largemagnitudeeventsduringinjectionsin ... · relation computation. such methods were already...
TRANSCRIPT
This paper was published in Geothermics,doi:10.1016/j.geothermics.2014.07.002.
Large magnitude events during injections in
geothermal reservoirs and hydraulic energy: A
heuristic approach
Clement Baujard∗1, Martin Schoenball2, Thomas Kohl2, and Louis Dorbath3
1Geowatt AG, Zurich, Switzerland2Karlsruhe Institute of Technology, Institute of Applied Geosciences, Karlsruhe, Germany
3Ecole et Observatoire des Sciences de la Terre, Universite de Strasbourg, Strasbourg,
France
Abstract
The occurrence of induced seismicity during reservoir stimulation re-quires robust real-time monitoring and forecasting methods for risk miti-gation. We propose to derive an estimation of Mmax (here defined as thelargest single seismic event occurring during or after reservoir stimulation)using hydraulic energy as a proxy to forecast the total induced seismicmoment and to model the transient evolution of the seismic moment dis-tribution (based on the Gutenberg-Richter relation). The study is appliedto the vast dataset assembled at the European pilot research project atSoultz-sous-Forets ( Alsace, France), where four major hydraulic stimula-tions were conducted at 5 km depth. Although the model could reproducethe transient evolution trend of Mmax for every dataset, detailed resultsshow different agreement with the observations from well to well. Thismight reveal the importance of mechanical and geological conditions thatmay show strong local variations in the same EGS.
1 Introduction
Induced seismicity is a crucial issue for Enhanced Geothermal Systems (EGS)development. Large magnitude events (in the following defined as events show-ing a moment magnitude larger than 2) can occur during the stimulation phaseof the reservoir or during the operational (circulation) phase. Such eventswere observed in many EGS: in Soultz-sous-Forts, France (Gerard et al., 2006;
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Charlety et al., 2007; Dorbath et al., 2009) , in Basel, Switzerland (Haring et al.,2008), or in Cooper Basin, Australia (Baisch et al., 2006) for example. In thefollowing, we will focus on seismic events observed during the reservoir develop-ment only, i.e. during stimulation phases (during and after injection) conductedby high pressure injections of water or brine. We restrict our analysis to thestimulation phase as it is generally associated with high seismicity rates, whichhelps to reduce the statistical uncertainty, e.g. compared to the lower seismicactivity during long-term production. Our study is based on monitoring dataacquired during the stimulation of the 5 km deep boreholes of the EGS of Soultz-sous-Forts (France). Seismicity prediction in geothermal reservoirs using severalmethods has been developed for years (Baujard, 2003; Kohl and Megel, 2007).Reservoir models are based on the numerical simulation of physical processesoccurring during injection or circulation. Flow in porous and fractured me-dia, mechanical coupling and thermal transport are the most important ones.Examples of such models are FRACTure (Kohl and Hopkirk, 1995), Tough2(Rutqvist, 2011), or FRACAS (Bruel, 2005). Seismic events magnitudes weresuccessfully simulated using e.g. rate- and state-dependent friction models (Mc-Clure and Horne, 2012), block-slider mechanisms (Baisch et al., 2010), discreteparticle models (Yoon et al., 2014) or by combining probabilistic approach andempirical observation (Bachmann et al., 2011; Shapiro et al., 2007; Shapiro andDinske, 2009). Goertz-Allmann and Wiemer (2013) present a model that mayexplain the observed variation of b-value. It has been showed that cyclic pres-surization of a geothermal reservoir could enhance permeability and reducesinduced seismicity (Zang et al., 2013). Our work aims at developing a heuristicmodel that can give indications on the largest magnitude event Mmax that couldbe induced during a given pumping sequence in a reservoir. To that purpose,we propose to correlate the hydraulic energy provided to the reservoir by fluidinjection and the seismic moment released by induced seismicity, and to use thiscorrelation to derive a prediction of Mmax, using a real-time Gutenberg-Richterrelation computation. Such methods were already applied, as one can find inthe literature examples of comparison of the pumped energy, or of the injectedvolume with the highest magnitude event obtained or with the total seismicmoment (see for example McGarr, 1976; Baisch et al., 2009b; McGarr, 2014).Here, we propose to go one step further and to use a simple relation betweenthe hydraulic energy and the total induced seismic moment in order to predictMmax evolution during reservoir stimulations resolved by time bins.
