 Research
 Open Access
Borehole damaging under thermomechanical loading in the RN15/IDDP2 deep well: towards validation of numerical modeling using logging images
 M. PeterBorie^{1}Email authorView ORCID ID profile,
 A. Loschetter^{1},
 I. A. Merciu^{2},
 G. Kampfer^{2} and
 O. Sigurdsson^{3}
https://doi.org/10.1186/s4051701801027
© The Author(s) 2018
 Received: 14 April 2018
 Accepted: 16 August 2018
 Published: 29 August 2018
Abstract
A wider exploitation of deep geothermal reservoir requires the development of Enhanced Geothermal System technology. In this context, drilling and stimulation of highenthalpy geothermal wells raise technical challenges. Understanding and predicting the rock behavior near a deep geothermal wellbore are decisive to implement stimulation strategies to reach the couple temperature/flowrate target. Numerical modeling can contribute to enhanced stimulation processes thanks to a better understanding of impact of stress release, pressure changes and rock cooling in the nearwellbore area. In this paper, we use Discrete Element Method (code PFC2D, © Itasca Consulting Group), and more specifically bondedparticle model to capture the thermomechanical processes at metric scale. The application case corresponds to the beginning of thermal stimulation at Reykjanes in well RN15/IDDP2 (Iceland, IDDP2 project and H2020 project DEEPEGS). A cold fluid is injected at a depth of 4.5 km where the rock temperature is above 430 °C and the well pressure is around 34 MPa. Since we have sitespecific data and logging images after drilling, we attempt to link the simulations with the reality. The numerical results are confronted with incipient interpretation of logging images and with analytical solution to go towards validation of the modeling approach. Numerical results show breakouts and thermally and/or mechanically induced fractures consistent with the analytical solutions. Moreover, the sensitivity analysis on uncertain parameters yields important clues regarding some logging features as, for example, asymmetric damaging or caving.
Keywords
 EGS (Enhanced Geothermal System)
 Borehole
 Thermal stimulation
 Fracture initiation
 DEM (Discrete Element Model)
 PFC2D
 LWD
 Borehole logging images
Background
EGS (enhanced/engineered geothermal system) constitutes a potential renewable energy technology to produce heat and electricity from geothermal reservoirs deficient in fluid or in permeability. In most cases, reaching an economically viable temperature target requires drilling down to several kilometers depth, where the permeability of the system is generally naturally low. The implementation of stimulation strategies is then necessary to increase the injectivity or the productivity of the wells (Tester et al. 2006). The deployment of such EGS method in a wide range of geological contexts is still a technical challenge, and the number of projects in operation is currently limited. According to EGEC (2017), concerning EGS, three electricity plants (Insheim and Landau in Germany, SoultzsousForêts in France; the reservoir temperatures are, respectively, > 160 °C, 160 °C and > 180 °C; Lu 2018) and one heat plant (Rittershoffen in France, the reservoir temperature is 177 °C; Baujard et al. 2017) are now in operation, with a further ten plants under development.
In this context, the EUfunded H2020 DEEPEGS (Deployment of DEEP Enhanced Geothermal Systems for sustainable energy business) project aims at demonstrating the feasibility of EGS in highenthalpy reservoirs (temperature up to 550 °C, with an Icelandic demonstrator) and in deep hydrothermal reservoirs (temperatures around 200 °C, with French demonstrators), to deliver new innovative solutions and models for wider deployments of EGS. The first demonstrator deployed in the frame of the DEEPEGS project is located in the Reykjanes geothermal system in southwest Iceland. The deepening of the wellbore RN15 from 2500 m depth (RN15/IDDP2) began in August 2016 and the well is completed at a depth of 4659 m MD (measured depth, ~ 4.5 km vertical depth) in January 2017 (temperature around 500–530 °C) (Friðleifsson et al. 2017; Friðleifsson and Elders 2017a, b; Stefanson et al. 2017). RN15/IDDP2 provides information about the deep geology and the deep rock behavior in the Icelandic context. Notably, borehole images provide a unique view of the geological structure of the Icelandic crust. To improve the productivity of the well (estimated injectivity index around 1.7 L s^{−1} bar^{−1} at the end of drilling), stimulations in the form of coldwater injection (mainly thermal stimulations) have been performed to connect the wellbore to existing hydraulic pathways, i.e., preexisting natural fracture network.
