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Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs

Rock Mechanics and Rock Engineering

June 2015
49(3)

DOI:10.1007/s00603-015-0776-0

Authors:

Pengcheng Fu

Lawrence Livermore National Laboratory

Yue Hao

Lawrence Livermore National Laboratory

Stuart Duncan Christopher Walsh

Monash University (Australia)

Charles R. Carrigan

Lawrence Livermore National Laboratory

We investigate the flow-channeling phenomenon caused by thermal drawdown in fractured geothermal reservoirs. A discrete fracture network-based, fully coupled thermal–hydrological–mechanical simulator is used to study the interactions between fluid flow, temperature change, and the associated rock deformation. The responses of a number of randomly generated 2D fracture networks that represent a variety of reservoir characteristics are simulated with various injection-production well distances. We find that flow channeling, namely flow concentration in cooled zones, is the inevitable fate of all the scenarios evaluated. We also identify a secondary geomechanical mechanism caused by the anisotropy in thermal stress that counteracts the primary mechanism of flow channeling. This new mechanism tends, to some extent, to result in a more diffuse flow distribution, although it is generally not strong enough to completely reverse flow channeling. We find that fracture intensity substantially affects the overall hydraulic impedance of the reservoir but increasing fracture intensity generally does not improve heat production performance. Increasing the injection-production well separation appears to be an effective means to prolong the production life of a reservoir.

Reservoir fracture flow field and reservoir temperature field for different fracture networks and inter-well separation distances.

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ORIGINAL PAPER

Thermal Drawdown-Induced Flow Channeling in Fractured

Geothermal Reservoirs

Pengcheng Fu

•Yue Hao

•Stuart D. C. Walsh

•Charles R. Carrigan

Received: 31 March 2015 / Accepted: 1 June 2015 / Published online: 30 June 2015

Springer-Verlag Wien (outside the USA) 2015

Abstract We investigate the ﬂow-channeling phe-

nomenon caused by thermal drawdown in fractured

geothermal reservoirs. A discrete fracture network-based,

fully coupled thermal–hydrological–mechanical simulator

is used to study the interactions between ﬂuid ﬂow, tem-

perature change, and the associated rock deformation. The

responses of a number of randomly generated 2D fracture

networks that represent a variety of reservoir characteris-

tics are simulated with various injection-production well

distances. We ﬁnd that ﬂow channeling, namely ﬂow

concentration in cooled zones, is the inevitable fate of all

the scenarios evaluated. We also identify a secondary

geomechanical mechanism caused by the anisotropy in

thermal stress that counteracts the primary mechanism of

ﬂow channeling. This new mechanism tends, to some

extent, to result in a more diffuse ﬂow distribution,

although it is generally not strong enough to completely

reverse ﬂow channeling. We ﬁnd that fracture intensity

substantially affects the overall hydraulic impedance of the

reservoir but increasing fracture intensity generally does

not improve heat production performance. Increasing the

injection-production well separation appears to be an

effective means to prolong the production life of a

reservoir.

Keywords Geothermal Enhanced geothermal system 

Hot wet rock Thermal breakthrough Flow channeling 

THM model

1 Introduction

Engineered (or enhanced) geothermal systems (EGS) are

usually located in fractured rock formations, where the

permeability of the intact rock matrix is very low and the

inter-connected fracture network provides the primary

conduit of ﬂuid between the injection well(s) and the

production well(s). Since heat conduction in the rock

matrix is much slower than convective heat transfer asso-

ciated with ﬂuid ﬂow along fractures, it is highly desirable

to have ﬂow patterns dispersed throughout a large volume

of rock. The understanding of ﬂow patterns in EGS reser-

voirs plays a critical role in the optimization of reservoir

exploration, stimulation, and operation.

The term ‘‘ﬂow channeling’’ generally refers to con-

centration of the ﬂow network in a relatively small number

of ‘‘ﬂow channels’’ or ‘‘ﬂow pathways’’, as opposed to

evenly dispersed ﬂow in the medium. In the context of ﬂow

in fractured media, its meanings are manifold. When ﬂuid

ﬂow along a given single fracture is concerned, ‘‘ﬂow

channeling’’ is used to describe the distinctive linear

channels forming along this planar fracture (Tsang and

Tsang 1987; Tsang and Neretnieks 1998; Auradou et al.

2006). In the reservoir scale involving a network of frac-

tures, ‘‘ﬂow channeling’’ refers to a ﬂow pattern in which a

small portion of the fractures carry the majority of the ﬂuid

ﬂow. The primary reason for channelized ﬂow in these two

cases is the heterogeneous spatial distribution of fracture

transmissivity, along a given fracture plane and within the

fracture network, respectively. ‘‘Flow channeling’’ also

refers to the process through which a channelized ﬂow

pattern forms or evolves due to various mechanisms.

The present study focuses on the evolution of ﬂow

channeling at the reservoir scale associated with thermal

drawdown in EGS. An intuitive mechanism for this process

&Pengcheng Fu

fu4@llnl.gov

Atmospheric, Earth, and Energy Division, Lawrence

Livermore National Laboratory, Livermore, CA 94550, USA

123

Rock Mech Rock Eng (2016) 49:1001–1024

DOI 10.1007/s00603-015-0776-0

is illustrated in Fig. 1as follows: at the commencement of

the production phase of an EGS (before signiﬁcant thermal

drawdown has taken place), the ﬂow pattern from the

injection well(s) to the production well(s) is likely to be

somewhat channelized, owing to the inherent heterogeneity

of the fracture system (i.e. the second phenomenon descri-

bed in the previous paragraph). The thicker and thinner lines

in Fig. 1a represent ﬂow paths with higher and lower ﬂow

rates, respectively. During heat production, fractures that

carry higher ﬂow rates are likely to cool faster. Thermal

stress in the cooled rock (the blue zone in Fig. 1b) is typi-

cally a tensile increment in addition to the original com-

pressive in situ stress. It tends to reduce the magnitude of

the total compressive stress on fractures inside the cooled

rock, thereby increasing the permeability along these frac-

tures. Therefore, a likely scenario is that ﬂow will further

concentrate in these cooled fractures and diminish in others

as shown in Fig. 1b. This is undesirable for EGS because it

reduces the effective heat exchange area of the reservoir and

undermines long term thermal performance. This mecha-

nism has been demonstrated by numerical models, such as

those in Hicks et al. (1996), DuTeaux et al. (1996), and Koh

et al. (2011). It has been observed in several EGS projects

that the overall ﬂow impedance between the injection and

production wells decreases with heat production (Kohl et al.

1995), which could be a manifestation of the hypothetical

mechanism. However, tracer tests at the Fenton Hill EGS

site indicated that the ﬂow pattern became more diffuse at

certain stages of the heat production operation (DuTeaux

et al. 1996). Flow channeling, particularly the mechanisms

of ﬂow channeling, in EGS during heat production deserves

further investigation.

The phenomenon to be studied herein entails coupled

mechanical, hydrological, and thermal processes. Hence,

the numerical model must simulate all the three aspects of

the problem and their coupling. Various coupled thermal–

hydrological–mechanical (THM) models and models cou-

pling two of the three aspects for geothermal reservoirs

have been developed and reported in the literature. Models

for conventional geothermal resources, namely hydrother-

mal systems dominated by ﬂow in porous rock formations,

typically handle ﬂuid and heat ﬂow using porous medium

ﬂow theories (see a review in O’Sullivan et al. 2001).

Mechanical coupling capability can be added to these

models through rock constitutive models based on contin-

uum mechanics, which quantiﬁes the stress–strain rela-

tionship of the porous medium (Hart and St. John 1986;

Rutqvist et al. 2002; Taron et al. 2009; Taron and Elsworth

2009). For EGS reservoirs dominated by ﬂow in fractures,

the porous medium models have been found to be inade-

quate (Nicol and Robinson 1990), and explicit represen-

tation of the fracture system is necessary. A number of

models in the literature focus on the ﬂow and deformation

of a single fracture. Such models could be useful for

reservoirs that are dominated by a single fracture (Bo

¨d-

varsson and Tsang 1982; Ghassemi et al. 2007). Several

coupled THM models based upon discrete fracture network

(DFN) ﬂow have been developed. The early models usually

handle simple fracture network patterns whereas the more

advanced ones can deal with random fracture networks.

Many complex and interesting phenomena in EGS reser-

voirs have been revealed by the application of these

models, but a comprehensive study of thermal drawdown-

induced ﬂow channeling is still missing.

Fig. 1 Conceptual illustration

of the ﬂow channeling concept

in an idealized fracture network:

athe ﬂow ﬁeld in the initial

state, and bthe ﬂow ﬁeld after a

cooled zone has developed due

to heat production. The solid

arrowed line represents ﬂow

paths with the ﬂow rate denoted

by the line thickness

1002 P. Fu et al.

123

We present a fully coupled THM model for ﬂuid and

heat ﬂow in discrete fracture networks and use the model to

gain insight into the ﬂow channeling phenomenon associ-

ated with thermal drawdown. Despite the decades of effort

since the Fenton Hill experiment, EGS research is still in

the concept-validation phase and only a small number of

experimental sites have been developed so far (see reviews

in Jung 2013; McClure and Horne 2014). The objective of

the current study is to reveal physical mechanisms gov-

erning the ﬂow-channeling process through the study of a

set of reasonable synthetic reservoir conﬁgurations, and to

provide practically useful guidance for the development

and operation of EGS. We focus on behavior of hot-wet-

rock (HWR) geothermal systems (Willis-Richards et al.

1996), where the natural fracture network provides the

majority of the permeability and the reservoir is saturated

with water in its natural state.

2 Coupled THM Model

2.1 Modeling Strategy

Our strategy for modeling coupled THM processes in the

production phase of EGS reservoirs is based on the fol-

lowing considerations and assumptions:

•Matrix permeability of the rock formation is ignored

and all ﬂuid ﬂow is through the discrete fracture

network.

