Carbonation is the reaction of environmental carbon dioxide with alkaline species in concrete. It is one of the major degradation mechanisms affecting the durability of reinforced concrete structures. In this paper, a mathematical model of the carbonation process is formulated and simulated using the finite-element method. Nonlinear reaction rates, Robin boundary conditions and a decrease of the concrete porosity in time are taken into account. A dimensional analysis based on a nondimensionalisation of the entire model is introduced to identify the key parameters and the different characteristic time and length scales of the whole process. Numerical simulations show the occurrence of an internal reaction layer travelling through the material. The speed and the width of the layer are rigorously defined via dimensionless quantities. A parameter study shows that the speed and the width are strongly related to the size of the Thiele modulus which is typically large. The relevance of other parameters is also investigated. The model is validated for accelerated and natural carbonation settings.