Understanding all the processes that lead to fracture initiation in the EGS nearwellbore remains challenging due to the high temperatures. In this context, numerical modeling contributes to improve our understanding and it allows for predictions in the future. The objective of this article is to propose a physical modeling approach contributing to the understanding of phenomena occurring in the wellbore vicinity during drilling and EGS operations. We focus on the thermomechanical processes induced by the rock cooling. The choice of the numerical method is based on assumptions drawn from onsite information. The results are compared with results from analytical equations and with observations made during drilling to critically discuss the numerical results and go towards validation of the chosen approach.
In this paper, after briefly describing the geological and geothermal context, we first present data and borehole images from well RN15/IDDP2. Then we describe the numerical modeling tool, based on the Discrete Element Method (DEM), and the chosen setup for the numerical simulations. Numerical results show breakouts and thermally and/or mechanically induced fractures consistent with the analytical solutions and with observations made during drilling. We finish with words of conclusion and with discussion on the experienced limitations and perspectives.
Geological knowledge
Regional data
The in situ geological, mechanical and thermal conditions are little known in the deep part of the Reykjanes field. The deepest well in this area was shallower than 3 km before drilling the IDDP2 well. Besides, geophysical methods are limited for investigations at several kilometers depth. We summarize below the information concerning the regional geology, the regional stress state and the rock behavior.
Geology
Regional stress state
The in situ stress field is poorly characterized in the deep part of the Reykjanes field. The World Stress Map (Heidbach et al. 2008, 2016) indicates that the stress regime varies by short distances around Reykjanes. Most data (e.g., Ziegler et al. 2016 in the vicinity of wellbore RN15/IDDP2) consist of principal stress directions, with no indication of the stress magnitudes. It is not even certain that the vertical direction is a principal stress axis (Keiding and Lund 2009; Kristjánsdóttir 2013). Pieces of information concerning the orientation and magnitude of principal stresses were found in Keiding and Lund (2009), Batir et al. (2012), and Kristjánsdóttir (2013) but the characterization of in situ stress at such depth in this complex area remains very uncertain.
Rock behavior
Foulger et al. (2003) suggest that the brittle–ductile transition occurs deeper than the targeted depth considering gabbrolike rocks and the geothermal gradient. The analysis of earthquake swarms indicates that the brittle–ductile boundary is at 5.5–6 km depth under Reykjanes (Khodayar et al. 2017), thus below the considered depth. Observations from core retrieved between 4643 and 4652 m MD show fractures, which are supposed to be open and fluidfilled downhole, indicated by precipitations on the fracture surface. For that reason, we only assume brittle formation behavior in the presented study.
Sitespecific data acquired during drilling operations
The drilling of IDDP2 provides new knowledge concerning the rock composition, the rock properties and the in situ temperature at depth.
Rock composition
Indepth logging and coring lend credibility to the thesis of sheeted dyke complex. Cores retrieved from 4 km depth show mainly rocks with finegrained igneous texture: microgabbro/dolerite to finegrained basaltic intrusive (cf. Fig. 1c), with heterogeneous grain size (Friðleifsson et al. 2017). The mineral composition was assessed (see "Numerical settings and scenarios" section) and the porosity is found to be very low (matrix porosity between 3.6 and 0.1%—Claudia Kruber, Equinor internal report in progress).
Rock properties
Knowing the rock mineralogy and an estimate of the in situ temperature range, we can use results of Keshavarz (2009) to confirm the assumption of brittle rock behavior. His experimental results indeed show that the physical and mechanical properties of this gabbro remain on the same trend up to the critical temperature of 600 °C, thus sufficiently above the estimated formation temperature in the IDDP2 well.
