Numerical study on variable thermophysical properties of heat transfer fluid affecting EGS heat extraction

International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Numerical study on variable thermophysical properties of heat transfer fluid affecting EGS heat extraction Wenjiong Cao, Wenbo Huang, Fangming Jiang ⇑ Laboratory of Advanced Energy Systems, CAS Key Laboratory of Renewable Energy, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences (CAS), Guangzhou 510640, China

a r t i c l e

i n f o

Article history: Received 21 April 2015 Received in revised form 27 September 2015 Accepted 29 September 2015

Keywords: Enhanced geothermal systems Local thermal non-equilibrium Variable properties Numerical simulation Super-critical carbon dioxide

a b s t r a c t Thermophysical properties of heat transfer fluid may experience significant changes during heat extraction process in enhanced geothermal system (EGS). The present work extends a previous EGS model by implementing pressure- and temperature-dependent thermophysical properties of real water and supercritical carbon dioxide (SCCO2), and employed the new model to simulate the long-term heat extraction processes of water-EGS and SCCO2-EGS. Comparison between the model results finds at a given fluid injection pressure, the lifetime of water-EGS is longer than that of SCCO2-EGS while the heat extraction rate of the latter is higher than the former, leading to approximately the same cumulative heat extraction amount at the end of EGS operation. Relative to water, larger density-temperature dependence of SCCO2 leads to stronger natural convection of fluid flow in EGS reservoir and makes the heat extraction process of SCCO2-EGS more prefers to perform in the reservoir bottom region. The natural convection flow in the reservoir of SCCO2-EGS is found to be relatively stronger if the reservoir permeability is smaller, the fluid injection pressure is lower, or the reservoir is of a larger volume. Simulations with respect to two groups of cases, one of which consists of water-based heat transfer fluids and the other SCCO2-based fluids, comprehensively reveal variable thermophysical property effects on EGS heat extraction. The production performance of SCCO2-EGS is generally more sensitive to the variation of fluid thermophysical properties; for both water- and SCCO2-EGS, the net electric power output is positively related with the density and specific heat capacity of fluid, and negatively related with the viscosity of fluid, whereas the thermal conductivity of fluid has little effect on the net electric power output. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Enhanced or engineered geothermal systems (EGS), aimed to exploit heat from deep-subsurface low permeability/porosity sedimentary rocks and basement formations, show tremendous potential for electricity generation [1–3]. Since the first EGS project implemented at Fenton Hill in the early 1970s, EGS field tests have been widely launched around the world. These projects [2,4], mostly for research and demonstration purpose, corroborate the conceptual feasibility of EGS at least on the following two aspects: (i) the subsurface low permeability rock can be stimulated (hydraulically and/or chemically) to form an artificial heat reservoir of adequate volume and hydraulic conductivity, and (ii) a fluid circulation system can be constructed to mine heat from the reservoir. However, the commercialization of EGS powerplant sets strict requirements on the circulation fluid flow rate, ⇑ Corresponding author. Tel.: +86 20 87057656. E-mail address: [email protected] (F. Jiang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.09.081 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

the production temperature, and the sustainability of the system etc. [4,5] and needs considerable research and development efforts on the related scientific and technical issues [2,5]. Water is commonly used as the heat transfer fluid in EGS-s due to its high volumetric heat capacity and ease of obtaining [2,4]. In the year of 2000, Brown [6] proposed a novel EGS concept that used supercritical CO2 (SCCO2) as the heat transfer fluid instead of water, which initiated the research topic about heat transfer fluid of EGS-s. SCCO2 has liquid-like density and gas-like viscosity. It is the unique properties that make SCCO2 a very attractive heat transfer fluid of EGS-s. Pruess [7,8] did comparisons between water and SCCO2 when used as heat transfer fluid of EGS-s. Atrens et al. [9,10] presented a hypothetical SCCO2 geo-thermosiphon. Numerical modeling and/or theoretical analyses [7–13] have partially detailed the thermal–hydraulic performance of SCCO2-EGS. Borgia et al. [14] focused mainly on the effects of salt precipitation on the performance of SCCO2-EGS and simulated the process of SCCO2 replacing the natural geothermal brine in the reservoir, which is often encountered during the initial phase of SCCO2-EGS operation.

1206

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Nomenclature cp dw g h ha k K p Q t T Tg u x, y, z We

heat capacity (J/kg/K) distance between the injection well and a production well (m) acceleration of gravity (m/s2) specific enthalpy of fluid (J/kg) volumetric heat transfer coefficient (W/m3/K) thermal conductivity (W/m/K) permeability (m2) pressure (Pa) mass flow rate (kg/s) time (s) temperature (K) ground temperature (K) velocity vector (m/s) Cartesian coordinates net power output (W)

Greek symbols q density (kg/m3)

Atrens et al. [15] and Mohan et al. [16] assessed the economic viability of SCCO2-EGS, when used simultaneously as a means of carbon storage and sequestration. Major findings from these works are summarized below.
Chemically, SCCO2 is not an ionic solvent and the performance of SCCO2-EGS would not be that vulnerable to degradation due to dissolution and precipitation of rock minerals as waterbased EGS [6–8,14].
SCCO2 has large compressibility and expansivity. The buoyancy caused by temperature difference along the reservoir/wellbore depth direction facilitates the fluid circulation and lowers the parasitic power consumption [6–8].
The low viscosity of SCCO2 largely reduces the flow resistance [6–8].
Simple earth-surface equipment is required as the produced hot CO2 fluid can be used directly in the electricity generation cycle [6].
Fluid loss during SCCO2-EGS operation brings an additional advantage of carbon sequestration [9,10].
Benefiting from the gas-like viscosity that leads to much higher mass flow rate at a given pump work, SCCO2-EGS was predicted to have larger energy extraction rates than water-EGS [7,8].
The smaller volumetric heat capacity (smaller specific heat and lower density) means to transmit the same amount of heat as water the mass flow rate of SCCO2 must be larger [7,8].
SCCO2-EGS may extract less energy than water-EGS due to evident temperature decreases caused by the Joule–Thompson expansion of SCCO2 in the production wellbore. This disadvantage of SCCO2-EGS may be alleviated when it is applied to a shallower reservoir or the borehole has been drilled with larger diameter [7].
The economic viability of SCCO2-EGS system depends strongly on the availability of water and the price associated with CO2 [15,16]. Thermophysical properties of heat transfer fluid may experience significant changes during EGS operation. Especially for SCCO2, its thermophysical properties have very strong dependence on temperature and pressure. Variable thermophysical properties of heat transfer fluid may lead to unusual thermal–hydraulic behaviors during EGS operation. Although some literature works [6–8] studied the EGS production behavior affected by

e l h hL

g

porosity viscosity (m2/s) heat extraction ratio local heat extraction ratio efficiency

