In the Upper Rhine Graben, several innovative projects based on
enhanced geothermal system (EGS) technology exploit local deep-fractured
geothermal reservoirs. The principle underlying this technology consists of
increasing the hydraulic performances of the natural fractures using
different stimulation methods in order to circulate the natural brine at
commercial flow rates. For this purpose, knowledge of the in situ stress
state is of central importance to predict the response of the rock mass to
different stimulation programs. Here, we propose a characterization of
the in situ stress state from the analysis of ultrasonic borehole imager (UBI) data
acquired at different key moments of the reservoir development using a
specific image correlation technique. This unique dataset has been obtained
from the open-hole sections of the two deep wells (GRT-1 and GRT-2,
∼2500m) at the geothermal site of Rittershoffen, France. We
based our analysis on the geometry of breakouts and drilling-induced
tension fractures (DITFs). A transitional stress regime between strike-slip
and normal faulting consistent with the neighboring site of
Soultz-sous-Forêts is evident. The time-lapse dataset enables us to
analyze both in time and space the evolution of the structures over
2 years after drilling. The image correlation approach developed for time-lapse UBI images shows that breakouts extend along the borehole with time and
widen (i.e., angular opening between the edges of the breakouts) but do not
deepen (i.e., increase in the maximal radius of the breakouts). The breakout
widening is explained by wellbore thermal equilibration. A significant
stress rotation at depth is evident. It is shown to be controlled by a
major fault zone and not by the sediment–basement interface. Our analysis
does not reveal any significant change in the stress magnitude in the
reservoir.
Introduction
Several deep geothermal projects located in the Upper Rhine Graben based
on enhanced geothermal system (EGS) technology exploit local geothermal
reservoirs, such as those located in Soultz-sous-Forêts and in
Rittershoffen (Baujard et al., 2017; Genter et al., 2010). The principle
underlying this technology consists of increasing the hydraulic performance
of the reservoir through different types of simulations to achieve
commercially interesting flow rates. The stimulation techniques are
typically based on high-pressure injection (hydraulic stimulation), cold
water injection (thermal stimulation) or chemical injection (chemical
stimulation). During the injections, a thermo-hydro-chemo-mechanical
perturbation induces an increase in permeability due to the reactivation of
existing structures or the generation of new ones (Cornet, 2015;
Huenges and Ledru, 2011). The in situ stress state is a key parameter controlling
rock mass response during stimulation and is required to design stimulation
strategies and forecast the response of the reservoir to varying injection
schemes.
Despite its importance, the in situ stress state is difficult to assess,
particularly in situations in which the rock mass is only accessible through a
few deep boreholes. In such cases, the assessment of borehole walls using
borehole logging imaging is a useful technique to provide information on the
type, the orientation and the size of fractures or breakouts, which are due
to stress perturbations related to the existence of the well (drilling and
fluid boundary conditions). Subsequently, it gives useful constraints on the
in situ stress state surrounding the wellbore (Schmitt et al., 2012; Zoback et al.,
2003). Borehole breakouts provide indirect information on the stress
orientation that it is difficult to extract, in particular for robust
quantitative stress magnitudes. Indeed, it relies on the choice of the
failure model used to interpret borehole wall images. The mechanisms
that control the failure evolution of the borehole wall are not well
understood in space or time, and there is no consensus on the most
appropriate failure criteria to be used. Parameterizing failure criteria is
also a challenge since intact core material is often not available from deep
boreholes. Finally, the set of images used to identify borehole failures is
typically acquired a few days after drilling completion when it is unclear
if the geometry has reached a new stationary state. The present analysis
addresses these difficulties as we attempt to characterize the stress state
at the Rittershoffen geothermal site (France).
We first present in this paper the geological and geodynamical context of
the Rittershoffen geothermal site (France). We describe the borehole imaging
data acquired in the GRT-1 and GRT-2 wells at the Rittershoffen geothermal
project. We then proceed to a brief review of the methods used for ultrasonic borehole imager (UBI)
analyses with their underlying assumptions. We applied the methodology
proposed by Schmitt et al. (2012) and Zoback et al. (2003) in order to
assess the stress state at this site. To analyze the three successive images
of the wellbore acquired up to 2 years after drilling completion, we
developed an image processing method for the UBI data to compare in time the
geometry of breakouts. We deduce from this study the evolution of breakouts
with time and evaluate its impact on our in situ stress state assessment. We
finally propose our best estimate of the in situ stress state for the Rittershoffen
site, both in orientation and magnitude.
Rittershoffen project context
The Rittershoffen geothermal project, also referred to as the ECOGI project, is
located near the village of Rittershoffen in northeastern France (Alsace).
It is an EGS geothermal project initiated in 2011 (Baujard et al., 2015,
2017). The doublet has been drilled between Rittershoffen and Betschdorf, 6 km east of the Soultz-sous-Forêts geothermal project in northern
Alsace, France (Genter et al., 2010). The aim of the project is to deliver
heat through a long pipeline loop to the Roquette Frères
bio-refinery located 15 km away. The power plant capacity is 24 MWth,
intending to cover up to 25 % of the client heat need. Figure 1 gives an
overview of the project location and presents in the right insert the
trajectory and completion of the wells, GRT-1 and GRT-2, that have been
drilled (Baujard et al., 2017). GRT-1 was completed in December 2013. It was
drilled to a depth of 2580 m (MD, depth measured along hole), corresponding
to a vertical depth (TVD) of 2562 m. The well penetrates the crystalline
basement at a depth of 2212 m MD and targets a local complex fault structure
(Baujard et al., 2017; Lengliné et al., 2017; Vidal et al., 2016). The
8′′1/2 diameter open-hole section of the well starts at 1922 m MD. The
borehole is almost vertical with a maximum deviation of 9∘ only.
The first hydraulic tests concluded with an insufficient injectivity of the
injection well GRT-1. Therefore, the well was stimulated in 2013, which
resulted in a fivefold increase in the injectivity (Baujard et al., 2017).
The target of the production well GRT-2 and its trajectory have been
designed to benefit from the results of additional seismic profiles acquired
in the meantime. GRT-2 targets the same fault structure but more than 1 km away from GRT-1. Local complexities of the fault structure such as “in-step” geometry have been observed a posteriori from micro-seismic monitoring during
GRT-1 stimulation (Lengliné et al., 2017). The GRT-2 borehole was drilled
in 2014 to a total depth of 3196 m MD (2708 m TVD) (Baujard et al., 2017).
The granite basement is penetrated at a depth of 2493.5 m MD. The 8′′1/2
diameter open-hole section starts at a depth of 2120 m MD. This borehole is
directed to the north and is strongly deviated with a mean deviation of
37∘ over the interval of interest. The left insert of Fig. 1
shows more specifically the geological units penetrated by the deep
boreholes of the geothermal sites in Rittershoffen and
Soultz-sous-Forêts. It consists of sedimentary layers from the Cenozoic
and Mesozoic that are overlaying a crystalline basement made of altered and
fractured granitic rocks (Aichholzer et al., 2016). Natural fractures are
well developed in the Vosges sandstones and Annweiler sandstones, as in the
granitic basement. The fracture network was observed from acoustic wall
imagery in the open-hole sections of GRT-1 and GRT-2 and analyzed by Vidal
(2017). The analysis of the major continuous natural fractures concluded, in
GRT-1, with a global orientation of N 15∘ E to N 20∘ E with a
dip of 80∘ W. In GRT-2, the main fracture family is oriented N
155∘ E to N 175∘ E with a dip of 80∘ E to
90∘ E. Fracture density is the highest on the roof of the granitic
basement (Vidal, 2017). Oil and gas exploration in the area led to good
knowledge of the regional subsurface, including measures of temperatures at
depth. The unusually high geothermal gradient encountered in
Soultz-sous-Forêts, which is one of the largest described so far in the
Upper Rhine Graben, encouraged the development of the ECOGI project in this
area (Baujard et al., 2017).
Geological and structural map of the main Upper Rhine
Graben with the location of the Rittershoffen and Soultz-sous-Forêts
sites. The map also shows the location and status of other neighboring deep
geothermal projects. It includes stress data from the World Stress Map database
(Heidbach et al., 2016). The upper left insert shows a geological section
highlighting the main units crossed by the wells in Rittershoffen and
Soultz-sous-Forêts (Aichholzer et al., 2016; Baujard et al., 2017).
The lower right insert is a sketch of wells GRT-1 and GRT-2 drilled in
Rittershoffen, which includes their geometry, depths and crossed lithology
(after Baujard et al., 2015, 2017).
The geological context is characterized in the vicinity of the
Soultz-sous-Forêts and Rittershoffen sites from numerous studies owing
to extended geophysical exploration in the region (Aichholzer et al.,
2016; Cornet et al., 2007; Dezayes et al., 2005; Dorbath et al., 2010; Evans
et al., 2009; Genter et al., 2010; Rummel, 1991; Rummel and Baumgartner,
1991). Given that the GRT-1 and GRT-2 wells penetrate geologic units similar to
those in Soultz-sous-Forêts, information from the Soultz-sous-Forêts
site can be used to better characterize the geological units through which
the wells in Rittershoffen are drilled (Aichholzer et al., 2016; Vidal et
al., 2016). It can be used, in particular, for the strength and mechanical
characteristics of these geological units, which are poorly characterized at
the Rittershoffen site since no coring was made during drilling (Heap et al.,
2017; Kushnir et al., 2018; Villeneuve et al., 2018). The World Stress Map
(WSM) released in 2016 also compiles the information available on the
present-day stress field of the Earth's crust in the vicinity and gives an
overview of the values and results which can be expected in Rittershoffen
(Cornet et al., 2007; Heidbach et al., 2010; Rummel and Baumgartner, 1991;
Valley and Evans, 2007a). The data collected from WSM are presented in
Fig. 1 and indicate that an orientation of the maximum principal stress
close to N 169∘ E and a normal to strike-slip faulting regime are
expected for our study area. The drilling direction of GRT-2, which is northward, is therefore close to the direction of one of the principal
stresses, which has implications for the assessment of the principal stress
directions as demonstrated in Sect. 4.
