 189 °C.The time step takes 15d.

6.2.1. Initial and boundary conditions

(1) Seepage field: The given pressure boundary and initial conditionsare used to ensure water circulating in the system. In order tocompare the simulation results with the commercial standard, theinjection rate of injection well is fixed at 50 kg/s and the pressure ofproduction well is a constant 6.5 MPa. The upper and lowerboundary and lateral boundary conditions are treated as im-permeable. The initial pressure of reservoir is set as 11.8 MPa.

(2) Thermal field: On the basis of static temperature data, the influenceof temperature gradient is not considered, which means the tem-perature variation along the depth is overlooked. For the otherexternal conditions, a thermal insulated boundary is selected. Theinitial average temperature of reservoir is 210 °C and the injectiontemperature in injection well is 60 °C.

(3) Displacement field: Seen Section 4.3

6.2.2. Model parametersIt is essential to make reasonable estimation of some reservoir

parameters due to the limit of measurement method. Material para-meters used in the numerical model are listed in Table 3 (Robertson-Tait et al., 2005; Carlson et al., 2004; Sanyal and Butler, 2005; Zenget al., 2013; Lutz et al., 2003).

6.3. Evaluation system of heat extraction performance

The evaluation parameters and criterion for commercial productionof geothermal heat reservoir are: (i) The average reservoir temperature

should higher than 190 °C and the real-time temperature of productionwater declined is supposed to be lower than 10% during a productionperiod of 15–20 years without re-stimulation. (ii) When the injectiontemperature and rate is 60 °C and 50 kg/s, commercial objectives for adoublet well system are thermal power of 25MW with electrical powerof 3.5 MW (Evans, 2010). The key indicators of the evaluation system ofheat extraction performance are discussed as follows.

6.3.1. Heat production timeGenerally, geothermal energy is regarded as a kind of renewable

energy. However, the heat reserve of the EGS porous reservoir willreduce dramatically as a result of heat mining operation for about20–30 years, which may take almost 100 years to recharge heat fromthe surrounding rock (Elsworth, 1990). Therefore, in order to extractheat from heat reservoir as much as possible for a comparatively longtime, it is the optimal time to cease operation when the average re-servoir temperature has declined by 10 °C (Tester et al., 2006), or theproduction temperature has declined by 10% (Baria et al., 1999), andthe latter is adopted in this study.

6.3.2. Outlet average temperatureThe average outlet temperature is calculated by the following

equation,

∫ ∬∫ ∬

=++

Tu d T dL uT dΓ

u d dL udΓoutL f f f Γ s

L f f Γ (13)

Where, the line integration term represents the fractures while thesurface integration term represents the rock matrix blocks.

6.3.3. Heat productionWith the exploitation system of an injection well and a production

well, the heat production can be calculated as,

= −W q h h( )h pro inj (14)

Where, hinj is the injection specific enthalpy, hpro is the productionspecific enthalpy. The heat exchange between wellbore fluid and sur-roundings can be ignored for a long time of production (Pruess, 2006).

6.3.4. Energy efficiencyThe system energy efficiency η is defined as the ratio of the total

produced energy of the overall energy consumption.

(i) Overall energy production

It is assumed that all of the produced thermal energy are utilized togenerate electricity. Based on the second law of thermodynamics, theavailable work converted from thermal energy can be described as,

− −q h h T T( )(1 / )pro inj o pro

If the converting efficiency coefficient from the available work to

Fig. 21. Mesh system of the EGS considered (tetrahedron elements 425080).

Table 3Reservoir parameters at site DP23-1 in Desert Peak field.

ρf/(kg/m3) η/(Pa·s) g/(m/s2) Cf/(J/kg/K) λf/(W/m/K) h/(W/m2/K) αB

1000 0.001 10 4200 0 3000 1.0

ρs/(kg/m3) κ/(m2) S/(1/Pa) E/(GPa) v Cs/(J/kg/K) λs/(W/m/K)

2850 1.0× 10−17 1.0× 10−8 30 0.25 1100 2.395

αT/(1/K) ε df/(m) κf/(m2) Sf/(1/Pa) kn/(GPa/m) ks/(GPa/m)

5.0× 10−6 0.02 0.0005 1.0×10−11 1.0× 10−9 1200 400

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28

electrical power is 0.45 (Sanyal and Butler, 2005), and then the elec-trical power can be calculated as,

= − −W q h h T T0.45 ( )(1 / )e pro inj o pro (15)

Where, To is the heat rejection temperature of 288.75 K at Desert PeakSite, which is employed in the form of absolute temperature (Sanyaland Butler, 2005).

• Overall energy consumption

The overall energy consumption is determined by counting up theenergy consumption of injection pump Wp1 and that of productionpump Wp2 and they are calculated by the following equations,

∫= = −W p dV q P ρgh ρη( )/( )p inj inj p1 1 (16)

∫= = −W p dV q ρgh P ρη( )/( )p pro pro p2 2 (17)

= + =− − −

W W Wq P P ρgq h h

ρη( ) ( )

p p pinj pro

p1 2

1 2

(18)

Where, dV is the injection/production water volume per second, h1 andh2 are the mid-depth of injection well and production well, respectively.ηp is pump efficiency.