Subscripts/superscripts eff effective f fluid water H2O H heat-to-electricity conversion in injection; inlet ini initial out production; outlet P pump s solid or rock SCCO2 super critical carbon dioxide L local

thermophysical properties of heat transfer fluid, there is generally lack of a thorough and comprehensive study, e.g. the timedependent natural flow convection, which is mainly caused by the temperature- and pressure-dependent fluid density, has been rarely studied to date. The present work is aimed to further the study on EGS heat transfer fluid effects and a trifold purpose it has. One is to further the model development of a new EGS model [17,18] developed previously. The second is to numerically study the heat extraction processes of water-EGS and SCCO2-EGS with particular focus on the natural convection of fluid flow in EGS heat reservoir. The third is to conduct a comprehensive study on the effects of variable (i.e. time-dependent) thermophysical properties of heat transfer fluid on EGS heat extraction performance for both water-EGS and SCCO2-EGS. 2. EGS heat extraction model We developed a transient three-dimensional numerical model for the simulation of EGS long-term heat extraction processes [17,18]. The model treats the geothermal reservoir as porous medium while considers local thermal non-equilibrium between the solid rock matrix and fluid flowing in the fractures to realize the simulation of local convective heat exchange in the porous reservoir. Most recently, this model was successfully used to explore the well layout effects of multi-well EGS-s and to assess the recoverable heat of EGS geothermal resource [19]. The cases considered in Refs. [17–19] all assume constant thermophysical properties for the heat transfer fluid. The present work furthers the model development by implementing sub-modules that describe temperature- and pressure-dependent thermophysical properties of EGS heat transfer fluid. 2.1. Mathematical model 2.1.1. Model equations The model focuses on the complete subsurface heat exchange (i.e. thermal and hydraulic) process and the governing equations were formulated as follows. [17,18] Continuity equation for fluid:

@ðeqf Þ þ r  ðqf uÞ ¼ 0 @t

ð1Þ

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Momentum conservation equation for fluid:

@ðqf uÞ qf u l ru ¼ rp þ r  lru  u þ eqf g þ @t e K

ð2Þ

Energy equation for heat transport in the rock matrix of geothermal reservoir or in the surrounding impermeable rocks:


   @ ð1  eÞqs cps T s eff ¼ r  ks rT s  haðT s  T f Þ @t


ð3Þ

Energy equation for fluid flowing in the fractures:

   @ eqf cpf T f eff þ r  ðuqf cpf TÞ ¼ r  kf rT f þ haðT s  T f Þ @t

ð4Þ

The variables: u, p, Tf and Ts, are the primary variables to be solved, denoting the superficial fluid velocity vector, fluid pressure, fluid temperature and rock temperature, respectively. The last term of Eqs. (3) and (4), ±ha(Ts  Tf), describe heat exchange between rock matrix and heat transfer fluid, where the ha denotes the volumetric heat exchange coefficient between rock matrix and fluid in the fracture. The fluid thermophysical properties including the fluid density qf, viscosity l, specific heat capacity cpf, and heat conductivity kf are considered to be temperature- and pressuredependent, more details about which will be given in the following subsection. As annotated by the superscript, eff, the heat conductivity of fluid and rock matrix in the reservoir are implemented 1.5 1.5 with the effective forms i.e. keff and keff , where s = ks(1  e) f = kfe e denotes the reservoir porosity. Note that the Brugegmann approximation has been implemented here, which assumes effective transport property can be approximated by the intrinsic physical property of the medium multiplied by its component volume fraction raised to power 1.5. 2.1.2. Thermophysical properties of water and SCCO2 We model the thermophysical properties of water in terms of the IAPWS (International Association for the Properties of Water and Steam) data [20–22], and the density, specific heat capacity, thermal conductivity, and viscosity of SCCO2 in terms of data available in Refs. [23–26], respectively. Fig. 1 compares the thermophysical properties of water and SCCO2 as functions of pressure and temperature. The thermophysical properties of water including density, viscosity, specific heat capacity, and thermal conductivity are generally larger than those of SCCO2. The effect of pressure on the thermophysical properties of water is relatively weaker, whereas it can be very significant on the thermophysical properties of SCCO2, particularly for the property, density. The density of SCCO2 and the viscosity of water both exhibit strong temperature effects. For typical EGS applications, the density of water may vary within the range of 900–1000 kg/m3, while that of SCCO2 may vary within 500–900 kg/m3; the viscosity of water may vary within 2.0  104– 8.0  104 Pa  s, while that of SCCO2 may vary within 4.0  105– 1.0  104 Pa  s. The stronger temperature-dependent density of SCCO2 may arouse larger buoyancy along the reservoir/wellbore depth direction [8,27]. The notably smaller viscosity of SCCO2 leads to smaller flow resistance for the seepage flow of SCCO2 in EGS reservoirs. The viscosity of SCCO2 shows stronger pressure-dependence than that of water, e.g. at 400 K temperature with the pressure being changed from 20 MPa to 60 MPa, the viscosity of water varies from 2.2  104 Pa  s to 2.3  104 Pa  s, while that of SCCO2 varies from 3.2  105 Pa  s to 7.4  105 Pa  s. Pruess [8] used the fluid mobility (i.e., density divided by viscosity) to explain different heat extraction performance between water-EGS and SCCO2-EGS. The evidently larger fluid mobility of SCCO2 leads to larger heat extraction rate. However, the specific heat capacity and thermal conductivity of SCCO2 are lower than those of water, which may diminish the heat extraction rate of SCCO2-EGS. In the sub-figure for the specific heat