Synthesis of the data used in this analysis of borehole GRT-1.
The measurements are expressed as a function of measured depth (MD) and
vertical depth (TVD). (a) Simplified lithologic column: (1) Couches de Rehberg, (2) Couches de Trifels, (3) Annweiler
sandstone, (4) Permian layers older than Annweiler sandstone, (5) rubefied granite, (6) hydrothermally altered granite and (7) low
altered granite. The UBI images are presented, as are the data picked
from the visual analysis of the double transit time image for the datasets for
2012 (b, c, d), 2013 (e, f, g) and 2015 (h, i, j)
collected in GRT-1. The radius of the borehole computed from the double
transit time image is displayed in panels (b)–(e) and (h). In panels (d)–(g)
and (j), blue dots represent the azimuth of the drilling-induced tension
fractures (DITFs), black dots represent the azimuth of the maximal radial
depth of the breakouts and red bars represent the extension between the
edges of the breakouts. Panel (k) presents information about the breakout (BO)
confidence level applied to these results. Panel (l) summarizes the width
(black dots; ∘) and the enlargement radius (red dots; mm)
measured in the 2012, 2013 and 2015 images.
Rittershoffen well dataGRT-1 data
Several extensive logging programs accompanied the drilling of wells GRT-1
and GRT-2. One was conducted in December 2012 in the open-hole section of
GRT-1 a few days after drilling (Vidal et al., 2016). UBI acquisitions were
carried out (Luthi, 2001). Figure 2b shows the amplitude image acquired
in 2012 in GRT-1, and Fig. 2c displays the radius of the borehole computed
from the double transit time image. The well logging also included caliper,
spectral gamma ray and gamma–gamma acquisitions that enable an estimation of
rock alteration and bulk density. The injectivity measured during the first
hydraulic test between 30 December 2012 and 1 January 2013 showed a
low injectivity (Baujard et al., 2017). To enhance the injectivity, the
hydraulic connectivity between the well and the natural fracture network was
increased through a multi-step reservoir development strategy. First, a
thermal stimulation of the well was performed in April 2013. A cold
fluid (12 ∘C) was injected at a maximum rate of 25 Ls-1 with
a maximum wellhead pressure of 2.8 MPa. The total injected volume was 4230 m3. Second, a chemical stimulation followed in June 2013. Using open-hole packers, a glutamate-based biocide was injected in specific zones of
the open-hole section of GRT-1 (Baujard et al., 2017). Finally, a hydraulic
stimulation of the well was performed in June 2013 with extensive seismic
monitoring at the surface (Lengliné et al., 2017; Maurer et al., 2015).
During these two last phases, a moderate-volume injection of 4400 m3 was
injected in the open hole. The hydraulic stimulation lasted 30 h, with
a major phase of stepwise flow rates from 10 to 80 Ls-1
(Baujard et al., 2017). As a result, the injectivity was improved fivefold
due to this thermal, chemical and hydraulic (TCH) stimulation program. Two
other borehole imaging programs were conducted in December 2013 shortly
after stimulation of the well and significantly later in June 2015. The
amplitude and travel time (or radius) images used in the analysis are respectively shown
in Fig. 2e and f for the logging program in 2013
and in Fig. 2h and i for the logging program in 2015.
Data acquired in GRT-1 and GRT-2 and the specificities of UBI
acquisition programs.
WellAcquisition dateStimulationLogging depth range Transducer diameter(m – MD)(m – TVD)(inch)GRT-130 Dec 20124 d after drilling completion1913–25681902–25504.979 Dec 20131 year after drilling completion1912–25311901–25132.925 months after TCH stimulation30 Jul 20152.5 years after drilling completion1911–25001900–24834.972 years after TCH stimulationGRT-223 Jul 20144 d after drilling completion2118–25311869–21964.9729 Jul 20151 year after drilling completion2111–28691863–24644.97
This time-lapse UBI dataset, whose characteristics are summarized in Table 1, provides the essential information for the present study as it enables us to
identify evidence of irreversible deformation and failure (natural and
induced fractures, breakouts, fault zones, damage zones, etc.) along the
borehole wall. Vidal et al. (2016) analyzed the images acquired in
GRT-1 and identified fractured zones impacted by the TCH stimulation
without assessing the stress state and its evolution. Hehn et al. (2016),
whose measurements are discussed later in Sect. 9.2, analyzed the
orientation of drilling-induced
tension fractures (DITFs) in GRT-1 in the granitic basement but also in the upper
sedimentary layers, investigating the orientation of the stress field with
depth.
We identify wellbore wall failure and use these observations to characterize
the stress state in the reservoir, including its evolution in time. Wellhead
pressure measurements of the hydraulic stimulation are also used to estimate
a lower bound of the minimum horizontal stress (Sh).
GRT-2 data
An extended logging program was also conducted in GRT-2, including repeated
UBI borehole imaging (see Table 1). Figure 3c and d respectively show
the amplitude image acquired in 2014 between 2404 and 2412 m and the
radius image acquired in 2015 between 2468 and 2472 m in GRT-2. No
hydraulic stimulation was performed in this well since its initial
injectivity was sufficient (Baujard et al., 2017).
Example of image artifact observed on the GRT-1 and GRT-2 dataset. (a) Comparison of data from 2012, 2013 and 2015 collected in GRT-1
presenting a signal loss artifact in sandstones, clearly highlighted by
persisting white patches in the radius signal. (b) Processing noise
resembling wood grain textures, visible on the 2015 GRT-1 image both on
the amplitude and radius image in granite. (c) Alternating compression and
stretching of the image characteristic of stick-slip artifacts, highlighted
along the entire GRT-2-2014 image. (d) Erroneous radius record observable on
the GRT-2-2015 image in granite, possibly related to tool decentralization.
Stress estimation methodology
The approaches proposed by Zoback et al. (2003) and by Schmitt et al. (2012)
are used to fully characterize the in situ stress field at the Rittershoffen
geothermal project. In the following, the symbol S refers to the total stress, while σ refers to the effective stress (Jaeger and Cook, 2009). We
suppose that one of the principal stresses of the in situ stress tensor is
vertical, which is a common assumption. This hypothesis is justified by the
first-order influence of gravity on the in situ stress state, although this
assumption may not be valid locally. Moreover, no “en échelon”
patterns are highlighted in GRT-1 or GRT-2, which would be the case if the
direction of any of the principal stresses differs from the well inclination
by more than 20∘, as was observed, for example, by Wileveau et al. (2007) in highly deviated wells. We show that the breakouts measured in
GRT-1 are collinear with the borehole axis, which confirms that the vertical
direction is principal. In the following, we denote the vertical principal
stress Sv. The magnitude of the vertical stress Sv is obtained from the weight
of the overburden. It is calculated by the integration of density logs
(see Sect. 8.2). The two other principal stresses act horizontally: SH, the
maximum horizontal stress, and Sh, the minimum horizontal stress. The magnitude
of the minimum horizontal stress Sh is estimated from the wellhead pressure
measurements carried out during the hydraulic stimulation of GRT-1 and from
the hydraulic tests performed in the reservoir of Soultz-sous-Forêts
(see Sect. 8.3). The analysis of the borehole failures is evaluated using
televiewer image data (Zemanek et al., 1970; Zoback et al., 1985). The
orientation and magnitude of SH are assessed using a failure condition at the
borehole wall with the three common failure criteria considered in our analysis,
i.e., the Mohr–Coulomb criterion (Jaeger and Cook, 2009), the Mogi–Coulomb
criterion (Zimmerman and Al-Ajmi, 2006) and a true triaxial version of the
Hoek–Brown criteria (Zhang et al., 2010), and are presented in Sect. 4.2.
Wellbore stress concentration
To express the stress concentration around the quasi-vertical borehole GRT-1
(maximum deviation is only about 9∘), we assumed its shape to
be a cylindrical hole and used the well-known linear elastic solution,
often referred to as the Kirsch solution (Kirsch, 1898; Schmitt et al.,
2012). For the deviated well GRT-2 where the plane strain approximation is
no longer valid, we used a 3-D solution taking into account the constant
deviation of 37∘ measured along the section of interest. The
equations that involve the geometry parameters of the well, the far-field stresses and the fluid pressure are well documented in the
literature. We refer to the summary proposed in the review from Schmitt et
al. (2012) for the general case of a 3-D well randomly inclined in regard to
the far-field stresses. The same methodology has been, for example, proposed
by Wileveau et al. (2007). A summary of the steps leading to the equations
used to compute the SH stresses for the deviated well GRT-2 is presented in
Appendix A. Note that we included in our solution a thermal stress component
that accounts for the thermal perturbation induced by the drilling process.
This component is detailed later in Sect. 8.4. We used the formulation of
the thermo-elastic stresses arising at a borehole given by
Voight and Stephens (1982), also recalled in Schmitt et al. (2012). We
computed the effective stress at the borehole wall considering a hydrostatic
pore pressure given by Pp=ρf⋅g⋅z, i.e., with
the head level located at the surface. The fluid density ρf is
taken as 1000 kgm-3 and the gravitational acceleration g as
9.81 m2s-1; z is the vertical depth (TVD) in meters from the ground
surface.
Failure criterion
At the scale of the surroundings of the borehole (a few decameters), we assume a
linear elastic, homogeneous and isotropic rock behavior prior to failure.
