L6-1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at...
-
Upload
meryl-cannon -
Category
Documents
-
view
228 -
download
1
Transcript of L6-1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at...
L6-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
XA A
A0A0
dXt=N
-r V XA dXAV =FA0 -rA0
Review: Logic of Isothermal Reactor Design
V jj0 j j
dNF F r dV
dt
In Out- +Generation =Accumulation1. Set up mole balance for specific reactor
2. Derive design eq. in terms of XA for each reactor
Batch
A0 A
A
F XV =
-r
CSTR PFR
3. Put Cj is in terms of XA and plug into rA
j0 j A0 A 0 0j
A 0
C C X T ZPC
1 X P T Z
n
A jr kC
nj0 j A0 A 0 0
AA 0
C C X T ZPr k
1 X P T Z
4. Plug rA into design eq and solve for the
time (batch) or volume (flow) required for a specific XA
(We will always look conditions where Z0=Z)
Examples of combining rates & design eqs follow!
L6-2
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Batch Reactor Operation
Batch Volume is constant, V=V0
AAA0
dXN V
dtr Mole balance
Rate law A2
Ar kC
Stoichiometry (put CA in terms of X)
A A0 AC C (1 X )
Combine AA02
AA 2
0C 1d
Vdt
kN XX
22A0 A
AA0 0k CN 1
tX
dXV
d
A → B -rA = kCA2 2nd order reaction rate
Calculate the time required for a conversion of XA in a constant V batch reactor
Integrate this equation in order to solve for time, tB
e a
ble
to
do
th
es
e 4
ste
ps,
an
d
the
n in
teg
rate
to
so
lve
fo
r ti
me
for
AN
Y R
EA
CT
ION
A
A0 A
X1t
kC 1 X
L6-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: CSTR OperationA → B -rA = kCA
Calculate the CSTR volume required to get a conversion of XA
Mole balance
Rate law A Ar kC
Stoichiometry (put CA in terms of X)
A A0 AC C (1 X )
Combine A0
A0 A
F XV
kC 1 X
A0 0 A
A0 A
C XV
kC 1 X
1st order reaction rate
r
XFV
A
A0A
Put FA0 in terms of CA0
0 A
A
XV
k 1 X
Volume required to achieve XA for 1st order rxn
Be able to do these steps for any order reaction!
L6-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
A0
A
X
kV
1 X
Review: Scaling CSTRs
0 A 0 A
small biggerA A
X Xknown: V want: V
k 1 X k 1 X
Space time t (residence time) required to achieve XA for 1st order irreversible rxn
• If one knows the volume of the pilot-scale reactor required to achieve XA, how is this information used to achieve XA in a larger reactor?
k in the small reactor is the same as k in the bigger reactor
Want XA in the small reactor to be the same as XA in the bigger reactor
0 in the small reactor must be different from 0 in the bigger reactor
Suppose for a 1st order irreversible rxn:
A
0 A
XVk 1 X
Separate variables we will vary from those held constant
So the reactor volume must be proportional to the volumetric flow rate 0
0Vt A
A
X
k 1 Xt
Be able to do this for any order rxn!
Eq is for a 1st order rxn only!
L6-5
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Damköhler Number, DaA0
A0
r V rate of reaction reaction rateDa
F enterinat en
g flow rate of A convection rattrance
e
Estimates the degree of conversion that can be obtained in a flow reactor
First order irreversible reaction:
A0
A0 A0 0
A0kr V VCDa
F C
0
kVDa
Da kt
1st order irreversible reaction
Second order irreversible reaction:
A02
A
0 A0 0
0
A
r V VD
kCa
F C
A0
0
kC VDa
A0Da kC t
2nd order irreversible reaction
Ak
X1 ktt
How is XA related to Da in a first order irreversible reaction in a flow reactor?
If Da < 0.1, then XA < 0.1
If Da > 10, then XA > 0.9A
DaX
1 Da
0Vt Substitute
From slide L6-7:
L6-6
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
A0 A0
A0
1 2 kC 1 4 kCX
2 kC
t tt
Review: Sizing CSTRs for 2nd Order Rxn
• Mole balance
• Rate laws
• Stoichiometry
• Combine
A
A0 0 A0
Ar r
F X C XV
A2
Ar kC
A A0C C (1 X)
A22
0
0
A0
kC X
C XV
1
or
t
0 A
20kC 1
V
X
X
1 2Da 1 4DaX
2Da
Calculate the CSTR volume required to get a conversion of XA
A → B -rA = kCA2 Liquid-phase 2nd order reaction rate
In terms of conversion?
In terms of space time?
In terms of XA as a function of Da?t A0Da kC
Eq is for a 2nd order liquid irreversible rxn
Be able to do these steps!
L6-7
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: n CSTRs in SeriesCA0u0
CA1uCA2u 0
For n identical CSTRs, then:
A0An n
CC
1 kt
How is conversion related to the # of CSTRs in series?
