Resolution of Interfaces, Curvatures, and Common Lines in General Porous Media

Multiphase porous medium systems present a number of modeling challenges that have yet to be resolved. Studying processes as they occur within the pores provides a basis for the development of both an improved fundamental understanding and more reliable larger scale mathematical models. In order to accomplish these small scale studies, information must be extracted about the morphology and topology of the phases using data sets derived from pore-scale experiments or simulation. Of particular interest are the interfaces between phases, but also of potential importance are common lines forming at the intersection of three phases which have received only limited study in the porous medium literature. In most cases appearing to date, the marching cubes algorithm has been used to obtain an approximate representation of the surfaces. We build upon this work to design a variant of the marching cubes method that allows us to construct and quantify the interfaces and common line in a three-phase system with improved accuracy compared to methods reported to date. Values of the curvature of the interface between the fluid phases are also computed. The developed algorithms represent a significant improvement over the standard marching cubes algorithm for resolving porous medium morphology to study multiphase processes at the pore scale.