1207

capacity in Fig. 1, there appears a singularity for the SCCO2 graph, which indicates the critical point (Temperature 304.13 K, Pressure 7.3773 MPa) of SCCO2. 2.2. Case setup 2.2.1. EGS heat transfer fluid We consider three groups of cases, as listed in Table 1. The EGS heat transfer fluid differs by case. Group 1 consists of 2 cases, case 1 takes the real water as working fluid (i.e. heat transfer fluid) and case 2 the real SCCO2; all the thermophysical properties of the fluid are temperature- and pressure-dependent, as described in Section 2.1.2. Group 2 and 3 both consist of 12 cases, in which the working fluid has one of the four thermophysical properties (i.e., density, viscosity, specific heat capacity, and thermal conductivity) being assumed temperature- and pressure-independent for each case. All the cases in group 2 have water-based working fluid while those in group 3 all have SCCO2-based working fluid. For each thermophysical property, the 3 constants considered are approximately the minimum, median, and maximum value, respectively, when the fluid is in normal EGS circumstance. 2.2.2. EGS subsurface geometry and other model parameters The modeled EGS subsurface geometry is treated as a single domain consisting of three sub-regions [17–19]: (i) injection and production wells, (ii) the geothermal reservoir, and (iii) the rock that enclosing the reservoir. Different sub-regions have different geo-physical properties: the injection and production wells having unity porosity and infinite permeability; the porous reservoir having finite porosity and permeability; the surrounding rock having zero porosity and permeability if considering zero fluid loss. Specially, the present work follows the works of Pruess [7,8] and takes a quintuplet EGS (one injection well and four production wells) as the model geometry, dimensions of which are schematically shown in Fig. 2(a). The simulated EGS subsurface domain is a 2000  6000  2000 m volume. (The xy-plane at z = 0 indicates the earth surface.) The reservoir, a 500  500  500 m porous cube, is located at about subsurface 4000 m depth. On horizontal xysectional planes of the reservoir, the injection well is positioned at the center and the four production wells are arranged close to the four corners, respectively. The distance between a production well center and the nearby reservoir boundary is 50 m. The injection and production wells are all 0.2  0.2 m square-shaped on xy-sectional planes. Due to geometrical symmetry (see Fig. 2a), only one quarter of the EGS geometry is simulated. Structural hexahedral meshes are used to discretize the simulated domain and the meshes are elaborately designed to ensure sufficient fine meshes in the injection and production wells and in the reservoir. Totally, there are about 270,000 numerical elements. The numerical mesh system is displayed in Fig. 2(b). Reservoir permeability and porosity may be the two most important parameters dominating EGS heat extraction process. They dictate the flow distribution and the flow resistance (i.e. the needed external pump work) and thereby directly affect the EGS performance, including the heat extraction performance, lifetime, and economic performance etc. We assume that the EGS reservoir has been homogeneously fractured, being of constant and uniform porosity and permeability, which are 0.01 [19] and 1.0  1014 m2 [19], respectively. The density, specific heat capacity and thermal conductivity of the rock are set as qs = 2650 kg/m3, Cps = 1000 J/kg/K, ks = 2.4 W/m/K, respectively [19]. The volumetric heat transfer coefficient ha is set to be 1.0 W/m3/K [18,19]. Initial temperature of the rock is set to increase linearly against the reservoir depth with 4 K per 100 m gradient, while the ground temperature (Tg, meaning the temperature at the earth surface) is fixed at 300 K

1208

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Fig. 1. Thermophysical properties of water and SCCO2 as functions of temperature and pressure.

[14]. Initially, the temperature of working fluid is assumed to be locally the same as the rock. During heat extraction processes, cold fluid of 343.15 K temperature is injected into the reservoir; at the inlet of injection well and the outlets of production wells, fixed pressure boundary conditions are imposed and a 10 MPa pressure difference between the injection inlet and production well outlets is prescribed. The pressure at the center of the reservoir is set at 40 MPa, approximately according with its subsurface 4000 m location. No-slip flow boundary condition and zero-flux heat transfer boundary condition are considered at the walls of all the wells. Fixed temperature (at the location-dependent initial value) boundary condition is assumed for all the external boundaries of the simulated domain. Since the simulated domain is sufficiently large and the thermal disturbance in the reservoir will not propagate to the external boundaries of the domain during EGS operation time of interest, the thermal boundary condition at the domain external boundaries actually has no influence on the simulation results. In the injection and production wells, the fluid flow may experience turbulence due to the high flow rate. We do not employ any turbulence model to resolve the flow turbulence, meaning the turbulent flow is solved by the DNS (direct numerical simulation) method. The model equations, Eqs. (1)–(4), confined by the abovementioned initial and boundary conditions, are solved in the commercial multi-functional CFD software package, FLUENTÒ 6.3. [17,18] Eqs. (1) and (2) are the standard transient continuity

equation and momentum conservation equation, respectively, for incompressible flow in porous media. Eqs. (3) and (4) are both non-standard energy conservation equation. We define two scalars for the variables Ts and Tf, respectively, and let the FLUENT itself solve the variables p and the vector u after customizing the non-standard terms in Eqs. (1)–(4) with the FLUENT user defined functions (UDF). The SIMPLEC (Semi-Implicit Method for Pressure Linked Equation Consistency) method is used to resolve the coupling of pressure and velocity. The first order upwind discretization scheme is used to discretize the transient terms. Grid-independence tests conducted in a previous work [19] indicates the present mesh system can give solutions of satisfying accuracy. 3. Results and discussion 3.1. Comparison of water-EGS and SCCO2-EGS 3.1.1. Flow behaviors Fig. 3 displays the calculated fluid pressure distribution in the reservoir at four representative time instants: 1, 5, 10, and 15 years into the EGS operation for both the water-EGS and SCCO2-EGS cases. The displayed pressure values relative to the reference pressure, 40 MPa, which is the assumed absolute pressure value at the

