Page 325 - Introduction to chemical reaction engineering and kinetics

306 Chapter 12: Batch Reactors (BR)

values of C, for A, R, and S are, respectively, 185.6, 104.7, and 80.9 J mol-’ K-l. The
enthalpy of reaction is -6280 J (mol A)-l, and the reaction is first-order with respect to A,
with kA = 1()‘4e-‘0,000/T h-l. D t and T versus t, if the process
e ermine the profiles of fA
is adiabatic, and T and t for fA = 0.99.

SOLUTION

We first obtain the appropriate forms of the material-balance and energy-balance equations
(12.3-3 1 and 12-3-29, respectively) for use in the above algorithm.
From the given rate law, we have

(-YA) = kAcA = k,n,lV = k,n,,(l - fA)IV

so that equation 12.3-3 1 becomes
t= d f* (4

k,(l - fA)
where

kA = 1014e-10,000/T
(B)
For equation 12.3-29, we may not be able to use the simplified result in equation 12.3-
30, since n,Cp may not be constant but depend on fA; to investigate this, we form

= n, C xiCpi = n, 2 (niln,)Cpi
%CP
= 2 nicpj = nACpA + nRCpR + nscpS
= nA,(l-f~)C~~ $- nAofACPR +nAofACPS
= nA,[CPA + ccPR + cPS - cPA)fA]
= 1856n,,

Since ntCp is independent of fA, we cm use equation 12.3-30:

T = 300 + ;;;e2A; fA = 300 + 33.8fA 0

Equations (A), (B) and (C) are used in the algorithm to obtain the information required.
Step (3) is used to calculate kA from equation (B), and step (4) is not required. Results are
summarized in Table 12.2, for the arbitrary step-size in fA indicated; G = ll[k,( 1 - fA)],
and G* represents the average of two consecutive values of G. The last column lists the
time required to achieve the corresponding conversion in the second column. These times
were obtained as approximations for the value of the integral in equation (A) by means of
the trapezoidal rule:

tj = tj-1 + 0*5(G, + Gj-l)(fAj - fA,j-1)
The estimated time required to achieve a fractional conversion of 0.99 is 1.80 h, and the
temperature at this time is 333.5 K, if the reactor operates adiabatically. The fA(t) profile
is given by the values listed in the second and last columns; the T(t) profile is given by
the third and last columns.