We propose a model for describing polymer blends dynamics close to the glass transition. The dynamical model incorporates an extension of the Flory Huggins model to the case of compressible blends for calculating the driving forces. Spatial dynamics follows then from an Onsager like description. The model is solved on a 2D lattice corresponding to spatial scales of about a few tens to 100 nm and a resolution corresponding to the scale of dynamical heterogeneities, allowing to study inter-diffusion mechanisms of species in polymer blends close to Tg, in particular during the process of phase separation. We deal with non-entangled polymers having a degree of polymerization smaller than 50 typically. In the course of spinodal decomposition, we observe slow structures building, which coexist with fast ones. Domains are found to grow like the logarithm of the time. We study also the reverse process, after the temperature is increased again in the totally miscible range. We observe a temporal asymmetry between the aging and the rejuvenation dynamics: the slow domains melt much faster than the elapsed time required to build them during the separation process and total miscibility is recovered after a much shorter time. This model allows also for describing solvent diffusion in polymers close to and below Tg and for explaining the so-called case-II diffusion.