Multiphase Chemical Reactor Engineering Quak Foo Lee Ph.D. Candidate Chemical and Biological...
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Transcript of Multiphase Chemical Reactor Engineering Quak Foo Lee Ph.D. Candidate Chemical and Biological...
Multiphase Chemical Multiphase Chemical Reactor EngineeringReactor Engineering
Quak Foo LeePh.D. Candidate
Chemical and Biological Engineering
The University of British Columbia
Different Types of Different Types of ReactorReactor
Fluidized Bed Reactor
Trickle Column ReactorSlurry Bubble Column ReactorBatch Reactor
Fixed Bed Reactor
Fluidized Bed ReactorFluidized Bed Reactor
Fluidized Bed Reactor using H2SO4 as a catalyst to bond butanes and iso-butanes to make high octane gas
Straight Through Straight Through Transport ReactorTransport Reactor
Riser
Standpipe
Settling Hopper
The reactor is 3.5 m in diameter and 38 m tall. Sasol/Sastech PT Limited
CA,in
CA,out
Gas + solids
Plug Flow ModelPlug Flow Model
V
Ht
out,Ain,A CC
Particle surrounding by Particle surrounding by fluid of essential fluid of essential constant concentration, constant concentration, CCA,mA,m
Batch Mix Flow: Charge Batch Mix Flow: Charge ReactorReactor
Residence time Residence time distributiondistribution
Particle stays in the Particle stays in the reactor for certain reactor for certain length of timelength of time
Countercurrent FlowCountercurrent Flow
If solids are moving plug If solids are moving plug flow and we have constant flow and we have constant flow composition flow composition
Residence time of solids:Residence time of solids:
Heat Effects !! Heat Effects !!
V
Ht
AC
Heat Effects on Reactions Heat Effects on Reactions of Single Particlesof Single Particles
Normally (developed) dealing with exothermic and Normally (developed) dealing with exothermic and endothermic reaction.endothermic reaction.
If reaction occurs at a rate such that the heat absorbed If reaction occurs at a rate such that the heat absorbed (endothermic) or generated (for exothermic) can’t be (endothermic) or generated (for exothermic) can’t be transferred rapidly enough, then non-isothermal effects transferred rapidly enough, then non-isothermal effects become important:become important:
The particle T The particle T ≠ the fluid T≠ the fluid T For exothermic reaction, TFor exothermic reaction, Tpp will increase and the rate of will increase and the rate of
reaction will increase above that expected for the isothermal reaction will increase above that expected for the isothermal case.case.
Two conditions:Two conditions: i) Film i) Film ∆T (external ∆T) T∆T (external ∆T) Tff (bulk fluid) ≠ T (bulk fluid) ≠ Tp p
(particle)(particle) ii) Intraparticle ∆T (internal ∆T) Tii) Intraparticle ∆T (internal ∆T) Tr=Rpr=Rp ≠ T ≠ Tr=∞r=∞
Non-ReactingNon-Reacting
1.1. Small particles Small particles highly conductive highly conductive particlesparticles
2.2. Small particles Small particles volumetric volumetric reactionreaction
1)1)Small Particles: Small Particles: Highly Conductive Highly Conductive
ParticlesParticles Particle initially at uniform Particle initially at uniform
T = TT = Tpp
At t = 0, we drop it into our At t = 0, we drop it into our furnacefurnace
Fluid at Tf
Tp
Energy BalanceEnergy Balance
dt