Put CAn in terms of XA (XA at the last CSTR):
A0A0 A n
CC 1 X
1 kt
A n
11 X
1 kt
An
11 X
1 kt
1st order irreversible liquid phase rxn run in n CSTRs with identical V, t and k
An
1or 1 X
1 Da
1st order irreversible liquid-phase rxn run in n CSTRs with identical V, t and k
Rate of disappearance of A in the nth reactor:
A0
An An n
Cr kC k
1 kt
L6-8
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Isothermal CSTRs in Parallel
FA0
FA01
FA02same T, V,
1 2 n X =X =...=X =X
A1 A2 An Ar r ... r r
Subscript i denotes reactor i
Aii A0i
Ai
XV F
r
FA01 = FA02 = … FA0n
iV total volume of all CSTRs
Vn # of CSTRs
Volume of each CSTR
A0A0i
F total molar flow rateF
n # of CSTRs
Molar flow rate of each CSTR
A0 Ai
Ai
F XV
n n r
Mole Balance
AA0
A
XV F
r
Conversion achieved by any one of the reactors in parallel is the same as if all the reactant were fed into one big reactor of volume
V
AA0
A
XV F
r
L6-9
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Liquid Phase Reaction in PFRLIQUID PHASE: Ci ≠ f(P) → no pressure drop
Calculate volume required to get a conversion of XA in a PFR
2A → B -rA = kCA2 2nd order reaction rate
Mole balance
Rate law
Stoichiometry (put CA in terms of X)
AA
A0
d rX
dV F
2A Ar kC
A A0 AC C (1 X )
Combine
A0 A
A0
2A
2C 1X Xd
V F
k
d
X VAA0 A
220 0A0 A
F dXdV
k C 1 X
A0 A
2AA0
F XV
1 Xk C
Liquid-phase 2nd order reaction in PFR
Be
ab
le t
o d
o t
he
se
4 s
tep
s,
inte
gra
te &
so
lve
fo
r V
fo
r A
NY
O
RD
ER
RX
N
See Appendix A for integrals frequently used in reactor design
L6-10
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Liquid Phase Reaction in PBRLIQUID PHASE: Ci ≠ f(P) → no pressure drop
Calculate catalyst weight required to get a conversion of XA in a PBR
2A → B -r’A = kCA2 2nd order reaction rate
Mole balance
Rate law
Stoichiometry (put CA in terms of X)
AA
A0
rX 'd
dW F
A2
Ar ' kC
A A0 AC C (1 X )
Combine
A0 A
A0
2A
2C 1X Xd
W F
k
d
X WAA0 A22
0 0A0 A
F dXdW
k C 1 X
A0 A
2AA0
F XW
1 Xk C
Liquid-phase 2nd order reaction in PBRBe
ab
le t
o d
o t
he
se
4 s
tep
s, in
teg
rate
&
so
lve
fo
r V
fo
r A
NY
OR
DE
R R
XN
L6-11
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Isobaric, Isothermal, Ideal Rxns in Tubular Reactors
GAS PHASE:j0 j A0 A 0 0
jA 0
C C X T ZPC
1 X P T Z
1 1 1
j0 j A0 Aj
A
C C XC
1 X
Gas-phase reactions are usually carried out in tubular reactors (PFRs & PBRs)
• Plug flow: no radial variations in concentration, temperature, & ∴ -rA
• No stirring element, so flow must be turbulent
FA0 FA
Stoichiometry for basis species A:
A0 AA0 A0 AA A
A A
C 1 XC C XC C
1 X 1 X
L6-12
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Isobaric, Isothermal, Ideal Rxn in PFRGAS PHASE: Ci = f( ) → no DP, DT, or DZ
Calculate PFR volume required to get a conversion of XA
2A → B -rA = kCA2 2nd order reaction rate
Mole balance
Rate law
Stoichiometry (put CA in terms of X)
AA
A0
d rX
dV F
A2
Ar kC
Combine
22A0 AA
02
AA
C 1 X
1
kdX
V FXd
2XA AA0A22
0A0 A
1 XFV dX
k C 1 X
22 AA0A A2
AA0
1 XFV 2 1 ln 1 X X
1 Xk C
Gas-phase 2nd order rxn in PFR no DP, DT, or DZ
A0 AA
A
C 1 XC
1 X
Integral A-7 in appendix
L6-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Effect of e on u and XATf T0 A
T0
N N Change in total # moles at X 1
N total moles fed
: expansion factor, the fraction of change in V per mol A reacted0: volumetric flow rate
00 A
0 0
PZ T1 X
Z T P
varies if gas phase & moles product ≠ moles reactant, or if a DP, DT, or DZ
occursNo DP, DT, or DZ occurs, but moles product ≠ moles reactant → 0 A1 X
• = 0 (mol product = mol reactants): 0: constant volumetric flow rate as XA increases
• < 0 (mol product < mol reactants): < 0 volumetric flow rate decreases as XA increases
• Longer residence time than when 0
• Higher conversion per volume of reactor (weight of catalyst) than if 0
• > 0 (mol product > mol reactants): > 0 with increasing XA
• Shorter residence time than when 0
• Lower conversion per volume of reactor (weight of catalyst) than if 0
L6-14