Rock temperature
At the end of drilling, the fluid temperature measured at 4560 m MD of IDDP2 was 426 °C (Friðleifsson et al. 2017), after the deepest part of the well had the possibility to warm up for 6 days. It should be noted that this measurement is probably an underestimation of the in situ formation temperature since extensive cooling occurred during drilling the well. The in situ formation temperature was estimated in the range 536–549 °C, based on warmup measurements and a Horner plot at 4565 m MD (Tulinius 2017).
Borehole response to drilling
During drilling, shear and tensile rock failures may threaten wellbore stability. We mainly distinguish between shear failureinduced breakouts and drillinginduced fractures (opening mode fractures) as the two main sets of mechanical instabilities when drilling with overly low and overly high mud weights, respectively. Breakouts are aligned with the minimum horizontal stress whereas drillinginduced fractures are aligned with the maximum horizontal stress in a vertical well. In the present case, severe mud losses were observed during drilling, leading to the conclusion that the pressure in the well exceeded the minimum compressive hoop stress around the wellbore, inducing a drillinginduced fracture or opening a preexisting fracture. Since the volumes of mud loss are high, it is very likely due to leakage into a naturally existing fracture network (swarm of fractures of the sheeted dyke complex). Either the well directly crossed such a discontinuity, or induced damages connected the wellbore and natural discontinuities. Logging images (see next section) give insight into possible damages in the wellbore. It should be noted that as a consequence of the total mud loss, it was not possible to influence the well pressure. The pressure measured at the bottom of the well after completing the drilling operations was 34 MPa (thus below the hydrostatic pressure expected at such depths, around 45 MPa) and is supposed to represent an equilibrium between gain and loss from the formation along the whole open section which intersects several fracture zones of different productivity and injectivity, respectively. The low pressure, however, can also result from the change in density as the formation water is heated up to abovesupercritical reservoir conditions.
Logging images
Borehole images recorded during drilling campaign of IDDP2 well provide a unique view into the geological structure of the Icelandic crust.
For a selected IDDP2 drilled interval from 2940 to 3410 m MD in a 21.6cm (8.5 in.) hole, two sets of images are available for our exemplification: ultrasonic images and electrical microimages (Stefanson et al. 2017) with no caliper measurement available. Ultrasonic amplitude images are collected using wireline standard televiewer ABI 43 (ALT advanced logic technology 2018) from 9 5/8 in. (24.5 cm) casing shoe at 2940 m MD down to 3410 m MD. Electrical microimages are collected using Logging While Drilling SineWave™ MicroImager Tool (Weatherford International logging while drilling SinWave 2018) images from 9 5/8 in (24.5 cm) casing shoe at 2940 m MD to 4513 m MD (Friðleifsson et al. 2017; Friðleifsson and Elders 2017a, b; Stefanson et al. 2017).
Ultrasonic amplitude image data are affected by poor centralization and lack of measurement references at surface (Stefanson et al. 2017). The eccentralization of the sensor affects heavily the reflection coefficients that may be extracted from the amplitude envelope and postprocessing artifacts are present on the images in the form of vertical shades. Further processing on ultrasonic amplitude images is limited due to challenging acquisition conditions.
Electrical microimages are affected by the high resistivity of the formation and the general raw values are accumulating towards 0 mA and exhibit sandy texture in dynamic normalization window which is further corrected by applying a median filter.
As a large data integration effort is ongoing at the time of this publication, we are selecting representative image examples for the scope of numerical simulation validation with intervals where both ultrasonic and electrical microimages are recorded and refraining from an indepth evaluation of logging results.
Numerical simulations
Observationdriven modeling

