Insights From Closed‐Form Expressions for Injection‐ and Production‐Induced Stresses in Displaced Faults. Issue 7 (31st July 2019) - Jansen, J. D.; Singhal, P.; Vossepoel, F. C.
Abstract: 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. Plain Language Summary: Injection of waste water or CO2 in the deep subsurface, or production of natural gas from subsurface reservoirs, may produce earthquakes. Earlier studies have shown that these are especially likely to occur when the reservoir contains faults that have undergone earlier movements ("displaced faults"). We derive mathematical expressions that allow for an improved understanding of the stresses in these faults compared to earlier computer studies. We conclude, among other findings, that there is an essential difference between injection and production: for injection the fault movement is much more likely to propagate outside the reservoir than for production. Our theoretical insights do not have direct quantitative predictive value but are relevant for the interpretation of experimental and computer studies. They may also help to drastically speed up computer studies, for example, for hazard and risk assessments of injection into or production from deep reservoirs. Key Points: Closed‐form expressions exist for fluid‐induced elastic stresses in displaced vertical and inclined (normal or reverse) faults Slip in a reservoir with displaced faults will already occur for small amounts of injection or production Injection always causes slip in the over/underburden; for production, slip may remain in the reservoir