A three-phase, transient model for hydrogen degassing of molten steel in an argon-stirred, slag-covered ladle has been developed based on the Eulerian method. The slag layer is treated as a separate phase with bubble coalescence and breakup accounted for using a discrete population balance model. A k-e turbulence model with a bubble induced source term is included along with drag, lift, turbulence dispersion, and wall lubrication submodels for the interfacial force terms. The model predictions are validated using industrial data from a vacuum arc degasser at Sheffield Forgemasters International Ltd. The effect of different ladle design and process parameters are subsequently investigated. Raising the argon injection rate from 0.07 to 0.21 m3min-1 is found to double the hydrogen degassing efficiency. The optimum efficiency is obtained for a porous plug placement at a radial distance of r/R=0.6, which is 24% more efficient than a central plug. A ladle aspect ratio of L/D=2 produces an increase in degassing efficiency of 32% compared to an aspect ratio of L/D=1.25, while the presence of a 10mm slag layer is shown to reduce efficiency by 26% in comparison to a slag free melt.