Effective Fluid Bulk Modulus in the Partially Saturated Rock and the Amplitude Dispersion Effects

Abstract

Frequency dispersion is a well‐known effect in geophysics, which means that waves of different wavelengths propagate at different velocities. Amplitude dispersion is a less‐known effect, which means that waves of different amplitudes propagate at different velocities. Herewith, we consider the alteration of the interfacial energy during wave‐induced two‐phase fluid flow in a partially saturated rock and demonstrate that this leads to a nonlinear amplitude dispersion effect. When the wave amplitude is small, seismic waves cause bending of the interface menisci between immiscible fluids at the pore scale. However, when the wave amplitude is sufficiently large, the interface menisci will slip at the pore scale, causing attenuation of the elastic energy by the contact line friction mechanism. At the zero frequency limit, all viscous dissipation models predict zero attenuation of the elastic wave energy, while this approach predicts a nonzero attenuation due to a static contact angle hysteresis effect. Herein, we extend the Gassmann's theory with three extra terms, which can be obtained from standard laboratory tests: pore‐size distribution and interfacial tension between immiscible fluids and rock wettability (advancing and receding contact angles). We derive closed‐form analytical expressions predicting the effective fluid modulus in partially saturated rock, which falls between Voigt and Reuss averages. Next, we demonstrate that the nonlinear amplitude dispersion effect leads to energy transfer between different frequencies. This may explain the low‐frequency microtremor anomalies, frequently observed above hydrocarbon reservoirs, when the low‐frequency energy of ocean waves (0.1–1 Hz) is converted to higher frequencies (2–6 Hz) by partially saturated reservoirs.

Possible Effects of Multiphase Methane Evolution During a Glacial Cycle on Underpressure Development in Sedimentary Basins: An Analysis With Application to the Northeast Michigan Basin

“…Simulation 30 shows the effects of a parameter adjustment that may be justified based on previous theoretical analyses of hydromechanics in multiphase systems by Rozhko (2020). In addition, the measured values of bulk compressibility from Walsh (2011) that were used to calculate K U2 ranged from 8.19 × 10 −11 Pa −1 to 4.88 × 10 −10 Pa −1 (i.e., the maximum value was ∼six times greater than the minimum).…”

“…In Simulation 30, a parameter adjustment was made to test whether it would improve the fit of the model results to the observed pressure profile. Specifically, the bulk modulus of Unit 2 was divided by two from that of the base case, which may be appropriate for multiphase simulations based on theoretical analysis by Rozhko (2020).…”

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

“…It should be noted that partial saturation has great influence on the frequency‐dependent seismic properties (e.g. White, 1975; Müller and Gurevich, 2004; Amalokwu et al ., 2014; Solazzi et al ., 2020; Rozhko, 2019, 2020), and the study of the seismic dispersion and attenuation in layered and fractured rocks with partial water saturation will be investigated in future studies.…”

Seismic tuning of dispersive thin layers

“…We assume a thin layer that disperses according to the standard linear solid model (Ursin and Toverud, 2002) and calculate the shift induced by attenuation in its tuning curves as well as the upper bound in this shift. It should be noted that we do not consider different dissipation mechanisms that is due to solid–solid friction or contact‐line movement (Winkler and Nur, 1982; Rozhko, 2020) in which dispersion depends on wave amplitude rather than frequency, but postpone such considerations for future work. Likewise, the wedge model we discuss here is assumed homogeneous although this is not always the case, particularly in the context of CO 2 monitoring (Glubokovskikh et al ., 2020).…”