Corrosion of steel reinforcements in concrete constructions is a worldwide problem. To assess the degradation of rebars in reinforced concrete, an accurate description of electric current, potential and concentrations of various species present in the concrete matrix is necessary. Although the concrete matrix is a heterogeneous porous material with intricate microstructure, mass transport has been treated in a homogeneous material so far, modifying bulk transport coefficients by additional factors (porosity, constrictivity, tortuosity), which led to so-called effective coefficients (e.g., diffusivity). This study presents an approach where the real 3D microstructure of concrete is obtained from high-resolution X-ray computed tomography (XCT), processed to generate a mesh for finite element method (FEM) computations, and finally combined with a multi-species system of transport and electric potential equations. This methodology allows for a more realistic description of ion movements and reactions in the bulk concrete and on the rebar surface and, consequently, a better evaluation of anodic and cathodic currents, ultimately responsible for the loss of reinforcement mass and its location. The results of this study are compared with a state-of-the-art model and numerical calculations for 2D and 3D geometries.