When the maximum principal stress exceeds the compressive rock strength,
rock fails in compression (Jaeger and Cook, 2009). Failure at the borehole
wall is assessed using the elastic stress concentration solutions presented
in Sect. 4.1, combined with an adequate failure criterion. There is currently
no consensus concerning the appropriate failure criteria to assess wellbore
wall strength. In the case in which the pore pressure and the internal
wellbore pressure are in equilibrium, the radial effective stress at the
borehole wall is equal to zero, so a common assumption is to consider the
uniaxial compressive strength (UCS) to be a good estimate of wellbore strength
(Barton et al., 1988; Zoback et al., 2003). Others suggest that the strength
of borehole walls in low-porosity brittle rocks could be less than the UCS
because the failure could be controlled by extensile strains (Barton and
Shen, 2018; Walton et al., 2015) or fluid pressure penetration
(Chang and Haimson, 2007). The presence of nonzero minimum principal
stress and the strengthening effect of the intermediate principal stress,
however, suggest that the borehole wall strength should be larger than the UCS
(Colmenares and Zoback, 2002; Haimson, 2006; Mogi, 1971). In view of this
situation and because stress magnitude evaluation differs according to the
criterion used in the analysis, we compared the estimates obtained with
three commonly used failure criteria in borehole breakout analyses: (1) the
Mohr–Coulomb criterion (Jaeger and Cook, 2009), (2) the Mogi–Coulomb
criterion (Zimmerman and Al-Ajmi, 2006) and (3) a true triaxial version of
the Hoek–Brown criteria (Zhang et al., 2010). The formulation is given in
Eq. (1) for the Mohr–Coulomb criterion in the principal effective stress
space σ1–σ3. The Mogi–Coulomb and Hoek–Brown
criteria include a so-called “effective mean stress” (Zimmerman and
Al-Ajmi, 2006) expressed as a function of the principal effective stresses
as σm=σ1+σ32 and an octahedral
shear stress given by τoct=σ1+σ22+σ2+σ32+σ3+σ12. Equations (2) and (3) express the Mogi–Coulomb
and Hoek–Brown criteria in the space (τoct, σm).
Mohr–Coulomb
σ1≥C0+q⋅σ3
Mogi–Coulomb
τoct≥a+b⋅σm
Hoek–Brown
92.C0⋅τoct2+322⋅mi⋅τoct-mi⋅σm≥C0C0 is the uniaxial compressive strength and q is a material constant
that can be related to the internal friction angle, φ, through
q=π4+φ2. The variables a and
b in the Mogi–Coulomb criteria and mi in the Hoek–Brown criteria are
parameters that are related to material friction and cohesion.
Elastic (Poisson ratio) and strength parameters (used in the
Mohr–Coulomb, Mogi–Coulomb and Hoek–Brown failure criteria) for the four
geological units retained in the model, for both the GRT-1 and GRT-2 wells, as a
function of measured depth (MD) and vertical depth (TVD). Elastic and
strength parameters for granites are based on a data compilation of tests
conducted on samples from Soultz-sous-Forêts. For the Buntsandstein
sandstones, we use the usual strength parameters based on Hoek and Brown
(1997).
Four simplified lithological categories have been used for the strength
characterization of the rock at depth in the Rittershoffen reservoir. The
open-hole section of GRT-1 and GRT-2 crosses Vosges sandstones and Annweiler
sandstones of the Buntsandstein. All the lower Triassic sandstones have been
grouped in a single category. The granitic section has been separated in
three categories according to the type and intensity of alteration. The
simplified lithologic profile for the GRT-1 and GRT-2 wells is indicated in
Table 2. Considering the methodology used here, the relevance and accuracy
of the stress characterization are highly conditioned by the values of the
rock strength parameters and by the failure criterion chosen. In
Rittershoffen, the drilling was performed exclusively in destructive mode
and no sample is available to measure rock moduli and strength
characteristics. The GRT-1 and GRT-2 wells penetrate geologic units similar to
those in the nearby Soultz-sous-Forêts site. Information from the
Soultz-sous-Forêts site is thus used to better characterize the
strength and mechanical characteristics of the geological units through
which the wells in Rittershoffen are drilled (Heap et al., 2017, 2019;
Kushnir et al., 2018; Villeneuve et al., 2018). Mechanical
tests that have been carried out on core samples from the
Soultz-sous-Forêts site are used to characterize the rock properties
(Rummel, 1991; Valley and Evans, 2006). At the Soultz-sous-Forêts site,
the EPS-1 borehole was continuously cored from 930 to 2227 m (Genter et al.,
2010; Genter and Traineau, 1992, 1996), providing samples of the sandstones
in the Buntsandstein and in the crystalline basement. Some cores have also
been obtained in borehole GPK-1 from various depth sections and were
analyzed by Rummel (1991). For the Buntsandstein sandstones, Heap et al. (2019) studied in detail the strength evolution with depth of the
Buntsandstein mechanical properties. They identified significant variations
of the compressive strength together with elastic modulus changes. They also
pointed out the role of the fluid content in the UCS. However, these
variations are limited compared to the statistical fluctuations of our
measurement. Accordingly, we gathered the Buntsandstein sandstones as a
single unit. The elastic and strength parameters used for our analyses are
summarized in Table 2. The variability range given for elastic parameters,
cohesion and UCS reflects natural rock heterogeneities and depicts the
variability in values encountered. Indeed, we recognize different sources of
uncertainty on the mechanical and strength parameters which limit our
approach. In addition to the absence of direct strength measurements for the
study site, the mechanical and strength parameters are selected from core or
cutting analyses performed in laboratory conditions. The parameters are
thus not necessarily representative in situ under large-scale conditions due to, for
example, the presence of core damage.
Images processing and borehole failure identification
Stress-induced failures are identified and measured from acoustic borehole
images. The confidence and accuracy of these determinations depend on the
quality of the images. In the following, we describe the original data as
well as the processing we applied to improve the quality and comparability
of the images. We also explain how we measure borehole failure on these
images and the limitations associated with these measurements.
Quality of the acoustic televiewer images
Several artifacts can deteriorate the quality of acoustic image data (Lofts
and Bourke, 1999). The images acquired in Rittershoffen suffer from some of
these limitations. The quality of the image depends of the tool
specification, the acquisition parameters and logging conditions. All
acoustic images at Rittershoffen were acquired by Schlumberger with their
UBI (ultrasonic borehole imager) tool. The tool and acquisition parameters
were similar between each log but not identical. For example, the GRT-1 log
in 2013 was acquired using a smaller acquisition head (see the changes in
transducer diameter detailed in Table 1). The acquisition resolution was the
same for every log, i.e., 2∘ azimuthal resolution and 1 cm depth
sampling step.
The 2012 log of GRT-1 has the best-quality image of the entire suite. The
image suffers from a signal loss artifact (Lofts and Bourke, 1999) in some
limited sections, most commonly related to the presence of breakouts or
major fracture zones. The zones of signal loss are clearly identified in the
radius image presented in Fig. 3a by persisting white patches.
The 2013 log of GRT-1 is of comparable quality as the 2012 log and also suffers
from some limited signal loss artifacts. The major issue with the image
of GRT-1 acquired in 2013 is that the orientation module was not included in
the tool string, and thus the image cannot be oriented with magnetometer data
as is usually done for this type of data.
The 2015 log of GRT-1 generally suffers from signal loss issues, not only in
areas with major fracture zones and breakouts. In the lower part of the log,
wood grain textures (Lofts and Bourke, 1999) related to processing noise
are also observable (see Fig. 3b). Wood grain textures are especially
encountered below 2431 m MD.
The quality of log data from GRT-2 is generally lower than for GRT-1. This
is due to the deviation of GRT-2 that makes wireline logging more difficult.
The 2014 log of GRT-2 suffers from stick-slip artifacts on its entire
length. The effects of the alternating compression and stretching on the
images highlighted in Fig. 3c are particularly significant and
possibly lead to errors in the recording of the fractures. The 2015 log in
GRT-2 does not show any sign of stick-slip but presents an erroneous
borehole radius record, leading to an incorrect borehole geometry assessment
(Fig. 3d).
Despite these difficulties, the images collected in the GRT-1 borehole are
of excellent quality. Signal loss is the main problem and it prevents us from
measuring the depth in the radial direction of the breakout in some zones.
Given the extent of the artifacts highlighted in GRT-2, the measurements of
the breakout parameters in this borehole are much more uncertain.
Processing of the UBI images
Prior to the use of the images for assessing borehole failure, the images went
through the following preprocessing steps:
transit time was converted to radius using the fluid velocity recorded
during the probe trip down the borehole;
images were filtered to reduce noise; and
digital image correlation was applied across the successive logs in order
to correct the image misalignment both in azimuth and depth.
The borehole radius was computed from the transit time following Luthi
(2001):
r=ttwt⋅vm2+d,
with ttwt the two-way travel time, vm the acoustic wave velocity in
the drilling mud and d the logging tool radius. Images are filtered using a
selective despiking algorithm implemented in WellCad™ using a
cutoff high level (75 %) and a cutoff low level (25 %) in a 3×3 pixel
window. The goal of this process is to replace outliers by cutoff values
when the radius exceeds the cutoff high or low level. Finally, digital
image correlation was used to ensure proper alignment of the UBI images.