•Fluid pressure is lower than the ‘‘jacking’’ pressure,

namely the minimum in situ principal stress (effective

stress, compression is positive) in the rock formation.

In this pressure regime, the change of ﬂuid pressure in

fractures only induces minimal change of the stress

state in the surrounding rock matrix (Fu et al. 2012).

Therefore, the interaction between neighboring frac-

tures through a ‘‘stress shadowing’’ effect (Kresse et al.

2013) is insigniﬁcant and ignored in our model.

Because fractures in this pressure regime are still

closed, we consider the solid phase in the reservoir as a

continuum for the calculation of thermal stress.

•Thermal drawdown in EGS reservoirs is a relatively

slow process. Field observation and numerical model-

ing have both indicated that its effect on reservoir

behavior is only noticeable over a time scale of months

(Bruel 2002). We assume that the ﬂow ﬁeld is in a

steady state within each time step. We use a time step

that is sufﬁciently small so that the simulation results

are insensitive to further reduction of the time step size.

•The simulations are performed in two-dimensional

(2D) space under plane-strain conditions. The 2D

model can be considered as a horizontal cut through a

rock body containing steeply dipping fractures in the

normal stress regime (i.e. vertical stress is the major

principal component). Although it is well recognized

that many characteristics of random fracture networks

cannot be adequately represented by 2D models, and

the quantitative values from 2D models should not be

directly used for real world projects, we can still use 2D

models to gain insight into the physical processes

governing EGS reservoir performance, which would be

very useful for optimizing stimulation and production

strategies. Results of 2D models also inspire the

development of more sophisticated 3D models (Fu

et al. 2013; Settgast et al. 2012).

The numerical model consists of four main modules as

illustrated in Fig. 2. We brieﬂy describe the framework of

the numerical method and discuss the coupling strategy

between different modules. The details of each module are

provided in subsequent sections.

In each time step, a rock joint model and a DFN-based

ﬂuid ﬂow solver are ﬁrst invoked iteratively to calculate the

steady-state ﬂow ﬁeld in the fracture network. In this paper,

the word ‘‘joint’’ is used as a generic term referring to any

uncemented discontinuity in rock formations in a similar

fashion to Cook (1992). In each iteration, the ﬂow solver

determines the pressure distribution within the fracture

network for the given aperture width distribution and

boundary conditions. The rock joint model then returns the

aperture width of each ﬂow element for the next iteration,

determined by a function of the local total stress, the ﬂuid

pressure provided by the ﬂow solver, and the intrinsic joint

characteristics at each fracture segment. Once these itera-

tions converge, we obtain a fracture transmissivity ﬁeld and

a ﬂow ﬁeld that are consistent with the given stress

boundary conditions, ﬂow boundary conditions, and rock

joint characteristics for the current time step. Figure 3a

shows a random DFN and Fig. 3b shows the ﬂow rate ﬁeld

near the injection well solved by the DFN model where the

direction and width of the black triangles denote the ﬂow

direction and ﬂow rate, respectively.

Next, we use a porous medium-based heat and ﬂow

transport model (i.e. a TH ﬂow model) to advance the

temperature ﬁeld for the present time step. To this end, we

Fig. 2 Main modules of the coupled THM model. Symbols t,Dt, and

Tdenote time, time increment, and temperature, respectively

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1003

123

map the DFN-based transmissivity ﬁeld onto the perme-

ability ﬁeld of a regular grid used by the porous medium

model. The ﬂuid ﬂow solution obtained by the TH ﬂow

model is equivalent to that obtained by the DFN ﬂow

solver. The ﬂow solution is used to calculate the heat

transfer between the solid phase and the ﬂuid phase, as well

as the convective heat transport along the fratures. At the

end of the time step, the reservoir temperature ﬁeld is

obtained from the TH ﬂow model, and mapped onto a ﬁnite

element method (FEM) solid mesh for calculation of the

thermal stress. Finally, we update the total stress on each

fracture segment used in the DFN ﬂow module and start the

next time step. The time increment for a whole cycle

shown in Fig. 2is 4 months for all the simulations pre-

sented. We found that further reducing cycle duration did

not signiﬁcantly alter the simulation results. Note that each

cycle involves many (typically hundreds of) time steps of

the porous medium solver.

2.2 DFN Flow Solver

The DFN ﬂow solver uses a simple FEM formulation based

on two-node line elements. In two-dimensional space,

discrete fractures are geometrically represented by line

segments, and each fracture is discretized into line ele-

ments of approximately equal lengths. Intersection points

between fractures have to be represented by nodes, which

imposes an additional constraint on the discretization of the

fractures. According to the parallel plate laminar ﬂow

assumption, the ﬂow rate through a ﬂow element between

node iand node jis

Qij ¼ðPiPjÞw3

12lijlF

ð1Þ

where P

and P

are the ﬂuid pressure at two adjacent

nodes; l

is the length of the element; l

is the dynamic

viscosity of the ﬂuid; and wis the aperture width, which

Fig. 3 The mapping of variables used by different modules of the

coupled model. aA random discrete fracture network. bThe ﬂow

ﬁeld near the injection well in the DFN model after 3 years of

injection. cThe regular Cartesian grid used by the porous medium

model overlaid on the DFN. The DFN elements are shown in thin blue

lines. The darkness (gray to black) of the thickened cell–cell interface

lines quantiﬁes the transmissivity between adjacent cells, with darker

color denoting greater transmissivity. dPressure ﬁeld in the Cartesian

grid solved by the porous medium model. High pressure cells are

shown in red and unpressurized solid medium is in yellow.eThe

temperature ﬁeld (red denotes high temperature and blue low

temperature) solved by the porous medium model. fThe thermal

stress (yy component; tensile stress in red color and compressive in

blue) ﬁeld solved by the solid ﬁnite element model. These ﬁgures only

conceptually illustrate the mapping of variables between

meshes/models, so the color tables are not provided (color ﬁgure

online)

1004 P. Fu et al.

123

will be discussed in Sect. 2.3. A global system of gov-

erning equations is established by enforcing the mass

conservation condition that the net ﬂow into each node is

balanced by the net ﬂow out.

2.3 Rock Joint Model

The closure behavior of a fracture, namely the variation of

the aperture width wwith respect to the effective stress r0

is often characterized by joint models in rock mechanics, of

which the Barton-Bandis model (Bandis et al. 1983; Barton

et al. 1985) is a classical example. The model states

r0¼wmax w

aJbJðwmax wÞ;ð2Þ

where r0is the effective compressive stress, i.e. the dif-

ference between the total normal stress r

acting on the

fracture and the ﬂuid pressure Pwithin the fracture; w

max

the aperture width at the zero-effective stress state, which

is essentially the maximum joint closure in the original

joint model of Bandis et al. (1983); a

and b

are two

material- and state-speciﬁc constants. This constitutive

model for rock joints has been widely used in various

numerical models for fracture-dominated geothermal

reservoirs (Kohl et al. 1995; Bower and Zyvoloski 1997;

Bruel 2002). If we identify a second reference state with

effective normal stress r0

ref

and the corresponding aperture

width w

ref

, the two material constants can be calculated as

aJ¼wmax

wmax wref

rref wref

and bJ¼wmax

wmax wref

rref wref

:ð3Þ

In our previous work (Fu and Carrigan 2012), we have

proposed to use parameters a

and b

as state variables to

reﬂect the effects of shear dilation on closure behavior of

rock joint. Since we focus on the production phase instead

of the stimulation phase of the reservoir, the two state

variables are constants for all fracture elements in the

current study. Note that the aperture width of individual

fracture segments can still vary based on the total stress and

ﬂuid pressure.

2.4 Modeling Heat Transfer Using an Effective

Porous Medium Model

Heat transfer in the fractured reservoir is simulated using a

dual-continuum model implemented in a porous medium-

based ﬂow and transport code NUFT (Nonisothermal

Unsaturated–saturated Flow and Transport). NUFT is

based on Darcy’s ﬂow approximation and models multi-

phase, multi-component heat and mass ﬂow and reactive

transport in unsaturated and saturated porous medium

(Nitao 1998; Hao et al. 2012). The formulation and veri-

ﬁcation of the dual-continuum model have been detailed in

Hao et al. (2013) and are not repeated here. In this section,

we present the procedure of converting the ﬂow ﬁeld

obtained by the DFN-based model to that on a regular

Cartesian grid used by NUFT.

Because the heat ﬂow in fractured geothermal reser-

voirs is closely associated with ﬂuid ﬂow in the medium,

we have to create a ﬂow ﬁeld that is consistent with that

obtained by the DFN-based solver and compatible with the

regular Cartesian grid usedbyNUFT.Wedevelopeda

method similar to the ‘‘fracture continuum’’ method pro-

posed by Botros et al. (2008) and Reeves et al. (2008)and

overlay the DFN-based fracture elements onto the Carte-

sian grid used by NUFT as shown in Fig. 3c. In NUFT, the

permeability ﬁeld is represented by the conductivity

between any two adjacent cells. In the two overlaid

meshes, if a fracture element geometrically intersects the

interface (a line segment in 2D) between two adjacent

porous medium cells in the regular grid, this fracture

segment’s contribution to the conductivity between these

two cells is

Dk¼ChðÞw3

12Að4Þ

where kis the permeability of the porous medium

according to Darcy’s law; Ais the area (length in 2D) of

the interface between the two cells; his the angle between

the fracture element and the Cartesian grid axis; and

C(h)=|sinh|?|cosh|, is a correction factor to compensate

for the longer ﬂow paths in the Cartesian grid than the

corresponding length of the fracture. This mapping is

illustrated in Fig. 3c, where the darkness of the thickened

cell–cell interface lines denotes the transmissivity between

these two cells. The permeability of an inter-cell interface

can be contributed to by multiple fractures and the prin-

ciple of superposition applies. Only the fracture elements

that carry non-zero ﬂow are included in the mapping, and

that is why most of the cell–cell interface lines are not

thickened, even though many of them are intersected by

fractures that do not carry ﬂow. This is an advantage of our

proposed method compared to the fracture continuum

method (Botros et al. 2008; Reeves et al. 2008) in which a

similar mapping is carried out. In the latter the DFN are

pure geometrical entities and the ﬂow ﬁeld is only solved

by the porous medium solver. If the Cartesian grid spacing

is comparable to or greater than discrete fracture spacing,

false transmissivity can be generated by discrete fracture

segments that do not carry ﬂow, a well known phenomenon

that causes over-prediction of ﬂow (Botros et al. 2008;

Reeves et al. 2008). By ignoring DFN elements that do not

carry ﬂow, our method maps the actual ‘‘ﬂow ﬁeld’’ solved

by the DFN solver instead of mere DFN geometries.

