![Schematic diagram of the injection-production system in a vertical fracture [38].](https://www.researchgate.net/profile/Sanbai-Li/publication/332415170/figure/fig1/AS:747908324405250@1555326648929/Schematic-diagram-of-the-injection-production-system-in-a-vertical-fracture-38_Q320.jpg)
![Comparison of simulation results of temperature distributions after 5 y produced by the model of this work (left) and by TOUGH2 EOS1 (right) [38].](https://www.researchgate.net/profile/Sanbai-Li/publication/332415170/figure/fig2/AS:747908324397066@1555326648950/Comparison-of-simulation-results-of-temperature-distributions-after-5-y-produced-by-the_Q320.jpg)
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1
Coupled Thermo-Hydro-Mechanical Analysis of Stimulation and Production for
Fractured Geothermal Reservoirs
Sanbai Li,1 Xia-Ting Feng,1 Dongxiao Zhang,2,* and Huiying Tang 3
1 Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, PR China
2 BIC-ESAT, ERE, and SKLTCS, College of Engineering, Peking University, Beijing 1000871, PR China
3 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, PR China
*Corresponding author, E-mail address: dxz@pku.edu.cn (D. Zhang).
Abstract
Commercial development of enhanced geothermal systems in low-permeability rocks relies on fracturing
treatments to create complex-fracture networks and an appropriate circulation strategy to maintain high flow
rates at sufficiently high temperatures. However, it remains challenging to model complex-fracture
propagation and heat energy extraction as a whole. This paper develops a fully coupled thermo-hydro-
mechanical model to simulate reservoir stimulation and heat production in naturally fractured geothermal
reservoirs. The proposed model is validated against a widely used model, TOUGH2, concerning heat sweep
in a vertical fracture. This model is then applied to study multi-staged fracturing and geothermal extraction
related to a doublet of horizontal wells. The hydro-geomechanical properties are chosen from the Soultz
geothermal reservoir at a depth of approximately 3600 m. Numerical results demonstrate that: (1) mixed tensile
and shear fracturing can constitute an important stimulation mechanism for naturally fractured geothermal
reservoirs; (2) well interlinked, zigzag artificial fractures between injection and production wells readily lead
to channeling flow; (3) keeping a segment of horizontal wells open and placing them further apart are
beneficial to the formation of sufficiently diffuse flow pathways; (4) increasing well spacing tends to improve
thermal performance; however, for the case of a one-stage opening, the improvement of heat sweep efficiency
is not significant; and (5) an alternating circulation scheme could achieve superior thermal performance. This
study establishes an effective modeling workflow for the design and optimization of naturally fractured
geothermal reservoirs, and provides an integrated modeling framework for evaluating recoverable energy
potential from geothermal reservoirs.
Keywords: enhanced geothermal system; hydraulic fracturing; thermo-hydro-mechanical model; complex-
fracture propagation; shear stimulation.
1. Introduction
Geothermal energy is considered as one of the best alternative energies to fossil fuels due to its considerable
reserves and reproducibility. The enhanced/engineered geothermal system (EGS), which includes the earlier
concept of hot dry rock (HDR), has been shown to constitute a viable resource for recovery of geothermal
energy since the 1970s, when the pioneering work was performed at the Fenton Hill project by the Los Alamos
National Laboratory [1, 2]. The basis of EGS is to create an abundant fracture surface via fracturing stimulation,
providing connected pathways for fluid flow and heat extraction. Although technical and commercial success
2
has been achieved in many geothermal projects (e.g., Fenton Hill, Soultz-en-Foret, Cooper Basin, etc.) [3],
numerous complex, unresolved issues remain related to commercial production from EGS reservoirs [4]. The
primary reason for this lies in the lack of a clear understanding of stimulation mechanisms, and multi-physics
system behavior and performance during production. This is probably the direct consequence of the inability
of simple stimulation and production models to describe complex-fracture propagation, and fluid flow and
heat transfer in stimulated EGS volume [4, 5].
The technique of fracturing treatments in EGS reservoirs was borrowed from the oil/gas industry. Conventional
fracturing models assume that artificial fractures are of planar, bi-wing geometry, such as classical KGD [6],
PKN [7], and Penny-shaped models [8]. However, the development of complex fracture networks has been
observed in various rock mass at scales from micrometers, over hundreds of meters, to kilometers [9]. In
addition, mineback experiments, highly scattered microseismic events, abnormal response of treating pressure,
and imaging logging also indicate complex, non-planar fracture network growth during fracturing treatments
[9-11]. Besides in-situ stress, material-property contrast, and fluid-pressure gradient, pre-existing natural
discontinuities (i.e., faults, bedding planes, fractures, and joints) could constitute the primary reasons for
generating complex fracture networks [12, 13]. To take geological discontinuities into consideration, numerous
researchers have investigated the mechanics that control the various behaviors at the fracture intersection point
of artificial and natural fractures, which is a highly localized phenomenon [14]. As a result, various crossing
criteria were established to predict fracture interaction behaviors, i.e., direct crossing, being arrested, and offset
crossing [13, 15, 16], which combined with fracture initiation, propagation, and reactivation criteria provide a
viable means for modeling complex fracture networks.
Once the fracturing stimulation has been completed, the next step is to perform heat extraction via circulating
fluid from the stimulated EGS volume [1]. Geothermal fluid flow through interlinked discrete fractures is a
coupled thermo-hydro-mechanical process, which is dominated by discrete fracture behaviors. When a cool
working fluid (e.g., water [17], carbon dioxide [18]) is injected into one well, most fluid will penetrate into
artificial fractures, leading to the enhancement of fracture aperture due to fluid pressurization. Achieving
commercial production from EGS reservoirs demands a sufficiently high flow rate with a sufficiently high
temperature, an adequate residence time of the injected cold fluid, and a sufficiently large rock mass volume
to access the required amount of geothermal energy [9]. A viable way to achieve this may be to stimulate a
complex, interconnected fracture network [9, 19], and to adopt an optimal heat production scheme. Kant et al.
[20] suggested a technique that uses thermal spallation to enlarge borehole diameter, which would help
stimulate a more complex fracture network. Currently, a quantitative framework, driven by static and dynamic
field data, was proposed to assess unconventional well development [21, 22], such that operators could
comprehensively evaluate the economic feasibility of target EGS reservoir. In the aspect of modeling
assessment, Ghassemi [23] pointed out that geomechanics research based on numerical and analytical solutions
3
plays a critical role in optimizing reservoir design and heat extraction strategies. Pioneering work, regarding
analytical/semi-analytical solutions for heat extraction from a single fracture, has been performed [24-26],
which is of fundamental importance for benchmarking complex numerical models. However, previous studies
mainly focused either on complex-fracture propagation or on heat production from stochastic fracture
networks. Comprehensive thermo-hydro-mechanical analysis of fracturing stimulation and heat production, as
a whole, based on a discrete fracture network model remains scarce.
