*2.3. Formulation of Mathematical Model*

The burden structure model in COREX MG is formulated as follows.

(1) Whenever the coal-gimbal distributor or the DRI-flap distributor is used, the burden pile is formed in a ring at certain radius and uniformly distributed in the circumferential direction. It is assumed that the two-dimensional section of the burden profile is a triangle, the shape of the triangle is determined by the width of the burden flow and the volume of the burden batch together, and the position of the triangle in radius direction is determined by the chute angle or flap angle.

(2) As mentioned above, the formation of COREX burden pile is in a developing phase, therefore, the width (*W*) of the burden pile is considered to be equal to the width of the burden flow arriving at the burden surface. The measured results for the width (*W*) of burden piles, the locations of the pile's left (*L*) and right (*R*) edges for coal, and DRI for different rings in physical experiment are listed in Table 1 [15].

**Table 1.** Measured results of the width of burden piles for coal and DRI in physical experiment (Units: mm).


Through regression analysis of the experimental data, the relationships between burden pile width and ring radius were obtained as shown by Equations (4) and (5) for coal and DRI respectively.

$$\mathcal{W}\_{\text{coal}} = 41.667 \mathcal{R}\_i + 177.92 \tag{4}$$

$$\mathcal{W}\_{\rm DRI} = 2\Im R\_i + 257 \tag{5}$$

(3) The impinging effect and the mixing between sequential layers (rings) are ignored. Based on observations from physical experiments, it was found that the larger and lighter coal particles more easily to roll than the ore particles if they charged on an inclined surface. Therefore, a modification coefficient (greater than 1) is introduced to take it into account.