Therefore, the ﬂow ﬁeld solved by the porous medium

solver is nearly identical to the DFN ﬂow ﬁeld and the

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1005

123

results are insensitive to the resolution of the Cartesian

grid.

To continue the example illustrated by Fig. 3a–c,

Fig. 3d shows the pressure ﬁeld solved by the porous

medium solver and Fig. 3e shows the temperature ﬁeld

evolved by NUFT. Additionally, an example of a DFN-

based ﬂow ﬁeld and its equivalent representation with a

regular grid is presented in Fig. 13 along with the

numerical examples in Sect. 4.2.

2.5 Calculation of the Thermal Stress

As discussed in Sect. 2.1, we treat the rock body containing

closed fractures as a continuum for the calculation of

thermal stress. The ﬁnite element mesh for this purpose can

be established independently. We map the temperature

ﬁeld onto the continuum FEM mesh at the center of each

element. The thermal stress ﬁeld is calculated following the

procedure outlined in Sect. 2.10 of Cook et al. (2001). The

approach is a standard method employed in thermo-me-

chanical ﬁnite element analysis and not repeated here. The

thermal stress (yy-component) corresponding to the tem-

perature ﬁeld in Fig. 3e is shown in Fig. 3f.

Initially, the ﬂuid pressure is lower than the minimum

principal in situ stress, ensuring that all fractures are

closed. Over time, however, changes in the thermal stress

can reduce the total stress in the rock to the extent that

some fractures open due to the contraction of surrounding

rock. In this situation, the aperture size cannot be deter-

mined by the joint model in Sect. 2.3 and ideally should be

calculated with a fully coupled model, such as that of Fu

et al. (2013), with open fractures explicitly meshed in the

FEM model. For all of the simulations in the present paper,

this condition only occurs within a limited area near the

injection well. When these fractures (usually a small

number) open, the ﬂow rate is determined by the closed

fractures that are connected to these open fractures, and

thus the transmissivity of the open fractures has minimal

effect on the overall ﬂow ﬁeld. Therefore, we assign a large

value, for instance 2w

max

to the aperture width of opened

fractures.

The three main modules in the numerical model use

three distinct meshes: the DFN solver uses an FEM mesh

composed of two-node line elements; NUFT uses a regular

Cartesian grid; and the thermal stress module uses a solid

mechanics FEM mesh. The three meshes do not need to

conform with each other as long as variable mapping

between meshes is correctly handled. In all the simulations

presented, the minimum distance between any two sub-

parallel fractures is 10 m, and the resolutions for the DFN

models, NUFT models, and the thermal stress FEM models

are all approximately 8 m, unless explicitly speciﬁed

otherwise.

3 A Highly Idealized Baseline Case

In this section, we study a reservoir with a highly idealized

fracture system as the baseline case, which enables us to

identify expected common behavior of fractured geother-

mal reservoirs, as well as a new mechanism that counter-

acting the ﬂow channeling mechanism described in Sect. 1.

3.1 Model Setup

The idealized reservoir consists of two orthogonal fractures

sets forming a regular grid as shown in Fig. 4.A2D

coordinate system is established so that the x-axis points

east and the y-axis points north. We term the fracture set

parallel to the x-axis the ‘‘x-set’’ and the other the ‘‘y-set’’.

The domain, as well as the fracture network, is assumed to

be inﬁnite, and the numerical model is made large enough

to minimize the effects of far-ﬁeld boundaries. Fracture

spacing for both sets is 20 m. The in situ stress components

are r

=18 MPa and r

=25 MPa, where r

and r

are the minimum and maximum horizontal princi-

pal stresses, respectively. Note that r

happens to be the

normal stress acting on the y-set and r

acts on the x-set.

The production well is 600 m north of the injection well,

and each well is at an intersection of two fractures. The

original natural ﬂuid pressure in the fracture system is

15 MPa, and the pressure boundary condition at the far-

ﬁeld boundary is ﬁxed at this value. The resolution of the

Fig. 4 Layout of the idealized reservoir consisting of two inﬁnite

orthogonal fracture sets. Note that only the center portion of the

numerical model is shown. In all the layout maps in the present paper,

the locations of the injection well and the production well are denoted

by small circles

1006 P. Fu et al.

123

DFN mesh is 4 m. Some other important parameters are

shown in Table 1. Note that properties of real water are

functions of the water’s state such as temperature and

pressure. Using constant properties introduces certain

amount of error in the calculated results, mainly in calcu-

lated the pressure loss. However, since the main phe-

nomenon investigated by the current study, namely ﬂow

channeling associated with reservoir temperature drop, is

caused by thermal–mechanical coupling that is indepen-

dent of water property change, these constant properties are

not expected to affect the comparison between the sce-

narios investigated herein.

Although we use the same rock joint parameters for the

two joint sets, their initial apertures are affected by the

anisotropic in situ stress and thus not the same. According

to the joint model described by Eq. (2), the aperture widths

for the x-set and y-set with zero-ﬂuid pressure are 0.066

and 0.082 mm, respectively. The y-set has signiﬁcantly

higher hydraulic transmissivity than the x-set, which is the

primary reason for the north–south well layout. We term

the y-set fractures the primary set and the x-set the sec-

ondary set.

3.2 Pumping Pressure—Circulation Rate Response

of Reservoir Before Thermal Drawdown

For all the simulations in the present paper, we use ﬂow

rate–controlled boundary conditions at the two wells. The

injection rate is ﬁxed at the same value as the production

rate, emulating a common circulating strategy used in

existing EGS sites (Genter et al. 2012,2013; Hogarth and

Bour 2015). To determine an appropriate ﬂow rate, we run

a series of simulations at different circulation rates and

obtain the injection and extraction pressure required as

shown in Fig. 5. Note that all pressures presented in the

current paper are the pressure at the reservoir depth. The

results indicate that a higher circulation rate would require

higher injection pressure and lower extraction pressure

(higher net extraction pressure or stronger ‘‘suction’’), as

expected. Both curves are nonlinear, especially the

extraction curve, which reﬂects the fact that as we increase

the net extraction pressure (the absolute difference between

the extraction pressure and the far-ﬁeld pore pressure) the

aperture near the extraction well decreases and the system

hydraulic impedance increases. This implies that with

increased pressure signiﬁcantly more pumping power is

required for the same amount of marginal increase of cir-

culation rate. Based on the results, we choose 20 liters per

second per 100 m thick reservoir (L/s/100 m) as the cir-

culation rate at an initial injection pressure of 16.5 MPa

and an initial extraction pressure of 9.7 MPa for the anal-

ysis in the rest of Sect. 3. Since 9.7 MPa is the hydrostatic

pressure at approximately 1 km depth, a downhole pump

would be required if the reservoir is deeper than 1 km.

3.3 Reservoir Behavior Without

Thermo-Mechanical Effects

Figure 6shows the ﬂow ﬁeld obtained by the DFN solver

at the beginning of the production phase (i.e. no signiﬁcant

temperature change in the reservoir has occurred). In this

ﬁgure and all subsequent ﬁgures quantifying DFN ﬂow

ﬁelds, we use the orientation and width of the gray trian-

gles to denote the ﬂow direction and ﬂow rate, respectively.

Assuming 100 m thick reservoir, a fracture ﬂow rate of

1.0 L/s is corresponding to a triangle 2.4 m wide. The scale

of ﬂow visualization, i.e. the ratio of triangle width to

fracture ﬂow rate is the same for all plots in the current

Table 1 Model parameters for

the idealized baseline

simulation

Parameter Value

Original in situ stress r

=18 MPa (east–west)

=25 MPa (north–south)

Original pore pressure P

=15 MPa

Rock joint parameters w

max

=1.0 mm

ref

=20 MPa

ref

=0.08 mm

Initial reservoir temperature T

=150 C

Injection ﬂuid temperature T

=50 C

Mechanical properties of rock Young’s modulus E=20 GPa

Poisson’s ratio m=0.2

Linear thermal expansion coefﬁcient a

=8910

-6

Thermal properties of rock Thermal conductivity K

=3 W/m/C

Heat capacity C

=2.5 MJ/m

/C

Fluid properties Dynamic viscosity l

=0.001 Pa s

Heat capacity C

=4.2 MJ/m

/C

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1007

123

paper. A few y-set fractures near the center of the domain

carry the majority of the ﬂow. In this region, the ﬂow rate

in the y-set fractures is substantially higher than in the x-set

fractures, because the total stress on y-set is lower than that

on x-set, resulting in wider apertures. However, because

only one fracture in the y-set is directly connected to the

two wells, ﬂow in all the other y-set fractures must be

‘‘fed’’ by x-set fractures intersecting with them. Therefore,

the low conductivity of the x-set fractures is the main

reason why more dispersed ﬂow patterns cannot form

under the given conditions. We term the ﬂow along the

y-direction the primary ﬂow and that along the x-direction

the secondary ﬂow. Clearly, ﬂow in both directions is

needed to form a ﬂow network. Also note that there is a

signiﬁcant amount of ﬂuid injected into the reservoir ﬂows

along the negative y-direction, i.e. the direction away from

the production well. Figure 6b shows that such ‘‘runaway’’

ﬂow is gradually diverted by x-set fractures, and it even-

tually reaches the production well through peripheral ﬂow

channels. The ﬂow into the production well that originates

from the far-ﬁeld (as shown in Fig. 6c) is caused by the

same mechanism. In this paper, we refer to such ﬂow as

‘‘peripheral ﬂow’’. The aforementioned behaviors of the

ﬂow network are clearly illustrated by Fig. 7, where ﬂow

diversion and merging have caused discontinuity in the

ﬂow rate along the two fractures shown, at x=0 and

x=60 m, respectively.

