Application of rock physics modelling to investigate the differences between static and dynamic elastic moduli of carbonates

Abstract

SUMMARY The elastic moduli estimated through geophysical studies carried out in wells (logging data) differ from those obtained from the triaxial tests conducted in laboratory on the available core samples. Terminologically former and latter are referred to as dynamic and static elastic moduli, respectively. Since the structural characteristics of rocks at the different scales, from micrometre to larger scales (tens of metre), are the controlling parameters of their dynamic and static moduli and their difference at the respective scale, in this study we aim to investigate the influence of the measurable (or quantifiable) parameters of the pore space on these elastic moduli. To do so, 19 dry carbonate samples of different structural characteristics were collected. Their basic petrophysical properties such as porosity and permeability were measured in laboratory. The ultra-sonic tomography was carried out to determine the heterogeneity degree, anisotropy system and average acoustic wave velocities for each core sample. SEM images were analysed to investigate the visual textural properties. The mineralogical composition of these samples was determined by the X-ray diffraction method. Based on the conducted experimental studies and using of the effective medium theory, a unique rock physics model (‘petroelastic model’) was constructed for each core sample. The average (effective) microstructural parameters characterizing the pore space of the studied carbonate samples, along with their elastic moduli were estimated through solving the inverse problem and the measured acoustic wave velocities. A multistage statistical approach, including computation of correlation coefficients, optimized regression analysis, factor analysis and bootstrap resampling, was suggested to investigate the effect of each microstructural parameters on the static and dynamic Young's moduli, ratio of dynamic to static Young's moduli (k-value), dynamic Poisson's ratio and mechanical properties (including unconfined compressive strength and internal friction angle). The obtained results show that the microstructural characteristics have different degrees of influence on the elastic moduli and can be successfully classified based on their physical nature. It was also concluded that the dynamic Poisson's ratio is independent of the studied, in this work, microstructural parameters.