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Pressure Drop in PFRs & PBRsGAS PHASE:
j0 j A0 A 0j
A 0
C C X TPC
1 X P T
Considering ideal gas phase behavior (Z0=Z)
Concentration is a function of P so pressure drop is important in gas phase rxns
Why? Take a 1st order reaction A → B in a PBR with –r’A = kCA
Substitute concentration of A into the rate law:
A0 A0 A 0
A 0A
C C X TPr
1 X Tk
P'
If P drops during the reaction, P/P0 is less than one, so CA ↓ & the rxn rate ↓
A
A0 A 3
dX molesF r
dV dm min
A
A0 AdX moles
F r ' dW g catalyst min
For tubular reactors:
PFR PBR
Use the differential forms of the design equations to address pressure drop
Pressure drops are especially common in reactions run in PBRs → we will focus on PBR applications
L6-15
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Pressure Drop in PBRs
A0 AA
A 0
C 1 X PC
1 X P
AA
A0dX
Fd
r 'W
GAS PHASE: A → B -r’A = kCA2
Calculate dXA/dW for an isothermal ideal gas phase reaction with DP
2nd order reaction rate
Mole balance
Rate law A2
Ar ' kC
Stoichiometry (put CA in terms of X)
Combine
A0 A
0A
2 22
2A
A0
C 1 X PP
dX
dW
k
F 1 X
22AA0A
20 0A
1 XkCdX PdW P1 X
We need to relate P/P0 to W
This eq. is solved simultaneously with an eq. that describes how the
pressure drops as the reactant moves down the reactor
Function of XA and pressure
L6-16
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Ergun Equation relates P to W
A0
dy T1 X
dW 2y T
0
c c 0
2
A 1 P
Differential form of Ergun equation for pressure drop in PBR:
0
Py
P Tf T0
A0T0
N Ny
N
AC: cross-sectional area C: particle density
: constant for each reactor, calculated using a complex equation that depends on properties of bed (gas density, particle size, gas viscosity, void volume in bed, etc)
: constant dependant on the packing in the bed
volume of solid1 : fraction of solid in bed =
total bed volume
0A
0 0
PdP T1 X
dW 2 T P P
This equation can be simplified to:
L6-17
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Gas Phase Reaction in PBR with ΔP
AA
A0dX
Fd
r 'W
GAS PHASE: A → B -r’A = kCA2
Calculate dXA/dW for an isothermal ideal gas phase reaction with DP
2nd order reaction rate
Mole balance
Combine with rate law and stoichiometry
22
2A
0
AA0
0A
1 XC Pk
P1 X
dX
dW
Relate P/P0 to W
0A
0 0
PdP T1 X
dW 2 T P P
Ergun Equation can be simplified by using y=P/P0 and T=T0:
Ady
1 XdW 2y
Simultaneously solve dXA/dW and dP/dW (or dy/dW) using Polymath
L6-18
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Analytical Solutions to P/P0
Sometimes P/P0 can be calculated analytically. When T is constant and = 0:
A0
dy T1 X
dW 2y T
1
0
1
dydW 2y
2ydy dW
Evaluate
Py
P W0
P 01P0
2ydy dWP P02
1y W
2
0
P1 W
P
0
P1 W
P Only for isothermal
rxn where e=0
From no pressure change
To pressure change
L6-19
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Pressure Drop Example GAS PHASE: A → B 2nd order reaction rate
This gas phase reaction is carried out isothermally in a PBR. Relate the catalyst weight to XA Tf T0
T0
N N 1 10
N 1
A0 A0 A 0A
A 0
C C X TPC
1 X P T
10
A A0 A
0
PP
C C 1 X
= 0 and isothermal, so:0
P1 W
P Plug
into CA
A A0 A0 AC C X 1C W
Plug into PBR design eq:
AA
A0dX
Fd
r 'W
22A A
A0 AA A0 A0dX dX
C C 1 Xk 1F FdW
kdW
W
22AA0 A0 A
dXF kC 1 X 1 W
dW
X WAA0 A2 2
0 0A0 A
F dX1 W dW
kC 1 X
-r’A = kCA2
Simplify, integrate, and solve for XA in terms of W or W in terms of XA:
L6-20
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Pressure Drop Example A → B -r’A = kCA
2 2nd order gas phase rxn non-elementary rate
This gas phase reaction is carried out isothermally in a PBR. Relate the catalyst weight to XA
X WA A2
0 0A
A02
A0
dX1 W d
FW
k XC 1
A0
A0
A
A
X WW
k X 2C1
1
A0A
A 0
kCX WW 1
1 X 2
Solve for XA
A0 A0
A A0 0
kC kCW WX W 1 W 1 X
2 2
A0 A0
A A0 0
kC kCW WX W 1 X W 1
2 2
A0
0A
A0
0
kCW1
2X
kCW1 1
2
0 A
A0 A
2 X1 1
kC 1 XW
Rearrange eq. for W:
L6-21
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Next Time
•Startup of a CSTR under isothermal conditions
•Semi-batch reactor