Page 53 - Introduction to chemical reaction engineering and kinetics

2.4 Plug-Flow Reactor (PFR) 35

t = v/q, (constant density) (2.4-8)

whether V represents the total volume of the vessel, in which case t is the residence time
of fluid in the vessel (- ffor a CSTR in equation 2.3-l), or part of the volume from the
inlet (V = 0). Equation 2.2-10 is the same for both a BR and a PFR for constant density
with this interpretation oft for a PFR.

Calculate (a) the residence time, t, and (b) the space time, r, and (c) explain any difference
between the two, for the gas-phase production of C,H, from C,H, in a cylindrical PFR of
constant diameter, based on the following data and assumptions:

(1) The feed is pure C,H, (A) at 1 kg s-l, 1000 K and 2 bar.
(2) The reaction rate is proportional to cA at any point, with a proportionality constant
of kA = 0.254 s-l at 1000 K (Froment and Bischoff, 1990, p. 351); that is, the rate
law is (-rA) = kAcA.
(3) The reactor operates isothermally and at constant pressure.
(4) fA = 0.20 at the outlet.
(5) Only C,H, and H, are formed as products.
(6) The flowing system behaves as an ideal-gas mixture.

SOLUTION

(a) In Figure 2.4, the gas flowing at a volumetric rate q at any point generates the control
volume dV in time dt. That is.

dV = qdt o r dt = dVlq

The total residence time, t, is obtained by integrating from inlet to outlet. For this, it is
necessary to relate V and q to one quantity such as fA, which is zero at the inlet and 0.2 at
the outlet. Thus,

(2.4-9)

= FAodfJd- TA) from equation 2.4-4
I

= FAodfAlqkACA from rate law given
I
= (FAolkA) dfA/FA from equation 2.3-7
I

= (F/,olkA) dfAIFAo(l - fA) from equation 2.3-5
I
0.2
= (l/k,) dfA/(l - fA)
I
= (1/0.2&- ln(O.*)] = 0.89 s