Page 54 - Introduction to chemical reaction engineering and kinetics

36 Chapter 2: Kinetics and Ideal Reactor Models

(b) From the definition of space time given in Section 2.1, as in equation 2.3-2,

7 = v/q, (2.3-2)

This is the same result as for residence time t in constant-density flow, equation 2.4-8.
However, in this case, density is not constant through the PFR, and the result for r is
different from that for t obtained in (a).
Using equation 2.4-4 in integrated form, V = 1 FAodfAl( -I*), together with the stoi-
chiometry of the reaction, from which the total molar flow rate at any point is

Ft = FA +FC,H, +FH2
= FA,(~ - .fA) +FAO~A +FAO~A
= F,,(l + fA)
and the ideal-gas equation of state, from which the volumetric flow rate at any point is

q = F,RTIP

where R is the gas constant, and the inlet flow rate is

qO = F,,RTIP = FA,RTIP

we obtain, on substitution into equation 2.3-2,
1
7= FAodfAl(-rA) I(FA,RTIP)

(1 + fA)dfAl(l - fA)

= 0.99s

(c) T > t, because T, based on inlet conditions, does not take the acceleration of the flowing
gas stream into account. The acceleration, which affects t, is due to the continuous increase
in moles on reaction.

2.5 LAMINAR-FLOW REACTOR (LFR)

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a
flow pattern that is relatively difficult to attain experimentally. However, the model
based on laminar flow, a type of tubular flow, may be useful in certain situations,
both in the laboratory and on a large scale, in which flow approaches this extreme (at
low Re). Such a situation would involve low fluid flow rate, small tube size, and high
fluid viscosity, either separately or in combination, as, for example, in the extrusion of
high-molecular-weight polymers. Nevertheless, we consider the general features of an
LFR at this stage for comparison with features of the other models introduced above.
We defer more detailed discussion, including applications of the material balance, to
Chapter 16.
The general characteristics of the simplest model of a continuous LFR, illustrated
schematically in Figure 2.5, are as follows:
(1) The flow through the vessel is laminar (LF) and continuous, but not necessarily
at constant rate.