  In this work we consider a mathematical model of the water treatment process
and determine the effective characteristics of this model. At the microscopic
length scale we describe our model in terms of a lattice random walk in a
high-contrast periodic medium with absorption. Applying then the upscaling
procedure we obtain the macroscopic model for total mass evolution. We discuss
both the dynamic and the stationary regimes, and show how the efficiency of the
purification process depends on the characteristics of the macroscopic model.
