Page 243 - Introduction to chemical reaction engineering and kinetics

9.1 Gas-Solid (Reactant) Systems 225

in which, for ease of notation, the stoichiometric coefficient b replaces I/~ used else-
where; b = \vsl > 0.
Examples of the other type in which the products are all gaseous, and the solid shrinks
and may eventually disappear are:

C(s) + O,(g) + CO,(g) 09
C(s) + WW -+ CO(g) + Hz(g) 09

We write a standard form of this type as

A(g) + bB(s) 4 products(g) (9.1-2)

The first type of reaction is treated in Section 9.1.2, and the second in Section 9.1.3.

9.1.2 Constant-Size Particle

9.1.2.1 General Considerations for Kinetics Model
To develop a kinetics model (i.e., a rate law) for the reaction represented in 9.1-1, we
focus on a single particle, initially all substance B, reacting with (an unlimited amount
of) gaseous species A. This is the local macroscopic level of size, level 2, discussed in
Section 1.3 and depicted in Figure 1.1. In Chapter 22, the kinetics model forms part of a
reactor model, which must also take into account the movement or flow of a collection
of particles (in addition to flow of the gas), and any particle-size distribution. We assume
that the particle size remains constant during reaction. This means that the integrity of
the particle is maintained (it doesn’t break apart), and requires that the densities of
solid reactant B and solid product (surrounding B) be nearly equal. The size of particle
is thus a parameter but not a variable. Among other things, this assumption of constant
size simplifies consideration of rate of reaction, which may be normalized with respect
to a constant unit of external surface area or unit volume of particle.
The single particle acts as a batch reactor in which conditions change with respect to
time t. This unsteady-state behavior for a reacting particle differs from the steady-state
behavior of a catalyst particle in heterogeneous catalysis (Chapter 8). The treatment
of it leads to the development of an integrated rate law in which, say, the fraction of B
converted, fn, is a function oft, or the inverse.
A kinetics or reaction model must take into account the various individual processes
involved in the overall process. We picture the reaction itself taking place on solid B sur-
face somewhere within the particle, but to arrive at the surface, reactant A must make
its way from the bulk-gas phase to the interior of the particle. This suggests the possibil-
ity of gas-phase resistances similar to those in a catalyst particle (Figure 8.9): external
mass-transfer resistance in the vicinity of the exterior surface of the particle, and inte-
rior diffusion resistance through pores of both product formed and unreacted reactant.
The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius
R at a particular instant of time, in terms of the general case and two extreme cases.
These extreme cases form the bases for relatively simple models, with corresponding
concentration profiles for A and B.
In Figure 9.1, a gas film for external mass transfer of A is shown in all three cases. A
further significance of a constant-size particle is that any effect of external mass transfer
is the same in all cases, regardless of the situation within the particle.
In Figure 9.l(b), the general case is shown in which the reactant and product solids
are both relatively porous, and the concentration profiles for A and B with respect to
radial position (r) change continuously, so that cn, shown on the left of the central axis,