Page 49 - Introduction to chemical reaction engineering and kinetics

2.3 Continuous Stirred-Tank Reactor (CSTR) 31

It is important to understand the distinction between the implications of points [3]
and [5]. Point [3] implies that there is instantaneous mixing at the point of entry be-
tween the input stream and the contents of the vessel; that is, the input stream instanta-
neously blends with what is already in the vessel. This does not mean that any reaction
taking place in the fluid inside the vessel occurs instantaneously. The time required for
the change in composition from input to output stream is t; point [5], which may be
small or large.

2.3.2 Material Balance; Interpretation of ri

Consider again a reaction represented by A + . . . + products taking place in a single-
stage CSTR (Figure 2.3(a)). The general balance equation, 1.5-1, written for A with a
control volume defined by the volume of fluid in the reactor, becomes

rate of accumulation
= of A within (1.5la)
control volume

or, on a molar basis,

FAo - FA + rAV = dn,ldt (2.3-3)
(for unsteady-state operation)

FAO - FA + r,V = 0 (2.3-4)

(for steady-state operation)

where FAO and FA are the molar flow rates, mol s-l, say, of A entering and leaving the
vessel, respectively, and V is the volume occupied by the fluid inside the vessel. Since a
CSTR is normally only operated at steady-state for kinetics investigations, we focus on
equation 2.3-4 in this chapter.
As in the case of a batch reactor, the balance equation 2.3-3 or 2.3-4 may appear in
various forms with other measures of flow and amounts. For a flow system, the fractional
conversion of A (fA), extent of reaction (0, and molarity of A (cA) are defined in terms
of FA rather than nA:

.f~ = (FA,, -FAYFAO (2.3-5)
1
5 = AFAIvA = (FA - FAo)Ivp, Flow system (2.3-6)
(2.3-7)
CA = F,iq

(cf. equations 2.2-3, -5, and -7, respectively).