An intrinsic problem related to fluid-heat flow within fractured porous media is channeling-flow. It is
necessary to introduce a fully coupled THM model to capture and understand the phenomenon of flow
concentration into a small portion of artificial fractures. Fu et al. [27] used a dual-continuum THM model
embedded into the code of NUFT (Nonisothermal Unsaturated-saturated Flow and Transport) to investigate
thermal drawdown-induced flow channeling. However, their discussion was limited to the production phase
without consideration of fractures’ propagation. In reality, long-term injection of cold fluid into EGS reservoirs
could induce significant cooling stresses around major flow paths, which inevitably creates new
fractures/fissures around cooling fractures and speeds up fractures’ propagation. Thermally induced fractures
can be another mechanism for channeling flow due to its positive feedback for high flow-rate.
In this paper, we develop an integrated, thermo-hydro-mechanical model for mixed tensile and shear fracturing,
and fluid-heat flow in naturally fractured EGS reservoirs. For the stimulation module, the mechanisms that are
of great importance for EGS fracturing are taken into consideration, such as cooling stress, shear dilation,
reactivation of isolated pre-existing fractures, and interaction behaviors between artificial and natural fractures.
In this way, the evolution of artificial fracture networks in a complex geological environment can be modeled
more precisely. For the heat production part, geothermal fluid flow is under the control of thermo-hydro-
mechanical coupling, in which both stabilized natural fractures and artificial fractures are stress-sensitive. This
integrated model could provide insight into complex-fracture propagation and flow channeling phenomena
related to heat extraction, and offer a realistic assessment of recoverable geothermal energy from EGS
reservoirs.
2. Methodology
2.1 Equivalent continuum model for fractured rock mass
The concept of the equivalent continuum model is to introduce a single material, which behaves in the same
way as fractured rock mass consisting of several sets of joints and rock matrix [28]. Thus, the compliance of
the fractured rock mass can be written as [29]:
(1)
where ,
, and
are the elastic compliance tensor of the fractured rock mass, the intact matrix,
and joint sets, respectively; the superscripts I and J denote intact matrix and joint sets, respectively; and the
4
subscripts i, j, k, and l denote the tensor indices. For the intact rock matrix, the compliance tensor can be
formulated as a function of Poisson ratio, , and Young’s modulus, , as [30]:
(2)
The general compliance tensor for joint sets is defined as a function of fracture spacing, , fracture shear
stiffness, , and fracture normal stiffness, , as [29]:
(3)
where is the unit vector outwardly perpendicular to the joint surface;
is the transformation tensor
which is composed of direction cosines between the local systems n (i.e., normal direction), s (i.e., strike
direction), and t (i.e., dip direction) and the global system , , and ; superscript n denotes the n-th set of
parallel joint planes; and
(J, L = n, s, t) represents the compliance tensor of the joint in the local coordinate
system, which can be written in matrix form as:
(4)
where the stress-dependent shear and normal stiffness can be expressed as [31, 32]:
(5)
where
is the effective normal stress in the unit of MPa; is the initial normal stiffness; is the
allowed maximum closure; is the maximum value of ; and denotes the uniaxial compressive
strength of the rock material. The constitutive relation of the fractured rock mass obeys generalized Hook’s
law, submitting Eqs. (2) and (3) into Eq. (1), as:
(6)
where
is the effective stress tensor, which can be expressed under the thermoporoelastic framework,
based on the principle of effective stress, as:
(7)
where is the Cauchy total stress tensor; is Biot’s coefficient; is the pore pressure; is the
coefficient of linear solid thermal expansion; denotes the drained bulk modulus; represents
the temperature variation; and and are the current and reference temperature, respectively.
2.2 Estimation of rock permeability
For rock mass with randomly distributed fractures, the equivalent permeability tensor, , is the sum of the
permeability of the intact rock,
, and the embedded fracture sets:
(8)
where is the hydraulic fracture aperture. This aperture is suitable for the cubic law that is usually employed
5
for describing fluid flow through fractures consisting of two smooth, parallel plates. It is necessary to build
the relationship for linking the hydraulic fracture aperture and the mechanical aperture, which is stress-
dependent. Details regarding how to describe the stress-dependent aperture are introduced as follows.
Li et al. [13] proposed a fracture constitutive model to describe the evolution of fracture aperture at various
stress states, i.e., tensile, shear, or both (Fig. 1). Under shear and normal stresses, the shear stress-dilation
relationship consists of four parts: (1) linear elastic stage
; (2) hardening stage
; (3) softening stage
; and (4) residual stage
. With the increase of shear displacement, worn asperities will significantly
reduce fracture roughness, and then lower the friction coefficient to decrease fracture shear strength. By use
of a monotonic direct shear tests (MDST) database [33], the roughness mobilization, , for both pre-
and post-peaks are given in Fig. 1, which is a function of shear displacement, . Shear induced dilational
displacement, , can be written as [33]:
(9)
where is the peak shear displacement; and is the dilational displacement corresponding to the
peak shear displacement. They are empirical parameters and can be characterized by MDST as [33]:
(10)
(11)
where is the size (in unit m) of a block facet.
Fig. 1.
Nonlinear fracture constitutive model in (a) tensile or compression, and (b) shear modes [13].
Pre-peak Post-peak
1
(a) (b)
6
Under pure tensile or compressive stress, Barton et al.’s model [34] can be utilized to calculate the fracture’s
closure (i.e., the change of fracture aperture due to the perturbation of normal effective stress) as:
(12)
where
is the effective normal stress in the unit of MPa; is the initial normal stiffness , i.e., the applied
normal effective stress equals zero; is the allowed maximum closure (i.e., the magnitude of fracture
aperture as the applied normal effective stress goes to infinity); and is the fracture closure in the unit of
mm. and can be linked to the joint roughness coefficient (JRC) and joint compressive strength (JCS)
as [31]:
(13)
(14)
where denotes the initial mechanical fracture aperture under zero normal effective stress, and
. Therefore, given the stress state of the fracture, one can estimate the mechanical aperture as [13]:
(15)
To consider the effect of asperities on fracture walls, Barton et al. [34] proposed an empirical relation relating
mechanical aperture, , to hydraulic aperture, , on the basis of experimental data:
(16)
where is the mobilized value of JCR. Note that a linear interpolation is used to determine the value
of a hydraulic aperture when , and both and are in the unit of mm.
