Page 247 - Introduction to chemical reaction engineering and kinetics

9.1 Gas-Solid (Reactant) Systems 229

Equation 9.1-15 equates the rate of heat transfer by conduction at the surface to the rate
of heat transfer by conduction/convection across a thermal boundary layer exterior to
the particle (corresponding to the gas film for mass transfer), expressed in terms of a
film coefficient, h, and the difference in temperature between bulk gas at Tg and particle
surface at T,;

at r = 0, (dT/&& = 0 (9.1-16)

Equation 9.1-16 implies no heat transfer through the center of the particle, from con-
sideration of symmetry.
Taken together with the continuity equations, the energy equation complicates the
solution further, since cA and T are nonlinearly coupled through (-Y*).

9.1.2.3 Shrinking-Core Model (SCM)

9.1.2.3.1. Isothermal spherical particle. The shrinking core model (SCM) for an
isothermal spherical particle is illustrated in Figure 9.l(a) for a particular instant
of time. It is also shown in Figure 9.2 at two different times to illustrate the ef-
fects of increasing time of reaction on the core size and on the concentration pro-
files.
Figure 9.2(a) or (b) shows the essence of the SCM, as discussed in outline in Sec-
tion 9.1.2.1, for a partially reacted particle. There is a sharp boundary (the reaction
surface) between the nonporous unreacted core of solid B and the porous outer shell
of solid product (sometimes referred to as the “ash layer,” even though the “ash” is
desired product). Outside the particle, there is a gas film reflecting the resistance to
mass transfer of A from the bulk gas to the exterior surface of the particle. As time in-
creases, the reaction surface moves progressively toward the center of the particle; that
is, the .unreacted core of B shrinks (hence the name). The SCM is an idealized model,
since the boundary between reacted and unreacted zones would tend to be blurred,
which could be revealed by slicing the particle and examining the cross-section. If this

, - G a s f i l m 7

Figure 9.2 The shrinking-core model
Solid & Gas Solid A Gas (SCM) for an isothermal spherical par-
Profile Profile ticle showing effects of increasing re-
(a) t = tl (b) t = t2 > tl action time t