Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 457

The polymerization reactions (9.166) through (9.168) can have a significant effect on the
extraction and/or hydrolysis process.
Reactions (9.148), (9.150), (9.151), (9.154), (9.156), (9.159), (9.161), (9.162), and (9.164)
through (9.168) are pseudo-elementary steps. There have been numerous studies aimed at
revealing the chemistry of these steps. However, for our purposes, we will consider them
elementary steps. The reaction rate so defined represents that from the rate-controlling sub-
steps based on detailed chemistry.
With the reaction mechanism given by Eqns (9.146) through (9.168) , one can write reaction
rate expressions for any given component of interest. However, the reaction rate expressions
could potentially involve a large number of kinetic parameters due to the number of reactions
involved. The kinetic parameters are not easy to determine theoretically based on chemistry
and physics of matter. Therefore, further simplification is desirable. The following assump-
tions are made:

1. The condensation reactions are neglected, i.e. reactions (9.166) through (9.168) are
neglected;
2. The breakage of glycosidic bonds has an equal rate or reactivity as long as they are in the
same phase;
3. The affinities of glycosidic bonds to hydrogen ions (H þ and H 3 O þ ) are the same, as long
as they are in the same phase.

The above three assumptions form the basis for the discussions to follow.
It is assumed that the adsorption and desorption reactions occur at much faster rates
than those of surface reactions on the woody biomass surface. Therefore, one can assume
that the adsorption steps are always in equilibrium. The adsorption process can be repre-
sented as the elementary reversible reactions such as that shown by Eqn (9.153) . Thus,
at the timescale of the surface reactions, the adsorption isotherm for hydrogen ions is
given by

q nH þ
q nV C H þ

K S ¼ (9.169)

where K S is the adsorption equilibrium constant of H þ onto X n on the biomass solid surface
(or R-X n OH); q n-H þ is the concentration or fraction of X n on the biomass solid surface that is
associated with H þ . q nV is the concentration or fraction of X n on the biomass solid surface that
is not associated with H þ ; and C H þ is the concentration of H þ in the extract liquor. The total
concentration of xylan on the biomass solid surface is given by

q nH þ þ q nV ¼ q n (9.170)

Substituting Eqn (9.169) into Eqn (9.170) , we obtain

K S C H þ q n
1

q nH þ ¼ (9.171)

þ K S C H þ

Ideally, q j is the surface concentration of component j on the woody biomass surface. q j can be
conveniently expressed as moles per g-inert (or water insoluble/undissoluble) biomass. The
total surface area can be assumed to be constant during the extraction process.