2.3 Governing equations for the thermoporoelastic model
We treat the porous medium as the superimposition of two continua, i.e., the skeleton continuum and the fluid
continuum. The physical model is based on thermoporoelasticity theory [35]. We assume that the porous
medium is of anisotropy and of infinitesimal transformation, and that the pore fluid is non-isothermal, single-
phase, and compressible [36]. The governing equations for fluid and heat flow, and mechanics are obtained
from mass, energy, and linear-momentum balances, respectively.
When neglecting the inertia force, based on Newton's second law, the governing equation of geomechanical
deformation of rock mass can be written as:
(17)
where is a deformable body; is the gravity vector; is the traction force; is the concentration force;
is the range on which the surface force acts; ρb=ρfρs is the bulk density; ρf is the fluid
density; ρs is the solid density; is the true porosity; is the pore pressure; is Biot’s coefficient;
7
is the rank-2 identity tensor; denotes the drained bulk modulus; represents the temperature
variation; and are the current and reference temperature, respectively; is the rank-4 drained
elasticity tensor; and is the coefficient of linear solid thermal expansion. Here, is the linearized strain
tensor under the assumption of infinitesimal transformation:
(18)
where is the displacement. Note that we use the convention that tensile stress is positive. The governing
equations for single phase fluid-heat flow in porous media can be written as:
(19)
for fluid flow, and
(20)
for heat flow, respectively, where is the simulation time; is Biot’s modulus; is the fluid viscosity;
is a sink/source term for fluid or heat; is the formation volume factor of fluid; is the absolute
permeability tensor; is the total thermal expansion; denotes the fluid thermal
expansion; is the total volumetric heat capacity; and denote skeleton
and fluid volumetric heat capacity, respectively; is enthalpy; is the thermal conductivity tensor of the
porous skeleton; and the subscripts , and denote solid, fluid, heat, and bulk, respectively. The
governing equations of fluid and heat flow share the same form, in which the source term is equal to the sum
of the accumulative term and the flow term.
3. Model Validation
As introduced above, the in-house model integrates fracture propagation modeling with heat production
forecasting. For the part of complex-fracture propagation, validation cases and additional details can be found
in Li and Zhang [37] and Li et al. [13]. In this work, we provide two simple validation/verification cases for
the part of heat production against (a) an analytical solution [26] and (b) a widely used, commercial simulator,
TOUGH2 [38].
3.1 1D fracture case: validation by an analytical solution
By neglecting the heat dispersion effect and heat storage term in the fracture, Gringarten et al. [26] derived an
accurate analytical solution to consider fluid-heat flow in a single fracture but only heat conduction in the
surrounding rock matrix, in which temperature versus time along the fracture is given as:
(21)
where is the dimensionless temperature in the fracture; is the temperature
in the fracture; is the temperature of injected water; is the temperature for both the fracture and rock
8
matrix; is the density; is the rock thermal conductivity; is the fluid average velocity in the fracture;
is the elapsed time; is the fracture aperture; is the coordinate along the strike direction of the fracture;
the subscript and denote the rock matrix and water, respectively; the symbol is the error function;
and denotes the unit step function.
Fig. 2.
Comparison between numerical and analytical solutions: (a) numerical model setup showing the
temperature distribution in the fracture and the surrounding matrix after 3 y circulation, and (b) temperature
distributions along the fracture at various times produced by the model of this work and by an analytical solution
[26].
Table 1.
Parameters for the fracture flow problem.
Properties
Value
Unit
1D fracture case [24]
2D fracture case [38]
Thermal conductivity of matrix
2.59
2.1
W/(m)
Specific heat of matrix
1048.5
1000
J/(kg)
Matrix density
2650
2650
kg/
Matrix permeability
0
0
mD
Fracture height
10
200
m
Fracture length
300
240
m
Fracture aperture
0.003
0.04
m
Fracture permeability
2
mD
Fracture porosity
1.0
0.5
-
Reservoir temperature
15
300
Reservoir average pressure
1.0
10.0
MPa
Temperature of injected water
5
100
Injection rate
0.15
4
kg/s
Productivity index
Flowing pressure in production well
0.91
9.65
MPa
In the numerical model, the fracture with an aperture of 3.0 mm is embedded in the matrix domain with the
dimension of . In the fracture length direction, there are 60 grids, and each grid has a
length of 5 m; it is divided into nine grids, i.e., 10 m, 3 m, 2 m, 1 m, 0.003 m, 1 m, 2 m, 3 m, and 10 m, along
the normal direction of the fracture; and only one grid (i.e., 10 m) is provided in the fracture height direction
(Fig. 2a). To minimize the boundary effect along the Y direction (Fig. 2a), the total simulation time is confined
to 5 y for water circulation with a constant injection/production rate of 0.15 . Using the same parameters
(a) (b)
9
for analytical and numerical models as listed in Table 1, we obtain the solutions for the fluid-heat flow problem.
Comparison results are plotted in Fig. 2b, which shows a good agreement with each other.
3.2 2D fracture case: verification against a numerical solution
The present problem is designed to investigate the rapid mitigation of injected fluid along preferential flow
paths, and pre-existing or artificial fractures, via modeling non-isothermal injection into and production from
a vertical fracture (Fig. 3). The matrix around the fracture is impermeable, but can provide a conductive heat
supply. As shown in Fig. 3, water is injected at one side of the fracture, while heat production is performed at
the other side. The input parameters for modeling heat sweep in the vertical fracture are given in Table 1. The
comparison of simulation results produced by TOUGH2 EOS1 and this in-house model, regarding temperature
distribution and production temperature history, are presented in Fig. 4 and Fig. 5, respectively. Very close
simulation results further confirm the accuracy of the developed model in this work. Based on two
validation/verification cases, we believe that this numerical model is reliable for predicting the geothermal
production process.
Fig. 3.
Schematic diagram of the injection-production system in a vertical
fracture [38].
Fig. 4.
Comparison of simulation results of temperature distributions after 5 y
produced by the model of this
work (left) and by TOUGH2 EOS1 (right) [38].
Injection
=0.5
=0.04 m
H=200 m
L=240 m
Production
10
Fig. 5.
Comparison of simulation results of produced fluid temperature versus time for a
vertical
fracture problem
produced by the model of this work and by TOUGH2 EOS1
[38].
4. Modeling Results
4.1 Model setup for numerical case studies
The target geothermal reservoir volume has a side length of m along -, -,
and -direction, respectively (Fig. 6). The in-situ stress condition belongs to a normal faulting environment,
i.e., . The hydro-geomechanical properties are chosen from the Soultz geothermal
reservoir at a depth of approximately 3600 m [39-42]. There are two sets of pre-existing natural fractures with
the number of 248, residing in a 100-m thick reservoir (Fig. 6). These discrete natural fractures are borrowed
from the Patchawarra reservoir in Australia, which are generated by a combination of deterministic and
stochastic techniques based on tectonic history and characteristic data available in the open literature [40]. The
naturally fractured geothermal reservoirs are saturated with water, and their initial temperature and pressure
are 150 and 36.5 MPa, respectively. No flow boundary conditions are applied for fluid and heat at the
boundaries of the reservoirs, and the injection/production wells are treated as sink/source terms in this model.
