Page 277 - Introduction to chemical reaction engineering and kinetics

258 Chapter 9: Multiphase Reacting Systems

grate moved at 0.3 m mm-‘, and 0.5 when the grate moved at 0.7 m mu-‘. Clearly state
any assumptions made.
(b) What is the value of each tt for 2-mm particles at the same T and P?
(c) For the particles in (b), what is the speed of the grate, if fn = 0.92?
9-8 Consider the reduction of relatively small spherical pellets of iron ore (assume Pam = 20 mol
L-l) by hydrogen at 900 K and 2 bar partial pressure, as represented by the shrinking-core
model, and

4H2 + FesO.&) = 4H20 + 3Fe(s)

(a) Show whether gas-film resistance is likely to be significant in comparison with ash-layer
resistance at relatively high conversion (fa + 1). For diffusion of Hz, assume D = 1 cm’
s-l at 300 K and D m T3’*; assume also that D, = 0.03 cm* s-t for diffusion through the
ash layer. For relatively small, free-falling particles, kAg = D/R.
(b) Repeat (a) for fa + 0.
9-9 (a) According to the shrinking-particle model (SPM) for a gas-solid reaction [A(g)+bB(s) +
gaseous products], does kAg for gas-film mass transfer increase or decrease with time of
reaction? Justify briefly but quantitatively.
(b) (i) For given c&, fluid properties and gas-solid relative velocity (u), what does the result
in (a) imply for the change of ch (exterior-surface, gas-phase concentration of A)
with increasing time? Justify.
(ii) What is the value of ch as t + tl, the time for complete reaction? Justify.
(iii) To illustrate your answers to (i) and (ii), draw sketches of a particle together with
concentration profiles of A at 3 times: t = 0,O < t < tl, and t + tl .
Assume that the particle is spherical and isothermal, that both gas-film mass transfer resistance
and reaction “resistance” are significant, and that the Ranz-Marshall correlation for kAg is
applicable. Do not make an assumption about particle “size, ” but assume the reaction is first-
order.
9-10 For a gas-liquid reaction, represented by 9.2-1, which occurs only in the bulk liquid, the rate
law resulting from the two-film model, and given by equation 9.2-18, has three special cases.
Write the special form of equation 9.2-18 for each of these three cases, (a), (b), and (c), and
describe what situation each refers to.
9-11 For A(g) + bB(9 + products (B nonvolatile) as an instantaneous reaction:
(a) Obtain an expression for the enhancement factor E (i.e., EC) in terms of observable quan-
tities [exclusive of (-IA)]; see Figure 9.9, equation numbered 9.2-56.
(b) Show Ei = &l6.
(c) Show, in addition to the result in (a), that

DBecB
Ei=l+p
DAd’cAi
(d) Show that the same result for Ei for liquid-film control is obtained from the expressions
in (a) and (c).
9-12 (a) For the instantaneous reaction A(g) + bB(Q + products, in which B is nonvolatile, it has
been shown that, according to the two-film model, the significance of the reaction plane
moving to the gas-liquid interface (i.e., 6 + 0, where 6 is the distance from the interface
to the plane) is that the gas-film resistance controls the rate. What is the significance of
this for Ei, the enhancement factor?
(b) What is the significance (i) in general, and (ii) for Ef, if the reaction plane moves to the
(imaginary) inside film boundary in the liquid phase (i.e., 6 + &, the film thickness)?
9-13 From equations 9.2-45 and 9.2-45a, show the significance of each of the two limiting cases
(a) Ha + large and (b) Ha + 0.