Simulating fluid transport in microporous media is challenging due to their inherent heterogeneity and multiscale nature. This study presents a multi-scale domain discretization approach coupled with a dual porosity numerical solver to address these challenges and determine representative elementary volumes (REVs) within the media. A hybrid formulation combining two-phase Darcy equation, single-phase compressible Navier-Stokes and continuity equations, and volume of fluid advection scheme is integrated. This enables accurate simulation of complex multiphase dynamics across both micro- and macro-porosity domains. Additionally, a dedicated domain discretization technique caters to the specific demands of microporous regions, ensuring tailored treatment of distinct porosity scales. This methodology was implemented on two distinct carbonate samples: Savonnieres carbonate and Mount-Gambier limestone. Prior studies had successfully determined an REV for Savonnieres carbonate. However, incorporating dual porosity made REV determination elusive due to sample size limitations stemming from the presence of clustered heterogeneity regions. Conversely, for Mount-Gambier limestone, with its more evenly distributed heterogeneity, an REV at 1200 cubic voxels was successfully established. The results closely align with existing core-scale estimates, further validating the proposed approach’s effectiveness. Notably, this success also underscores the method’s potential for broader application to diverse microporous media with varying heterogeneity distributions.