The same constant injection rate, 15.89 L/s, and the same constant production pressure, 35.5 MPa, are adopted
for fluid circulation. Water’s thermodynamic properties (i.e., density, enthalpy, compressibility, viscosity, heat
conductivity, and heat capacity) are functions of temperature and pressure [43]. The input parameters for the
simulation, including rock matrix, fracture and fluid properties, and initial and boundary conditions, are listed
in Table 2. Although the parameters used in this work are extracted from extant literatures, they can also be
characterized from in-situ tests and laboratory experiments for practical applications. The common sources of
the computing parameters are listed in Table 3.
11
Table 2.
Rock and fracture properties used in the simulation from literature data.
Properties
Value
Dimension
Source and remarks
Rock properties
Young’s modulus
40
GPa
[17, 39]
Poisson’s ratio
0.25
-
[17, 39]
Density
2744
kg/
[44]
Thermal conductivity
2.79
W/(m)
[44]
Specific heat
1098
J/(kg)
[39]
Permeability
5.2
[39]
Porosity
0.1
-
[45]
Thermal expansion coefficient
1.0
1/
[46]
Tensile strength
2.0
MPa
assumed
Fracture properties
Fracture number
248
-
[40], Fig. 6
Fracture density
0.0664
/
[40], Fig. 6
Joint roughness coefficient JRC
8
-
[47], refer to weathered joint
Joint compressive strength JCS
180
MPa
refer to the range from [47]
Uniaxial compressive strength
35
MPa
refer to the range from [48]
Friction angle
34
°
[39, 41]
Residual friction angle
30
°
[39]
Dilation angle
3
°
[39, 41]
In-situ fracture permeability
200
mD
assumed
Fluid properties
Fluid density
kg/
[43], calculated
Fluid viscosity
mPa
[43], calculated
Fluid specific heat
J/(kg)
[43], calculated
Fluid thermal conductivity
W/(m)
[43], calculated
Initial and boundary conditions
Initial reservoir temperature
150
[42], at 3600 m depth
Hydrostatic fluid pressure
36.5
MPa
[43], at 3600 m depth
Injection fluid temperature
25
assumed
Vertical stress
65.0
MPa
assumed, normal fault regime
Maximum horizontal stress
44.0
MPa
assumed, normal fault regime
Minimum horizontal stress
41.0
MPa
assumed, normal fault regime
Injection rate, stimulation
7.949
refer to the range from [9, 49]
Injection rate, circulation
1.5898
refer to the range from [5]
Production pressure
35.5
MPa
assumed
Table 3.
Common sources of the computing parameters [13, 50].
Parameters
Sources (i.e., in-situ tests and laboratory experiments)
In-situ stresses
Mini-fracturing tests, borehole breakouts image
Elastic properties
Core-based compressibility test, shear sonic imager
Reservoir pressure, permeability
Injection fall off test (IFOT), drill stem test, mud log
Reservoir temperature
Frac job, temperature logging, IFOT
Porosity
Gas expansion, well logging
Fluid properties
PVT tests, mud log
Geometries of hydraulic fractures
Micro-seismic mapping, tilt meters, tracers
Mechanical properties of the fracture
Monotonic direct shear tests
Thermal conductivity and capacity of rock mass
Temperature logging, core tests
The key for economical EGS energy extraction is to develop a complex fracture network [9]. This goal can be
achieved by using multi-staged fracturing in a double/triplet of horizontal wells, which could provide a
12
sufficient fracture surface area for heat exchange and achieve an adequate flow rate by creating high
permeability. Although channeling-flow is inevitable for fractured EGS reservoirs [27], complexity might be
desirable for relieving this phenomenon [19], which also depends on achieving effective fracturing. In addition,
choosing a reasonable circulation strategy through parameter optimization is expected to be another way to
relieve thermal short-circuiting due to channeling-flow. In this study, we perform a numerical investigation of
the development of EGS reservoirs using a doublet of horizontal wells for both stimulation and circulation. As
shown in Fig. 6, two horizontal wells are drilled into the target reservoirs for the purpose of stimulation and
circulation. Multi-staged fracturing treatments with a staggered sequence are performed in these two horizontal
wells from the toe to the heel, as depicted in Fig. 7a. Subsequently, fluid circulation is operated to extract
geothermal energy. It should be noted that the results obtained from the stimulation phase serve as the initial
conditions for the circulation operation, such as artificial fracture pattern, permeability of matrix and fractures,
pore pressure, stress distribution, etc. Fracture aperture change, throughout the entire process under the
condition of tensile stress, compressive stress, or both shear and compressive stress, is estimated by a fracture
constitutive model reported by Li et al. [13].
Fig. 6.
Numerical model setup. An EGS doublet of horizontal wells with a spacing of 200 m are drilled into the
naturally fractured reservoirs along the direction of minimum horizontal stress. The coal stripe denotes the pre-
existing natural fracture.
13
Fig. 7.
Schematics of operation strategies related to stimulation and circulation. The development of EGS
reservoirs starts with multi-staged fracturing stimulation in two horizontal wells with a spacing of 200 m (a);
then, fluid circulation is carried out to extract geothermal energy using three production schemes: (b) five-stage
opening, (c) three-stage opening, and (d) one-stage opening for fluid injection and production.
4.2 Multi-staged fracturing in an EGS doublet of horizontal wells
After finding and confirming a suitable site for EGS operations, the next step is to stimulate the rock in the
target reservoirs at depth [1]. Conventional fracturing design is assumed to artificially create simple, tensile
fractures with a planar, bi-wing shape [6, 7, 51]. However, quite scattered microseismic events and abnormally
high treating pressure imply that the artificial fractures can be more complicated, rather than simple, planar
tensile fractures. Then, the concept of “shear stimulation” or “hydroshearing” [19, 52] was proposed to
understand the stimulation process in EGS reservoirs, in which the artificial fracture networks consist of
reactivated pre-existing natural fractures in the shear slip. In addition, mixed-mode propagation (i.e., large
wing-cracks) was discussed by Min et al. [53] and Jung [54] based on field observations and numerical analysis.
This work mainly focuses on complex-fracture propagation in naturally fractured EGS reservoirs based on the
concept of a mixed tensile and shear fracturing mechanism.
14
Fig. 8.
Bottom hole pressure history of two parallel wells (solid lines in pink and blue) and the pumping schedule
(solid line in green).
