chemical reaction engineering 1 chapter 4 isothermal reactor design 반응공학 1
TRANSCRIPT
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Chemical Reaction Engineering 1Chemical Reaction Engineering 1
Chapter 4Chapter 4
Isothermal Reactor DesignIsothermal Reactor Design
반응공학 반응공학 11
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• Describe the algorithm that allows the reader to solve chemical reaction engineering problems through logic rather than memorization.
• Sizing batch reactors, semi-batch reactors, CSTRs, PFRs, and PBRs for isothermal operation given the rate law and feed conditions.
• Studying a liquid-phase batch reactor to determine the specific reaction rate constant needed for the design of a CSTR.
• Design of a tubular reactor for a gas-phase reaction.
• Account for the effects of pressure drop on conversion in packed bed tubular reactors and in packed bed spherical reactors.
• The principles of unsteady operation and semi-batch reactor.
Objectives
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Fig. 4-1 Isothermal Reaction Design Algorithm for Conversion
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Algorithm for isothermal reactor designAlgorithm for isothermal reactor design1. Mole balance and design equation2. Rate law3. Stoichiometry4. Combine5. Evaluate
4.1 Design structure for isothermal reactors
We can solve the equations in the We can solve the equations in the combine step eithercombine step either
A. Graphically (Chapter 2)
B. Numerical (Appendix A4)
C. Analytical (Appendix A1)
D. Software packages (polymath)
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Algorithm for Isothermal Reactors
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French Menu Analogy
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Scale-up of Liquid-Phase Batch Reactor to the Design of a CSTR
To make this jump successfully requires a through understanding of the chemical kinetics and transport limitations.
Pilot plant Pilot plant OperationOperation
Full-scale Full-scale ProductionProduction
Laboratory Laboratory ExperimentExperiment
PAST
Full-scale Full-scale ProductionProduction
MicroplantMicroplant(Lab-bench-scale unit) (Lab-bench-scale unit)
High cost of a pilot-plant leads to jump pilot plant operation
FUTURE
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Algorithm for isothermal reactor designAlgorithm for isothermal reactor design
1. Mole balance and design equation
2. Rate law
3. Stoichiometry
4. Combination
5. Analytical Evaluation
Batch Operation
tCCk
dtC
dC
k
dtkC
dC
kCdt
dC
AinorderndleirreversibkCrBA
rdt
dC
dt
VNd
dt
dN
V
rdt
dN
V
AA
tC
CA
A
A
A
AA
AA
AAAA
AA
A
A
0
02
2
2
2
0
0
111
1
2,
/1
1
0
CA=CAo(1-X)
CAo dtdX
=kCAo2(1-X)2
kCAo
1 0
X dX
(1-X)2 = dt 0
t
t= kCAo
1 ( ) 1-X X
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Batch Reaction Times
BA
Mole balance
)1(00
0
XCV
NC
VN
r
dt
dX
AA
A
A
A
Rate law
Xkt
Xkdt
dX
kCr AA
1
1ln
1
)1(
order-First
)1(
)1(
order Second
0
20
2
XkC
Xt
XkCdt
dX
kCr
A
A
AA
Stoichiometry (V=V0)
Combine
Integration
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Batch Reaction Times
hr
s
k
k
Xkt
s
R
4.6
sec000,23
10
3.2
3.2
9.01
1ln
1
1
1ln
1
)10k 0.9,(Xorder -1st
14
1-4
hr
s
kC
kC
XkC
Xt
s
A
A
AR
5.2
sec000,9
10
9
9
)9.01(
9.0
)1(
)10kC 0.9,(Xorder 2nd
13
0
0
0
13A0
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Batch Reaction Times (Table 4-2)
1st-orderk (s-1)
2nd-orderkCA0 (s-1)
Reaction timetR
10-4 10-3 Hours
10-2 10-1 Minutes
1 10 Seconds
1,000 10,000 Milliseconds
The order of magnitude of time to achieve 90% conversion
For first- and second-order irreversible batch reactions
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Reaction Time in Batch Operation (Table 4-3)
0
111
AA CCkt
This time is the time t needed to reduce the reactant concentration in a batch reactor from an initial value CA0 to some specified value CA.
1. Heat to reaction temperature, te
2. Charge feed to the reactor and agitate, tf
3. Carry out reaction, tR
4. Empty and clean reactor, tc
1.5-3.01.0-2.0
Varies (5-60)0.5-1.0
Total cycle time excluding reaction 3.0-6.0
Activity Time (h)
2nd orderIsothermal
Liquid-phaseBatch reaction
Typical cycle times for a batch polymerization process
tt = tf + te + tR + tc
Decreasing the reaction time with a 60-h reaction is a critical problem. As the reaction time is reduced, it becomes important to use large lines and pumps to achieve rapid transfer and to utilize efficient sequencing to minimize the cycle time
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Example 4-1: Design a Reactor Producing Ethylene Glycol
Design a CSTR to Produce 200 million pounds of ethylene glycol per year by hydrolyzing ethylene oxide. However, before the design can be carried out , it is necessary to perform and analyze a batch reactor experiment to determine the specific reaction rate constant (kA). Since the reaction will be carried out isothermally, kA will need to be determined only at the reaction temperature of the CSTR. At high temperature there is a significant by-product formation, while at temperature below 40oC the reaction does not proceed at a significant rate; consequently, a temperature of 55oC has been chosen. Since the water is usually present in excess, its concentration may be considered constant during the course of the reaction. The reaction is first-order in ethylene oxide.
