  We study in this paper compression effects in heterogeneous media with
maximal packing constraint. Starting from compressible Brinkman equations,
where maximal packing is encoded in a singular pressure and a singular bulk
viscosity, we show that the global weak solutions converge (up to a
subsequence) to global weak solutions of the two-phase
compressible/incompressible Brinkman equations with respect to a parameter
$\varepsilon$ which measures effects close to the maximal packing value.
Depending on the importance of the bulk viscosity with respect to the pressure
in the dense regimes, memory effects are activated or not at the limit in the
congested (incompressible) domain.
