Viscous deformation of unconsolidated reservoir sands—Part 1: Time‐dependent deformation, frequency dispersion, and attenuation

Abstract

Laboratory experiments on dry, unconsolidated sands from the Wilmington field, California, reveal significant viscous creep strain under a variety of loading conditions. In hydrostatic compression tests, following initial loading to 10 MPa, the creep strain that accompanies 5-MPa loading steps to 15, 20, 25, and 30 MPa exceeds the magnitude of the instantaneous strain (∼3 × 10 −3 ). We observed a two-fold increase in bulk modulus with frequency over the range of frequencies tested (10 −6 to 10 −2 Hz), which is consistent with a viscoelastic rheology of unconsolidated sand. The data demonstrate that the effective static bulk modulus is approximately one-third of that at seismic frequencies. By measuring the phase lag between stress and strain during the loading cycles, we were also able to show that inelastic attenuation is nearly constant (Q ≈ 5) over the four-decade range of frequencies tested at a strain amplitude of 10 −3 . Interestingly, the viscous effects only appear when loading a sample beyond its preconsolidation. Triaxial tests show that the relationship between differential stress and axial strain is positively dependent on axial strain-rate, and that unconsolidated sand continues to deform viscously even at large strains (∼7%). All experiments were conducted at room temperature and humidity. A limited number of experiments with unconsolidated reservoir sand from the Gulf of Mexico show similar behavior.

Earthquake triggering and large-scale geologic storage of carbon dioxide

“…Moreover, weak, poorly cemented sandstones are expected to deform slowly in response to applied geologic forces. In such reservoirs, the stresses relax over time, and such formations are not prone to faulting (20). In this regard, the Utsira formation is ideal for CO 2 sequestration.…”

Application of rate‐and‐state friction laws to creep compaction of unconsolidated sand under hydrostatic loading conditions

“…Previous studies of volumetric compaction in unconsolidated sands under hydrostatic pressure [e.g., Hagin and Zoback, 2004] show that the compaction is functionally dependent on time, pressure, and porosity. In the next section, we modify equation (7) to include hydrostatic compression in order to test whether rate-and-state friction laws can be used to describe volumetric creep of unconsolidated sands.…”

“…For compaction of quartz sand in friction experiments [e.g., Richardson and Marone, 1999], strain rate decays according to a power law function of porosity during a hold. In volumetric creep tests on unconsolidated sands from the upper terminal zone of the Wilmington field (and others from the Gulf of Mexico), strain rate decays according to a power law of time, under conditions of hydrostatic stress [Ostermeier, 1995;Chang et al, 1997;Hagin and Zoback, 2004].…”

“…First, we begin by finding appropriate stress and strain invariants to convert the rate-and-state equations from simple shear to hydrostatic stress boundary conditions. Second, existing volumetric creep data (from Hagin and Zoback [2004]) are replotted to show volumetric strain rate as a function of volumetric strain. Finally, the stateporosity relationship by Segall and Rice [1995] is used to test whether volumetric creep of unconsolidated sand can be described using rate-and-state friction laws.…”

“…[2] Given that the deformation of most unconsolidated sands has been observed to depend on both state (contact area or porosity) and deformation rate, it is necessary to include these effects when constructing an appropriate constitutive law [Yale et al, 1993;Ostermeier, 1995;Chang et al, 1997;Hagin and Zoback, 2004]. A natural choice for such a law is the rateand-state variable friction law, since it already contains the necessary terms and was empirically derived from laboratory observations in a concise mathematical form [e.g., Dieterich, 1978Dieterich, , 1979 and has a physical basis in thermally activated creep at high-stress asperity contacts [Nakatani, 2001;Rice et al, 2001;Beeler, 2004;Nakatani and Scholz, 2004].…”