O CH2-OH
CH2-CH2 + H2O CH2-OHH2SO4
A + B C Catalyst
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Example 4-1: Determining k from Batch Data
Time Concentration of EG (min) (kmol/m3) 0.0 0.000 0.5 0.145 1.0 0.270 1.5 0.376 2.0 0.467 3.0 0.610 4.0 0.715 6.0 0.84810.0 0.957
In the lab experiment, 500mL of a 2 M solution (2 kmol/m3) of EO in water was mixed with 500mL of water containing 0.9 wt % sulfuric acid catalyst. At T=55oC, the CEG was recorded with time.
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Problem Solving AlgorithmExample 4-1 Determining k from Batch Data
A. Problem statement. Determine the kA
B. SketchC. Identify
C1. Relevant theoriesRate law:
Mole balance:C2. Variables
Dependent: concentrationsIndependent: time
C3. Knowns and unknownsKnowns: CEG = f(t)Unknowns: 1. CEO = f(t) 2. kA
3. Reactor volumeC4. Inputs and outputs: reactant fed
all at once a batch reactorC5. Missing information: None
AAA Ckr
Vrdt
dNA
A
D. Assumptions and approximations:Assumptions1. Well mixed2. All reactants enter at the same time3. No side reaction4. Negligible filling and emptying time5. Isothermal operationApproximations1. Water in excess (CH2O~constant)
E. Specification. The problem is neither overspecified nor underspecified.
F. Related material. This problem uses the mole balances developed in Chap. 1 for a batch reactor and the stoichiometry and rate laws developed in Chap. 3.
G. Use an Algorithm.
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dtdCA = -kCA
CA0
CA dCA-CA
0
t= k dt ln
CA
CAo = kt CA = CAoe-kt
A + B C
NC=NAoX=NAo-NA
CC=NC/V=NC/Vo= CAo-CA=CAo- CAoe-kt =CAo(1-e-kt)
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Rearranging and taking the logarithm of both side yields
We see that a plot ln[(CA0-CC)/CA0] as a function of t will be a straight line with a slope –k.
ktC
CC
A
CA
0
0lnAA Cr
ttk
)min311.0(
min311.055.195.8
3.210ln
1
1
12
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Design of CSTR
Design Equation for a CSTR
A
AA
A
AA
exitA
A
r
CC
v
V
r
CCvV
r
XFV
0
0
00
0
)(
For a 1st-order irreversible reaction, the rate law is
A
AA
AA
kC
CC
kCr
0
Mole balance
Rate law
Combine
Solving for the effluent concentration of A, we obtain
k
kX
XCk
CC A
AA
1
)1(1 0
0
the space time
Relationship between space time and
conversion for a 1st-order liquid-phase rxn
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Reaction Damköhler number
rate" convection a"
rate"reaction a"
A of Rate Flow Entering
Entranceat Reaction of Rate
0
0
A
A
F
VrDa
The Damkohler is a dimensionless number that can give us a quick estimate of the degree of conversion that can be achieved in continuous-flow reactor.
For 1st-order irreversible reaction
For 2nd-order irreversible reaction
Da 0.1 will usually give less than 10% conversion.Da 10.0 will usually give greater than 90% conversion.
