The purpose of this thesis is to study an evolving system of SUperNOva CONdensateS (SUNOCONS) within the Interstellar Medium (ISM). This is done via a Monte Carlo process where refractory dust grains formed within supernova remnants are subjected to the processes of sputtering and collisional fragmentation in the diffuse phase and accretion within the cold molecular cloud phase. In order to record chemical detail, we take each new particle to consist of a superrefractory core plus a more massive refractory mantle. The particles are allowed to transfer to and fro between the different phases of the ISM until either the particles are destroyed or the program finishes. The resulting chemical and size spectrum(s) are then applied to various astrophysical problems with the following results: (1) after six thousand million years roughly 10 to 20% by mass of the most refractory material (Al\sb2O\sb3) survives the rigors of the ISM intact, which leaves open the possibility that 'fossilized' isotopically anomalous material may have been present within the primordial solar nebula. (2) structured or layered refractory dust grains within our model cannot explain the observed interstellar depletions of refractory material. (3) fragmentation due to grain-grain collisions in the diffuse phase plus the accretion of material in the molecular cloud phase can under certain circumstances cause a bimodal distribution in grain size.