The accurate prediction of the tritium inventory and permeation fluxes in the water-cooled lithium-lead (WCLL) breeding blanket of the European DEMO fusion reactor is a key aspect for future thermonuclear power plant licensing. In this context, a tritium transport analysis is essential for the evaluation of the tritium retention in LiPb (15.7 at. % Li) and in the structural components and tritium permeation fluxes into the cooling water. This study presents a COMSOL Multiphysics model of a portion of the minimum functional unit of the outboard equatorial module of the WCLL. The neutronics analysis, performed with the MCNP Monte Carlo transport code, allows for the assessment of the tritium generation rate and the volumetric power deposition in the lithium-lead, both of which are used as an input for tritium transport modeling. Moreover, the buoyancy forces and the magnetohydrodynamic effect are also included. In order to take into account a pulsed operation for the DEMO reactor, a suitable algorithm was developed. The results show peak velocities in LiPb up to 24.1 mm  with a maximum temperature at the first wall (FW) of 441°C. Most of the tritium is concentrated between the FW and the baffle plate, with partial pressures between 0.15 and 0.4 Pa considering Aiello’s correlation and in-house measurements of Sieverts’ constant on the HyPer-QuarCh II (HQ-II) device, whereas from 70 to 180 Pa adopting Reiter’s correlation. This has an impact also on the inventory in the Eurofer and in permeation fluxes to the water pipes. For Reiter’s correlation, the inventories in the Eurofer are about one order of magnitude lower with respect to LiPb, and the inventory in water is five orders of magnitude higher with respect to HQ-II and Aiello’s correlation.