For first order reaction, X = =
kCv
VkC
F
VrDa
A
A
A
A
00
0
0
0 0
000
20
0
0A
A
A
A
A kCCv
VkC
F
VrDa
k1 + k
Da1 + Da
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CSTRs in SeriesCA1, X1
CA2, X2
CA0
v0
-rA1, V1 -rA2, V2
For first-order irreversible reaction with no volume change (v=v0) is carried out in two CSTRs placed in series. The effluent concentration of A from reactor 1 is
11
01 1 k
CC A
A
From a mole balance on reactor 2,
22
210
2
212
A
AA
A
AA
Ck
CCv
r
FFV
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CSTRs in SeriesSolving for CA2, the concentration exiting the second reactor, we get
1122
0
22
12 111 kk
C
k
CC AA
A
If instead of two CSTRs in series we had n equal-sized CSTRs connected in series (1 = 2 = … = n = i = (Vi/v0)) operating at the same temperature (k1 = k2 = … = kn = k), the concentration leaving the last reactor would be
nA
nA
AnC
k
CC
Da1100
The conversion and the rate of disappearance of A for these n tank reactors in series would be
nkX
1
11 n
AAnAn
k
kCkCr
10
X= 1-CA/CAo
1(1+Da)n
= 1 -
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Conversion as a Function of Reactors in Series for different Damkohler numbers for a first-order recation
Da 1, 90% conversion is achieved in two or three reactors; thus the cost of adding subsequent reactors might not be justifiedDa ~0.1, the conversion continues to increase significantly with each reactor added
Da=k=1
Da=k=0.5
Da=k=0.1
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CSTRs in Parallel
-rA1, V1, X1
-rAi, Vi
-rAn, Vn
FA0
FA0 i
1
i
n
A balance on any reactor i, gives the individualreactor volume
n
FF
n
VV
rrrr
XXXX
r
XFV
AiAi
AAnAA
n
Ai
iiAi
00
21
21
0
The volume of each individual reactor, Vi, is related to the total volume, V, of all the reactors, and similar relationship exists for the total molar flow rate
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CSTRs in Parallel
-rA1, V1
-rAi, Vi
-rAn, Vn
FA0
FA0i
1
i
n
Substituting these values into Eq (4-12) yields
A
A
Ai
iA
Ai
iA
Ai
iiAi
r
XF
r
XFV
r
X
n
F
n
V
r
XFV
00
0
0
The conversion achieved in any one of the reactors in parallel is identical to what would be achieved if the reactant were fed in one stream to one large reactor of volume V
n
FF A
iA0
0
n
VVi
FA01
-rA1, V1, X1
-rAi, Vi, Xi
-rAn, Vn, Xn
FA0n
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A Second-Order Reaction in a CSTR
20
20
0
200
)1( XkC
X
kC
CC
v
V
kC
XF
r
XFV
A
A
AA
A
A
A
A
For a 2nd-order liquid-phase reaction being carried out in a CSTR, the combination of the rate law and the design equation yields
For const density v=v0, FA0X=v0(CA0-CA)
We solve the above eq. for X:
Using our definition of conversion, we have
Da2
Da41Da21
2
4121
2
22121
0
00
0
20
200
A
AA
A
AAA
kC
kCkC
kC
kCkCkCX
The minus sign must be chosen in the quadratic equation because X cannot be greater than 1.
(4-16)
(4-15)
(4-14)
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A Second-Order Reaction in a CSTR
606
0.670.88
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Example 4-2: Producing 200 Million Pound/Year in a CSTR
A 1 lb mol/ft3 solution of ethylene oxide (EO) in water is fed to the reactor together with an equal volumetric solution of water containing 0.9 wt% of the catalyst H2SO4. The specific reaction rate constant is 0.311 min-1.
(a) If 80% conversion is to be achieved, determine the necessary CSTR volume.
(b) If two 800-gal reactors were arranged in parallel, what is the corresponding conversion?
(c) If two 800-gal reactors were arranged in series,what is the corresponding conversion?
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Tubular Reactors
- 2nd-order gas-phase reaction- Turbulent- No dispersion- No radial gradients in T, u, or C
PLUG-FLOW REACTOR
PFR mole balance
AA rdV
dXF 0
must be used when there is a DP or heat exchange between PFR & the surrounds. In the absence of DP or heat exchange, the integral form of the PFR design equation is used.
X
AA r
dXFV
00
X
AA
kC
dXFV
0 20
Rate law
For Liquid-Phase Reaction
X
AA
kC
dXFV
0 20 0
X= FAo
dX
kCAo2(1-X)2
= kCAo
vo ( ) 1-X X
V/vo= = kCAo
1 ( ) 1-X X
kCAo
1+kCAo
Da2
1 + Da2
X= =
(Da2=Damköhler number for a 2nd-order RXN)
For n-th order RXN, Dan=kCAon-1
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For Gas-Phase Reaction
X
AA
kC
dXFV
0 20
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Conversion as a Function of Distance Down the Reactor
0)5.01( vXv
The volumetric flow rate decreases with increasing conversion, and the reactant spends more time in the reactor than reactants that produce no net change in the total number of moles.
the reactant spends more time
0)21( vXv the reactant spends less time
öV(m3)
v=vo(1+X)
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Change in Gas-Phase Volumetric Flow Rate Down the Reactor
v=vo(1+X)
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Example 4-3: Determination of a PFR Volume
Determine the PFR volume necessary to produce 300 million pounds of ethylene a yearfrom cracking a feed stream of pure ethane. The reaction is irreversible and follows an elementary rate law. We want to achieve 80% conversion of ethane, operating the reactor isothermally at 1100K at a pressure of 6 atm.
