Publications

Pore shape and geometry are essential in determining the elastic properties of porous rocks, as they influence fluid content, which affects the bulk response. In carbonate reservoirs, complex (primary and secondary) porosity creates additional challenges because of the wide variation in pore shapes and sizes, from nanoscale to meter scale. This variability complicates the development of rock physics models.

Rock Physics, grounded in effective medium theory (EMT), characterizes rock properties by understanding seismic wave propagation, which in turn depends on the rock’s stress-strain relationship. When pore fluids are included, the objective shifts to correlating seismic-derived impedance and elastic parameters—such as Young’s, Shear, and Bulk moduli—with specific rock properties.

EMT-based analytical models are widely used in geophysics to study rocks’ macroscopic properties, including seismic velocities, mineral shapes, sizes, volumes, and elastic moduli. These properties are influenced by the mineral composition, porosity, and saturation of the rock. EMTs provide approximations of a medium based on the properties and proportions of its key components.

Among the most recognized EMT approaches are Differential Effective Medium (DEM) and Self-Consistent Approximation (SCA). The DEM model involves adding inclusions incrementally into a host material, useful when inclusions do not form a continuous network, producing effective elastic moduli within known bounds for heterogeneous media. The SCA model provides an iterative approach, inserting inclusions into an unknown background medium and finding a self-consistent solution that can account for multiple components.

In this paper, we develop two effective medium models that incorporate pore shape data into DEM and SCA models using statistical and machine learning techniques. Our results demonstrate that the DEM model yields superior outcomes in partitioning porosity within carbonates compared to the SCA model. This advancement could improve predictive models for complex carbonate reservoirs, aiding in more accurate assessments of rock and fluid properties.