2 Physical background
The hydraulic energy applied to a reservoir can be estimated through the inte-gration of pumping power over time or through the integration of the pressuredistribution in the reservoir over its volume. The pumped hydraulic energy canbe computed with:
Eh,pumped =
∫
Q∆Pdt, (1)
2
with Eh,pumped [J] being the pumped hydraulic energy, Q [m3/s] the flowrate,∆P [Pa] the overpressure and t [s] the injection time. The integration of theoverpressure distribution over the reservoir volume also represents a quantity ofenergy. The advantage of this estimation of energy is that, on the contrary tothe pumping energy (which is zero if computed in a time interval after shut-in),there is still some residual energy after shutting in the well. This energy willbe called in the following reservoir hydraulic energy and can be computed withthe following relation:
Eh,res =
∫∫∫
∆PdV, (2)
with Eh, res [J] being the hydraulic reservoir energy, ∆P [Pa] the overpres-sure and V [m3] the reservoir (rock and fluid) volume. The seismic moment isobtained by:
M0 = µSd (3)
with M0 [Nm] being the seismic moment, µ [Pa] the shear modulus, S [m2] thesurface of rupture and d [m] the displacement. The moment magnitude of theevents is computed using the following relation (Hanks and Kanamori, 1979):
Mw =2
3log(M0)6.07. (4)
With Mw [-] being the moment magnitude and M0 [Nm] the seismic moment.
3 Dataset
Our work is based on the unique data set acquired from the three deep boreholesof the European research pilot-EGS site at Soultz-sous-Forts, France (Dorbathet al., 2009). The following data will be used:
• GPK2 stimulation, starting 30.06.2000. Approx. 23 400m3 of water wereinjected during 6 days. A total number of 6 947 seismic events wererecorded and located by a surface network. The highest magnitude recordedwas 2.6.
• GPK3 stimulation, starting 27.05.2003. Approx. 37 500m3 were injectedduring 11 days. A total number of 7 175 events were recorded. Only 2 253events were located. The highest magnitude recorded was 2.9.
• GPK4 first stimulation, starting 13.09.2004. Approx. 9 300m3 were in-jected during 3.5 days. A total of 1 182 events were recorded. Only 794events were located. The highest magnitude recorded was 2.3.
• GPK4 second stimulation, starting 09.02.2005. Approx. 12 500m3 wereinjected during 4 days. A total of 1 246 events were recorded. Only 764events were located. The highest magnitude recorded was 2.7.
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Figure 1: Hydraulic stimulation data of GPK2, 2000. From bottom to top:imposed flowrate and wellhead pressure, event rate and ratio of the numberof events of magnitude greater than 1 over the total number of events using12 hours bins, and distance vs. time of the seismic events with symbol sizeproportional to magnitude.
These data were acquired using the surface network of EOST (Ecole et Ob-servatoire des Sciences de la Terre - University of Strasbourg). It consisted of14 temporary stations in 2000, and was upgraded through the installation ofnine permanent stations in 2003. For the stimulations in 2004 and 2005 thepermanent network was enhanced by a temporary network of only six tempo-rary stations (Dorbath et al., 2009). It must be underlined that the catalogs forGPK4 might be incomplete. The injection scheme considered for each stimula-tion sequence as well as the time-distance representation for the localized eventsare represented in figure 1 for the stimulation of GPK2, in figure 2 for GPK3,in figures 3 and 4 for the stimulations of GPK4.
