Page 211 - Modelling in Transport Phenomena A Conceptual Approach

7.3. CONSERVATION OF TOTAL MASS 191

Integration gives
-
nA = - exp(- k t)] (7)
[l
kt
Substitution of Eq. (7) into Eq. (5) and the use of Eq. (3) gives the concentration
as a function of time as

The concentration c> at the instant the tank is full, i.e., at t = t* = VT/Qin, is

ii) The unsteady-state period
Since the total volume of the reactor VT is constant, then the inlet and outlet
volumetric flow rates are the same, i.e.,
&in = Qout = Q (10)

The inventory rate equation on the moles of species A, Eq. (7.2-6), is

~(cAVT)
QCA, - QCA - kCAVT = (11)
dt
Equation (11) can be rearranged in the form

where 7- is the residence time defined by
VT
e
7=- (13)

Equation (12) is a separable equation and can be written in the form

Integration of Eq. (14) gives the concentration distribution as