Fault stability changes induced beneath a reservoir with cyclic variations in water level

Abstract

The stress and pore pressure changes produced by a steady periodic variation of water level on the surface of a uniform porous elastic half‐space are evaluated using the fully coupled (Biot) equations of elastic deformation and pore fluid flow. Diverse choices of material properties all give a coupled stress field differing from the elastic stress field by at most 0.035 po, where po is the water pressure at the bottom of the reservoir. Peak coupled pore pressure change can lag peak water level in the depth range 0 < (ω/2c)1/2z < π, where ω is frequency of the cyclic change in water level, c is diffusivity, and z is depth. The maximum lag increases as B decreases, where B is the ratio of pore pressure increase to mean compressive stress increase under undrained conditions. Directly beneath the reservoir, for example, peak pore pressure in an annual cycle can lag peak water level by at most 10 days if B = 0.80, but can lag by up to 122 days if B = 0.11. When cyclic water level changes are superimposed on the steady state reservoir level, the time during the cycle at which a fault is most destabilized depends on whether the weight of the reservoir stabilizes or destabilizes the fault, which, in turn, depends on its orientation and location relative to the reservoir. B and c also influence the timing of the greatest destabilization. If B and c are low, maximum destabilization at low water level is possible for faults that are stabilized by the weight of the reservoir; this mechanism may have operated at Lake Mead. The analysis suggests that induced seismic events should be separated into groups having a common focal mechanism and occurring in similar locations relative to the reservoir before studying the time at which the events occur relative to the water level. The fully coupled solution is compared with an uncoupled solution, with a solution that is coupled but which assumes incompressible solid and fluid constituents (consolidation) and with a decoupled solution in which the difference between the pore pressure field and B times the elastic mean compressive stress obeys a homogeneous diffusion equation. The uncoupled and consolidation solutions respectively underestimate and overestimate pore pressure during short‐term reservoir level fluctuations as well as at times short compared to that required to achieve steady state. In contrast, the decoupled solution agrees closely with the fully coupled solution for the problem studied here.

In situ measurements of hydraulic properties of a shear zone in northwestern South Carolina

“…The dependence of the pore pressures at depths on the frequency of lake level fluctuations was observed and confirmed theoretical prediction of Roeloffs [1988]. These results also offer an explanation for the observed phenomenon of protracted reservoir induced seismicity [Talwani, 1997].…”

“…Those values of C inferred from seismicity data cluster around 1 m 2 s Ϫ1 and range between 0.1 and 10 m 2 s Ϫ1 [Talwani and Acree, 1984;Rastogi et al, 1986]. Roeloffs [1988] noted that C obtained from seismicity data by Talwani and Acree [1984] tended to be an upper bound value of C as it did not consider the undrained response of the reservoir. Shapiro et al [1997] obtained C ϳ 0.5-1 m 2 s Ϫ1 from seismicity data associated with hydraulic-fracturing in the German Continental Drilling Borehole (KTB).…”

“…Values of B calculated from laboratory measurements of elastic moduli vary with effective pressure. Roeloffs [1988] lists calculated values based on laboratory measurements for two granites. They range from 0.23 to 0.99 depending on the effective pressure.…”

“…Both theoretical models and observations attest to the importance of pore pressure diffusion in triggering tectonic and induced seismicity [see, e.g., Healy et al, 1968;Nur and Booker, 1972;Howells, 1974;Talwani, 1976;Hill, 1977;Bell and Nur, 1978;Hsieh and Bredehoeft, 1981;Talwani and Acree, 1984;Roeloffs, 1988;Rice, 1992;Rajendran and Talwani, 1992;Henderson and Maillot, 1997;Talwani, 1997]. However, in all cases, the value of the critical hydraulic parameter, hydraulic diffusivity, was assumed or inferred, for example, from the spreading of seismicity [e.g., Talwani and Acree, 1984;Shapiro et al, 1997] or the lag between the onset of seismicity and impoundment of reservoirs [Talwani and Acree, 1984].…”

Investigations related to scientific deep drilling to study reservoir-triggered earthquakes at Koyna, India

“…The occurrence of reservoir-triggered seismicity (RTS) has been associated with a number of potential factors including the rate of loading, highest water level reached and the duration of retention of high water levels (Kaiser 1953;Gupta et al 1972a, b). Other studies have investigated the role of reservoir loading (e.g., Gough and Gough 1970a, b;Bell and Nur 1978;Roeloffs 1988) and the influence of pore fluid pressure (Snow 1972;Talwani et al 1999;Do Nascimento et al 2004). While major advancements have been made towards elucidating the role of individual parameters in triggering earthquakes, an integrated model that explains the genesis of RTS is unavailable.…”