The immiscible displacement of a wetting fluid by a non-wetting one in heterogeneous porous media is modeled using a multi-scale network-type analysis: (1) The pressure-controlled immiscible displacement of water by oil in pore-and-throat networks (1st length scale ~ 1 mm) is simulated as a capillary-driven process. (2) The pressure-controlled immiscible displacement in uncorrelated cubic lattices (2nd length scale ~ 1 cm) is simulated as a site percolation process governed by capillary and gravity forces. At this scale, each node represents a network of the previous scale. (3) The rate-controlled immiscible displacement of water by oil in cubic networks (3rd length scale ~ 10 cm), where each node represents a lattice of the previous scale, is simulated by accounting for capillary, gravity, and viscous forces. The multi-scale approach along with the information concerning the pore structure properties of the porous medium can be employed to determine the transient responses of the pressure drop and axial distribution of water saturation, and estimate the effective (up-scaled) relative permeability functions. The method is demonstrated with application to data of highly heterogeneous soils.
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This article is dedicated to the memory of Professor Alkiviades Payatakes (deceased on 29 November 2009) who taught us the principles and disciplines of scientific research, and inspired us to conduct systematic and hierarchical studies toward the development of true-to-the mechanism numerical models.
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Tsakiroglou, C.D. A Multi-Scale Approach to Model Two-Phase Flow in Heterogeneous Porous Media. Transp Porous Med 94, 525–536 (2012). https://doi.org/10.1007/s11242-011-9882-y
- Multi-scale models
- Two-phase flow
- Heterogeneous media
- Relative permeability
- Capillary pressure
- Network analysis