Model-Free Relative Permeability Estimation and Oil Recovery Prediction in Reservoir Rocks from Capillary Pressure Curves

Elena M. Avraham 

This paper presents and validates a model-free method for predicting the relative permeability and oil recovery of reservoir rocks directly from the shape of the capillary pressure curve, tested against real reservoir core, digital rock models, and a large soil-hydraulic dataset. Relative permeability is the key saturation function governing production forecasts, water cut, and oil recovery in reservoir simulation, yet its direct measurement requires costly special core analysis (SCAL), while capillary pressure curves are obtained routinely and at low cost from mercury injection porometry (MICP) or capillarimetry. We introduce a spectral relative-permeability exponent, computed as the mean logarithmic slope of the Mualem integral kernel, requiring no selection or fitting of a parametric capillary pressure model; the classical Brooks–Corey exponent emerges as its limiting special case. On real Berea sandstone reservoir core from two independent published datasets — oil as the wetting phase and gas as the non-wetting phase — the method reproduces the measured relative permeability with a logarithmic coefficient of determination of 0.995 and 0.978, respectively, using a single calibrated scale factor and no fitted shape parameters. On four digital rock models (Bentheimer and Doddington sandstones, Estaillades and Ketton limestones), the exponent predicted from capillary pressure alone agrees with pore-network flow simulation on the same segmented pore geometry, with a logarithmic coefficient of determination of 0.82–0.98. Statistical robustness is further confirmed on a combined dataset of 283 real capillary pressure/relative permeability pairs, where the method matches the accuracy of the best-fitting parametric models without fitting any shape parameters. Beyond validation, the method quantifies its own fundamental limit: the residual gap to the best achievable power-law fit is shown to be structural, linked to pore-space connectivity, rather than random noise. A closed-form analytical expression for the sensitivity of the water-free oil recovery factor to the exponent enables a confidence interval for oil recovery to be constructed from a single capillary pressure curve, and an economic criterion is formulated for the cost-effectiveness of direct flow experiments, expressed in barrels of movable oil. The results provide a laboratory- and pore-scale-validated basis for core analysis optimization and for populating geological and reservoir simulation models with saturation functions at scale, particularly relevant for hard-to-recover reserves and polymodal carbonate reservoirs.