Numerical simulation of heat production potential from hot dry rock by water circulating through a novel single vertical fracture at Desert Peak geothermal field

Energy 63 (2013) 268e282

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Numerical simulation of heat production potential from hot dry rock by water circulating through a novel single vertical fracture at Desert Peak geothermal field Yu-Chao Zeng, Neng-You Wu*, Zheng Su, Xiao-Xing Wang, Jian Hu Key Laboratory of Renewable Energy and Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, No. 2 Nengyuan Road, Guangzhou 510640, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 March 2013 Received in revised form 10 October 2013 Accepted 12 October 2013 Available online 7 November 2013

Based on the geological data of well DP23-1 under the EGS (enhanced geothermal system) project at Desert Peak geothermal field, we numerically investigated the heat production potential from deep HDR (hot dry rock) at this site by water circulating through a novel single vertical fracture. A technically feasible fracture aperture of 2 mm is assumed. The injected water is assumed to sweep the fracture along the diagonal and the effect of high pressure and temperature on water density is taken into considerations. The results indicate that desirable heat production efficiency can be attained under suitable fracture permeability and water production rate, however the heat and electricity production power remains a relative low situation and the water flow impedance retains a relative high level during production process. The sensitivity analysis indicates that the electricity production power mainly depends on rock thermal conductivity, water production rate and injection temperature; water flow impedance mainly depends on the fracture permeability, the rock thermal conductivity, the water production rate and the injection temperature; and energy efficiency mainly depends on the fracture permeability, the water production rate and the rock thermal conductivity. When the fracture permeability and water production rate are under reasonable conditions, the energy output and production efficiency will be optimized. However, rock contraction due to temperature reduction and watererock interaction are not taken into considerations in this study, so the practical heat output and efficiency through one single vertical fracture needs further study in the future. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Single vertical fracture Heat production potential Circulating water Desert Peak geothermal field Enhanced geothermal system

1. Introduction 1.1. Background The key to exploiting the EGS (enhanced geothermal system) resource is the creation of a well-constructed fractured reservoir in the deep hot dry rock [1]. The reservoir structure determines the system’s performance to a great extent [2]. However, because the geological structure, formation lithology, geophysical and geochemical conditions are complex and site-specific, even though the reservoir stimulation methods are the same, the structures of the reservoirs at different sites always differ significantly. Therefore investigation into the system performances of differently constructed reservoirs is very important [1e3].

* Correspondence author. Tel./fax: þ86 20 87052746. E-mail addresses: [email protected], [email protected] (N.-Y. Wu). 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.10.036

The structure of fractured EGS reservoir experiences three stages of conceptual model: the artificial fracture, the natural joints and the graben settings [1e3]. The artificial fracture, originating from a “penny-shaped” fracture, is formed in a rock mass which behaves as an isotropic continuum within a uniform stress field. The implication of the creation of a reservoir in such a medium is the effect of water injection under high pressure that would be to create a new fracture and jack the new fracture open, thus forming the heat exchange surface [3]. The main artificial fracture form is a single vertical fracture, and the internal water flow can be regarded as plane [2,3]. Fractures in the natural joints and the graben settings models are three-dimensional and reticular, so internal flow paths are also three-dimensional and reticular. The actual fracture structure is highly complex due to complex geological conditions, so one of key problems in EGS reservoir simulation is to properly characterize the fracture [1,4]. The structure of the single fracture is relatively simple, and can be relatively easily modeled by analytical methods, thus it can provide a basic understanding for the heat

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

Nomenclature A d dV f g h1 h2 hinj hpro I IR K k L P P0 PI

cross-sectional area of flow path, m2 distance, m water injection rate, m3/s safety factor gravity, 9.8 m/s2 depth of the injection well, m depth of the production well, m injection specific enthalpy, kJ/kg production specific enthalpy, kJ/kg water flowing impedance, MPa/(kg/s) water flow impedance, MPa/(kg/s) hydraulic conductivity, m/s average reservoir permeability, m2 flow path length, m pressure, MPa wellbore production pressure, MPa productivity index, m3

transfer process between hot rock and water [4e7]. Furthermore, the single fracture model can be used to analyze the heat transfer process in an uneven fracture; thus, many investigations have been conducted revolving around this model [4]. The single fracture concept was initially proposed by Smith in the Los Alamos Scientific Laboratory in 1972, and was the first generation of EGS reservoir model [3]. The initial thought was to fracture the dry rock between the injection well and the production well using highly pressurized water, which forms water flow channel and heat transfer area [4]. Then the Fenton Hill EGS project (phaseⅡ) and the Rosemanowes EGS project (phaseⅡ) proved that there are various naturally weak stress planes or natural joints embedded in the rock mass, allowing the fracture to be created by hydrofracture [2e4]. 1.2. Heat production through a single vertical fracture The method for recovering heat through a closed loop cycle of surface water from previous fractured dry geothermal sites was described in detail in 1971 [8]. Robinson et al. developed the technique of drilling two parallel deep boreholes connected by a vertically oriented crack in 1971 [9]. Harlow et al. conducted a supporting theoretical analysis indicating that many tens of megawatts of thermal power could be supplied for several decades [10]. Raleigh suggested geothermal wells be drilled at an angle in a direction perpendicular to the expected orientation of fractures and this could greatly increase the economic life of hot rock geothermal systems [11]. The thermodynamics characteristics of the single fracture system were systematically investigated using analytical and numerical methods by Bödvarsson in 1969 and 1972 [12,13]. Gringarten et al. presented the theory of heat extraction from fractured hot dry rock based on an infinite series of parallel vertical fractures of uniform aperture [14]. Based on the CGDD (Christianovich Geertsma Deklerk Daneshy) and PKN (Perkins Kern Nordgren) models from the oil and gas industry, Abé established the planar penny-shaped fracture model in 1976 [15]. Wunder et al. conducted a detailed study on thermal drawdown and recovery of single and multiply fractured hot dry rock reservoirs [16]. The analytical solutions of temperature and pressure for the rectangular fracture system were derived by Cheng et al., in 2001, assuming that there was only one-dimensional heat conduction perpendicular to the fracture wall [17]. The poroelasticity and thermoelasticity

q q0 T0 T W x, y, z 4

h hp r m l

e h inj max pro p

269

total water production rate, kg/s partial water production rate, kg/s heat rejection temperature, 288.75 K temperature,  C energy production power, MW Cartesian coordinates, m porosity energy efficiency pump efficiency, 80% density of water, kg/m3 average water viscosity, Pa s rock thermal conductivity, W/(m K) electricity heat injection maximum production pump

effects on the fracture aperture were studied by Ghassemi and Zhang in 2006, assuming that the reservoir pressure is evenly distributed [18]. The aperture and pressure variations within a single vertical rectangular fracture during water circulation were analytically investigated by Ghassemi; in particular, the equation describing the change of fracture aperture controlled by thermoelasticity and poroelasticity effects was derived for the first time [6]. The previous studies provide some guidelines for heat extraction through a single vertical fracture. Increasing permeability in a zone with a high geothermal gradient will trigger free convection, and if there is weak or no free convection in an EGS reservoir, economic exploitation of the geothermal energy will rapidly end [5]. High rock stiffness and low fluid diffusivity cause poroelastic contraction of the fracture opening to slowly develop in time and the maximum reduction of aperture occurs at the injection point and become negligible near the extraction point [6]. The forced convection between circulating water and the fracture surface has an important role in the heat transfer mechanism only in the early stage of heat extraction; the assumption that the temperature of the flowing water is equal to that of the fracture wall is valid in practice for estimation of production temperature [7]. Heat storage and dispersion effects are not important due to dominant advective transport in the fracture flow; two-dimensional heat conduction in hot rock can significantly influence the prediction of the production temperature and reservoir lifetime [17]. For a fixed fracture area, low injection rates will result in thermal drawdown around the fluid inlet with heat conduction in the parallel direction becoming significant [19]. Though realistic reservoirs consist of fracture networks, the single fracture model adequately captures thermal extraction through heat conduction from the hot rock surrounding the reservoir [19]. However, the concept models deviate from a practical injection-reservoir-production system, and these theoretical models cannot fully represent the actual fracture flowing system. First, the injection interval of the injection well and the production interval of the production well are located at different depths, and only part of the connection between the well and reservoir is perforated, so the water flow does not sweep parallel to the fracture wall, while most of the previous models assume water flows parallel to the fracture wall [1,6,17,18]. Second, water flow in the fracture is compressible because of high temperature and pressure, so water density within the fracture is not constant [1,5e7,17e19].

