Simulation of the effect of stress-induced anisotropy on borehole compressional wave propagation

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This can lead to an incorrect estimation of formation elastic properties measured from sonic logs. Previous work has focused on estimating the elastic properties of the formation surrounding a borehole under anisotropic stress loading. We studied the effect of borehole stress concentration on sonic logging in a moderately consolidated Berea sandstone using a two-step approach. First, we used an iterative approach, which combines a rock-physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole subjected to an anisotropic stress loading. Second, we used the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response of the borehole. Although we neglected the effects of rock failure and stress-induced crack opening, our modeling results provided important insights into the characteristics of borehole P-wave propagation when anisotropic in situ stresses are present. Our simulation results were consistent with the published laboratory measurements, which indicate that azimuthal variation of the P-wave velocity around a borehole subjected to uniaxial loading is not a simple cosine function. However, on field scale, the azimuthal variation in P-wave velocity might not be apparent at conventional logging frequencies. We found that the low-velocity region along the wellbore acts as an acoustic focusing zone that substantially enhances the P-wave amplitude, whereas the high-velocity region caused by the stress concentration near the borehole results in a significantly reduced P-wave amplitude. This results in strong azimuthal variation of P-wave amplitude, which may be used to infer the in situ stress state

Investigation of borehole cross-dipole flexural dispersion crossover through numerical modeling

Crossover of the dispersion of flexural waves recorded in borehole cross-dipole measurements is interpreted as an indicator of stress-induced anisotropy around a circular borehole in formations that are isotropic in the absence of stresses. We have investigated different factors that influence flexural wave dispersion. Through numerical modeling, we determined that for a circular borehole surrounded by an isotropic formation that is subjected to an anisotropic stress field, the dipole flexural dispersion crossover is detectable only when the formation is very compliant. This might happen only in the shallow subsurface or in zones having high pore pressure. However, we found that dipole dispersion crossover can also result from the combined effect of formation intrinsic anisotropy and borehole elongation. We found that a small elongation on the wellbore and very weak intrinsic anisotropy can result in a resolvable crossover in flexural dispersion that might be erroneously interpreted as borehole stress-induced anisotropy. A thorough and correct interpretation of flexural dispersion crossover thus has to take into account the effects of stress-induced and intrinsic anisotropy and borehole cross-sectional geometry

Fracture clustering effect on amplitude variation with offset and azimuth analyses

Traditional amplitude variation with offset and azimuth (AVOAz) analysis for fracture characterization extracts fracture properties through analysis of reflection AVOAz to determine anisotropic parameters (e.g., Thomsen’s parameters) that are then related to fracture properties. The validity of this method relies on the basic assumption that a fractured unit can be viewed as an equivalent anisotropic medium. As a rule of thumb, this assumption is taken to be valid when the fracture spacing is less than λ/10. Under the effective medium assumption, diffractions from individual fractures destructively interfere and only specular reflections from boundaries of a fractured layer can be observed in seismic data. The effective medium theory has been widely used in fracture characterization, and its applicability has been validated through many field applications. However, through numerical simulations, we find that diffractions from fracture clusters can significantly distort the AVOAz signatures when a fracture system has irregular spacing even though the average fracture spacing is much smaller than a wavelength (e.g., ≪λ/10). Contamination by diffractions from irregularly spaced fractures on reflections can substantially bias the fracture properties estimated from AVOAz analysis and may possibly lead to incorrect estimates of fracture properties. Additionally, through Monte Carlo simulations, we find that fracture spacing uncertainty inverted from amplitude variation with offset (AVO) analysis can be up to 10%–20% when fractures are not uniformly distributed, which should be the realistic state of fractures present in the earth. Also, AVOAz and AVO analysis gives more reliable estimates of fracture properties when reflections at the top of the fractured layer are used compared with those from the bottom of the layer