For each injection sequence, an event rate has been calculated for the largestmagnitude events (in number of events of magnitude higher than 1, 1.5 and 2using 12 hours intervals). The ratio of the number of events of magnitude greaterthan 1 over the total event number was also computed. It can be observed
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Figure 2: Hydraulic stimulation data of GPK3, 2003. From bottom to top:imposed flowrate and wellhead pressure, event rate and ratio of the numberof events of magnitude greater than 1 over the total number of events using12 hours bins, and distance vs. time of the seismic events with symbol sizeproportional to magnitude.
that the ratio has a tendency to increase after the shut-in of the well, so theproportion of larger events increases. Similar observations have been made bySchindler et al. (2008), who found that the mean amplitudes recorded at theseismic stations increased significantly after shut-in. Furthermore, there arenumerous examples where the largest event induced by hydraulic stimulationwas observed after shut-in (Baisch et al., 2006, 2009b; Haring et al., 2008). Itwas also shown, that the b-value tends to decrease after shut-in (Bachmannet al., 2011), which results in a larger proportion of large magnitude events.
The total energy pumped into the system during the pumping sequence andthe total seismic moment have been calculated for each stimulation (see table 1and figure 5). The total seismic moment is the sum of the seismic moments ofall events. Deriving a universal relation between the total seismic moment andthe pumped energy is not possible using simple physical considerations. Never-theless, as it seems that the total seismic moment increases with the pumped
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Figure 3: Hydraulic stimulation data of GPK4, 2004. From bottom to top:imposed flowrate and wellhead pressure, events rate and ratio of the numberof events of magnitude greater than one over the total events number using 12hours bins, and distance vs. time of the seismic events.
energy, an empirical linear relation will be assumed in the following betweenhydraulic energy and total seismic moment released, as follows:
M0 = cEh (5)
With M0 [Nm] the seismic moment, Eh [J] the hydraulic energy, and c a con-stant.
4 Methodology
The proposed methodology aims at predicting the total seismic moment thatwill be released at time t+ t, using a comparison between the hydraulic energyinjected into the system and the total seismic moment released at time t. Thegeneral methodology can be summarized by the following steps:
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Figure 4: Hydraulic stimulation data of GPK4, 2005 (right). From bottomto top: imposed flowrate and wellhead pressure, events rate and ratio of thenumber of events of magnitude greater than one over the total events numberusing 12 hours bins, and distance vs. time of the seismic events.
• Step 1: at time t, computation of the ratio R of total seismic momentrecorded M0,t [Nm] and the hydraulic energy injected Eh,t [J]:
R =M0,t
Eh,t
(6)
• Step 2: at time t, the b-value is computed, following the Gutenberg-Richter relation (Gutenberg and Richter, 1944). The value of the seismicmoment obtained for N = 1 and N = 10 is computed, where N is theevents number of a given magnitude.
• Step 3: at time t + ∆t, the total predicted seismic moment is computedafter:
M0,t+∆t = REh,t+∆t (7)
M0,t+∆t [Nm] and Eh,t+∆t [J] being the total seismic moment predictedand the hydraulic energy injected or present in the system at a time t+∆t,
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Hydraulic Energy Seismic MomentEh [J] logEh M0 [Nm] logM0
Stim GPK2 2000 3.00× 1011 11.48 1.47× 1014 14.17Stim GPK3 2003 5.50× 1011 11.74 1.50× 1014 14.18Stim GPK4 2004 1.47× 1011 11.17 1.29× 1013 13.11Stim GPK4 2005 1.99× 1011 11.30 3.79× 1013 13.58
Table 1: Pumped hydraulic energy and total seismic moment released the for thestimulations of GPK2 (2000), GPK3 (2003), GPK4 (2004) and GPK4 (2005).
Log (E h)
Log
(M0)
11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 1213
13.2
13.4
13.6
13.8
14
14.2
14.4
14.6
GPK4, 2004
GPK4, 2005
GPK2, 2000 GPK3, 2003
Figure 5: Comparison of the total seismic moment released with the hydraulicpumped energy for the stimulations of GPK2 (2000), GPK3 (2003), GPK4(2004) and GPK4 (2005).
respectively. Thus, we assume that the hydraulic energy that will beinjected into the system during the next phase is known. The way to derivethe hydraulic energy will be discussed in more detail in the following.
• Step 4: at time t+∆t, a new distribution of the predicted seismic eventsis computed, that fits the predicted total seismic M0,t+∆t, assuming thatthe b- value remains the same as during the previous time bin. Thus,it is possible to derive the seismic moment of an event that has a givenoccurrence. We suggest in the following to take the occurrences N=1 andN=10 as proxies for the determination of Mmax.
