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## Tortuosity |

The tortuosity is defined as the tortuous path taken by an ion through the unit cell, compared with the length of the direct path through the unit cell, i.e. the unit cell size in the z-axis direction.

The calculation takes a very long time for large unit cells, up to a few days, so we recommend you consider using batch mode so that it runs in the background.

The tortuosity operation screen allows choice of two different type of tortuosity, based on the diffusion of dissolved ions, or liquids (or dense gases not exhibiting Knudsen flow - i.e dense gases, or less dense gases in void networks with no narrow (< 1 μm) throats ), as explained further in the tortuosity background science section.

Tortuosity operation screen

The algorithm outputs a histogram of the lengths of paths taken through the cell. We define the tortuosity as the median value of the distribution of path lengths, which is shown as a green line on the output graph.

Tortuosity output for a 10 x 10 x 10 unit cell representation of deltaic sandstone

The y-axis displays the probability of the relative path length. Note that in the illustrated case the x-axis starts at 1.2. This is the shortest path length discovered by the algorithm, so below this value, the probabilities of paths are not defined. At the first value, in this case a 46% probability of a path length of 1.2, both the Average Probability (i.e. the probability of that particular path length) and the Cumulative Probability (i.e. the probability of all paths of 1.2 or shorter) are the same. The single-valued tortuosity is taken to be the median path length. This is a more stable statistic than the mathematical average, because it is less affected by extreme high values of the distribution, even when these values have low probability.

After clicking Accept on the Output screen, you will be returned to the Operations list, which will display the single valued (median) tortuosity.

Tortuosity result shown on the Home screen