Measurements of the Effective Stress Coefficient for Elastic Moduli of Sandstone in Quasi-Static Regime Using Semiconductor Strain Gauges

Numerous experimental and theoretical studies undertaken to determine the effective stress coefficient for seismic velocities in rocks stem from the importance of this geomechanical parameter both for monitoring changes in rock saturation and pore pressure distribution in connection with reservoir production, and for overpressure prediction in reservoirs and formations from seismic data. The present work pursues a task to determine, in the framework of a low-frequency laboratory study, the dependence of the elastic moduli of n-decane-saturated sandstone on the relationship between pore and confining pressures. The study was conducted on a sandstone sample with high quartz and notable clay content in a quasi-static regime when a 100 mL tank filled with n-decane was directly connected to the pore space of the sample. The measurements were carried out at a seismic frequency of 2 Hz and strains, controlled by semiconductor strain gauges, not exceeding 10-6. The study was performed using a forced-oscillation laboratory apparatus utilizing the stress-strain relationship. The dynamic elastic moduli were measured in two sets of experiments: at constant pore pressures of 0, 1, and 5 MPa and differential pressure (defined as a difference between confining and pore pressures) that varied from 3 to 19 MPa; and at a constant confining pressure of 20 MPa and pore pressure that varied from 1 to 17 MP. It was shown that the elastic moduli obtained in the measurements were in good agreement with the Gassmann moduli calculated for the range of differential pressures used in our experiments, which corresponds to the effective stress coefficient equal to unity.

Experimental Studies of the Influence of Dynamic Loading on the Elastic Properties of Sandstone

Under dynamic loading, the geomechanical properties of porous clastic rocks differ from those in quasistatic loading. A small experimental rig was built to directly assess the influence of vibrations on the uniaxial compressive strength (UCS), Young modulus, and Poisson’s ratio. A piezoelectric actuator powered by a signal from an oscillator was used in the rig as a generator of vibrations. A laser sensor and eddy current probe measured the longitudinal and transverse deformation. Tinius Hounsfield and Instron Series 4483 installations were used to determine the geomechanical properties of new red sandstone in a quasistatic regime. The boundaries of elastic deformations determined in the quasistatic loading were implemented in the dynamic loading. To perform the experiments in the elastic zone (on the graph of stress (σ)–strain (ε)), small samples with diameters ranging between 7.5 and 24.7 mm were manufactured. The investigation demonstrated that the Young’s modulus of the sandstone increased with increasing values of the dynamic load and frequency.

An enhanced broad-frequency-band apparatus for dynamic measurement of elastic moduli and Poisson's ratio of rock samples

We built a broad-frequency-band measurement system for rock elastic parameters based on the stress-strain method following Batzle et al., Geophysics 71, N1-N9 (2006). The system gives strain amplitude anomalies at some measurement frequencies. These anomalies put limitations on the range of the measurement frequency and jeopardize the credibility of the measurement results over a broad frequency band. To overcome these limitations, we investigated the cause of these anomalous strains by numerical model simulations with a finite element method based on the experimental apparatus. Through the systematic analysis of the modeling results, we conclude that the resonances caused by non-axial perturbations lead to such anomalous measurement results. Based on the analysis, we give a solution to reduce the effect of the resonances and shift the first resonance frequency beyond the frequency band of 1-2000 Hz. The enhanced measurement system can provide robust and reliable measurements on the elastic parameters of rocks between 1 and 2000 Hz, which is crucial for a quantitative study of the frequency-dependent phenomenon related to fluid effects. This in turn will provide a powerful tool for the experimental characterization of elastic properties of oil/gas reservoir rocks, thus laying a solid foundation for low-frequency rock physics analysis and quantitative seismic interpretation.

Giant strain-sensitivity of acoustic energy dissipation in solids containing dry and saturated cracks with wavy interfaces

Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10(-8) produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.

Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes

Self-action and effects mutually induced by oscillations interacting in hysteretic media are investigated analytically and numerically. Special attention is paid to non-simplex processes for which presence of intermediate extrema results in appearance of minor nested loops inside the main hysteretic stress-strain loop. Non-simplex regimes are typical of interaction of excitations having different frequencies and amplitudes, but comparable strain rates. It is found that, due to transition between the regimes, frequency and amplitude dependencies of the variations in elasticity and dissipation induced by one wave for another one may become non-monotonous. Either additional dissipation or induced transparency may occur in different regimes. The results obtained are important for correct interpretation of experimental data on nonlinear acoustic interactions in rocks and many other microstructured (mesoscopic) solids that are known to exhibit elastic hysteresis and memory properties.

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.

Strain wave evolution equation for nonlinear propagation in materials with mesoscopic mechanical elements

Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.