Carbonate rocks have unique attributes that distinguish them from siliciclastics and that require diferent methods of study to characterize their texture. Carbonates rocks are formed as a result of close interactions between biological and chemical depositional processes. The underlying diagenetic processes that form and alter these rocks contribute to a build-up of heterogeneities. Because of the high heterogeneity content measured properties (e.g. porosity and permeability) change with the scale of investigation and studies have struggle with a trade-off between significance of details and space representativeness. Extending a smaller scale to a larger requires scaling up procedures that preserves the essence of physical processes at one level to be summarized at the coarser level. Simplistic methods for scaling-up non-additive properties such as permeability generally do not honour the original heterogeneity present in complex systems. Therefore the dynamics of fluid flow in complex rocks demand more sophisticate methods and approaches. This study was focused in developing a methodology to evaluate the permeability as a scaling-up parameter for heterogeneous porous media. The permeability is back-calculated by emulating Darcy s experiment and solving the pore-scale ow using a Finite element formulation of Brinkman flow equation. The study was initially focused on parametric systems of periodic cells and later extended to two micro-tomography carbonate samples in which one has been selected for a spatial representativeness study. The parametric cells were used to evaluate the shape effects of channels and void spaces in an analogy to geological fractures and vugs as well as the permeability of the porous matrix. The micro-tomography carbonate samples consisted of a real case scenario in which, to a certain degree, could be observed a combination of the previously studied periodic cells. Finally a representativeness study was conducted segmenting the micro-tomography sample into suficiently sub-samples that would be capable of reproducing the spatial heterogeneity of the sample.