| Cubic lattice models were used to represent sedimentary deposits and their role as georeservoirs. The percolation of high-permeability zones was studied using both analytical and simulation approaches. The analytical approach was developed for single-scale sedimentary architecture. The approach showed that percolation is affected by cluster spatial correlation and by lattice size. It showed that correlation affects both high-permeability and low-permeability clusters equally, and thus correlation does not likely affect the percolation threshold for infinite lattices. On finite lattices, the analysis showed that the effect of correlation on lowering the percolation threshold can be understood through the truncation of low-permeability cluster-size distributions, without the need for Monte Carlo simulations.;The simulation approach was used to study multiscale, hierarchical sedimentary architecture. A computer code was developed to create a digital model representing hierarchical stratal architecture found in channel-belt deposits. The code uses a geometric-based approach to simulate strata observed over multiple scales (levels). Larger-scale unit types form the bounding surfaces of associations of smaller-scale unit types. The different scales of bounding surfaces were each found to create a finite lattice effect on percolation. When using realistic length distributions, the high-permeability zones percolate across boundaries at all hierarchical levels if volume proportions are above 0.18, as is common. This threshold value is lower than the threshold proportion of 0.3116 required for percolation on the infinite random lattice. Thus, in sedimentary deposits as represented here, percolation in the high-permeability zones is expected. |
