The efficient extraction of tritium from the breeder blanket (BB) in a fusion reactor is vital for maintaining the tritium economy for a sustainable and self-sufficient fusion power plant. The vacuum permeator (VP) design is one of several promising technology platforms for extracting tritium from the BB with the advantages of being capable of operating continuously at high temperatures with the aim of achieving high tritium extraction efficiencies. The Tritium Extraction eXperiment (TEX), under construction at the Safety and Tritium Applied Research (STAR) Facility at Idaho National Laboratory (INL), is designed to test the viability of VP technology by introducing atomic hydrogen (H, D, and T) from a source permeator (SP) into a forced convection lead lithium eutectic (PbLi) loop and determining the hydrogen extraction rates from the vanadium VP. Presented here is a computational analysis of the hydrogen inventory and permeation behavior in TEX using the hydrogen transport and accident analysis code MELCOR-TMAP developed at INL. The results of a sensitivity analysis based on MELCOR-TMAP simulations of hydrogen extraction efficiencies from the TEX test section using varying PbLi flow rates, hydrogen source rates from the SP, and material property uncertainties are also reported. Operation scenarios for TEX in consideration of the analyses based on results from MELCOR-TMAP are discussed.