  In this work we study analytically and numerically the transport properties
of non-interacting active particles moving on a $d$-dimensional disordered
media. The disorder in the space is modeled by means of a set of
non-overlapping spherical obstacles. We assume that obstacles are reactive in
the sense that they react in the presence of the particles in an attractive
manner: when the particle collides with an obstacle, it is attached during a
random time (adsorption time), i.e., it gets adsorbed by an obstacle;
thereafter the particle is detached from the obstacle and continues its motion
in a random direction. We give an analytical formula for the effective
diffusion coefficient when the mean adsorption time is finite. When the mean
adsorption time is infinite, we show that the system undergoes a transition
from a normal to anomalous diffusion regime. We also show that another
transition takes place in the mean number of adsorbed particles: in the
anomalous diffusion phase all the particles become adsorbed in the average. We
show that the fraction of adsorbed particles, seen as an order parameter of the
system, undergoes a second-order-like phase transition, because the fraction of
adsorbed particles is not differentiable but changes continuously as a function
of a parameter of the model.
