Topology and Geometry Setup

Pore locations of a default cubic network.

OpenPNM comes with a machinery to create various topologies and geometries. The topology generates the number of pores (or nodes in network theory language) and connects them by  throats (edges). Basic operations can now be executed: check for connected regions, connectivity plots and some others. The geometry generators attach some geometric information to the topolgy: e.g. pore sizes, throat sizes, throat lengths, …

In the statistical plot below, we can observe that the pore and throat diameters are discretely drawn from a normal distribution. The coordicantio number shows the eight corner node with a coordination number of three, the edge nodes (4), face nodes (5) and internal node (6).

MIP algorithm

The drainage algorithm simulates a capillary drainage experiment by applying a list of increasing capillary pressures and invading all throats that are accessible and invadable at the given pressure.

The capillary pressure is calculated based on the throat radius, the surface tension of the invading phase and the contact angle. In this particular case the invading fluid is mercury. The algorithm returns the drainage curve (right) and attaches the step in which a praticular pore was invaded as well as the pressure at invasion time. This allows us to create a visualization of the invasion sequence in Paraview (below).

MIP simulation on a cubic network conducted by OpenPNM. 3D scene generated with Paraview, movie generated with GIMP.

Topology and Geometry Setup

Topology of a network generated with the Delaunay/Voronoi algorithm.

In the previous example, we have generated a simple cubic network. In this example we will use randomly placed points to generate our network. The main problem for random points is to figure out which points should be connected. One solution to this problem is to utilize a suite of tools used in the meshing community: Delaunay Triangulations and Voronoi Diagrams. The image on the left shows one example of such a network. Additional pores were added on the cube boundary to allow for an easy identification of injection pores. The very simplistic approach used in this algorithm generates artificially large pores close to the outer faces of the geometry. To generate a more realistic porous medium, the detection and generation of boundary face pores has to be done with more care and sophistication.

Geometric properties

Now the sizes of pores and throats needs to be calculated. IN this example we will use the Voronoi diagram of the Delaunay tessellation to find the shape of pores and throats. The image below shows the pores and pore edges generated by the Voronoi diagram. The green dots denote the pore centres given by the Delaunay points.

Visualization of the pore and throat space of the based on the Voronoi algorithm.

To simplify the visualization, OpenPNM allows to select a specific pore and draw the cross sections of all connected pores. The pore selected in the plot before is connected to six other pores (hence coordination number of 6)

Calculation of the fibre sizing. The black and green lines denote the polygonal cage of connected pores, the red circle denotes the throat diameter.

As observed before, our simplistic addition of boundary pores, leads to some obvious anomalies in the distributions shown below: The boundary pores only connect to one internal pore, hence their coordination number is 1. The boundary pores have volume 0, to not influence the saturation calculation.

Histogram of the key geometric properties: throat diameter, pore diameter, throat lengths and coordination numbers.

Similarity to fibrous materials

A cross section of the porous network defined by the Delaunay/voronoi algorithm pair. White denotes fibres, black the void space.

One of the attractions of this type of network is the similarity to fibrous materials. OpenPNM allows to visualize (see right image) a cross section of this geometry type and one can observe a striking similarity to real materials (e.g. gas diffusion layers for fuel cell applications).

Graph of the porosity of a single slice along the three Cartesian axis.

MIP algorithm

Simulation of a MIP based on a random Delaunay network.

The drainage algorithm simulates a capillary drainage experiment by applying a list of increasing capillary pressures and invading all throats that are accessible and invadable at the given pressure.

The capillary pressure is calculated based on the throat radius, the surface tension of the invading phase and the contact angle. In this particular case the invading fluid is mercury. The algorithm returns the drainage curve (right) and attaches the step in which a praticular pore was invaded as well as the pressure at invasion time. This allows us to create a visualization of the invasion sequence in Paraview (below).

MIP intrusion simulation of a network generated by the Delaunay and Voronoi algorithms.

Topology and Geometry Setup

The topology and geometry for ths section is identical to the previous one.

OP algorithm

Invasion percolation of a water phase into a Delaunay/Voronoi random network.

The drainage algorithm simulates a capillary drainage experiment by applying a list of increasing capillary pressures and invading all throats that are accessible and invadable at the given pressure. In contrast to the previous section, the invading fluid is now water instead of mercury.

The capillary pressure is calculated based on the throat radius, the surface tension of the invading phase and the contact angle. In this particular case the invading fluid is mercury. The algorithm returns the drainage curve (right) and attaches the step in which a praticular pore was invaded as well as the pressure at invasion time. This allows us to create a visualization of the invasion sequence in Paraview (below).

Ordinary percolation simulation of water into a porous network generated by the Delaunay/Voronoi algorithm. Simulation with OpenPNM and visualization with Paraview.