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The tight oil/gas reservoirs in China have showed the great exploration prospects and high production potential, with the characteristics of low porosity, low permeability, and significant heterogeneity in formation rocks. It remains a challenge to sort out the relations between reservoir wave responses and rock physical properties, and the further studies on the wave response patterns of tight reservoirs are in an urgent demand. The shear modulus and S- (shear) wave attenuation of rocks are affected by the properties of pore fluid and confining pressure. The ultrasonic wave experiments are performed on eight partially-saturated tight sandstone samples at different confining pressures, and we estimate S-wave attenuation with the spectral-ratio method. Results show that S-wave attenuation decreases with increasing confining pressure, and the water saturation case shows more loss compared to the oil saturation case, while the gas saturation case gives the lowest attenuation. We observe the S-wave relaxation peak at an intermediate water saturation for the gas-water partial-saturation case in general. S-wave attenuation increases with increasing porosity or permeability. Based on the measured rock physical properties, and combined with the Voigt–Reuss–Hill (VRH) average, differential effective medium (DEM) model and squirt-flow model, a tight rock attenuation model is proposed for analyzing the attenuation characteristics of fluid-saturated rocks at different confining pressures. The model reasonably describes the S-wave attenuation characteristics. The model predictions of S-wave attenuation show apparent pressure- and fluid-sensitivity at full saturation and partial saturation conditions. For sample TS1-19 at full saturation with different confining pressures, the S-wave peak attenuation predicted by the model ranges from 11.6 to 69.5, and decreases with confining pressure, while the relaxation frequency shifts to high frequency end. For the partial saturation condition of the sample, the predicted S-wave peak attenuation ranges from 15.5 to 39.8 at a confining pressure of 30 MPa and increases with water saturation, while the relaxation frequency shifts to low frequency end. For all the samples at 30MPa confining pressure, the predicted S-wave attenuation ranges from 5.6 to 38.6. At the full-saturation case, the predicted S-wave attenuation increases with porosity and decreases with confining pressure. For the partial saturation case, the S-wave attenuation predicted with the model and the Voigt and Reuss bounds generally increases with water saturation, whereas the experimentally-measured attenuation exhibits the peak attenuation at an intermediate saturation. [ABSTRACT FROM AUTHOR]

The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs. [ABSTRACT FROM AUTHOR]

We perform seismic and ultrasonic measurements in carbonate and shaley sandstone samples as a function of differential pressure. The velocities show a strong frequency and pressure dependence. The dispersion disappears with increasing pressure and the squirt flow in turn inhibits the pressure dependence. To model these effects, we combine the Gurevich's squirt-flow model with the Mori–Tanaka scheme and the David Zimmerman model, and extend it with third-order elastic constants, to obtain a frequency-dependent acoustoelasticity model. Comparisons between measurements from this study and literature and modelling results show that the P -wave velocity increases non-linearly first and then nearly linearly, dominated by crack closure and acoustoelasticity, respectively. The pressure dependence of wave velocities is reduced by liquid substitution and further by the squirt-flow mechanism. The effects of fluid properties and crack closure on P -wave velocity decrease with differential pressure. The results will feed a new model and help better understanding the wave propagation in pre-stressed rocks at different scales. [ABSTRACT FROM AUTHOR]

Knowledge of how temperature affects the oil–sand acoustic response is useful to exploit these reservoir rocks with seismic methods. We propose three models: double-porosity coherent potential approximation (CPA), lower-bound Hashin–Shtrikmann (HS-), and contact cement (CC), based on different spatial distributions of heavy oil and temperature and frequency-dependent empirical equations. The shear modulus and S-wave velocity are affected by temperature in all the cases. Moreover, the properties of oil sands with heavy oil as a continuous matrix and higher viscosity are more sensitive to temperature. The models can provide theoretical support for the establishment of rock physical models in heavy oil reservoirs so as to quantitatively characterize the seismic response changes caused by thermal mining. [ABSTRACT FROM AUTHOR]

