Page 471 - Elements of Chemical Reaction Engineering Ebook

442 Steady-State Nonisothermal Reactor Design Chap. 8

TABLE 8- 1. CSTR ALGORITHM
The first-order irreversible liquid-phase reaction
A-B
is carried out adiabatrcally.
1. CSTR design equation:
v=- (T8- 1.1)
- TA
2. Rate law: -IA kC, (T8- 1.2)
=
with k = A~-E/RT (T8- 1.3)
An algorithm 3. Stoichiometry (liquid-phase, u = u, ):
c, = CA0(l -X)
4. Combining yields
(T8-1.4)
Divide and
conquer Case A. The variables X, uo , CAo, and F,, are specified and the reactor volume, K
must be determined. The procedure is:
- A
5A. Solve for the temperature, T, for pure A entering, and cp, = Cp,(ACp = 0).
For the adiabatic case, solve Equation (8-52) for T:
X (-AH& 1
T=T,+ - (T8-I .5)
CPA
For the nonadiabatic case with Q = UA(T, - T), solve Equation (8-51) for T:
FAOX(-AH;Ix) + FAoCP,To+ UAT,
T= (T8-1.6)
+
FAOCPA UA
6A. Calculate k from the Arrhenius equation.
7A. Calculate the reactor volume, K from Equation (T8-1.4).
Case B. The variables u, , C,,, V, and F,, are specified and the exit temperature, Z:
and conversion, X, are unknown quantities. The procedure is:
5B. Solve the energy balance (adiabatic) for X as a function of T.

Energy balance (T8- 1.7)
For the nonadiabatic with Q = UA(T, - T) case, solve Equation (8-51) for
XEB
UA(T - T,) /FA, + e,,( T - To)
XEB = -AH& (T8- 1.8)
6B. Solve Equation (TS-1.4) for X as a function of T.
,Ae-E/RT
Mole balance XMB = 1 + TAe-E/RT where ‘I = V/u, (T8-1.9)
7B Find the values of X and T that satisfy both the energy balance [Equation
(TS-1.7)] and the mole balance [Equation (T8-1.9)]. This result can 8e
achieved either numencally or graphically [plottmg X vs T using Equauons
(T8-1 7) and (T8-1 9) on the same graph]