The rock matrix has brittle elastoplastic material properties.

The porosity of the matrix is below 3%. As a consequence, it is considered reasonable to neglect the poroelastic effects (referring to the poroelasticity theory, this would mean assuming a zero Biot coefficient, which can be supported in such a situation, see Fjar et al. (2008), sections 1.3, 2.9 and 6.2; subsequently effective stresses are simplified and assumed as total stresses).

The hole stability is ensured mainly by the rock matrix rigidity, with little influence from fluid pressure in the fractures of the surrounding rock.

The rock has a finegrained texture, with heterogeneous grain size and different mineral grain composition.
The stress state has a strong influence on the failure initiation and propagation, but we lack quantitative data to make solid assumptions. Hence, it was decided to work with a series of possible scenarios for the stress state (see "Numerical approach" section).
Logging images reveal numerous features, between other breakouts and induced fractures. From the drilling operation without any return of fluid to surface (for depths beyond around 3300 m) we can assume that the pressure in the wellbore during drilling was very close to the pressure in the fluidfilled fracture systems intersected by the well. With this limited hydraulic pressure in the well, it is not expected to observe drillinginduced fractures in conventional wells. A possible explanation for this observation is coolinginduced fracture (e.g., Yan et al. 2014). In such hightemperature environments, cooling of the rock necessarily occurs during drilling operations (even before dedicated thermal stimulation). In the following, we provide insight into the initial fracture mechanism based on thermomechanical stress mechanism.
The role of the thermal stimulation is often unclear, and determining which mechanisms lead to observed injectivity increase is still challenging (Flores et al. 2005; Grant et al. 2013; Héðinsdóttir 2014). Covell (2016) shows that thermal stimulation is driven by thermal contraction caused by the significant temperature difference between cold injection fluid and hot reservoir rock. The involved mechanisms lead to opening preexisting discontinuities (contraction of discontinuity walls) or creating new ones. The thermal solicitation induces differential strains at the origin of thermomechanical stresses. When these stresses exceed the mechanical resistance of the rock, microcracks and failures could appear. Strains at the origin of this process can be mainly due to two causes: on the one hand, a thermal gradient in the rock mass, on the other hand, the heterogeneity of the grain contraction in the rock matrix. Because of this heterogeneity, two adjacent minerals can contract at different rates and this can generate uneven strains at the grain boundary (Wanne and Young 2008). In addition, petrographic characteristics (including grain size, grain shape, packing density, packing proximity, degree of interlocking, type of contacts and mineralogical composition) are known to affect mechanical properties (Ulusay et al. 1994). A critical review concerning DEM and its application to borehole stability was proposed by Kang et al. (2009). Santarelli et al. (1992) were among the first to study borehole stability using DEM. Yamamoto et al. (2002) used DEM to study the wellbore instability of laminated and fissured rocks. Karatela et al. (2016) studied the effect of in situ stress ratio and discontinuity orientation on borehole stability in heavily fractured rocks using DEM. DEM seems fairly adapted to take into account the physical phenomena at the granular phase level (micro scale), and to analyze their impact on the mechanical behavior of the nearwellbore zone (macro scale). We propose to implement this approach using the code Particle Flow Code—2 Dimensions (PFC2D) (Itasca Consulting Group Inc. 2008a, b), and to question the role of thermal loadings in the wellbore. Chemical interaction of the drilling fluid may play a role in the thermal stimulation, for instance, through dissolution or precipitation of the minerals, triggered by temperature change. The quantification of these chemical effects in the specific context of IDDP2 remains a scientific challenge. Thus, in the absence of available data, indirect chemical effects of thermal stimulation are not considered in this study.
It is worth mentioning that the thermal stimulation by injecting cold water may not necessarily have a longterm effect because of the thermal expansion and closure of fractures during production. Only the naturally propped fractures keep some permeability and hence improve productivity.
Contrary to common analytical approaches (see Appendix), the proposed numerical approach enables quantifying the depth and shapes of damages. The results will be compared with the logging observations (breakouts, induced fractures, petal fractures), trying to identify what the simulation captures successfully and what it does not. Note as a limit of the method that the logging is performed several days after the drilling: throughout this time lapse, the well has been exposed to more mechanical and thermal stresses than simulated in the numerical approach.
Numerical approach
PFC2D calculates the movement and interaction of stressed assemblies of rigid circular particles using the DEM. As a discrete element code, it allows finite displacements and rotations of discrete bodies (including complete detachment), and recognizes new contacts automatically as the calculation progresses. The setup is composed of distinct particles that displace independently of one another, and interact only at contacts or interfaces between them. The calculations performed in the DEM alternate between the application of Newton’s second law to the particles and a force–displacement law at the contacts, characterized by normal and tangential stiffnesses. Newton’s second law is used to determine the motion of each particle arising from the contact and body forces acting upon it, while the force–displacement law is used to update the contact forces arising from the relative motion at each contact (Itasca Consulting Group Inc. 2008a).
For a plutonic rock, we choose bonding behavior for contacts (also called “parallel bond”—PB), which allows to reproduce the behavior of cohesive materials (Potyondy and Cundall 2004; Itasca Consulting Group Inc. 2008b). A rupture criterion based on the beam theory is used for PB; when the bond stress exceeds its yielding strength (in tension or in shear), the bond breaks.
The integration of radii increment in the force–displacement law creates induced mechanical response of the system.
Numerical settings and scenarios
The calculation setup consists of a twodimensional cross section perpendicular to the well. The numerical simulations focus on the deepest part of the well. As far as possible, the conditions observed at 4560 m MD of IDDP2 are used in the numerical simulations. The wellbore section is assumed to be 21.6 cm (8.5 in.). The temperature of the rock is assumed to be 426 °C (corresponding to the fluid temperature measured at the end of drilling). For thermal stimulation, we assume a temperature of 30 °C for the injected fluid (corresponding to the targeted temperature of the cooling fluid). Please note that temperatures recorded during logging operations are above 70 °C, thus using 30 °C overestimates the cooling during drilling operations (but may be appropriate for the subsequent thermal stimulation). The direction of the wellbore dip direction is N220°E and the deviation from the vertical is approximated at 30°. The modeled 2D cross section is thus oriented N130°E–60°NE.
We focus our study on the behavior of the matrix of the finegrainedtextured rock. The welldetailed description of the dolerite (weekly report IDDP2, 2016) cored at 4 km depth is used as a reference for the numerical rock model. Deeper coring shows that similar rocks exist in the deeper part of the wellbore.
Description of the four configurations considered to address uncertainties on the stress state
Name  “Andersonian” stress state (MPa)  Transformed stress state, aligned with a local coordinate system which is aligned with the wellbore axis (MPa)  

