Effective permeability of a porous carbon composite is computed using the direct simulation Monte Carlo technique. The microstructure of the carbon composite is synthetically generated using an in-house solver. Permeabilities obtained using synthetic microstructures of the precursor (carbon fibers) is compared to two independent experimental dataset and good agreement is observed. An approach to digitally infuse matrix into the precursor is proposed. Comparison of the permeability for the full composite (carbon fibers with matrix) with experimental data demonstrates good agreement indicating that representative microstructures generated digitally can be used to compute and predict effective permeability of porous carbon composites. Simulations of gases penetrating the full composite are performed, and an intrinsic material permeability (Ko) of 11.866 × 10−11 m2, and a Klinkenberg constant (b∗) of 5.655 × 10−8 that is only dependent on the temperature and the molecular weight of the gaseous species is obtained.