The geometry of primary drainage

Area of Science:

• Pore-scale physics
• Computational geometry
• Geology

Background:

• Understanding fluid flow in porous media is crucial for various geoscience applications.
• Capillary pressure and meniscus configuration govern fluid distribution during primary drainage.
• Existing methods for predicting entry pressure have limitations in accuracy for real pore structures.

Purpose of the Study:

• To develop a computational geometry-based method for determining arc meniscus configuration in capillary tubes and porous media.
• To accurately predict entry pressure and meniscus radius during primary drainage.
• To evaluate the effectiveness of geometric parameters in predicting these properties.

Main Methods:

• Applied medial axis analysis from computational geometry to model arc meniscus configuration.
• Developed a solution for arbitrary polygonal cross-sections at various pressures and wetting angles.
• Analyzed over 21,500 throats from computed tomography images of Fontainebleau sandstone core samples.

Main Results:

• The ratio of throat area (A) to throat perimeter (P) was identified as an excellent predictor of entry pressure meniscus radius and entry pressure.
• Medial axis analysis provided highly accurate solutions for meniscus radius.
• Inscribed and area equivalent radii were found to over-predict meniscus radius by 1.5-3 times, proving to be poor predictors.

Conclusions:

• The A/P ratio offers a robust and accurate method for predicting entry pressure in primary drainage for real porous materials.
• Medial axis analysis provides a powerful theoretical framework for understanding pore-scale fluid configurations.
• This approach enhances the prediction of fluid flow behavior in rocks and soils.