C2H6 (A) C2H4 (B) + H2 (C)
FB=300x106 lb/year=0.340 lb-mol/sec
FB=FAoX
FAo=FB/X=0.340/0.8=0.425 lb-mol/sec
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Pressure Drop in Reactors
In liquid-phase reaction
- the concentration of reactants is insignificantly affected by even
relatively large change in the total pressure
- ignore the effect of pressure drop on the rate of reaction
when sizing liquid-phase chemical reactors
- that is, pressure drop is ignored for liquid-phase kinetics calculations
In gas-phase reaction
- the concentration of the reacting species is proportional to
the total pressure
- the effects of pressure drop on the reaction system are a key factor
in the success or failure of the reactor operation
- that is, pressure drop may be very important for gas-phase reactions
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Pressure Drop and Rate Law
• For an ideal gas,
- determine the ratio P/P0 as a function of V or W
- combine the concentration, rate law, and design equation
- the differential form of the mole balance (design equation) must be used
)/)(/)(1( 000
0
TTPPXv
XvF
v
FC iiAi
i
00 1 P
P
X
XvCC ii
Ai
기상반응에서는 반응 성분의 농도가 반응압력에 비례
하므로 압력강하에 대한 고려가 필수적이다 .
To
T(4-18)
![Page 46: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/46.jpg)
Pressure Drop and Rate Law
• For example,
- the second order isomerization reaction in a packed-bed reactor
2A B + C
-the differential form of the mole balance
- rate law
-from stoichiometry for gas-phase reactions
mincatalyst g
gmoles0 AA r
dW
dXF
2AA kCr
T
T
P
P
X
XCC AA
0
00 1
1
![Page 47: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/47.jpg)
Pressure drop and the rate law
• Then, the rate law
- the larger the pressure drop from frictional losses, the smaller the reaction rate
• Combining with the mole balance and assuming isothermal operation (T=To)
• Dividing by FA0
20
00 1
1
T
T
P
P
X
XCkr AA
2
0
20
0 1
)1(
P
P
X
XCk
dW
dXF A
A
2
0
2
0
0
1
1
P
P
X
X
v
kC
dW
dX A
(4-20)
![Page 48: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/48.jpg)
Pressure Drop and Rate Law
• For isothermal operation (T =T0)
-a function of only conversion and pressure
-Another equation is needed to determine the conversion as a function of
catalyst weight
- that is, we need to relate the pressure drop to the catalyst weight
),( PXfdW
dX
)(WfP
(4-21)
![Page 49: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/49.jpg)
Flow Through a Packed Bed
• The majority of gas-phase reactions are catalyzed by passing the reactant through a packed of catalyst particles
• Ergun equation: to calculate pressure drop in a packed porous bed
• The gas density is the only parameter that varies with pressure on the right-hand side. So, calculate the pressure drop through the bed laminar turbulent
G
DDg
G
dz
dP
ppc
75.1)1(1501
3
laminar turbulent
(4-22)
G=u=superficial mass velocity [g/cm2s]; u=superficial velocity [cm/s]; Dp=diameter of particle in the bed [cm]; =porosity=volume of void/total bed volume; 1- =volume of solid/total bed volume
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Flow through a Packed Bed
• Equation of continuity
- steady state the mass flow rate at any point is equal to the entering
mass flow rate
• Gas-phase volumetric flow rate
• Then,
vv
mm
00
0
00
00
T
T
F
F
T
T
P
Pvv
T
T
F
F
T
T
P
P
v
v 00
00
00
mo = m
(3-41)
(4-23)
![Page 51: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/51.jpg)
Pressure Drop in a Packed Bed Reactor
• then, Ergun equation
• Simplifying
• The catalyst weight,
00
00
T
T
F
F
T
T
P
P
dz
dP
cc zAW )1(
00
03
0
75.1)1(150)1(
T
T
ppc F
F
T
T
P
PG
DDg
G
dz
dP
GDDg
G
ppc
75.1)1(150)1(
30
0
Volume ofsolid
Density of solid catalyst
dzAdW cc )1(
(4-24)
dW
dPWe need
(4-26)
(4-25)
![Page 52: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/52.jpg)
Pressure Drop in a Packed Bed Reactor
• then, Ergun equation
• Simplifying
00
00
)1( T
T
cc F
F
T
T
P
P
AdW
dP
0
0
)1(
2
PA cc
00
0
0 /2 T
T
F
F
PP
P
T
T
dW
dP(4-27)
X
F
FFXFFF
T
ATTTT
0
0000 1 X
F
F
T
T 10
0
00
T
AA F
Fy
)1(/2 0
0
0
XPP
P
T
T
dW
dP
(4-28)
(4-29)
Let y=P/Po 2ydy FT
FTo
![Page 53: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/53.jpg)
Pressure drop in a packed bed reactor
ε < 0, the pressure drop (P) will be less than ε = 0
ε > 0, the pressure drop (P) will be greater than ε = 0
(4-30)
• For isothermal operation
),( PXfdW
dP ),( PXf
dW
dXand
• The two expressions are coupled ordinary differential equations. We can solve them simultaneously using an ODE solver such as Polymath.
• For the special case of isothermal operation and ε = 0, we can obtain an analytical solution.
