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We simulate the effects of diagenesis, cementation and compaction on the elastic properties of shales and sandstones with four different petro-elastic theories and a basin-evolution model, based on constant heating and sedimentation rates. We consider shales composed of clay minerals, mainly smectite and illite, depending on the burial depth, and the pore space is assumed to be saturated with water at hydrostatic conditions. Diagenesis in shale (smectite/illite transformation here) as a function of depth is described by a fifth-order kinetic equation, based on an Arrhenius reaction rate. On the other hand, quartz cementation in sandstones is based on a model that estimates the volume of precipitated quartz cement and the resulting porosity loss from the temperature history, using an equation relating the precipitation rate to temperature. Effective pressure effects (additional compaction) are accounted for using the Athy equation and the Hertz–Mindlin model. The petro-elastic models yield similar seismic velocities, despite the different levels of complexity and physics approaches, with increasing density and seismic velocities as a function of depth. The methodology provides a simple procedure to obtain the velocity of shales and sandstones versus temperature and pressure due to the diagenesis-cementation-compaction process. [ABSTRACT FROM AUTHOR]

The acoustic properties of rocks depend on porosity, pressure, and pore fluid and also on pore geometry. Anelasticity (attenuation and velocity dispersion) is more affected by crack aspect ratio and fraction (soft pores) than by equant (stiff) pores. To study this fact, we have performed ultrasonic measurements on two dolomite samples under variable pressure and fluid content, and used the EIAS (equivalent inclusion-average stress) model to obtain the crack aspect ratio and fraction from the bulk and shear moduli of the rock. The theory has an excellent agreement with the experimental data, and the results show that the crack attributes decrease with increasing differential pressure and are higher for a stiffer fluid. In fact, the interpretation of the experiments with the model shows that crack fraction and aspect ratio increase with the bulk modulus of the fluid (water and oil). Then, by extending the theory to all frequencies, using the Zener mechanical model, we obtain the phase velocities and quality factors as a function of frequency. Our findings reveal the importance of considering differential pressure and fluid type to analyze pore geometry and rock anelasticity. [ABSTRACT FROM AUTHOR]

Wave-induced fluid flow generates a dominant attenuation mechanism in porous media. It consists of energy loss due to P-wave conversion to Biot (diffusive) modes at mesoscopic-scale inhomogeneities. Fractured poroelastic media show significant attenuation and velocity dispersion due to this mechanism. The theory has first been developed for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a poroelastic medium containing planar fractures. In this work, we consider the theory for all propagation angles by obtaining the five complex and frequency-dependent stiffnesses of the equivalent TI medium as a function of frequency. We assume that the flow direction is perpendicular to the layering plane and is independent of the loading direction. As a consequence, the behaviour of the medium can be described by a single relaxation function. We first consider the limiting case of an open (highly permeable) fracture of negligible thickness. We then compute the associated wave velocities and quality factors as a function of the propagation direction (phase and ray angles) and frequency. The location of the relaxation peak depends on the distance between fractures (the mesoscopic distance), viscosity, permeability and fractures compliances. The flow induced by wave propagation affects the quasi-shear (qS) wave with levels of attenuation similar to those of the quasi-compressional (qP) wave. On the other hand, a general fracture can be modeled as a sequence of poroelastic layers, where one of the layers is very thin. Modeling fractures of different thickness filled with CO embedded in a background medium saturated with a stiffer fluid also shows considerable attenuation and velocity dispersion. If the fracture and background frames are the same, the equivalent medium is isotropic, but strong wave anisotropy occurs in the case of a frameless and highly permeable fracture material, for instance a suspension of solid particles in the fluid. [ABSTRACT FROM AUTHOR]

The triaxial nature of the tectonic stress in the earth’s crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as $$[{\varvec{ \kappa}}\cdot {\bf u} + {\varvec{\eta}} \cdot {\bf v} ],$$ where the brackets denote discontinuities across the fracture surface, $${\varvec{\kappa}}$$ is a fracture stiffness, and $${\varvec{\eta}}$$ is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir’s theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low- to the high-frequency limits in the case of a particle–velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP–qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis. [ABSTRACT FROM AUTHOR]

We obtain the reflection and transmission coefficients at a fracture in transversely isotropic media, whose symmetry axis is perpendicular to the fracture surface. We consider dissimilar upper and lower media. The fracture is modeled as an interface with boundary discontinuities in the displacement and the particle velocity. The stress components are proportional to the displacement and velocity discontinuities through the specific stiffnesses and specific viscosities, respectively. The stiffness introduces frequency-dependence and phase changes in the fracture response and the viscosity is related to the energy loss. We also calculate the energy balance at the fracture and the dissipated energy. The theory is illustrated by computing the reflection coefficient of a fracture present in the Antarctic ice cap. In this case, the reflection coefficient decreases with increasing incidence angle and then approaches 1 at grazing angle. [ABSTRACT FROM AUTHOR]

We present a new petro-elastical and numerical-simulation methodology to compute synthetic seismograms for reservoirs subject to CO2 sequestration. The petro-elastical equations model the seismic properties of reservoir rocks saturated with CO2, methane, oil and brine. The gas properties are obtained from the van der Waals equation and we take into account the absorption of gas by oil and brine, as a function of the in situ pore pressure and temperature. The dry-rock bulk and shear moduli can be obtained either by calibration from real data or by using rock-physics models based on the Hertz-Mindlin and Hashin-Shtrikman theories. Mesoscopic attenuation due to fluids effects is quantified by using White's model of patchy saturation, and the wet-rock velocities are calculated with Gassmann equations by using an effective fluid modulus to describe the velocities predicted by White's model. The simulations are performed with a poro-viscoelastic modeling code based on Biot's theory, where viscoelasticity is described by generalizing the solid/fluid coupling modulus to a relaxation function. Using the pseudo-spectral method, which allows general material variability, a complete and accurate characterization of the reservoir can be obtained. A simulation, that considers the Utsira sand of the North Sea, illustrates the methodology. [ABSTRACT FROM AUTHOR]

A correction to the article "Fracture-Induced Anisotropic Attenuation" in the December 2013 issue is presented.