Page 48 - Introduction to chemical reaction engineering and kinetics

30 Chapter 2: Kinetics and Ideal Reactor Models

t l t l

CA CA I

Distance coordinate + Distance coordinate --+

(a) Single CSTR (b) 2 CSTRs in series
Figure 2.3 Property profile (e.g., CA for A + . . -+ products) in a CSTR

[l] Since the fluid inside the vessel is uniformly mixed (and hence elements of fluid
are uniformly distributed), all fluid elements have equal probability of leaving
the vessel in the output stream at any time.
[2] As a consequence of [l], the output stream has the same properties as the fluid
inside the vessel.
[3] As a consequence of [2], there is a step-change across the inlet in any property
of the system that changes from inlet to outlet; this is illustrated in Figure 2.3(a)
and (b) for cA.
[4] There is a continuous distribution (spread) of residence times (t) of fluid ele-
ments; the spread can be appreciated intuitively by considering two extremes:
(i) fluid moving directly from inlet to outlet (short t), and (ii) fluid being caught
up in a recycling motion by the stirring action (long t); this distribution can be
expressed exactly mathematically (Chapter 13).
[5] The mean residence time, t; of fluid inside the vessel for steady-state flow is

t = v/q (CSTR) (2.3-1)

where 4 is the steady-state flow rate (e.g., m3 s-i) of fluid leaving the reactor; this
is a consequence of [2] above.
[6] The space time, r for steady-state flow is

7 = v/q, (2.3-2) 1

where go is the steady-state flow rate of feed at inlet conditions; note that for
constant-density flow, go = q, and r = t: Equation 2.3-2 applies whether or not
density is constant, since the definition of r takes no account of this.
[7] In steady-state operation, each stage of a CSTR is in a stationary state (uniform
cA, T, etc.), which is independent of time.