Transcript Plug Flow Model - Biodiesel Projects

Fixed Bed Reactor
Quak Foo Lee
Chemical and Biological Engineering
The University of British Columbia
Fixed Bed Reactor


Solids take part in reaction  unsteady state or semi-batch
mode
Over some time, solids either replaced or regenerated
CA,out
Breakthrough
curve
1
2
CA,in
CA,out/CA,in
Regeneration
t
Isothermal Reaction:
Plug Flow Reactor

Plug flow of fluid – no radial gradients, and
no axial dispersion

Constant density with position

Superficial velocity remains constant
Plug Flow Model
z + dz
z
CA,f + dCA,f
CA,f
U0 (m/s) superficial velocity
U0 

Vgas m2 / s
 
Axs m2

Mass Balance
Input – Output – Reaction = Accumulation


U 0C A , f  U 0 C A , f  dC A , f    rAv   dz  

  C A, f  z 
t
Divide by ∂z and take the limits as ∂z  0

C A , f
t
ε is void fraction in bed
U0
C A , f
z
 rAv  0
Void fraction
For first order reaction, fluid only:
mol

 1 dNA
''
rAv  3


k
v 1   C A , f

 m reactor s  Vr dt
For steady state:
C A , f
t
Volume of reactor
0
Therefore,
U0
dCA , f
dz
 kv'' 1   C A , f  0
Conversion as a function of Height
Integrating with CA,f = CA,f,in at z = 0
X A  1
C A, f
C A , f ,in
 kv'' 1    
 1  exp 
z 
U0


Note 1: Same equation as for catalytic reactor with 1st order reaction
Note 2: Can be used in pseudo-homogeneous reaction
Balance on Solid



aA (fluid) + S (solid)  Products
Input – Output – Reaction = Accumulation
Over increment of dz: input = 0, output =0
C s
 rsv   z  1     z
t
Volume fraction of solid =
m3 of solid
m3 of reactor volume
mol
m3 of solid · s
Balance on Solid
Cs
1     rsv  0
t

 rav   a   rsv 
Cs
rAv

0
t a1   
Solve These Equations
= 0 (In quasi steady state, we ignore the
accumulation of A in gas)

C A , f
t
U0
C A , f
z
 rAv  0
a1    Cs

0
z
U 0 t
C A, f
C 'A , f
Cs
rAv

0
t a1   
Cs'

0
z
t
C 'A , f  f z ,t 
Cs'  f z ,t 
Non-Isothermal Packed Bed
Reactor


For mass continuity  did balance on fluid
and on solid
For energy balance, we do balance on each
phase
Non-Isothermal Packed Bed
Reactor

Assumptions:
1)
2)
3)
4)
Adiabatic reaction – no heat lost through shell to
surroundings (no radial temperature gradients) q
=0
Biλ is small – uniform T within particle (an
exothermic reaction Tp > Tg)
Plug flow of gas and use Tref =0 for enthalpy
calculations
Assume an average density can be used (ρg =
constant)
Modeling
q =0
Tf + dTf
z + dz
Tf
z
Tf,0
U0
 kg 
G 2   U0g
m s
Governing Equations
Solve all these equations together.

Fluid
 f C p ,

T f
f
t
 U 0  f C p, f
T f
z
 hAs Ts  T f   0
Solid
r  H
Av
r
  hA T
s
s  Tf
   C 1    T
s
s
p,s
t
Quasi Steady State
Cs
rAv

0
t a1   
C A, f
z
 rAv  0
For Heat Transfer

Z=0
all t
Tf = Tf,0; Ts = Ts,0

T = 0 all z

Generally, require a numerical solution for the
solution of the set of equations.
Ts = Ts,0; Tf = Tf,0