270

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

1.3. Evaluation of heat production performance Garnish and Shock proposed that performance parameters and their requirements for commercialization are: (1) mean reservoir temperature should be no less than 190  C and production temperature drop is lower than 10% during a production period of 15e20 years without re-stimulation; (2) water production rate q is about 100 kg/s and water loss is lower than 10%; (3) stimulated reservoir volume is higher than 2  108 m3; (4) effective heat transfer area is higher than 2  106 m2; (5) water flow impedance IR is lower than 0.1 MPa/(kg/s) [3]. Commercial objectives for a two-well system are thermal power of 25 MW with electrical power of 3.5 MW, and IR lower than 0.2 MPa/(kg/s), when the injection temperature Tinj is 60  C and water production rate q is 50 kg/s [20]. Based on the results of the past 30 years of EGS field tests, there is still a long way to go to realize these objectives [1,20]. Sanyal and Butler proposed that the temperature production profile and net electricity production profile, along with heat recovery, are three most important criteria for evaluating the system’s performances [21]. 1.4. Enhanced geothermal system at Desert Peak geothermal field The Desert Peak EGS project was initiated in 2002, and it is located on the eastern edge of the Desert Peak geothermal field, which is located about 130 km ENE of Reno, Nevada. The ultimate goal of this project is to develop 2e5 MW of EGS-derived power from a stand-alone binary power plant supplied by a well doublet or triplet [22e25]. Part detailed geological data on this project have been published in Ref. [25]. Because the EGS resource potential around well DP23-1 had been systematically evaluated in 2002e 2005 and much geological data had been obtained, this work still adopts well DP23-1 data to perform the numerical research [22e 27]. The target formation is buried at depth from 1219 m to 2743 m (4000e9000 feet), in which the uppermost layer is the pT1 metasediments; and the lowermost layer is the Two-Mica granodiorite [25]. Other formations within above depth range are pT2 quartz monzodiorite, pT2 metasediments and pT2 hornblende diorite in turn [22,25]. The temperature is between 207  C and 216  C, with an average value of 210  C [22,23]. The natural joints are evenly distributed in the target formation and their intersection with the well wall appears as a sine curve shape. The vertical stress is larger than the maximum horizontal principal stress, so the fracture must appear as vertical [27]. The porosity is about 2% over a 439 m investigation radius around well DP23-1, and the permeability is about 0.01 mD (1 mD ¼ 1015 m2) [21,27]. To simplify the analysis, we neglect the changes of lithology in the target formation and assume the whole target formation is granodiorite, and its density is evenly distributed and constant [21,22,25e27]. Based on the data of well spacing and reservoir thickness from the EGS field tests [1], this study aims to exploit the geothermal energy buried in a reservoir at depth of 1219 m to 1619 m (4000e5311.7 feet), the corresponding lithostatic pressure of this interval is from 9.65 MPa to 13.10 MPa, and the pressure gradient is approximately 8.63 MPa/ km [22,25]. 1.5. Objectives The main objective of this study is evaluation of the heat production potential over a 20 year period by water circulating through a single vertical fracture in the deep hot dry rocks of the Desert Peak geothermal field based on data from well DP23-1. The sensitivity of heat production to various operational and formation parameters and conditions are assessed. As mentioned above, the novelty of this study mainly lies in three features. First, the injection interval of the injection well and

the production interval of the production well are located at different depths, making the system more realistic rather than more theoretical [1,6,17,18]. Second, the influence of temperature and pressure on water density is taken into consideration, and the influence of water density on energy efficiency is also analyzed [1,5e7,17e19]. Third, the most important point that differs from the previous studies is that all the data are based on the real geological background at Desert Peak site, and the research conclusions are more practical for engineering applications [21]. 2. Method of production and well design 2.1. Reservoir design and stimulation of the single vertical fracture Field tests have proven that the vertical fracture connecting the injection well and the production well can be created by hydrofracturing [2,3,28,29]. The fractures are always vertical or rather sloped because of the deep stress field [29,30]. When there is only one vertical fracture in the reservoir, the fracture can penetrate the well wall and connect with other wells [1]. Based on this, we assume well DP23-1 is employed as the injection well, and a new well named DPnew-1 is drilled as the production well to the depth of 1619 m, 400 m away from DP23-1 [21,31]. Especially, we assume that hydrofracture creates a vertical rectangular fracture connecting the injection well and the production well. The height of the fracture is 400 m, the length is 400 m and the fracture aperture is 2 m, as shown in Fig. 4. In actual tests, the fracture aperture cannot be measured directly and must be inferred from impedance measurements, tracer studies or radon emanations [32]. The range of aperture estimates at the Rosemanowes reservoir is 0.05e0.60 mm, with fracture spacing a few meters; at Fenton Hill reservoir, the mean joint aperture just prior to joint opening by pressurization is of the order of 0.2 mm; the fracture aperture near the Hijiori injection well is 1.4e2.6 mm while injection at a rate sufficient to extend the fracture based on numerical analysis, while according to tracer experiments the fracture aperture estimates to a range of 2e14 mm [32]. Fracture aperture ranges from 0.2 to 0.5 mm at hydrostatic pressure to 1.0e2.0 mm at fracture extension pressure in a reservoir at Falkenberg, Germany [32]. Based on these field data, a fracture aperture of 2 mm is completely possible under current hydrofracturing technology or water circulation method. However, to simplify the analysis, in this work we don’t discuss the detailed method to stimulate such a fracture reservoir and just assume the fracture has been created for water circulation and heat extraction. In addition, while the enhancement of fractures with time due to thermal contraction of the rock is possible, gradual closing of fractures or degradation of fractures due to scaling is equally possible. Therefore, in our research we have assumed that, after hydrofracturing the fracture characteristics remain unchanged over the project life [21]. Previous studies show that although mineral precipitation may partially close or heal some open fissures, it doesn’t lead to a major decrease of the hydraulic conductivity of the hydrofractured reservoir [5]. Consequently, the geometry of the hydraulic fracture is assumed to maintain constant during the entire production period. Because the underground granodiorite formation is big enough, with permeability lower than 0.01 mD in this site [22], we can assume the fracture is basically bounded by semi-infinite half-space of impermeable rock [17]. For purposes of this study, the assumption is a smooth fracture wall on the rectangular fracture in the dry rock and the thickness of the reservoir is constant at the facture height [17]. The fracture aperture is assumed constant; hence, the solution geometry is reduced to two-dimensional, as shown in Fig. 1 [17]. Because the temperate is 210  C all over the reservoir and there is no geothermal gradient, the free convection effect of the fracture water

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

271

2.3. Water injection and production method Production

Injection well

Fractured reservior

Production well

Injection

Fig. 1. Conceptual model of heat production through a novel single vertical fracture, and the fracture is bounded by semi-infinite half-spaces of impermeable hot rock.

can be neglected [5]. Thus the heat is transported mainly by conduction and forced convection in the circulating water, and only by conduction in the hot rock [5,17]. Because of the high water velocity across the rock surface of the aperture, we assume the heat flow perpendicular to the rock surface is the most important and ignore that parallel to the surface [17e19]; consequently only one dimensional heat conduction is considered in this study [17e19]. Based on these assumptions, the heat extraction system through a single vertical fracture can be reduced into the process of heat sweep in a vertical fracture [33,34], and this process can be well simulated with TOUGH2 codes [34]. Because the 2-D heat conduction case always predicts a higher extraction temperature than the 1-D case, the 1-D heat conduction case can provide an estimation of lower limit of heat production, which is of great importance for geothermal energy exploitation schedule design [1,17,19]. Both thicknesses of the overburden and underburden are 50 m, and the temperature is 210  C. The pressure at the top surface of the overburden, 1169 m depth, is 9.22 MPa, and that at the bottom surface of the underburden, 1669 m depth, is 13.53 MPa [22]. 2.2. Well design There is only one groove along the circumference of the injection well and the production well (Fig. 2) and this groove connects the well with the fracture. In injection well DP23-1, the groove is located at the depth of 1579 m to 1599 m, while in production well DPnew-1, the groove is located at the depth of 1239 m to 1259 m, as shown in the colored parts in Fig. 2. Based on experience derived from the oil and gas industry, this type of design will lower the difficulties of well drilling, completion and perforation [20,31].

