We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: micro- macro). The geometry we have in mind includes regions of low diffusivity arranged in a locally-periodic fashion. We choose a prototypical advection-diffusion system (of minimal size), discuss its formal homogenization (the heterogenous medium being now assumed to be made of zones with circular areas of low diffusivity of x-varying sizes), and prove the weak solvability of the limit two-scale reaction-diffusion model. A special feature of our analysis is that most of the basic estimates (positivity, L^inf-bounds, uniqueness, energy inequality) are obtained in x-dependent Bochner spaces. Keywords: Heterogeneous porous materials, homogenization, micro-macro transport, two-scale model, reaction-diffusion system, weak solvability
