Percolation in a fractional Brownian motion lattice
- Univ. of Southern California, Los Angeles, CA (United States)
Many applications of engineering interest involve spatially correlated properties obeying the statistics of fractional Brownian motion (fBm). Of specific interest to this note are percolation processes in a field described by fBm. There are two applications where such processes may arise: The immiscible displacement of one fluid by another in a 2-D fracture, the aperture of which obeys fBm statistics; and the same displacement in a heterogeneous porous medium, the permeability of which obeys fBm statistics. In either case, it is assumed that capillary forces dominate the displacement. In previous works, Yortsos and Chang (1990) and van Batenburg et al. (1991) simulated displacements in such fields by considering both capillary and viscous forces. Here, the authors consider the case where viscous forces are small (low flow rates). As capillary-controlled displacement is described by invasion percolation (IP), the problem of interest is one of percolation in a correlated lattice. In this note the authors present numerical results of both ordinary percolation and IP in an fBm lattice, which expand on their previous study (Satik and Yortsos, 1991) and support the findings of Isichenko (1992) and Schmittbuhl et al. (1993). The statistics of the random variables p{sub c} and P(p, H) obtained should be useful in problems involving fBm lattices. More generally, the results should be useful in the study of invasion processes in correlated media.
- OSTI ID:
- 367873
- Journal Information:
- AIChE Journal, Journal Name: AIChE Journal Journal Issue: 8 Vol. 42; ISSN 0001-1541; ISSN AICEAC
- Country of Publication:
- United States
- Language:
- English
Similar Records
Gravity destabilized non-wetting phase invasion in macro-heterogeneous porous media: Near pore scale macro modified invasion percolation simulation of experiments
Crossover from capillary fingering to compact invasion for two-phase drainage with stable viscosity ratios