Fig. 7a presents the fracturing strategy, in which the landed two wells with a length of 500 m consist of five
stages with the same length. Each stage with a length of 100 m is stimulated with five perforation clusters. The
pumping schedule for each stage can be found in Fig. 8, i.e., a constant pumping rate of 79.49 L/s for 40 min
followed by a 30 min well shut-in phase. The total time simulated is 420 min.
Fig. 9 shows the propagation process of a complex-fracture network during stimulation operations. Although
pure shear stimulation mechanisms were discussed in depth by McClure and Horne [19] and supported by
interpretations of field data [55-57], numerical simulation results here demonstrate that the mixed tensile and
shear stimulation mechanism could constitute another such mechanism. In order to understand this stimulation
mechanism, it is necessary to consider the processes of fractures’ initiation, propagation, reactivation, and
intersection with other fractures. When fracturing fluid is pumped into the wellbore, the pressurized fluid
pressure may exceed the minimum principle stress at some point. Fractures could then initiate from each
perforation away from the wellbore. Subsequently, fracture propagation occurs when the threshold value of
the stress intensity factor is reached or exceeded, according to the theory of subcritical fracture growth [58,
59]. In naturally fractured reservoirs, preexisting isolated fractures experience stress perturbation in response
to the change of pressure and temperature. Once the shear strength is overcome, shear slip on the fracture plane
could occur. Shear slippage causes energy release and triggers microseismic events, which are the so-called
reactivation-induced dry events. As propagating artificial fractures encounter pre-existing natural fractures,
various interaction results, i.e., termination, direct crossing or offset crossing, can occur, depending on the
15
stress condition and hydromechanical properties of the matrix and fractures [13]. As a result, complex-fracture
networks that consist of reactivated pre-existing natural fractures that may or may not be isolated, and newly
created opening fractures are generated during stage-by-stage fracturing treatments (Fig. 9). Fig. 8 shows the
bottomhole pressure (BHP) history. First, fluid pressure is gradually elevated, due to the increased fluid volume,
to reach the breakdown pressure. Then, nearly steady propagation of fractures lowers the BHP with a
fluctuation characteristic related to fracture interaction behaviors as analyzed above. This is followed by the
shut-in phase, during which the BHP reduces slowly due to fluid leak-off. This typical fracturing pressure
curve can be observed in the fracturing stages shown in Fig. 8. Table 4 shows the computational performance
of the proposed model and the production performance of each circulation scenario. The statistics illustrate
that the fracturing phase is much more computationally expensive than the circulation phase, and the
alternative scheme achieves the best thermal performance.
Fig. 9.
Illustration of the stimulated fracture network evolution during multi-staged fracturing. The patterns of
stabilized (coal), reactivated (green), and newly opened fractures (red) after: (a) 70 min corresponding to the 1st
stage stimulation; (b) 140 min corresponding to the 2nd stage stimulation; (c) 210 min corresponding to the 3rd
stage stimulation; and (d) 420 min corresponding to the 5th stage stimulation. Note that the stabilized fracture
means the naturally preexisting fracture without any shear and/or normal displacement, in which two fracture
surfaces contact each other; the reactivated fracture means that the natural fracture has experienced certain shear
displacement because its shear strength is overcome; and the newly opened fractures means the tensile fracture
for which the maximum tensile strength or the critical stress intensity factor of the rock is overcome.
(b)(a)
(d)(c)
16
Fig. 10 presents the evolution process of different kinds of fractures that correspond to the fracture patterns
depicted in Fig. 9. Artificial fractures are composed of shear fractures and opening fractures. Shear fractures
form the majority of the artificial fractures, accounting for 94.48%, 92.58%, 88.41%, 85.53%, and 82.44%
after one-, two-, three-, four-, and five-stage fracturing, respectively. It can be seen that only a small part of
natural fractures (6.05%) maintains stability after five stages of fracturing. The numerical results are consistent
with the assertion that natural fractures are the major source of artificial fracture networks, and one cannot
create a fracture network but can only activate pre-existing natural fracture networks [60, 61]. These
quantitative statistics also confirm the mixed stimulation mechanism.
Fig. 10.
Statistics of the fracture area of newly opening fractures, shear fractures, stabilized fractures, and total
artificial fractures during multi-staged fracturing.
4.3 Heat extraction using a doublet of horizontal wells
Achieving commercial development of EGS reservoirs relies not only on the success of hydraulic fracturing
treatments in creating complex fracture networks, but also on an optimal heat production strategy to avoid
thermal short-circuiting, as well as to maintain a sufficiently high flow rate. We perform heat extraction
modeling based on the stimulation results, in which the most important component is the artificial fracture
pattern (Fig. 9d). McClure and Horne [19] pointed out that one of the most important obstacles to the economic
development of EGS reservoirs is thermal short-circuiting. Previous studies [9, 27] have found clear evidence
that channeling flow concentrated into a small portion of fractures can be readily built between injection and
production wells. Our goal is to elucidate why channeling flow can form and to provide an alternative strategy
for circulation operations.
0.00E+00
3.00E+05
6.00E+05
9.00E+05
1.20E+06
1.50E+06
1.80E+06
2.10E+06
1 2 3 4 5
Fracture area (m2)
Shear fractures Opening fractures
Stabilized fractures Artificial fractures
one stage two stages three stages four stages five stages
Fracture area ()
17
Table 4.
Statistics on computational performance on a single CPU core and EGS performance of each circulation scenario.
Case description
Total time
Simulation
CPU
With 20 reduction
at the production well
Fracturing case
Multi-staged fracturing, 200-m well spacing
420 min
10.5 h
N/A
Base case for production
Five-stage, 200-m well spacing
2245 d
3.6 h
2083.3 d
Effect of active well length
Three-stage, 200-m well spacing, heel operation
2453 d
3.7 h
828.7 d
One-stage, 200-m well spacing, heel operation
3190 d
5.1 h
886.6 d
Effect of well spacing
280-m well spacing, five-stage
2500 d
4.0 h
1527.8 d
360-m well spacing, five-stage
2905 d
4.6 h
2155.8 d
280-m well spacing, one-stage, heel operation
3190 d
5.1 h
2141.2 d
360-m well spacing, one-stage, heel operation
3190 d
5.1 h
2291.7 d
Various operation schemes
Toe operation, 200-m well spacing, one-stage
3190 d
5.1 h
2118.1 d
Alternative, 200-m well spacing, one-stage
3190 d
5.3 h
3113.4 d
4.4 The effect of active well length for injection and production
Three injection-production scenarios with different active sections, as shown in Fig. 7b-d, are designed to
investigate the process of geothermal energy development under the framework of thermo-hydro-mechanical
coupling. We keep one, three, and five stage/stages of each well open to communicate with EGS reservoirs,
i.e., the working fluid is prevented from flowing into the rest of the stages.
Fig. 11.
