  We consider a multicontinuum model in porous media applications, which is
described as a system of coupled flow equations. The coupling between different
continua depends on many factors and its modeling is important for porous media
applications. The coefficients depend on particle deposition that is described
in term of a stochastic process solution of an SDE. The stochastic process is
considered to be faster than the flow motion and we introduce time-space scales
to model the problem. Our goal is to pass to the limit in time and space and to
find an associated averaged system. This is an averaging-homogenization
problem, where the averages are computed in terms of the invariant measure
associated to the fast motion and the spatial variable. We use the techniques
developed in our previous paper to model the interactions between the continua
and derive the averaged model problem that can be used in many applications.
