Porosity is a key parameter controlling the physico-chemical behavior of porous rocks. Digital rock physics offers a unique technique for imaging the inherently heterogeneous rock microstructure at fine spatial resolutions and its computational reconstruction, through which a better understanding and prediction of the rock behavior can be achieved. In this study, we propose a simple but accurate method to build a 3D porosity map of centimeter-scale carbonate rock cores from X-ray Micro Computed Tomography (XMCT) imaging data. The method consists of 3 main steps: i) decomposition of 3D volumetric XMCT data into sub-volumes, ii) processing of equidistributed 2D cross-section images in each sub-volume and iii) 2D slice-by-slice calculation of porosity and its assembly to reconstruct a 3D continuum porosity map over the whole core domain using a MATLAB code. The proposed approach significantly conserves the required memory to manipulate large image datasets. The digitized porosity representations are used to build 3D permeability maps of the cores by applying an explicit permeability-porosity relationship. The permeability maps are used as input for numerical simulation of the rock response to the percolation of reactive fluids through which the general validity of the approach is verified. The developed digital rock model paves the way for an improved understanding of reactive transport in carbonate rocks.