1209

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217 Table 1 Simulated cases. Group #

Working fluid

Case #

q (kg/m3)

l (Pa  s)

Cp (J/kg/K)

k (W/m/K)

1

Water SCCO2

1 2

qH2 O (p,T) qSCCO2 (p,T)

lH2 O (p,T) lSCCO2 (p,T) lH2 O (p,T) lH2 O (p,T) lH2 O (p,T)

C pH2 O (p,T) C pSCCO2 (p,T)

kSCCO2 (p,T)

C pH2 O (p,T)

kH2 O (p,T)

C pH2 O (p,T)

kH2 O (p,T)

C pH2 O (p,T)

kH2 O (p,T)

C pH2 O (p,T) C pH2 O (p,T) C pH2 O (p,T) 4300

kH2 O kH2 O kH2 O kH2 O

4200 C pH2 O (p,T)

kH2 O (p,T) kH2 O (p,T) 0.7

C pH2 O (p,T)

0.65

2

Water-based fluid

3

1000

4

950

5

900

6 7 8 9

14

qH2 O qH2 O qH2 O qH2 O qH2 O qH2 O qH2 O qH2 O qH2 O

15

900

16 17

700 500

18 19 20 21

qSCCO2 qSCCO2 qSCCO2 qSCCO2 qSCCO2 qSCCO2 qSCCO2 qSCCO2 qSCCO2

10 11 12 13 3

SCCO2-based fluid

22 23 24 25 26

center of the reservoir. For both cases, the fluid pressure at the injection well is highest and decreases, first dramatically in the vicinity of the injection well, with increasing distance to the injection well. However, the pressure drop for the water-EGS case is more concentrated in the vicinity region of the injection well due to the smaller fluid mobility [7]. Fig. 4 compares the fluid mass flow rate of the water-EGS and the SCCO2-EGS. The mass flow rate for both cases declines significantly during the very early period of EGS operation as the cold fluid (of higher viscosity) is being injected into the reservoir; later on, the fluid mass flow rate slightly declines as the rock is gradually cooled down by the heat transfer fluid. For most time during EGS operation, the fluid mass flow rate for the SCCO2-EGS maintains at 64 kg/s, more than 3 times of that for the water-EGS. During EGS operation, heat exchange in the reservoir relies partially on natural convection of fluid. Fig. 5 depicts Z-velocity contour plots on a plane confined by the injection well and a production well in the reservoir at four representative time instants: 1, 5, 10, and 15 years into the EGS operation for both the water-EGS and SCCO2-EGS cases. For both cases, upon EGS operation, there forms first a negative Z-velocity region originates from the injection well and then expands toward the production well; at a relatively later instant into EGS operation (say, 5, 10, or 15 years), two disparate regions of negative and positive Zvelocity, respectively, coexist. Near the injection well, Z-velocity is negative as the cold fluid is injected downward; near the production well, it is positive as the hot fluid is mined upward. The Zvelocity magnitude for the SCCO2-EGS case is significantly larger than that for the water-EGS case, indicating much stronger natural convective heat exchange for the former. The Z-velocity contour for the SCCO2-EGS case also shows stronger time-dependence than that for the water-EGS case as the thermophysical properties of the former are generally more sensitive to the variations of fluid temperature and pressure.

(p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T)

(p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T) (p,T)

1.0  103 6.0  104 2.0  104 lH2 O (p,T)

lH2 O (p,T) lH2 O (p,T) lH2 O (p,T) lH2 O (p,T) lH2 O (p,T) lSCCO2 (p,T) lSCCO2 (p,T) lSCCO2 (p,T)

(p,T) (p,T) (p,T) (p,T)

C pH2 O (p,T)

0.6

C pSCCO2 (p,T)

kSCCO2 (p,T)

C pSCCO2 (p,T) C pSCCO2 (p,T)

kSCCO2 (p,T)

C pSCCO2 (p,T) C pSCCO2 (p,T) C pSCCO2 (p,T) 1800

kSCCO2 kSCCO2 kSCCO2 kSCCO2

(p,T)

1700

kSCCO2 (p,T)

(p,T)

1600

(p,T)

C pSCCO2 (p,T)

kSCCO2 (p,T) 0.12

(p,T)

C pSCCO2 (p,T)

0.09

(p,T)

C pSCCO2 (p,T)

0.06

1.0  104 7.0  105 4.0  105 lSCCO2 (p,T)

lSCCO2 lSCCO2 lSCCO2 lSCCO2 lSCCO2

4100

kH2 O (p,T)

kSCCO2 (p,T) (p,T) (p,T) (p,T) (p,T)

