there. Experiments were carried out to determine the amount of the material
effectively bypassed and the volume of the dead zone. A simple modification
of an ideal reactor successfully modeled the essential physical characteristics
of the system and the equations were readily solvable.
Three concepts were used to describe nonideal reactors in these exam-
ples: the distribution of residence times in the system, the quality of mixing,
and the model used to describe the system. All three of these concepts are con-
sidered when describing deviations from the mixing patterns assumed in ideal
reactors. The three concepts can be regarded as characteristics of the mixing in
nonideal reactors.
One way to order our thinking on nonideal reactors is to consider model-
ing the flow patterns in our reactors as either CSTRs or PFRs as a first approx-
imation. In real reactors, however, nonideal flow patterns exist, resulting in
ineffective contacting and lower conversions than in the case of ideal reactors.
We must have a method of accounting for this nonideality, and to achieve this
goal we use the next-higher level of approximation, which involves the use of
macromixing information (RTD) (Sections 13.1 to 13.4). The next level uses
microscale (micromixing) information to make predictions about the conver-
sion in nonideal reactors. We address this third level of approximation in Sec-
tions 13.6 to 13.9 and in Chapter 14.
13.1.1 Residence-Time Distribution (RTD) Function
The idea of using the distribution of residence times in the analysis of chemi-
cal reactor performance was apparently first proposed in a pioneering paper by
MacMullin and Weber.1 However, the concept did not appear to be used exten-
sively until the early 1950s, when Prof. P. V. Danckwerts2 gave organizational
structure to the subject of RTD by defining most of the distributions of interest.
The ever-increasing amount of literature on this topic since then has generally
followed the nomenclature of Danckwerts, and this will be done here as well.
In an ideal plug-flow reactor, all the atoms of material leaving the reactor
have been inside it for exactly the same amount of time. Similarly, in an ideal
batch reactor, all the atoms of materials within the reactor have been inside it
for an identical length of time. The time the atoms have spent in the reactor is
called the residence time of the atoms in the reactor.
The idealized plug-flow and batch reactors are the only two classes of
reactors in which all the atoms in the reactors have the same residence time. In
all other reactor types, the various atoms in the feed spend different times
inside the reactor; that is, there is a distribution of residence times of the mate-
rial within the reactor. For example, consider the CSTR; the feed introduced
into a CSTR at any given time becomes completely mixed with the material
already in the reactor. In other words, some of the atoms entering the CSTR