This was required for the GRT-1 2013 image because this image was not
oriented with a magnetometer–accelerometer tool. The process was also
applied to the 2015 GRT-1 data to facilitate comparison between images. For
this purpose, we developed a technique based on a particle image velocimetry
(PIV) method (Thielicke and Stamhuis, 2014) that relies on optical image
correlation but being applied to travel time UBI images. This image
alignment process is illustrated in Fig. 4. Figure 4a shows, as an example,
the “correlation box” in the travel time UBI image of reference – i.e.,
2012 in this case – and the corresponding one in the image to compare with
– i.e., the image of 2013 – which is shifted for a given displacement
vector (dX, dY) within the “search box”. The cross-correlation function, which
is a measure of the similarity between the thumbnails, is computed between
the correlation boxes for each displacement vector (dX, dY). Figure 4a shows a map of the cross-correlation function computed for every
displacement vector in a given search box. The two-dimensional
cross-correlation function is an operator acting on two intensity functions,
s(X,Y) and r(X,Y), defined as a norm of the color levels at each position of each
thumbnail. Csr is defined at a position (X,Y) and for a shift (dX, dY) by Eq. (5).
CsrdX,dY=sX,Y⊗rX,Y=∬-∞+∞sX,YrX-dX,Y-dYdXdY
The position (dX, dY) within the search box with the highest cross-correlation
corresponds to the best alignment (see Fig. 4a). The operation is repeated
along the image for each position of the search box. Importantly, the
correlation box is taken with an anisotropic shape to account for the rigid
rotation of the UBI tool and the linear property of the acoustic camera. The
size of the correlation box is 180×20 pixels. This configuration is
appropriate to principally identify the azimuthal offset, while it is less
sensitive to the depth mismatch. We investigated offset up to 180 pixels
horizontally, corresponding for our 2∘ resolution to a complete
360∘ rotation. We considered a vertical offset of ±10 pixels,
corresponding to offsets of about ±10cm. Figure 4b gives an
example of image realignment and shows the efficiency of the process. This
correlation process allows us to finely align the successive images and thus to
study the borehole shape evolution with time more accurately.
(a) Sketch presenting the process used to orient the images of
GRT-1. A correlation box is defined in the double transit time image of
reference (acquired in 2012) and is progressively shifted in the image to
compare with (red windows) within the limits of the search box (black
window). We compute the correlation between the correlation box in its
initial position in the image of reference and the shifted correlation box
in the image to compare with for each position (right insert). The
displacement maximizing the correlation factor enables, at a given depth, us to
rotate and adapt the image of 2013 and 2015 according to the image of 2012.
(b) Example of original and reoriented time transit images of 2013 at a
depth of 2414 m (TVD) in GRT-1.
Determination of the borehole failure
For GRT-1, the breakouts have been determined through a visual analysis of
borehole sections computed every 20 cm from 1926 to 2568 m (MD) from the
double transit time data. The borehole sections are computed by stacking
(averaging using the median) the data collected every 1 cm over 20 cm
borehole intervals (with no overlap between two successive sections). The
median is thus used because it is less sensitive to extreme values than the
mean and is thus efficient at removing local noise from the data. Prior to
determining breakout geometrical parameters, the actual borehole center is
determined by adjusting the best-fitted ellipse to the borehole section.
This process corrects for eventual logging probe decentralization. For each
section presenting the characteristic elongated shape of breakouts due to
stress-induced failure, the azimuthal position of the edges and the center
of each limb are determined by visual inspection. Figure 5 gives examples of
such a determination to depict the process. The breakout edges are defined as
the location where the wellbore section departs from a quasi-circular
section adjusted by the best-fitted ellipse. As can be seen in Fig. 5,
this typically spans an azimuthal range much broader than the low-amplitude
reflections visible as dark bands on the amplitude images and justifies the
choice to use the double transit time data. The positions of the breakout
edges are not easy to determine in a systematic and indisputable manner, and
significant uncertainty is associated with these measurements. Related to
this issue, it is not possible to determine on the images what azimuthal
range of the wellbore is enlarged by purely stress redistribution processes
and what part is enlarged subsequently by the effects of drill string wear.
These uncertainties about the physical process controlling the enlargement
of the breakout could limit the comparisons between the three successive
logs acquired in GRT-1. Breakout measurements were thus performed on all
three images concomitantly and consistently. We ensured, for example, that
within a tolerance dictated by the uncertainties of the measurements, the
width of breakouts only remains identical or increases: no decrease in width
is measured between successive logs.
Example of breakout geometry determination in sandstones. (a) Amplitude images for GRT-1 at 2140.8 m for the logs from 2012, 2013
and 2015. (b) Wellbore section at 2140.8 m computed from the
transit time images from the 2012, 2013 and 2015 logs, respectively. The
breakout extent is determined on the wellbore section. The blue and green
dashed lines represent the extent of the breakout, while the plain lines
represent the azimuth of the maximum radial extension of the breakout.
Figure 2d, g and j summarize all the measurements of the breakout
geometry performed in GRT-1 for the images acquired in 2012, 2013 and 2015.
Black dots indicate the azimuth at which the radius of the breakout is
maximum and red bars link the azimuthal position of the breakout edges used
to compute the width of the breakouts. Given the difficulty of measuring
breakouts as discussed previously (i.e., artifacts affecting the images,
disputable positions of the breakout edges), a confidence ranking has been
established for each breakout. This confidence level is presented in Fig. 2k. From the geometry of the breakouts, we compute the breakout widths
which are obtained from the breakout edge azimuths. The deepest point of the
breakout is used to determine the enlargement radius. In some situations,
signal loss issues prevent the determination of the enlargement radius, as
shown in Fig. 5 for the image of GRT-1 acquired in 2015. The measured
width (black dots; in degrees) and enlargement radius (red dots; mm) are
determined from the GRT-1 dataset acquired in 2012 and presented in Fig. 2l.
Examples of drilling-induced tension fractures (DITFs) observed
in the granitic section of GRT-1 in the amplitude images acquired in 2012,
2013 and 2015. The azimuth of the DITFs is measured every 20 cm (green
crosses).
Drilling-induced tension fractures (DITFs) are also identified from the
GRT-1 borehole images using the same procedure as for the breakout
determination. For example, clear DITFs are evident in the amplitude image
from 2395 to 2400 m in GRT-1 and presented in Fig. 6. Green crosses show
the azimuth of the DITFs measured in GRT-1 every 20 cm. Blue dots in
Fig. 2d, g and j summarize the azimuth of the DITFs measured in
GRT-1 in 2012, 2013 and 2015, respectively. Given the poor quality of the
double transit time images acquired in GRT-2, less focus has been given to
the analysis of the borehole failure in this well. The dataset consists of
the acquisitions made in 2014 after completion of the borehole and in 2015.
The investigated depths vary from the 2014 to the 2015 dataset. The depth is from
1950 m (vertical depth – 2220 m MD) down to 2125 m (TVD – 2440 m MD) in
2014, while it is down to 2160 m (TVD – 2480 m MD) in 2015. The well is
strongly deviated. The concentration of stresses within the borehole wall is
expressed under the assumption of a constant deviation of 37∘, and
measurements are carried out as a function of the true vertical depth to be
comparable with the results obtained in GRT-1, which is considered to be
vertical. Borehole sections are computed every 50 cm. To this end, borehole
sections are stacked using the data collected every 1 cm over 50 cm borehole
intervals, all along the transit time image. As for GRT-1, the actual
borehole center is determined by adjusting a best-fitted ellipse to the
borehole section. Breakouts are analyzed by visual analysis in the same manner
as for GRT-1 data. The difficulties encountered with the identification of
breakout geometry are more pronounced for images acquired in GRT-2, as
artifacts are more developed. The deviation of this well results in
pronounced stick-slip effects. For a more accurate comparison between the
measurements carried out on the images acquired in 2014 and 2015,
measurements are performed for the two images concomitantly. No DITFs are
identified on the GRT-2 borehole images.
Analyses of temporal borehole failure evolution
The characterization of the stress tensor derived from the analysis of
borehole failures typically relies on a single borehole image dataset. From
this snapshot in time, stresses are estimated, while information on the
evolution of breakout shape in time is not available. Interestingly, for the
ECOGI project, the acquisition of three successive image logs allows us to
study this evolution. Here, the time evolution of breakouts, referred to as
breakout development, is analyzed to characterize the time evolution of the
borehole failure. A common hypothesis concerning borehole breakout evolution
is that breakout width remains stable and is controlled by the stress state
around the well at the initial rupture time. Progressive failure is assumed, however, to lead to breakout deepening until a stable profile is reached
(Zoback et al., 2003).
Examples of breakout shape evolution between the three successive
images collected in GRT-1 in sandstones. (a) The amplitude
images and the radius computed from the time transit images for a section of
GRT-1 from 2124 to 2128 m (MD) in 2012, 2013 and 2015. (b) The
mean section computed at 2125.6 and 2126.2 m (MD) from the time transit
images averaged over 60 cm intervals. The sections are represented along with
an 8.5 inch radius circle representing the unaltered open-hole section. The
sections from the images of 2012, 2013 and 2015 are superposed on the far right
of panel (b).
An example of a time-lapse comparison of breakout shapes is presented in
Fig. 7. Images of GRT-1 from 2012, 2013 and 2015 show a clear breakout at a
depth of about 2126 m in the Couches de Trifels in the Buntsandstein.
Breakouts can present three types of evolution.
They can develop along the well, corresponding to an increase in the
vertical length of breakouts. We refer to this process as breakout extension.
They can widen, corresponding to an apparent opening between the edges of
the breakouts. We refer to this process as breakout widening.
They can deepen, corresponding to an increase in the maximal radius of
the breakout (or “depth” of the breakout) measured in the borehole cross
section at a given depth. We refer to this process as breakout deepening.
Figure 7 shows the evolution from 2012 to 2015 of the breakouts at 2125.6 m. Failure did not occur in 2012, while breakouts are visible in 2013 and
2015. When superposing the 2013–2015 borehole sections, no change in
breakout shape is highlighted for the west limb although a slight widening
is visible on the east limb. Possible deepening of the east limb is occulted
by signal loss issues. The borehole section computed at 2126.2 m shows, in
contrast, no modification of the breakout shape from 2012 to 2015 in
GRT-1.
Development of breakouts along the GRT-1 borehole between 2012 and
2013. (a) Simplified lithologies along the GRT-1 borehole as a function of measured
depth (MD) or vertical depth (TVD). BuntR stands for Couches de Rehberg,
BuntT for Couches de Trifels, BuntA for Annweiler sandstone, BuntP for
Permian layers older than Annweiler sandstone, GranR for rubefied granites,
GranA for hydrothermally altered granite and GranF for low altered granite.
The major fault zone crossing GRT-1 at 2368 m is represented as a black band.
(b) Breakout positions in GRT-1 in 2012. (c) Breakout positions in GRT-1 in
2013. (d) Intervals at which breakouts are present in 2013 but not in 2012. (e) Breakout length increase (m) along the borehole between 2012 and 2013 in
5 m bins. (f) Fraction (%) of wellbore length that was free of a breakout
in 2012 but presents a breakout on the 2013 image, computed in 5 m bins.
The development of borehole failures also depends on the lithology. Breakout
extension (longitudinal failure development) is quite common in the
Buntsandstein, while it is very limited in the basement granites, which is
highlighted in Fig. 8. The evolution occurs exclusively between the
2012 and 2013 datasets, while no longitudinal extension occurs during 2013 and
2015. In 2012, a total breakout length of 404 m is observed. It increases to
504 m in 2013 and then remains stable in 2015 with a length of 506 m. There
is no clear evolution of DITFs along the GRT-1 well despite the hydraulic
and thermal stimulation performed between 2012 and 2013.
Evolution of breakout width in the GRT-1 borehole as a function of
measured depth (MD) or vertical depth (TVD). (a) Simplified lithologies along
the GRT-1 borehole (see Fig. 8 for the legend). (b) Width increase between the
2012–2013 time interval (black circles) and the 2013–2015 time interval (red
crosses) presented as a function of the vertical depth. (c) Histograms in
2∘ classes of breakout width changes for the 2012–2013 interval
(black) and the 2013–2015 interval (red).
Figure 9 shows an increase in breakout width. We first compare the data
acquired in 2012 and in 2013; 73 % of the change of width is within an
interval -10∘/+10∘, i.e., within our measurement
uncertainty. For these breakouts no changes in width can be highlighted
within our level of uncertainty. However, for 27 % of our data, we observe
an increase in width larger than 10∘. This is reflected by the
long tail (with values higher than 10∘) of the histogram computed
from the width of breakouts (see Fig. 9c). The widening of these
breakouts is undisputable. When comparing the data acquired in 2013 and in
2015, very few changes are observed. Indeed, most of the measured changes
remain below our uncertainty level of ±10∘ (red histogram
in Fig. 9c).
The evolution of the maximum radial extension (breakout deepening) of the
breakout measured in the borehole cross sections is presented in Fig. 10.
This parameter is more delicate to track because of signal loss issues (see,
for example, Fig. 3a). In our analysis, we filtered out obvious incorrect
depth measurements related to these artifacts, i.e., when the computed radius
from the transit time image is clearly shorter than the drill bit radius. For
both time intervals (2012–2013 and 2013–2015), the change in the depth of the
breakout is symmetrically distributed around 0 mm and spans a variability of
about ±15mm. We interpret this distribution as an indication that if
any deepening occurred, it remained within our uncertainty level. Our data
analysis does not enable us to draw the conclusion of a general deepening of the
breakouts.
Evolution of the depth of the breakouts in the GRT-1 borehole as a
function of measured depth (MD) or vertical depth (TVD). (a) Simplified
lithologies along the GRT-1 borehole (see Fig. 8 for the legend). (b) Increase in
the maximum radial extension between the 2012–2013 time interval (black
circles) and 2013–2015 time interval (red crosses) presented as a function of
depth. (c) Histograms in 2 mm classes of breakout width changes for the
2012–2013 interval (black) and 2013–2015 interval (red).
Stress characterization
We propose in this section a complete stress characterization at different
periods in both the GRT-1 and GRT-2 wells, including a thermal history and
thermal stress analyses, and discuss the impact of breakout widening in time
on stress estimation. To that purpose, we first determine the orientation of
the stress tensor. We then detail how we estimate the minimum horizontal
stress component Sh, the vertical stress component Sv and the thermal component.
Finally, we propose an estimation of the maximum horizontal stress component
SH from the measurement of the width of breakouts.
Maximum horizontal stress SH orientation
The orientations of breakouts and DITFs are a direct measure of the
principal stress directions in a plane perpendicular to the well. As
discussed previously, we assume that Sv is overall vertical, which is a
common hypothesis in such an approach and is justified by the first-order
effect of gravity on in situ stresses. In GRT-1, which is considered to be vertical,
DITFs are aligned with the direction of the maximum horizontal stress (SH) and
breakouts are aligned with the direction of minimum horizontal stress
(Sh).
Evolution in the orientation of the maximum principal stress as a
function of measured depth (MD) and vertical depth (TVD) in GRT-1 in 2012
and 2015. (a) Simplified lithologies along the GRT-1 borehole (see Fig. 8 for the
legend). (b) Orientation of SH from the azimuth of the maximum radial extension of
the breakouts (BOs) from the datasets of 2012 (in blue) and 2015 (in red)
acquired in GRT-1. In green is the orientation of SH from the azimuth of drilling-induced tensile fractures (DITFs). The red line is a moving average of the
orientation data. (c) Orientation in
rose diagrams from the datasets displayed in panel (b).
Figure 2d, h and i show the orientation of breakouts (black dots)
and DITFs (blue dots) measured in GRT-1. The measurements are compiled in
Fig. 11 as circular histograms. We chose to only analyze data from the
images acquired in 2012 and in 2015. Indeed, data acquired in 2013 were
obtained without orientation, since the device was not functioning correctly,
and are reoriented with respect to the 2012 data. Subsequently, the
measurements carried out for the 2013 image do not bring additional
constraints in terms of stress orientation.
In the Buntsandstein sediments, the failure orientation is stable and
indicates that the principal stress SH is oriented 15∘ N ±19∘ (one circular standard deviation). The same failure
orientation persists in the upper section of the granite down to about 2270 m. Below this depth borehole failure orientation is much more variable as it
seems to be influenced by the presence of major fault zones crossing the
GRT-1 borehole at a depth of 2368 m (MD) (Vidal et al., 2016). Below 2420 m,
which is the deepest large structure visible on the GRT-1 borehole image,
the failure orientation indicates that SH is oriented 165∘±14∘. This is significantly different from the orientation in the
sediments with a 30∘ counterclockwise rotation. Such differences
in orientation with lithology have already been noted by Hehn et al. (2016) from an analysis of the orientation of drilling-induced fractures
observed on borehole acoustic logs acquired in GRT-1. The orientation of
SH proposed by Hehn et al. (2016), i.e., globally N 155∘ E in the
basement and N 20∘ E in the sedimentary layer, is consistent with
our measurements.
Mean density retained for each lithological layer and vertical
depth (TVD) in each well.
The geological study of the cuttings from the drilling of GRT-1 and GRT-2
enabled the determination of the rock density profile in both wells (Aichholzer et
al., 2016). Thanks to this analysis, we estimate the mean density of each
lithological layer. Table 3 shows the rock volumetric mass density as a
function of the vertical depth (TVD). The magnitude of the vertical
component Sv at depth is computed accordingly by integrating the volumetric
mass density profile from the surface. A linear regression is fitted to the
measurements obtained for the depth range studied here, i.e., 1900–2600 m.
In the following, the vertical component Sv is computed from a linear trend
expressed as a function of vertical depth (TVD) z:
Sv[MPa]=0.0248⋅z[m]-0.83.
As the linear trend is expressed as a function of the vertical depth, we use
the same equations in the computation steps leading to the SH stress estimates
in GRT-1 and GRT-2. As the density profile is integrated from surface to
reservoir depth, the uncertainty on density adds up and the uncertainty on
the vertical stress increases with depth consequently. Considering an
uncertainty of 50 kgm-3 on the densities leads to a 2.5 MPa uncertainty on Sv at reservoir depth. This uncertainty is not significant
compared to other uncertainties involved in the analysis, for example
those related to the mechanical parameters chosen in the inversion of the
maximum horizontal stress SH.
Stabilized wellhead pressure (MPa) as a function of flow rate
(Ls-1) measured during the hydraulic stimulation of the GRT-1 well in
2013 (after Baujard et al., 2017).
Minimum horizontal stress Sh
We take the first-order assumption that the minimum horizontal stress Sh
varies linearly with depth. Usually, the minimum horizontal stress Sh is
estimated at depth from hydrofracture tests (i.e., Haimson and Cornet,
2003) but this was not done at the Rittershoffen site. As the data available
for the ECOGI project do not enable us to compute a profile for the Sh stresses,
our analysis of the minimum stress component is based on the numerous
injection tests that were conducted in Soultz-sous-Forêts. We present in
Fig. 12 the main trends computed from pressure-limiting behavior during
hydraulic injections. For large depths, the injection tests performed in the
deep wells (GPK-1, GPK-2, GPK-3 and/or EPS-1) of Soultz-sous-Forêts
(Cornet et al., 2007; Valley and Evans, 2007b) give important constraints
for the minimum horizontal stress Sh at the Rittershoffen site. In addition,
the study of Rummel and Baumgartner (1991) provides estimates at shallow
depth. In our analysis of the stress state in GRT-1 and GRT-2, we compute
the horizontal minimum stress Sh as a function of the true vertical depth (TVD)
z from the linear trend proposed by Cornet et al. (2007) for the site of
Soultz-sous-Forêts (Fig. 15):
Sh[MPa]=0.015⋅z-7.3.
From the data available for the Rittershoffen site, i.e., the wellhead
pressure measured during the hydraulic stimulation of GRT-1 (Baujard et al.,
2017), we estimated a lower bound of the minimum horizontal stress Sh at 1913 m in Rittershoffen. The measurement enables us to verify the applicability of
the linear trend inferred from acquisitions in Soultz-sous-Forêts to the
Rittershoffen site. Figure 13 shows that the variation of wellhead pressure
with the flow is slower during the high-rate hydraulic stimulation (above 40 Ls-1) than during the low-rate hydraulic stimulation (below 40 Ls-1). The change in behavior highlighted for higher values of the
flow rate is interpreted as the beginning of a pressure capping resulting
from fracture reactivation. Hydraulic stimulation operations aim at
increasing pore pressure, which reduces the effective stress until pressure
equals Sh in magnitude. In theory, an increase in pressure could activate new
fractures, which results in the capping of the recorded pressure: in such a
case, minimum horizontal stress is inferred at depth from the maximum
pressure achieved during the hydraulic operations. Meanwhile, other
processes (shearing of existing weak fractures, for example) could possibly
result in the capping of pressure for lower pressure values.
Minimal horizontal stress Sh (MPa) as a function of vertical depth
(TVD) measured at the Soultz-sous-Forêts site from the analysis of
high-volume injections in the GPK-1, GPK-2, GPK-3 and EPS-1 wells. The lower
bound for the minimal horizontal stress Sh obtained from the analysis of the
wellhead pressure measured during the stimulation of well GRT-1 in
Rittershoffen is represented for comparison as a black circle.
The maximum pressure reached at 1913 m (TVD) during the hydraulic test is
22.6 MPa for a flow rate of 80 Ls-1 (Fig. 12). As the measurement is
recorded at the end of a gradual but not definitive stabilization of the
pressure with the flow rate, the 22.6 MPa stress measured at 1913 m consists
of a lower bound for the minimum horizontal stress Sh at depth. It is compared
to the Soultz-sous-Forêts trends in Fig. 13, and the measurement shows
the consistency of the linear trend used in our analysis and inferred from
the operations carried out at the Soultz-sous-Forêts site.
Thermal stresses
The cooling of the well imposed during drilling results in a thermal stress
contribution. Accordingly, the characterization of the stress tensor
necessitates the inclusion of a thermal stress analysis, which requires good
knowledge of the thermal history of the well. We define the thermal
contributions in the stress concentration at the borehole wall as
σΔTr, σzΔT and σθΔT, which are respectively
the radial, vertical and tangential components. The thermal stresses
resulting from the temperature difference, Δt, between the borehole
wall and the so-called ambient temperature, i.e., the initial temperature at
that depth before the drilling phase or the temperature at a significant
distance from the borehole (not influenced by the borehole perturbation),
are expressed from Voight and Stephens (1982). These authors adapted the
thermo-elastic solutions proposed by Ritchie and Sakakura (1956) for a
hollow cylinder to study the stress concentrations at the borehole wall due
to the application of a temperature difference. The radial component is
null, and the tangential component is expressed as
σθΔT=σzΔT=α⋅E⋅ΔT1-ν,
where α is the volumetric thermal expansion, E the Young modulus and
ν the Poisson ratio. The volumetric thermal expansion, which is kept
constant in the different layers crossed by the borehole, is α=14×10-6K-1. The Young modulus and Poisson ratio values applied at
the different layers are indicated in Table 2. Figure 14 (green curve)
presents the temperature log acquired in 2015 in GRT-1 (Baujard et al.,
2017). It is plotted along with the temperature log acquired in 2013 (red
curve). The comparison shows that temperature is close to be stable during
that period in GRT-1. As a result, the temperature log acquired in 2015 in
GRT-1 is used as an estimate of the ambient temperature since it is
considered to be in equilibrium with the reservoir. Temperature at the borehole
walls at drilling completion is best estimated from the temperature log
acquired 4 d after drilling competition. The temperature log is
presented in Fig. 14 (blue curve) as is the difference in temperature
Δt computed from these logs. Interestingly, these temperature logs show a clear anomaly at 2360 m
where the wells cross the main fault zone associated with a major
permeable structure that controls two-thirds of the total flow during flow
tests (Baujard et al., 2017).
(a) Variation of temperature (∘C) as a function
of measured depth (MD) or vertical depth (TVD) estimated from the
temperature log acquired in 2015 in GRT-1 (green curve), plotted along with
the temperature log acquired in 2013 (red curve). The temperature log
acquired 4 d after drilling completion (blue curve) enables us to
estimate the temperature at the borehole wall during drilling. (b) Estimation of the difference between the wellbore temperature
and the borehole wall temperature after completion Δt used in the
evaluation of the thermal stress components.
Maximum horizontal stress SH magnitude
The determination of the azimuthal position of the breakout edges and of
their width from the analysis of the UBI images acquired in GRT-1 and GRT-2
enables us to estimate the maximum horizontal stress SH, and to evaluate its
evolution with depth and time. Here, we present the results of our
inversion for multiple dates in GRT-1 and GRT-2.
In situ stress state components Sh, Sv and SH (MPa). Maximum horizontal
stresses SH are inverted with three distinctive failure criteria for the
images acquired in 2013 in GRT-1. Error bars are calculated considering the
error on the measurement of the breakout width, on the estimates of the
elastic parameters, and on the Sh and Sv trends. The right column illustrates the
four major lithological units retained in the model, and the horizontal band
locates the major fault zone crossed by GRT-1.
In GRT-1, we obtain for each UBI log (in 2012, 2013 and 2015) three
estimates of the magnitude of SH, according to the failure criterion. Figure 15 shows estimates of the magnitude of SH. The maximum horizontal stress SH in
GRT-1 is presented for the 2013 UBI log as a function of the true vertical
depth (TVD), along with the Sh and Sv obtained previously (Eqs. 6 and 7).
The horizontal error bars are calculated from the uncertainty on the elastic
parameters, on the Sh and Sv estimates, and on the measurements of the width of
the breakouts. The uncertainty ΔSH is obtained by integration, taking
into account the uncertainty Δxi on each variable xi involved in
the estimation of SH, i.e., the strength parameters, the Sh and Sv trends, and the width
of the breakouts.
Δf=∑i∂f∂xi⋅Δxi
Figure 15 shows that the SH magnitudes vary significantly with the failure
criterion. In particular, it shows that the SH stresses computed using a
criterion that considers the strengthening effect of the intermediate
principal stress (i.e., in Mogi–Coulomb or Hoek–Brown) are higher than those
calculated from a criterion that considers only the minimum and maximum
principal stresses (i.e., in Mohr–Coulomb).
Normalized stress polygon defining stress states (SH/SV, Sh/SV) at a depth of
2500 m in GRT-1, according to a Coulomb law with a coefficient of friction
μ=1. The borders of the polygon correspond to an active fault situation.
RF – reverse faulting, SS – strike-slip regime and NF – normal faulting refer to Anderson's faulting
regimes. The plot includes stresses (SH/SV–Sh/SV) calculated from the image
of GRT-1 from 2013 for three different failure criteria (circles in
color).
To choose the criterion that best describes the failure in the borehole, we
use the approach proposed by Zoback et al. (2003) to display the stress
state estimates presented in Fig. 15 in the stress polygon whose
circumference is defined by a purely frictional, critically stressed Earth
crust. For this purpose, we suppose that crustal strength is limited by a
Coulomb friction criterion with a friction coefficient μ=1. We
considered a depth of 2500 m to evaluate the vertical stress and assumed a
hydrostatic pore pressure. The possible stress states from the 2013 UBI images
are shown in Fig. 16 in a normalized SH vs. Sh space. Because 2500 m is an upper
boundary for the investigated depths in our study, the circumference of the
polygon sets a maximum value for the maximum and minimum horizontal stresses
SH and Sh. The stresses are normalized by the vertical stress magnitude Sv to
facilitate the comparison. The maximum principal stresses SH measured using
both our parameterized Hoek–Brown and Mogi–Coulomb criteria (blue and black
dots) exceed the polygon boundaries. With our selection of parameters, the
Mohr–Coulomb criterion was therefore retained as the most suitable for
characterizing rock failure in our study. The same conclusion was drawn by
Valley and Evans (2009) in Basel.
In situ stress components Sh, Sv and SH (MPa) in the deviated well GRT-2. SH
stresses are inverted using a Mohr–Coulomb failure criterion and represented
as a function of vertical depth (TVD) for the images acquired in 2014
and 2015. Error bars are calculated considering the errors on the
measurements of the breakout widths, on the elastic parameters, and on the
Sh and Sv trends. The right column illustrates the lithological unit retained in
the model.
For GRT-2, we calculated the SH magnitudes using only the Mohr–Coulomb
criterion retained in the previous analysis. GRT-2 is highly deviated and
the well was imaged in 2014 and 2015. The deviation is constant in the
section of interest (i.e., the open hole): 37∘ N, 355∘ E.
SH stresses are shown as a function of vertical depth (TVD) in Fig. 17
with the corresponding error bars and plotted along with the Sh and Sv trends in
GRT-2.
The impact of breakout widening on stress estimation can be evaluated from
our time-lapse characterization of the stress tensor in GRT-1 and GRT-2. For
GRT-2, Fig. 17 shows that SH magnitude changes are limited between 2014 and
2015, given the uncertainty on the estimates. Figure 18 compares the SH
stresses estimated using the Mohr–Coulomb criterion on different dates in
both the GRT-1 and GRT-2 wells. The systematic shift observed between the
estimates in both wells suggests that the lower stresses estimated in the
deviated well lead to a borehole wall stress concentration closer to the
failure condition than in the vertical well. Figure 18 provides evidence of a time
evolution of the SH stress estimates in GRT-1. Panel (b) quantifies the
differences in SH stress between 2012 and 2015 in GRT-1 in a 1 MPa bins
histogram. The confidence in the time evolution is discussed in the next
section considering the error on SH.
