  We apply local mean-field (i.e. density functional) theory to a lattice model
of a fluid in contact with a dilute, disordered gel network. The gel structure
is described by a diffusion-limited cluster aggregation model. We focus on the
influence of porosity on both the hysteretic and the equilibrium behavior of
the fluid as one varies the chemical potential at low temperature. We show that
the shape of the hysteresis loop changes from smooth to rectangular as the
porosity increases and that this change is associated to disorder-induced
out-of-equilibrium phase transitions that differ on adsorption and on
desorption. Our results provide insight in the behavior of $^4$He in silica
aerogels.
