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The shale oil reservoir within the Yanchang Formations of Ordos Basin harbors substantial oil and gas resources and has recently emerged as the primary focus of unconventional oil and gas exploration and development. Due to its complex pore and throat structure, pronounced heterogeneity, and tight reservoir characteristics, the techniques for conventional oil and gas exploration and production face challenges in comprehensive implementation, also indicating that as a vital parameter for evaluating the physical properties of a reservoir, permeability cannot be effectively estimated. This study selects 21 tight sandstone samples from the Q area within the shale oil formations of Ordos Basin. We systematically conduct the experiments to measure porosity, permeability, ultrasonic wave velocities, and resistivity at varying confining pressures. Results reveal that these measurements exhibit nonlinear changes in response to effective pressure. By using these experimental data and effective medium model, empirical relationships between P-and S-wave velocities, permeability and resistivity and effective pressure are established at logging and seismic scales. Furthermore, relationships between P-wave impedance and permeability, and resistivity and permeability are determined. A comparison between the predicted permeability and logging data demonstrates that the impedance–permeability relationship yields better results in contrast to those of resistivity–permeability relationship. These relationships are further applied to the seismic interpretation of shale oil reservoir in the target layer, enabling the permeability profile predictions based on inverse P-wave impedance. The predicted results are evaluated with actual production data, revealing a better agreement between predicted results and logging data and productivity. [ABSTRACT FROM AUTHOR]

We develop a numerical algorithm for simulation of wave propagation in anisotropic thermoelastic media, established with a generalized Fourier law of heat conduction. The wavefield is computed by using a grid method based on the Fourier differential operator and a first-order explicit Crank-Nicolson algorithm to compute the spatial derivatives and discretize the time variable (time stepping), respectively. The model predicts four propagation modes, namely, a fast compressional or (elastic) P wave, a slow thermal P diffusion/wave (the T wave), having similar characteristics to the fast and slow P waves of poroelasticity, respectively, and two shear waves, one of them coupled to the P wave and therefore affected by the heat flow. The thermal mode is diffusive for low values of the thermal conductivity and wave-like (it behaves as a wave) for high values of this property. As in the isotropic case, three velocities define the wavefront of the fast P wave, i.e, the isothermal velocity in the uncoupled case, the adiabatic velocity at low frequencies, and a higher velocity at high frequencies. The heat (thermal) wave shows an anisotropic behavior if the thermal conductivity is anisotropic, but an elastic source does not induce anisotropy in this wave if the thermal properties are isotropic. [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]

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 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]

Underground carbonate deposits are widespread worldwide and have considerable hydrocarbon potential. They are generally characterized by a complex microscopic structure that affects the properties of the macroscopic fluid flow and the relevant petrophysical behavior. In recent years, advances in digital technology have helped reveal the microstructures (i.e., pore connections, cracks, pore size and radius, etc.) of rocks in the subsurface. In this work, drill cores (cylinder) are taken from a deep carbonate deposit in the Sichuan Basin in western China to perform computed tomography (CT) scans, thin sections and mineral analysis. The characteristics of lithology and pore structure are investigated. Ultrasonic experiments with different fluid types and pressures are conducted to determine rock samples’ wave velocities, attenuation and crack porosity. The experimental data show that the rocks have low porosity/permeability and a complex pore/crack system, leading to significant pressure, crack and fluid type effects on the velocities, dispersion and attenuation. We develop a model of multiple pore-crack structures for carbonates by considering the complex structure and fluid properties. Digital cores are reconstructed based on CT scans, image processing and threshold segmentation. The aspect ratios of pores and cracks are extracted with their volume fractions to simulate the rock skeleton with the differential effective medium theory. The Biot–Rayleigh wave propagation equations are applied to simulate the effects of different pore and fluid types on the velocity and attenuation of P-waves. The agreement between the modeling results and the ultrasonic and log data confirms that the model can validly reproduce the wave responses. [ABSTRACT FROM AUTHOR]

The quality factor Q is a dimensionless measure of the energy loss per cycle of a wave field, and a proper understanding of this factor is important in a variety of fields, from seismology, geophysical prospecting to electrical science. Here, the focus is on viscoelasticity. When interpreting experimental values, several factors must be taken into account, in particular the shape of the medium (rods, bars or unbounded media) and the fact that the measurements are made on stationary or propagating modes. From a theoretical point of view, the expressions of Q may differ due to different definitions, the spatial dimension and the inhomogeneity of the wave, i.e. the fact that the vectors of propagation (or wavenumber) and attenuation do not point in the same direction. We show the difference between temporal and spatial Q, the relationships between compressional and shear Q, the dependence on frequency, the case of poro-viscoelasticity and anisotropy, the effect of inhomogeneous waves and various loss mechanisms, and consider the analogy between elastic and electromagnetic waves. We discuss physical theories describing relaxation peaks, bounds on Q and experiments showing the behaviour of Q as a function of frequency, saturation and pore pressure. Finally, we propose an application example where Q can be used to estimate porosity and saturation. [ABSTRACT FROM AUTHOR]