• Polymath will combine the mole balance, rate law and stoichiometry
(4-31)
)1(/2 0
0
0
XPP
P
T
T
dW
dP
2y(1+X)
dy
![Page 54: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/54.jpg)
Pressure Drop in a Packed Bed Reactor
Analytical Solution
If ε = 0 or ε X ≪ 1, we can obtain an analytical solution to Eq. (4-30) for isothermal operation (i.e., T=T0). For isothermal operation with ε = 0, Eq. (4-30) becomes
)/(2 0
0
PP
P
dW
dP Isothermal (T=To)
with ε = 0
(4-30))1(/2 0
0
0
XPP
P
T
T
dW
dP
2y(1+X)
dy
dy
2y
2ydydW = -
dy2
dW = -
At W=0, y=1 (P/Po=1) y2= 1- w
![Page 55: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/55.jpg)
Pressure Drop in a Packed Bed Reactor
If ε = 0 or ε X ≪ 1, we can obtain an analytical solution to Eq. (4-30) for isothermal operation (i.e., T=T0). For isothermal operation with ε = 0, Eq. (4-30) becomes
0
0
)1(
2
PA cc
Pressure ratio only for ε = 0
WP
P 1
0
0
0
0
21
P
z
P
P
cc zAW )1(
(4-33)
(4-34)
(4-26)
Pressure as a function of reactor length, z
y=
y= =f (z)
![Page 56: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/56.jpg)
Pressure Drop in Pipes
D
fG
dL
dG
dL
dP
22
Integrating with P=P0 at L=0, and assuming that f = constant
Pressure drop along the length of the pipe
02 2
2
00
D
fG
PdL
dPG
dL
dP
P
P
P
P
D
Lf
PG
PP 0
0
0222
0 ln22
0
Rearranging, we get
DAP
fGV
P
P
cpp
00
20 4
1
Example 4-4: 1½” schedule 40 x1000-ft L (p=0.018), P<10%
![Page 57: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/57.jpg)
Analytical Solution for Reaction with Pressure DropConversion as a function of catalyst weight
AA rdW
dXF 0
A B
2nd-order isothermal reaction
Mole balance:
2AA kCr
Rate law:
00 )1(
P
PXCC AA
Stoichiometry: Gas-phase isothermal with =0
WP
P 1
0
2/10 )1)(1( WXCC AA
22/12
0
20 1)1( WX
F
kC
dW
dX
A
A
Combining
21
1
0,0
1)1(
0
0
000
220
0
WW
X
X
kC
v
vCFandWXat
dWWX
dX
kC
F
A
AA
A
A
Separating variable and Integrating
211
21
0
0
0
0
W
v
WkC
W
v
WkC
XA
A
(4-38)y=
![Page 58: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/58.jpg)
Reaction with Pressure DropConversion as a function of catalyst weight
211
21
0
0
0
0
W
v
WkC
W
v
WkC
XA
A
(4-38)
2/100 )1/(/)2(11 XXkCv
W A (4-39)
Catalyst weight for 2nd-order isothermal reaction in PFR with P
![Page 59: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/59.jpg)
Reaction with Pressure DropConversion as a function of catalyst weight
For gas phase reactions, as the pressure drop increases, the concentration decreases, resulting in a decreased rate of reaction, hence a lower conversion when compared to a reactor without a pressure drop.
![Page 60: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/60.jpg)
Example 4-5 and Example 4-6
지금까지 배운 지식을 활용하여 적들이 방심하고 있는 사이에
이 예제들은 집에서 풀어 봐야지 ...
![Page 61: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/61.jpg)
Spherical Packed-Bed Reactors
Spherical Ultraformer Reactor (Amoco) for dehydrogenation reaction such as
Paraffin Aromatic + 3 H2
Spherical reactor
- minimize pressure drop
- inexpensive
- the most economical shape for high pressure
![Page 62: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/62.jpg)
Coordinate system and variables used with a spherical reactor
![Page 63: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/63.jpg)
Synthesizing a Chemical Plant
Always challenge the assumptions, constraints, and boundaries of the problem
The profit from a chemical plant will be the difference between income from sales and the cost to produce the chemical
Profit = (value of products) – (cost of reactants)
– (operating costs) – (separation costs)
The operating cost: energy, labor, overhead, and depreciation of equipment
![Page 64: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/64.jpg)
Production of Ethylene Glycol
C2H4O(aq)
7 8 H2O, 0.9wt% H2SO4
200 millionlb EG/yr
9
V=197 ft3, X=0.8
CH2OHC2H4O + H2O CH2OH
Cat.
