  The paper investigates the linear growth of the mixing zone during polymer
slug injection into a water reservoir. The velocities of the slug front and of
the boundaries of the mixing zone are analyzed as key parameters. Using two
different numerical methods (finite volumes and finite elements), the impact of
the slug size, reservoir dimensions, Peclet number, and viscosity curve shape
on the corresponding velocities is examined. Notwithstanding the realization of
the solution by two computational schemes, the simulation results coincide with
sufficient accuracy. The numerically obtained velocities are compared with
theoretical estimates within the transverse flow equilibrium approximation and
Koval model. Based on the comparison pattern, recommendations are presented on
the use of specific analytical methods for estimating the growth rate of the
mixing zone depending on the characteristics of the polymer.

Fluid Dynamics;Numerical Analysis;Analysis of PDEs;Numerical Analysis