If we disregard the thermo-mechanical (TM) effects on

ﬂow channeling, we can directly use NUFT to simulate the

temperature ﬁeld evolution in the reservoir without

requiring the full procedure shown in Fig. 2. The results

provide a useful baseline reference for the study of ﬂow

pattern changes due to TM effects. The evolution of pro-

duction temperature for this scenario is shown in Fig. 8as a

solid line, and the reservoir temperature ﬁelds 5, 10, 20,

and 30 years into the production phase are shown in Fig. 9.

According to the simulation results, the cooling front

arrives at the production well in less than 5 years of pro-

duction. The production temperature gradually decreases

afterwards and is approximately 98 C after 30 years of

production.

Fig. 5 Pumping pressure—circulation rate relationship of the ideal-

ized reservoir. The unit of circulation rate is liter per second for a

100 m thick reservoir. The pressure is that at the intersection between

the wellbores and the reservoir

Fig. 6 Initial ﬂow ﬁeld in the idealized reservoir. The direction and

width of the gray triangles denote the ﬂow direction and ﬂow rate,

respectively. Assuming 100 m thick reservoir, a fracture ﬂow rate of

1.0 L/s is corresponding to a triangle 2.4 m wide. This ratio applies to

all ﬂow rate visualizations throughout the paper wherever applicable.

The simulation domain is 1600 m 91600 m and not fully shown.

Fractures with ﬂow rates smaller than 0.2 L/s are not shown. aThe

domain enclosing the two wells; bmagniﬁes the region around the

injection well; and cmagniﬁes the region around the production well

1008 P. Fu et al.

123

3.4 Coupled THM Simulation Results

If we invoke the THM coupling loop shown in Fig. 2, the

ﬂow pattern will evolve with the temperature ﬁeld. The

production temperature history obtained by the coupled

simulation is shown as the dotted line in Fig. 8. Snapshots

of the temperature and ﬂow ﬁelds are shown in Fig. 10.

By comparing the temperature and ﬂow ﬁelds between

Figs. 9and 10 at year 5, we see that the TM effects tend to

divert ﬂow from the center fracture in the y-set, which

directly connects the two wells, to a few y-set fractures

running parallel to the center fracture. This causes a

slightly more diffuse ﬂow pattern. This phenomenon is also

evident in Fig. 7: after 5 years, the ﬂow rate in the fracture

at x=0 m between y=-300 m and y=-200 m is

substantially lower than the initial state; and in the fracture

at x=60 m ﬂow rate has signiﬁcantly increased in the ﬁrst

5 years. This trend is also consistent with the observed

response of the temperature ﬁeld: when the TM effects are

considered, the cooled zone is wider and the cooling front’s

propagation toward the projection well is slightly slower.

The TM effects substantially impede peripheral ﬂow

(deﬁned in Sect. 3.3) in the reservoir. After 20 years, ﬂow

is almost completely concentrated in the cooled rock vol-

ume. This is one of the factors contributing to the fast

decrease of production temperature after thermal break-

through. In the scenario ignoring TM coupling, nearly half

of the ﬂow into the production well is through peripheral

ﬂow channels, and this portion of the ﬂuid is not affected

by the cooling of the interior reservoir. Therefore, the ﬂuid

extracted from the production well is indeed a mix of the

relatively cold ﬂuid from the interior ﬂow and the hot ﬂuid

from the peripheral ﬂow. On the other hand, because TM

coupling impedes peripheral ﬂow, the ﬂow into the pro-

duction well is primarily through the cooled reservoir, so

the production temperature declines rather rapidly. Due to

the same mechanism, the cooled zone extends quite far in

the negative y-direction if TM coupling is ignored, while

this extension is impeded when the full TM coupling is

considered.

3.5 Anisotropic Thermal Stress and its Implication

for Flow Channeling

We observe in Figs. 9and 10 that the cooled zone in the

reservoir elongates along the primary ﬂow direction

because of the fast cooling of rock adjacent to the fractures

that carry high ﬂow rate. Understanding of the anisotropy

in thermal stress caused by this elongated cooling geometry

is critical for gaining insight into the TM effects on ﬂow

channeling. To this end, we consider an idealized case for

which closed-form solutions for thermal stress are avail-

able. This inﬁnite 2D medium (plane-strain) has homoge-

neous physical and mechanical properties except that the

temperature of an elliptical zone is DTlower than that of

the rest of the medium, as illustrated in Fig. 11. The two

principal axes of the ellipse align with the two coordinate

axes, respectively, and the dimensions are 2aalong the

x-direction and 2balong the y-direction. Thermal stress

develops in this cooled zone as well as in the medium

surrounding it as a result of the cooling. The thermal stress

inside the cooled zone is homogeneous, which can be

calculated using our ﬁnite element model and can also be

calculated using the following equations, which are

Fig. 7 Flow rate along two y-set fractures, one at ax=0 and the

other one at, bx=60 m as marked in Fig. 5. The injection well is

located at x=0, y=-300 m and the production well at y=300 m.

Flow along the positive direction of the y-axis is considered to have a

positive ﬂow rate and against this direction negative. Flow rate along

each straight fracture is continuous within each 20 m segment

between intersections but appears discontinuous due to the diversion

of ﬂow to or from the x-set fractures

Fig. 8 Evolution of ﬂuid temperature at the production well for the

idealized reservoir

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1009

123

simpliﬁed forms of the solution provided by Mindlin and

Cooper (1950):

x¼aEDTaL

ðaþbÞð1mÞ;ð5Þ

y¼bEDTaL

ðaþbÞð1mÞ;ð6Þ

where Eis the Young’s modulus of the medium; mis the

Poisson’s ratio of the medium; and a

is the linear thermal

expansion coefﬁcient. Both normal components are tensile,

which result in the negative sign. The ratio of the magni-

tude of the two thermal stress components rT

x.rT



happens to be the aspect ratio of the ellipse. Note that

closed-form solutions for thermal stress are only available

for such a highly idealized case. Thermal stress for all the

cases in the current paper is calculated using coupled

thermal–mechanical ﬁnite element analysis.

Although the shape of the cooled zones shown in Figs. 9

and 10 is not exactly elliptical and the temperature in the

cooled zone is not uniformly distributed, the anisotropy in

thermal stress, shown in Fig. 12, resembles that of the

elliptical cooled zone scenario to some extent. Therefore,

the thermal stress along the primary ﬂow direction (i.e.

y-direction) is substantially greater (in absolute magnitude)

than that along the secondary ﬂow direction. Since thermal

stress in the cooled zone is tensile and it tends to reduce the

total normal stress (compressive) on fractures, the aniso-

tropic thermal stress opens the secondary fracture set (the

x-set) more than it does the primary set. As discussed in

Sect. 3.3, this results in a more diffuse ﬂow pattern, and

thus ﬂow must be fed into more primary set fractures

through secondary set fractures. However, under aniso-

tropic in situ stress, the secondary set acts as a bottleneck in

the system and prevents highly diffuse ﬂow patterns from

forming. The anisotropic thermal stress is likely to

Fig. 9 Reservoir temperature

distribution in the idealized

reservoir if thermo-mechanical

effects are ignored. The ﬂow

ﬁeld is overlaid onto the

temperature ﬁeld but it does not

evolve over time since the THM

coupling is disabled

Fig. 10 Reservoir temperature

distribution in the idealized

reservoir if thermo-mechanical

coupling is engaged. The ﬂow

ﬁeld is overlaid onto the

temperature ﬁeld and evolves

over time along with the

temperature ﬁeld evolution

1010 P. Fu et al.

123

counteract the anisotropic in situ stress and enhance the

conductivity of the secondary set fractures. This is the main

reason for the more diffuse ﬂow pattern and wider cooled

zone in Fig. 10 than those in Fig. 9.

In Fig. 12 we also observe signiﬁcant compressive

thermal stress (denoted by the blue regions) develops along

the periphery of the reservoir. This compressive stress

increment tends to further compress the fractures around

the cooled reservoir, which is an important mechanism that

impedes peripheral ﬂow.

In summary, the analysis of the highly idealized reser-

voir reveals the primary effect of TM coupling: it causes

more open fractures inside the cooled reservoir and tighter

fractures in the exterior compared with the initial states.

The combined effect is that ﬂow tends channelize inside

the cooled reservoir, inducing rapid temperature decreases

once thermal breakthrough has taken place. As a secondary

effect, the anisotropy in the thermal stress increment tends

to open the secondary set more than it does the primary set,

which encourages a more diffuse ﬂow pattern well before

thermal breakthrough takes place, at least for fracture

networks with intensive interconnectivity. This effect can

delay thermal breakthrough.

4 Behavior of Random Fracture Networks

In this section, we investigate the THM responses of

reservoirs with various fracture network patterns and well

spacing. In real world reservoirs, natural fractures were

created by a variety of geophysical and geological pro-

cesses in rock formations. Certain characteristics of the

natural fracture system in a given formation can be quan-

tiﬁed, at least to some extent, through observations on

formation outcrops and wellbore logs (e.g. Engelder et al.

