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Trapping thresholds in invasion percolation
Lincoln Paterson1, Adrian P Sheppard, Mark A Knackstedt
1Australian Petroleum Cooperative Research Centre, CSIRO Division of Petroleum Resources, P.O. Box 3000, Glen Waverley, Vic 3150, Australia.
Summary
Numerical simulations reveal that invasion percolation and ordinary percolation thresholds typically align on 3D lattices. However, thresholds diverge for coordination numbers below five, impacting porous rock simulations.
Area of Science:
- Physics
- Geology
- Materials Science
Background:
- Percolation theory is crucial for understanding fluid flow in porous media.
- Invasion percolation models fluid displacement, while ordinary percolation describes random site occupation.
Purpose of the Study:
- To numerically estimate site percolation trapping thresholds for invasion percolation on 3D lattices.
- To compare these thresholds with those of ordinary percolation.
Main Methods:
- Numerical simulations were performed on various three-dimensional lattices.
- Site percolation trapping thresholds were calculated for invasion percolation.
Main Results:
- In most cases, invasion percolation and ordinary percolation thresholds were found to coincide.
- A divergence in thresholds was observed for lattices with coordination numbers less than five.
Conclusions:
- The findings highlight that standard percolation models may not accurately represent residual saturation in porous rocks with low coordination numbers.
- Careful selection of simulation rules is necessary for accurately modeling porous rock networks, particularly those with coordination numbers below five.