Temperature distribution at various times with a full wellbore opening. Thermal snapshots at: (a)
s (250 d); (b)
s (500 d); (c)
s (900 d); and (d)
s (2245 d).
The distance between the injection well and the production well is 200 m. The dashed lines in white color inside
of the rectangle are active sections of the operation wells.
Temperature ()
(b)(a)
(d)
(c)
18
Following the work of Hofmann et al. [9], we first keep the doublet of the two horizontal wells fully open, as
shown in Fig. 7b. From Fig. 9d, it can be seen that the injection and production wells with a distance of 200
m are well connected through a complex, interlinked fracture network. Driven by the pressure gradient built
between the injection and production wells, a majority of the working fluid tends to flow into artificial fractures
that link one well to another in a zigzag configuration. During circulation, fractures that carry higher flow rates
are likely to cool faster [27]. Then, a tremendously high cooling stress, , will be produced to
increase tensile stress acting on fractures and matrix, so as to enhance permeability inside of the cooled rock
(cf. Eqs. 12, 15, 16, and 8). Enhancement of fracture permeability, in turn, accelerates flow rates through these
fractures, which further strengthens the flow channeling phenomenon. Fig. 11 shows that thermal drawdown-
induced flow channeling is gradually built up, accompanied by a thermal conductivity-induced temperature
halo along the flow paths, and that the regions outside of the couple of wells become dead zones. This is
detrimental for long-term operation in EGS reservoirs, because it reduces the effective heat exchange area
tremendously [27] and causes the thermal breakthrough to occur earlier.
Fig. 12.
Thermal snapshots with a three-stage opening at the heel sides. Temperature distribution at various
times: (a)
s (250 d); (b)
s (500 d); (c)
s (900 d); and (d)
s
(2245 d). These two operation wells have a spacing of 200 m. The white dashed frames denote active segments
of wells, and the black solid lines indicate inactive segments.
Temperature ()
(b)(a)
(d)(c)
19
Fig. 12 shows thermal propagation in EGS reservoirs during fluid circulation between two horizontal wells.
Each well only provides a 300-m-long segment for fluid and heat exchange (Fig. 7c). In this scenario, a side-
by-side segment exists between the range of 200 m and 300 m along the direction. Between these two
segments is a range that favors inducing channeling flow due to the existence of direct pathways. The direct
pathways carry a high rate of fluid from the injection well to the production one. Fig. 12b presents the cooling
front contacting the production well after 250 d of circulation. Subsequently, cooling-induced enhancement of
permeability causes a more concentrated flow therein. After approximately 750 d (Fig. 12c), other cooling
fronts, traveling a longer way through interconnected artificial fractures, touch the production well. It is evident
that the produced fluid is a mix of relatively cold fluid from a certain location and hot fluid from another
location. Therefore, horizontal wells possess an advantage over vertical wells in receiving more heat from the
surrounding hot rock and the inflow of hot fluid.
Fig. 13.
Thermal snapshots for the case of a one-stage opening at the heel sides. Temperature distribution at
various times: (a)
s (250 d); (b)
s (500 d); (c)
s (900 d); and (d)
s (2245 d).
Fig. 13 depicts the temperature behavior corresponding to the scenario of a one-stage opening, in which
(b)
(a)
(d)
(c)
Temperature ()
20
abundant circuitous fractures exist to carry high flow rates. The lack of direct pathways linking the doublet of
wells facilitates a very diffuse initial flow pattern. Moreover, a long pathway for fluid to travel provides a
sufficiently long time for heat exchange between working fluid and hot rock. Thus, the early thermal
breakthrough is postponed such that effective production life is prolonged effectively. Although channeling
flow into cooled zones is inevitable [27], keeping a segment of horizontal wells open as long as possible and
placing them further apart are beneficial for forming highly diffuse flow pathways. Compared with scenarios
of five-stage opening and three-stage opening, this scenario produces the most diffuse flow pathways (Fig.
13c).
Fig. 14.
Thermal behaviors. (a) Production temperature profiles for three circulation strategies. The enlarged
part (b) clearly shows the thermal breakthrough at times of
s (185 d),
s (115 d), and
s (355 d) for 500-, 300-, and 200-m-long segment openings, respectively (Fig. 7b-d). (c) Reservoir
power generation for three circulation strategies. The zoomed part (d) shows the thermal drawdown behaviors
of different circulation schemes.
(a) (b)
(c) (d)
21
Fig. 15.
Pressure perturbations during the circulation phase. Pressure distribution at various times for three
circulation scenarios: (a) 8.64
s (1 d) and (b) 8.64
s (100 d) for the case of a one-stage opening; (c)
8.64
s (1 d) and (d) 1.04
s (100 d) for the case of a three-stage opening; and (e) 8.64
s (1 d)
and (f) 1.17
s (100 d) for the case of a five-stage opening.
Fig. 14 displays the thermal performance of the three circulation schemes mentioned above. They share the
same thermal drawdown behavior, in which a period of very low thermal drawdown prior to thermal
breakthrough is followed by a period of rapid temperature decline. Among these circulation strategies, the case
of the one-stage opening (i.e., 100-m-long segment for injection/production) provides the longest resident time
for cold fluid to heat up, prolongs the thermal breakthrough of the cold fluid plume at the production well, and
Pressure (Pa)
Pressure (Pa)
Pressure (Pa)
Pressure (Pa)
Pressure (Pa) Pressure (Pa)
(a)
(c)
(e)
(b)
(d)
(f)
22
effectively delays temperature decline after thermal breakthrough. Fig. 14c and d show the corresponding
power generation , which can be estimated as:
(22)
where is the volumetric flow rate; and the subscript denotes the production well. The power generation
follows a similar tendency to that of production temperature (comparing Fig. 14a with Fig. 14d) after the
establishment of a relatively steady pressure system, before which the fluctuation of pressure and flow rate
causes a complex response of power generation (Fig. 14d).
Fig. 16. Thermal snapshots for different well distances. Temperature distribution at various times: (a) s (250
d) and (b) s (2500 d) are the results of the case of 280-m well distance; and (c) s (250 d) and (d)
s (2500 d) are the results of the case of 360-m well distance.
Fig. 15 presents pressure distributions for three circulation schemes at different times. After 1 d of fluid
circulation, the pressure discrepancy becomes evident, in which overpressure occurs around the injection well
and depletion-induced low pressure forms close to the production well. Approximately 100 d later, a relatively
Temperature ()
(b)(a)
(d)(c)
23
steady state pressure system is built. Comparing Fig. 15 with Fig. 11, Fig. 12, and Fig. 13, it can be seen that
the propagation velocity of pressure is much more rapid than that of the cooling front. Although
accomplishment of thermal sweep for a field scale problem requires several decades, only several days are
needed for pressure propagation.
