What makes a petrophysical model robust is the understanding of the relationships between its petrophysical properties, typically porosity, permeability, and saturation. In carbonates, and particularly in limestones, the pore geometry and connectivity are often not uniform which can lead to lack of correlation between porosity, permeability, and saturation.

This study explains how the combination of core analyses, Nuclear Magnetic Resonance (NMR), and borehole image logs was used to build a permeability transform that considers the pore size distribution and connectivity. The permeability model is based on a dual medium pore network concept that combines the macro pore network with the micro and meso pore network according to their relative pore volume. The saturation height functions are defined based on the rock characteristics that honor the capillary pressure (Pc) core data behavior.

The comparison of the pore size partitioning from NMR logs or borehole image processing with the core description and digital core photos provided important information on how to process and interpret both log and core data. The pore size distribution was associated with depositional and diagenetic processes that were used during the 3D modeling of the macro porosity. After the porosity and the macro-porosity were modelled using geological concepts and geostatistics, the permeability in the 3D static model is directly computed using the function defined from core and logs. The saturation height functions (SHF) are defined from routine and capillary pressure (Pc) core data to be consistent with the pore size classification used to define the permeability model. The saturation height modeling is ultimately adjusted by combining the free water level (FWL) from pressure data, SHF from Pc data, and log-derived water saturation.

All the properties of the model are consistent between each other and can be updated with new wells very easily since only porosity and its macro porosity volume need to be re-populated with the data from the new wells.

The construction of empirical permeability models in particular in carbonates that use the pore size distribution has been established in the past generally at the core to log level. This work revisits the construction of those analytical permeability models by using a dual-media pore network concept and illustrates the advantages to use those functions directly in the 3D modeling construction and update.

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