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

1 2

CA,in

CA,out

Regeneration

t

CA

,out/C

A,in

Breakthrough curve

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 CA,f + dCA,f

z CA,f

U0 (m/s) superficial velocity 2

2

0 mA

s/mVU

xs

gas

Mass Balance

zCt

dzrdCCUCU f,AAvf,Af,Af,A

00

Input – Output – Reaction = Accumulation

Divide by ∂z and take the limits as ∂z 0

00

Avf,Af,A rz

CU

t

C 00

Av

f,Af,A rz

CU

t

C

ε is void fraction in bed

f,A''v

A

rAv Ck

dt

dN

Vsreactorm

molr

1

13

0

t

C f,A

For first order reaction, fluid only:

For steady state:

Therefore,

010 f,A''v

f,A Ckdz

dCU

Volume of reactor

Void fraction

Conversion as a function of HeightIntegrating with CA,f = CA,f,in at z = 0

z

U

kexp

C

CX

''v

in,f,A

f,AA

0

111

z

U

kexp

C

CX

''v

in,f,A

f,AA

0

111

Note 1: Same equation as for catalytic reactor with 1st order reactionNote 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

zt

Czr s

sv

1

Volume fraction of solid = m3 of solid m3 of reactor volume

mol m3 of solid · s

Balance on Solid

01

01

a

r

t

C

rar

rt

C

Avs

svav

svs

Solve These Equations

00

Avf,Af,A rz

CU

t

C 00

Av

f,Af,A rz

CU

t

C

01

a

r

t

C Avs

01

a

r

t

C Avs

0

1

0

t

C

U

a

z

Csf,A

01

0

t

C

U

a

z

Csf,A

= 0 (In quasi steady state, we ignore the accumulation of A in gas)

Sub

stitu

te r Av

t,zfC

t,zfC

t

C

z

C

's

'f,A

's

'f,A

0

t,zfC

t,zfC

t

C

z

C

's

'f,A

's

'f,A

0

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) Adiabatic reaction – no heat lost through shell to

surroundings (no radial temperature gradients) q = 0

2) Biλ is small – uniform T within particle (an exothermic reaction Tp > Tg)

3) Plug flow of gas and use Tref =0 for enthalpy calculations

4) Assume an average density can be used (ρg = constant)

Modeling

Tf + dTf

Tf

z + dz

z

Tf,0

U0

q =0

gUsm

kgG 02

Governing Equations

Fluid

Solid

t

TCTThAHr

TThAz

TCU

t

TC

spsfssrA

fssf

pff

pf

sv

ff

1

0

,

,0,

0,

Av

fA rz

C 01

a

r

t

C Avs

Solve all these equations together.

Quasi Steady State

For Heat Transfer

Z=0 all t Tf = Tf,0; Ts = Ts,0

T = 0 all z Ts = Ts,0; Tf = Tf,0

Generally, require a numerical solution for the solution of the set of equations.