5
O2, C2H4, N2, C2H4O
6
separator
2
H2, C2H4
C2H6
separator
H2O C2H4O
absorber
C 2H 6 C 2H 4 + H 21
V=81 ft3, X=0.8
402 million lbC2H6 /yr
3C2H4
4 Air
W=45,440 lb, X=0.6
C2H4+ ½ O2 C2H4OAg
![Page 65: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/65.jpg)
Synthesizing a Chemical Plant
Ethylene glycol = $0.38/lb (2x108 lb/yr)
Ethane = $0.04/lb (4x106 lb/yr)
Sulfuric acid = $0.043/lb (2.26x108 lb/yr)
Operating cost = $8x106/yr
Profit = ($0.38/lb x 2x108 lb/yr) – ($0.04/lb x 4x108 lb/yr)
-($0.043/lb x 2.26x106 lb/yr) – ($8x106/yr)
= $52 million
How the profit will be affected by conversion, separation, recycle stream, and operating costs?
![Page 66: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/66.jpg)
Using CA (liquid) and FA (gas)
in the mole balance and rate laws
More convenient to work in terms of the number of moles or molar flow rate rather than conversion.
Must write a mole balance on each species when molar flow rates (Fi) and concentrations (Ci) are used as variables
Membrane reactor, multiple reaction, and unsteady state
BAAA
DCBA
CCkr
d
r
c
r
b
r
a
r
Da
dC
a
cB
a
bA
![Page 67: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/67.jpg)
Liquid Phase
Mole balance for liquid-phase reactions
AA
AA
A
AA
AA
rdW
dCv
rdV
dCv
r
CCvV
rdt
dC
0
0
00 )(
AB
AB
A
BB
AB
ra
b
dW
dCv
ra
b
dV
dCv
rab
CCvV
ra
b
dt
dC
0
0
00
)/(
)(
Batch
CSTR
PFR
PBR
DCBA dcba
DCBAa
d
a
c
a
b
For liquid-phase reaction with no volume change Concentration is the preferred variable
![Page 68: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/68.jpg)
Gas Phase For gas phase reactions
need to be expressed in terms of the molar flow rates
T
T
P
P
F
FCC
T
jTj
0
00
Total molar flow rate
n
jjT FF
1
jj r
dV
dF
y
(4-28, T=To)dydW
=2y-
FTo
FT
(1-11)
(3-42)
= FA + FB + FC + FD + FI
![Page 69: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/69.jpg)
Algorithm for Gas Phase Reaction
dDcCbBaA
Mole balances:
Vrdt
dN
Vrdt
dN
Vrdt
dN
Vrdt
dN
DD
CC
BB
AA
D
DD
C
CC
B
BB
A
AA
r
FFV
r
FFV
r
FFV
r
FFV
0
0
0
0
DD
CC
BB
AA
rdV
dF
rdV
dF
rdV
dF
rdV
dF
Batch CSTR PFR
![Page 70: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/70.jpg)
Algorithm for Gas Phase Reaction
Rate law: BAAA CCkr
Stoichiometry:
DCBAT
T
DTD
T
CTC
T
BTB
T
ATA
ADACAB
DCBA
FFFFF
T
T
P
P
F
FCC
T
T
P
P
F
FCC
T
T
P
P
F
FCC
T
T
P
P
F
FCC
ra
drr
a
crr
a
br
d
r
c
r
b
r
a
r
0
00
0
00
0
00
0
00
Relative rate of reaction:
Concentration:
Total molar flow rate:
y
![Page 71: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/71.jpg)
Algorithm for Gas Phase Reaction
Combine:
T
B
T
ATA
B
T
B
T
ATA
C
T
B
T
ATA
B
T
B
T
ATA
A
F
F
F
FCk
a
d
dV
dF
F
F
F
FCk
a
c
dV
dF
F
F
F
FCk
a
b
dV
dF
F
F
F
FCk
dV
dF
00
00
- Specify the parameter values: kA, CT0, T0, a, b, c, d
- Specify the entering number: FA0, FB0, FC0, FD0, and final value: Vfinal
Use an ODE solver
![Page 72: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/72.jpg)
Microreactors
Microreactors are used for the production of special chemicals, combinatorial chemical screening, lab-on-a-chip, and chemical sensors.
Example 4-7: Gas-Phase Reaction in a Microreactor
The gas phase reaction, 2NOCl 2NO + Cl2, is carried out at 425oC and 1641 kPa (16.2 atm). Pure NoCl is to be fed, and the reaction follows an elementary rate law. It is desired to produce 20 tons of NO per year in a micro reactor system using a bank of ten microreactors in parallel.Each microreactor has 100 channelswith each channel 0.2 mm square and250 mm in length. Plot the molar flowrates as a function of volume down thelength of the reactor. The volume of each channel is 10-5 dm3.
![Page 73: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/73.jpg)
Rate constant and activation energy (given): k=0.29 dm3/mol-sec at 500K with E=24 kcal/molTo produce 20 tons/year of NO at 85% conversion would require a feed rate of 0.0226 mol/s.