To shed more light on the Z-velocity distribution in the reservoir, we set a monitoring line, line AB, which connects the injection and production well centers on the mid-Z horizontal plane of the reservoir (see the first plot of Fig. 5 for its position), and make a quantitative comparison of Z-velocity profile along line AB between the water-EGS case and the SCCO2-EGS case. To facilitate the comparison, we define a dimensionless parameter, which is the local Zvelocity divided by the velocity magnitude, i.e. uz/|u|. Fig. 6 shows the uz/|u| profiles along line AB for both the water-EGS and the SCCO2-EGS cases at two time instants: 1 and 10 years into the EGS operation. It is worth pointing out that for both cases uz/|u| is about 1.0 in the injection well and 1.0 in the production well. However, in Fig. 6, the vertical axis is truncated to keep the view window remaining within the range from 0.45 to 0.2 for better view. For the SCCO2-EGS case, the uz/|u| profile is seen to have a peak negative value of about 0.05 at 1 year and 0.2 at 10 years, and a peak positive value of about 0.01 at 1 year and 0.08 at 10 years, which are evidently larger than the corresponding counterparts for the waterEGS. At 1 year, the uz/|u| values are all slightly negative in the reservoir of the water-EGS. These findings corroborate again that much stronger natural convection flow exists in the SCCO2-EGS reservoir. 3.1.2. Heat extraction performance During EGS operation, the heat stored in the subsurface reservoir is extracted along with the seepage flow of heat transfer fluid. Evolution of rock temperature, which can be indicative of heat extraction rate, is presented in Fig. 7 for case 1 and 2 both. The rock in the vicinity region surrounding the injection well is first cooled down by the injected cold fluid and a low temperature region forms therein; this low temperature region is seen to gradually expand toward the production wells. The expanding speed of low rock temperature region for the SCCO2-EGS case (i.e. case 2) is faster than that for the water-EGS case (i.e. case 1), indicating the SCCO2-EGS case has higher heat extraction rate.

1210

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Fig. 2. Geometry and mesh system. (a) Geometry and geometrical dimensions of the considered quintuplet EGS; (b) meshes of the simulated geometry.

To evaluate the heat extraction performance of EGS, we define a parameter, heat extraction ratio, as

R hðtÞ ¼

ðQ out ðtÞhout ðtÞ  Q in ðtÞhin Þdt R q c ðT s;ini  T g Þdv Vh s ps

ð5Þ

On the right hand side of the above equation, the denominator represents the total heat stored in the geothermal reservoir in reference to the ground temperature, Tg; the numerator denotes the cumulative heat extracted by the heat transfer fluid, where, Q denotes the fluid mass flow rate, hout and hin the specific enthalpy of the hot fluid at the production well outlet and that of the cold fluid at the injection well inlet, respectively; the term (Qout(t)hout(t)  Qin(t)hin) represents the heat extraction rate; Ts,ini represents the rock initial temperature and Vh the volume of geothermal reservoir. Further, we can define the local heat extraction ratio in terms of the rock temperature, as

hL ðtÞ ¼

T s;ini  T s ðtÞ T s;ini  T g

ð6Þ

where, Ts (t) represents the rock temperature at time t. Fig. 8 makes a comparison of EGS production temperature and heat extraction ratio between the water-EGS and SCCO2-EGS case, i.e. case 1 and 2. The production temperature remains high, about 460 K, which is the initial average rock temperature in the reservoir, during the early stage of EGS operation, and then decreases for both cases, whereas the duration for the production temperature maintaining high is shorter and the subsequent temperature drop speed is faster for the SCCO2-EGS case. Taking the production temperature to be 10 K lower than the early-stage maximum production temperature as the EGS abandonment temperature [2,19], we can determine the EGS lifetimes are 12.5 and 16.3 years for the SCCO2-EGS and water-EGS case, respectively. It is seen from Fig. 8 that the heat extraction ratio for the SCCO2-EGS case is higher than that for the water-EGS case. However, if we compare the heat extraction ratio values at the EGS ceasing-operation time, we see very small difference

between them, about 0.44 for the SCCO2-EGS case and 0.46 for the water-EGS case. The slightly larger heat extraction ratio that the water-EGS case has is caused by its longer lifetime and more thermal compensation the reservoir gets from the surrounding rocks. [19] Fig. 9 displays the heat extraction ratio distribution in the reservoir at the end of EGS operation. The two cases show approximately the same distribution, which accords well with the observation from Fig. 8. However, careful inspection of Fig. 9 finds easily that more heat has been extracted from the reservoir deep regions for the SCCO2-EGS case, that is to say, the heat extraction for the SCCO2-EGS case prefers to perform in the reservoir deep regions. This phenomenon is caused by the stronger natural convection of SCCO2 fluid occurring in the reservoir, which has been discussed in detail in relation with Figs. 5 and 6.

3.1.3. Additional parametric study on natural convection flow in SCCO2-EGS Since the natural convective heat exchange may play an important role in the heat extraction process of SCCO2-EGS, an additional parametric study is particularly conducted to shed more light on the natural convection flow in SCCO2-EGS reservoir. The parameters considered are the reservoir permeability (K), the fluid injection pressure (pin), and the reservoir volume that is indicated by the distance (dw) between the injection well and a production well. The base case is the SCCO2-EGS case, listed as case 2 in Table 1. For the base case, K = 1.0  1014 m2, pin = 10 MPa and dw = 282.8 m. To perform the parametric study, we simulate additionally three couples of cases with (i) K = 1.0  1013 m2 or K = 1.0  1015 m2; (ii) pin = 5 MPa or pin = 20 MPa; (iii) dw = 141.4 m or dw = 565.7 m. At the same time instant, the temperature distribution and the fluid density distribution in the reservoir can be very different between cases. To make the results more comparable, we take the simulated results at the end of EGS operation, i.e. at the time instant when the production temperature decreases to be 10 K lower than the early-stage maximum production temperature, for comparison.

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

1211

Fig. 3. Fluid pressure distribution in the reservoir. (Upper row: water-EGS; lower-row: SCCO2-EGS. The plots from left to right correspond to time instants: 1, 5, 10, and 15 years, respectively.)

Fig. 4. Mass flow rate of water-EGS and SCCO2-EGS.

