The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure

Abstract

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 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. We used a data set consisting of 323 samples from different lithologies including tight, sandstone and carbonate reservoirs. The semi-analytical (Huet) model correlates permeability with porosity (), irreducible wetting phase saturation (Swi), displacement pressure (pd), and the pore-size distribution index () obtained from MICP data. The resulting correlation equation generated in this work shows very good coherence for permeabilities higher than 1 md and reasonably good coherence for permeabilities less than 1 md. In this work we have refitted the Huet model to our database of 323 samples and over the entire range of permeabilities considered (i.e., 1x10^-7 to 1x10^4 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% 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 showed in this work that our proposed model outperformed 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. Based on this derivation, we propose a new method to determine the Brooks-Corey capillary pressure model parameters as an alternative to the regression method. In short, this work has confirmed the power-law relationship between permeability and the mercury injection capillary pressure data to be valid for both sandstone and carbonate reservoirs. The new correlation model proposed should provide an improvement for the prediction of permeability from the mercury injection capillary pressure data. This work also holds promise in relating the Huet semi-analytical model to the Swanson empirical model directly, and we expect that (eventually) a type of "hybrid" model will evolve which will include the influence of both the Brooks-Corey and the Swanson capillary pressure models.