Two models were developed, based on different approaches for estimatinghydraulic energy used in eqs. 6 and 7.
4.1 Model 1
In the first model, the ratio R (see eq. 6) is computed by assuming Eh,t =Eh,pumped and computed after eq. 1. In order to compute the energy at a time
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t + ∆t, it is necessary to know the flowrate during ∆t, and the correspondingwellhead pressure. In the following, it is assumed that the flowrate is knownfor the next ∆t time interval. The wellhead pressure is predicted assuming thatthe well injectivity remains constant during the next time interval ∆t. Theinjectivity at a time t is computed after:
It =Qt
Pt
(8)
with Qt [m3/s] being the flowrate at a time t and Pt [Pa] the wellheadpressure at a time t. Thus, the pressure at t+∆t is computed after:
Pt+∆t =Qt+∆t
It(9)
The main limitation of this model is that hydraulic energy remains constantafter the shut-in of the well, as the flowrate drops down to zero. Thus, noprediction can be done for the shut-in phase. According to the number of dataavailable, at a given time t, the seismic moment and the pumped hydraulicenergy can be computed from the beginning of the pumping sequence or onlyfor the last period ∆t.
4.2 Model 2
In order to predict the seismic response of the reservoir during shut-in phases,another strategy was developed. As described above, the hydraulic energy addedto the system can also be obtained by integrating the reservoir overpressureinduced by the injection over the reservoir volume. In this model, physicalquantities are derived at a reservoir scale. The pressure integration is done overthe entire reservoir volume (i.e. the pressurized rock and fluid volume), and notonly additional fluid volume. The method assumes that the pressure distributionat a time t and at a time t+∆t, is known. In this model, the pressure distributionat different times is computed assuming the Dupuit steady-state solution of thediffusion equation (de Marsily, 1986), following an isotropic natural logarithmicdecrease of the pressure with distance from the injection, after:
Pres,t(r) = a lnb
r, (10)
with Pres,t [bar] being the reservoir pressure, r [m] being the distance to theborehole, and a and b two constants. An example of the pressure curve is shownin figure 6. The constants a and b are determined by the following boundaryconditions: Pres,t(r = r0) = Pt, r0 [m] being the borehole radius and Pt [bar]the injection pressure at a time t, and Pres,t(r = rcloud) = constant, rcloud beingthe radius of the seismic cloud at a time t. The constant is a parameter of themodel (usually relatively low, as it is the minimum shearing pressure). Thisformulation of the pressure distribution in the reservoir implicitly assumes thatthe reservoir behaves like a porous medium when observed at a large scale. This
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Distance to borehole [m]
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200 400 600 800 1000 12000
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Figure 6: Reservoir pressure model for a wellhead pressure of 120 bar (12MPa)and a seismic cloud extension of 1 200m after eq. 9.
assumption is certainly arguable and will be discussed in the last section of thispaper. Nevertheless, this formulation will be here accepted as its purpose is toprovide a simple analytical solution of the pressure distribution to be integratedin space in order to derive the energy.
In order to be able to compute the reservoir hydraulic energy at a time t+∆t,one has to know the extension of the cloud at that time. In order to overcomethat issue, we propose to compute the seismic diffusivity at a time t, based onthe propagation of the triggering front of the hydraulic-induced microseismicity(Shapiro et al., 1999). The extension of the cloud as a time t + ∆t is thencomputed after:
rcloud,t+∆t =√
4πD(t+∆t) (11)
With D [m2/s] being the diffusivity. The diffusivity is fitted using an iter-ation scheme at every time t, using a tolerance ratio. The diffusivity value isiteratively increased until the envelope drawn by the diffusion equation reachesa tolerance value (see table 2). Thus, it is possible to predict the hydraulic reser-voir energy, as one knows at a time t+∆t the extension of the cloud as well asthe pressure at the borehole (which is derived assuming a constant injectivity,see model 1).
