In 2005 Huet proposed a semi-analytical model to correlate between rock permeability and capillary pressure data. The model was proposed with the intention to be a "universal" model where the correlation was to be unique over a wide range of rock types. The objectives of this study are to verify the power-law relationship between permeability and the mercury injection capillary pressure (MICP) parameters in Huet's semi-analytical model and to propose a new correlation to predict permeability from the MICP data. The semi-analytical (Huet) model correlates permeability with porosity (ϕ), irreducible wetting phase saturation (Swi), displacement pressure (pd), and the pore-size distribution index (λ) obtained from MICP data.
In this work we have refitted the Huet model to our database of 323 samples from different lithologies including tight, sandstone, and carbonate reservoirs. The resulting correlation equation generated in this work shows very good coherence for permeabilities greater than 1 md and reasonably good coherence for permeabilities less than 1 md. Over the entire range of permeabilities considered (i.e., 1×107 to 1×104 md), 95 percent of the data are related to the proposed model by a factor of 9.1 or less, and 58 percent of the data are related to the proposed model by a factor of 2 or less. When the data are "partitioned," we find that our refitted model has a 95 percent prediction interval within a factor of 3.97 for permeability values greater than 1 md and 12.70 for permeability values less than 1 md. We also show in this work that our proposed model (slightly) outperforms the Swanson model to predict permeability from MICP data.
In addition to the statistical work, we performed analytical derivations to establish an analytical relationship between the semi-analytical (Huet) model and the Swanson model. Our derivation results support the application of the semi-analytical model as a viable (and possibly superior) alternative to the Swanson model. Our analytical work also provides an insight into the viability of the Swanson model, which was developed empirically.