We utilize an injection pump on the ground at well DP23-1 to provide a constant flow rate injection, while utilizing a suction pump on the ground at well DPnew-1 to extract the heated water in order to keep bottom-hole pressure Ppro of the production well constant (for reference case, Ppro is 6.50 MPa). By pumping the production well in conjunction with moderate pressurization of the injection well, the circulating fluid is drawn to the producer throughout the stimulated fractured rock, minimizing fluid loss to the far field [1,35]. Thus the water is injected into the fracture and extracted out through the production well, then is input into a binary power generation system. The outflow from the power plant is cooled back down to 60  C and reinjected into the injection well. This forms the complete water circulation and heat extraction process [21]. For reference case, we assume the water production rate q is 7 kg/s, and the injection temperature Tinj is 60  C. The effluent temperature of 60  C is not only necessary to maintain reasonable pinch-point temperature difference in the heat exchangers, but also to limit scaling and chemical deposition phenomena in subsurface reservoir depending on the fluid composition, because the scaling and chemical deposition will increase and cause low efficiency and damages when the injection temperature is lower than 60  C [1,20]. When the bottom-hole injection pressure Pinj is larger than reservoir minimum principal stress, the fracture will be stimulated again and will expand to a larger range. This is called “secondary reservoir development” [1,13]. This effect may change the geometry of the fracture, cause water loss and short circuits, and finally damage the geothermal reservoir [1,20]. So generally Pinj should be lower than the reservoir minimum principal stress [1,20]. However, the Fenton Hill EGS test had proven that a fully confined fractured reservoir can still work even when water pressure exceeds the rock critical failure pressure; furthermore, the water loss may be very low under this condition [1,35]. Based on measurements at the Desert Peak site, in our study we limit downhole injection pressure buildup to 6.90 MPa and limit production well drawdown to 3.40 MPa [21]. Intermediate depth of the injection perforated interval is 1589 m, corresponding to an initial formation pressure of 12.84 MPa; intermediate depth of the production perforated interval is 1249 m, corresponding to an initial formation pressure of 9.9 MPa. In order to avoid the second reservoir growth, Pinj must be maintained lower than Pc ¼ (12.84 þ 6.90) MPa ¼ 19.74 MPa. For the production well, we assume the bottomhole pressure Ppro is maintained at (9.90e3.40)MPa ¼ 6.50 MPa. Based on current pump technology, production wells are limited to a maximum flow rate of 126 L per second [21]. Then our water production rate of 7 kg/s is feasible from technological viewpoint. In an actual EGS reservoir, some circulating water may be lost into the surrounding rock [1e 3,20,35]. In this work we assume the fracture walls are fully impermeable and there are no water losses. This assumption is consistent with that of other recent studies [36,37].

2.4. Heat production time

Injected or produced fluids

Groove

Fig. 2. Connection method for the well and the fracture. The inside and outside rings are the inside and outside of the steel pipe, with a 20 m long groove in it.

Generally, geothermal energy is regarded as renewable. However, over a normal project life of about 20e30 years, a fractured EGS reservoir will be cooled significantly as a result of heat mining operations, and recovery can take as long as 100 years [38e40]. Regarding this factor we must limit the maximum extent to which the geothermal energy can be exploited. Previous researches have proved that it is best to stop the heat extraction when the average reservoir temperature has declined by 10  C [1], or the production temperature has declined by 10% [3]. However, to fully understand the changing characteristics of production temperature, energy

272

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

For the production system with an injector and a producer, the heat production power is calculated by (1) [41,44]:

with temperature and pressure in the well-reservoir system, in Equations (4)e(6), we adopt the average value of r for analysis. In the reference case, the maximum density is 992.00 kg/m3, the minimum density is 857.00 kg/m3, so the average value of 924.50 kg/m3 is adopted (see Section 4.7). It is readily found that both hh and he increase with r according to (5) and (6), so a sensitivity analysis is conducted to research the influence of water density on system energy efficiency in Section 4.4.


 Wh ¼ q hpro  hinj

3. Numerical models and simulation approach

production, reservoir temperature and pressure, we have modeled the heat production for a period of 20 years in this work. 2.5. Energy production power, water flow impedance and energy efficiency

(1)

where hinj is the injection specific enthalpy, for the reference case hinj ¼ 261.90 kJ/kg; hpro is the bottomhole production specific enthalpy, calculated with bottomhole temperature and pressure of the production well [41]. For long time circulation, the heat transfer between wellbore fluid and surroundings can be ignored, and the wellbore flow can be regarded as isenthalpic [41]. We assume all the produced heat is used for electrical power generation. Based on the second law of thermodynamics, the available work converted from above heat is qðhpro  hinj Þð1  ðTo =Tpro ÞÞ, where To is the heat rejection temperature of 288.75 K at Desert Peak site [21], and To =Tpro is calculated by absolute temperature [21]. If the utilization efficiency factor of available work transferred to electrical power is 0.45 [21], the electrical power We can be calculated by (2):

3.1. The numerical simulation code



 We ¼ 0:45q hpro  hinj 1  To =Tpro

The geological system in this study corresponds to the depth from 1169 m to 1669 m of well DP23-1 at the Desert Peak geothermal field, as shown in Fig. 3a. The geological system consists of three layers: an overburden layer (OB, 1219 m  z  1169 m), a fractured reservoir layer (FR, 1619 m  z  1219 m) and an underburden layer (UB, 1669 m  z  1619 m). Based on experience from the oil and gas industry, the 50 m thickness of overburden and underburden are sufficient to provide accurate estimates of heat and pressure transfer in the reservoir [43,44]. Based on the geological data at well DP23-1, there are many natural joints in the dry rock, so the actual geological system should be classified as a “fractured-porous media” [22e26], which consists of matrix blocks of low permeability and fractures distributed in the network (in other words, a double-porosity system). Rock matrix and fractures may exchange fluid or heat locally by means of “interporosity flow”, which is driven by the difference in pressure or temperature between matrix and fractures. However, because the rock permeability at this site is too low and the water flow mainly takes places within the artificial fracture [22,26], we regard the rock as a porous media with very low single porosity. Fig. 3b shows the discrete grids for the above simulated domain. Because the heat transfer and water flow around the wells changes very quickly, the resolution of the area within 0  x  100 m and 300 m  x  400 m, along with that within 1319 m  z  1219 m and 1619 m  z  1519 m (excluding the overburden and underburden) is blocks of 4 m  4 m. The domain within 100 m  x  300 m is discretized into 40 elements, whose length is 5 m; the domain within 1519 m  z  1319 m is also discretized into 40 elements, whose length is also 5 m. The overburden and underburden is discretized into 10 elements in the vertical direction, respectively. Because the fracture aperture is only 0.002 m, the change of temperature and pressure in the y direction within the fracture is very small, the heat storage and dispersion effects within the fracture are not important, therefore the forced heat convection in the y direction can be neglected [10,12,17,33,34] and the water temperature is controlled by the forced heat convection along the x and z directions and the heat conduction along the onedimensional y direction [17]. In hot rock, the temperature is controlled by the 1-D heat conduction along the y direction, perpendicular to the vertical fracture under high water flowing rate

(2)

The water flow impedance IR (MPa/(kg/s)) is calculated by (3) [2,20]:

IR ¼

Pinj  Ppro q

(3)

IR represents the power consumption of the unit production rate for penetrating the fractured reservoir. The energy efficiency of the system h is defined as the ratio of the total produced thermal energy to the internal energy consumption. The internal energy consumption Wp, mainly includes the energy consumption of the injection pump Wp1 and that of the suction pump Wp2. The injecR tion pump power should be calculated as Wp1 ¼ Pinj dV, where dV is injected water volume per second. Based on Fig. 4, if the energy loss due to duct friction and water internal friction is neglected [41], the pump efficiency hp is 80% [42], thus the injection pump power Wp1 can be calculated as Wp1 ¼ ðqðPinj  rgh1 Þ=ðrhp ÞÞ, whereh1 is the depth of the injection well; the suction pump power Wp2 can be calculated as Wp2 ¼ ðqðrgh2  Ppro Þ=ðrhp ÞÞ, where h2 is the depth of production well. It follows then that the internal energy consumption Wp is (4):

Wp ¼


 q Pinj  Ppro  rqgðh1  h2 Þ

rhp

(4)

