CHAPTER 4 Chemical Kinetics and Applications

CHAPTER 10: Basic reactor models and evaluation of rate expressions
from experimental data
In spite of the advances made by absolute kinetic rate theories, the
ultimate determination of the kinetic rate form and the evaluation of the
appropriate kinetic parameters has to be based on experimental results.
Only when the rate form has been confirmed in the laboratory and the rate
parameters evaluated, preferably at conditions close to those contemplated
for the large scale process, can an engineer use with some confidence the
rate and its parameters for design purposes or for predictions of events in
the atmosphere.
The question then arises, if the reaction rates have to be determined
by experiments of what help are the kinetic theories to chemical or
environmental engineers? The knowledge of reaction mechanism leads to
postulated rate forms. It is always much easier to check a postulated rate
form, find out whether the experimental data confirm it in its entirety or
indicate that a limiting case is sufficient, than to find what rate form
experimental data conform to without the prior knowledge of that form. In
other words, it is clear that if one knows the expected rate form one can
plan well the experiments, and minimize the number of necessary
experiments, in order to confirm the postulated rate expression and
determine its parameters. Without "a priori" knowledge of the rate
expression more experimentation and more work is necessary in order to
extract all the information. At the same time prediction of kinetic
constants and activation energies from transition state theory helps in
setting up the expected upper limits on the kinetic constants and in
assessing the temperature sensitivity of reaction. This also helps in
planning properly the experiments.
In order to understand how rate expressions are evaluated from
laboratory experimental measurements it is instructive to consider first
what types of experiments are usually possible and in what environments and
under what conditions are they done. We will restrict ourselves here to
experiments performed in homogeneous systems. 10.1 Reaction environments and conditions for determination of reaction
rates in homogeneous systems
Typically laboratory experiments can be performed in one of the
reactor types described below. Each of the reactor types can be operated
(more or less successfully) under isothermal, adiabatic, or non-isothermal
conditions. Under isothermal experimental conditions the temperature of any point of
the reaction mixture in the reactor should be the same and constant (equal
to the desired experimental temperature) at all times during the run. Adiabatic experimental conditions are achieved when the reaction mixture
does not exchange any heat with the surroundings (other than sensible heat
of the inflow and outflow stream in flow reactors) and no work is done on
or by the reaction mixture (other than PV work of the fluid entering and
leaving the vessel in flow reactors). Non-isothermal experimental conditions are achieved: a. either when a temperature program with respect to time or position in
the reactor is established
b. or when the reactor establishes its own temperature profile in time
and space while exchanging heat with the surroundings. From the point of view of determination of kinetic rates, isothermal
conditions are preferred. Kinetic data for simple reactions with well
defined stoichiometry can also be obtained from adiabatic runs, but
interpretation of non-isothermal runs is usually extremely tedious and is
to be avoided. The typical reactor types in which experiments are performed are: 10.1.1 BATCH REACTOR |[pic] | |
| |[pic] | A typical batch reactor [pic] is a vessel of constant volume (i.e., a
flask, autoclave, etc.) into which the reactants are charged at the
beginning of the run. The reactor is equipped either with a
cooling/heating coil or jacket, or is well insulated, and can be run
isothermally (or close to it) or adiabatically. A mixer provides for
vigorous agitation of the reaction system. The progress of reaction can be
monitored by taking samples of the reaction mixture in specified time
intervals and analyzing their composition, i.e. concentrations of certain
components are observed as a function of time. In case of gas phase
reactions, which proceed with the change in the number of moles, the change
of the overall pressure in the system can be monitored in time and tied to
reaction progress in case of single reactions.
Another type of batch reactor, which is infrequently used in practice
to generate rate data but which illustrates an important concept to be used
later, is the constant pressure batch system where the volume of the
reaction mixture may change in time (i.e. in case of gas phase reactions
which proceed with the change in the total number of moles). 10.1.2 SEMIBATCH REACTOR: [pic] In the case of a semibatch reactor some of the reactants are charged at
the beginning of the run while one or more reactants are added continuously
throughout the run. Again, the reactor can be run isothermally or
adiabatically, and sampling of the reaction mixture is performed in time in
order to monitor the progress of reaction. This reactor type may be quite
useful when one is trying to determine the reaction order with respect to
say reactant [pic] and constantly keeps adding reactant [pic] in large
excess. It is also a convenient device in complex reaction systems to
study the effect of the order of reactant addition on selectivity and yield
etc. 10.1.3 CONTINUOUS FLOW REACTOR: | |[pic] |
|[pic] | | Reaction rates and rate expressions can also be determined in
continuous flow systems run at steady state. Two basic types of continuous
flow reactors are: the ideal plug flow reactor (PFR) and the ideal
continuous flow stirred tank reaction (CFSTR). 10.1.4 PLUG FLOW REACTOR (PFR):
The main assumption of the ideal plug flow reactor is that the fluid
is perfectly mixed in the direction perpendicular to main flow and that
there is absolutely no mixing in the axial direction, i.e. in the direction
of flow. Thus, it is visualized that all fluid molecules move at a uniform
velocity [pic], i.e. the molecules that enter at [pic] form a front (plug)
that moves at velocity [pic] all the way to the exit. Therefore, there are
no variations in composition and temperature in the direction perpendicular
to flow, while concentration changes in the axial or [pic] direction as one
proceeds downstream.
The assumptions of the plug flow reactor are frequently met in
industrial practice and in the laboratory. High Reynolds number flow in
sufficiently long tubes, i.e. tubes of high [pic] (length/diameter) ratio,
will usually approximate well the plug flow reactor. Flow in packed beds
can also be treated as plug flow. This reactor can be operated
isothermally or adiabatically. 10.1.5 CONTINUOUS FLOW STIRRED TANK REACTOR (CFSTR):
The CFSTR is also frequently called the backmixed reactor, ideal
stirred tank reactor (ISTR), etc. The main assumption is that the reaction
mixture in a CFSTR is ideally or perfectly mixed. Thus, when the reactor
operates at steady state every point (i.e. every portion) in the reactor
has the same composition and temperature. Since there is nothing to
distinguish the points in the exit line from the points in the reactor,
this implies that the composition and temperature in the exit stream is
identical to the composition and temperature of the reaction mixture in the
reactor. This ideal reactor in practice is approached by devices that
provide a very vigorous mixing of the reaction mixture. It can be operated
isothermally or adiabatically.
Other flow type reactors which do not approach a PFR or CFSTR
behavior are not useful for evaluation of rate expressions.
We have mentioned before that it is desirable to perform kinetic runs
at constant temperature. Of the above reactor types CFSTR is the easiest
to run at isothermal conditions. When operated at steady state, the
composition in the reactor is constant and the heat released (or taken) per
unit time is constant and can be readily removed or provided. In contrast,
in a batch reactor, since the composition changes in time so will the heat
released or absorbed; thus, one must have sufficient flexibility to meet
varying heat requirements. Similarly, in a PFR fluid composition changes
along the reactor, and thus the heat released or taken per unit reactor
length changes along the reactor. Cooling or heating must meet this
varying requirements.
It also should be pointed out that flow reactors (especially
laboratory ones) operate essentially at constant pressure conditions since
the pressure drops are usually negligible. In making energy balances,
friction losses, or the work done on the fluid by the impeller, can
generally be neglected in comparison to heats of reaction. At the same
time, since the volume of the reaction mixture is fixed in flow reactors
and also [pic], this means that in the case of gas phase reactions which
proceed w