4.5 The effect of well spacing
Well spacing plays a key role in both geothermal energy production and thermal enhanced heavy oil recovery
[62]. To assess the impact of well spacing on the efficiency of heat extraction, we increase the well spacing
from 200 m to 280 m, and then to 360 m for both one-stage opening and five-stage opening scenarios.
Fig. 16 shows that thermal sweep primarily occurs in the region between injection and production wells for
the situation of full opening. This is because well connected injection and production wells, due to multistage
fracturing, tend to form steady flow within the sandwich region. However, extensive reservoir volume outside
of the connected wells contributes little to heat production, depending on heat conduction rather than heat
advection. Less well spacing means more connectivity, as well as shorter flow paths, for the full opening
scenario. Thus, major flow paths can be more easily built, and less residence time is provided for working
fluid to absorb sufficient heat energy. This situation usually leads to earlier thermal breakthrough, which results
in quicker thermal drawdown. We can observe from Fig. 17 that the thermal breakthrough time of the 200-m
well spacing case is earlier than that of the other two cases (i.e., 280 m and 360 m), and the power generation
of 200-m well spacing case reduces more sharply in the long term than the latter two cases do. Furthermore, a
negative relationship exists between the speed of thermal drawdown and well spacing. After s
(approximately 2200 d) circulation, production temperature differences are 16 , 25 , and 41 for each
of the two well spacings, i.e., 360-280 couple, 280-200 couple, and 360-200 couple, respectively.
Fig. 17. Thermal behaviors. (a) Production temperature profiles and (b) reservoir power generation for various well
spacings (i.e., 200 m, 280 m, and 360 m) with a five-stage opening.
(a) (b)
24
For the case of the one-stage opening, attempts are also made to understand the impact of well spacing through
changing the well distance from 200 m to 280 m, and then to 360 m. Previous case studies demonstrate that
the one-stage opening is favorable for creating diffusive flow paths to prolong the heat exchange time
compared to a longer active opening. Based on this understanding, we further increase the well distance to
investigate thermal production performance. Fig. 18 together with Fig. 13 displays the flow paths, temperature
distributions, and thermal sweep areas at various times, revealing a significantly similar heat exchange pattern.
Temperature curves and power generation profiles plotted in Fig. 19 also indicate a very close heat extraction
behavior, in which the temperature discrepancy is less than 2 from beginning to end of the simulation time.
It seems somewhat counterintuitive that increasing well distance does not achieve significant enhancement in
heat production. The reason for this is that the multiple stage fracturing has created a very complex fracture
network prior to heat production via generating newly tensile fractures and reactivating pre-existing natural
fractures. These well-connected artificial fractures could provide a sufficiently large fracture surface area for
heat exchange and high-rate flow paths for the communication of injection and production wells. Under this
circumstance, the well spacing of 200 m is sufficiently large to make use of artificial fracture networks to
access most energy contained in EGS reservoirs in this study.
Fig. 18. Thermal snapshots for the case of a one-stage opening at the heel sides. Temperature distributions at various
times: (a) s (250 d); (b) s (900 d); and (c) s (3190 d) are the simulation results of
the case of 280 m well spacing; and (d) s (250 d); (e) s (900 d); and (f) s (3190 d)
correspond to the case of 360 m well spacing.
Temperature ()
(b)(a)
(e)
(d)
(c)
(f)
(e)
25
Fig. 19. Production temperature profiles (a) and corresponding reservoir power generation curves (b) for different well
spacings (i.e., 200 m, 280 m, and 360 m). The power generation curve is composed of four phases: the first phase is
characterized by a rapid decline in power generation due to a deficiency in fluid supply, even though the production
temperature remains unchanged at 150 ; the second phase is then produced power that is gradually elevated due to
increased fluid supply; in the third stage, a steady flow rate between injection and production wells is subsequently built,
resulting in a steady power generation period; and the fourth phase corresponds to the temperature decline stage.
4.6 Alternative injection-production schemes
Two injection-production schemes are adopted here to determine how to increase heat sweep efficiency. The
first scenario is to change the active segment location from the heel side (Fig. 13) to the toe side (Fig. 20) with
a one-stage opening, which is accessible by adjusting the control valve. Although the location of cooled regions
differs from each other when comparing the heel operation case and the toe operation case, the pattern of
cooled regions is very similar. However, dead zones can be found at corner parts and in regions far away from
major flow paths linking injection and production wells. This phenomenon stimulates an idea to improve heat
sweep efficiency by employing an alternating operation scheme. The strategy is that heat circulation starts
from the heel operation for a period of time (250 d); the toe operation is then performed for 900 d, which is
followed by another period of time for 2040 d using the heel operation again. Fig. 21 displays the temperature
distributions at different times associated with the alternating operation. The aim of the alternating operation
is to make use of heat recovery taking place in the cooled region via altering active segments of
injection/production wells.
Ⅰ Ⅱ Ⅲ Ⅳ
(a) (b)
26
Fig. 20. Thermal snapshots for the case of a one-stage opening at the toe sides. Temperature distribution at various times:
(a) s (25 d); (b) s (250 d); (c) s (900 d); and (d) s (3190 d).
From Fig. 22, it can be seen that a slight discrepancy in production temperature exists between the heel
operation and the toe operation. However, the alternating operation possesses a significant advantage over both
heel and toe operations. As shown in Fig. 21b, the cooled region has a period of time to be heated (i.e., thermal
recovery) prior to thermal breakthrough of the heel operation. Because the production well is very close to the
cooled region, the producer experiences thermal drawdown from 250 d to 1150 d. At the moment of 1150 d,
the active segments are moved back to heel sides, which provides an opportunity for the cooled region induced
by the previous operation stage to recover (Fig. 21c and d). In such a way, the speed of thermal drawdown of
the alternating operation is much slower than that of either heel or toe operation (Fig. 22a). It can be expected
that the alternating operation will achieve much higher heat sweep efficiency than do the other two circulation
schemes. The advantage of the alternating scheme lies mainly in lowering the declining rate in the later stage.
The power generation curves, as shown in Fig. 22b, also indicate the advantage of the alternating scheme. The
reason for this is that those major flow paths that formed during the previous phase could still deliver a portion
of heated fluid from the injection well to the production well, which mitigates fluid concentration into a
minority of artificial fractures to some extent. Therefore, the temperature decline of the heel or the toe
operation is more pronounced than that of the alternating operation.
Temperature ()
(b)(a)
(d)(c)
27
Fig. 21. Thermal snapshots for the case of an alternating operation with a one-stage opening. Temperature distribution at
various times: (a) s (500 d); (b) s (1150 d); (c) s (1200 d); and (d) s
(3190 d).
