TY - JOUR
T1 - Phase connectivity in pore-network models for capillary-driven flow
AU - Petrovskyy, Dmytro
AU - van Dijke, Marinus I. J.
AU - Jiang, Zeyun
AU - Geiger, Sebastian
N1 - Funding Information:
The authors would like to thank Petrobras and Shell for their sponsorship of the International Centre for Carbonate Reservoirs (ICCR). Sebastian Geiger further thanks the Energi Simulation Foundation for supporting his chair programme.
Publisher Copyright:
© 2020 Elsevier Ltd
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/1
Y1 - 2021/1
N2 - Pore-network representations of permeable media provide the framework for explicit simulation of capillary-driven immiscible displacement governed by invasion-percolation theory. The most demanding task of a pore-network flow simulation is the identification of trapped defending phase clusters at every displacement step, i.e. the phase connectivity problem. Instead of employing the conventional adjacency list we represent the connectivity of a phase cluster as a tree accompanied by a set of adjacent non-tree edges. In this graph representation, a decrease in phase connectivity due to a pore displacement event corresponds to deletion of either a tree or a non-tree edge. Deletion of a tree edge invokes a computationally intensive search for a possible reconnection of the resulting subtrees by an adjacent non-tree edge. The tree representation facilitates a highly efficient execution of the reconnection search. Invasion-percolation simulations of secondary water floods under different wetting conditions in pore-networks of different origin and size confirm the efficiency of the proposed phase connectivity algorithm. Moreover, a systematic simulation study of runtime growth with increasing model size on regular lattice networks demonstrates a consistent orders-of-magnitude speed-up compared to conventional simulations. Consequently, the proposed algorithm proves to be a powerful tool for invasion-percolation simulations on large multi-scale networks and for extensive stochastic analysis of typical single-scale pore-networks.
AB - Pore-network representations of permeable media provide the framework for explicit simulation of capillary-driven immiscible displacement governed by invasion-percolation theory. The most demanding task of a pore-network flow simulation is the identification of trapped defending phase clusters at every displacement step, i.e. the phase connectivity problem. Instead of employing the conventional adjacency list we represent the connectivity of a phase cluster as a tree accompanied by a set of adjacent non-tree edges. In this graph representation, a decrease in phase connectivity due to a pore displacement event corresponds to deletion of either a tree or a non-tree edge. Deletion of a tree edge invokes a computationally intensive search for a possible reconnection of the resulting subtrees by an adjacent non-tree edge. The tree representation facilitates a highly efficient execution of the reconnection search. Invasion-percolation simulations of secondary water floods under different wetting conditions in pore-networks of different origin and size confirm the efficiency of the proposed phase connectivity algorithm. Moreover, a systematic simulation study of runtime growth with increasing model size on regular lattice networks demonstrates a consistent orders-of-magnitude speed-up compared to conventional simulations. Consequently, the proposed algorithm proves to be a powerful tool for invasion-percolation simulations on large multi-scale networks and for extensive stochastic analysis of typical single-scale pore-networks.
KW - Invasion-percolation
KW - Phase connectivity
KW - Pore-network modelling
KW - Simulation runtime growth
UR - http://www.scopus.com/inward/record.url?scp=85095805851&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2020.103776
DO - 10.1016/j.advwatres.2020.103776
M3 - Article
AN - SCOPUS:85095805851
SN - 0309-1708
VL - 147
JO - Advances in Water Resources
JF - Advances in Water Resources
M1 - 103776
ER -