• System energy efficiency

In this study, two kinds of energy efficiency are studied, one is basedon the produced thermal energy ηh, and the other is based on thegenerated electrical energy ηe. With the definition of energy efficiency,they are derived as,

= =−

− − −η W

Wρη h h

P P ρg h h( )

( ) ( )hh

p

p pro inj

inj pro 1 2 (19)

= =− −

− − −η W

Wρη h h T TP P ρg h h

0.45 ( )(1 / )( ) ( )e

e

p

p pro inj o pro

inj pro 1 2 (20)

6.3.5. Heat recoveryFor the purpose of explaining the local heat exchange in the re-

servoir and seeking for some methods to improve heat extraction per-formance, the local heat extraction ratio γL is employed and defined asthe extracted heat divided by the stored or maximum extractable heat,which can be expressed as (Jiang et al., 2013),

= −−

γ t T T tT T

( ) ( )L

r s

r inj (21)

Where, Tr and Ts(t) is the initial rock temperature and the rocktemperature at time instant t, respectively.

Furthermore, the overall heat recovery is obtained by the volumeintegral of local heat extraction ratio, which represents the ratio of thecumulative produced heat energy to the extractable heat energy. Simplederivation leads to the following equation.

∭∭

=γ tγ t dV

dV( )

( )V L

V (22)

6.4. Results and analysis

6.4.1. Fluid production temperature and injection pressureFig. 22 depicts the evolution of the dimensionless fluid production

temperature, fluid production temperature, and specific enthalpy ofproduction water. It can be observed that two stages existed which arestabilization stage and declining stage over the whole productionperiod. Based on the condition that ceasing the operation when theproduction temperature has declined by 10%, the service-life of EGS

project is almost 30 years which meets the commercial objective, aproduction period of 15–20 years. As for the stable stage, the averageoutlet temperature remains constant at 210 °C for about 10 years, andthe corresponding specific enthalpy of production water is fixed at880 kJ/kg. During the declining stage, the outlet temperature decreasesfrom 210 °C to 189 °C and the minimum specific enthalpy of productionwater declines to 795 kJ/kg.

Seen From Fig. 23, it shows the variation trend of the injectionpressure. In the stage of stable production for 10 years, the injectionpressure increases quickly from 33MPa to 35.75MPa, while that overthe declining stage gets larger from 35.75MPa to 36MPa gently. Theproduction pressure remains at 6.5 MPa as set. It can be inferred thatthe injection pressure should maintain at high level, to achieve therequirement of constant injection rate at 50 kg/s. So the relationshipbetween the injection pressure and reservoir stress condition are sup-posed to be considered, not just the actual production needs.

6.4.2. Spatial distribution of temperatureThe spatial distribution of temperature at different time is demon-

strated by Fig. 24. The low-temperature zone expands continually in thefractured heat reservoir and the temperature decreases faster along thefracture surface, which indicates that the connected fracture networksare the prime flow channels with the same conclusion in Section 5.2. As

Fig. 22. Evolution of the dimensionless fluid production temperature, fluid productiontemperature, and specific enthalpy of production water.

Fig. 23. Evolution of the injection pressure.

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Fig. 24. Spatial distribution of temperature in EGS at different time.

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shown in Fig. 24(b), the low-temperature part gradually moves to theproduction well as a result of temperature drop of production wateroccurred, which indicates that the continuous and steady heat outputstage of system is gone. The low temperature area will gradually ap-proach to the top and bottom boundaries along with the heat mining.

6.4.3. Heat production and electricity generationThe evolution of heat production and electricity generation is drawn

in Fig. 25. The heat production and electricity generation maintain at95.2MWe and 10.5MWe respectively, as the injection temperature,production temperature, specific enthalpy of injection fluid and pro-duction fluid are kept unchanged. With the decrement of productionwater temperature at the declining stage, the heat production andelectricity generation reduce from 95.2MWe, 10.5 MWe to 89.4MWe,7.9 MWe, apart. For the commercialization of a doublet well system, theheat production and electricity generation are required to be largerthan 25MWe and 3.5MWe, so this EGS case is suit for the commer-cialization.

6.4.4. Energy efficiencyThe evolution of the EGS energy efficiency is displayed in Fig. 26.

The energy efficiency on the basis of the produced thermal energy andthe generated electrical energy all declines along with heat exploiting.They are falling from 53, 6.0–45, 4.0 over the whole production period.Both of the energy efficiency are greater than 1 which means the energyproduced can balance the energy consumed, however, it is far from theeconomic exploitation goal due to the high expense of drilling andfracturing stimulation.

