Anisotropic rock physics templates constructed by the Mori–Tanaka-Benveniste Method and evaluated with classical micromechanics modeling and experimental data

Abstract

Lithologic and elastic interpretations of reservoir rocks and minerals are critical steps in hydrocarbon exploration and production. In this work, we developed an anisotropic micromechanical scheme known as the Mori–Tanaka-Benveniste Method (MTBM) to compute the effective elastic properties of isotropic and anisotropic composites. This led to the creation of new Anisotropic Rock Physics Templates (ARPTs), represented as Ternary Diagrams based on Young’s moduli and Poisson’s ratios, considering factors such as mineralogy, porosity, pore fluid type, and pore geometry. An essential aspect of this research is the pore aspect ratio (\(\alpha\)), a critical parameter influencing pore shape and significantly impacting rock characterization, pore fluid behavior, and mineralogy. We explored an isotropic scheme with a pore aspect ratio of \(\alpha =1\) (spherical pores). We compared it against established methods, including the Perfectly Disordered Method (PDM), Self-Consistent Method (SCM), and classic models like the Hashin–Shtrikman schemes, using Berea sandstone as a reference sample. The resulting ARPTs were constructed as Ternary Diagrams based on calcite, quartz, and clay, utilizing pore aspect ratios of 0.1 and 0.5 (representing aligned spheroidal pores). These templates were applied to various anisotropic samples and formation data, including Bazhenov, Niobrara, Lockatong, Woodford, Chicopee, and a Shale sample from 5000 ft depth, where they demonstrated a strong fit. MTBM provides analytical solutions in a tensorial form that minimizes numerical complexity, presenting a significant advantage over classical self-consistent approaches. This innovative integration of micromechanical modeling with petrophysical analysis enhances the understanding of reservoir characteristics and supports more effective hydrocarbon exploration and production.