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.