2009), but such knowledge is generally scarce. Therefore,

we investigate a number of artiﬁcially generated fracture

networks that collectively represent a variety of distinct

characteristics of fracture networks. The main objective is

to reveal how these network characteristics qualitatively

affect the thermo-mechanical-hydrological behavior of the

reservoir, rather than to quantify the performance of

speciﬁc reservoirs.

4.1 Reservoir Characteristics

We ﬁrst investigate ﬁve distinct fracture networks, Net-

works B through F, illustrated in Fig. 13. Network A

denotes the idealized case introduced in Sect. 3.

A few properties are shared by all of the fracture net-

works. All networks have the same fracture intensity in

terms of total fracture trace length (area in 3D) per unit

area (volume in 3D). The initial pore pressure, temperature,

and in situ stress of all the reservoirs are the same as those

of the baseline case. We also use the same circulation rate,

20 L/s/100 m thick reservoir for all the cases.

Geometrical characteristics of a fracture network in 3D

are usually statistically quantiﬁed by a rather complex set

of parameters (Dershowitz and Einstein 1988). In 2D, the

situation is simpler and the main difference between 2D

fracture networks is the fracture pattern, namely orientation

and length distributions. In Network B, the orientations of

fractures follow a uniform distribution within all possible

directions, and the concept of ‘‘fracture sets’’ does not

apply to this network. If we use a variable hto denote the

orientation of a fracture with respect to the x-axis, hfol-

lows a continuous uniform distribution in the interval

Fig. 11 Geometry of an elliptical-shaped cooling zone in an inﬁnite

medium. The analytical solution for the thermal stress in the cooling

zone demonstrates the relationship between the shape of the cooling

zone and the anisotropy of the thermal stress

Fig. 12 Thermal stress in the idealized reservoir after 20 years of

production. Compressive stress increment is positive

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1011

123

0Bh\180. Networks C through F each have two

distinct fracture sets. We term the set that is approximately

along the north–south direction the ‘‘primary set’’ and the

other the ‘‘secondary set’’, denoted by subscripts ‘‘P’’ and

‘‘S’’, respectively. The orientations and lengths (l) of each

fracture are randomly generated within a speciﬁed range.

These ranges are provided in Table 2for all the networks.

Note that the fracture generation algorithm enforces the

rule that no sub-parallel fractures should intersect with

each other. The two sets in Network C have similar fracture

lengths. The primary set in Network D has signiﬁcantly

longer fracture than the secondary set, whereas fractures in

the secondary set of Network E are signiﬁcantly longer

than those in the primary set. The two sets in Network F

have similar fracture lengths, but the fractures are much

shorter than those in Network C.

Although all networks have the same fracture intensity,

the permeability provided by each network also depends of

the connectivity of the fractures, which, to some extent, can

be quantiﬁed by the average number of fracture–fracture

intersections (n

) on each fracture. The n

values for all the

networks are shown in Table 2. Networks B through E are

all well above the percolation threshold (Berkowitz and

Ewing 1998), which means that many ﬂow paths can be

established within the fracture network between two given

points. On the other hand, Network F is barely above the

percolation threshold. In order to carry out a ‘‘fair com-

parison’’, it is highly desirable to study and compare

reservoirs under the same production rate, which requires

comparable overall hydraulic impedances. Among other

parameters, fracture intensity, fracture orientations, frac-

ture dimension, fracture connectivity, and in situ joint

characteristics directly affect the hydraulic impedance of

the reservoirs. We choose to alter the joint parameters of

these networks to compensate for the difference in fracture

connectivity so that the overall ﬂow impedances are com-

parable across all scenarios with the same fracture inten-

sity. The current study focuses on reservoir behavior

common to all the scenarios evaluated and none of the

conclusions to be drawn is a result of the speciﬁc joint

parameter values. We are primarily concerned with the

evolution of ﬂow impedance of each individual scenario,

and do not intend to compare the absolute values of ﬂow

impedance across different reservoirs. Therefore, the joint

parameters used for the different reservoir scenarios do not

affect the conclusions reached in this study. The approach

taken is analogous to a comparison of actual reservoirs

with different fracture connectivities but similar overall

hydraulic impedances.

For each network, excluding Network F, we evaluate

three inter-well distances: 400, 600, and 800 m. In the case

of Network F, only the 600 m inter-well distance is con-

sidered. The production well is due north of the injection

well. To establish a connection between the wells and the

in situ fracture network, we create a hydraulic fracture,

running 80 m to the north and to the south of each well. In

all other regards, we assume the hydraulic fractures to

behave in the same manner as the pre-existing natural

fractures. The simulation domain is 2400 m 92400 m in

size, sufﬁcient for simulating the thermal, hydrological,

and mechanical effects of the far ﬁeld. In Sects. 4.2–4.6,

we focus on the scenarios with 600 m inter-well distance

and study the effects of well distance in Sect. 4.7.

4.2 Initial Flow Field

The initial ﬂow patterns for the ﬁve fracture networks with

600 m well spacing are shown in Fig. 14. The same

Fig. 13 Fracture connectivity patterns for the ﬁve representative fracture networks. Only the center portion of each network is shown. The

injection well and production well denoted are 600 m apart, although 400 and 800 m spacings are also investigated

1012 P. Fu et al.

123

circulation rate (20 L/s/100 m) is applied to all the net-

works. The initial pressure drop between injection and

production wells for Networks B to F is 7.0, 10.6, 8.3, 12.9,

and 10.6 MPa, respectively. As different joint parameters

are used for each network, the comparison of these values

does not offer much insight into hydraulic behaviors of

these networks.

In Network B, the fracture orientations are isotropic, so

the concepts of primary and secondary fracture sets are

inapplicable. For Network C, the primary set and the sec-

ondary set are geometrically similar. However, their aper-

tures are signiﬁcantly different because the in situ stresses

in the x-direction (r

=18 MPa, acting on the y- or pri-

mary set fractures) and that in the y-direction (r

=25 -

MPa, acting on the x- or secondary set fractures) are rather

different. These two networks are similar to the baseline

regular Network A in the sense that the two fracture sets

cannot be differentiated based on geometrical features

only. Consequently, the initial ﬂow patterns of these three

networks exhibit certain similarities: Flow tends to con-

centrate in fractures along the north–south direction. Some

secondary set fractures (east–west oriented fractures in

Network B) have to be engaged as they are necessary for

connecting the primary set fractures together. In Network

D, the primary-set fractures are longer than the secondary-

set fractures and on average each primary-set fracture

intersects 6.74 secondary-set fractures while each sec-

ondary fracture intersects 2.48 primary-set fractures. Flow

in a primary set fracture in Network D can travel a rela-

tively long distance without having to diverge into sec-

ondary set fractures. Meanwhile, ﬂow in a secondary

fracture does not need to travel a long distance to ﬂow into

another primary set fracture. Therefore, the active ﬂow

paths in Network D do not spread as wide as those in

Network C in the east–west direction. The situation in

Network E is the opposite and consequently, the active

ﬂow paths spread more widely in the east–west direction

than those in Networks C and D. Network F is a special

scenario with low fracture connectivity that is barely above

the percolation threshold. Apart from ﬂow to and from the

far ﬁeld, there is only one major ﬂow path between the two

wells. Although this ﬂow path splits at some points along

the way, the branches soon merge back into a single path.

All the ﬁve initial ﬂow networks have signiﬁcant peripheral

ﬂow through the far ﬁeld network.

4.3 Reservoir Performance Without TM Coupling

If we ignore the TM coupling for the sake of understanding

the impact of channelized ﬂow, we can use NUFT alone to

calculate the responses of the reservoirs during heat pro-

duction. The production temperature evolution for all the

six fracture networks, including the regular grid discussed

in Sect. 3, is shown in Fig. 15. Note that simulations

ignoring TM coupling only have conceptual signiﬁcance,

since TM coupling always takes place in a real reservoir.

However, we can use the results as a proxy for character-

izing the diffusivity of the initial ﬂow network, and the

results are consistent with a visual assessment of Fig. 14:

ﬂow paths in Network B and those in Network C have

comparable diffusivity, and these two reservoirs have

similar thermal performance; ﬂow paths in Network D are

slightly more concentrated than those in Network C, and its

thermal performance is moderately worse; Network E has

the most diffuse ﬂow paths among all the six scenarios and

it also has the longest lasting thermal performance. Net-

work A and Network F have similar thermal performance

that is signiﬁcantly worse than that of the other four sce-

narios. Although they are at the two ends of the percolation

number (i.e. fracture connectivity) spectrum, they share

one common characteristic: the ﬂow ﬁeld is dominated by a

single ﬂow path. For Network A, it is the fracture directly

connecting the two wells; for Network F, only one viable

ﬂow path between the two wells can be established besides

peripheral ﬂow paths. The ﬂow path in Network A has

much lower hydraulic impedance that that in Network F,

Table 2 Characteristics of the ﬁve randomly generated fracture networks

Network B Network C Network D Network E Network F

Fracture orientation 0Bh\18075Bh

\85

-5Bh

\5

75Bh

\85

-5Bh

\5

75Bh

\85

-5Bh

\5

75Bh

\85

-5Bh

\5

Fracture length 150 m \l\300 m 150 m \l

\300 m

150 m \l

\300 m

150 m \l

\300 m

60 m \l

\120 m

60 m \l

\120 m

150 m \l

\300 m

60 m \l

\120 m

60 m \l

\120 m

Fracture connectivity n

=7.08 n

i_p

=6.38

i_s

=6.42

i_p

=6.75

i_s

=2.48

i_p

=2.50

i_s

=6.66

i_p

=2.63

i_s

=2.59

Joint model parameters w

max

=1.0 mm

ref

=20 MPa

ref

=0.12 mm

max

=1.0 mm

ref

=20 MPa

ref

=0.12 mm

max

=1.0 mm

ref

=20 MPa

ref

=0.15 mm

max

=1.0 mm

ref

=20 MPa

ref

=0.15 mm

max

=1.0 mm

ref

=20 MPa

ref

=0.3 mm

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1013

123

but this difference only affects the overall hydraulic

impedance of the reservoirs, not the thermal performance

without TM coupling.

