Preparations are currently underway at the OMEGA laser at the University of Rochester Laboratory for Laser Energetics (UR/LLE) to conduct direct drive laser implosion campaigns with inertial confinement fusion targets containing deuterium-tritium (DT) cryogenic ice layers. The OMEGA Cryogenic Target Handling System will fill plastic targets with high-pressure DT (150 MPa) at 300 to 500 K, cool them down to cryogenic temperature (<25 K), form the DT ice layer, and transport the targets to the OMEGA laser target chamber. Targets will then be shot with the 60-beam 30-kJ OMEGA laser. A tritium removal system has been designed to remove tritium from effluents associated with operation of the target chamber and its associated diagnostic antechambers, vacuum pumping systems, and target insertion systems. The design of the target chamber tritium removal system (TCTRS) is based on catalytic oxidation of DT and tritiated methane to tritiated water (DTO), followed by immobilization of DTO on molecular sieves. The design of the TCTRS presented a challenge due to the low tritium release limits dictated by the tritium license at UR/LLE. Aspen Plus, a commercial software package intended for the simulation and design of chemical processing systems operating at steady state, was used to simulate and design the TCTRS. A second commercial software package, Aspen ADSIM, was used to simulate and design the TCTRS molecular sieve beds, which operate at unsteady state. In this paper, we describe the design of the TCTRS and the benefits that were realized by use of the Aspen Plus and Aspen ADSIM software packages.