PUBLICATIONS. Geophysical Research Letters. Linking microearthquakes to fracture permeability change: The role of surface roughness

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1 PUBLICATIONS RESEARCH LETTER Key Points: A plausible scale dependence for channeling flow through joints and faults is formulated A quantitative relation between the moment magnitude of MEQs and the fracture permeability change is obtained Potential of in situ MEQ data that allow inverse mapping of permeability change is suggested Correspondence to: T. Ishibashi, takuya.ishibashi@aist.go.jp Citation: Ishibashi, T., N. Watanabe, H. Asanuma, and N. Tsuchiya (2016), Linking microearthquakes to fracture permeability change: The role of surface roughness, Geophys. Res. Lett., 43, , doi: / 2016GL Received 20 APR 2016 Accepted 6 JUL 2016 Accepted article online 11 JUL 2016 Published online 25 JUL American Geophysical Union. All Rights Reserved. Linking microearthquakes to fracture permeability change: The role of surface roughness Takuya Ishibashi 1, Noriaki Watanabe 2, Hiroshi Asanuma 1, and Noriyoshi Tsuchiya 2 1 Fukushima Renewable Energy Institute, National Institute of Advanced Industrial Science and Technology, Koriyama, Japan, 2 Graduate School of Environmental Studies, Tohoku University, Sendai, Japan Abstract Despite its importance, the relation between microearthquakes (MEQs) and changes in hydraulic properties during hydraulic stimulation of a fractured reservoir has rarely been explored, and it is still not well understood. To investigate this relation, we first formulate a plausible scale dependence, where fracture length and shear displacement are variables, for channeling flow through heterogeneous aperture distributions for joints and faults. By combining this formulation with the concept of the seismic moment, we derive quantitative relations between the moment magnitude (M w ) of MEQs and the fracture permeability change in the directions orthogonal to (k fault, /k joint ) and parallel to (k fault, /k joint ) the shear displacement, in the form k fault; =k joint ¼ 116:410 0:46Mw and k fault;===k joint ¼ 13:110 0:46Mw. Despite the simplicity of the derivation, these relations have the potential to explain the results of field experiments on hydraulic stimulation, such as the enhanced geothermal systems at Soultz-sous-Fôret and Basel. 1. Introduction Traditionally, fractured reservoirs such as geothermal or hydrocarbon reservoirs are stimulated hydraulically for the purpose of improving or maintaining their permeability [Evans et al., 2005; Häring et al., 2008]. During this stimulation, a massive amount of pressurized fluid is injected into the reservoir, and as a result, preexistent fractures undergo slip which induces microearthquakes (MEQs) [Ellsworth, 2013; Guglielmi et al., 2015]. In situ data on such MEQs are generally recorded, since they can be good indicators of active processes within the reservoir [Majer et al., 2007]. The mechanisms involved in (hydro-)shear slip of rock fractures have been widely investigated and such slip is generally explained in terms of the Mohr- Coulomb (MC) failure criterion. Specifically, changes in mechanical properties, e.g., based on the rate and state friction (RSF) model, have been actively studied [Marone, 1998], and by coupling the RSF concept with the MC failure criterion, McClure and Horne [2012] have recently been successful in reproducing the diversity of timings and magnitudes of MEQs induced by hydraulic stimulation of a fractured system. This has led to a better understanding of the link between MEQs and the mechanical properties of rock fractures. In contrast, the relation between MEQs and changes in hydraulic properties has rarely been explored and is still poorly understood. Recently, however, the link between MEQs and the change in permeability in fractures and faults has become one of the hottest topics in geo-engineering [McClure and Horne, 2012] and seismology [Shelly et al., 2013], since understanding this relation can potentially open the door to novel approaches for coupling hydraulic and seismic effects. Since the permeability of a fractured system has been shown to change during or after hydraulic stimulation [Evans et al., 2005; Häring et al., 2008], it is natural to explore a link with MEQs in such systems. In the present study, we focus specifically on the role of the surface topography (roughness) of rock fractures for the hydraulic properties of the fractured system. For a fracture consisting of two opposing rock faces, such roughness can produce asperities that give rise to self-propping of the fracture during a MEQ, and this is highly likely to change the hydraulic properties of the fracture or reservoir [Preisig et al., 2015]. Here the roughness of natural fractures and faults can be characterized by a self-affine fractal nature regardless of their scale (length) [Renard et al., 2013]. Thus, the distribution of apertures formed by these rough surfaces remains heterogeneous regardless of shear displacement [Ameli et al., 2013; Watanabe et al., 2009]. Considering such characteristics of rock fractures, we can determine the significance of geometrical properties of aperture distribution and resulting fluid flow through rock fractures with natural (field) scales. Ishibashi et al. [2015] recently proposed a prediction method for aperture distributions of beyond-laboratory-scale rock ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7486