The temperature distribution in the reservoirs after

20 years (TM effects ignored) of production is shown in

Fig. 16. The shapes of the cooled zones are consistent with

the ﬂow ﬁelds: if the ﬂow paths spread wide along the east–

west direction, the corresponding cooled zone is also wide.

The propagation of the cooling front is slower towards the

production well if the cooled zone is wider, implying more

desirable thermal performance. The cooled zones in all ﬁve

simulated reservoirs extend signiﬁcantly southwards due to

the peripheral ﬂow.

4.4 Reservoir Behavior With TM Coupling

The production temperature of the ﬁve random fracture

networks calculated by THM coupled simulations is shown

in Fig. 17 along with the results for Network A. The

temperature and ﬂow ﬁelds after 2.5, 5, 10, 20, and

30 years of production at the constant circulation rate of

20 L/s are shown in Fig. 18. The injection well and pro-

duction well are 600 m apart in all the results of the current

section.

The most striking observation when we compare the

results in Fig. 17 with those in Fig. 15 is the rapid tem-

perature decline in all cases after thermal breakthrough. In

Fig. 18 we see that in each reservoir as the cooling front

propagates towards the production well, ﬂow always con-

centrates in a small number of fractures in the cooled zone,

Fig. 14 Initial ﬂow pattern in the ﬁve random fracture networks with

600 m well distance. Fractures with ﬂow rate smaller than 0.2 L/s are

not shown. For Network B, ﬂow patterns obtained by both the DFN

solver and NUFT are shown. In the NUFT result for Network B,

porous medium cells with higher ﬂow rate are rendered darker

Fig. 15 Production temperature evolution without TM coupling for

the six fracture Networks (A–F) with an inter-well separation distance

of 600 m

1014 P. Fu et al.

123

regardless of how dispersed the initial ﬂow network had

been. The TM effect always impedes peripheral ﬂow, in a

fashion similar to that demonstrated in Sect. 3, due to the

compressive hoop thermal stress around the cooled zone.

This effect further increases the severity of the ﬂow

channeling.

Among all the fracture networks, Network E has the

most diffuse initial ﬂow pattern, owing to the lack of direct

ﬂow pathways connecting the two wells. As a result, the

thermal breakthrough in Network E takes place signiﬁ-

cantly later than that in other networks. Nevertheless, ﬂow

channeling into the cooled zone is inevitable. Because the

cooled zone does not extend straight between the two

wells, Network E has longer ﬂow paths after thermal

breakthrough than those in the other networks. This results

in a more gradual production temperature decline than that

in the networks with shorter ﬂow paths.

Network F is a special case with a low fracture con-

nectivity that is barely above the percolation threshold. The

TM coupling only has a moderate effect on the ﬂow ﬁeld in

this fracture network, because there is only one viable ﬂow

path between the two wells in the interior of the reservoir.

The TM effects tend to decrease hydraulic impedance of

the interior portion of the reservoir and reduce peripheral

ﬂow, but the change of overall ﬂow pattern is much less

substantial than that for Networks B through E. Therefore,

thermal breakthrough takes place in Network F the earliest

among all networks, because the ﬂow pattern is the least

diffuse, but the temperature decline is more gradual than

that of other networks, because a relatively long ﬂow path

is retained between the two wells. The decline in

Fig. 16 Reservoir temperature ﬁeld without TM coupling after 20 years of production. The initial ﬂow ﬁelds are overlaid onto the temperature

ﬁeld

100

120

140

160

0 5 10 15 20 25 30

Production temperature (°C)

Production time (year)

Network A

Fig. 17 Production temperature evolution with TM coupling for the

six fracture Networks (A–F) with an inter-well separation distance of

600 m

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1015

123

Fig. 18 Temperature and ﬂow ﬁelds of in the ﬁve random fracture networks during production. Inter-well distance is 600 m for all cases shown

1016 P. Fu et al.

123

production temperature from Network F is also relatively

gradual for a similar reason: the topological characteristics

of this reservoir do not allow for a short (and straight) ﬂow

path to form between the two wells.

Geometrical and topological characteristics of the frac-

ture network have profound effects on thermal perfor-

mance of a reservoir. Note that all networks we studied so

far have the same fracture intensity. Fracture aperture

width mainly affects the reservoir hydraulic impedance

while its effects on ﬂow ﬁeld patterns are insigniﬁcant.

Therefore, the observed differences are mainly caused by

the differences in fracture geometry and topology. Gener-

ally speaking, networks with more diffuse initial ﬂow

patterns (e.g. Network E) tend to have later thermal

breakthrough. However, the TM effects, which dictate the

ﬂow pattern evolution during heat production, are highly

dependent on characteristics of the fracture network in a

rather complex way.

4.5 The Evolution of Overall Hydraulic Impedance

As reservoir temperature decreases, the overall hydraulic

impedance between the two wells is expected to decrease

owing to less compressive total stress, and thereby smaller

effective stress on the fractures. This phenomenon has been

observed in real world EGS reservoirs (Kohl et al. 1995).

Figure 19 shows the evolution of overall hydraulic impe-

dance of each reservoir with respect to production time,

where DPis the pressure difference between the two wells

and the subscript ‘‘0’’ denotes the initial state. By com-

paring Figs. 19 with 17 we conclude that the reduction of

hydraulic impedance is highly correlated with the decline

of production temperature, which is a proxy for overall

reservoir temperature. A special case is Network A where

the impedance ﬁrst decreases and then moderately increa-

ses between year 1 and 7. This is believed to be caused by

the compressive thermal stress at the periphery of the

cooled zone, which tends to tighten the fractures. This

phenomenon is only observable on Network A but not the

other networks, likely due to the unique feature of Network

A that much of the permeability in the reservoir is provided

by the fracture directly connecting the two wells.

4.6 The Effects of Random Realizations

So far we only generated one random realization for each

set of fracture network characteristics. To evaluate whether

the results and conclusions are sensitive to random real-

izations, we generate ﬁve additional realizations for Net-

work B and simulate the ﬂuid circulation and heat

production with THM coupling. Figure 20 shows the initial

ﬂow ﬁeld and the ﬂow and temperature ﬁelds after 20 years

of heat production at 20 L/s/100 m thick reservoir for these

ﬁve random realizations. The evolution of production

temperature for these ﬁve realizations (‘‘Realization 1’’ to

‘‘Realization 5’’) along with that for the Network B real-

ization in Sect. 4.2 (‘‘Realization 0’’) is shown in Fig. 21.

Although the production temperature evolution curves

of the six realizations span a relatively wide range, the

variation does not call into question any of the observations

in Sect. 4.4 as summarized below.

1. All the six curves show rapid post-breakthrough

temperature decline.

2. The networks with more diffuse initial ﬂow patterns

(e.g. Realizations 3 and 4) have later thermal break-

through than those with more concentrated initial ﬂow

ﬁelds do.

3. Figure 21 compares the production temperature curves

of the six Network B realizations with those of

Network E and Network F. We argued in Sect. 4.4

that the heat production characteristics of Networks E

and F are rooted in their respective fracture network

features: Network E’s late breakthrough and gradual

post-breakthrough temperature decrease are caused by

the lack of direct short connections between the two

wells and the abundance of tortuous ﬂow paths,

whereas Network F’s early breakthrough and relatively

slow post-breakthrough temperature decrease are the

results of the low percolation number. Although the six

realizations of Network B show a relatively wide range

of variation in heat production characteristics, they still

share many characteristics that are distinctly different

from those of Networks E and F. The thermal

breakthrough time of all the six Network B realizations

is later than that of Network F but earlier than that of

0.2

0.4

0.6

0.8

0 5 10 15 20 25 30

ΔP/ΔP0

Production time (year)

Network A

Fig. 19 Evolution of hydraulic impedance for the six simulated

reservoirs (A–F) with a 600 m inter-well separation distance

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1017

123

Network E. Their post-breakthrough temperature

decrease is signiﬁcantly faster than those of Networks

E and F. This proves that the different behaviors of the

networks discussed in Sect. 4.4 are indeed primarily

caused by the distinct statistical characteristics of the

networks, not merely reﬂecting the random nature of

the problem.

4.7 The Effects of Well Distance

Intuitively, increasing the well distance should increase the

extractable heat by enlarging the accessible reservoir vol-

ume while potentially requiring greater pumping effort. To

study these effects, we perform simulations with well dis-

tances of 400 and 800 m in addition to the 600 m well

distance simulations for Networks B, C, D, and E. One

stochastic realization is generated for each combination of

well distance and network characteristics, except that

multiple realizations of Networks B and E at well distances

of 600 and 800 m are included to evaluate the effects of the

random process that creates the fracture networks. The

injection-extraction pressure drop in the initial state for

different fracture networks is summarized in Fig. 22. Each

column of data point(s) represents a combination of well

distance and fracture network characteristics. Multiple data

points are shown for those combinations (Networks

B-600 m, B-800 m, E-600 m, and E-800 m) with a series

of stochastic realizations.

The effects of well distance on ﬂow impedance do not

seem to be deﬁnitive. For the combinations with multiple

realizations, increasing the well distance seems to increase

the total impedance of the system, but the random variation

of the results is also very substantial. A closer inspection of

individual fracture network characteristics reveals that the

observed variation of ﬂow impedance is heavily affected

Fig. 20 Five additional random realizations with statistical characteristics identical to Network B. The images in the upper row show the initial

ﬂow ﬁeld, and those in the lower row show the ﬂow ﬁeld and reservoir temperature ﬁeld after 20 years of production

Fig. 21 Production temperature histories of six random fracture

network realizations with the same statistical characteristics as

Network B. The results of Networks E and F are also shown for

comparison

1018 P. Fu et al.

123

by the number of natural fractures intersecting the

hydraulic fractures connecting to the wells, particularly

those connecting to the production well. This factor is not

controlled in the randomly generated fracture networks.

