We have carried out computer simulation of miscible displacements in p
orous media in which the permeabilities vary spatially according to a
fractional Brownian motion. This distribution induces long-range corre
lations and has been found to describe the permeabilities of heterogen
eous rocks. Our simulation shows that conventional viscous fingers, wh
ich are the result of the contrast M between the viscosities of the di
splacing and displaced fluids, and are usually found in laboratory exp
eriments, do not exist. Displacement patterns and efficiency are contr
olled by the heterogeneities, and the viscosity contrast M, varied her
e between 1 and infinity, has essentially no effect.