10.4122/1.1000000735
Tsakiroglou, Christos
Christos
Tsakiroglou
ctsakir@iceht.forth.gr
Tsakiroglou, Christos
Christos
Tsakiroglou
ctsakir@iceht.forth.gr
A two-scale percolation approach to compute the effective two-phase flow coefficients of heterogeneous porous media in the general case of a shear-thinning nonwetting fluid
XVI International Conference on Computational Methods in Water Resources
2006
2006
Mechanistic simulators of the two-phase flow in pore networks (length scale~1 cm)
have widely been used to determine the effective transport coefficients (e.g.
capillary pressure curve-Pc, relative permeability curve of wetting phase-krw and
nonwetting phase-krnw, resistivity index-IR) of macroscopically homogeneous porous
media. However, in the classical 1-scale approach, very large networks, complicated
algorithms and enormous computational effort are required to (1) simulate the up-
scaled multiphase transport coefficients of macroscopically heterogeneous porous
media (length scale~1 m), and (2) take into consideration the effects of buoyancy
and viscous forces on Pc, krw, krnw, IR.
In the present work, a two-scale percolation approach is developed to simulate the
displacement of a Newtonian wetting fluid by a power law fluid in a heterogeneous
porous medium. First, a gradient percolation model is developed by taking into
account the power law rheology of the nonwetting fluid and the flow of wetting
fluid along pore edges. In this manner, the small-scale Pc, krw, krnw, IR of each
homogeneous unit are calculated. Then, the small-scale effective transport
coefficients are fed as input data into a large-scale site-percolation model, where
the pore sizes are replaced by the small-scale Pc curves, and instead of the
critical pore pressure of penetration the critical breakthrough pressure is
employed. The effects of the power law parameters, Bond number (Bo), capillary
number (Ca), and contact angle (θe) on the small (homogeneous) and large
(heterogeneous) scale displacement growth pattern as well as on the corresponding
Pc, krw, krnw, IR are investigated. Finally, the calculated growth patterns and
effective transport coefficients are compared to results of drainage experiments
performed on glass-etched dual pore networks.