Modeling Injection-Induced Seismicity with the Physics-Based Earthquake Simulator RSQSim by James H. Dieterich, Keith B. Richards-Dinger, and Kayla A. Kroll INTRODUCTION physics-based simulations include McClure and Horne (2011), who investigated the effects of fluid injection on a 1D fracture. Although the phenomenon of earthquakes induced by the sub- Here, we present a modeling approach for simulating seismicity surface injection of fluids has been recognized, and the basic induced by fluid injection in 3D over multiple earthquake mechanisms understood, for many decades (e.g., Healy et al., cycles. 1968), the recent increase in seismicity associated with oil and gas development, including large damaging events (e.g., Ells- worth, 2013; Keranen et al., 2013; Hough, 2014; Rubinstein INDUCED-SEISMICITY SIMULATIONS et al., 2014) makes clear the need to better understand the processes controlling such seismicity and to develop techniques We developed a method to simulate injection-induced seismicity to mitigate the associated seismic hazard. that couples the regional scale, multicycle earthquake simulator, The relationship of fault stress, fault strength, and fluid RSQSim, to reservoir models that give changes of effective pressure at the onset of fault slip in the most basic form is given stresses acting on the modeled faults due to fluid injection. by the modified Coulomb criterion, RSQSim is a computationally efficient 3D boundary-element code that incorporates rate–state fault friction to simulate long τ μ σ − P; 1 sequences of earthquakes in interacting fault systems. Although RSQSim (Dieterich and Richards-Dinger, 2010; Richards- Dinger and Dieterich, 2012) was specifically developed for ef- τ σ in which and are the shear and normal stress, respectively, ficient simulations of earthquakes and other fault slip processes P μ acting on the fault surface, is the pore-fluid pressure, and is in geometrically complex fault systems, our initial investigation σ − P the coefficient of fault friction. The term ( ) is the effec- reported here focuses on the characteristics of induced earth- tive normal stress (Terzaghi, 1925). From equation (1), a fault quakes arising from injection near a single isolated planar fault. can be brought to a critical state through an increase of shear RSQSim is a boundary element code in which faults are τ σ stress , a decrease of the normal stress , an increase of fluid represented by arrays of rectangular or triangular elements. Be- P pressure , or some combination of the three. Increase of pore- cause fully dynamic models of the rupture process are computa- fluid pressure is the most widely cited cause of earthquakes in- tionally intensive, the great efficiency of this code derives in part duced by human activities (National Research Council, 2012). from use of a quasi-dynamic approximation of rupture dynamics Consequently, investigations and models of induced seismicity wherein slip speed during an earthquake is fixed at a constant have tended to focus mainly on spatial changes of fluid pressures value consistent with the elastic shear impedance and earthquake (Hsieh and Bredehoeft, 1981; Shapiro and Dinske, 2009). stress drop. Slip on the fault elements is governed by a rate- and Although the immediate cause of injection-induced earth- state-dependent constitutive formulation of friction, quakes is the increase of fluid pressure that brings a fault to a critical stress state, models of the spatial changes of fluid pres- δ_ θδ_ sure alone are insufficient to either predict or understand the τ σ − P μ a b – 0 ln ln 2 space time characteristics of induced earthquakes. Compre- δ_ Dc hensive system-level models that couple physics-based simula- tions of seismicity with reservoir simulations of fluid pressure a changes can provide an experimental capability to investigate (Dieterich, 1978, 1979; Ruina, 1983; Marone, 1998), in which and b are experimentally determined dimensionless constants topics related to induced seismicity. These include (1) investi- − gation of the system-level interactions controlling the space– (with typical laboratory values of 10 2 ), δ_ is the instantaneous δ_ μ time characteristics of induced seismicity; (2) characterization slip speed, is a reference slip speed, 0 is the steady-state co- of the relationships among injection parameters, reservoir char- efficient of friction at the reference slip speed and constant nor- acteristics, and induced seismicity; (3) development of best- mal stress, Dc is a characteristic distance over which θ evolves, practice protocols for injection projects; (4) site-specific models and θ is a state variable (with dimensions of time) that evolves of injection-induced earthquakes; and (5) probabilistic hazard according to the aging