2 fractures at in situ reservoir conditions. However, the relation between MEQs and changes in fracture permeability has still not been clarified. In the present study, our main focus is achieving a quantitative relation between the magnitude of a MEQ and the change in permeability during hydraulic stimulation of a fractured system. Based on the results of numerical modeling, we derive the scale dependences of mechanical and hydraulic properties of subsurface rock fractures (joint/fault), where the shear displacement of the fracture is treated as a variable parameter rather than having a fixed value. Consequently, the dependence of mechanical and hydraulic properties of rock fractures on scale (length) and shear displacement can be successively determined. By introducing the concept of the seismic moment, which relates the magnitude of a MEQ to the fracture scale, we then obtain the relation between the MEQ magnitude and the permeability change. 2. Methods Based on the method developed by Ishibashi et al. [2015], heterogeneous aperture distributions for effective confining stresses of up to ~100 MPa (corresponding to depths of ~6 7 km in a continental crust) are simulated for rock fractures with various combinations of length l (m) and shear displacement δ (m). In their method, a pair of synthetic fractal surfaces were placed together, so that the fractures had a scaleindependent contact area (see Ishibashi et al. [2015] for details). The contact area of a fracture having shear displacement was 42%, whereas that of fracture having no shear displacement was 59%. In our study, shear displacements (δ) of more than ~0.4 mm were considered. This limitation was because of the change from joint to fault fracture characteristics for δ between 0 mm and ~0.4 mm [Chen et al., 2000]. Following Ishibashi et al. [2015], for the rough fracture surfaces (hanging wall and footwall), a fractal dimension, a standard deviation for a referential length of 200 mm, and a mismatch length were set as 2.3 mm, 1.3 mm, and 0.7 mm. The proportion of the power spectral density (PSD) of the initial aperture with a single contact point to the PSD of the footwall surface geometry, R(f), was expressed as Rf ðþ¼ef 6: ðln fþ 3 2: ðln fþ 2 þ2: ðln fþþ5: g, where f is the spatial frequency. These values and relationships are essential for numerical modeling of fracture surface topographies and were computed based on fractures in Inada granite (Ibaraki, Japan). Using the aforementioned parameter values, we numerically paired surface topographies of square fractures with fracture lengths of 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 m, using a 250 μm square-shaped grid. Heterogeneous aperture structures of fractures with shear displacement (i.e., faults) and without shear displacement (i.e., joint) were then modeled over various scales. To imitate natural faults, δ/l was kept constant, which corresponds to a linear increase in shear displacement with fracture length [Kanamori and Anderson, 1975]. However, since δ/l inherently depends on both rock properties and tectonic environment, values of , , , and were considered. Thus, a total of 35 aperture distributions were considered in this study. For each distribution, the geometrical average and standard deviation for nonzero aperture sizes were first calculated. Unidirectional fluid flow was then simulated by solving the Reynolds equation [Brown, 1987; Brush and Thomson, 2003]. In the simulations, flow both orthogonal and parallel to the imposed shear displacement direction was considered, since it has been reported that there is a large degree of hydraulic anisotropy associated with hydraulic fracturing in fractured reservoirs [Nemoto et al., 2009]. Based on the fluid flow simulations, changes in the fracture permeability and flow area which corresponds to the region of the channeling flow paths within a fracture were evaluated for different fracture lengths and shear displacements. Finally, the scale dependence of fracture flow was combined with equations defining the scale of earthquakes [Aki and Richards, 2002; Hanks and Kanamori, 1979], and the relation between MEQs and the change in the fracture permeability was investigated. 3. Results and Discussion 3.1. Scale Dependence of Channeling Flow Through Rock Fracture Regardless of the fracture length or the shear displacement, rock fractures contain a large number of contacting points, and the distribution of nonzero apertures is skewed and has a long tail, i.e., a lognormal appearing ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7487

