  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.