Tectonics  σ _{v}  σ _{H}  σ _{h}  σ _{ss}  σ _{dd}  τ _{sd}  
Case A  Intermediary normal/strikeslip fault (σ_{v} = σ_{H} = σ_{1})  134  134  60  125  85  21 
Case B  Normal fault—“low” horizontal isotropic stress (σ_{v} = σ_{1})  134  60  60  60  79  0 
Case C  Strikeslip fault (σ_{H} = σ_{1} and σ_{v} = σ_{2})  134  180  60  166  89  33 
Case D  Normal fault—“high” horizontal isotropic stress (σ_{v} = σ_{1})  134  80  80  80  94  0 

a low value (1000 W m^{−2} K^{−1}) simulating a slow cooling of the rock mass on the boundary of the wellbore;

a very high value (10,000 W m^{−2} K^{−1}) simulating an instantaneous cooling of the rock mass on the boundary of the wellbore.
Numerical rock setup
Following the conceptualization step, the properties of the numerical particles and bond are assigned. In this regard, quantified data from studied or analogue rock are required. For the present application case, the coring of finegrained dolerite retrieved at 4090.6 m depth (Zierenberg et al. 2017) provided detailed information on the rock composition (pyroxene 40%, plagioclase 55%, titanomagnetite 5%, grain size around 3 mm). The particles of the numerical dolerite model follow the same distribution. The heterogeneity of particles size is represented through the implementation of a particlesize distribution centered on 3 mm.
At the time of the study, macroscopic mechanical and thermal data were not available from the IDDP2 cored samples. Thus, we chose a limited analogue rock with available macroscopic properties. Since petrographic characteristics affect mechanical properties, analogues are selected depending on the proximity in terms of rock petrographic characteristics as mineral composition and grain size. A North African gabbro, characterized by Keshavarz (2009), is retained as reference analogue. It contains almost 40% pyroxene and 60% plagioclase, with traces of other elements (among others magnetite). Laboratory tests performed on pressurized (stepwise up to 650 MPa) and heated (stepwise up to 600 °C) samples provide mechanical properties of the analogue rock covering conditions similar to those expected in the bottom of IDDP2. As microgabbro/dolerite have very low porosity [below 0.5% in the analogue rock (Keshavarz 2009), matrix porosity between 3.6 and 0.1% (no microporosity included) for the cored dolerite (Claudia Kruber, Equinor internal report in progress)], we assume that the pores can be seen as singularities in the rock matrix. The numerical rock model does not integrate the rock porosity. Therefore, in our numerical approach, no poroelastic effects are considered. The heat transfer process is thus limited to conduction between grains.
Mechanical, thermal and thermomechanical properties of particles after calibration
Plagioclase  Pyroxene  Olivine  Titanomagnetite  

Young’s modulus (mean value, MPa)  84  162  178  230 
Ratio normal stiffness/shear stiffness  2.5  2.2  2.6  2.6 
Friction coefficient  0.9  0.9  0.9  0.9 
Tensile strength (MPa)  30  75  27  45 
Cohesion (MPa)  140  350  126  210 
Thermal conductivity (W m^{−1} K^{−1})  1.98  4.52  4.48  2.10 
Specific heat (J kg^{−1} K^{−1})  1112  800  800  910 
Linear thermal expansion coefficient (K^{−1})  6.81 × 10^{−6}  1.00 × 10^{−5}  3.85 × 10^{−6}  3.40 × 10^{−5} 
Mechanical properties of the selected analogue rocks and of the numerical rock model
Young’s modulus (GPa)  Poisson’s ratio  UCS (MPa)  UTS (MPa)  Cohesion (MPa)  Friction angle (°)  

