A Closed-Form Equation for Capillary Pressure in Porous Media for All Wettabilities

Abstract A saturation–capillary pressure relationship is proposed that applicable for all wettabilities, including mixed-wet and oil-wet or hydrophobic media. This formulation more flexible than existing correlations only match water-wet data, while also allowing saturation to be written as a closed-form function of capillary pressure: we can determine explicitly from saturation, vice versa. We propose $$P_{{\text{c}}} = + B\tan \left( {\frac{\pi }{2} - \pi S_{e}^{C} } \right)\,{\text{for}}\,0 \le S_{{\text{e}}} 1,$$ P c = A + B tan ? 2 - S e C for 0 ? e 1 , where $$S_{{\text{e}}}$$ the normalized saturation. indicates wettability: $$A>0$$ > medium, $$A<0$$ < small suggests mixed wettability. B represents average curvature pore-size distribution which much lower in compared media with same pore structure if menisci are approximately minimal surfaces. C an exponent controls inflection point asymptotic behaviour near end points. model accurately 29 datasets literature water-wet, media, rocks, soils, bead sand packs fibrous materials over four orders magnitude difference permeability porosities 20% nearly 90%. apply Leverett J-function scaling make expression dimensionless discuss analytical solutions spontaneous imbibition.