  Hydraulic fracturing increases reservoir permeability by opening fractures
and triggering slip on natural fractures and faults. While seismic slip of
small faults or fault patches is detectable as microseismic events, the role of
aseismic slip is poorly understood. From a modeling standpoint, geomechanical
analysis using the Coulomb criterion can determine if faults slip but not
whether slip is seismic or aseismic. Here we propose a computational
methodology to predict fault slip, and whether slip is seismic or aseismic,
using rate-and-state friction. To avoid computational costs associated with
resolving small faults, we use the spring-slider idealization that treats
faults as points. Interaction between faults is neglected. The method is
applied to study fault slip from a hydraulic fracture that grows past a fault,
without intersecting it. We represent the hydraulic fracture stressing using an
asymptotic expansion of stresses around the tip of a tensile crack. We
investigate the effect of fault length, orientation, and distance from the
hydraulic fracture. For velocity-weakening faults with stiffness smaller than a
critical stiffness, slip is seismic, whereas faults with stiffness greater than
the critical stiffness slip aseismically. Furthermore, we compare the
spring-slider idealization with a finite element analysis that resolves
spatially variable slip. The spring-slider idealization provides reasonably
accurate predictions of moment and even moment-rate history, especially for
faults having stiffness close to or larger than the critical stiffness.
Differences appear for large faults where rupture propagation is important,
though differences might still be negligible for many applications.