Fig. 10 displays the dependence of the dimensionless Z-velocity (i.e. uz/|u|) profile along line AB (refer to Fig. 5 for its approximate position) on the reservoir permeability. The uz/|u| reduces its peak negative and positive values both and the positions that have these peak values shift towards the injection well if the reservoir permeability K increases. Increasing the reservoir permeability means lowering the flow resistance. As the fluid injection pressure is fixed at 10 MPa for all the three cases, the fluid flow velocity in the reservoir is directly proportional to the reservoir permeability in terms of Darcy’s law. From Fig. 10, we can derive with ease that the fluid Z-velocity increases with the increase of reservoir permeability, whereas its increasing rate is lower than that of the velocity magnitude. Reducing the fluid injection pressure is to some extent equivalent to lowering the reservoir permeability in terms of Darcy’s law. Fig. 11 shows the effect of the fluid injection pressure on the uz/|u| profile along line AB. It is seen that increasing the injection pressure from 5 MPa to 15 MPa results in a reduction of the uz/|u| peak negative value from about 0.42 to 0.11 and a drop of the uz/|u| peak positive value from about 0.18 to 0.05. Since the reduction or

1212

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Fig. 5. Z-velocity contour plots on a plane confined by the injection well and a production well. (Upper row: water-EGS; lower-row: SCCO2-EGS. The plots from left to right correspond to time instants: 1, 5, 10, and 15 years, respectively.)

Fig. 12 shows the effect of reservoir volume on the uz/|u| profile along line AB in SCCO2-EGS. Enlarging the reservoir volume leads to broader fluid temperature and density distributions in the EGS reservoir, facilitating the flow convection. It is seen from Fig. 12 that increasing the injection and production well distance from 141.4 m to 565.7 m makes an increment of about 0.23 (from about 0.11 to 0.34) at the uz/|u| peak negative value, an increment of about 0.06 (from about 0.05 to 0.11) at the uz/|u| peak positive value. 3.2. Effects of variable thermophysical properties of fluid

Fig. 6. Profiles of uz/|u| along line AB for the water-EGS case and the SCCO2-EGS case.

For real fluids, e.g. water or SCCO2, all the thermophysical properties are functions of temperature and pressure, thus are locationdependent and vary with time during EGS heat extraction. This section gears to understand the effects of variable thermophysical properties of heat transfer fluid on EGS heat extraction performance. The cases considered have been listed in Table 1 as group 2 and 3 cases. We evaluate the heat extraction performance of different cases by monitoring the real-time net electric power output We, which is defined as

W e ¼ gH ðQ out ðtÞhout ðtÞ  Q in ðtÞhin Þ  drop rate of the uz/|u| peak value is larger than the fluid injection pressure increasing rate, it is speculated that the Z-velocity does not change much and there may form stronger preferential flow along line AB in the reservoir when increasing the fluid injection pressure.

DpQ in ðtÞ gP qin ðtÞ

ð7Þ

where gH denotes heat-to-electricity conversion efficiency, assumed to be constant, 0.14 [2] in the present work in terms only of the approximate production temperature range; (Qout(t)hout(t)  Qin(t)hin) is the heat extraction rate, the same as

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

1213

Fig. 7. Rock temperature in the reservoir. (Upper row: water-EGS; lower-row: SCCO2-EGS. The plots from left to right correspond to time instants: 1, 5, 10, and 15 years, respectively.)

Fig. 8. Production temperature and heat extraction ratio of water-EGS and SCCO2-EGS.

Fig. 9. Local heat extraction ratio distribution in the reservoir at the end of EGS operation. (a) Water-EGS at 16.3 years; (b) SCCO2-EGS at 12.5 years.

1214

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

Fig. 10. Effect of SCCO2-EGS reservoir permeability on the uz/|u| profile along line AB.

Fig. 12. Effect of reservoir volume on the uz/|u| profile along line AB in SCCO2-EGS.

Fig. 11. Effect of fluid injection pressure on the uz/|u| profile along line AB in SCCO2EGS.

in Eq. (5). The second term on the right hand side of Eq. (7) represents the external pump work consumed to drive the heat transfer fluid flow through the geothermal reservoir; pressure head of the pump (Dp) is fixed at 10 MPa for all the cases; working efficiency of the pump (gP) is assumed to be 0.9.

3.2.1. Effects of variable density Fig. 13 illustrates dependence of the net electric power output on fluid density. The temporal evolution of net electric power output show three distinct stages for both water- and SCCO2-based cases. During the very early first stage, as short as a few months, the net electric power rapidly decreases. The second stage can last around 10 years for water-EGSs and 7.5 years for SCCO2-EGSs, during which the EGS has relatively stable electric power output. During the third stage, the net electric power of EGS turns to decrease again, meaning the EGS is close to the end of its lifetime. Quantitatively, we define the time instant, at which the relative change of the net electric power output within one day is less than 5%, as the end of the first stage, and the time instant, at which the production temperature starts to decline from its high value, as the end of the second stage. Recalling the mass flow rate curves in Fig. 4, the production temperature curves in Fig. 8, and the results

Fig. 13. Net electric power output for cases with different fluid density scenarios. (a) Water-based cases; (b) SCCO2-based cases.

of rock temperature distribution presented in Fig. 7, we deduce with ease the underlying mechanisms. The speedy drop of net electric power output during the first stage is associated with the fast mass flow rate decrease due to the significant increase of fluid viscosity, and the decline of the net power output during the third stage is associated with the so-called ‘‘thermal breakthrough” [17–19] of heat transfer fluid. For the two real fluid cases, the water

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

density is varying within 904.1–1000.0 kg/m3 and the SCCO2 density is varying within 522.1–909.1 kg/m3. Seen from Fig. 13, the curve of net electric power output falls in-between the curves of 950 and 1000 kg/m3 constant density cases for the real water case and 700 and 900 kg/m3 constant density cases for the real SCCO2 case. To a great extent, the magnitude of net power output during the second stage represents the capacity of EGS power plant and the duration of this stage reflects the lifetime of this plant. Seen from Fig. 13, the magnitude of net power output during the second stage is greatly affected by the density of fluid. For cases with waterbased heat transfer fluid, the net power output during the second stage is 4.31 MW (a time-averaged value) at 1000 kg/m3 fluid density, 4.06 MW at 950 kg/m3 fluid density and 3.81 MW at 900 kg/m3 fluid density; for cases with SCCO2-based heat transfer fluid, the net power output during the second stage is 4.57 MW at 900 kg/m3 fluid density, 2.77 MW at 700 kg/m3 fluid density, 0.95 MW at 500 kg/m3 fluid density. The net power output is approximately directly proportional to the density of fluid. Moreover, every 50 kg/m3 decrease of fluid density leads to about 0.25 MW loss of the net power output for water-based cases, whereas about 0.45 MW loss for SCCO2-based cases, indicating that the production performance of SCCO2-EGS is more sensitive to the density variation of heat transfer fluid.

