The permeability algorithm calculates the network capacity for any of the liquids or gases in the materials database, which is related to the absolute permeability of the network. PoreXpert does not yet automatically calculate relative permeabilities.
Background
The network capacity is based on the flow capacity of the simulated void network for the trickle flow of non-compressible fluids. Each arc of the network has flow capacity Farccalculated from parametrized Navier-Stokes equations (Matthews, Canonville and Moss, 2006):
where h is the length of a throat of radius r connecting two cubic pores with sides L1 and L2, respectively, and λ is the mean free path between collisions in the fluid.
Except for very straight forward pore networks, such as those within clean, highly porous outcrop sandstone and track etch membranes, the network capacity is less than the actual absolute permeability. The extent of the discrepancy is shown in our property simulation validation, and arises because of the simplifying flow assumptions, and the fact that PoreXpert cannot replicate the true complexity and intricacy of void networks in most natural materials. Larger unit cells provide more realistic values of permeability because there are fewer unit cell replications to represent the experimental sample, but take longer as detailed below.
The network capacity is calculated in milliDarcy units.
The calculated value includes the slip/Knudsen flow of molecules of gases, caused by molecules bouncing their way through throats within the network. The effect is most noticeable, relative to laminar / Poiseuillian flow, for small molecules in low density gases passing through narrow throats. The difference between gas and liquid permeability corresponds to the Klinkenberg effect.
Performing a permeability calculation
To start a calculation, choose a wetting liquid or gas from the list. If what you want to model is not there, then Go home. Then on the File dropdown menu, Edit available materials.
The permeability screen during a calculation
Once calculating, the permeability icon, faintly visible in the screenshot above, will pulsate. As the algorithm finds more and more trickle flow routes through the network, the Maximum flow will increase. Finally, at the end of the calculation, it will revert to the Home screen, and display the network capacity in the operations list.
The network capacity result
Note that in the result screen shown above, there is a Precise permeability estimate. This is based on the results of the property simulation validation, and the method of calculation is described in the Permeability Calibration section. Currently, precise estimates are only available for air at atmospheric pressure flowing through sandstones, based on the void size and permeability validation. The further a sample deviates from that, the less accurate the estimate. The accuracy categories are, in decreasing order, Very precise, Precise, Moderately precise, Possible, Default and Generic. Unit cells with less than 8000 pores, i.e. smaller than 20x20x20 for a cubic unit cell, are too small for either network capacity or permeability estimates. Note that a precise estimate is not an accurate one - you still need to generate many stochastic generations to gain a reliable value of permeability, as emphasised in the discussion of the permeability validation.
Clicking on the permeability operation in the list will reveal the unit cell. Viewing the unit cell in 3D will display the major routes though the structure. Colouring shows net flow on a linear scale, whereas in fact the flow is often logarithmically distributed through the network. So only the most major flow routes, close to maximum flow, will be highlighted, as shown below.
For complete flow details, save the permeability calculation as an uncompressed PoreXpert file. A screenshot of part of an uncompressed file, showing flow into and out of the pore nearest the Cartesian axes origin (ID = "0"), is shown under calculation speed. The trickle-flow approximation allows separate trickles of flow in the +x, -x, +y, -y and -z directions, but not in the +z direction (i.e. not back towards the fluid reservoir position).
Detail of the unit cell for sandstone sample 5 in the permeability validation exercise. Blue / purple voids indicate net flow in the -x, -y or -z directions. Yellow spectrum voids show net flow in the positive Cartesian directions.
This operation may take a long time to complete, depending on your hardware capabilities and the unit cell size. The amount of RAM available on your system will also restrict the largest unit cell size that your system can calculate. You will receive a warning if the calculation is beyond the capability of your computer's RAM. To find out how long a permeability calculation takes, run the calculation in Batch mode, save the output in uncompressed .porexpert format, open the output file using e.g. NotePad++, and search for TimeStamp.