Throat Finding Algorithms based on Throat Types

Abstract: The three-dimensional geometry and connectivity of pore space determines the flow of single-phase incompressible flow. Herein I report on new throat finding algorithms that contribute to finding the exact flow-relevant geometrical properties of the void space, including high porosity samples of X2B images, three-dimensional synchrotron X-ray computed microtomographic images, and amounting to over 20% porosity. These new algorithms use the modified medial axis that comes from the 3DMA-Rock software package. To find accurate throats, we classify three major throat types: mostly planar and simply connected type, non-planar and simply connected type, and non-planar and non-simply connected type. For each type, we make at least one algorithm to find the throats. Here I introduce an example that has a non-planar and simply connected throat, and my solution indicated by one of my algorithms. My five algorithms each calculate the throat for each path. It selects one of them, which has the smallest inner area. New algorithms find accurate throats at least 98% among 12 high porosity samples (over 20%). Also, I introduce a new length calculation in the digitized image. The new calculation uses three mathematical concepts: i) differentiability, ii) implicit function theorem, iii) line integral. The result can convert the discrete boundary of the XMCT image to the real boundary. When the real boundary has an arc shape, the new calculation has less than 1% relative error.