Kovenklioglu and De Lancey (1979) proposed an approximation to
optimal heat exchange and consequently, to the optimal
temperature-profile, by specifying the insulation thickness for a
given reactor diameter.Kovenklioglu and De Lancey, 1979, found
higher conversions than those corresponding to adiabatic operation
for some insulation thicknesses and inlet temperatures.The
objective of this present work is to study the possibility of
improving upon adiabatic operation, e.g., achieving a higher
conversion for a fixed reactor-size or reducing the size of the
latter for a given conversion, by accepting heat losses.In order to
simplify the calculations, a plug-flow model was used to describe
the reactor instead of describing more complicated models (Pereira
and coworkers, 1984 and 1984b). In spite of the generality of the
present work, a specific reaction must be considered, because of
the uniqueness of the kinetic equation. The reaction so selected
was the oxidation of SO2, which was, also, employed in other
studies (Calderbank, 1953, Mars and Van Krevelen, 1954, and
Kovenklioglu and De Lancey, 1979). In addition, this important
reaction incorporates some of the problems encountered in practice,
namely, hyperbolic kinetics and resistance to internal
diffusion.System studiedAs has been indicated, the reaction is
catalyzed by n solid consisting primarily of V2O5. It in well-known
that the kinetic equation for this reaction is quite complicated
(Azevedo, 1982), and that it takes place in a liquid phase inside
the pores of the catalyst. Following a pseudo homogeneous model,
the kinetic equation incorporates two effectiveness factors. One
for the gaseous phase no, and another one for the liquid phase nt.
Of the large number of kinetic equations proposed, more than thirty
(Azevedo, 1982), the one by Mars and and Messen (1964) was chosen,
namely,WhereThe values used for the constants areAnd, for the
equilibrium constant (Lifjberg and Villadsen, 1972),The
effectiveness factor in the liquid phase was estimated in agreement
with Neth and coworkers (1980):WhereAndReactor modelThe material
and heat balances for plug flow, in dimensionless variable, are
andFundamentally, Da represents the conditions at the reactor
inlet, while Da takes into consideration the generation of heat
inside the reactor. The ratio NTUH indicates the heat transfer
through the wall, and is proportional to the overall heat transfer
coefficient U, representing the influence of the thickness of
insulation.Equations (8) and (9) were solved by employing a
fourth-order Runge-Kutta method for the system of two differential
equations.Comparison between operations with different heat
transfer conditionsCalculations for different cases, varying the
values of Da and Da and for different values of To and NTUH were,
then, performed. Figure 1 is an example the results obtained for To
= 703K, three combinations of Da and Da, and different values of
NTUH. In all of these cases, To = 300K.A series of values for NTUH
exists, which improves the results at the reactor exit over
adiabatic operation (NTUH = 0). Moreover, one of these values
exhibits a maximum in the outlet conversion. This maximum is
dependent upon the values of the remaining parameters.All of the
preceding agrees substantially with the results of Kovenklioglu and
De Lancey (1979). The equilibrium conversion under adiabatic
operation is, often, achieved much earlier than the reactor exit;
as a result, the entire reaction is not utilized, and, somewhere
along the length of the reactor, the variable r 0. Consequently,
any comparison made under conditions where NTUH =/= 0 cannot be too
realistic. In order to make a comparison under equivalent
conditions, to return to the study of adiabatic operation is
essential.Study of adiabatic operationWhen NTUH = 0, Equation (9)
is simplified. After dividing Equation (8) by Equation (9),
integrating and substituting = T/ T0.
