Ensuring a secure and reliable execution of the International Fusion Materials Irradiation Facility (IFMIF) and the DEMO-Oriented Neutron Source (DONES) requires their liquid lithium loops to be purified from hydrogen isotopes which are generated during operation. For this purpose, an yttrium pebble-bed will serve as a hydrogen hot trap. Former intentions to predict the retention behavior of an yttrium pebble-bed are based on the consideration of the trap as a black box with a predetermined trap efficiency. Disregarding the internal physical mechanisms of the gettering process these models are built on simplified assumptions and should be extended to allow reliable trap designs for IFMIF/DONES. Therefore, a detailed numerical model describing the hydrogen transport from flowing liquid lithium into an yttrium pebble-bed has been developed from scratch within the scope of this work. It enables simulating the hydrogen retention process into an arbitrarily dimensioned getter bed for the low concentration regime by solving a system of differential equations with a finite-difference approach. The model is used to calculate the time evolution of the hydrogen concentrations in a simplified loop system which is connected in line with an yttrium pebble-bed. Special focus is placed on the observation of a case relevant for IFMIF/DONES considering a constant generation of tritium in the loop. Simulation results reveal that the trap efficiency decreases with time and that lower system temperatures significantly improve the trap efficiency. It is found that for heavier pebble-beds the tritium inventory build-up in the lithium is slowed down more efficiently. These findings are of great importance for the design of the hot traps for IFMIF/DONES. To demonstrate the reliability of the model experimental data of a previous deuterium retention experiment are successfully reproduced.