2.5.2. Freeboard

The freeboard consists of a gas phase with a small amount of very fine particles with almost the same velocity. The gas component balance is

$$\frac{dM\_{f,j}^{m}}{dt} = 0 = \dot{M}\_{f,j}^{m-1} - \dot{M}\_{f,j}^{m} + \mathcal{M}\mathcal{W}\_{j} \cdot \sum\_{I\_{f}} \nu\_{i,j} \mathcal{R}\_{f,i}^{m} \tag{25}$$

and the solid component balance is

$$\frac{dM\_k^m}{dt} = 0 = \dot{M}\_k^{m-1} - \dot{M}\_k^m + M\mathcal{W}\_k \cdot \sum\_{l\_k} \nu\_{i,k} R\_{k,i}^m \tag{26}$$

Therefore, the overall mass balance expression is written as

$$\frac{dM^m}{dt} = 0 = \dot{M}\_f^{m-1} + \dot{M}\_k^{m-1} - \dot{M}\_f^m - \dot{M}\_k^m \,. \tag{27}$$

The linkage of the freeboard with the fluidized bed is carried out by applying Equation (28) for gases and Equation (29) for solids:

$$
\dot{M}\_f^{m=0} = \dot{M}\_d^{n=N} + \dot{M}\_b^{n=N} \tag{28}
$$

$$
\dot{M}\_k^{m=0} = \dot{M}\_{\text{clut}} \tag{29}
$$