3 Figure 1. Representative results for channeling flow within heterogeneous aperture distribution for model fractures (a) with no shear displacement and (b) with constant shear displacement of δ/l = distribution. Hence, preferential flow paths are always formed through the heterogeneous aperture distribution (i.e., channeling flow). Figure 1 shows typical aperture maps (gray scale) and flow rate maps (color scale) for (a) a joint (δ/l=0) and (b) a fault (δ/l= ); for both fractures, channeling flow can clearly be seen. These results are completely different than those for conventional parallel-plate fractures. Note that the flow rates are normalized, normalized flow rates of less than 0.01 are colorless, and the shear displacement is in the direction orthogonal to the fluid flow. As shown in Figure 2a, the average aperture size of joints/faults increases with fracture length. In addition, the average aperture size for faults with a constant length increases with shear displacement (i.e., δ/l), as a result of the shear dilation effect [Chen et al., 2000; Watanabe et al., 2009]. In the case of a joint, the average aperture size can be approximated by e m;joint ¼ 1:310 1 l 0:10 ; (1) where e m, joint and l are the average aperture size for the joint (mm) and the fracture length (m), respectively. For a fault with a constant δ/l, the average aperture size can be approximated by e m;fault ¼ α 1 l β 1 ; (2) Figure 2. Predicted fracture-length dependence of (a) average aperture size and (b) standard deviation, for fractures with no shear displacement (joints) and fractures with constant shear displacement to fracture length ratios (faults). Curves from equations (1) and (2) are also shown. ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7488

4 Figure 3. Predicted fracture-length dependence of (a) permeability in direction orthogonal to shear displacement, k ; (b) permeability in direction parallel to shear displacement, k // ; (c) permeability anisotropy ratio k /k ; and (d) flow area for joints and faults. Curves from equations (4) and (6) are also shown. where e m, fault is the average aperture size for the fault (mm) and α 1 and β 1 are a preexponential factor and an exponent, respectively. Curves from equation (2) are also shown in Figure 2a, and they yield α 1 = (δ/l) 0.59 and β 1 = Equation (2) can then be rearranged to give e m;fault ¼ 1:310 δ 0:59 l 0:71 : (3) l Equations (1) and (3) indicate that the scale dependence of e m, joint is weak, whereas that of e m, fault is strong. This discrepancy is due to differences in the degree of matedness, which is defined by how well matched the opposing fracture surfaces are [Olsson and Barton, 2001]. As shown in Figure 2b, the standard deviation is approximately 3, and its dependence on l or δ/l is ambiguous. The predicted fracture-length dependence of hydraulic properties is shown in Figure 3. Figure 3a shows that fracture permeability (k ) in the direction orthogonal to the shear displacement increases with fracture length for both joints and faults. For joints, the permeability can be approximated by k joint ¼ 9: l 0:16 ; (4) where k joint is the joint permeability (m 2 ). For faults with a constant δ/l, the permeability can be approximated by k fault; ¼ α 2 l β 2 ; (5) where k fault, is the fault permeability (m 2 ) and α 2 and β 2 are a preexponential factor and an exponent, respectively. Curves from equation (5) yield α 2 = (δ/l) 1.18 and of β 2 = Equation (5) can then be rearranged to give k fault; ¼ 2:310 6 δ 1:18 l 1:08 : (6) l Figure 3b shows fracture permeability (k // ) in the direction parallel to the shear displacement. The line and the shaded region represent the k values shown in Figure 3a. Figure 3c shows the permeability anisotropy ratio, ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7489

5 Figure 4. (a) Model used to link microearthquakes to permeability change during hydraulic stimulation, and estimated relations between moment magnitude and (b) fracture length and shear displacement, (c) average aperture size, and (d) fracture permeability. which is defined as k /k //. For the joint, this ratio is about 1 regardless of the fracture length, indicating that the permeability anisotropy is low. For faults, the ratio varies from 2 to 40, indicating a high degree of permeability anisotropy. Since the permeability anisotropy ratio is poorly correlated with fracture length or shear displacement (Figure 3c), we evaluate the arithmetic mean value of permeability ratio as 8.9. The fault permeability (k fault, // ) in the direction