Analogue  85–90  0.18  225  12  68  43 
Numerical model  87  0.17  214  15  61  35 
Nearwellbore setup
Simulation stepwise
The numerical simulation is performed stepwise with the aim to reproduce, as far as possible, the state of the rock in the vicinity of the wellbore before the thermal stimulation. Randomization is used for the construction of the numerical model. The radius of each particle is randomly drawn following the normal distribution \({\mathcal{N}}\,(1.37,0.62)\) for pyroxene and plagioclase, and following \({\mathcal{N}}\,(1.25,0.5)\) for titanomagnetite (based on cores observations). A periodic sample duplication process is used to build the numerical model faster.
After the initial stress field is established, the borehole drilling is simulated by removing the particles located on the wellbore surface (Fig. 9 step 1). To avoid a sudden increase of the unbalanced forces of particles placed on the surface of the wellbore, leading to numerical instabilities, a forcereduction procedure is used at this step to release progressively the unbalanced forces of particles situated along the wellbore surface (Shiu et al. 2011). Note that this step is a very rough and simplified approximation of the drilling impact on the formation stability. On the one hand, the impact of the drilling bit at the excavation step is not considered. On the other hand, the pressure considered in the wellbore is assumed zero, due to limitation in the calculation procedure, which can lead to damage overestimation as pressure actually exists in the well during real drilling at ECDs (equivalent circulation densities) even above the static fluid column.
During the fluid injection step of the calculation schedule, the wellbore is subjected to a hydraulic pressure and to a thermal loading. The fluid injection is assumed to act only on particles forming the wellbore surface. A specific procedure (Itasca Consulting Group Inc. 2008c; Shiu et al. 2011) is used to detect a set of closed linked particles (connected by parallel bonds) around the wellbore. These particles are recorded in a specific list and will be referred to as the wellbore list in the following description. To simplify the numerical modeling setup, and to limit the computational time, the hydraulic pressure and the thermal loading are applied in two steps. The hydraulic pressure is applied first (Fig. 9 step 2) and the thermal loading (Fig. 9 step 3) takes place later (assuming that no significant thermal propagation occurs before the hydraulic pressure is fully installed on the wellbore surface). The underlying assumption is that the characteristic time for pressure effects is far shorter than the characteristic time for thermal effects. The list of the wellbore particles is updated automatically when cracks appear between particles in the wellbore list. Hence, once the cracks start propagating from the wellbore, the injection pressure and the fluid temperature can penetrate into the crack as well.
Results
Simulation of the drilling of the well
Results of the analytical approach for breakouts
Name  Principal stress in the 2D plane perpendicular to the well  Breakout characteristics  

P_{well} = 0 MPa  P_{well} = 34 MPa  
σ_{A*} (MPa)  σ_{B*} (MPa)  σ_{90°, R = r} (MPa)  r_{θ = 90°,} σ_{θ = UCS} (cm)  σ_{90°, R = r} (MPa)  r_{θ = 90°,} σ_{θ=UCS} (cm)  
Case A  76  134  326  14.8  292  13.6 
Case B  60  79  175  < R  141  < R 
Case C  76  178  459  23.0  425  21.0 
Case D  80  94  200  < R  166  < R 

In numerical simulation, cracks coalesce until creating a caved area; this area represents only a limited part of the area where the rupture criterion is exceeded in the analytical model.

Cracks in the numerical model also occur outside of the area where the rupture criterion is exceeded according to the analytical solution.

As contact properties depend on the adjacent particle properties, the PB do not have all the same strength (the criterion of the analytical solution is the mean strength of the rock). Cracks may occur outside of the analytical breakout area when the strength of the PB is locally exceeded by the stress, even if it is lower than the criterion. Conversely, stronger bonds may resist in the numerical model, even if the analytical area predicts rupture.

Because of the heterogeneity of the properties of the particles and of the PB, stress local modification can occur. Thus, locally, a higher stress can lead to PB breaking, or a lower stress to PB integrity.

The caving in the breakout area will affect the stress further—this case cannot be taken into account in the analytical solution.
Impact of increased well pressure
In this section, we discuss the mechanical impact of increased well pressure, without thermal loading effects, with tensile failure as expected result.
Results of the analytical approach for the computation of the breakdown pressure (P_{frac})
Name  Tectonics  Principal stresses  P _{frac, UTS=15 MPa}  

