Modelling of Drainage Capillary Pressure: A Comparative Study of Various Analytical Capillary Pressure Formulations in Matching Laboratory Results

摘要

Capillary pressure relationships (drainage) is of importance in both, reservoir engineering and petrophysics. Reservoir engineers use capillary pressure relationships in reservoir engineering calculations and petrophysicists use such relationships in saturation-height modelling. The overall objective of the study presented is to perform a comparative study of various capillary pressure models commonly used by the petroleum industry and to access their ability to match diverse laboratory data. Over the years many capillary pressure formulations have been proposed to match laboratory data, from the well-known Leverett J-function approach to more recent methods. Generally, formulations may be theoretical, semi-empirical, empirical or statistical basis. The comparative study presented involves the following analytical formulations: modified Leverett J-function, modified Brooks-Corey (MBC), Thomeer, Skelt-Harrison, Lambda (λ) and the more recently established, Modified Carman-Kozeny-Purcell (MCKP) model. Various types of pore structures may be modelled: homogeneous (narrow), broad (poorer sorting) and bimodal (two distinct distributions) where one of the distributions is often related to pore-fill, or a mixture of distribution types. Results presented in this paper compare application of the above-mentioned methods for homogeneous plugs. It is demonstrated that the MCKP method consistently outperforms the other methods and it is the only method that is able to identify the type of pore throat distribution without any further input data. The advantage of the MCKP method is that it does not contain any fitting parameters. The degree of accuracy of the MCKP model is typically R~2 > 0.99. The MCKP model also lends itself very easily to predict capillary pressure relationships from more basic parameters. Presented are examples with data from two Australian fields, one offshore and one onshore.