We report here a simple algorithm to create 2D lattice-based models of porous deposits of preformed nano-metric particles, by mimicking to some extent the physics of the actual deposition/aggregation mechanism. The heterogeneous porous networks obtained exhibit anisotropic properties unlike lattice-based models of porous materials in the existing literature, such as those of porous Vycor glass. We have then used calculations based on the mean field kinetic theory, in order to study the thermodynamics and dynamics of fluid adsorption and desorption in these lattice based porous models. We showcase the influence of pore heterogeneity on the phase equilibrium of the confined fluid, studying both heterogeneity in pore size distribution and chemical heterogeneity of the internal surface.