5 Results
Both models need the same input data, which are: hydraulic data: pressureand flowrate with time, seismic data: location and magnitude of events withtime The input parameters are the following: the prediction time interval ortime bin ∆t, a tolerance ratio for the computation of the diffusivity (whichis the proportion of events located under the envelope given by eq. 11 for a
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Parameter Valuetime interval ∆t 12 hoursdiffusivity tolerance factor 80%magnitude bin length DeltaMw 0.2magnitude interval for b-value determination 0 - 1.2
Table 2: Model parameters used in the following computations.
given diffusivity) the size of the magnitude bin for the determination of theb-value in the Gutenberg-Richter relation, the magnitude interval used for thedetermination of the b-value. As the extreme values of magnitude do not followthe Gutenberg-Richter relation (Dorbath et al., 2009), it is necessary to set-upa fixed interval for the determination of the b-value. The influence of theseparameters in the computations will be discussed later on in this paper. Theparameters used in the following are summarized in table 2. The results obtainedfor every stimulation campaign are presented in the following. A prediction ofthe seismic rate and magnitude for the next 12 hours is made every 12 hours.On the following figures, the prediction is shown 12 hours later in order to becompared with the observation. Both models have been run, with the model1 being limited to the injection sequence. At each time step, the seismic rateand the predicted magnitude of events for occurrence N = 1 and N = 10 arepresented.
GPK2, 2000
The results obtained for the stimulation of GPK2 are shown in figure 7. As thepressure was not monitored after 168 hours (see figure 1), the pressure decreaseat the borehole was linearly extrapolated during the next 72 hours in order toallow a prediction. Both models give comparable results. As it can be observed,the predicted seismic rate is well correlated with the observations, for bothmodels. The magnitude of the event with occurrence N=1 is higher than theobserved highest magnitude event. The magnitude of the events of occurrenceN = 10 correlates relatively well with the highest observed magnitude. It mustbe pointed out that both predicted magnitudes of the event of occurrence N = 1and N = 10 do not decrease during the shut-in of the well.
GPK3, 2003
The results obtained for the stimulation of GPK3 are shown in figure 8. Again,both models give comparable results. As for GPK2, the predicted seismic rateis well correlated with the observations, for both models. On the contrary ofthe GPK2 stimulation, the magnitude of the event with occurrence N=1 givesa realistic prediction of the highest magnitude event that was observed. It isinteresting to note that, at the end of the injection (240 hours), the magnitudeof the event of occurrence N = 1 is 2.8, which seems overestimated in regard
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Figure 7: Results of the predictions obtained for the stimulation of GPK2. Frombottom to top: imposed flowrate and wellhead pressure, predicted magnitudesof events of occurrence N=1 and N=10, compared with the highest magnitudeobserved, and predicted seismic events rate compared with the observations.
to the observed highest magnitude events. But, an event of magnitude 2.9 wasrecorded around 4 days later, i.e. 350 hours after the beginning of the injection.
GPK4, 2004
The results obtained for the stimulation of GPK4 (2004) are shown in figure 9.If the correlation between the predicted seismic events rate and the observationsis realistic during the injection, the predicted seismic event rate is overestimatedduring the shut-in phase of the stimulation. The observed highest magnitudeevent for each time bin has a very high time variability, making the interpre-tation of the results of our magnitude prediction relatively problematic. Themagnitude of the event of occurrence N = 1 (Mmax = 2.5 after 96 hours ofinjection) corresponds to the largest event observed.
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Figure 8: Results of the predictions obtained for the stimulation of GPK3. Frombottom to top: imposed flowrate and wellhead pressure, predicted magnitudes ofevents of occurrence N = 1 and N = 10, compared with the highest magnitudeobserved, and predicted seismic events rate compared with the observations.
GPK4, 2005
The results obtained for the second stimulation of GPK4 (2005) are shown infigure 10. The prediction does not correlate very well with the observations.The first prediction of the model can be made only after 50 hours of injections,as the model has to collect enough magnitudes in order to derive a b-value(see also figure 4). The poor quality of the results can be explained by thelack of data recorded during this phase of the stimulation, thus making thedetermination of a b-value quite problematic. The reason for this anomalousbehaviour of the reservoir is the history of the well and a prominent Kaiser effect(see for example Baisch et al., 2009a), that plays a dominant role in the firsthalf of the stimulation. Due to this effect, no seismicity is induced as long asthe injection pressure is lower, than the maximum pressure achieved during the
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Figure 9: Results of the predictions obtained for GPK4 (2004). From bottom totop: imposed flowrate and wellhead pressure, predicted magnitudes of events ofoccurrence N = 1 and N = 10, compared with the highest magnitude observed,and predicted seismic events rate compared with the observations.
first stimulation in 2004.