The energy efficiency hh based on thermal energy production is (5), and the energy efficiency he based on the electric energy production is (6):


 rhp hpro  hinj Wh  hh ¼ ¼
Wp Pinj  Ppro  rgðh1  h2 Þ

he ¼



 0:45rhp hpro  hinj 1  To =Tpro We 
¼ Wp Pinj  Ppro  rgðh1  h2 Þ

(5)

(6)

The Tpro and Pinj versus time are first calculated, and then hpro ¼ hpro (Ppro, Tpro) versus time is calculated. Based on these and Equations (1)e(6), Wh, We,Wp, IR, hh and he versus time are all calculated, respectively [21]. Because water density r is varying

In this numerical study, we used the TOUGH2-EOS1 code, which has been developed at Lawrence Berkeley National Laboratory. TOUGH2 is a numerical simulator for non isothermal flows of multicomponent, multiphase fluids in one, two and threedimensional porous and fractured media. The conservation equations of mass, momentum and energy are numerically solved by the integral finite difference method [34]. For subsurface water flow, the EOS1 module provides a useful simulation [34]. 3.2. Geometry, domain discretization, and system properties

Y.-C. Zeng et al. / Energy 63 (2013) 268e282 (0,0,-1169)

273

(400,0,-1169)

-1169 50m

Overburden

-1219

Production

-1319

-1419

400m

Fractured reservoir

-1519 Injection (400,0,-1619)

-1619 50m

Underburden

-1669 z(m)

0

100

200

300

400

x(m)

a)

b)

Fig. 3. A schematic of a) the fractured reservoir at DP23-1 and b) the corresponding grid used in the simulation.

[17e19]. To provide the lateral fracture wall with a heat conductive boundary, a semi-analytical method is used to describe heat conduction in the confining hot rock, reducing the dimensionality of the problem from 3-D of the fracture and rock matrix to 2-D of the fracture [45e47]. The TOUGH2 codes provide an easy but very exact approach to implement this method [34]. For the simulated fluid flowing domain within the fracture, there are total 90 blocks along the x direction, 1 block along the y direction and 110 blocks along the vertical direction; the 2D grid system is comprised of 9900 elements, of which 9720 elements are active (the remaining being the uppermost and lowermost boundary cells). The groove of the injection at a depth from 1579 m to 1599 m is discretized to 5 injection cells connecting with the whole gird system, and the injection water is averagely divided into 5 parts for the 5 injection cells. Similarly, the groove of the production at depth from 1239 m to 1259 m is also divided into 5 production cells, from which the heated water is extracted out [34]. Field measurement data from DP23-1 are limited, and a reasonable estimation of the system properties is necessary. The system properties and the initial conditions used in this study are shown in Table 1 [21e27], in which the productivity index is referred to reference [34]. 3.3. Boundary and initial conditions In this work, the fracture aperture is only 0.002 m, heat exchange area perpendicular to the fracture aperture in Fig. 6b is only about 0.0005% of that perpendicular to the fracture wall, so the heat exchange perpendicular to the fracture aperture can be neglected when compared with that perpendicular to the fracture wall. Based on this and the assumption of impermeable rock the left and right sides in Fig. 6b are considered as no-flow for mass and heat. Both fracture walls are regarded as no-flow for mass and only conductive heat transfer by method from Vinsome et al. in Ref. [45] with TOUGH2 codes [34]. The pressures and temperatures of the uppermost and lowermost layers in Fig. 6b are 9.22 MPa, 210  C and 13.53 MPa, 210  C, respectively, and all are constant during the entire heat production period. Based on the measurements of static temperature and pressure in 2002, we neglect the temperature variance within depths from 1169 m to 1669 m and assume the initial average reservoir

temperature is 210  C [22]. For the pressure, we take P ¼ 0.00862z0.85678 (MPa) as the initial value according to the relationship between pressure and depth [22]. 4. Heat production through a single vertical fracture at Desert Peak field 4.1. The reference case As shown in Table 1, in the reference case, the water injection rate is 7 kg/s, and the injection temperature is 60  C. The bottomhole pressure at production well is 6.50 MPa, and the productivity index is 5  1012 m3. In our study we performed the heat production for 20 years. 4.2. Temperature and specific enthalpy production Fig. 4 shows the evolution of Tpro and hpro during the 20 years of production. It can be readily found the whole production process Table 1 Actual and assumed reservoir parameters at site DP23-1 in Desert Peak field [21e 27,34]. Parameter

Value

Rock thermal conductivity Rock specific heat Rock density Rock porosity Rock permeability Fracture height Fracture length Fracture aperture Fracture porosity Fracture permeability Overburden thickness Overburden top surface pressure Underburden thickness Underburden bottom surface pressure Injection rate (reference case) Injection specific enthalpy (reference case) Productivity index Production flow pressure Initial temperature Initial pressure

2.395 W/(m K) 1100 J/(kg K) 2850 kg/m3 0.02 0 400 m 400 m 0.002 m 0.6 400  1012 m2 50 m 9.22 MPa (constant) 50 m 13.53 MPa (constant) 7 kg/s 261.90 kJ/kg (about 60  C) 5  1012 m3 6.50 MPa 210  C P ¼ 0.00862z0.85678 (MPa)

274

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

can be divided into two stages: a stable stage and a declining stage based on the variance of Tpro and hpro [21,48]. In the stable stage, Tpro attains a maximum level of 210  C since the production begins, and this level lasts for about 1 year; the corresponding hpro maintains at a maximum level of about 899.40 kJ/kg because Ppro is kept at a constant level of 6.50 MPa. During the following declining stage, Tpro begins to decline from 210  C and reaches at a final minimum of 146.93  C at the end of the production, reduced by about 30.03%; hpro gradually reduces from 899.40 kJ/kg to the finial minimum of 622.83 kJ/kg, reduced by about 30.75%. If we take the 10% drawdown of Tpro to cease the production, lifetime of the project is only about 5.10 years [3]. Consequently, in the reference case, the single fracture system can’t strictly support the heat mining for a lifetime of 15e20 years for commercial objectives. Wu et al. developed a semi-analytical model for the single fracture model to calculate the enthalpy production and thermal recovery efficiency based on similar assumptions [49]. In his study, the semiinfinite matrix is revised to finite matrix because of symmetry, however the fluid density and viscosity are assumed as constant under reservoir conditions, and the influences of this constant density and viscosity assumptions on heat production performance have not been assessed in previous analytical solutions [32,49e52]. It can be readily found that the change pattern of hpro in Fig. 4 is very close to that in Ref. [49] from both numerical and semianalytical solution, except the durations of the stable stage are different arising from the difference of operational conditions. Fig. 5 shows the comparison of dimensionless Tpro between this work and [17], in which Tpro is normalized by TD ¼ ðTpro  Tinj Þ=ðTr  Tinj Þ, where Tr ¼ 210  C and Tinj ¼ 60  C. It can be readily found that the durations of stable stage in three cases are all 1 year. In the declining stage, TD decreases much slower than the two situations in Refs. [17]; at the end of production, TD in this work reaches at 0.58, reducing by about 42.0%, while TD of the 2-D conduction case in Ref. [17] decreases by 43.3%, our work shows a final 1.3% higher TD than the 2-D conduction case in Refs. [17], and a final 9.8% higher TD than the 1-D conduction case. Under similar conditions, this effect may arise from the diagonal flow from the injector to the producer in this work, because different from the parallel flow along the fracture from the injector to the producer in Refs. [17], the diagonal flow path is relatively much longer and this prolongs the hydraulic retention time in the fracture, allowing the water to extract more heat in the rock. Indeed, we can conclude that the use of correct of reservoir geometryis important in predicting the production temperature and lifetime of a HDR (hot dry rock) reservoir [17].

Fig. 4. Evolution of Tpro and hpro during the 20 year period.

Fig. 5. Comparison of dimensionless Tpro between this work and reference [17].

