Ammonia is a promising carrier for storing and transporting hydrogen, but its efficient decomposition into high-purity hydrogen remains a challenge. Catalytic membrane reactors (CMRs) equipped with palladium-based membranes offer an elegant solution by integrating reaction and separation, yet their performance is critically influenced by complex transport phenomena and potential inhibition by ammonia. This thesis develops and rigorously validates a predictive, multi-physics model for hydrogen permeation through a supported Pd-Ag membrane to de-risk its application in ammonia cracking environments. The model is constructed incrementally, coupling external gas-film mass transfer, a modified Sieverts' law for the dense Pd-Ag layer, and dusty gas model (DGM) for the porous support.