Solution
For one channel,
FAo=22.6 mol/s
FB=19.2 mol/s, X=0.85
2NOCl 2NO + Cl2
2A 2B + CA B +1/2C
1. Mole balance: jj r
dV
dF
dFA
dV= rA
dFB
dV= rB
dFC
dV= rC
2. Rate law:
-rA=kCA2, k=0.29 dm3/mol-sec
![Page 74: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/74.jpg)
3. Stoichiometry: Gas phase with T=To and P=Po, then v=vo(FT/FTo)
3-1. Relative rate
rA
-1=
rB
1=
rC
1/2
rB = -rA, rC= -0.5rA
3-2. Concentration
By applying Equation (3-42)
CA=CTo(FA/FT), CB=CTo(FB/FT), CC=CTo(FC/FT) with FT=FA+FB+FC
4. Combine
-rA=kCA2=kCTo
2(FA/FT)2
dFA
dVdFB
dVdFC
dV
= -kCTo2(FA/FT)2
= kCTo2(FA/FT)2
= 0.5kCTo2(FA/FT)2
5. Evaluate
CTo=Po/RT=(1641)/(8.314)(698K)=0.286 mol/dm3=0.286 mmol/cm3
Use Polymath to solve the ODE
![Page 75: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/75.jpg)
FAFB
FC
![Page 76: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/76.jpg)
Membrane Reactors
Membrane reactors can be used to achieve conversions greater than the original equilibrium value. These higher conversions are the result of Le Chatelier's Principle; you can remove one of the reaction products and drive the reaction to the right. To accomplish this, a membrane that is permeable to that reaction product, but is impermeable to all other species, is placed around the reacting mixture
By having one of the products pass throughout the membrane, we drive the reaction toward completion
![Page 77: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/77.jpg)
What kinds of membrane reactors are available?
Membrane reactors are most commonly used when a reaction involves some form of catalyst, and there are two main types of these membrane reactors: the inert membrance reactor and the catalytic membrane reactor.
The inert membrane reactor allows catalyst pellets to flow with the reactants on the feed side (usually the inside of the membrane). It is known as an IMRCF, which stands for Inert Membrane Reactor with Catalyst on the Feed side. In this kind of membrane reactor, the membrane does not participate in the reaction directly; it simply acts as a barrier to the reactants and some products.
A catalytic membrane reactor (CMR) has a membrane that has either been coated with or is made of a material that contains catalyst, which means that the membrane itself participates in the reaction. Some of the reaction products (those that are small enough) pass through the membrane and exit the reactor on the permeate side.
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Membrane Reactors
Inert membrane reactor with catalyst pellets on the feed side (IMRCF)
C6H12 C6H6 + 3H2
H2 molecule is small enough to diffuse through the small pore of the membrane while C6H12 and C6H6 cannot..
![Page 79: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/79.jpg)
Membrane Reactors
Catalytic membrane reactor (CMR)
C6H12 C6H6 + 3H2
Membrane reactors are commonly used in dehydrogenation reactions (e.g., dehydrogenation of ethane), where only one of the products (molecular hydrogen) is small enough to pass through the membrane. This raises the conversion for the reaction, making the process more economical.
![Page 80: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/80.jpg)
Dehydrogenation Reaction
A B + C
CH2CH3 CH=CH
+ H2 (B)
C4H10 C4H8 + H2 (B)
C3H8 C3H6 + H2 (B)
According to The DOE, an energy saving of 10 trillion Btu per year could result from the use of catalytic membrane reactors as replacements for conventional reactors for dehydrogenation reactions such as the dehydrogenation of ethylbenzene to styrene.
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RB=kcCB
A B + CFA
FB
V
FA
FB
FCmembrane
V+V
KC=0.05 mol @227oCP=8.2 atmT=227oCFA0=10mol/min
RB
1. Mole balance:
AA
AVVAVA
rdV
dF
VrFF
0
BBB
BBVVBVB
RrdV
dF
VrVRFF
0
for a differential mole balance on A in the catalytic bed at steady state
for a differential mole balance on C in the catalytic bed at steady state C
C rdV
dF
There are two “OUT”
terms
for a differential mole balance on B in the catalytic bed at steady state
Basic Algorithm for Membrane Reactor (Example 4-8)
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2. Rate law:
ACABC
CBAA rrrr
K
CCCkr
;;
kc is a transport coefficient. kc=f(membrane & fluid properties, tube diameter…) constant
3. Transport out the sides of the reactor:
BCB CkR
4. Stoichiometry:
CBA
CBAT
T
CTC
T
BTB
T
ATA
rrr
FFFF
F
FCC
F
FCC
F
FCC
000 ;;
Basic Algorithm for Solving Reaction in the Membrane Reactor
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5. Combining and Summarizing:
6. Parameter evaluation: CT0=0.2 mol/L, k=0.7 min-1, KC=0.05 mol/L, kc=0.2 min-1
FA0=10 mol/min, FB0=FC0=0
CBAT
T
C
T
B
C
T
T
ATcA
AC
T
BTcA
BA
A
FFFF
F
F
F
F
K
C
F
FCkr
rdV
dF
F
FCkr
dV
dFr
dV
dF
00
0 ;;
7. Numerical solution:Solve with POLYMATH or MATLAB
Basic Algorithm for Solving Reaction in the Membrane Reactor
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Reactor volume, V [L]
FA
FB
FC
10
5
00 100 200 300 400 500
FA
FB
FCkc=0.20 min-1
Effects of Side Stream, RB=kcCBin a membrane reactor
Reactor volume, V [L]
FA
FB
FC
10
5
00 100 200 300 400 500
FAFB
FCkc=20 min-1
Large side stream
Reactor volume, V [L]
FA
FB
FC
10
5
00 100 200 300 400 500
FA
FB FC
kc=0.0022 min-1
Little side stream
ConversionX=(10-4)/10=0.6
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Unsteady-State Operation of Stirred Reactors
Determine the time to reach steady-state operation
Predict the concentration and conversion as a function of time
Semibatch reactor
(b) ammonolysis, chlorination, hydrolysis
(c) acetylation reaction, esterification reaction
A
B
A, B
C
![Page 86: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/86.jpg)
Startup of a CSTR
Time to Reach Steady State for a First-Order Reaction in a CSTR
To determine the time to reach steady-state operation of a CSTR, we begin with the general mole balance equation applied to a well-mixed CSTR.