Sensitivity analysis of fracture scattering

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 40-42).We use a 2-D finite difference method to numerically calculate the seismic response of a single finite fracture in a homogeneous media. In our experiments, we use a point explosive source and ignore the free surface effect, so the fracture scattering wave field contains two parts: P-to-P scattering and P-to-S scattering. We vary the fracture compliance within a range considered appropriate for field observations, 10-12 m/Pa to 10-9 m/Pa, and investigate the variation of the scattering pattern of a single fracture as a function of normal and tangential fracture compliance. We show that P-to-P and P-to-S fracture scattering patterns are sensitive to the ratio of normal to tangential fracture compliance and different incident angle, while radiation pattern amplitudes scale as the square of the compliance. We find that, for a vertical fracture system, if the source is located at the surface, most of the energy scattered by a fracture propagates downwards, specifically, the P-to-P scattering energy propagates down and forward while the P-to-S scattering energy propagates down and backward. Therefore, most of the fracture scattered waves observed on the surface are, first scattered by fractures, and then reflected back to the surface by reflectors below the fracture zone, so the fracture scattered waves have complex ray paths and are contaminated by the reflectivity of matrix reflectors.by Xinding Fang.S.M

Seismic characterization of fractured reservoirs using 3D double beams

We propose an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. We use both singly scattered and multiply scattered seismic waves by fractures. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation. If multiple targets are used, the interference pattern is spatially varying and the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.Eni-MIT Energy Initiative Founding Member Progra

Efficient Double-Beam Characterization for Fractured Reservoir

We proposed an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.Massachusetts Institute of Technology. Earth Resources Laborator

Double-beam stacking to infer seismic properties of fractured reservoirs

We develop a theory for using 3D beam interference to infer scattering properties of a fractured reservoir using reflected seismic P data. For the sake of simplicity, we use Gaussian beams. The scattering properties are important to infer fracture spacing, orientation and compliance. The method involves the interference of two beams, one from the source region and the other from the receiver region. Each beam is formed by first windowing the data in space and time and then performing f-k filtering. The interference pattern depends on frequency, the incident angle, the reflection angle, and the azimuth. We try to interpret the interference pattern using local Born scattering in the target region. This interpretation is motivated by the observation that full-wave finite difference simulation of waves propagating through a set of vertical fractures using Schoenberg’s linear-slip boundary condition and fracture compliances consistent with those inferred from field and laboratory data shows that single scattering dominates in the reflection data. The methodology is versatile in that by adjusting the window sizes we can obtain plane wave interference as well as interference for a single shot or receiver gather. By suitable choice of pairs of source and receiver beams, the spatially varying fracture properties as well as the fracture orientation can be inferred.Eni-MIT Energy Initiative Founding Member Program; Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Member Postdoctoral Fellowship

Sensitivity analysis of fracture scattering

The understanding of seismic scattering of a finite fracture is very important in reservoir fracture characterizations, but the analytical solution of this problem is not available. Thus, in this paper, we present an approach for numerical study of the seismic response of a finite fracture.Eni-MIT Energy Initiative Founding Member Program (Eni Multiscale Reservoir Science Project)Massachusetts Institute of Technology. Earth Resources Laborator

A robust method for fracture orientation and density detection from seismic scattered energy

The measurements of fracture parameters, such as fracture orientation, fracture density and fracture compliance, in a reservoir is very important for field development and exploration. Traditional seismic methods for fracture characterization include shear wave birefringence (Gaiser and Dok, 2001; Dok et al., 2001; Angerer et al., 2002; Vetri et al., 2003) and amplitude variations with offset and azimuth (AVOA) (Ruger, 1998; Shen et al., 2002; Hall et al., 2003; Liu et al., 2010; Lynn et al., 2010). These methods are based on the equivalent medium theory with the assumption that fracture dimension and spacing are small relative to the seismic wave length, so a fracture zone behaves like an equivalent anisotropic medium. But fractures on the order of seismic wave length are also very important for enhanced oil recovery, and they are one of the important subsurface scattering sources that generate scattered seismic waves. Willis et al. (2006) developed the Scattering Index method to extract the fracture scattering characteristics by calculating the transfer funtion of a fracture zone. This method has two sources of uncertainty: (1) calculation of the transfer function is sensitive to the analysis time window; (2) the interpretation of the transfer function is based on the assumption that the background reflectivity of the medium is white. Here we propose a modification of the SI methods that addresses these issues and leads to a more robust fracture characterization.Eni-MIT Energy Initiative Founding Member Progra