A New Capillary Pressure Model from Fractal Characterization of Porous Medium: A Case Study from Malaysia

Abstract

Capillary pressure is an essential input in reservoir modeling and simulation. Laboratory
measurements of capillary pressure are costly and time-consuming; hence, a limited number of core plugs
are tested, and capillary pressure models were required to fill this gap. Several capillary pressure models
were presented in the literature to match the measured laboratory data, e.g., Brooks and Corey’s model.
However, matching capillary pressure remains a challenge for reservoir engineers and petrophysicists. On
the other hand, various publications demonstrated the fractal characteristics of porous media and employed
the fractal theory to develop capillary pressure models for drainage and imbibition processes. This study
developed a new capillary pressure model by representing the pore structure as bundles of capillaries with
equilateral triangular cross-sections whose inscribed radii follow a fractal distribution. Using triangular
tubes reflects the angularity of the actual pores; therefore, providing a better representation of the pore
structure. The genetic algorithm, GA, is then utilized to match the measured capillary pressure and
determine the parameters of the developed model. Capillary pressure data for five core samples from an
offshore well in Malaysia were used to validate the developed model. The error analysis indicated that the
fractal model matches the experimental data with reasonable accuracy. Moreover, compared with Brooks
and Corey’s model, the newly developed fractal model provides a better match to the experimental data,
especially for low permeability rock samples.