dHmQQ radiationconvection
dt
TCdmTTTThR pp
pwmpfcv 4424
Heat in by convection and radiation = change in enthalpy of particle
Where,Area of sphere = 4πR2
Hcv = convection coefficientσ = Stefan-Boltzman constantЄm = emissivity of the particle (wall has Є = 1)
Energy BalanceEnergy Balance
pF
pwmr TT
TTh
44
dt
dT
A
CmTThh ppp
pFrcv
Can solve this equation to get Tp =f(t)
Find hFind hcvcv
Have film: Have film: ∆H T∆H Tff ≠ T ≠ Tpp
Use mass transfer analogy to get hUse mass transfer analogy to get hcvcv
31
21
602 PrRe.Nuk
dhp
f
pcv 31
21
602 PrRe.Nuk
dhp
f
pcv
;k
CPr;
VdRe
f
ppp
2. Small Particles: 2. Small Particles: Volumetric ReactionVolumetric Reaction
Small such that no Small such that no internal gradientsinternal gradients
fpprAvp TThAHrV
Heat generated by reaction = Heat transferred to surroundingHeat generated by reaction = Heat transferred to surrounding
Steady State:
Volume of particle Rate of
reaction
3
R
h
rHTT Avr
fp
Exothermic Rxn:-∆Hr = (+)-rAv = (+)
3. Large Particles:3. Large Particles:Possible Internal Particle Possible Internal Particle
GradientsGradients We have to solve the conduction equationWe have to solve the conduction equation Non reacting particle: the conduction equation for sphere:Non reacting particle: the conduction equation for sphere:
t
TC
r
Tkr
rr s,pe
2
2
1
Rrpf
Rre TThdr
dTk
:Surface
Heat conducted into particle at r =Rp
Heat transferred into particleNote: accommodate radiation in the definition of h if that is the case
Ke = effective thermoconductivity within the particle∂T/∂r = 0 at steady state
Boundary ConditionsBoundary Conditions
0
0
rr
T
p,pp T)r(T;TT;t 00
00
00
Rrrrr
rr
TT
RTT
Symmetry condition
Initial condition
Internal gradient
External gradientRrrf TT
Reacting SystemsReacting Systems
General equation for volumetric General equation for volumetric reactions reactions
(Reaction in porous particles)(Reaction in porous particles)
Recall continuity equation:Recall continuity equation:
continuity for Acontinuity for A
Solve (1), (2), (3) Solve (1), (2), (3) TogetherTogether
AvA
eA r
r
CDr
rrt
C
22
1
AvnS
mAr
rAvep
rCCk
Hrr
Tkr
rrt
TC
22
11
Continuity for A
Energy balance
AvnS
mAr rCCTk
(1)
(2)
(3)
Cou
pled
thr
ough
the
re
actio
n ra
te
In Steady State In Steady State Showed that for steady conditions:Showed that for steady conditions:
rA
ee Hdr
dCD
dr
dTk r
Aee H
dr
dCD
dr
dTk
rr,As,Ae
eSr HCC
k
DTT 00
rr,As,Ae
eSr HCC
k
DTT 00
Integrate at r = 0, r = R
For sphere
RrrS TT
Some NotesSome Notes If we know If we know CCA,sA,s (surface concentration) and (surface concentration) and CCA,r=0A,r=0 ( (CCAA
within pellet at r = 0), we can calculate temperature within pellet at r = 0), we can calculate temperature gradient, previous equation tell us either we need or gradient, previous equation tell us either we need or don’t need to worry about T gradient within particle.don’t need to worry about T gradient within particle.
Where isothermal (approach) approximation can be Where isothermal (approach) approximation can be used and where internal T gradients must be used and where internal T gradients must be considered.considered.
Volumetric reaction for porous particles, heat is Volumetric reaction for porous particles, heat is generated in a volume.generated in a volume.