parallel to the shear displacement is then arranged as k fault;== ¼ k fault; 8:9 ¼ δ 1:18 2:610 7 l 1:08 : (7) l The permeability anisotropy may be caused by contacting asperities grouped along the direction orthogonal to the shear displacement that partially block the fluid flow [Nemoto et al., 2009]. As shown in Figure 3d, the flow area is limited to about 5 20% of the fracture plane for fluid flow in the direction orthogonal to the introduced shear displacement. This is typical of fluid flow within rock fractures, matching the results of field investigations [Tsang and Neretnieks, 1998] Relation Between Microearthquakes and Change in Fracture Permeability Having established the dependence of the average aperture size and fracture permeability on the fracture length and shear displacement, we introduce the concept of seismic moment. This concept relates the scale of an earthquake to the fracture length, allowing a quantitative relationship between the change in permeability and the magnitude of MEQs. As shown in Figure 4a, we consider a simple configuration of hydroshear failure for the MEQs generated during stimulation of fractured reservoirs. A shear displacement of δ (m) is uniformly applied to a square fracture plane with a fracture length of l (m), although in reality the shear displacement would have a nonuniform distribution [Preisig et al., 2015]. For such a MEQ, the seismic moment is defined as [Aki and Richards, 2002] M 0 ¼ μ 0 Aδ; (8) where M 0 is the seismic moment (N m), μ 0 is the shear modulus for the host rock, and A is the surface area of the fracture (m 2 ). This seismic moment can be converted into the equivalent moment magnitude as log M 0 ¼ 1:5M w þ 9:1; (9) ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7490

6 where M w is the moment magnitude [Hanks and Kanamori, 1979]. As long as the stress drop has a unique value, A and δ can be estimated as functions of M w using empirical scaling relations [Zoback and Gorelick, 2012] and assuming a static stress drop. According to Leonard [2010], for strike-slip earthquakes of relatively small magnitude, the seismic moment is related to the fracture surface area as log M 0 ¼ 1:5log A þ 6:09: (10) Because the fracture surface area is equivalent to the square of the fracture length (i.e., A = l 2 ), equation (10) can be rearranged to yield The shear displacement is given by l ¼ 10 0:5Mwþ1:00 : (11) log δ ¼ 0:5log A 4:43 ¼ log l 4:43; (12) which indicates that δ/l is constant (δ/l= ). The small value of δ/l is due to the fact that a fault experiences a single slip when using the scaling for fracture surface area (equations (10)) and shear displacement (equation (12)). Since these scaling of strike-slip earthquakes (i.e., equations (10) and (12)) are virtually identical to those of dip-slip earthquakes, the following discussions are generally acceptable for both strikeslip and dip-slip earthquakes. Thus, M w, l, and δ can be quantitatively correlated. For a fracture that has not experienced shear failure (i.e., a joint prior to hydraulic stimulation), we assume zero shear displacement. This allows the initial values for average aperture size (e m, joint ) and fracture permeability (k joint ) for a fracture with a given length to be estimated using equations (1) and (4). In contrast, for a fracture that has experienced a MEQ (i.e., a fault after hydraulic stimulation), the average aperture size (e m, fault ), the permeability (k fault, ) in the direction orthogonal to the shear displacement, and the permeability (k fault,// ) in the direction parallel to the shear displacement can be estimated using equations (3), (6), and (7), respectively. Here the shear displacement is limited to values larger than ~0.4 mm (M w > 0 from equations (11) and (12)). In this manner, the quantitative change in average aperture size and fracture permeability can be expressed in terms of M w for a MEQ. By combining equations (1), (4), (11), and (12), the change in the average aperture size is e m;fault =e m;joint ¼ 1:010 0:35Mw : (13) Similarly, by combining equations (3), (6), (11), and (12), the corresponding change in the fracture permeability in the orthogonal direction to the shear displacement can be formulated as k fault; =k joint ¼ 116:410 0:46Mw : (14) Finally, by combining equations (3), (7), (11), and (12), the change in the fracture permeability in the parallel direction to the shear displacement is k fault;===k joint ¼ 13:110 0:46Mw : (15) The generality of these expressions is clearly limited, because they can be influenced by rock type, the roughness of fracture surface, fault gouge formation, and the absolute value of the static stress drop. Next, l and δ are estimated for a MEQ with a M w of 0 2, and the average aperture size and the fracture permeability are calculated before and after the earthquake. Figure 4b shows the relation between l and M w