Acoustic anisotropy measurements and calibration of the non-hydrostatic in-situ stresses in a wellbore.

Abstract

The comparison of the static and dynamic stress-strain data (measured from borehole strain gages and velocities) indicates that velocities have to be calibrated according to the rock type to take into account the specific rock mechanical properties and their stress anisotropy dependence when stresses are estimated from the velocities in and around the borehole geometry. Also, estimated in-situ stresses from borehole velocity measurements based on the non-linear model that is currently used by the industry showed significant difference in the magnitude of the actual experimentally measured stresses; yet, an empirical calibration at this stage is necessary for each type of reservoir.

Quasi-static and dynamic uniaxial compressive tests were performed initially on cylindrical core samples corresponding to the different types of rock to evaluate their mechanical properties and their stress dependency which then were used to calibrate the measurements on large cubical block samples. Furthermore, the uniaxial compressive tests under small strain loading and unloading procedures were used to correlate the quasi-static and dynamic behaviors of each rock type and extrapolate them with the measurements performed on the large cubical block samples with the borehole geometry included.

The purpose of the work reported in this dissertation is to estimate experimentally the effect of both inherent and stress-induced anisotropies on rock mechanical properties and on the in-situ stress measurements within the geometry of the borehole for different types of rock. In particular, the effective in-situ stress estimation is immediately linked to the pore pressure coefficients (also known as Biot's effective stress coefficients), which relate total stresses with pore pressure and weighs the effect of the pore pressure on the value of effective stresses according to Terzaghi's principle.

In-situ stress induced anisotropy and inherent rock formation anisotropy have in many instances been hard to distinguish by most deep in-situ tools designed to estimate the deep earth stress anisotropy and/or rock inherent anisotropy. In the oil and gas industry, in particular, the prior knowledge of the magnitude of in-situ stresses is essential in many aspects including exploration, well planning, reservoir stimulation, reservoir subsidence, and production. Present techniques for measuring rock stresses in a borehole can predict two out of the three principal stresses with acceptable engineering errors. These are the vertical and the minimum horizontal stresses. However, the measurement of the maximum horizontal stress remains the least explored. Moreover, the presence of intrinsic rock anisotropy around the borehole, along with the in-situ stress anisotropy, makes an accurate estimation of the latter extremely challenging when using acoustic techniques.

The role of both inherent and stress-induced anisotropies on stiffness components, elastic moduli, and Biot's pore pressure coefficients using both acoustic and quasi-static measurements is first investigated. Lyons Colorado sandstone cores with observable finely-layered dipping beds are assumed to exhibit a transverse inherent anisotropy. The core samples are used and tested under a non-hydrostatic state of stress to emphasize and maximize both inherent and stress-induced effects on the measurements. The effect of stress-induced anisotropy appears to have significant control on measured stiffness components, elastic moduli, and Biot's effective stress coefficients compared with inherent anisotropy effect. For example, the presence of transverse inherent anisotropy in these sandstones has shown an increase in the magnitude of the Biot's effective stress parameter in transverse plane by 16% whereas a reduction of 60% is observed in the same plane due to the stress-induced anisotropy over an applied stress range of 21,000 psi.

The measured induced tangential compressive stresses at the borehole for the tested rock materials were found to be non-linearly correlated with the external applied stress at the boundary. As a result, assumptions of borehole stress concentration factor of 3 based on Kirsch's equations for a uniaxial stress field may under or over estimate the actual induced compressive stresses at the borehole wall in rocks. Four empirical correlations were reported for each rock type being tested that estimate the maximum induced compressive stresses at the borehole by knowing the uniaxial far field stresses. The measurements show that stress magnitude measured at the wellbore wall varies considerably depending on the type of rocks being tested and their stress dependence has to be taken into account for stress estimation. Borehole failures, including breakouts, were observed during the rock experiments and confirmed from borehole strain measurements. The applied boundary stress level at which tensile failure and breakouts occur at the borehole is observed to be correlated with the measured tensile strength from Brazilian tests and the uniaxial compressive strength of each tested rock material, respectively.

In the second part of this work, the technique of estimating the in-situ stresses is revisited by studying experimentally the effect of stresses on borehole strains, displacements, and acoustic wave velocities within the theory of elasticity. The experiments involve measurement of acoustic velocities (compressional and shear), radial, axial and transversal strains, and corresponding displacements around a borehole for different rock types including Berea sandstone, chalk, white limestone and Pierre shale. The borehole strain, displacement, and velocity measurements were first conducted on an aluminum block sample to validate the measurements by comparing them with the theoretical behavior of such medium from the dynamic and static equations of elasticity. The borehole acoustic measurements for aluminum showed constant velocities as a function of stress indicating that properties of the material do not vary with stress (i.e., Young's modulus and Poisson's ratio). The basic understanding of aluminum behavior under applied stress was then extended for the rock samples.