4.3. Injection pressure and water flow impedance Fig. 6 shows the evolution of Pinj and IR during the 20 year period. In the first year of stable stage, Pinj quickly increases from 14.51 MPa to 17.73 MPa, meanwhile Ppro remains at 6.50 MPa throughout, so IR goes up from 1.14 MPa/(kg/s) to 1.60 MPa/(kg/s). During the following declining stage, Pinj continually increases from 17.73 MPa to the ultimate maximum of 19.98 MPa slowly, and the corresponding IR gradually goes up from 1.60 MPa/(kg/s) to the ultimate maximum of 1.93 MPa/(kg/s). During the whole production, IR increases to 1.69 times the initial value, and maintains a level of about 11.4e19.3 times the commercial standard (0.1 MPa/ (kg/s)); the maximum Pinj attains 19.98 MPa, very slightly higher than the Pc ¼ 19.74 MPa. When water flows through the fracture, based on Darcy’s law, the flow impedance IR can be calculated as (7) [1,29]:

IR ¼

mL krA

(7)

where m, L, k, A is the average water viscosity, flow path length, permeability and cross-sectional area of flow path, respectively. It’s obvious that L, k, A in this study are basically constant, so we deduce that it is the change of m=r that causes the continual increase of IR. In TOUGH2-EOS1 module, water viscosity m is computed with the equation of state m ¼ m(p,T), and m is strongly dependent on temperature when P ranges from 6.50 MPa to 20.00 MPa [34]. The

Fig. 6. Evolution of Pinj and IR during the 20 year period.

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

variation range of the temperature is from 60  C to 210  C, and that of the pressure is from 6.50 MPa to 20.00 MPa in this study. Fig. 7 shows the change of m=r versus water temperature with pressure ranging from 6.50 MPa to 18.50 MPa, and it can be readily found m=r clearly increases with temperature decreasing, and m=r is basically not influenced by pressure within our study range [36,41,51]. So, it can be concluded that as heat production goes on, the average reservoir temperature declines gradually, and the water temperature goes down gradually, which causes m=r to increase with time, and this finally arouse the continual increasing of Pinj and IR. These accord well with [36,53]. In fact, in order to increase the expansivity of working fluid to generate large density difference between wells and provide more buoyancy force to reduce the pump power consumption, and in order to lower viscosity to yield larger flow velocities for a given pressure gradient, Pruess has proposed to adopt CO2 as working fluid for generating renewable energy with simultaneous sequestration of carbon [41]. So the sensitive change of viscosity with temperature has a significant influence on the productivity of EGS reservoir [36]. 4.4. Power production and energy efficiency In our numerical model, h1 ¼ 1599 m andh2 ¼ 1259 m. The average value of r ¼ 924.50 kg/m3 is adopted in Equations (4)e(6). Fig. 8 shows the evolution of Wh, We, Wp, hh and he in the 20 year period. In the first year of stable stage, Wh maintains at a constant level of 4.46 MWa, We maintains at a constant level of 0.81 MWa because the Tinj, Tpro, hinj and hpro are all basically constant. As a result of the increasing of IR, based on Equation (4), Wp gradually increases from 0.05 MWa to 0.08 MWa. During the following declining stage, as a result of continual decreasing of Tpro and hpro, Wh decreases from 4.46 MWa to a final minimum of 2.53 MWa, We decreases from 0.81 MWa to a final minimum of 0.36 MWa, and Wp increases from 0.08 MWa to a final maximum of 0.10 MWa. The continual decline of We will cause many problems for the operation and management of the surface power plant, so this energy production profile is not satisfactory enough [21]. Compared with the commercial standards (see Section Section 1.3) a level of 0.81e 0.36 MWa of We is too low: the maximum of 0.81 MWa is only about 23.14% of 3.50 MWa. As a result of continual increasing of IR and Wp, both hh and he declines with heat production. In the first 1 year of stable stage, due to the very quick increasing of IR, hh sharply decreases from 99.03 to 57.70, and the corresponding he decreases from 17.93 to 10.43. During the following declining stage, hh gradually decreases from

Fig. 7. Change of m=r with water temperature T and pressure P.

275

Fig. 8. Evolution of power production and energy efficiency during the 20 year period.

57.70 to the final minimum of 25.68, and the corresponding he decreases from 10.43 to the final minimum of 3.61. So both energy efficiency are far higher than 1, showing a very promising prospect of energy production. Fig. 9 shows the sensitivity of he to the water density. From Equations (4)e(6), the water density may influence the energy efficiency. As the water density increases, he becomes larger. An increment of r from 924.50 kg/m3 to 992.00 kg/m3 results in an increment of he from level of 17.93e3.61 to 20.19e3.96, increased by about 12.60%e9.66%; a decrement of r from 924.50 kg/ m3 to 857.00 kg/m3 results in a decrement of he from level of 17.93e 3.61 to 15.87e3.28, reduced by about 11.49%e9.14%. So even the error induced by the variance of water density in Equations (4)e(6) is considered, relative error of he is still within 15.00%, and he is still higher than 1. 4.5. Spatial distribution of temperature Fig. 10 shows the evolution of temperature distribution over the 20 year period. Some nested annular regions of low temperature are formed around the injection well in the initial stage, and the radii of the temperature annulus increase with time. The heat production process corresponds to the expansion process of the annular low temperature regions in the early stable stages (Fig. 10aec). This marks the geothermal energy around the production well is extracted first, when the heat reserve in the rock around the production well is not influenced (the cold front has not

Fig. 9. Sensitivity of he to the water density.

276

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

Fig. 10. Evolution of the spatial distribution of temperature during the 20 year period.

broken through the fractured reservoir). When the radius of the temperature annulus increases to about 320 m (Fig. 10c), the isothermals begin to bulge out towards the production well (Fig. 10ce e), the temperature near the production well begins to decline, and the low temperature area finally expands to the whole reservoir (Fig. 10eei). One important characteristic of the declining stage is that the rock temperature around the producer is affected by heat production process and continually decreases (the cold front has broken through the fractured reservoir).

It is worth noting that in Fig. 10 the left and right boundaries are considered as no-flow for mass and heat in this work, as stated above due to the too small heat transfer area and impermeable rock. We can find the cold areas in Fig. 10aef are strictly inside the fracture, and the cold front has never reached the right boundary, so during this period the numerical simulation is quite accurate. However, since about 10.45 years later, the cold front has reached the right boundary, and this will cause slight boundary effect and arouse a little simulation errors. In this work this slight boundary

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

effect is neglected. Strictly, for exact modeling the temperature field, the model domain should be much larger to include some impermeable rock in the left and right sides of the fracture. Due to the impermeable rock, highly accurate modeling of the boundary temperature field will require large numbers of grid blocks, causing expensive calculation and storage [34,45]. Studies of Pruess et al. prove that it is reasonable to neglect this conductive heat exchange from impermeable rock [44], so in this work we neglect the slight boundary effect and still perform the simulation for 20 years. Fig. 11 shows a comparison of temperature evolution along the fracture from inlet to outlet between this work and [17], where LD ¼ ðx=Lf Þ is the dimensionless distance from the inlet to the outlet of the fracture system. In Refs. [17], fracture length ¼ 300 m; in this work, Lf ¼ 524.9762 m is the distance from point (0 m, 0.001 m, 1589 m) to point (400 m, 0.001 m, 1249 m). It can be found the temperature at outlet decreases with time, continually changing the temperature profile along the fracture. Within the range from 0.7 to 1 of LD, this model simulates basically the same temperature with [17], greatly supporting our results. Especially, this greatly prove the reliability of predicting Tpro, as shown in Fig. 8. Within range of LD from 0 to 0.7, our model simulates lower temperature than [17], especially around the injection well. This may arise from the geometry of injection-production method. In Refs. [17], the water is injected into the reservoir through all height of the fracture, while in this work, as shown in Fig. 3a, the water is injected through only the partial height of the fracture, namely the perforated interval, and the latter is obviously much closer to practice [1,30]. Under conditions of this work, the injected cold water is all concentrated around the shorter perforated interval of the fracture height, with a much higher heat convection rate between the water and the confined rock, so near the injecting interval, the heat extraction rate is much higher than [17], forming a relatively lower temperature zone near the injection interval, shown as Fig. 11. 4.6. Spatial distribution of pressure Fig. 12 shows the evolution of the spatial distribution of pressure during the 20 year production period; the two white horizontal lines represent the boundaries between the overburden or underburden and the reservoir. Similar to the evolution of the temperature field, some nested annular regions of high pressure are formed around the injection well in the initial stage (Fig. 12aec), and the radius of the pressure annulus goes up in correspondence with the entire heat production process (Fig. 12aei). At the same time, the

Fig. 11. Comparison of temperature evolution along the fracture from inlet to outlet between this work and [17].