and between δ and M w. Figures 4c and 4d, respectively, show the change in the average aperture size and the fracture permeability due to MEQs with a specific M w. MEQs with M w 0 cause an increase in the average aperture size due to shear dilation. In contrast, the impact of shear dilation is expected to be small or absent for MEQs of M w < 0, and this is consistent with previously reported experimental results [Chen et al., 2000; Javadi et al., 2014]. As a result, the increase in permeability due to a MEQ with M w < 0 is expected to be very small or zero, so that during stimulation of a fractured reservoir, such increases would only be expected for zones experiencing seismic events with M w 0. Although the mechanisms of fracture shear are much more complicated than is assumed here (e.g., a heterogeneous slip distribution along the fracture), we feel that the proposed approach is valuable as a first step toward linking MEQs to fracture permeability change. ISHIBASHI ET AL. LINKING MEQS TO PERMEABILITY CHANGE 7491

7 3.3. Comparison With Results of Field Experiments We next compare the permeability increases predicted using the proposed method with the results of actual field experiments. According to Evans et al. [2005], the hydraulic stimulation for creating an enhanced geothermal system (EGS) at Soultz-sous-Fôret, France, caused several MEQ events with local magnitudes of , and as a result, the reservoir transmissivity increased from ~ to ~ m 2 (approximately 200 times). Similar transmissivity gains (400 times) were reported at the EGS project in Basel, Switzerland, where the local magnitude of observed MEQs was 2.5 [Häring et al., 2008]. In comparison, for a MEQ with M w = 2.5, equations (14) and (15), respectively, predict permeability gains of 1640 and 185 times. Since these equations represent extreme cases with regard to the slip direction, the actual permeability increase would be expected to be between these values. This is consistent with the results of the field experiments, and thus supports the validity of the approach proposed here. In future work, we will attempt to refine this method, for example, by considering uncertainties in the stress drop [Zoback and Gorelick, 2012] or the difference between the characteristics of a single rock fracture and those of a discrete rock fracture network. The results of the present study suggest that the relationship between earthquake dynamics and crustal fluids is likely influenced by the in situ characteristics of the Earth s crust, including the stress field and the fault geometry (size and morphologic characteristics), as well as by the characteristics of the crustal fluid. This relationship can be simply formulated and constrained by considering both scale-independent parameters (ratio of asperity contact and flow area) and scale-dependent parameters (average aperture, fracture permeability, and shear displacement). This raises the possibility of new interpretations of subsurface hydraulic properties based on seismic data. 4. Conclusions We explore the linkage between MEQs and fracture permeability change during hydraulic stimulation of a fracture reservoir. Plausible scale dependencies were systematically formulated for channeling flow within heterogeneous aperture structures for the case of joints (fractures having no shear displacement) and faults (fractures having shear displacement), for different fracture lengths and shear displacements. These formulations were then combined with the concept of the seismic moment, which connects the scale of the earthquake with the fracture length. Consequently, expressions were obtained for the relation between the increase in fracture permeability and the moment magnitude of MEQs during hydraulic stimulation, in the form k fault; =k joint ¼ 116:410 0:46Mw and k fault;===k joint ¼ 13:110 0:46Mw. This may allow rough inverse mapping of changes in fracture permeability using in situ MEQ data and possibly lead to novel views into fluid migration phenomenon within the Earth s crust. This is also intimately connected to the development of fractured reservoirs of hydrocarbon/geothermal or could lead to breakthrough for earthquake mechanisms. Acknowledgments The authors thank Steven Ingebritsen for his thoughtful comments that significantly improved the manuscript. This work also benefitted from discussions with Derek Elsworth, Yi Fang, Atsushi Okamoto, and Nobuo Hirano. The present study was supported in part by JSPS through Postdoctoral Fellowships for Research Abroad, (to T.I.), a Grant-in-Aid for Specially Promoted Research, (to N.T.), and by METI, Japan through International Research Program for Innovative Energy Technology (to H.A.). The data to reproduce the work are available from the corresponding author: Takuya Ishibashi (takuya.ishibashi@aist.go.jp). 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