Pressure drop mechanism
The results of our numerical simulations demonstrate that a direct link between seismicity and pressure drops can be established. The formation of pressure drops seems to be related to the activation of slip along a pre-existing fracture during seismic events in regions near fracture intersections. This process operates in a series of steps summarised in Fig. 13.
In situations where the fluid is injected in a fracture segment at a low angle with σ1 (e.g. model “88–60”), the fracture high fluid storage capacity or transmissibility allows it to be initially pressurised without seismicity. Once the pressure front reaches the intersection between fracture segments, and a seismic segment is stimulated, microseismicity occurs. When the tensile strength is overcome in the seismic segment (i.e., α = 60°), the fracture slides and the relative displacement between walls induces stress concentration at fracture tips. In our models, this stress was high enough to open the tensional segments, producing a slight decrease of fluid pressure next to the intersection zones (for example see Fig. 3 around t = 0.5 × 104 s). After that, a time lapse is required to re-pressurise the region prior to the onset of a new pressure drop. This pressurisation is followed by new seismic events that assist the opening of additional tensional segments. These processes are repeated until all the seismic segments are completely stimulated. While the injected fluid progressively flows from the well throughout the fracture network, seismic events migrate from intersections located next to the injection well to more distant ones. Tensional segments are stimulated as aseismic segments or result in seismic events with very low magnitude. Larger events are located along seismic fractures and tend to occur near the intersections. With ongoing stimulation, seismic events progressively occur at longer distances from the injection point and the induced pressure drops are, thus, hardly observable by looking at the fluid pressure measured at the well. Nevertheless, they are continually happening, as illustrated in Figs. 3, 7 and 10 or in Fig. 12b, in which the difference between pressure drops at the well and in the simulation domain increases with increasing of fracture length.
In cases where fluid injection is carried out in a low-transmissivity fracture segment (model “60–88”; Fig. 7), pressure drops are difficult to be detected at the injection point. The fracture acts as a barrier for the pressure drop propagation due to its low storage capacity and low hydraulic aperture. The process producing pressure drops operates in a similar way as in the model previously described. When the tensile strength is overcome in a seismic segment, a sudden aperture change of the intersection is induced, causing the aseismic/tensional segments (i.e., high-capacity fractures) to get open, generating a new volume and producing the pressure drop (for example, see those at t ~ 3.25 × 104 s in Figs. 7, 8 and 9 or between t = 4 and 4.5 × 104 s in Fig. 7).
Another process associated with void aperture can be detected when pressure drops are analysed in detail (Figs. 5, 6, 8 and 9). The opening of aseismic fractures was not homogenous in our models, and regions along the same fracture segment experienced closing and opening during stimulation of the fracture intersections. Some regions are opened suddenly, while others are closed suddenly (e.g. points 1 and 6 in Fig. 6). Since a sudden fracture opening should imply a pressure drop, its sudden close should be associated with a local fluid pressure rise. Such local pressure rises, which get quickly dissipated, are likely to be felt more intensively in low-permeability fractures, i.e. in fractures that are shear stimulated (this can be detected for example in the curve t + 10 s in Fig. 8 for injection in the 60° segment).
Models “60–88” and “88–60” were carried out to explore the influence of the orientation of the fracture in which the fluid was injected. Despite the initial differences between the two models, their dynamic behaviour is very similar, and both show similar pressure drop phenomena. Similarly, the variation of the dilation angle or the length scale does not modify the described processes, but only determines the absolute values of pressure drops (Fig. 12) and the magnitude of microseismicity. Increasing the dilatational angle produces a permeability increase in the shear-stimulated fractures, allowing the propagation of pressure drops up to the well (Fig. 12a). However, the pressure drop process is similar to that in models “60–88” and “88–60”, and is related to the reactivation by sliding of a shear-stimulated fracture and the opening of the tensile conjugated fractures. Figure 13 shows a synthesis of the processes related to pressure drops. The influence of the injection rate was tested (from 2 kg/s up to 100 kg/s), producing a reduction of pressure drop values. However, the main pressure drop values in the system are independent of this parameter.
The same pattern was observed in the model with wing cracks (model “60–hydro”). When the seismic segment is stimulated, the wing crack is forced to open, producing a pressure drop and enhancing its propagation. In our simulations, pressure drops were not related to wing crack propagation, which was associated with the stress concentration at the edges of the pre-existing fracture. Sliding of the seismic segment allowed wing crack propagation, given that injection pressure in our models was lower than the minimum principal stress (σ3). This resulted in hydrofracture propagation with injection fluid pressures below σ3 and in accordance with the model proposed by McClure and Horne (2014), as an explanation of the mixed-mechanism stimulation for EGS projects (i.e., shear stimulation operates jointly with new tensile fracture generation).
As previously mentioned, Meyer et al. (2017) concluded that pressure drops could be produced by the propagation of tensile fractures as a wing crack. This process could be interpreted in a similar way, as observed in breakdown tests and used to identify the minimum principal stress (Prabhakaran et al. 2017). In these tests, the generation of a new hydrofracture produces a pressure drop because the fluid quickly migrates into the newly formed fracture, oriented normal to the minimum stress. However, the process of hydraulic fracture propagation as a wing crack due to the stress concentration at fracture tips was achieved under conditions of fluid pressure below σ3. According to the modelling parameters used in our simulations (specifically the injection fluid pressure and the tensile strength of the material), sudden changes as those observed in breakdown tests (in which the injection pressure reaches σ3) are not observed. Moreover, as discussed above, pressure drops in our models are linked with the tensile fracture opening rather than its propagation, regardless of whether this fracture is a pre-existing or a newly formed one.
