  The paper presents a stochastic analysis of the growth rate of viscous
fingers in miscible displacement in a heterogeneous porous medium. The
statistical parameters characterizing the permeability distribution of a
reservoir vary over a wide range. The formation of fingers is provided by the
mixing of different-viscosity fluids -- water and polymer solution. The
distribution functions of the growth rate of viscous fingers are numerically
determined and visualized. Careful data processing reveals the non-monotonic
nature of the dependence of the front end of the mixing zone on the correlation
length of the permeability (describing the medium graininess) of the reservoir
formation. It is demonstrated that an increase in graininess up to a certain
value causes an expansion of the distribution shape and a shift of the
distribution maximum to the region of higher velocities. In addition, an
increase in the standard deviation of permeability leads to a slight change in
the shape and characteristics of the density distribution of the growth rates
of viscous fingers. The theoretical predictions within the framework of the
transverse flow equilibrium approximation and the Koval model are contrasted
with the numerically computed velocity distributions.
