Rejuvenation - Spent Hydroprocessing Catalysts - page 207

where t is time of leaching; X B is fractional conversion; τ is time for a complete conversion of
a single solid particle.

Diffusion through reaction rim controls
t
τ =

− X B ) 2 / 3 − + − X B )

1 3(1 2(1 (7.2)

Surface chemical reaction controls
t
τ =

− X B ) 1 / 3 1 − (1 (7.3)

7.1.2.2 Particle Changing Size (Shrinking Particle) Model

Chemical reaction controls
t
τ =

X B ) 1 / 3 1 − (1 − (7.4)

Liquid phase diffusion through the pores controls
t
τ =

X B ) 2 / 3 1 − (1 − (7.5)

Comparison of the data predicted by these models with the experimental data should identify
the rate-controlling process involved during leaching. It is obvious that diffusion in liquid
phase cannot be rate-controlling process. The data from leaching of pure metal sulfides
( Table 7.6 ) [480] gave the best-fit using the Eqn (7.4) ( Fig. 7.13 ), suggesting that chemical
reactions were the rate-controlling process. This is not surprising considering very low
porosity and surface area of the metal sulfides used for leaching.

For coked catalyst, the presence of the layer of coke has to be considered. Thus, in order for
leaching to take place, the acid molecules have to diffuse through the layer to contact catalyst
surface. Therefore, the mass transfer through the layer of coke deposited on catalyst surface is
the rate-controlling process. This is confirmed by the near-perfect fit of the experimental data
using Eqn (7.2) shown in Fig. 7.14 [480] . However, it may not be easy to describe the leaching
of metals from the pores of spent catalysts. According to Fig. 7.10 [490] leaching process

Table 7.6: Surface properties of metal sulfides [From ref. 480 . Reprinted with permission].

Surface area (m 2 /g)

Compound Pore volume (mL/g)

V 2 S 3 7 0 . 11

MoS 2 4 . 3 < 0 . 01

CoS 1 . 5 < 0 . 01

NiS 1 . 2 < 0 . 01