Seismicity and pressure drops
In terms of the seismicity associated with pressure drops, we can distinguish two types of events. The first type of seismic event is produced in the seismic segments by fluid pressurisation, acting as a trigger for the pressure drop phenomenon and usually producing high magnitudes (M > 1.5). The second type of seismic event is produced at the aseismic fracture segments next to the regions that are opening. Normally, the latter events appear as low-magnitude seismic swarms (events with magnitude below one or zero), produced to accommodate the displacement generated by the sliding of seismic segments and the opening of the aseismic ones. A similar behaviour can be observed in the model containing a pre-existing fracture combined with wing cracks. This duality of the system’s seismicity was proposed and analysed by Fischer and Guest (2011). In their model, the higher magnitude events are located at the critically stressed natural fractures, while lower magnitudes occur at pre-existing tensile fractures or new hydrofractures. Such behaviour would be expected in a mixed-stimulation mechanism, where these different stimulation mechanisms operate jointly (McClure and Horne 2014; Norbeck et al. 2018).
A key aspect in our simulations is the tendency of microseismicity to cluster next to the intersections between fractures. The influence of intersections between fractures on the seismicity population and location was already proposed by Rutledge et al. (2004). Their interpretation of microseismicity generated during fluid stimulation in the Cartage Cotton Gas field (Texas) showed anomalous dense clusters of seismic events following intersections between fractures. Clusters showed location patterns diverging in time, progressively migrating from the injection zone to far away regions. Additionally, clustering of events was related to fewer and larger precursor events along critically stressed fractures, while other segments oriented at low angles to σ1 experienced an aseismic behaviour. After injection shut-in, new large-magnitude and clustered seismic events were observed. This phenomenon was interpreted by Rutledge et al. (2004) as a result of fluid flow forced by slip-induced loading along critical seismic fractures. During injection, the increase of fluid pressure critically stimulated pre-existing fractures and fracture intersections, allowing fluid migration along the fracture network.
Rittershoffen sensitivity analysis
To evaluate the applicability of our results, stress drops and microseismicity data from the stimulation of the GRT1 well in Rittershoffen (Meyer et al. 2017) were analysed using a sensitivity analysis similar to that presented here. The stress and injection conditions used for these models are described in the Model Setup section. For this setup, pressure drops and seismic magnitudes are lower than those previously described, as stress magnitudes are substantially lower. The relationship between pressure drops mean values in the well and in the simulation domain with respect to the seismic magnitudes is shown in Fig. 14. Pressure drops were not detected at the well for fractures with length scales below 30 m. The maximum was observed for 50-m-long fractures, while those longer than 80 m produced pressure drops that could hardly be detected at the well. As expected, a proportional relationship between the seismic magnitude and pressure drops in the system was observed. For the range of seismic magnitudes and pressure drops observed in the Rittershoffen case (box grey area in Fig. 14; from Meyer et al. 2017), we can infer that fracture sizes of stimulated fractures could range between 40 and 60 m. A better constraint could potentially be obtained if pressure drop data were linked to magnitude and epicentre (unreported in Meyer et al. 2017), because in such case, the distance to the well could be utilised for the analysis. However, a handicap is that large uncertainty is normally associated with earthquake location data, normally longer than hundreds of metres (e.g., Kinnaert 2016).
Furthermore, our models show that the time lapse between the main earthquake event and the pressure drop at the well occurs after a few seconds (less than 2–4 s). This very short time interval probably implies that both phenomena will be almost simultaneously detected in real cases, requiring a highly precise time synchronisation between injection and seismicity data.
Our models use simplified geometries and are intended to help in investigating and understanding physical processes, rather than providing a perfect representation of reality. We chose not to use a model with complex multifracture networks, such as that utilised by Meyer et al. (2017), to isolate the main processes controlling pressure drops and seismicity. With a more complex network, the superposition of effects could attenuate the phenomena. Simulations by Meyer et al. (2017) with multifracture networks also produced pressure drops next to the intersections between fractures. However, their signal in the fluid pressure evolution at the well was attenuated. Additionally, there is a higher chance that more fractures can act as barriers to the propagation of transient variations of fluid pressure in multifracture systems. Our results confirm the interpretation by Meyer et al. (2017) that the conditions required to observe pressure drops in wells are very specific and unlikely to be observed in all reservoir formations. For injection wells located at a fracture with high transmissibility (i.e. model “88–60”), pressure drops at the well are potentially observable. However, pressure drops are hardly detectable in situations where the wells are located in low-transmissibility fractures (i.e. model “60–88”). However, as demonstrated by the numerical simulations presented here, pressure drops may occur in the reservoir even if they are not detected at the injection well.
Our simulations were carried out in isothermal conditions and, therefore, thermal drawdown effects are not modelled. In terms of stress reduction and seismicity, Gan and Elsworth (2014) observed that a second seismic cycle is developed related to the thermal drawdown that could potentially produce a second pressure drop cycle. It would be useful to repeat our analysis with a fully 3D model, since 2D models may enhance the magnitude of early events. Furthermore, the height used in our models (Table 1) is only an assumption required to take into account the third dimension, assuming plain strain for height values much larger than the fracture size (Shou and Crouch 1995).