277

pressure near the production well basically maintains unchanged as the process continues as a result of constant production backpressure of 6.50 MPa. Therefore, the average reservoir pressure gradually increases with the entire production process going on. As mentioned above, Pinj attains a maximum value of 19.98 MPa. In actual fracture system, thermally induced stress increases the fracture aperture near the injection point and water pressure at this point is greatly reduced, so the actual bottomhole injection pressure will be much lower than this simulation [6]. Because the permeability of the overburden and the underburden is considered to be 0, the pressure within those areas remain unchanged during the entire production period, as shown in Fig. 10aei and Fig. 12aei. 4.7. Spatial distribution of water density Fig. 13aei shows the evolution of the spatial distribution of water density during the 20 year production period. Due to the fact that the pressure around the injection well is highest and the temperature is lowest, as shown in Figs. 10 and 12, the water density around the injection well reaches at maximum. Some nested annular regions of high density are formed around the injection interval in the initial stage, and the radius of the density annulus goes up with time because of the migrations of cold front and high-pressured front in Figs. 10 and 12. In other words, the heat production process is driven by the expansion process of the annular high density regions during the early stage (Fig. 13aec). When the radius of the density annulus increases to about 340 m (Fig. 13c), the isodenses begin to bulge out towards the production well (Fig. 13def), and at last the high density area is full of the fracture (Fig. 13gei). On the whole, we can see the water density in the fractured reservoir ranges from 857 kg/m3 to 992 kg/m3, the previous r ¼ 924.50 kg/m3 is within a reasonable range, and the constant density assumption in the fracture in Refs. [5e7,17e19] is not exact in fact. The sensitivity analysis of energy efficiency to water density in Section 4.4 shows that he is indeed greater than 1 even the error from water density is taken into considerations. 4.8. Comparing the reference case with the actual EGS tests Comparation of production performance between the reference case and EGS field tests is shown in Table 2 [1,3,20]. Strictly speaking, the single fracture system can only operate for 5.1 years according to commercial requirements (see Sections 1.3 and 4.2). Though this period is far less than 20 years, it is still comparable with the actual EGS tests. Tpro, q and IR during this period are all within the observed range of field EGS, so, to a great extent, the single fracture system in our study is technically feasible. However, it may be that the effective stimulated volume controlled by a single fracture is too small, and then Tpro declines quickly after the first 5.1 years of heat extraction [1,3,20,21]. The novel single fracture system attains a thermal power of 4.46e2.53 MW, an electrical power of 0.81e0.36 MW with a total pump power of 0.05e0.10 MW, arriving at an electrical efficiency of 17.93e3.61 and a thermal efficiency of 99.03e25.68 in 20 years at a water production rate of 7 kg/s and a reservoir impedance of 1.14e1.93 (MPa/(kg/s)). According to Evans’s suggestions, a double wells system should attain 0.50 MWt/ (kg/s) or 0.07 MWe/(kg/s) in 20 years [20], and this novel system attains 0.64e0.36 MWt/(kg/s) and 0.12e0.05 MWe/(kg/s), thus a too much shorter lifetime of the single fracture system is key barrier to develop such a system. However, Wu et al. proved that the enthalpy production from the fracture network is the summation of enthalpy production of individual fractures making up the actual networks [49], so actual energy production power from HDR reservoir must be higher than the novel single fracture system and the actual lifetime will also be pronged to sustain the heat production [20].

278

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

Fig. 12. Evolution of the spatial distribution of pressure during the 20 year period.

Although a multiply fracture system provides a more efficiency mechanism for heat extraction than a single fracture in HDR [14], the above analysis on productivity of single fracture is still very useful for understanding the heat mining process. 5. Sensitivity analysis of heat production through a single vertical fracture In this work, we investigate the sensitivity of heat production through a single vertical fracture to the following conditions and parameters: the fracture porosity, 4; the fracture permeability, k; the rock heat conductivity, l; the water production rate, q; and the injection temperature, Tinj. Based on the reference case (r), we have researched the following 5 scenarios: (a) increasing 4 to 4 ¼ 0.8; (b) increasing k to k ¼ 600  1012 m2 (1D ¼ 1.0  1012 m2); (c) increasing l to l ¼ 3.5 W/(m K); (d) reducing q to q ¼ 5 kg/s; (e) increasing Tinj to Tinj ¼ 80  C (increasing hinj to hinj ¼ 345.13 kJ/kg). Figs. 14e16 show the results of sensitivity analysis, and Table 3

shows the maximum, minimum and average water density in different scenarios for calculation the electrical energy efficiency he. 5.1. Sensitivity to 4 In this study, we assume the porosity is independent of the permeability [34], although previous investigations have proved the fracture permeability is empirically correlated to fracture aperture and porosity of the fracture [54]. Figs. 14ae16a show the dependence of We, IR and hh on 4, respectively. We can find We, IR and he at 4 ¼ 80% is basically the same as those in the reference case (4 ¼ 60%). This is because in this work the fracture permeability is assumed independent of porosity, and an increment of 4 doesn’t influence the flowing conditions for the forced convection confined within the fracture. Therefore the estimated value of 4 can be used for the numerical simulation and the fracture porosity 4 has only very slight effect on heat production through a single vertical fracture.

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

279

Fig. 13. Evolution of the spatial distribution of water density during the 20 year period.

5.2. Sensitivity to k Figs.14be16b show, respectively, the dependence of We, IR and he on the fracture permeability k. Fig.14b shows We is slightly increased by the increment of k from 400  1012 m2 to 600  1012 m2. Obviously, this will be correct only when k varies within a certain range. If the facture aperture exceeds a certain limit, causing the fracture permeability be too large and water retention time too short, Tpro will decline quickly. This is the so-called “short circuit”,

and it will greatly damage the EGS reservoir [1,6,20]. Therefore, the fracture permeability k cannot exceed a certain limit [1,20]. Fig. 15b shows that IR is greatly reduced with an increased k. This can be deduced from Equation (7). However, similar to Fig. 14b, a precondition is that k must be within a certain range. Fig. 16b shows he will be obviously improved with increased k. This is mainly because IR is reduced with increased k, thus Pinj is also declined based on Equation (3) (Ppro is a constant 6.50 MPa in this work), and it follows that he is obviously improved according to the Equation (6).

280

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

Table 2 Comparison of water temperature, flow, impedance and loss for specific locations and the conditions used in this work. EGS field test project

Tpro ( C)

q IR Water (kg/s) (MPa/(kg/s)) loss

Heat production target Fenton Hill, New Mexico (1972e1996) Shallow 2-well reservoir (2.8 km): 282 days circulation Deep 2-well reservoir (4.2 km): 112 days circulation Rosemanowes, UK (1978e1991) 3-well reservoir (2.2 km): about 200 days circulation Hijiori, Japan (1985e2002) Shallow 4-well reservoir (1.8 km) 90 days circulation Deep 3-well reservoir (2.2 km) 10 month circulation Soultz, France (1987-present) Shallow reservoir (2.9e3.5 km) 120 days circulation In this work single fracture reservoir (1.2e1.7 km) 5.1 years circulation

180

40

0.2

10% of q

155

5.5

1.7

10%

183

5.7

4.0

16%

70

16

0.6

21%

165

12.8

0.4e0.7

23%

180

5.8

1.4e2.1

64%

0.2

0

1.14e1.93

0

135

210e190

25

7

To sum up, though We won’t be obviously improved when k increases, the internal energy consumption of pumps Wp will be greatly reduced, and thus he will be greatly improved. Therefore, that it’s very important to control and stimulate the fracture permeability only to a specific extent [1e3]. 5.3. Sensitivity to l

Fig. 15. Sensitivity of water flow impedance to various parameters.

with rock, the convective heat transfer is dominated, so the rock heat conductivity has only very slight effect on the heat production performance [1,25]; the stable stage will last much longer and the reduction in productivity over time will be much weaker [1,25]. Fig. 15c shows that IR declines as l increases. Similarly, this is because the water temperature is raised and at the same time m=r is reduced. As discussed above, the reduction of IR represents the drop of the internal energy consumption Wp, meanwhile We is increased, so he is improved to some extent, just as shown in Fig. 16c. 5.4. Sensitivity to q

Figs. 14ce16c show, respectively, the dependence of We, IR and he on the rock heat conductivity l. Fig. 14c shows that We is obviously increased as l increases from 2.395 W/(m K) to 3.5 W/(m K). This is because a higher l scenario increases the heat transfer rate conducted to the fracture wall which is then transferred to the flowing water at the same time, thus slowing down the decline rate of Tpro (with the result that the water temperature is increased), and this effect finally improves We. We can find that limitation of this kind of geothermal is the conductivity of heat through the rock of the specific formation, and this limitation makes this kind of geothermal unlikely for large scale production of electricity only through single or few fractures. So the stable stage only lasts for about 1 year and then the electric power begins to decline quickly. However, in natural hydrothermal system or fully fractured rock reservoir, the water within the aperture network is fully contacting

Figs.14de16d show, respectively, the dependence of We, IR and he on the water production rate q. Fig. 14d shows that the initial maximum of We is reduced and the ultimate minimum of We is increased when q is reduced from 7 kg/s to 5 kg/s, so the production profile of We versus time becomes more stable. This is because a lower q means a longer time of higher Tpro, based on Equations (1) and (2) We will be increased to some extent. This is beneficial to the operation and management of the surface power plant [21]. Fig.15d shows that a lower q means a lower IR. This is because a lower q means a higher average temperature of water, and thus a lower water viscosity m. So the energy efficiency of the system is greatly improved, just as shown in Fig. 16d. Fundamentally, a lower q means a much lower Pinj and a much higher Tpro, thus, based on Equations (5) and (6), the energy efficiency of the system is greatly improved.