The complex seismic responses of heterogeneous reservoirs can be related to the fabric structure, pore/microcrack shape, mineral composition and fluid distribution of the rock in situ. The pore structure refers to the geometric shape, size, spatial distribution and interconnectedness of pores, microcracks and throats. It is closely related to the storage space of reservoirs and the spatial distribution of oil/gas. Understanding the pore structure is crucial for the development of processes to increase oil/gas production capacity. Six dolomite samples from the Gaoshiti-Moxi Longwangmiao Formation are sorted out for measurements, and the ultrasonic and seismic attenuation are determined by using the spectral ratio method and the enhanced frequency shift method, respectively. When predicting the pore structure, we assume that the aspect ratio and volume fraction of pores and microcracks correspond to a normal distribution. On this basis, a model with the Voigt–Reuss–Hill average (VRH), differential effective medium (DEM) theory and infinituple-porosity media (IPM) theory is proposed. The acoustic wave responses in terms of reservoir porosity and standard deviation of normal distribution are analyzed, and multiscale 3D rock physics templates (RPT) are created. The calibrations of the templates are performed with the ultrasonic and seismic data, and then the templates are applied to the field data. The results show that the estimated porosity and pore structure (corresponding to the mean aspect ratio and standard deviation of a normal distribution, respectively) are in substantial agreement with the log data and the actual gas production results. [ABSTRACT FROM AUTHOR]

Tight sandstone reservoirs basically have low porosity and permeability, a complex pore structure and a heterogeneous distribution of immiscible fluids. With the development of theoretical models, it is common to characterize rock properties, i.e., pore structure, microfractures, fluid type and saturation, etc., based on acoustic and electrical properties. We have taken four tight sandstone samples and performed X-ray diffraction and cast thin section analyses. We measure porosity and permeability as well as ultrasonic properties and electrical conductivity at different confining pressures and fluid saturations. These measurements show that the P-wave velocity, P-wave attenuation and conductivity strongly depend on the type and saturation of the fluid and the microstructure of the rock. We propose a combined acoustic-electrical model based on the concept of equivalent medium and on the double porosity, patchy saturation and squirt flow models. We then create rock physics templates calibrated with wellbore log data to estimate fluid saturation and equant and soft porosities, which are well corroborated by gas production reports. This work demonstrates the link between combined acoustic-electrical responses and rock properties and provides an effective approach for applications in reservoirs. [ABSTRACT FROM AUTHOR]

The rheological models of Lomnitz and Jeffreys have been widely used in earthquake seismology (to simulate a nearly constant Q medium) and to describe the creep and relaxation behavior of rocks as a function of time. Other similar models, such as those of Becker, Scott Blair and Kolsky, show similar properties, particularly the Scott Blair model describes a perfectly constant Q as a function of frequency. We first give a historical overview of the main scientists and the development and versions of the various models and priorities of discovery. Then, we clarify the relationship between the different versions of these models in terms of mathematical expressions of the complex modulus and calculate the phase velocity and quality factor Q as a function of frequency, illustrating the various special cases. In addition, we give useful hints for the numerical calculation of these moduli, which include special cases of the hypergeometric function. [ABSTRACT FROM AUTHOR]

Petrophysics and fluid-flow simulations are used to build a realistic pre- and post- CO 2 injection geological model for the Utsira formation at the Sleipner field, and the Fourier pseudospectral method is employed to compute synthetic seismograms. The methodology can be used to perform a seismic sensitivity analysis for the detection of carbon dioxide. We built the model solely based on the porosity and clay content of the formations with the aid of fluid-flow and seismic simulations. The pressure map before the injection is assumed to be hydrostatic for which a reference porosity map is defined. The injection induces pore pressure variations and partial saturation, which affect the poroelastic properties and hence the associated seismic response. A proper porosity–permeability–clay content relation is one of the key factors since permeability determines the preferential flow directions and the distribution of the CO 2 plume. The petrophysical model is based on a shaly sandstone (or sandy shale) to represent the caprock, Utsira Sand and embedded mudstone layers. The composite permeability (anisotropic) is analogous to the inverse electrical resistance model. Gas viscosity depends on pressure and temperature. The P- and S-wave velocities are obtained from Gassmann equation (pre-injection) and White's mesoscopic model (post-injection), which also yields the P-wave quality factor in the case of partial (patchy) saturation. To model a realistic situation, we implement a fractal variation of the porosity and clay content, based on the von Kármán correlation function. We then compare the real and synthetic seismograms (pre-injection and post-injection) and show the effect of attenuation on the seismic data. Simulations and real data show a remarkable match. [ABSTRACT FROM AUTHOR]

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord–Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case. [ABSTRACT FROM AUTHOR]