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# Auto Cluster Ratio

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# Auto Cluster Ratio

Percolation involves forcing a non-wetting fluid into a porous material.  If it encounters a small pore-throat, then it will not intrude until sufficient pressure is applied.  When an appropriate pressure is reached, it will intrude everything accessible beyond that pore-throat, until it encounters voids that are even smaller.  So the intrusion may be into a single pore, or a cluster of voids larger than the pore-throat that are all connected to each other with connections larger than the pore-throat.  Traditionally, the single pore assumption has been made.  However, that is usually very wrong.  To understand why, it is essential to download and read our 2018 publication.

(To understand the range of possible Cluster Ratio values, and how to enter a Cluster Ratio manually, see Manual Cluster Ratio. )

Since that publication, we have carried out much programming work, and you now have the unique ability to identify which pores are probably clusters.  Having read our publication, you will realise that a criterion for correct choice of Cluster Ratio is that the total void size distribution does not kink at maximum size.  Having tried many methods to find an objective method to determine that, which works for a range of different sample types, we have chosen a method whereby the second derivative of the total void size distribution is extrapolated to maximum size, and then the second derivative of the kink at the highest size is compared to the extrapolated value. If that is greater than or equal to 3 (the default setting), then the cluster ratio is chosen.

In practice you do not have to worry about the science, mathematics and programming.  The increment and test ratio settings are set for you to the values shown below, and the maximum number of increments is set automatically to cover the valid range.

Click Run sequence at the bottom of the screen, wait for the search for Cluster Ratio to be successful, and you should get a meaningful answer (although for small unit cells, less than 15x15x15, the algorithm is likely to crash or give an anomalous answer). Note that the cluster ratio is only defined to 2 decimal points at most, so do not worry about imprecision - differences in cluster ratio at higher precision make no difference.  In some samples, all voids are found to be clusters, whereupon the cluster ratio = 1, and you will be told of that.

The cluster ratio is the means to an end - the absolute value of the number itself means little, and may vary between stochastic realisations.  What are important are the details of the void size distributions that the auto cluster (or manual cluster) generates.

Once the cluster ratio has been found, click Accept.  You will be taken back to the Operations List.  The outputs can be viewed by clicking on Unit Cell Building, and looking at e.g. 3D full-screen view, whereupon the clusters are shown stippled. Also you can click on Size Distribution. As this calculation is new for PoreXpert version 2.0, it has not yet been propagated into other simulated properties - see our void size and permeability validation for the consequence of that on the microtoming simulation.