Pv. Joshi et al., Detailed kinetic models in the context of reactor analysis: Linking mechanistic and process chemistry, ENERG FUEL, 13(6), 1999, pp. 1135-1144
Detailed kinetic models for the modeling of complex chemistries, including
thermal cracking, catalytic reforming, catalytic cracking, and hydroprocess
ing, offer the compelling advantage chemical significance at the mechanisti
c level. They carry a considerable burden, however, in terms of species, re
actions, and associated rate parameters. This, together with the batch and
the plug flow reactor balances, requires solution of a large system of eith
er stiff ordinary differential equations (ODE) or stiff differential algebr
aic equations (DAE), for both homogeneous and heterogeneous processes. It i
s often faster numerically to solve a stiff system of ODEs and, thus, it ca
n be useful to convert a system of DAEs to ODEs for numerical solution sche
mes. For heterogeneous PFR systems, the reactor steady-state balances resul
t in a set of DAEs, and it would therefore be desirable to construct the as
sociated set of ODEs to minimize CPU demand. To this end, we propose that s
uch a transformation can be achieved by making the "flowing surface species
" approximation. This involves approximating the overall rate of reaction o
f surface species, which is identically equal to zero at reactor steady sta
te, by a spatial derivative. We show that this approximation becomes better
as the system of equations becomes stiffer, and, hence, is a reverse analo
gy of the kinetic steady-state approximation in the case of batch systems.
To validate the proposition, we analyze various contrived and real examples
of mechanistic kinetics for heterogeneous systems.