law (with the variable normal stress modi- evaluations of the potential for inducing earthquakes. Previous fication of Linker and Dieterich, 1992): doi: 10.1785/0220150057 Seismological Research Letters Volume 86, Number 4 July/August 2015 1 τ θδ_ aθ min, then no events will ever nucleate. An analagous argument θ_ 1 − − α σ_; 3 Dc bσ to that leading to equation (4), but including the effect of the changing effective normal stress on the state variable, gives α in which is an additional empirical constant and overdots in- dicate time derivatives. A key property of rate–state friction is θ δ_ τ ≈ σ − P μ b − a 0 that nucleation of unstable slip is highly time dependent (Diet- min 0 max 0 ln D c erich, 1992), which results in earthquake clustering, foreshocks, b − a P and aftershocks that follow the Omori aftershock decay law (Di- − α − max ; b ln 1 σ 5 eterich, 1994). 0 For the simulations of injection-induced seismicity de- P scribed below, tectonic stressing rates are set to zero in order in which max is the largest pore-fluid pressure perturbation at to simulate regions that were formerly tectonically active but the location of a given fault element. are now completely or nearly inactive. We construct models Figure 1 illustrates the fault model and some features of a with two different patterns of initial shear stress heterogeneity: typical simulation. The fault is a 3km× 5kmplanar surface and (1) Gaussian white noise with a standard deviation of 5 MPa consists of 37,500 20 m × 20 m elements. The upper edge of the (Figs. 3 and 4) or 15 MPa (Figs. 1 and 6) smoothed with a 3 × fault is buried at 3 km depth. The injection point is even with the 3 running mean filter (so that stresses are correlated over a top edge of the fault and 200 m from the nearest point on the maximum distance of ∼170 m ) and (2) the remnant pattern fault. The injection rate is 0:01 m3=s (26:9 × 103 m3=month), M > after an w 5 rupture from a previous simulation (Figs. 2 which is roughly comparable to injection rates associated with and 5). The effective normal stress on the fault elements (initially the Rocky Mountain Arsenal induced earthquakes (7:5 × 103 set to 100 MPa) is controlled by fluid pressure histories from an to 17 × 103 m3=month; Healy et al.,1968) and Paradox external reservoir simulation of fluid injection. The earthquake simulator can accept pore-fluid pressure (and/or poroelastic Event A: 2.9 years Event B: 9.4 years Event C: 15.5 years stressing) histories from arbitrarily sophisticated reservoir models, (a) 3 20 but all the results presented here use pressure histories generated 5 from the simple analytic Green’s function for pore-fluid pressure 15 due to injection at a point source into a uniform, isotropic half- 4 8.19 60 6.19 (b) Closest point on the space immediately below an impermeable layer, based on Wa ng 0 4.19 50 fault from well 2.19 (2000). Because of the unbounded nature of the medium we use 40 10 30 Depth (km) Shear Stress (MPa) Δ 5 Time (years) here, the pressure perturbation due to an infinitely long, constant 0.19 20 500 m –5 rate injection will approach a steady-state value at large times. In 10 5 1800 m Pore Pressure Change (MPa) 0 contrast, injection into a bounded compartment will lead to ever- 0 51510 20 Time (years) 6 increasing pore-fluid pressures once the pressure front begins to 12345 interact with the boundaries of the compartment. Distance Along Strike (km) Even with zero tectonic stressing rates and zero pore-fluid (c) 4 Event A: Event B: Event C: pressure perturbation, earthquakes will nucleate spontaneously 2.9 years 9.4 years 15.5 years τ if the initial shear stress 0 is high enough. Specifically, this will 3 occur if the initial shear stress on any fault element is greater τ than some max, which is offset above the steady-state stress by an Magnitude 2 amount controlled by the critical element stiffness for instability (Ranjith and Rice, 1999), which in turn is inversely proportional 1 to Dc. In these simulations, we use Dc 10 μm, which results in very large values for the critical stiffness compared with the 0 5 10 15 20 25 τ Time (years) element stiffness. In this case, the offset is very small and max is nearly the steady-state friction, giving ▴ Figure 1. Fault model and an example of simulation results. (a) Fault surface (gray) with hypocenter locations (colored by time θ δ_ τ ≈ σ μ b − a 0 ; since injection began and scaled by magnitude). The injection well max 0 0 ln 4 Dc is located at 1.5, −0:2,and−3kmin the along-strike, out of plane, and depth directions, respectively. The contours indicate pressure σ θ in which 0 is the initial normal stress and 0 is the initial value of change (in MPa) at the end of the 20-year injection interval. The back- the state variable on that element.