Reliable Quantification of Pore Geometry in Carbonate Rocks Using NMR and Electrical Resistivity Measurements for Enhanced Assessment of Permeability and Capillary Pressure

Reliable and real-time assessment of directional permeability and saturation-dependent capillary pressure are utterly important because they significantly affect the exploitation strategies. Conventional well-log-based methods (e.g., NMR-based, saturation-height analysis, resistivity-based, correlation-based) are either highly dependent on calibration efforts or rely on model parameters which are difficult to obtain in real-time and make them dependent on core measurements. Moreover, most conventional methods for assessment of directional permeability and saturation-dependent capillary pressure fail in the presence of multi-modal pore-size distribution. Recent publications suggested that integration of transverse Nuclear Magnetic Resonance (T2 NMR) and resistivity measurements enables assessment of pore-throat-size distribution as well as permeability and capillary pressure. However, the reliability of these methods is questionable in rocks with complex/multi-modal pore geometry. The objectives of this paper include (a) reliably estimating a variable constriction factor (a geometric parameter which relates the pore- and throat-size) in rocks with complex pore geometry to accurately quantify pore geometry, which is the main contribution of this work, (b) developing a new rock physics workflow for integrating NMR and electrical conductivity for assessment of permeability and capillary pressure that takes into account a variable constriction factor, and (c) verifying the reliability of the introduced workflow using core scale measurements. The proposed workflow starts with calculating pore-body-size distribution from NMR T2 distribution. Then, we combine electrical resistivity and pore-size distribution to estimate the distribution of constriction factor in the pore structure. Next, we determine pore- throat-size distribution using the estimated variable constriction factor. We then introduce a new permeability model which takes variable constriction factor into account. The inputs to the permeability model include throat-size distribution, tortuosity, and porosity. Finally, we calculate saturation-dependent capillary pressure using the estimated throat-size distribution. We successfully verified the reliability of the introduced workflow in the core-scale domain in carbonate rock samples with complex pore structure. The permeability estimates obtained by the new workflow yielded less than 7% average relative error when compared against core measurements. We also observed a good agreement between the throat-size distribution and capillary pressure estimated from the new workflow and the ones acquired from MICP (mercury injection capillary pressure) measurements. Results also confirmed that integration of a variable constriction factor improves directional permeability estimates compared to cases where an effective constriction factor was used to quantify pore-throat size distribution in rocks with multi-modal pore-size distribution.