Panel (a) shows the in situ stress components Sh, Sv and SH (MPa) in the
deviated wells GRT-1 and GRT-2. SH stresses (MPa) inverted with a Mohr–Coulomb
criterion are obtained from an analysis of the images acquired in 2012–2013 and 2015 (black, blue and red circles, respectively) in GRT-1 and in
2014 and 2015 (black and red crosses, respectively) in GRT-2 as a function
of vertical depth (TVD). The right column illustrates the four major
lithological units retained in the model. Panel (b) is a histogram with 1 MPa
bins representing the difference between the SH stresses measured in GRT-1 in
2015 and in 2012.
Discussion
The dataset from the Rittershoffen geothermal project and our analyses
allow us to discuss the evolution of the
observed borehole failures both over time and with depth. The impact of these evolutions on our ability to
estimate stress magnitude from borehole failure indicators is important.
Evolution of breakout geometry with time
Our analysis of the evolution of the breakout geometry with time proves a
development of breakouts along well GRT-1 during the first year after
drilling (Fig. 8). Indeed, we highlighted the fact that sections without breakouts in
2012, 4 d after drilling, present characteristic breakouts in 2013 and
2015, 1 year and 2.5 years after drilling, respectively. We also observe
numerous length increases in the existing 2012 breakouts with time, in
particular in the Buntsandstein. The difficulty is to link this evolution
with time to a specific process: the time-dependant rheology of the rock (i.e.,
creep) or the effects of one of the stimulations (thermal, chemical or
hydraulic). Moreover, the 2012 data were acquired at a period during which
the thermal perturbations due to the drilling operations were still present.
The data they are compared with were collected in 2013 or 2015 after
hydraulic, thermal and chemical stimulations of the well. As a result, the
observed changes could have taken place during the thermal equilibrium of
the borehole after drilling or during the simulation operations, i.e., directly
after drilling or later.
The conclusion from our time evolution analysis of the breakout
geometry contradicts the usual assumption that breakouts deepen (i.e., an
increase in the maximum radius measured in the borehole cross sections) but
do not widen (i.e., an opening between the edges of the breakouts) with time
(Zoback et al., 2003). However, the statistical approach applied in our study
along the open hole of well GRT-1 must be interpreted with caution. Even
if we propose a systematic analysis of a time-evolutive dataset, signal loss
artifacts prevent an accurate measurement of borehole radius at some depths.
This locally limits our ability to reliably estimate the depth of the
breakout, i.e., the extension of the breakout in the radial direction. Given
this limitation, we do not completely exclude the possibility that breakouts could have deepened
with time. Our breakout width evaluation is also affected by uncertainty:
deviation from the nominal cylindrical geometry of the borehole
adds complexity to the measurements made considering the disputable
positions of breakout edges. Meanwhile, we mitigated this difficulty by
proposing a systematic analysis of all datasets to ensure a more consistent
measurement and by attributing an uncertainty level to these values. Our
study is thus more conclusive concerning this geometric parameter given that
measured changes exceed our uncertainty level.
The widening observed in our dataset can be explained by the process of
thermal stress dissipation. Indeed, the 30 to 35 ∘C of cooling
observed at the time of the 2012 logging is dissipated by the time of the
2013 logging (see Fig. 14). Assuming thermo-elastic properties of the
material, the thermal hoop stresses implied by the cooling reach -17 to
-20MPa (Eq. 8). This will be sufficient to explain the change in breakout
width without including additional time-dependent failure processes.
Evolution of breakout geometry with depth
The development of breakouts depends on the rock rheology and subsequently
on the lithology. For our dataset, breakouts are more numerous and extended
in the sedimentary cover than in the granitic basement (Fig. 2). Moreover,
their development is more pronounced in the sedimentary cover when they
develop with time vertically along the well (Fig. 8). Both observations are
consistent with the fact that the sediments have on average a lower strength
compared to the granitic rocks (Evans et al., 2009; Heap et al., 2019;
Kushnir et al., 2018); i.e., conditions are closer to failure in the
sediments.
Another important aspect of the variation of breakout geometry with depth is
the evolution of their mean orientation. From the combined measure of the
azimuth of the maximum radial extension of the breakouts (BOs) and the
azimuth of drilling-induced tensile fractures (DITFs), we analyze in Fig. 11 the evolution with depth of the orientation of the maximum principal
stress SH. The measurements are repeated for the images acquired in GRT-1 in
2012 and in 2015. The consistency in orientation between our data
and the 2012 and 2015 datasets (the 2013 dataset was not oriented)
builds confidence in the reliability of these indicators.
Figure 11 suggests that the orientation measured in the granitic layers
below 2420 m in Rittershoffen is consistent with the measurements carried out
in the basement of Soultz-sous-Forêts (Valley and Evans, 2007b) and
tends to reach regional orientation. The red line in Fig. 11 is a moving
average of the orientation data. It is computed over a 20 m window in depth.
The measurement is carried out only if 50 individual measurements or more
are present in the averaging window. It shows that the orientation of the
maximum principal stress SH varies in the studied section. Another important
aspect of Fig. 11 is the significant rotation of 30∘ from NNW to
NNE highlighted between the bottom and the top of our analyzed section. Such
a rotation with depth has already been shown in the Upper Rhine Graben
area in the Basel geothermal boreholes (Valley and Evans, 2009), in potash
mines (Cornet and Röckel, 2012) and at the neighboring geothermal site
of Soultz-sous-Forêts (Valley and Evans, 2007b). Hehn et al. (2016)
have also provided evidence of local stress rotations in the sedimentary section of
GRT-1 up to the upper Triassic (Keuper) from analyses of DITFs. The
orientation measured here, which is above the limit set close to 2400 m MD (Fig. 11),
is also consistent with the measurements of Hehn et al. (2016). They
interpreted these variations to be related to mechanical contrasts between
stiffer and softer rock layers. Another explanation for the stress rotation
has been proposed by Cornet (2016). He suggested that the rotation is the
result of the hydrostatic pressure effect on the effective friction angle in
the Hoek–Brown failure criterion. In such a case, the rotation would be
mainly a depth effect not linked to the presence of the Rittershoffen
fault. The particularity of the measurements proposed in Fig. 11 is that the
orientation of the maximum principal stress SH deviates from the regional trend
within the granitic basement, while the measurement in the upper basement
aligns with the orientation of the sedimentary cover (Fig. 11). The presence
of a major fault crossing the GRT-1 borehole at a depth of 2368 m MD (Vidal
et al., 2016) could be the explanation for this rotation. The location of the
observed stress rotation, i.e., in the basement and around 50 m above the
major fault zone, does not assume that it is related to the stiffness
contrast or decoupling between the sedimentary cover and the underlying
basement, as typically assumed, but rather to the presence of a neighboring
major fault zone. Considering a high-dipping fault geometry for this fault
zone, it suggests that the geothermal well is tangent to the fault zone,
explaining why breakouts are observed below but also above the major drain
of the fault zone located at 2368 m (Fig. 11). Moreover, it was clearly
demonstrated, based on continuous granite core analyses at Soultz, that the
fault zone could have a significant thickness due to the presence of a
damaged zone characterized by an intense hydrothermal alteration
(Genter et al., 2010). Therefore, the absence of breakouts visible in the
altered granitic section located just above the main fault drain and the
anticipated rotation of the stress field at some distance in the hanging
wall and the footwall of the fault zone confirm its major mechanical
influence.
Evaluation of stress magnitude from breakout width
Our study shows the sensitivity of our approach toward the failure criterion
chosen to describe the stability of the wellbore wall at a
centimetric scale. The absence of consensus regarding the appropriate
failure criterion to be used in the analysis of the borehole breakouts is a
first limitation in our approach. Our analyses suggest that the Mogi–Coulomb
and Hoek–Brown criteria tend to overestimate borehole wall strength because
they lead to stress estimates that violate the frictional strength limit of the
crust (Fig. 16), while the Mohr–Coulomb strength model leads to acceptable
results. This conclusion is, however, dependent on the detailed
parameterization of the failure criterion, which in Rittershoffen
is supported by sparse data. The rock strength is among the main parameters
that impact the stress magnitude assessment. Direct strength measurements
are not available for the Rittershoffen project, since no cores were
collected. We rely on measurements at the neighboring Soultz-sous-Forêts
site where cores are available. However, even at Soultz-sous-Forêts, a
systematic characterization of the rock strength of the various lithologies
is not achievable, particularly for the sediments. Also, the mechanical and
strength parameters are selected from an analysis of the core or cuttings
performed at the laboratory scale. The measurements are thus not necessarily
representative of the in situ conditions.
In addition to the uncertainty on the strength parameterization, the
uncertainty on width determination and the evolution of width with time also
impact the stress estimation. In the case of GRT-1, significant changes
occur between the 2012 dataset (prior to reservoir stimulation operations)
and the 2013–2015 datasets (after stimulation). Panel (b) of Fig. 18 shows
that the changes in the SH stresses between 2012 and 2015 in GRT-1 are larger
than our measurement uncertainty for 15 % of the measurements and
show principal stress increases. This change can be fully explained by
the thermal equilibration of the well. The uncertainty on our data does not
allow us to relate stress changes to the reservoir stimulation operations.
