Transverse Anisotropy in Biot's Constant through Dynamic Measurements on Cordoba Cream Limestone

Abstract

Abstract Biot's constant is an important poroelastic parameter that has a major influence on various petroleum-related rock mechanical applications. It is needed to compute the in-situ stresses accurately (σ' = σ − α*pr, or effective stress = total stress - Biot's constant * pore pressure). The in-situ stresses play a key role in the design of hydraulic fracturing, sanding tendency prediction, and in optimizing borehole trajectory to combat instability problems in drilling. In regards to in-situ stress and Biot's constant, most rocks are not isotropic, as is commonly assumed in many of the above applications. This leads to inaccurate determination of key parameters resulting in hole failure or loss of productivity, which translate into losses amounting to millions of dollars. This underscores the importance of determining the Biot's constant experimentally. In most cases where Biot's constant is used, it is either assumed or derived empirically. Another aspect of this assumption is that the directional variation of Biot's constant is not considered at all, which results in further approximation. To address both these problems, we have developed a laboratory testing procedure to evaluate the dynamic (ultrasonic) transverse anisotropy in Biot's constant on Cordoba Cream limestone samples obtained from a quarry in Texas. Cylindrical samples (NX-size) were cored from cubical blocks and were subjected to triaxial and hydrostatic compression stress paths in a triaxial cell. Ultrasonic compressional and shear waves were transmitted in both axial and radial directions and travel times were recorded simultaneously with load and deformation recordings. Biot's constant was evaluated as a function of axial and confining stresses in both axial (αv) and lateral (αh) directions, thus allowing for anisotropy determination. Dynamic values of Biot's constant obtained in the axial direction are compared with those obtained from static rock mechanical measurements. Results show that the limestone material behaves in a transversely anisotropic manner, with dynamic αv values being lower than the corresponding αh at almost all confining and deviatoric (shear) stresses. With increasing deviatoric stress, αv was found to decrease slightly or remain constant, while αh increased considerably. A comparison between static and dynamic values shows that αv obtained statically is more than αv obtained dynamically, for all confining pressures and deviatoric stresses. The information presented in this paper shows that the Biot's constant is not a constant; rather, it is dependent on stress magnitude as well as principal stress directions. We present a case study to show the optimization of borehole trajectory in terms of mud weight as a function of borehole inclination. It is found that the computed critical mud weight is considerably sensitive to Biot's constant and its directional variation, when the borehole inclination is greater than 40°. Similar case studies can be shown on hydraulic fracture design and sanding tendency prediction also, which will be discussed in subsequent papers.