Stable blast furnace operation is required to reduce energy consumption and CO 2 emission in iron and steelmaking industry. For the stable blast furnace operation, precise controlled drainage is one of the important factors. Therefore, in this work, the effect of coke diameter, void fraction, coke diameter distribution, coke free space, impermeable zone, slag viscosity in a blast furnace hearth on drainage rates, gas-slag and slag-iron interfaces shapes and maximum gas-slag interfaces height were examined with a three-dimensional mathematical model.The results indicate that the conditions of the peripheral region at the taphole level determine the residual slag volume. The packed bed in the region 2.0 m from the taphole has about 50 % of contribution to the residual slag volume. The void fraction change has the largest effect on the gas-slag interfaces height. The coke diameter distribution has little effect on the total drainage rate as well as the coke diameter of the uniform packed bed, coke free space, and impermeable zone bellow the taphole level. The taphole conditions dominate the total drainage rate under the terms of the assumed blast furnace conditions. The conditions of the peripheral region in the hearth determine the drainage rate patterns of the iron and slag. The peripheral region's permeability can be predicted from the drainage rate patterns of iron and slag, if precise measurement of the drainage rate patterns can be achieved. A drainage pattern, whether iron drains prior to slag or slag drains prior to iron, is largely affected by a drainage interval.