1215

pump work, and the net electric power output thus benefits from a larger mass flow rate of heat transfer fluid. Dependence of the net electric power output on fluid viscosity is shown in Fig. 14. Different from Fig. 13, the first stage of net electric power temporal evolution is not seen for all the constant fluid viscosity cases as the early stage speedy drop of fluid mass flow rate shown in Fig. 4 will not occur. Furthermore, the net electric power output prior to its last stage decline has negative correlation to the constant fluid viscosity assumed. For water-based cases, it is about 1.25 MW for the 1.0  103 Pa  s viscosity case, 2.30 MW for the 6.0  104 Pa  s viscosity case, and 7.55 MW for the 2.0  104 Pa  s viscosity case; for SCCO2-based cases, it is about 1.38 MW for the 1.0  104 Pa  s viscosity case, 3.25 MW for the 7.0  105 Pa  s viscosity case, and 7.86 MW for the 4.0  105 Pa  s case. SCCO2-EGS shows stronger effects of variable fluid viscosity than water-EGS. For the two real fluid cases, the water viscosity is varying within 1.6  104–1.0  103 Pa  s and the SCCO2 viscosity is varying within 4.4  105–9.4  105 Pa  s during EGS operation. Deduced from the results shown in Fig. 14, simulations with constant fluid viscosity assumed may not be able to well predict the net electric power output of real EGS, especially during its early operation stage.

3.2.2. Effects of variable viscosity The viscosity of fluid affects the heat extraction performance of EGS as a lower viscosity would yield larger fluid velocities at a given

3.2.3. Effects of variable specific heat capacity Fig. 15 describes dependence of the net electric power output on fluid specific heat capacity. The specific heat capacity of fluid has positive effects on the net electric power output of EGS. For water-based cases, the net electric power output prior to its last stage decline is about 4.33 MW for the 4300 J/kg/K case, 4.21 MW

Fig. 14. Net electric power output for cases with different fluid viscosity scenarios. (a) Water-based cases; (b) SCCO2-based cases.

Fig. 15. Net electric power output for cases with different fluid specific heat capacity scenarios. (a) Water-based cases; (b) SCCO2-based cases.

1216

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217

for the 4200 J/kg/K case, and 4.09 MW for the 4100 J/kg/K case; for SCCO2 based cases, it is about 3.53 MW for the 1800 J/kg/K case, 3.12 MW for the 1700 J/kg/K case, and 2.69 MW for the 1600 J/kg/K case. The variable specific heat capacity of fluid must have stronger effects on the production of SCCO2-EGS than that of water-EGS. For the two real fluid cases, the specific heat capacity of water is varying within 4093.0–4279.1 J/kg/K and the specific heat capacity of SCCO2 is varying within 1593.9–1848.8 J/kg/K during EGS operation. Seen directly from Fig. 15, a simulation with suitably assumed constant specific heat capacity of fluid is able to well predict the net electric power output of real EGS. 3.2.4. Effects of variable thermal conductivity Fig. 16 displays dependence of the net electric power output on fluid thermal conductivity. Regardless of water- or SCCO2-based cases, the net electric power output curve exhibits little difference between cases of different thermal conductivity values, indicating negligible effects of variable thermal conductivity of heat transfer fluid. We further deduce that heat extraction in EGS relies mainly on heat exchange between heat transfer fluid and hot rock. From the above case studies we find that the net electric power output of EGS has positive correlation to the density and specific heat capacity of heat transfer fluid, and negative correlation to the viscosity of fluid, whereas the thermal conductivity of fluid only has negligible effects on the net electric power output of EGS. It is worth pointing out that the heat-to-electricity conversion efficiency (gH) is certainly not a constant [2], which varies during EGS operation and alters for different EGS-s. The assumption of

0.14 constant gH for both water-EGS and SCCO2-EGS in the present work should not alter the qualitative results, particularly where there are large differences in the calculated electric power data of the water-based EGS and SCCO2-based EGS cases. However, one must be cautious when taking the estimated electric power data for relevant predictions of practical EGS power plants. 4. Concluding remarks We upgraded a previously developed model by implementing pressure- and temperature-dependent thermophysical properties of real water and SCCO2, and employed it to simulate the longterm heat extraction processes in water-EGS and SCCO2-EGS. The heat extraction performance of EGS shows evident dependence on the heat transfer fluid used. For the special quintuplet EGS (one injection well and four production wells) considered, at a given pressure drop between the injection well inlet and production well outlet, (1) the SCCO2-EGS has much higher fluid mass flow rate than the water-EGS; (2) the SCCO2-EGS has faster heat extraction rate, but with the same ceasing-operation criterion, the SCCO2-EGS has shorter lifetime and the cumulative heat extraction amount at the end of operation for the SCCO2-EGS is approximately the same as that for the water-EGS; (3) stronger natural convection of fluid makes the heat extraction of SCCO2-EGS more prefer to perform in the reservoir deep regions. Furthermore, the SCCO2-EGS is found to have relatively stronger natural convection flow if the reservoir permeability is smaller, the fluid injection pressure is lower, or the reservoir is of a larger volume. Effects of variable thermophysical properties of heat transfer fluid on EGS heat extraction performance were studied more comprehensively. For both water- and SCCO2-EGS, the net electric power output was found to be positively related with the density and specific heat capacity of fluid, and negatively related with the viscosity of fluid, whereas the thermal conductivity of fluid shows little effect on the net electric power output. Nevertheless, the production performance of SCCO2-EGS is generally more sensitive to the variation of fluid thermophysical properties. From viewpoint of pure numerical prediction, a simulation with suitably-assumed constant fluid density, specific heat capacity, and thermal conductivity may well predict the production performance of real EGS, whereas a simulation with constant fluid viscosity may not, especially during the very early stage operation of real EGS, the simulation gives completely wrong result. Conflict of interest None declared. Acknowledgments Financial support received from the China National ‘‘863” Project (2012AA052802), the China National Science Foundation and Guangdong-Province Joint Project (U1401232), the Key Scientific Development Project of Guangdong Province (2014A030308001), the CAS ‘‘100 talents” Program (FJ), and the China National Science Foundation (51406213, 51206174) is gratefully acknowledged. References

Fig. 16. Net electric power output for cases with different fluid thermal conductivity scenarios. (a) Water-based cases; (b) SCCO2-based cases.

