3.3.3. Screen

The screen apparatus is a steady-state unit, which is described in terms of the grade efficiency *<sup>G</sup>*(*x*), calculated according to the model of Plitt [61] as

$$G(\mathbf{x}) = 1 - \exp\left(-0.693 \left(\frac{\mathbf{x}}{\mathbf{x}\_{\rm cut}}\right)^{\alpha}\right). \tag{63}$$

*<sup>G</sup>*(*x*) determines the mass fraction of material of size *x*, which leaves the screen through an outlet for coarse particles; *xcut* is the cut size of the classification model; α is the separation sharpness.

For proper consideration of the distributed parameters, each deck of the screen unit formulates two diagonal transformation matrices for the particle size distribution (PSD): for coarse (*Tc*) and for fines (*Tf*) output, so that

$$\begin{aligned} T\_{i,i}^c &= G(\mathbf{x}\_i) \\ T\_{i,i}^f &= 1 - G(\mathbf{x}\_i) . \end{aligned} \tag{64}$$

The total mass flows of coarse .*mcout* and fines .*mfout*outlets can be calculated as

$$\begin{aligned} \dot{m}\_{\text{out}}^c &= \dot{m}\_{\text{in}} \sum\_{i=1}^{L\_1} G(\mathbf{x}\_i) \cdot \mathbf{c}\_i \\ \dot{m}\_{\text{out}}^f &= \dot{m}\_{\text{in}} \Big(1 - \sum\_{i=1}^{L\_1} G(\mathbf{x}\_i) \cdot \mathbf{c}\_i\Big) \end{aligned} \tag{65}$$

where .*min* is the mass flow at the inlet, *ci* is the mass fraction of particles of size *xi*, and *L*1 is the number of size classes.

Application of the transformation matrices was performed according to Equations (52) and (55).
