Page 567 - Elements of Chemical Reaction Engineering Ebook

Sec. 91.2 Unsteady Operation of CSTRs and Semibatch Reactors 537
9.2.1 Batch Reactors

A batch reactor is usually well mixed, so that we may neglect spatial
variations in the temperature and species concentration. The energy balance on
this reactor is found by setting FAo equal to zero in Equation (9-9) yielding

(9- 1 1)

Equation (9-1 1) is the preferred form of the energy balance when the number
of moles, N,, is used in the mole balance rather than the conversion, X. The
number of moles of species i at any X is

Consiequently, in terms of conversion, the energy balance becomes

dT Q-ws+(-AHR,S(-rAV) (9-12)
NA, (C 0, C,, + Ac,X)

Batch reactor energy Equation (9-12) must be coupled with the mole balance
and mole balances

and the rate law and then solved numerically.

9.2.2 Adiabatic Operation of a Batch Reactor

For adiabatic operation (e = 0) of a batch (F[, 3 0) reactor and when
the work done by the stirrer can be neglected (W, z 0), Equation (9- 12) can be
written as

cp, = c OiCPi (9-14)
From the mole balance on a batch reactor we have

dX
NAO 7 -rAV

We combine Equations (9-13) and (2-6) to obtain
dT
dX
-[AH, +AC,(T-TR)] - = [C,,+AC,X] - (9-15)
dt dt