  We consider a lattice gas interacting by the exclusion rule in the presence
of a random field given by i.i.d. bounded random variables in a bounded domain
in contact with particles reservoir at different densities. We show, in
dimensions $d \ge 3$, that the rescaled empirical density field almost surely,
with respect to the random field, converges to the unique weak solution of a
non linear parabolic equation having the diffusion matrix determined by the
statistical properties of the external random field and boundary conditions
determined by the density of the reservoir. Further we show that the rescaled
empirical density field, in the stationary regime, almost surely with respect
to the random field, converges to the solution of the associated stationary
transport equation.