σ_{A*} (MPa)  σ_{B*} (MPa)  
Case A  Intermediary normal/strikeslip fault (σ_{v} = σ_{H} = σ_{1})  76  134  110 
Case B  Normal fault—“low” horizontal isotropic stress (σ_{v} = σ_{1})  60  79  116 
Case C  Strikeslip fault (σ_{H} = σ_{1} and σ_{v} = σ_{2})  76  178  65 
Case D  Normal fault—“high” horizontal isotropic stress (σ_{v} = σ_{1})  80  94  161 
In the RN15/IDDP2 wellbore, the pressure remained limited (below breakdown pressures computed in this section). Neither the analytical solution nor the numerical simulation results can explain the tensile fractures observed by the low well pressures. However, numerous features that may be interpreted as tensile fractures are observed in the image logs (see "Logging images" section and Fig. 2). Therefore, we study the effects due to the thermal cooling in the next section.
Cooling effects on wellbore stability
Numerical simulations are proposed here for an indepth view of the failure under thermal loading. Our motivation is twofold: first, the DEM approach allows to take into account thermal effects at the microscale (notably the differential expansion of the grains of the rock) and thus the approach is indeed more detailed for simulating the thermal effects. Second, the shape and size of damages can be retrieved and analyzed in comparison with observations. We investigate the impact of the thermal flux (through the heat transfer coefficient values) and of the pressure in the well. For the sake of comparison, and after a brief presentation of the stress state impact, a sensitivity analysis is presented.
Thermomechanical tensile failures depending on the stress state
Impact of the thermal flux at the wellbore boundary
Impact of the pressure in the wellbore
Discussion
The presented study may shed light on the effects of the wellbore drilling and of the thermal stimulation in a deep and very hot finegrained rock. Drilling and pressurization impacts on the wellbore stability have been studied first. The formation of breakouts and induced tensile fracture have been successfully described by the calculation results, even though we consider total deconfinement of the wellbore during drilling and no dynamic processes as tools impact in a first approach. Slight differences can be explained by the level of greater detail included in the numerical approach compared to the analytical solution: grain heterogeneity in the rock matrix, caving processes allowed and not predefined. From both analytical solution and numerical results, a fluid pressure no less than 65 MPa is needed for inducing tensile fracture without considering thermal effects. During the drilling phase and after, the pressure in the bottom of the well is under the breakdown pressure. However, numerous induced fractures have been observed in the logging images; a thermal component appears to be necessary to explain the observations.
In the RN15/IDDP2 well, there is a drastic difference in temperature between the fluid in the well and formation, probably higher than 150 °C during the drilling phase and even higher during the thermal stimulation (up to 400 °C). From both analytical and DEM calculations, which take into account thermomechanical loadings, this constant thermal stimulation induces tensile fracture. Note that considering the high temperature difference, fluid pressure in the well is not necessary for fracture inducing.
Complementary to the analytical solution, DEM allows a more detailed study of the thermomechanical processes; beyond the “macro” thermomechanical processes, the impact of the differential behavior of the minerals composing the rock can be considered thanks to a modeling at the grain scale. In addition, this approach allows notably the quantification of the damage around the wellbore, the visualization of the pathway of the induced fractures.
Beyond the abovepresented results fitting with the observations, and as for any model, it is important to keep in mind the limitations when analyzing modeling results. Among the model limitations, we can quote the two dimensionality, the matrix considered as impermeable, and the impossibility to generate intragranular cracks.
Other limitations of simulations come from the complexity of the model and from the difficulty to have wellcharacterized parameters to feed into the model. The long computational time (on average 4–5 weeks to simulate a few hours of thermal loading) makes these limitations more pronounced since the number of possible investigations is limited. The variety of rock behavior under thermal loading, depending on the different studied parameters as the stress state, the thermal flux or the pressure in the wellbore, illustrates the necessity of data acquisition to reduce uncertainties. Indeed, the efficiency of the thermal stimulation as well as the stability of the borehole during the drilling evaluation need a sound knowledge of the in situ conditions (thermal and mechanical properties of the rock, direction and magnitude of stress state among others), and the control of the thermal stimulation (depending notably on the flow rate, the temperature at surface, the pressure and the composition of the injected fluid). In addition to these influent uncertainties, the influence of the rock model should also be further investigated.
A second layer of uncertainties is introduced when comparing the modeling results with logging images, since these latter are also subject to uncertainties. Besides, note that the logging is performed more than 48 h after drilling while exposing the well to both thermocycling and pressure cycling; as a consequence, comparisons are mainly qualitative, but provide nonetheless a preliminary evaluation on the ability of the numerical approach to replicate successfully the observations.
Further investigations and numerical developments are needed to confirm the assumption and for a better understanding of the linked processes. Indeed, some limitations of the used version of the numerical code can lead to a misevaluation of the pathway and the propagation speed of the fractures: the energy of propagation of the fractures is not taken into account (Kanninen and Popelar 1985); the stability/instability of fracture growth in and out the zone of increased stress should be further investigated depending on the stimulation mechanism (either thermal or pressure effects). We have observed that the results are not accurately capturing the propagation of fractures into the far field once the close wellbore region is fractured when well pressures are larger than the minimum horizontal stress. The reason for that is found to be in the definition of the 2D plane strain cross section and the definition of the boundary conditions. The principal stress direction of the far field stresses is not aligned with the plane in which the 2D calculations are performed and also the axial stresses are not taken into the lower dimensional setup. For that reason, the system does not recognize that the outofplane, farfield stress is not a principal stress direction, but rather rotating with distance from the wellbore. This simplification overestimates the overall resistance against fracturing in the far field which in reality would be simply the minimum horizontal stress and rock resistance. Therefore, a fully 3D setup including all components of the stress tensor is proposed in future studies, which will shed light on stable vs unstable fracture growth beyond the closewellbore region in the case of inclined wells exposed to temperature and pressure loading. This enhanced setup would then also enable a discussion of the paths of fractures propagating from the well into the far field eventually creating socalled “hackles”.
Further developments are also in progress for interpreting the induced fractures in terms of injectivity and later on also for studying productivity gains. The goal of such future simulations will be to enable the numerical reproduction of transient productivity loss as the previously created fracture closes due to thermal expansion of the matrix.
Conclusion

