  We study a particle model for a simple system of partial differential
equations describing, in dimension $d\geq 2$, a two component mixture where
light particles move in a medium of absorbing, fixed obstacles; the system
consists in a transport and a reaction equation coupled through pure absorption
collision terms. We consider a particle system where the obstacles, of radius
$\var$, become inactive at a rate related to the number of light particles
travelling in their range of influence at a given time and the light particles
are instantaneously absorbed at the first time they meet the physical boundary
of an obstacle; elements belonging to the same species do not interact among
themselves. We prove the convergence (a.s. w.r.t. the product measure
associated to the initial datum for the light particle component) of the
densities describing the particle system to the solution of the system of
partial differential equations in the asymptotics $ a_n^d n^{-\kappa}\to 0$ and
$a_n^d \var^{\zeta}\to 0$, for $\kappa\in(0,\frac 12)$ and $\zeta\in (0,\frac12
- \frac 1{2d})$, where $a_n^{-1}$ is the effective range of the obstacles and
$n$ is the total number of light particles.
