Insights From Closed-Form Expressions for Injection- and Production-Induced Stresses in Displaced Faults

We consider fluid-induced seismicity and present closed-form expressions for the elastic displacements, strains, and stresses resulting from injection into or production from a reservoir with displaced faults. We apply classic inclusion theory to two-dimensional finite-width and infinite-width reservoir models. First, we simplify the fault model to the bare minimum while still maintaining its essential features: a vertical fault in a homogeneous reservoir of infinite width in an infinite domain. We confirm and sharpen findings from earlier numerical studies and furthermore conclude that the development of infinitely large elastic shear stresses in a displaced fault, at the internal and external reservoir/fault corners, implies that even small amounts of injection or production will result in some amount of slip or other nonelastic deformation. Another finding is that there is a marked difference between the shear stress patterns resulting from injection and production in a reservoir with a displaced fault. In both situations two slip patches emerge but at the start of injection some amount of slip occurs immediately in the overburden and underburden, whereas during production the slip may remain inside the reservoir region. Next we derive similar but more complicated expressions for displaced inclined (normal or reverse) faults and conclude that our findings for vertical faults also apply to inclined faults.