We consider the homogenization of a coupled system of PDEs describing flows in highly heterogeneous porous media. Due to the coupling, the effective coefficients always depend on the slow variable, even in the simple case when the porosity is taken purely periodic. Therefore the most important part of the computational time for the numerical simulation of such flows is dedicated to the determination of these coefficients. We propose a new numerical algorithm based on Reduced Basis techniques, which significantly improves the computational performances.