[1] G.L. Wang, K.W. Li, D.G. Wen, W.J. Lin, L.J. Lin, Z.M. Liu, W. Zhang, F. Ma, Assessment of geothermal resources in China, in: The 38th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2013. [2] J.W. Tester, B.J. Anderson, A.S. Batchelor, D.D. Blackwell, R. Dipippo, E.M. Drake, et al., The future of geothermal energy: impact of enhanced geothermal systems (EGS) on the United States in the 21st Century, in: Final Report to the US Department of Energy Geothermal Technologies Program, Massachusetts Institute of Technology, Cambridge, 2006.

W. Cao et al. / International Journal of Heat and Mass Transfer 92 (2016) 1205–1217 [3] J. Brasz, G. Holdmann, Power production from a moderate-temperature geothermal resource, Geotherm. Resour. Counc. Trans. 29 (2005) 729–733. [4] K. Breede, K. Dzebisashvili, X. Liu, G. Falcone, A systematic review of enhanced (or engineered) geothermal systems: past, present and future, Geotherm. Energy 1 (2013) 4. [5] U.S. Department of Energy, An Evaluation of Enhanced Geothermal Systems Technology, 2008. [6] D.W. Brown, A hot dry rock geothermal energy concept utilizing supercritical CO2 instead of water, in: The Twenty-Fifth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2000. [7] K. Pruess, Enhanced geothermal systems (EGS) using CO2 as working fluid – a novel approach for generating renewable energy with simultaneous sequestration of carbon, Geothermics 3 (2006) 51–67. [8] K. Pruess, On production behavior of enhanced geothermal systems with CO2 as working fluid, Appl. Therm. Eng. 49 (2008) 1446–1454. [9] A.D. Atrens, H. Gurgenci, V. Rudolph, CO2 thermosiphon for competitive geothermal power generation, Energy Fuels 23 (2009) 553–557. [10] A.D. Atrens, H. Gurgenci, V. Rudolph, Electricity generation using a carbondioxide thermosiphon, Geothermics 39 (2010) 161–169. [11] M.H. Fard, K. Hooman, H.T. Chua, Numerical simulation of a supercritical CO2 geothermosiphon, Int. Commun. Heat Mass Transfer 37 (2010) 1447–1451. [12] J.B. Randolph, B. Adams, T.H. Kuehn, M.O. Saar, Wellbore heat transfer in CO2based geothermal systems, GRC Trans. 36 (2012) 549–554. [13] F. Luo, R.N. Xu, P.X. Jiang, Numerical investigation of fluid flow and heat transfer in a doublet enhanced geothermal system with CO2 as the working fluid (CO2-EGS), Energy 64 (2014) 307–322. [14] A. Borgia, K. Pruess, T.J. Kneafsey, C.M. Oldenburg, L. Pan, Numerical simulation of salt precipitation in fractures of a CO2-enhanced geothermal system, Geothermics 44 (2012) 13–27. [15] A.D. Atrens, H. Gurgenci, V. Rudolph, Economic optimization of a CO2-based EGS power plant, Energy Fuels 25 (2011) 3765–3775. [16] A.R. Mohan, U. Turaga, V. Shembekar, D. Elsworth, Utilization of carbon dioxide from coal-based power plants as a heat transfer fluid for electricity generation in enhanced geothermal system, Energy 57 (2013) 505–512.

1217

[17] F.M. Jiang, L. Luo, J.L. Chen, A novel three-dimensional transient model for subsurface heat exchange in enhanced geothermal systems, Int. Commun. Heat Mass Transfer 41 (2013) 57–62. [18] F.M. Jiang, J.L. Chen, W.B. Huang, L. Luo, A three-dimensional transient model for EGS subsurface thermo-hydraulic process, Energy 72 (2014) 300–310. [19] J.L. Chen, F.M. Jiang, Designing multi-well layout for enhanced geothermal system to better exploit hot dry rock geothermal energy, Renewable Energy 74 (2015) 37–48. [20] The International Association for the Properties of Water and Steam, Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, Switzerland, 2007. [21] The International Association for the Properties of Water and Steam, Lamda Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance, Czech Republic, 2011. [22] The International Association for the Properties of Water and Steam, Viscosity Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance, Germany, 2008. [23] E. Heidaryan, A. Jarrahian, Modified Redlich–Kwong equation of state for supercritical carbon dioxide, J. Supercrit. Fluids 81 (2013) 92–98. [24] R. Span, W. Wagner, A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPa, J. Phys. Chem. Ref. Data 25 (1996) 1509–1596. [25] A. Jarrahian, E. Heidaryan, A novel correlation approach to estimate thermal conductivity of pure carbon dioxide in the supercritical region, J. Supercrit. Fluids 64 (2012) 39–45. [26] E. Heidaryan, T.H. Hatami, M. Rahimi, J. Moghadasi, Viscosity of pure carbon dioxide at supercritical region: measurement and correlation approach, J. Supercrit. Fluids 56 (2011) 144–151. [27] A. Bataillé, P. Genthon, M. Rabinowicz, B. Fritz, Modeling the coupling between free and forced convection in a vertical permeable slot: implications for the heat production of an enhanced geothermal system, Geothermics 35 (2006) 654–682.