Shrinking Core: Non-Shrinking Core: Non-IsothermalIsothermal
Heat generated at reaction Heat generated at reaction frontfront, not throughout the volume, not throughout the volume
In Steady State, In Steady State,
SolveSolve
t
TC
r
Tkr
rr s,pe
2
2
1
02
2
r
Tr
rr
ke
21111
11
r
TT
dr
dT;
TT
TT
cc
c
rR
sc
rR
rr
sc
c
R
r
rc
Ts
Tf
Tc
Boundary Condition 1: Boundary Condition 1: rr = = rrcc
Heat is generated = Heat conducted out through product layer Area
ce
rc,A,SrSC
rrerc,A,Sr
rRk
HCCakTT
dr
dTkHCCak
c
110
0
Boundary Condition 2: Boundary Condition 2: rr = = RR
Heat arriving by conduction = Heat removed forfrom within particle convection
crR
eSCfS
fSRr
e
RhR
kTTTT
TThdr
dTk
11
1
Bi-1Can be obtained from B.C. 1
SolutionSolution Combine equations and eliminate Combine equations and eliminate TTS S to get to get TTcc--TTf f
20
21111
crc,A,Sr
ce
fC rHCCak
hRRrk
TT
2
0
21111
crc,A,Sr
ce
fC rHCCak
hRRrk
TT
Recall from Isothermal Recall from Isothermal SC ModelSC Model
RBirrCakD
rCak
D
C
C
mcc,sr
e
c,Sr
e
f,A
c,A
111
11
0
20
Substitute CA,c into (Tc –Tf) equation
TTcc - - TTff
220
2
111111111RkrCakRrD
HC
hRRrk
TT
mc,Srce
rf,A
ce
fC
220
2
111111111RkrCakRrD
HC
hRRrk
TT
mc,Srce
rf,A
ce
fC
Conduction Convection Diffusion inProduct Layer
Reaction MassTransfer
Can Heat Transfer Control Can Heat Transfer Control the Rate in Endo- and the Rate in Endo- and
Exothermal Rxn?Exothermal Rxn? Consider Consider CCA,cA,c ≈≈ CCA,fA,f; initially rapid reaction; initially rapid reaction
a)a) EndothermicEndothermicwith poor heat transfer, heat will be consumed in reaction, with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, and if can’t transfer heat in, TTCC will drop will drop reaction rate reaction rate ↓↓ markedly and rate of reaction become markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of the slow step occurring at a rate dictated by the flow of heat.heat.
b)b) ExothermicExothermic
initial rapid reaction and with poor initial rapid reaction and with poor QQ, , TTCC will increased, will increased, then then rate of reaction rate of reaction ↑↑ and eventually reach point where and eventually reach point where gaseous reactant can’t be transferred fast enough gaseous reactant can’t be transferred fast enough (external mass transfer or diffusion). Hence (external mass transfer or diffusion). Hence rate is limitedrate is limited..
Fixed Bed ReactorFixed Bed Reactor
Solids take part in reaction Solids take part in reaction unsteady state or semi-batch mode unsteady state or semi-batch mode Over some time, solids either replaced or regeneratedOver some time, solids either replaced or regenerated
1 2
CA,in
CA,out
Regeneration
t
CA
,out/C
A,in
Breakthrough curve
Isothermal Reaction:Isothermal Reaction:Plug Flow ReactorPlug Flow Reactor
Plug flow of fluid – no radial Plug flow of fluid – no radial gradients, and no axial dispersiongradients, and no axial dispersion
Constant density with positionConstant density with position
Superficial velocity remains Superficial velocity remains constantconstant
Plug Flow ModelPlug 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 BalanceMass 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 r
z
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 Conversion as a function of Heightof Height
Integrating 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 SolidBalance on Solid
aA (fluid) + S (solid) aA (fluid) + S (solid) Products Products Input – Output – Reaction = AccumulationInput – Output – Reaction = Accumulation Over increment of dz: input = 0, output Over increment of dz: input = 0, output
=0=0
zt
Czr s
sv
1
Volume fraction of solid = m3 of solid m3 of reactor volume
mol m3 of solid · s
Solve These EquationsSolve These Equations
00
Avf,Af,A r
z
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
a)a) Shrinking Core ModelShrinking Core Modelb)b) Uniform reaction in porous particleUniform reaction in porous particle, zero order , zero order