Cornet (2016) showed that large-scale fluid injections conducted at the
Soultz-sous-Forêts site generated large-scale failure zones whose
orientation varies with depth. Based on the analyses of borehole failures,
considerable stress orientation variations were also highlighted with depth
at Rittershoffen (Hehn et al., 2016), at Soultz-sous-Forêts (Valley and
Evans, 2007b) and at other sites (e.g., Valley and Evans, 2009; Cornet
and Röckel, 2012). In this respect, our measurements at the
Rittershoffen site confirm the conclusions drawn at many other sites
regarding the change in stress orientation. However, given the difference in
the fluid volumes injected into the wells of the two sites during the
stimulation processes and in injection pressures, it is difficult to
associate the rotation with depth with the hydraulic stimulation of GRT-1
and to apply the conclusions reached by Cornet (2016) in
Soultz-sous-Forêts to the Rittershoffen site.
Stress magnitude evolution with depth
Stresses estimated in GRT-1 and GRT-2 suggest that SH, in regards to the
uncertainty, is generally close to the vertical principal stresses Sv, consistent
with a transition between a strike-slip and a normal faulting
regime (Anderson, 1951). This result is consistent with the stress
characterization of the neighboring site of Soultz-sous-Forêts, where
measurements have highlighted a normal faulting regime in the top granitic
layers evolving into a strike-slip regime at greater depth. The uncertainty
about our measurements and about the strength parameterization does not
allow, however, for a decision on the faulting regime and its evolution with
depth in Rittershoffen. A step in SH magnitude is visible on our estimate in
Fig. 18 at large depth (below 2250 m). This step occurs at the sediment–basement interface
and could be explained by the effect of a stiffness contrast
between lithologies (Corkum et al., 2018).
Conclusion
Thanks to the repeated UBI logging of geothermal wells GRT-1 and GRT-2
in Rittershoffen (France), this study focuses on the analysis of the
evolution with time and depth of the borehole breakouts. The following
conclusions are drawn.
There is clear evidence of the time evolution of the breakout, in particular in the
sedimentary cover.
The evolution in time of the vertical length and the horizontal width of the
breakouts is measured, benefiting from the development of a UBI image
correlation technique. It is discussed in the limit of the estimated
uncertainties. The vertical length of the breakouts is shown to increase
with time. No variation in the depth of the breakouts in the radial
direction was observed within the limit of the uncertainty of our analysis.
However, width increases beyond the uncertainty of our determination were
highlighted. This contradicts the common assumption that breakouts do not
widen but only deepen until the borehole reaches a new stable state (Zoback et
al., 2003).
The changes in breakout width occur between datasets collected prior to and
after the reservoir stimulation that took place in 2013. However, the most likely
effect on breakout width is the thermal equilibration of the wellbore, and
our data do not provide evidence of stress changes resulting from reservoir stimulation.
In addition to this analysis, a study of the geometry of borehole failures
in both wells leads us to propose a characterization of the in situ stress tensor at
depth, including the orientation and magnitude of the three principal
stresses. This detailed stress state analysis includes the estimation of
thermal stresses. A Mohr–Coulomb criterion is retained here to estimate the
principal stress magnitude as it is in our parameterization, which is the most
consistent with a frictional strength limit in the crust. The strength
parameterization is, however, uncertain due to the lack of mechanical testing
on the Rittershoffen reservoir rocks. Given the uncertainties, we propose
the following careful interpretation of our measurements.
Our analyses of the breakout geometry variation with depth suggest a change
in mean orientation, with a 30∘ rotation from NNW to NNE
highlighted between the bottom and the top of our analyzed section. This
observation is robust and independent of the strength parameterization. The
rotation does not occur at the sediment–basement interface but is related to
a high, steeply dipping major fault zone crossing the GRT-1 borehole at a
depth of 2368 m (Vidal et al., 2016).
Our results also suggest a step in horizontal stress magnitude at the
sediment to basement transition that would be consistent with a stiffness
contrast between these two lithologies. However, such a step is determined by
the choice of the failure criterion and its parameterization, which is
uncertain at Rittershoffen.
SH is generally slightly larger than the vertical principal stresses Sv consistently
with a strike-slip to normal faulting transitional regime. This is
consistent with stress characterization at the neighbor site of
Soultz-sous-Forêts (Cornet et al., 2007; Klee and Rummel, 1993; Valley
and Evans, 2007b)
The Rittershoffen borehole imaging dataset is unique in that
repeated logging allowed for the study of the temporal evolution of borehole
breakouts and the possible stress changes induced by reservoir stimulation.
Our results change the common view that breakouts mostly deepen but do not
widen. Further work is, however, required to reduce the uncertainties related
to stress magnitude estimates from borehole breakouts and to
quantify stress changes induced by reservoir stimulation.
Data availability
Due to the industrial properties of the borehole datasets, raw data must
remain confidential and cannot be shared.
The Kirsch equations are derived under 2-D plane conditions. They provide
stress values in a case that is not suited to the one of real deviated
boreholes, in which out-of-plane normal and shear stresses also exist. We
consider two Cartesian coordinate frames: x–y–z having z aligned with the vertical
and x′–y′–z′, which is aligned with the three principal
stresses denoted [σx′x′, σy′y′, σz′z′]. We consider a long
cylindrical cavity of radius a. Its axis is arbitrarily oriented with respect to
the principal stress state in the Earth. The borehole axis tilts at an angle
ϕ relative to the x axis. The third cylindrical r–θ–ζ
coordinate frame is borehole centric with the ζ axis, which is
coincident with the borehole axis. The azimuth with respect to the borehole
axis is denoted θ.
The borehole centric stresses are expressed as a function of the direction of
cosines aij, enabling us to transform the principal axes x′–y′–z′ to the x–y–z frame according to Eq. (A1),
σ′=A.σ.AT,
where the rotation matrix A is composed of the direction cosines aij:
A=axx′axy′axz′ay′x′ayy′ayz′az′xaz′yazz′.
Equations (A2)–(A7) express the borehole-centric stresses as a function of
directional coefficients α1, α2, α3, γ1 and γ2. They include the contribution of fluid pressure Pf. Indeed, the
pressure of the fluid in the mud column increases with depth, which produces
tensile hoop stress and compressive radial stress. Equations (A2)–(A7) also include
the time-dependant contribution due to temperature changes. The thermal
stresses σθΔT and σrΔT,
resulting from the temperature difference, Δt, between the
temperature applied at the borehole wall and the initial temperature at that
depth before perturbation or the temperature at a significant distance from
the borehole (not influenced by the borehole perturbation), are expressed
from Voight and Stephens (1982). The radial component is null, and the
tangential component expressed in Eq. (8) shows that an increase in
temperature at r=a effects the compressive hoop stress.
A2σrr=Pf+σrΔTA3σθθ=2α1-4α2cos2θ-4α3sin2θ-Pf+σθΔTA4σζζ=β1-4ν(α2cos2θ+α3sin2θ)A5τθζ=2γ1cosθ+2γ2sinθA6τrζ=0A7τθr=0
The geometrical coefficients involved in Eqs. (A2)–(A7) are expressed as a
function of the three far-field principal stress states [σx′x′, σy′y′, σz′z′]
and as a function of the geometrical rotations aij.
A8α1=12[(ax′x2sin2Φ+ax′y2+ax′z2cos2Φ-2ax′z2ax′x2sinΦcosΦ)σx′x′+(ay′x2sin2Φ+ay′y2+ay′z2cos2Φ-2ay′z2ay′x2sinΦcosΦ)σy′y′+(az′x2sin2Φ+az′y2+az′z2cos2Φ-2az′z2az′x2sinΦcosΦ)σz′z′]A9α2=12[(-ax′x2sin2Φ+ax′y2-ax′z2cos2Φ+2ax′z2ax′x2sinΦcosΦ)σx′x′+(-ay′x2sin2Φ+ay′y2-ay′z2cos2Φ+2ay′z2ay′x2sinΦcosΦ)σy′y′+(-az′x2sin2Φ+az′y2-az′z2cos2Φ+2az′z2az′x2sinΦcosΦ)σz′z′]A10α3=(ax′yax′zcosΦ-ax′xax′ysinΦ)σx′x′+(ay′yay′zcosΦ-ay′xay′ysinΦ)σy′y′+(az′yaz′zcosΦ-az′xaz′ysinΦ)σz′z′A11γ1=[-ax′x2sinΦcosΦ+ax′z2cosΦsinΦ+ax′zax′x(cos2Φ-sin2Φ)]σx′x′+[-ay′x2sinΦcosΦ+ay′z2cosΦsinΦ+ay′zay′x(cos2Φ-sin2Φ)]σy′y′+[-az′x2sinΦcosΦ+az′z2cosΦsinΦ+az′zaz′x(cos2Φ-sin2Φ)]σz′z′]A12γ2=(-ax′yax′zsinΦ-ax′xax′ycosΦ)σx′x′+(-ay′yay′zsinΦ-ay′xay′ycosΦ)σy′y′+(-az′yaz′zsinΦ-az′xaz′ycosΦ)σz′z′
Author contributions
JA and BV measured the borehole failure. JA characterized the stress state under the guidance of BV, JS and AG. The analysis of the failure evolution was conducted mainly by BV. JA wrote the paper with help from all the coauthors. All authors read and approved the final paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank ÉS-Géothermie, a subsidiary company of Électricité de
Strasbourg (ÉS), for support and allowing us to use the borehole data on
wells GRT-1 and GRT-2 of the Rittershoffen ECOGI project. A part of this
work was conducted in the framework of the EGS Alsace project, which was
cofounded by ADEME.
We would like to thank the Swiss Competence Center for Energy
Research–Supply of Electricity (SCCER-SoE) for support of the study. The
present work has been done under the framework of LABEX
ANR-11-LABX-0050-G-EAU-THERMIE-PROFONDE and benefits from state funding
managed by the French National Research Agency (ANR) as part of the
“Investments for the Future” program.
Financial support
This research has been supported by the EU H2020 DESTRESS Project (grant no. 691728).
Review statement
This paper was edited by Federico Rossetti and reviewed by two anonymous referees.
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