SYNTHESIS GAS UTILIZATION FOR TRANSPORTATION FUEL PRODUCTION - Biomass as a Sustainable Energy Source for the Future - page 542

hydrogen (H 2 ) and carbon monoxide (CO) diffuse from the fluid at the outer
surface of a catalyst particle through the pores to the catalytic reactive sites
inside the particle, while the reaction products diffuse out of the particle. The
main issue of this problem is what would be a suitable molar H 2 /CO ratio at
the outer surface of the catalyst particles to favor the FT reactions throughout
the particles.
From a stoichiometric point of view, this H 2 /CO ratio should be close to

3 − α ,where α is the chain growth probability (see Section 17.2.2). However,

α is sensitive to the amount of hydrogen. The chain growth probability

increases with a lower H 2 /CO ratio by reducing the termination of chain
growth by hydrogen. Another complication is the effect of spatially distrib-
uted reaction

diffusion in the catalyst particle. H 2 diffuses faster than CO
and is consumed in larger amounts. Thus, the H 2 /CO ratio will vary along
the radial coordinate of the particle. This is borne out by the radially distrib-
uted concentrations of the reactants, which can be obtained by solving the
reaction

-

diffusion equations for a catalyst particle. Solving such equations
with realistic kinetics, e.g., Equation (17.1), requires a numerical approach
because coupled nonlinear differential equations are involved. Here, we will
use a simplified reaction

-

diffusion equation for which an analytical solution
can be obtained to illustrate effects of unequal diffusion. Our gross simpli-
fications (not suitable for real design cases) involve assuming:

-

￿ Zero-order kinetics (obtained by ignoring the partial pressure dependencies

in Equation (17.1))

￿ Constant α

￿ Fickian diffusion, which neglects flux interactions between reactants and

products inside the catalyst pores

The analytical solution to the reaction - diffusion equation is

=c ð i + s i

a
6

r 2 z 2 c i z ðÞ − for 0 ≤ z ≤ r

D i

=c ðÞ
i

c i r ðÞ i = CO,H 2

s jj
D i

a
6 r 2

c ðÞ
i

c i 0 ðÞ≥ 0 = > physical feasibility ≤

:

s −1 m −3

cat

a zero-order reaction rate coefficient kmol

:

c ðÞ
i

m −3

concentration of component i at surface kmol ð Þ

:

Fickian diffusion coefficient of component i m 2 s −1

D i ð Þ

:

r Radius of spherical catalyst particle m ðÞ

:

s i stoichiometric coefficient of component i ðÞ

:

Note s i < 0 for a reactant

:

z radial coordinate fromcenter to surface S ð Þ ðÞ m

: