Effects of pore fluids on quasi‐static shear modulus caused by pore‐scale interfacial phenomena

Abstract

It is evident from the laboratory experiments that shear moduli of different porous isotropic rocks may show softening behaviour upon saturation. The shear softening means that the shear modulus of dry samples is higher than of saturated samples. Shear softening was observed both at low (seismic) frequencies and high (ultrasonic) frequencies. Shear softening is stronger at seismic frequencies than at ultrasonic frequencies, where the softening is compensated by hardening due to unrelaxed squirt flow. It contradicts to Gassmann's theory suggesting that the relaxed shear modulus of isotropic rock should not depend upon fluid saturation, provided that no chemical reaction between the solid frame and the pore fluid. Several researchers demonstrated that the shear softening effect is reversible during re‐saturation of rock samples, suggesting no permanent chemical reaction between the solid frame and the pore fluid. Therefore, it is extremely difficult to explain this fluid–rock interaction mechanism theoretically, because it does not contradict to the assumptions of Gassmann's theory, but contradicts to its conclusions. We argue that the observed shear softening of partially saturated rocks by different pore fluids is related to pore‐scale interfacial phenomena effects, typically neglected by the rock physics models. These interface phenomena effects are dependent on surface tension between immiscible fluids, rock wettability, aperture distribution of microcracks, compressibility of microcracks, porosity of microcracks, elastic properties of rock mineral, fluid saturation, effective stress and wave amplitude. Derived equations allow to estimate effects of pore fluids and saturation on the shear modulus and mechanical strength of rocks.

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

“…Those features, observed on seismic data, are called in literature by "anomalies," because it is challenging to explain it using viscous dissipation models, which predict seismic attenuation to be proportional to the frequency (Q −1~f ) in the low-frequency limit, which gets negligibly small at the zero limit. This model and our previous publications (Rozhko, 2019(Rozhko, , 2020Rozhko & Bauer, 2019) predicted nonzero attenuation at the zero-frequency limit due to a static contact angle hysteresis effect, which was not previously considered in geophysical literature; however, this effect is well known in the physics literature (e.g., Bormashenko, 2013;de Gennes et al, 2013;Drelich, 2019). Figure 8 shows the dependence of Skempton's B we and B nw coefficients (ordinate) on the water saturation S we (abscissa) and the dimensionless wave amplitude Δσ Δσc (color scale).…”

“…According to our model, this effect is highly sensitive to the wettability of the rock. Effects of wettability on seismic wave velocities were observed more than 60 years ago, after Wyllie et al (), who were the first (to our knowledge) to report this effect (see also Waite et al, ; Wang et al, ; Rozhko, , ); however, the wettability effects are not mentioned in the literature review by Kazantsev (). If the rock is mixed wet (when contact angles are close to 90°), then equation would predict very high value of the critical wave amplitude ( ∆σ c ), required for the contact line slippage.…”

“…When the presence of microcracks is neglected, we can consider that fluids do not affect the shear modulus of the rock. Here we do not include the isotropic system of microcracks, considered by Rozhko () because the number of equations and input parameters will be increased. In this paper we aim to keep the minimum number of input parameters to predict the effective fluid bulk modulus in the partially saturated rock and demonstrate the energy transfer between different frequencies due to the amplitude dispersion effect.…”

“…In this paper we aim to keep the minimum number of input parameters to predict the effective fluid bulk modulus in the partially saturated rock and demonstrate the energy transfer between different frequencies due to the amplitude dispersion effect. Similarly, the aim of Rozhko () paper was to demonstrate the shear‐softening effect keeping the minimum number of input parameters; that is, only isotropic microcrack porosity was assumed.…”

“…Contrary, all input parameters in Gassmann's theory can be derived from the lab, because this theory does not depend on the pore geometry. In this paper we extend both approaches of Gassmann () and Rozhko (, ) by coupling of the interfacial energy to Gassmann's theory. Interfacial energy effects on seismic wave velocity dispersion have been reported in many publications (Knight et al, ; Knight & Nolen‐Hoeksema, ; Moerig et al, ; Murphy, ; Murphy et al, ; Papageorgiou et al, ; Rozhko & Bauer, ; Vo‐Thanh, ; Waite et al, ; Wang et al, ; Wyllie et al, ); see Rozhko () for detailed literature review.…”