Fig. 22. Illustrations of thermal performance for the case of a one-stage opening. Production temperature profiles (a) and
corresponding reservoir power generation curves (b) for the heel operation, the toe operation, and the alternative operation
with a well spacing of 200 m.
Temperature ()
(b)(a)
(d)
(c)
(a) (b)
28
5. Discussion
Comprehensive thermo-hydro-mechanical analysis of fracturing stimulation and heat production as a whole
based on a discrete fracture network model remains scarce. Difficulties lie primarily in multiple physical
processes and different time scales involved in a life cycle of an EGS reservoir [63]. A compromised method
is to couple a fracturing model with a heat production model using a loosely coupled approach via data
mapping [9]. However, numerous problems associated with computational accuracy and efficiency may be
induced. A data mapping method between two independent simulators/models may also not be available for a
refracturing situation, since this treatment usually does not support two-way coupling, i.e., the fracturing model
cannot be restarted based on the simulation results from the heat production model.
This model requires many kinds of prescribed parameters, such as in-situ stresses, hydraulic and mechanical
properties of the matrix and the fracture, fluid properties, geometries, the distribution of natural and hydraulic
fractures, etc., which can be characterized via in-situ tests and laboratory experiments (cf. Table 3). However,
experimental errors and uncertainties of field parameters may decrease the accuracy of the prediction model.
A viable solution may be to resort to the parameter inverse model based on production data. With reliable input
data, this model could be utilized for real applications. The simulation results are sensitive to parameters of
fracture geometries and grid resolution. Conductivity and connectivity of fractures have great impact on the
patterns of hydraulic fractures, as well as the fluid-heat flow paths. Therefore, the input data of fracture
geometries should be characterized carefully, which necessitates the application of an effective inverse model
for fractures [64]. In addition, users should employ local refined grids to represent the fracture since this model
is based on the continuum theory. Otherwise, the channeling flow would be underestimated. To reduce grid
dependency, we intend to adopt the embedded discrete fracture model to handle fractures in both fracturing
and circulation phases in our future work.
Although the model proposed in this work is capable of simulating fracture-network propagation and
geothermal energy production based on THM coupling, there still exist limitations and shortcomings. For
instance, no new artificial fractures are allowed to generate during the circulation phase. Actually, long-term
injection of cold fluid will induce multiple relatively small-scale fractures around major flow paths and might
trigger fractures’ propagation. These newly created fractures associated with fluid circulation have an influence
on fluid-heat flow patterns, as well as thermal performance, which should be taken into consideration. The
model is currently applicable for single phase problems. However, carbon dioxide and nitrogen have been
proposed to serve as working fluids for stimulation and heat extraction in which multiphase flow is involved.
In addition, an optimization scheme for multiple stage EGS doublets would need to consider marginal revenue
and marginal costs related to the project over the lifetime of the system [65]. These topics should be
investigated in future studies.
29
6. Conclusions
In this work, we developed a fully coupled thermo-hydro-mechanical model to simulate fracturing stimulation
and heat production with a seamless connection for enhanced geothermal systems (EGS). The proposed model
integrates critical mechanisms associated with stimulation and circulation as much as possible, including the
reactivation of isolated and/or hydraulically connected natural fractures, mechanical interaction between
artificial fractures and pre-existing natural fractures, shear dilation-induced permeability enhancement, and
thermal stress. A validation case against a commercial simulator, TOUGH2, for heat sweep in a vertical fracture
is provided, and validation for fracturing simulation in fractured reservoirs was given by Li et al. [13] and Li
and Zhang [37]. Using this model, we systematically investigated the operation processes for EGS reservoirs,
from which we have made the following findings and suggestions.
• In addition to the pure tensile, pure shear, and wing-crack simulation mechanisms, the mixed tensile
and shear simulation mechanism could constitute another important mechanism. Although
reactivating a pre-existing natural fracture is easier than initiating an artificial fracture, tensile
fractures’ propagation can still occur due to stress concentration in the vicinity of perforations, as well
as fracture tips. As a result, artificial fracture networks consist of newly opening fractures and
reactivated natural fractures, in which the shear fractures account for a major portion of up to 80% or
more based on this work.
• Various interaction behaviors, such as termination, direct crossing, or offset crossing, between
artificial and natural fractures make the induced fracture networks more complicated. As analyzed
above, complex artificial fracture networks can be expected during stimulation in naturally fractured
EGS reservoirs via multi-staged fracturing in horizontal wells. The numerical investigation carried
out in this study demonstrates that stimulation and circulation operations on an EGS doublet of
horizontal wells can be an effective means to tap geothermal energy.
• It is worth noting that an alternating operation among a doublet of long horizontal wells based on
valve control could significantly enhance heat sweep efficiency. A reasonable alternating strategy can
make optimal use of thermal recovery to delay the time of thermal breakthrough, as well as prolong
the thermal decline curve.
Concentrated flow into a small portion of well-interlinked artificial fractures leads to the so-called channeling
flow, which constitutes the primary reason for thermal short-circuiting. Previous studies [5, 27, 66] have shown
that increasing well spacing or lowering flow rate can be an apparent way to effectively delay thermal
breakthrough and prolong production life. Our study, using an EGS doublet of two horizontal wells to establish
an injection-production system, demonstrates that:
• Thermal performance is degraded if two horizontal wells are kept fully open, because the high
pressure gradient built between wells tends to deteriorate concentrated flow and makes regions
30
outside of the two wells become dead zones.
• Keeping a part of the horizontal wells open and placing them further apart are beneficial to the
formation of sufficiently diffuse flow pathways. Consequently, the residence time of the injected cold
fluid is prolonged, and effective heat sweep can be achieved within the stimulated EGS volume.
• Increasing well distance tends to enhance heat sweep efficiency, but the effect is not significant for
the case of a one-stage opening.
• The presented alternating circulation scheme could achieve better thermal performance than that of
the heel operation and the toe operation. Furthermore, horizontal wells possess an advantage over
vertical wells in receiving more heat as a mix of relatively cold fluid from a certain location and hot
fluid from another location due to a larger contact area between the production well and the
surrounding hot rock.
We believe that it is necessary to employ a thermo-hydro-mechanical model to understand EGS operations
since both the fracturing and production processes are controlled by thermomechanical effects. We also
conclude that it is essential to combine fracturing stimulation and heat extraction together in order to obtain
requisite insight into EGS performance and recoverable potential.
Acknowledgment
This work is partially funded by the National Natural Science Foundation of China (Grant No. 51804064,
U1663208 and 51520105005), the National Science and Technology Major Project of China (Grant No.
2016ZX05037-003), the Beijing Municipal Science and Technology Commission (Grant No.
Z171100002317022), and the Fundamental Research Funds for the Central Universities (Grant No.
N170103010).
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