Page 155 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.1 Design Structure for Isothermal Reactors 127

our general mole balance equation (level 1) to a specific reactor to arrive at the
design equation for that reactor (level 2). If the feeld conditions are specified
(e.g., NAo or FA0). all that is required to evaluate the (design equation is the rate
Use the algorithm
rather than of reaction as a fuinction of conversion at the same conditions as those at which
memorizing the reactor is to be operated (e.g., temperature and pressure). When -rA =
equations
f(X) is given, one can go directly from level 3 to level 7 to determine either the
time or reactor volume necessary to achieve the specified conversion.
If the rate of reaction is not given explibitly as a function of conversion,
the rate law must be determined (level 4) by either finding it in books or jour-
nals or by deterimining it experimentally in the laboratory. Techniques for
obtaining and analyzing rate data to determine the reaction order and rate con-
stant are presented in Chapter 5. After the rate law has been established, one
has only to use stoichiometry (level 5) together with the conditions of the sys-
tem (e.g., constant volume, temperature) to express concentration as a function
of conversion. By combining the information in levels 4 and 5, one can express
the rate of reaction as a function of conversion and arrive at level 6. It is now
possible to determine either the time or reactor volume necessary to achieve
the desired conversion by substituting the relationship relating conversion and
rate of reaction into the appropriate design equation. The design equation is
then evaluated in the appropriate manner (Le., analytically using a table of
integrals, or numerically using an ODE solver). Although this structure empha-
sizes the determination of a reaction time or volume For a specified conversion,
it can also readily be wed for other types of reactor calculations, such as deler-
mining the conversion for a specified volume. Different manipulations can be
performed in level 7 to answer the types of questions mentioned here.
The structure shown in Figure 4-1 allows one to develop a few basic con-
cepts and then to arrange the parameters (equations) associated with each con-
cept in a variety of ways. Without such a structure, one is faced with the
possibiliity of choosing or perhaps memorizing the correct equation from a
multitude of equations that can arise for a variety of different reactions, reac-
tors, and sets of conditions. The challenge is to put everything together in an
orderly and logical fashion so that we can proceed to arrive at the correct equa-
tion for a given situation.
Fortunately, by using an algorithm to formulate CRE problems, which
happens to be analogous to ordering dinner from a fixed-price menu in a fine
French restaurant, we can eliminate virtually all memorization. In both of these
algorithms we must make choices in each category. For example, in orderling
from a French menu, we begin by choosing one dish from the appetiz,ers
listed. Step 1 in the analog in CRE is to begin by choosing the mole balance
for one of the three types of reactors shown. In step 2 we choose the rate law
(eiztre'e), and in step 3 we specify whether the reaction is gas or liquid phase
(cheese or dessen). Finally, in step 4 we combine steps 1, 2, and 3 and obtain
an analytical solution or solve the equations using an ordinary differential
equation (ODE) solver. (See complete French menu on the CD-ROM)
We now will apply this algorithm to a specific situation. The first step is
to derive or apply the mole balance equation for the system at hand. Suppose
that we have, as shown in Figure 4-2, mole balances for three reactors, three