The long computational time resulting in limited number of possible investigations in the parametric study;

The two dimensionality of the model leading to a poor capture of the propagation of fractures into the far field;
Some of these limitations can be improved in future works, in particular, by considering a 3D setup.
Nonetheless, numerical results are consistent with the results of the analytical solutions. According to the numerical results, as well as to the analytical solution, and fitting with the observations in RN15/IDDP2, breakouts result from the drilling process—arguing for a quite high local deviatoric stress—and tensile fractures appear because of the high thermal loading. Overpressure in the wellbore speeds up the process.
Moreover, the numerical simulation allows a deeper investigation into the effect of the drilling and into the thermal stimulation. In particular, the impact of the differential behavior of the minerals composing the rock can be considered thanks to a modeling at the grain scale. In addition, this approach notably allows the quantification of the damage around the wellbore and highlights the caved areas and the pathway of the induced fractures in the near field.
As emphasized, a fresh aspect of this study is the consideration of the thermal flux at the wellbore boundary. We have shown that a high thermal flux between the fluid in the wellbore and the rock leads to tortuous pathways for induced fractures; In this case, pieces of rock can be separated from the rock mass. This could be one explanation for the observed induced fractures and cavings in the logging images, oriented perpendicular to the direction of breakouts due to low ECD.
Abbreviations
DEM: discrete element method; ECD: equivalent circulation density; EGS: enhanced/engineered geothermal system; IDDP: Iceland Deep Drilling Project; MD: measured depth; PB: parallel bond; PFC2D: particle flow code—2 dimensions; UCS: uniaxial compressive strength; UTS: ultimate tensile strength; VD: vertical depth.
List of symbols
\(\alpha_{L}\): linear thermal expansion coefficient (1 °C^{−1}); ∆P: difference between the fluid pressure in the borehole and that in the formation (P_{well}–P_{p}) (MPa); Δt_{th}: thermal time step (s); ΔT: temperature difference between the mud and the rock (°C); θ: Azimuth measured from the direction of σ_{B}* (°); ν: Poisson’s ratio; σ_{1}: major principal stress (MPa); σ_{2}: middle principal stress (MPa); σ_{3}: minor principal stress (MPa); σ_{H}: major horizontal stress (MPa); σ_{h}: minor horizontal stress (MPa); σ_{v}: vertical stress (MPa); σ_{A}*: 2D minimal principal stress component (MPa); σ_{B}*: 2D maximum principal stress component (MPa); σ_{dd}: stress component parallel to the dip direction of the plan perpendicular to the well (MPa); σ_{ss}: stress component parallel to the strike direction of the plan perpendicular to the well (MPa); σ_{r}: radial stress around the borehole (MPa); σ_{θ}: circumferential stress around the borehole (MPa); τ_{sd}: tangential shear stress component in the plane perpendicular to the well (MPa); \(\tau_{{r_{{_{\theta } }} }}\): tangential shear stress around the borehole (MPa); C_{v}: specific heat coefficient (J kg^{−1} °C^{−1}); E: Young’s modulus (GPa); L_{p}: pipe length (m); m: mass of the heat reservoir (kg); P_{frac}: fracture pressure (MPa); P_{well}: well pressure (MPa); P_{p}: pore pressure of the formation (MPa); Q_{p}: power in the thermal pipe (W); r: distance from the center of the hole (m); R: radius of the borehole (m); R_{th}: thermal resistance (°C W^{−1} m^{−1}); T_{i}: temperature of the numerical particle i (°C); T_{j}: temperature of the numerical particle j (°C).
Declarations
Authors’ contributions
BRGM’s authors performed modeling work and prepared the core of the manuscript. Equinor’s authors provided data from wellbore logging and enriched the discussion part. HsOrka provided data from RN15/IDDP2. All authors read and approved the final manuscript.
Acknowledgements
We would like to thank Kati TänavsuuMilkeviciene (Equinor) and Claudia Kruber (Equinor) who helped with the geology, mineralogy and porosity analyses; Théophile Guillon (BRGM) and Arnold Blaisonneau (BRGM) for fruitful discussion on modeling issues. The authors are grateful to the editor and to the two anonymous reviewers for their helpful comments and advice.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
Not applicable (commercial code).
Funding
This study was part of the DEEPEGS project, which received funding from the European Union HORIZON 2020 research and innovation program under Grant agreement no. 690771.
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Authors’ Affiliations
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