Page 210 - Modelling in Transport Phenomena A Conceptual Approach

190 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Solution

Assumptions
1. Well mixed system, i.e., the temperature and the Concentration of the contents
of the reactor are uniform.
2. The density of the reaction mixture is constant.

Analysis

System: Contents of the reactor
The problem should be considered in three parts: the filling period, the unsteady
state period, and the steady-state period.
i) The filling period
During this period, there is no outlet stream from the reactor. Hence, the conser-
vation of total mass, Eq. (7.3-1), is given by

Since an and p are constant, integration of Eq. (1) and the use of the initial
condition, msys = 0 at t = 0, gives

msys = Qinpt (2)
Since msys = pVsys, Eq. (2) can also be expressed as

Kys = Qin t (3)
F’rom Eq. (3), the time required to fill the reactor, t*, is calculated as t* = VT/Q~,
where VT is the volume of the reactor.
The inventory rate equation based on the moles of species A, Eq. (7.2-6),
duces to
dnA
&in CA, - ~cAV,,, = - (4)
dt
where the volume of the reaction mixture, is dependent on time. The molar
concentration can be expressed an terms of the number of moles as

such that Eq. (4) can be rearranged in the form