Mg scrap is notorious for the high cost and serious pollution of its recycling process due to the good wettability and similar density of Mg melt to its solid inclusions. To support the sustainable growth of Mg industry and application, intensive effort has been contributed to the development high efficiency, flux-free purification techniques for Mg scrap recycling. In the present study, the purification of Mg scrap melt via filtration was theoretically analyzed by multi-phase fluid hydrodynamics. The relationships between the nozzle size in the filtration medium, melt penetrating-through speed and other filtration parameters were formulated. To provide a guideline to filtration engineering, the influence of processing parameters on the filtering efficiency were discussed.