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

Abstract

Laboratory experiments on dry, unconsolidated reservoir 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 (10−6to 10−2Hz), 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.