Summary of the results
The predicted maximum magnitude for every stimulation campaign is shownin the table 3. As can be observed, except for GPK2, the highest predictedmagnitude of the events of occurrence N = 1 is generally quite close to thehighest magnitude observed in reality.
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Figure 10: Results of the predictions obtained for GPK4 (2005). From bottom totop: imposed flowrate and wellhead pressure, predicted magnitudes of events ofoccurrence N = 1 and N = 10, compared with the highest magnitude observed,and predicted seismic events rate compared with the observations.
Maximum magnitude Maximum magnitude Largest magnitudeof occurrence N=1 of occurrence N=10 observed
GPK2, 2002 3.5 2.6 2.5GPK3, 2003 2.8 1.8 2.9GPK4, 2004 2.5 1.6 2.3GPK4, 2005 2.6 1.3 2.3
Table 3: Comparison of the maximum magnitude of the events of occurrenceN = 1 and N = 10 with the highest magnitude observed
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6 Discussion
Several observations can be made on our results. Firstly, it can be observedthat the magnitude of the events with occurrence N = 1 or N = 10 hardly de-crease during the shut-in phase, for all wells. This is a consequence of the factthat the hydraulic energy that has been injected into the system only resorbsvery slowly after the end of the injection in the datasets used. Also, it must bepointed out that the seismic rate rapidly decreases after the shut- in, thus lim-iting the risk of obtaining a large magnitude seismic event. On the other hand,b-value decreases after shut-in which in turn increases Mmax. Secondly, resultsobtained for GPK2 and GPK3, which are the best datasets available, show verydifferent agreement with the observations. The predictions of the magnitudeof the events of occurrence N = 1 are much higher than the observed highestmagnitude events for GPK2, on the contrary to GPK3, for which the magni-tude of the events of occurrence N = 1 is quite closed to the observed highestmagnitude. Several reasons could explain these different behaviours:
• The lack of large scale structures (faults) in the vicinity of GPK2 (Dorbathet al., 2009; Schoenball et al., 2012). Indeed, an event of magnitude 3.5,which is the predicted magnitude of the events of occurrence N = 1 wouldrequire a fault of around 500m diameter. If no such structure is to befound in the neighbourhood of GPK2, no such event could happen.
• In the case of GPK3, it is well established that an important structure hasbeen met in the open section of the well at 4770m depth (Sausse et al.,2010; Held et al., 2014). Thus, this structure may allow movements oflarge areas and consequently leads to the occurrence of large magnitudeseismic events during the stimulation.
• The reservoir structure and rock properties vary from well to well. Theopen hole section of GPK2 is characterized by a higher clay content thanthe open hole section of GPK3 (Meller et al., 2014). The clay content isknown to be a critical parameter for the failure modes to be brittle, henceseismic, or ductile and aseismic (Tembe et al., 2010).
The sensitivity of the model response to the input parameters has to bementioned here. In fact, the sensitivity of the model to the time interval ∆t, tothe tolerance factor for the computation of the diffusivity and to the magnitudebin length ∆Mw is very limited. On the contrary, sensitivity of the modelresponse to the magnitude interval used for the determination of the b- value isrelatively high (see figure 11). This parameter has a direct influence on the b-value and thus on the predicted magnitude of the events of different occurrenceprobabilities. Despite the high sensitivity of the model to this parameter, theadvantage of the method here proposed is that the number of user-defined inputparameters remains very limited and that no manual data fit is needed. It istherefore suitable for real-time monitoring and prediction of seismic activityduring stimulation or operation in geothermal reservoirs.
