Modeling sub-resolution porosity of a heterogeneous carbonate rock sample

Accurately estimating the petrophysical properties of heterogeneous carbonate rocks across various scales poses significant challenges, particularly within the context of water and hydrocarbon reservoir studies. Digital rock analysis techniques, such as X-ray computed microtomography and synchrotron-light-based imaging, are increasingly employed to study the complex pore structure of carbonate rocks. However, several technical limitations remain, notably the need to balance the volume of interest with the maximum achievable resolution, which is influenced by geometric properties of the source-detector distance in each apparatus. Typically, higher resolutions necessitate smaller sample volumes, leading to a portion of the pore structure (the sub-resolution or unresolved porosity), that remain undetected. In this study, X-ray microtomography is used to infer the fluid flow properties of a carbonate rock sample having a substantial fraction of porosity below the imaging resolution. The existence of unresolved porosity is verified by comparisons with nuclear magnetic resonance (NMR) data. We introduce a methodology for modeling the sub-resolution pore structure within images by accounting for unresolved pore bodies and pore throats derived from a predetermined distribution of pore throat radii. The process identifies preferential pathways between visible pores using the shortest distance and establishes connections between these pores by allocating pore bodies and throats along these paths, while ensuring compatibility with the NMR measurements. Single-phase flow simulations are conducted on the full volume of a selected heterogeneous rock sample by using the developed pore network model. Results are then compared with petrophysical data obtained from laboratory measurements.