A simulation and data informed approach to porosity partitioning

Information about pore shape and geometry form one of the significant inputs in determining the effective elastic properties of porous rocks. The size and structure of the pores determine the amount of fluid contents which in turn determine their bulk response. Conventionally, effective medium models have been used to study the macroscopic properties of these rocks. These models often use a fixed set of microscopic variables (like the shape parameter) to describe their bulk behavior. Barring the specification of the elastic properties of the starting host material, their original formulations often lack the provision to integrate any experimental data, later. In the context of carbonates, the rocks exhibit a large variation in pore shapes and sizes, hindering the development of rock physics models. Therefore, they eventually require calibration. This is an important issue as the size of the pores here range from nanoscale to meter scale due the presence of primary and secondary porosity systems. In this paper we develop a method that can integrate the pore shape information into differential effective medium models using simple statistical and machine learning algorithms. Avoiding the use of conceptual values for the interparticle and vug type pores, our technique facilitates a data-based inference of the shape parameters from both the image data and forward model simulations. Micro-tomography images were used to extract the pore shape information for relatively larger pores such as the vugs. The information about the interparticle pores was deduced using a simulation-based approach from well-logs. Both of these were used to specify the properties of the new inclusions, hence aiding in data informed porosity partitioning. Finally, we outline a simple regression-based scheme using a first order polynomial model that can be used to calibrate any general rock physics model.