ABSTRACT:

  • The difference in stress magnitude during (quasi-)static rock compression (typically of the order of 10-3 m/m), and acoustic-wave propagation (typically<10-6 m/m);

  • The frequency dependence of the rock stiffness (dispersion). In laboratory studies, acoustic velocities are measured at ultrasonic frequencies (105 – 106 Hz), while in the field, velocities are measured at seismic or sonic frequencies (during seismic surveys: 1~100 Hz; sonic-log measurements in a wellbore: kHz range).

In this work, an experimental study was carried out with the aim of linking static and dynamic stiffness of shales. Four fully saturated field shales were tested. The experiments were carried out in SINTEF's low-frequency cell. The measurements included undrained quasi-static loading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (1 – 150 Hz), and ultrasonic velocity measurements (500 kHz). The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: All tested shales exhibited P-wave velocity dispersion of the order of 10-20% between seismic and ultrasonic frequencies. Much larger dispersion of up to 150% was observed for Young's moduli. In static tests, non-elastic deformations increase with increasing stress change, resulting in a reduction of the rock stiffness. The largest stress-amplitude effects were observed for Opalinus Clay: the static undrained average Young modulus, measured for a stress amplitude of 3 MPa is 50% lower than that measured for a 1 MPa stress cycle. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness measured at low frequency. One shale exhibited nearly perfect elastic behavior for stress amplitudes up to 5 MPa.

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