6.4.5. Local and overall heat recoveryFig. 27 shows the spatial distribution of local heat recovery at dif-

ferent time. At the initial time, the heat exchange between rock matrixand low temperature water is existed around the injection well whichmakes the temperature of rock matrix reduces quickly. The local heatrecovery of rock matrix surrounding the injection well is almost up to 1since the cold water is injected, indicating that the heat extracted fromrock matrix near the injection location contributes less and less to theproduced hot water. Therefore, the thermal energy produced awayfrom the injection domain should be improved in terms of the optimi-zation of heat production performance. The temperature of the pro-duction well reaches the limited exploiting temperature when the op-eration time lasts for 30 years. Seen from the 30-year recovery profile asFig. 27(d), it can be observed only the recovery of rock close to injec-tion area is high, while the recovery of most of the area, especiallyaround the production region, is relatively low. The thermal recoverycondition over a wide radius range of production well should be en-hanced, the optimization of well pattern can be adopted to figure outthe problems to some extent.

To evaluate the consequence of heat extraction from the geothermalheat reservoir under a doublet well system, the evolution of the overallheat recovery and average rock matrix temperature are illustrated inFig. 28. An important characteristic is that the overall heat recoveryand mean rock matrix temperature are nearly proportional to the time.This phenomenon can be explained by that the temperature drop barelyreaches the top and bottom boundary and then the energy supply isunchanged. It is speculated that the growth rate of overall heat recoverywill reduce when the temperature drop occurs at most boundaries. Theratio of the cumulative produced heat energy to the extractable heatenergy is very low, only 8%, at the end of production. A lot of thermalenergy still retained in the reservoir, so the improvement of workingcondition and heat reservoir stimulation remains to be conducted.

7. Conclusions

A 3D numerical model based on FEM is developed for effectivelymodeling the thermal–hydraulic–mechanical coupling process in frac-tured rock mass, which is utilized to study the heat extraction perfor-mance by enhanced geothermal system in HDR. The proposed modeland the numerical approach are validated by comparing with someanalytical solutions. An ideal 3D-EGS doublet model is presented tostudy the main features of heat transfer, water flow and mechanicalbehaviors in EGS reservoir. An EGS case based on the Desert Peakgeothermal field is simulated with a 3D stochastically generated frac-ture model to conduct evaluation of EGS heat production performance.

(1) The conductivity of rock mass is enhanced and the heat extractionefficiency is increased by the fracture networks, so they are ne-cessary to be explicitly modeled. The heat extraction performanceextremely depends on the circulation of water in the heat reservoir,thus the optimization of flow-field distribution, in other words thedistribution of fractures, plays a vital role in improving the per-formance of heat extraction. The change of permeability andnormal displacement of fracture coincide with the temperaturevariation in the heat reservoir as a result of the decrease of rocktemperature causing rock contraction deformation and fractureopen.

(2) Numerical results of an ideal 3D-EGS doublet model show thestrong coupling effects of THM is existent in the heat extraction ofEGS and further studies on the THM coupling in fractured rock massare required. Sensitivity analysis is performed to understand theeffects of some model parameters on the average outlet temperatureof EGS. The results show that the average outlet temperature issensitive to the conductive properties of fractures, the inlet tem-perature, the well distance between injector and producer, as wellas the rock elastic modulus, whereas the rock thermal conductivity

Fig. 25. Evolution of the heat production and electricity generation.

Fig. 26. Evolution of the EGS energy efficiency.

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Fig. 27. Spatial distribution of local heat recovery in EGS at different time.

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has a relatively limited effect, which obtain a similar results in 2Dnumerical simulation and reflect that 2D numerical model can beemployed to conduct quantitative analysis with a certain accuracy.

(3) In the EGS case study, a 3D stochastically generated fracture modeland the evaluation system of heat extraction performance areconstructed to guide the exploitation of geothermal heat reservoir.The results indicate that the running period, heat production andelectricity generation with appropriate parameters can meet thecommercial objectives of a doublet system, while the energy effi-ciency and overall heat recovery remain at relatively low. The ex-tremely low thermal recovery over a wide radius range of produc-tion well should be enhanced through the optimization of wellpattern, like employing triplet/quadruplet well layout with moreproduction wells, and drilling directional or horizontal wells.

In this study, treating water as heat transfer fluid, a doublet wellmodel incorporating THM coupling process is established to simulatethe heat extraction performance of EGS. However, the effect of che-mical reaction on the consequence of thermal recovery is not con-sidered over a long time scale, so more practical model should be de-veloped for simulating the actual EGS heat extraction process. In thefurther work, as for the low heat recovery of EGS, the reservoir schemesshould be optimized with the comparison of different heat transmissionfluids and the heat supplement by surrounding hot rocks.

Acknowledgements

This study was jointly supported by the National Natural ScienceFoundation of China (Grant No. 51404291, No. 51774317, No.51674278). We are grateful to all staff involved in this project.

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