Upscaling of elastic properties of anisotropic sedimentary rocks

Abstract

S U M M A R YIn this paper, the term 'upscaling' means the theoretical prediction of rock's elastic properties at lower frequency (seismic or cross-well data) using higher frequency logging data on sonic velocities (V P , V S 1 and V S 2 ), porosity and density. The mineral composition and water saturation derived from other logs are used. Due to the special treatment of sonic logging data provided by the dipole sonic probe, all the sonic velocities are obtained in the principal coordinate system of the rock's stiffness tensor. The upscaling procedure includes two steps. The first step involves the solution of an inverse problem on reconstruction of the parameters of the rock's microstructure from the logging data. The inversion is based on the effective medium theory. As a result of the inverse problem solution, the effective stiffness tensor is found for depths at which the sonic wave velocities are measured. At the second step, the velocities of waves at given lower frequencies are calculated as propagating in a layered medium. The number of layers in the medium depends on the given frequency and logging step. Each layer of the medium has the stiffness tensor found at the first step.This upscaling procedure has been applied to a wellbore for which the dipole sonic data are available. The rocks penetrated by the well are shales. In general, the resulting medium exhibits orthorhombic symmetry at sonic frequency. This symmetry results from the preferential orientation of clay platelets and grain-related cracks and vertical cracks. The existence of the latter is indicated by the dipole sonic tool. Depending on the microstructure parameters (orientation of clay platelets and cracks, pore/crack connectivity and shale mineralogical composition), the shales, at lower frequency, have either transversely isotropic symmetry (with the vertical axis of symmetry, a.k.a. VTI) or orthorhombic symmetry.

Evaluation of Non-Nuclear Techniques for Well Logging: Technology Evaluation

“…Challenges remain in many aspects of data interpretation. An example relating to scale is seen in simply correlating acoustically determined parameters (e.g., velocity, density, and porosity) from higher-resolution sonic-ultrasonic probes with that from lower-resolution (lower frequency) probes ortheoretical predictions (Bayuk et al 2008).…”

Velocity Modeling to Determine Pore Aspect Ratios of the Haynesville Shale

“…Upscaling means theoretically predicting the elastic properties in rocks at lower frequency from higher frequency sonic logging data (Bayuk et al, 2007). When the wavelength (λ) is large compared to the layer thickness (d), the wave velocity is estimated by an average of the properties in the individual layers (Backus, 1962), assuming each layer is isotropic.…”

Spatial variation of angle-dependent impedance through a thin-layered oil reservoir

“…Applying an upscaling process, the effective VTI stiffnesses of such layered structure can be estimated from bulk density and full-wave sonic logs. In this way, weighted arithmetic average formulas allows the calculation of the five effective VTI stiffnesses within a specified frequencydependent window length (Liner & Fei, 2006;Stovas et al, 2006;Bayuk et al, 2008;Tiwary et al, 2009).…”

“…Because of the fine-layering character of the formation containing the reservoir, we approximated the sedimentary column to a transverse isotropic medium with vertical axis of symmetry (i.e., a VTI medium). As the layer induced VTI anisotropy is the result of Backus-averaging effective medium theory (Backus, 1962;Stovas et al, 2006;Bayuk et al, 2008), we used this averaging technique to construct VTI stiffness logs from the Namorado reservoir well log data set. We then generated isotropic and VTI EI maps at a specific depth through the Namorado reservoir using the same interpolator and search radius scheme adopted in Augusto (2009).…”