Evaluation of Biot's Coefficient Using Sonic Logs and Elastic Moduli Minimization

Abstract

Biot's coefficient is one of the key parameters in estimating effective stresses, leading to understanding of the three stresses spatial distribution, namely vertical, minimum and maximum horizontal. Ultimately, these stresses shape up the behavior of a geomechanics model (either in 3D or in 1D). Thus, the robustness of any geomechanics model significantly depends on the precision of Biot's coefficient estimation. The proposed technique allows evaluating isotropic and anisotropic Biot's coefficients based on the log responses independent of the geological environment. The methodology is based on elastic moduli-minimization. In isotropic case, Bulk rock frame and Bulk rock grain moduli minimization produce the best fit to the measured Density, DTP and DTS. Then, isotropic Biot's coefficient can be computed directly. In the case of anisotropy, additional control on lamination is required. This can be achieved by comparing estimated laminated and dispersed clay volumes based on the anisotropic rock-physics model and derived from the Thomas-Stieber plot or any alternative lamination analysis technique. Anisotropy modeling allows to produce five independent VTI elastic moduli and as a result to compute anisotropic Biot's coefficient. The methodology has been tested in several fields: clastic (Western Siberia, Norwegian offshore, Argentina unconventional) and carbonates (Brazil, Middle East, North Sea chalks). It produces reliable results in all cases. This study shows good agreement of the Biot's coefficient computed from the proposed methodology with measurements of core-based Biot's coefficients. In practice, core-based Biot's coefficient measurements are rarely available and quite often done on a few samples, taken in the reservoir section only. The proposed methodology allows reliable estimates of Biot's coefficient for the entire wellbore section, where density and sonic logs are available. It utilizes a minimization technique instead of using geomechanics correlations. Thus, it is applicable for any rocks and geological settings and is not bounded to the area or formation compared to correlations specific to the particular formation. The novelty of the method is in the process of elastic-moduli minimization based on logs and allows direct extraction of the Biot's coefficient. Previous works were either concentrating on principles of the laboratory Biot's coefficient measurements or focusing on the correlations derived from core tests. Correlation derivation requires a significant number of core tests conducted for the same geological settings. However, the proposed methodology requires a few core samples for Q.C. purposes only.