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Log (M0) [-]
Lo
g(N
)[-
]
108
109
1010
1011
1012
101310
0
101
102
103
104
Observations
Gutenberg-Richter line - Mag. interval 0 - 1.6
Gutenberg-Richter line - Mag. interval 0 - 1.2
Time since 27.05.2003 18:37:50.2 [h]
Mm
ax
0 48 96 144 192 240 288 336 384 432 4800
1
2
3
4
Observations
Predictions - Model 1 - Mag. interval 0 - 1.6
Predictions - Model 2 - Mag. interval 0 - 1.6
Predictions - Model 1 - Mag. interval 0 - 1.2
Predictions - Model 2 - Mag. interval 0 - 1.2
Occurrence N=1
a
b
Figure 11: Top: sensitivity of the results to the magnitude interval used for thedetermination of the b-value (example with GPK3). Bottom: sensitivity of theGutenberg-Richter law computed at the end of the stimulation.
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The presented methodology shows several limitations. The implementedhydraulic model (pressure prediction assuming that injectivity remains constantfor the next time bin, and pressure distribution in the reservoir following aDupuit steady-state) is very simple. Further developments could couple thismethod with more complex 3D hydro-mechanical models (see for example Kohlet al., 2004). As mentioned with GPK4, the model does not take into accountpast injections/stimulations. Implementing a reservoir initial state and initial b-value could improve that point. The ability of the models to predict post shut-inseismic activity is limited, as aftershocks (Omori- Utsu seismicity decay) are nottaken into account. The spatial variation of b- values, as presented by Goertz-Allmann and Wiemer (2013) could not be taken into account in the models,as well as stress variations occurring into the reservoir (as the stress state ofthe reservoir is not considered). The presented model cannot take into accountaseismic slips that could occur in the reservoir during stimulation. Indicationsfor large-scale aseismic deformations have been obtained from 4D-tomography,revealing strong changes of seismic velocities (Calo et al., 2011). These canbe interpreted as strong changes of the stress field. This was underpinned bySchoenball et al. (2014), who found strong changes of the stress regime, thatare incompatible with co-seismic stress changes (Schoenball et al., 2012), andtherefore must occur aseismically.
7 Conclusions
We presented a heuristic approach to estimate the largest events induced dur-ing a reservoir stimulation treatment. Our approach relies on the observationof seismicity, determination of their magnitudes and the past and projectedhydraulic schedule for the operation. Since real-time seismic monitoring is stan-dard now, our approach is easy to implement in an action scheme for a plannedoperation. We use two different models for the calculation of the hydraulic en-ergy. The first one relies on the operational parameters pressure and injectionrate. In order to predict the post shut-in phase we use an analytical solutionwhich integrates the pressure perturbation over the reservoir volume. Resultsof both models are very similar during the injection phases; therefore the ap-plied analytical solution appears to be valid. The models could reproduce thetransient evolution trend of Mmax for every dataset. The predicted seismic rateis well correlated with the observations for all 4 stimulations. The magnitude ofthe events with a predicted occurrence N = 10 gives a realistic prediction of thehighest magnitude event that was observed for GPK2, whereas the magnitudeof the event with occurrence N = 1 correlates relatively well with the highestobserved magnitude during GPK3 stimulation. Concerning GPK4 stimulation,the observed highest magnitude event for each time bin shows a strong vari-ability, making the interpretation of the results of our magnitude predictionrelatively problematic. For a given dataset, the highest predicted magnitude ofthe events of occurrence N = 1 is generally quite close to the highest magnitudeobserved in reality. The observed differences of the seismogenic responses be-
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tween the stimulation appear to not be solely related to the reservoir treatment,i.e. the energy supplied to the system by fluid injection. Instead, the individualgeological conditions for each well at the Soultz reservoir, that is the hydraulicconnection to the local fracture network and its mechanical properties, definede.g. by the clay content plays a critical role.
Acknowledgements
This study was supported by the 7th EU framework programme for Researchand Technical Development and carried out within the framework of the GEISER( Geothermal Engineering Integrating Mitigation of Induced Seismicity in Reser-voirs) project. The authors would like to thank GEIE Soultz-sous-Forts andspecially Nicolas Cuenot for data and ideas exchange.
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