CE 561 Lecture Notes
Fall 2009
p. 1 of 12
Day 23: The ideal plug flow reactor
The next idealized reactor configuration we will consider is the ideal plug flow tubular reactor.
In this model, we assume that the reactor is a tube in which the velocity is in the axial direction
only.
We further assume that the velocity and
all other quantities
are constant across the tube
diameter, and that diffusion and conduction in the axial direction are negligible.
With these
assumptions, the species mole balance equations are
( )
1
M
x
k
ik i
i
d
vC
r
dx
α
=
=
∑
If the velocity is independent of axial position (which will be the case if density is constant), then
it can be taken out of the derivative to get
1
M
k
x
ik i
i
dC
vr
dx
=
=
∑
Defining a residence time
τ
(the time a fluid element has spent in the reactor when it reaches
position
x
) by
x
x
v
=
this equation becomes
1
M
k
ik i
i
dC
r
d
=
=
∑
which is identical to the constant volume batch reactor equation with the clock time
t
replaced by
the residence time
.
If the density in the reactor cannot be assumed to be constant (because of changes in the number
of moles or changes in the temperature of a gas, for example) then the plug flow reactor balances
are
not
identical to those for the batch reactor.
However, we can still define the residence time in
a similar way as
,
xo
x
v
=
where
v
x,o
is the axial velocity at the inlet.
Then the equation becomes
,
1
M
x
k
ik i
i
v
d
Cr
dv
=
=
∑
The velocity at a given point in the reactor can be related to the density at that point using the
total mass balance.
For the steadystate plug flow reactor, the mass balance reduces to
( )
0
x
d
v
dx
ρ
=
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Fall 2009
p. 2 of 12
which can directly be integrated between the inlet (where the velocity is
v
x,o
and the density is
ρ
o
)
and some other point in the reactor to give
v
x
=
o
v
x,o
The local velocity can often be computed from the ideal gas law using the local composition and
temperature.
For isothermal reaction among gases, it can be written in terms of the extent(s) of
reaction (for as many linearly independent reactions as we have) and the overall change in mole
number for those reactions.
For a mixture of ideal gases, the velocity is
,,
oo
x
xo
p
nT
vv
v
nT p
=
=
where
T
is the temperature,
n
/
n
o
is the ratio of the number of moles at a particular position to the
number of moles in the feed, and
p
is the pressure.
The most direct measure of the reactor’s capability to carry out the reaction is given by the total
residence time based on the inlet flow rate and total reactor volume.
Froment and Bischoff
designate this as
θ
, but most other authors (including me) use the symbol
τ
.
,
o
LV
vQ
=
=
Where
L
is the reactor length,
V
is the reactor volume, and
Q
o
is the volumetric flow rate of
reactant to the reactor.
In practice, reactors are often described in terms of the reciprocal of this,
which is usually called “space velocity”.
For catalytic reactions, it is not the volume of the
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 Fall '09
 Batch reactor, Plug Flow Reactor, PFTR

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