Rock Static Moduli From Borehole Sonic Data in Stress-Dependent Formations.

This article describes a novel technique to estimate static Young's modulus of stress-sensitive rocks using dynamic linear and nonlinear constants estimated from borehole sonic data. Two linear and three nonlinear constants are estimated from the transit time of compressional headwaves and inversion of borehole-guided Stoneley and crossdipole dispersions in tectonically stressed formations. A major advantage of this technique is that the rock static Young's modulus is determined from the dynamic elastic constants measured at a chosen reference state that is rather close to the in situ conditions. These dynamic elastic constants are used in the nonlinear constitutive relations for poroelastic rocks subject to finite deformations. These relations express the second Piola-Kirchhoff axial stresses in terms of elastic constants together with up to quadratic terms in Lagrangian axial strains. Strain derivatives of the second Piola-Kirchhoff stress yield the static Young's modulus as a function of incremental axial strains from a chosen reference state. Consequently, static Young's modulus can also be determined at other depths with different overburden stresses and associated incremental axial strains from a chosen reference state. In contrast, strain derivative of the second Piola-Kirchhoff axial stress expressed in terms of linear elastic constants and only linear terms in axial strain provides the dynamic Young's modulus. Two useful outputs from this workflow are the static stress-strain deformation curves for a core plug and static Young's modulus under in situ conditions as a function of logging depth. The proposed technique has been validated with the available experimental stress-strain data from Castlegate and Berea sandstones core plugs. Results have been obtained for the static Young's modulus and finite deformation stress-strain curves for two different stress-sensitive poroelastic formations using borehole sonic data.

Radial Profiles of Formation Mass Density, Bulk and Shear Moduli From Borehole Flexural and Stoneley Dispersions.

Exploration wells are liquid-filled boreholes drilled into formations with different geophysical and petrophysical properties. These boreholes support axisymmetric, flexural, and quadrupole family of guided modes that can probe radially varying formation properties at different frequencies. Radially varying formation properties are caused by drilling-induced fractures or near-wellbore stress concentrations. This work describes a novel workflow that inverts borehole flexural and Stoneley dispersions to obtain radially varying formation mass density and shear and bulk moduli away from the borehole surface. An integral equation relates fractional changes in guided mode velocities at different frequencies caused by fractional changes in radially varying mass density and shear and bulk moduli from a radially uniform reference state. A solution of this integral equation is based on extending the Backus-Gilbert (B-G) method for obtaining radial profile of a single to radial profiles of three formation properties away from the borehole surface. Inverted radial profiles from synthetic flexural and Stoneley dispersions have been validated against input formation parameters used to generate synthetic (measured) dispersions.

Analysis of noncircular fluid-filled boreholes in elastic formations using a perturbation model.

This paper presents a perturbation model to obtain flexural mode dispersions of noncircular fluid-filled boreholes in homogeneous elastic formations. The perturbation model is based on Hamilton's principle with a modified procedure for the reference state selection in order to handle the directional sensitivity of the flexural modes. The accuracy of the perturbation model has been confirmed by comparison to boundary integral solutions. Numerical results confirm that for a fast formation, even modes, and for a slow formation, odd modes are more sensitive to changes in the borehole elongation and azimuth. Even though the focus of this work is on elliptical boreholes and breakouts, the formulation is valid for any kind of noncircular borehole.

Stress- and temperature-compensated orientations for thickness-shear langasite resonators for high-temperature and high-pressure environment.

This paper describes an exhaustive study of the variations of the mean force sensitivity coefficients in the entire region of crystalline langasite (LGS). We also study the variation of temperature coefficients in the entire region of the crystalline LGS and its isomorphs. The computational results have been obtained from a procedure that has been successfully employed in the study of the planar and temperature stressinduced frequency shifts in thickness-mode resonators. Both the fast and slow thickness-shear modes have been studied. Among other things, the loci of orientations with zero stress and temperature coefficients of frequency have been identified for LGS.

Applications of piezoelectric materials in oilfield services.

Piezoelectric materials are used in many applications in the oilfield services industry. Four illustrative examples are given in this paper: marine seismic survey, precision pressure measurement, sonic logging-while-drilling, and ultrasonic bore-hole imaging. In marine seismics, piezoelectric hydrophones are deployed on a massive scale in a relatively benign environment. Hence, unit cost and device reliability are major considerations. The remaining three applications take place downhole in a characteristically harsh environment with high temperature and high pressure among other factors. The number of piezoelectric devices involved is generally small but otherwise highly valued. The selection of piezoelectric materials is limited, and the devices have to be engineered to withstand the operating conditions. With the global demand for energy increasing in the foreseeable future, the search for hydrocarbon resources is reaching into deeper and hotter wells. There is, therefore, a continuing and pressing need for high-temperature and high-coupling piezoelectric materials.

Inversion of guided-wave dispersion data with application to borehole acoustics.

The problem of inferring unknown geometry and material parameters of a waveguide model from noisy samples of the associated modal dispersion curves is considered. In a significant reduction of the complexity of a common inversion methodology, the inner of two nested iterations is eliminated: The approach described does not employ explicit fitting of the data to computed dispersion curves. Instead, the unknown parameters are adjusted to minimize a cost function derived directly from the determinant of the boundary condition system matrix. This results in an efficient inversion scheme that, in the case of noise-free data, yields exact results. Multimode data can be simultaneously processed without extra complications. Furthermore, the inversion scheme can accommodate an arbitrary number of unknown parameters, provided that the data have sufficient sensitivity to these parameters. As an important application, we consider the sonic guidance condition for a fluid-filled borehole in an elastic, homogeneous, and isotropic rock formation for numerical forward and inverse dispersion analysis. We investigate numerically the parametric inversion with errors in the model parameters and the influence of bandwidth and noise, and examine the cases of multifrequency and multimode data, using simulated flexural and Stoneley dispersion data.