Fig. 14. Sensitivity of electric power production to various parameters.

Fig. 16. Sensitivity of electrical efficiency to various parameters.

Y.-C. Zeng et al. / Energy 63 (2013) 268e282 Table 3 Maximum, minimum and average water density in different scenarios (kg/m3). Scenarios

Maximum density

Minimum density

Average density

(r) (a) (b) (c) (d) (e)

992.00 992.00 991.00 992.00 991.00 980.00

857.00 857.00 857.00 857.00 857.00 857.00

924.50 924.50 924.00 924.50 924.00 918.50

5.5. Sensitivity to Tinj Figs. 14ee16e show, respectively, the dependence of We, IR and he on the injection temperature Tinj. Fig. 14e shows that a higher Tinj means a lower We, this is because under this condition the variance of Tpro is very small, and it follows that Wh and We will be reduced based on Equations (1) and (2) when hinj is increased from 261.90 kJ/ kg to 345.13 kJ/kg while hpro basically keeps unchanged. Because Tinj is the lowest temperature in the reservoir, a higher Tinj means a higher average temperature of flowing water and lower water m=r, and thus means a lower IR, just as shown in Fig. 15e. However, he changes very little when both We and IR are declined, just as shown in Fig. 16e. So both We and IR decreases significantly with increased Tinj, while the effect of the increased Tinj on hh is very slight. 6. Model validation The above results are shortly verified from two aspects as follows. 6.1. Reliability of TOUGH2 code As stated in the userguide of TOUGH2 in Refs. [34], the accuracy of the code has been tested by comparison with many different analytical and numerical solutions, with results from laboratory experiments, and with field observations. With proper grid refinement around the well, the simulation results are greatly reliable. 6.2. Comparison with previous model and test results As stated above in Section 4.2, the pattern of production profile of hpro is very similar to that in Refs. [49]; in Section 4.5, Tpro is detailedly compared with that in Refs. [17]; and the results can greatly support our simulation results. In Section 4.8, the main performance parameters are compared with that from actual field tests and the modeled values are all within reasonable ranges. 7. Conclusions In this work, we numerically investigated the heat production potential from hot dry rock by water circulating through a novel single vertical fracture at site DP23-1 in Desert Peak geothermal field. A completely technically feasible fracture aperture of 2 mm is assumed. Based on the results of this study, the following conclusions are drawn: (1) In the reference case, the stable production stage lasts for about 1 year, and this reveals a tendency for stable heat extraction; during the declining stage, Tpro declines from 210  C to a final 146.93  C, and the corresponding hpro reduces to a final 622.83 kJ/kg. The diagonal flow path is relatively longer and this prolongs the hydraulic retention time in the fracture, allowing the water to extract more heat from the rock.

281

(2) In the reference case, Pinj increases from 14.51 MPa to a final maximum of 19.98 MPa, and IR goes up from 1.14 MPa/(kg/s) to a final maximum of 1.93 MPa/(kg/s). IR maintains a level of approximately 11.4e19.3 times the commercial standard, so the water flow impedance is very high for economic exploitation. (3) The reservoir temperature around the injection well declines gradually, this arouses a continuous increase of water viscosity, so water flow impedance continually increases with time. (4) In the reference case, the single fracture system attains an electrical power of 0.81e0.36 MW, a pump power of 0.05e 0.10 MW and an electrical efficiency of 17.93e3.61. The energy efficiency gradually declines during the heat production. (5) In the stable stage, the cold front has not broken through the reservoir and in the declining stage that has broken through the whole reservoir. (6) Analysis of sensitivity to k indicates that k is one of the most important factors that affect the project’s heat production performance. Though the electric power will not improve when k increases within a certain range, the pump power will be greatly reduced, and thus the energy efficiency will be greatly improved. (7) Analysis of sensitivity to l indicates that dry rock with higher heat conductivity will show better production performance as it provides more favorable conditions for heat transfer. In general, a higher l is associated with higher We and more favorable IR and he. (8) Analysis of sensitivity to q indicates that q is one of the most important factors that affect the heat production performance. A reasonable decrease of q will result in an obvious increase of We during a relative stable production stage and also a decrease of IR, which is more favorable for heat production from HDR. (9) Analysis of sensitivity to Tinj indicates that an increased Tinj has positive effect in reducing IR, but the energy efficiency will be only slightly influenced as higher Tinj involves less We. The results of the reference case and the sensitivity analysis show that desirable hh level can be obtained, but We of the single fracture system is too low and IR is too high compared with the commercial standards, because the single fracture system can only provide a low water production rate. Furthermore, sensitivity analysis indicates that heat production performance could be improved under more favorable conditions (including relatively higher k, larger l and reasonable q). Specifically, the facture permeability k and water production rate q are the most important parameters that affect the heat production performance. However, rock contraction from temperature reduction and watererock interaction effect are not taken into considerations in this work, so further discussion and analysis are needed from different perspectives to investigate the detailed process and mechanism of water circulating and heat mining through a single vertical fracture in the Desert Peak geothermal field. Acknowledgments This work was financially supported by the National High Technology Research and Development Program of China (Grant 2012AA052802); the Director Fund Projects of the Guangzhou Institute of Energy Conversion, the Chinese Academy of Sciences (Grant y107a41001); the Postdoctoral Start-up Fund of the Chinese Academy of Sciences (Grant y107b11001); the Science and Technology Innovation Special for Graduate Student, Chinese Academy of Sciences (Grant y207y81001).

