Page 220 - Elements of Chemical Reaction Engineering Ebook
P. 220
Sec. 4.7 Unsteady-State Operation of Reactors 191
(4-54)
with the initial condition V = Vo at t = 0, integrating for the case of constant
Vo yielcls
Semibatch
reactor
volume as a (4-,55)
function of time
Substituting Equation (4-54) into the right-hand side of Equation (4-52) and
rearranging gives us
Vdc,
- uoC, + Vr, = -
dt
The balance of A. [i.e. Equation (4-52)] can be rewritten as
- 1
Mole balance on A (4-56)
~
A mole balance of B that is fed to the reactor at a rate FBo is
(4-57)
dVCB dV VdCB = rBv+FBo
- -cB+-
dt = dt dt
Substituting Equation (4-55) in terms of V and differentiating, the mole bal-
ance on B becomes
Mole balance on B (4-58)
If the reaction order is other than zero- or first-order, or if the reaction is
nonisotliermal, we must use numerical techniques to determine the conversion
as a function of time. Equations (4-56) and (4-58) are easily solved with an
ODE solver.
Exaniple kll Isothermal Semibatch Reactor with Second-Order Reaction
The production of methyl bromide is an irreversible liquid-phase reaction that fol-
lows an elementary rate law. The reaction
CNBr + CH,NH, + CH,Br + NCNH,
is carried out isothermally in a semibatch reactor. An aqueous solution of melthyl
amine (B) at a concentration of 0.025 g mol/dm3 is to be fed at a rate of 0.05 drn3/s
to an aqueous solution of bromine cyanide (A) contained in a glass-lined reactor.