Permeation is investigated for the introduction of hydrogen isotopes into lead lithium (PbLi) for the Tritium Extraction eXperiment (TEX). TEX is a forced-convection PbLi loop under construction at Idaho National Laboratory that will test the vacuum permeator (VP) method of tritium extraction from PbLi. The source permeator (SP) delivers atomic hydrogen (H, D, and T) from a gas-phase reservoir into the PbLi via a permeable dense metal membrane. A modular system and a fixed SP system are presented. In the modular design, PbLi flows through the inside of a tubular membrane, and gas-phase hydrogen is introduced on the outside of the membrane. Atomic hydrogen permeates radially inward through the membrane into the PbLi. In the fixed design, PbLi flows into an expansion chamber with closed-ended tubular membranes inserted. Gas-phase hydrogen is introduced on the inside of the closed-ended membranes, and atomic hydrogen permeates radially outward into the flowing PbLi. Hydrogen transport models based on steady-state mass transport through PbLi and permeation through the metal membrane were developed to assess the operation of the SP relative to experimental variables and to allow understanding of uncertain parameter effects, such as PbLi hydrogen transport properties and the effective hydrogen permeability of the VP. This modeling effort considers iron as the SP material and vanadium as the VP material.