in fluidin fluidc)c) Uniform reactionUniform reaction, 1, 1stst order in fluid and in solid order in fluid and in solidd)d) Park et al., “An Unsteady State Analysis of Park et al., “An Unsteady State Analysis of
Packed Bed Reactors for Gas-Solid Reactions”, Packed Bed Reactors for Gas-Solid Reactions”, J. Chem. Eng. Of Japan, 17(3):269-274 (1984)J. Chem. Eng. Of Japan, 17(3):269-274 (1984)
e)e) Evans et al., “Application of a Porous Pellet Evans et al., “Application of a Porous Pellet Model to Fixed, Moving and Fluid Bed Gas-Model to Fixed, Moving and Fluid Bed Gas-Solid Reactors”, Ind. Eng. Chem. Proc. Des. Solid Reactors”, Ind. Eng. Chem. Proc. Des. 13(2):146-155 (1974)13(2):146-155 (1974)
a) In Shrinking Core a) In Shrinking Core ModelModel
o,Sc,AvAv CCakr 1
RBirrCakD
rCakD
C
C
mcco,Sr
e
co,Sv
e
f,A
c,A
111
11
2
3
R
rCC c
o,ss
Recall that
03
32
cc,Avc
c rCkR
t
rr 0
3
32
cc,Avc
c rCkR
t
rr
010
c,Ao,sv
f,A CCakz
CU 010
c,Ao,svf,A CCak
z
CU
Solid Phase
Liquid Phase
For SCM
SolveCA,f = f(z) rc = f(z,t)
Height Vs time Height Vs time (Graphical)(Graphical)
z/L
t/
All CA has been reacted
Particles at bed entrance are completed reacted
Unreacted bed depth
Reaction zone
Completely reacted
b) Uniform Reaction in Porous b) Uniform Reaction in Porous ParticleParticle
and Zero Order in Fluidand Zero Order in Fluid
SS Xk
dt
dX 1
S,S
S
SS
dCC
dX
C
CX
0
0
1
1
where
0
01
0
SS
Sf,A
kCt
C
kCz
C
a
U
0
01
0
SS
Sf,A
kCt
C
kCz
C
a
U
c) Uniform Reaction and 1c) Uniform Reaction and 1stst order in Fluid and in solidorder in Fluid and in solid
01
01
1
1
0
Ss,Avs,A
Ss,Avf,A
SvAv
SAvAv
CCakt
C
CCakz
CU
Cakr
CCakr
Non-Isothermal Packed Non-Isothermal Packed Bed ReactorBed Reactor
For mass continuity For mass continuity did balance did balance on fluid and on solidon fluid and on solid
For energy balance, we do balance For energy balance, we do balance on each phaseon each phase
Non-Isothermal Packed Non-Isothermal Packed Bed ReactorBed Reactor
Assumptions:Assumptions:1)1) Adiabatic reaction – no heat lost through Adiabatic reaction – no heat lost through
shell to surroundings (no radial shell to surroundings (no radial temperature gradients) q = 0temperature gradients) q = 0
2)2) BiBiλλ is small – uniform T within particle (an is small – uniform T within particle (an exothermic reaction Texothermic reaction Tpp > T > Tgg))
3)3) Plug flow of gas and use TPlug flow of gas and use Trefref =0 for =0 for enthalpy calculationsenthalpy calculations
4)4) Assume an average density can be used Assume an average density can be used ((ρρgg = constant) = constant)
Moving Bed Reactor Moving Bed Reactor (MBR)(MBR)
Steady state reactor where solids moving at Steady state reactor where solids moving at near their packed bed voidagenear their packed bed voidage
Counter or co-current operationCounter or co-current operation Solid usually move downward (vertical shaft Solid usually move downward (vertical shaft
reactor or furnace)reactor or furnace) Voidage is near that of a packed bedVoidage is near that of a packed bed
Slightly above random loose-packed Slightly above random loose-packed voidagevoidage
Solids move mainly in a plug floe, but region Solids move mainly in a plug floe, but region near wall have a velocity distributionnear wall have a velocity distribution
Advantages of MBRAdvantages of MBR
True counter-current flowTrue counter-current flow Uniform residence time (essentially plug Uniform residence time (essentially plug
flow)flow) Reasonable Reasonable ∆P∆P Throughput variableThroughput variable Generally larger particle dGenerally larger particle dpp > 2-3 mm > 2-3 mm Difficulties coping with wide size Difficulties coping with wide size
distribution of particles (fines tend to distribution of particles (fines tend to block up the void spaces)block up the void spaces)