For a modern blast furnace (BF), a smooth tapping is a key prerequisite to keep the furnace running efficiently. An understanding of the hearth drainage and the influence of associated operational factors is therefore vitally important. To investigate the hearth tapping, a 2D computational fluid dynamics (CFD) model is developed and verified based on results from an experimental Hele–Shaw model. A series of simulation cases are conducted with the CFD model, studying the effect of the blast pressure, packed bed permeability, coke-free zone, and initial accumulated amounts of liquids on the tapping behavior, using water and oil as liquids as in the experimental model. To quantify the simulation findings, the effect of the above process conditions on the evolution of some drainage parameters, i.e., the liquid levels and volumes, flow rates, ratio of oil and water in the outflow, as well as the angle of the interfaces, are analyzed. The results reveal interesting findings of the hearth drainage and also show similarities with the outflow patterns of the hearth liquids in operating BFs.