Page 157 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.2 Scale-Llp of Liquid-Phase Batch Reactor Data to the Design of a CSTR 129

rate laws, and the equations for concentrations for both liquid and gas phases.
In Figure 4-2 the algorithm is used to formulate the equation to calculate the
PFR reactor volume for a jirst-order gas-phase reaction and the pathwtiy to
arrive at this equation is shown by the ovals connected to the dark lines
through the algorithm. The dashed lines and the boxes represent other path-
ways for solutions to other situations. For the reactor and reaction specified we
will choose

We can solve the equa- 1. the mole balance on species A for a PFR,
tions in the combine step 2. the rate law for an irreversible first-order reaction,
either 3. the equation for the concentration of species A in the gas phase
1) Analytically (Ap- (stoichiometry), and then
pendix Al) 4. combine to calculate the volume necessary to achieve a given conver-
2) Graphically (Ch. 2) sion or calculate the conversion that can be achieved in a specified
3) Numerically, or reaction volume.
(Appendix A4)
4) Using Software Fur the case of isothermal operation with no pressure drop, we were able
(Polymath).
to obtain an analytical solution, given by equation IB, which gives the reatctor
volume necessary to achieve a conversion X for a gas-phase reaction carried
out isothermally in a PFR. However, in the majority of situations, analytical
solutions to the ordinary differential equations appearing in the combine step
are not possible. Consequently, we include POLYMATH, or some other ODE
solver such as MATLAB, in our menu in that it inakes obtaining solutions to
the differential eyuations much more palatable.

4.2 Scale-up of Liquid-Phase Batch
Reactor Data to the Design of a CSTFl
One of the jobs in which chemical engineers are involved is the scale-up of
laboratory experiments to pilot-plant operation or to full-scale production, In
the pasr, a pilot plant would be designed based on laboratory data. However,
owing to the high cost of a pilot-plant study, this step is beginning to be sur-
passed in many instances by designing a full-scale plant from the operation of
a laboratory-bench-scale unit called a microplant. To make this jump success-
fully requires a tliorough understanding of the chemical kinetics and transport
limitations. In this section we show how to analyze a laboratory-scale batch
reactor in which a liquid-phase reaction of known order is being carried out.
After determining the specific reaction rate, k, from a batch experiment, we use
it in the design OF a full-scale flow reactor.

4.2.1 Batch Operation

In modeling a batch reactor, we have assumed that there is no inflow or
outflow of material and that the reactor is well mixted. For most liquid-phase
reactions, the density change with reaction is usually small and can be
neglected (Le., V = VO). In addition, for gas phases in which the batch reactor