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The textural and geometrical properties of the pore networks (i.e., such as pore size distribution, pore shape, connectivity, and tortuosity) provides a primary control on the fluid storage and migration of geofluids within porous carbonate reservoirs. These properties are highly variable because of primary depositional conditions, diagenetic processes and deformation. This issue represents an important challenge for the characterization and exploitation plan in this type of reservoirs. In this study, the complementary properties of neutrons and X-ray experiments are carried out to better understand the effects of pore network properties on the hydraulic behavior of porous carbonates. Neutrons have unique properties and are particularly suitable for this study due to the sensitivity of neutrons to hydrogen-based fluids. The used methodology combines dynamic neutron radiography (NR), integrated X-ray and neutron tomography (XCT, NCT), and computational fluid dynamics simulations (lattice-Boltzmann method) of porous carbonate reservoir analogs from central and southern Italy. Dynamic 2D NR images provide information regarding the fluid transport and the wetting front dynamics related to the effect of heterogeneities (e.g., fractures and deformation bands) at the microscale. The combination of NCT (dry and wet samples) and XCT (dry), generates more information regarding the effective pore space contribution to fluid flow. The fluid flow simulations generate information about the connected pore network and the permeability evaluated rock sample at saturated condition.