To compare the thermal performances of different well

distances in a concise manner, we plot the production life

of each layout at production temperatures above 145 and

100 C in Fig. 23a and b, respectively. The ﬂow ﬁeld and

temperature ﬁeld after 20 years of production are shown in

Fig. 24. Overall, the effects of well distance on thermal

performance of the reservoir are very signiﬁcant. For

Networks B, C, and D, the percentage of production life

increase is greater than the percentage of the increase of

well distances. In other words, the production life of each

fracture network increases much more than 50 % when the

well distance increases from 400 to 600 m, and life

increases much more than 33 % when the well distance

increases from 600 to 800 m. The baseline realization of

Network E shown in Fig. 18 is an anomalous case, as the

layout of 800 m well distance has slightly worse thermal

performance than the layout with 600 m well distance. In

the 600 m layout, the fracture connectivity, especially that

near the injection well, dictates that ﬂow paths connecting

the two wells in a relatively direct manner cannot form,

resulting in long ﬂow paths. In contrast, the 800 m well

distance layout for Network E happens to produce less-

tortuous connections between the two wells. Although this

small anomaly does not affect the validity of the afore-

mentioned overall trend of the effects of well distance, it

reemphasizes the fact that in a random fracture network the

inter-fracture connectivity and fracture-well connectivity

play a remarkable role in determining behavior of the

reservoir.

4.8 The Effects of Fracture Intensity

The fracture intensity in all the above simulations is con-

stant (0.1 m fracture length per m

area in 2D) across all

the fracture networks generated. We investigate the effects

of increased fracture intensity in the current section. We

generate random fracture Network G with the same frac-

ture orientation and length distributions as those in Net-

work C while the fracture intensity has been increased by

67 %. We also generate Network H based on Network E in

a similar fashion. The injection well and production well

are 600 m apart for both cases. For a given fracture length

and orientation distribution, the inter-fracture connectivity

increases as fracture intensity increases. n

i_p

and n

i_s

are

10.47 and 10.57, respectively for Network G, and 4.11 and

11.03, respectively for Network H. The joint model

Fig. 22 Injection-extraction

pressure drop in the initial state

for different fracture networks

and various inter-well

separation distances

Fig. 23 Reservoir production life at temperature above 145 C and above 100 C for different fracture networks and inter-well separation

distances

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1019

123

parameters for Networks G and H are the same as those for

Networks C and E, respectively. At the same circulation

rate of 20 L/s, the initial pressure difference between the

injection well and the production well is 3.13 MPa for

Network G, and 2.91 MPa for Network H, much lower than

the values for their low fracture intensity counterparts,

which is a direct result of the lower per-fracture ﬂow rate.

Figure 25 shows the initial ﬂow network patterns for

these two reservoirs. When ﬂow in Network G is compared

with Network C (shown in Fig. 14) and H compared with E

(shown in Fig. 14), an expected consequence of the

increased fracture intensity is that ﬂow distributes into

more fractures with each fracture carrying a smaller ﬂow

rate. However, the overall ﬂow patterns of Networks G and

H resemble those of C and E, respectively. As explained in

Sect. 4.3, NUFT simulation results without TM effects can

be used as a proxy for the degree of ﬂow path diffusivity.

With the TM effects disabled, the evolution of production

temperature for Networks G and H is shown in Fig. 26a,

compared with the results of their low fracture intensity

counterparts (TM also disabled). Networks G and H per-

form slightly worse than Networks C and E, respectively.

Fig. 24 Reservoir fracture ﬂow ﬁeld and reservoir temperature ﬁeld for different fracture Networks (B, C, D, and E) and inter-well separation

distances (400, 600, and 800 m) after 20 years of production

1020 P. Fu et al.

123

This is caused by the high fracture intensity networks’

ability to form less-tortuous ﬂow paths than the low frac-

ture intensity networks can. Nevertheless, the difference is

small.

The THM coupled simulation results are shown in

Figs. 26b and 27. The cooled zone of a high fracture

intensity reservoir tends to be more consolidated into the

core of the reservoir than its low fracture intensity coun-

terpart. The thermal performance of Network G is com-

parable to that of Network C. The difference of thermal

performance between Networks H and E is remarkable.

Recall that the good thermal performance of Network E is

mainly caused by the lack of ﬂow pathways directly con-

necting the two wells, which is combined effect of network

features and the particular well locations. The higher

fracture intensity in Network H allows much more direct

(i.e. straight) ﬂow paths to form.

5 Concluding Remarks and Practical Implications

The current study investigates the effects of thermo-me-

chanical (TM) coupling on the performance of geothermal

reservoirs in discrete fracture networks, with a particular

focus on the phenomenon of ﬂow channeling. A series of

discoveries and observations have been made through a

systematic investigation.

In addition to conﬁrming the well-known ﬂow chan-

neling mechanism, where ﬂow concentrates into a small

number of ﬂow paths inside the cooled zone, our numerical

simulation reveals a new TM mechanism that counteracts

ﬂow channeling to some extent. This secondary mechanism

is related to the anisotropy in thermal stress caused by the

typically elongated cooling zone. Although the effects of

the secondary mechanism are not strong enough to sig-

niﬁcantly alter the fate of ﬂow channeling, it is possibly an

Fig. 25 Initial ﬂow patterns of

Networks G and H

Fig. 26 The evolution of production temperature for high fracture intensity scenarios for asimulations without TM effects and bwith TM

effects. The comparison with the low fracture intensity counterparts is included

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs 1021

123

important factor contributing to the temporarily more dif-

fuse ﬂow pattern suggested by tracer tests after some time

of production at Fenton Hill (DuTeaux et al. 1996).

Flow channeling seems to be inevitable in all of the

fracture networks simulated with TM coupling, despite the

wide variety of network characteristics under considera-

tion. The effects of ﬂow channeling on the pre-break-

through production life is modest. However, ﬂow

channeling causes very rapid production temperature

decline after thermal breakthrough, thereby severely

undermining the economic value of a post-breakthrough

reservoir. One reason for the rapid post-breakthrough

temperature drop is that the TM effects cause tensile stress

increments inside the cooled zone and compressive hoop

stresses along the periphery of the cooled zone, which

dramatically impedes peripheral ﬂow and eliminates ﬂuid

ﬂow’s access to the exterior hot rock body. We did not

consider spatial variation of fracture properties in the

paper, although in real reservoir fractures in some regions

could be tighter than those in other regions. However, the

phenomenon that fractures carrying higher ﬂow rate cool

the surrounding rock faster and ﬂow tends to concentrate

more in the cooled zone is universally true, because it is a

result of simple thermal–mechanical coupling.

The current study highlights the important role of frac-

ture connectivity in determining the general behavior and

thermal performance of a fractured reservoir. Intensively

inter-connected fractures offer low hydraulic impedance

and consequently low pumping cost, but also enable the

formation of direct ﬂow paths between the two wells,

which is a negative factor for reservoir thermal perfor-

mance. As long as fractures in the network are well

interconnected, increasing or decreasing fracture intensity

has no signiﬁcant and consistent effect on effective pro-

duction life, although it does signiﬁcantly affect the overall

hydraulic impedance of the system. Although the available

analysis does not point to speciﬁc network characteristics

that ‘‘optimize’’ reservoir performance, the current study

does highlight the importance of gaining deeper knowledge

on this subject.

For a given fracture system, it appears that the only

apparent way to effectively prolong the effective produc-

tion life is to place the two wells further apart. It is inter-

esting to observe that the overall hydraulic impedance is

not sensitive to well distance changes, and the modest

effect of well distance is often overshadowed by the ran-

dom nature of fracture networks.

Finally, we acknowledge that it would be inappropriate

to directly use our 2D model to quantitatively predict

actual reservoir performance. 3D fracture geometries and

ﬂow ﬁelds are necessarily more complex than those in 2D.

However, the ﬂow channeling and accelerated production

Fig. 27 Temperature and ﬂow ﬁelds of in the two random fracture Networks (G and H) with high fracture intensity during production. Inter-well

separation distance is 600 m in both cases

1022 P. Fu et al.

123

temperature decline phenomena revealed and investigated

in the current study are direct consequences of two simple

physical processes: (1) the aperture and transmissivity of

rock joints increases as effective stress decreases, and (2)

the cooling of a ﬁnite zone causes tensile thermal stress

within the cooled zone and compressive hoop thermal

stress in the surrounding medium. These two processes are

true for both 2D models and 3D reservoirs alike. Therefore,

we believe that the discoveries in the current paper apply,

at least qualitatively, to real world reservoirs.

Acknowledgments The authors gratefully acknowledge the

Geothermal Technologies Ofﬁce of the US Department of Energy for

support of this work. Additional support was provided by the LLNL

LDRD project ‘‘Creating Optimal Fracture Networks’’ (#11-SI-006).

An anonymous editor of the journal provided valuable advice that

substantially improved the quality of this paper, for which the authors

are especially grateful. This work was performed under the auspices

of the US Department of Energy by Lawrence Livermore National

Laboratory under Contract DE-AC52-07NA27344. This paper is

LLNL report LLNL-JRNL-644453.

