**6.2 Geometrical contraction models**

The basis of this model is that hydrogenation and dehydrogenation reactions transpire uniformly from the surface into the bulk of particle and the particles are uniform in size and shape [58]. The reaction fraction relationship between distances in particles of various shapes (sphere, plate and cylinder) is given by:

$$\varepsilon = \mathbf{1} - \left(\frac{r}{r\mathbf{o}}\right)^d \tag{4}$$

Where d = dimensionality, r = lengths of the unreacted part, *r*0= length of the whole particles, *ε* = reaction fraction.

The geometrical contraction models are derived from this relationship equation and assumptions of isothermal conditions ([59–62]; N [63]; Nobuyoshi [64]). These are the geometrical contraction models:
