Irregularly-bounded cross sections’ shape factors from high-order piecewise-polynomials

Abstract

In a two-dimensional domain, bounded cross-sections are interpretable from the generalized concept of “aperture” and embrace uncountable applications. Shapefactors for apertures confined by irregular boundaries are much less known than regular ones. Besides, they are poorly estimated due to restrictions in experimental measurements of underlying properties and do not have immediate determination. An example is the estimation of the Kozeny constant in models derived from the classical Kozeny-Carman equation. This paper presents a numerical Galerkinbasedintegral (GBI) model that computes shape factors for apertures confined by arbitrary boundaries, thus filling a knowledge gap regarding shape factor determination. The technique relies on two underlying pillars: accurate boundary reconstruction by high-order piecewise polynomials and shape factor recovery using the Poiseuille number. The GBI technique treats the fluid flow as fully developed under the laminar regime, thus allowing a reasonable comprehension of the cross-sectional dynamics. Our study stands on realistic apertures modeled from rock core samples and is additive to understanding transport mechanisms in fractured media. The outcomes are specifically helpful for people who deal with fluid injection of any kind and need to compute shape factors for ducts, fissures, or cracks, either for biotechnology, engineering, or medical applications.