282

Y.-C. Zeng et al. / Energy 63 (2013) 268e282

References [1] Tester JW, Livesay B, Anderson BJ, Moore MC, Bathchelor AS, Nichols K, et al. The future of geothermal energy: impact of enhanced geothermal systems (EGS) on the United States in the 21st century. An assessment by an MIT-led interdisciplinary panel; 2006. [2] Tenzer H. Development of hot dry rock technology. GHC bulletin; 2001. p. 14e22. [3] Baria R, Baumgärtner J, Rummel F, Pine RJ, Sato Y. HDR/HWR reservoir: concepts, understanding and creation. Geothermics 1999;28:533e52. [4] Hayashi K, Willis-Richards J, Hopkirk RJ, Niibori Y. Numerical models of HDR geothermal reservoirs- a review of current thinking and progress. Geothermics 1999;28:507e18. [5] Bataillé A, Genthon P, Rabinowicz M, Fritz B. Modeling the coupling between free and forced convection in a vertical permeable slot: Implications for the heat production of an enhanced geothermal system. Geothermics 2006;35: 654e82. [6] Ghassemi A, Nygren A, Cheng A. Effects of heat extraction on fracture aperture: a poro-thermoelastic analysis. Geothermics 2008;37:525e39. [7] Ogino F, Yamamura M, Fukuda T. Heat transfer from hot dry rock to water flowing through a circular fracture. Geothermics 1999;28:21e44. [8] A feasibility study of a geothermal power plant. American oil shale corporation and U.S. atomic energy commission. PNE-1550, Washington, D.C; 1971. [9] Robinson ES, Potter RM, Mcinteer BB, Rowley JC, Armstrong DE, Mills RL, et al. A preliminary study of the nuclear subterrange. Rep.LA-4547. Los Alamos, N. Mex.: Los Alamos Sci. Lab.; 1971. [10] Harlow FH, Pracht WE. A theoretical study of geothermal energy extraction. J Geophys Res 1972;77(35):7038. [11] Raleigh CB, Witherspoon PA, Gringarten AC, Ohnishi Y. Multiple hydraulic fracturing for the recovery of geothermal energy (abstract). Eos Trans AGU;1974;55(4):4026. [12] Bodvarsson G. On the temperature of water flowing through fracture. J Geophys Res 1969;74:1987e92. [13] Bodvarsson G. Thermal problem in the siting of reinjection wells. Geothermics 1972;1:63e6. [14] Gringarten AC, Witherspoon PA, Ohnishi Y. Theory of heat extraction from fractured hot dry rock. J Geophys Res 1975;80(8):1120e4. [15] Abé H, Mura FT, Keer LM. Growth rate of a penny-shaped crack in hydraulic fracturing of rocks. J Geophys Res 1976;81:5335e40. [16] Wunder R, Murphy H. Thermal drawdown and recovery of singly and multiply fractured hot dry rock reservoirs. Los Alamos, New Mexico: Los Alamos Scientific Laboratory of the University of California; 1978. [17] Cheng AH, Ghassemi A, Detournay E. Integral equation solution of heat extraction from a fracture in hot dry rock. Int J Numer Anal Methods Geomech 2001;25:1327e38. [18] Ghassemi A, Zhang Q. Porothermoelastic analysis of the response of a stationary crack using the displacement discontinuity method. J Eng Mech 2006;132(1):26e33. [19] Sutter D, Fox DB, Anderson BJ, Koch DL, Rohr PRV, Tester JW. Sustainable heat farming of geothermal systems: a case study of heat extraction and thermal recovery on a model EGS fractured reservoir. In: Proceedings in Thirty-Sixth workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, January 31eFebruayr 2, 2011. [20] Evans K. Enhanced/engineered geothermal system: an introduction with overviews of deep systems built and circulated to date. In: China geothermal development forum. Beijing Sep. 13, 2010. p. 395e418. [21] Sanyal SK, Butler SJ. An analysis of power generation prospects from enhanced geothermal systems. In: Proceedings of world geothermal congress 2005, Antalya, Turkey 2005. [22] Robertson-Tait A, Morris C, Schochet D. The Desert Peak East EGS project: a progress report. In: Proceedings world geothermal congress. Antalya, Turkey 24e29 April, 2005. [23] Carlson SR, Roberts JJ, Detwiler RL, Burton EA, Robertson-tait A, Morris C, et al. Fracture permeability evolution in rock from the Desert Peak EGS Site. In: Geothermal resources council annual meeting. CA, United States: Palm Springs; 2004. [24] Lutz SJ, Schriener A, Schochet D, Robert-Tait A. Geological characterization of pre-tertiary rocks at the Desert Peak East EGS project site, Churchill County, Nevada. Geotherm Resour Counc Transac 2003;27:865e70. [25] Zeng YC, Su Z, Wu NY. Numerical simulation of heat production potential from hot dry rock by water circulating through two horizontal wells at Desert Peak geothermal field. Energy 2013;56:92e107. [26] Stage-gate Review. Desert Peak EGS Project-Department of Energy. 2009. In: http://www1.eere.energy.gov/geothermal/pdfs/desert_peak_stage_gate_ review_2008.pdf, 2011.

[27] United States Department of Energy. EGS program review. Technical feasibility of an EGS development at Desert Peak, Nevada. In: DOE EGS program review. Marriott Denver West-Golden, Colorado 2006. [28] Hammond AL. Dry geothermal wells: promising experimental results. Science 1973;182:43. [29] ZHAO YS, WAN ZJ, Kang JR. Introduction to HDR geothermal development. Beijing: Science Press; 2004 [in Chinese]. [30] Ghassemi A, Tarasovs S, Cheng AHD. A 3-D study of the effects of thermomechanical loads on fracture slip in enhanced geothermal reservoirs. Int J Rock Mech Min Sci 2007;44:1132e48. [31] Polsky Y, Capuano L, Finger J, Huh M, Knudsen S, Chipmansure AJ, et al. Enhanced geothermal systems (EGS) well construction technology evaluation report. Sandia National Laboratories; 2008. [32] Murphy H, Brown D, Jung R, Matsunaga I, Parker R. Hydraulics and well testing of engineered geothermal reservoirs. Geothermics 1999;28:491e506. [33] Pruess K, Bodvarsson GS. Thermal effects of reinjection on geothermal reservoirs with major vertical fractures. Soc Pet Eng 1984;36(9):1567e78. [34] Pruess K, Oldenburg C, Moridis G. TOUGH2 user’s guide, version 2.0. Berkeley, CA, USA: Lawrence Berkeley National Laboratory; 1999. [35] Brown DW. Hot dry rock geothermal energy: important lessons from Fenton Hill. In: Proceedings in thirty-fourth workshop on geothermal reservoir engineering. Stanford, California: Stanford University; February 9-11, 2009. [36] Mcdermott CI, Randriamanjatosoa AR, Tenzer H, Kolditz O. Simulation of heat extraction from crystalline rocks: the influence of coupled processes on differential reservoir cooling. Geothermics 2006;35:321e44. [37] Shaik AR, Rahman SS, Tran NH, Tran T. Numerical simulation of fluid-rock coupling heat transfer in naturally fractured geothermal system. Appl Therm Eng 2011;31:1600e6. [38] Elsworth D. Theory of thermal recovery from a spherically stimulated HDR reservoir. J Geophys Res 1989;94(B2):1927e34. [39] Elsworth D. A comparative evaluation of the parallel flow and spherical reservoir models of HDR geothermal systems. J Volcanol Geotherm Res 1990;44:283e93. [40] Rybach L, Mégel T, Eugster WJ. At what time scale are geothermal resources renewable? In: Proceedings in World Geothermal Congress 2000, KyushuTohoku, Japan, May 28eJune 10, 2000. [41] Pruess K. Enhanced geothermal system (EGS) using CO2 as working fluid-A novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics 2006;35:351e67. [42] Davis AP, Michaelides EE. Geothermal power production from abandoned oil wells. Energy 2009;34:866e72. [43] Moridis GJ, Kowalsky MB, Pruess K. Depressurization-induced gas production from class 1 hydrate deposits. SPE Reserv Eval Eng 2007;10:458e81. [44] Pruess K. On production behavior of enhanced geothermal systems with CO2 as working fluid. Energy Convers Manag 2008;49:1446e54. [45] Vinsome PKW, Westerveld J. A simple method for prediction cap and base rock heat losses in thermal reservoir simulators. J Can Pet Technol 1980;19(3): 5. http://dx.doi.org/10.2118/80-03-04. [46] Pruess K, Wu YS. A semi-analytical method for heat sweep calculations in fractured reservoirs. In: Proceedings in thirteenth workshop on geothermal reservoir engineering, Standford University, Stanford, California, January 19e 21, 1988. [47] Pruess K, Wu YS. A new semi-analytical method for numerical simulation of fluid and heat flow in fractured reservoirs. SPE Adv Technol Ser 1993;1(2): 63e72. [48] Brown D, DuTeaux R, Kruger P, Swenson D, Yamaguchi T. Fluid circulation and heat extraction from engineered geothermal reservoirs. Geothermics 1999;28:553e72. [49] Wu X, Pope GA, Shook GM, Srinivasan S. Prediction of enthalpy production from fractured geothermal reservoirs using partitioning tracers. Int J Heat Mass Transf 2008;51:1453e66. [50] Lauwerier HA. The transport of heat in an oil layer caused by the injection of hot fluid. Appl Sci Res 1955;5(2e3):145e50. [51] Kocabas I. Geothermal reservoir characterization via thermal injection backflow and interwell tracer testing. Geothermics 2004;34:27e46. [52] Bodvarsson GS, Tsang CF. Injection and thermal breakthrough in fractured reservoirs. J Geophys Res 1982;87(B2):1031e48. [53] Watanabe K, Niibori Y, Hashida T. Numerical study on heat extraction from supercritical geothermal reservoir. In: Proc World Geotherm Congr. KyushuTohoku, Japan 2000. [54] Rossen WR, Gu Y, Lake LW. Connectivity and permeability in fracture networks obeying power-law statistics. SPE 59720. In: Proceedings of the 2000 Permian Basin Oil and Gas Recovery Conference, Midland, TX, March 21e23, 2000.