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Jan 2025

Shear-thickening fluids (STFs), especially nanofluids, are one of the key research areas in the world at the present time because of their ability to increase viscosity in response to specific shear conditions. This transition in viscosity is of great interest in various fields, including mechanical platforms and smart structures to advanced protective fabrics and armor. This increase in viscosity under applied shear conditions can be of great interest in the development of enhanced geothermal systems (EGSs). However, there is currently less research on the potential application of these shear-thickening nanofluids in EGS reservoirs. In this comprehensive review, the basic mechanisms of shear-thickening behavior in nanofluids are explained, while the effects of nanoparticle concentration, size, and temperature on this mechanism have been discussed in detail. This comprehensive review highlights how such factors can be optimized to adjust the rheological properties of nanofluids in order to improve their performance in fluid flow in highly fractured EGS reservoirs. An in-depth review of existing literature indicated that the combination of hydrolusters formation and the thermal properties of the shear-thickening nanofluids can be optimized to provide a potential solution to some of the EGS challenges such as thermal short-circuiting and low thermal energy extraction efficiency. Despite the huge potential of STF nanofluids in EGS development, extensive experimental and numerical investigations are needed to realize the effectiveness of these fluids further.

Real-Time Temperature Monitoring and Flow Control for Improved Heat Extraction in Enhanced Geothermal Systems

Article

Dec 2024
ENERGY

Influence of Fracture Network Characteristics of Hot Dry Rock on Heat Extraction Performance: A Numerical Simulation Study

Article

Nov 2024

Quantitative Analysis of Fracture Network Geometry on Fluid Flow and Heat Transfer in Hot Dry Rock Geothermal Reservoirs

Article

Nov 2024
ENERGY

Geothermal system lifetime with fracture heterogeneity and thermal non-equilibrium impact

Article

Nov 2024
APPL THERM ENG

Geothermal energy is a clean and sustainable alternative energy, and enhanced geothermal systems are an essential technology offering an industrial-scale method to tap geothermal energy. This technology stimulates numerous reservoir fractures, creating primary flow channels for fluids to extract heat. The important question of how the permeability of fracture swarm evolves during fluid circulation and how this evolution potentially affects the geothermal system life remains to be further answered. To address this, we develop and validate a fully coupled thermo-hydro-mechanical model based on the discrete fracture network. Results show a positive feedback mechanism between pore pressure/temperature changes and fracture permeability evolution, leading to monotone permeability-increasing in a limited number of specific fractures, indicating uneven permeability evolution of fracture swarm is crucial in shortening reservoir lifetime. Furthermore, we conduct a comparative analysis of multiple factors to determine what most significantly affects reservoir lifetime, including fracture heterogeneity, the local thermal non-equilibrium effect, and layout strategies. Results indicate the strong heterogeneity of the fracture network is dominant, and the inherent heterogeneity of hydraulic fractures is further exacerbated during geothermal production. Neglecting fractures’ mechanical response leads to an overestimated outcome. A simplified thermal-hydraulic analysis indicates a 34 % higher temperature and a 6 % higher heat extraction rate than the coupled thermo-hydro-mechanical modeling. In contrast, the impact of the local thermal non-equilibrium effect is negligible, with comparable results between equilibrium and non-equilibrium models. We further find the multi-well layout can effectively suppress the heterogeneity impact and prevent preferential flow paths. Compared to dual-well systems, the multi-well scheme has a 24 % higher temperature and a 6 % higher heat extraction rate.

Fundamentals of Rock Joint Deformation

Article

Full-text available

Jan 1983

This paper describes laboratory investigations of the deformation characteristics of rock joints under normal and shear loading. Normal deformability was studied by conducting loading~unloading and repeated load cycling tests on a wide variety of fresh and weathered joints in five different rock types. The data invariably showed non-linear behaviour, irrespective of the rock and joint type. A hyperbolic function is suggested to describe the stress-closure~opening curves of joints. Quantitative relations between normal deformability and revelant joint parameters (aperture, wall strength and roughness) are developed. Tentative conclusions on the changes in normal stiffness during shearing are also presen ted. The behaviour of dislocated (mismatching) joints is studied qualitatively and analytically. Shear deformability was studied by performing direct shear tests under normal stresses in the range of engineering interest. It is shown that behaviour in the pre-peak range is invariably non-linear depending on the joint type, and can be adequately described by easily measured parameters and hyperbolic functions.

Flow Performance of the Habanero EGS Closed Loop

Conference Paper

Full-text available

Apr 2015

Geodynamics Limited has been developing an Enhanced Geothermal System (EGS) in hot granite beneath the Cooper Basin in central Australia since 2002. Four wells have been drilled at the Habanero site to depths exceeding 4,200 m and all four wells have penetrated a major sub-horizontal fault which forms the reservoir within the granite. The temperature in the reservoir has been measured at 244°C at ~4,220 m below surface. From April to October, 2013, Habanero 4 and Habanero 1 were operated in closed-loop mode, with Habanero 4 as the producer and Habanero 1 as the injector. Circulation was established and maintained with the aid of a surface pump, re-injecting the produced geothermal brine back into the reservoir. The heat produced was used to power a 1 MW e pilot binary power station. During the trial, the performance of the closed-loop steadily improved. Production temperatures increased to 215°C and flow rates reaching 19 kg/s at the end of the trial. During the trial, two step-rate tests of the closed-loop system were conducted. These step-rate tests involved operating the closed-loop at several different pump speeds to assess the system performance and the potential for thermosiphon flow. In an effort to reduce temperature losses in the wellbore, Nitrogen was injected into the tubing-casing annulus part way through the trial period. At the end of the trial, production logs were run in both wells to provide temperature and pressure profiles for each well. These production logs were used to calibrate analytical models of both wellbores and to assess the effect of the Nitrogen. The performance of this closed-loop will be discussed and compared to an earlier closed-loop trial conducted at Habanero in 2009. By combining surface data, production logs and wellbore models, pressures, temperatures and fluid densities around the closed-loop will be discussed.

An investigation of stimulation mechanisms in Enhanced Geothermal Systems

Article

Full-text available

Dec 2014
INT J ROCK MECH MIN

We review ten historical Enhanced Geothermal Systems (EGS) projects and find that typically, during injection: (1) flow from the wellbore is from preexisting fractures, (2) bottomhole pressure exceeds the minimum principal stress, and (3) pressure-limiting behavior occurs. These observations are apparently contradictory because (1) is consistent with shear stimulation, but (2) and (3) suggest propagation of new fractures. To reconcile these observations, we propose that, in many cases, new fractures do not form at the wellbore, but away from the wellbore, and new fractures initiate from open and/or sliding natural fractures and propagate through the formation. Fracture initiation from natural fractures is aided by concentrations of stress caused by the fractures׳ opening and sliding. The propagating fractures may terminate against natural fractures, forming a complex network of both new and preexisting fractures. We perform computational modeling with a discrete fracture network simulator that couples fluid flow with the stresses induced by fracture deformation. The modeling results demonstrate that several geological conditions must be in place for stimulation to occur only through induced slip on preexisting fractures and to avoid significant opening of new or preexisting fractures. These conditions cannot be expected to be present at every EGS project, and our review of the literature shows that they typically are not. The simulation results indicate that pure shear stimulation is more likely to be possible in locations with thick faults present, and our review of the literature shows that EGS field experience is consistent with this hypothesis. We discuss field experiences from several EGS projects and describe how they are consistent with the idea that significant propagation of new fractures has occurred.

SIMULATION OF HYDRAULIC FRACTURE NETWORKS IN THREE DIMENSIONS

Article

Full-text available

Hydraulic fracturing has been an enabling technology for commercially stimulating fracture networks for over half of a century. It has become one of the most widespread technologies for engineering subsurface fracture systems. Despite the ubiquity of this technique in the field, understanding and prediction of the hydraulic induced propagation of the fracture network in realistic, heterogeneous reservoirs has been limited. Recent developments allowing the modeling of complex fracture propagation and advances in quantifying solution uncertainties, provide the possibility of capturing both the fracturing behavior and longer term permeability evolution of rock masses under hydraulic loading across both dynamic and viscosity dominated regimes. We present a framework for leveraging these advances in practical workflows for analyzing prospective and operating geothermal / hydrothermal sites. We will demonstrate the first phase of this effort through illustrations of fully three-dimensional, 2-way coupled hydromechanical simulations of hydraulically induced fracture network propagation and discuss preliminary results regarding the mechanisms by which fracture interactions and the accompanying changes to the stress field can lead to deleterious or beneficial changes to the fracture network.

Thermoelastic Stress Around a Cylindrical Inclusion of Elliptic Cross Section

Article

Sep 1950

The two-dimensional equations of thermoelasticity are solved for the case of a uniform temperature change of an infinite medium containing a cylindrical inclusion of elliptic cross section. The problem is treated as one of plane strain in elliptic co-ordinates, and the solution is given in closed form. Formulas and curves are given for the maximum values of various components of stress at the interface between the inclusion and the surrounding medium.

EGS — Goodbye or Back to the Future 95

Chapter

May 2013

Reinhard Jung

Modeling responses of naturally fractured geothermal reservoir to low-pressure stimulation

Article

Jan 2012

Hydraulic shearing is an appealing reservoir stimulation strategy for Enhanced Geothermal Systems. It is believed that hydro-shearing is likely to simulate a fracture network that covers a relatively large volume of the reservoir whereas hydro-fracturing tends to create a small number of fractures. In this paper, we examine the geomechanical and hydraulic behaviors of natural fracture systems subjected to hydro-shearing stimulation and develop a coupled numerical model within the framework of discrete fracture network modeling. We found that in the low pressure hydro-shearing regime, the coupling between the fluid phase and the rock solid phase is relatively simple, and the numerical model is computationally efficient. Using this modified model, we study the behavior of a random fracture network subjected to hydro-shearing stimulation.

Concepts and Applications of Finite Element Analysis: 4th Edition

Book

Jan 2002

Concepts and Applications of Finite Element Analysis

Book

Jan 1989

Thermoelastic Stress Around a Cylindrical Inclusion of Elliptic Cross Section

Article

Jan 1950

Thermal Drawdown-Induced Flow Channeling in Fractured Geothermal Reservoirs

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