dt
dNVrFF A
AAA 0
Conversion does not have any meaning in startup because one cannot separate moles reacted from moles accumulated. Consequently, we must use concentration as the variable in our balance equation. For liquid-phase reactions V =V0 and for a constant overflow, v =v0. After dividing by v0 and replacing V/v0 by the space time , we find that
dt
dCrCC A
AAA 0
(4-45)
(4-46)
Utilizing the definitions of FA and NA, we have
dt
VCdVrvCvC A
AAA)(
00
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Startup of a CSTR
AA kCr
01 AA
A CC
k
dt
dC
tk
k
CC A
A )1(exp11
0
For a first-order reaction:
Solution (4-47)
Letting ts be the time necessary to reach 99% of the steady state concentration, CAS:
k
CC A
AS
10
Rearranging (4-46) for CA=0.99CAS yields
ktS
16.4 (4-48)
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Startup of a CSTR
For slow reactions :
For rapid reactions:
ktS
16.4 (4-48)
kt
t
S
S
6.4
6.4
(4-49)
(4-50)
Time to reach steady state in an isothermal CSTRFor most first-order system, steady state is achieved in three to four space times
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Semibatch ReactorsCBA
B
A
Mole balance on specials A:
[ in ] - [ out ] + [ gen. ] = [ acc. ]
dt
dVC
dt
VdC
dt
VCdVr
dt
dNtVr
AAAA
AA
)(00
Mass balance of all specials:
[ in ] - [ out ] + [ gen. ] = [ acc. ]
00
00
for
)(00
vdt
dV
dt
Vdv
tVV 00
AAA
AAA
CV
vr
dt
dC
dt
VdCVrCv
0
0
(4-55)
(4-56)
(4-54)
(4-53)
(4-52)
(4-51)
B
A
0 0Semibatch
reactorvolume as a
function of time
Mole balance on specials B:
[ in ] - [ out ] + [ gen. ] = [ acc. ]
000
0
0
)(
)(0
BBBB
BB
BB
BBB
BBB
CvVrFVr
dt
dCV
dt
dVC
dt
VCd
dt
dN
FVrdt
dN
dt
dNtVrF
V
CCvr
dt
dC BBB
B )( 00
(4-57)
(4-58)
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Example 4-9: Isothermal Semibatch Reactor with 2nd–order Reaction
CNBr + CH3NH2 CH3Br + NCNH2
A + B C + D
Isothermal elementary reaction in a semibatch reactor
t=0, CA=0.05 gmol/, CB=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
tvVV
CCV
vCkC
dt
dC
CV
vCkC
dt
dC
CkCr
BBBAB
ABAA
BAA
00
00
0
)(
CC
CCCC
ACC
Cvdt
dCV
dt
dVC
dt
dCV
dt
VCd
dt
dN
VrVrdt
dN
0
)(
Mole balance of A, B, C, and D
A
B
C CBAC C
V
vCkC
dt
dC 0
DBAD C
V
vCkC
dt
dC 0D
Conversion, X
00
00
0
0
VC
VCVC
N
NNX
A
AA
A
AA
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Concentration-time Trajectoriesin Semibatch Reactor
CA
CC
CB
0.05
0.04
0.03
0.02
0.01
0.000 100 200 300 400 500
CNBr + CH3NH2 CH3Br + NCNH2
(A) (B) (C) (D)
t=0, CA=0.05 gmol/, CB=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
Time
Co
nc
entr
ati
on
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Reaction Rate-time Trajectoriesin Semibatch Reactor
0.0025
0.0020
0.0015
0.00010
0.00005
0.000 50 100 150 200 250
CNBr + CH3NH2 CH3Br + NCNH2
(A) (B) (C) (D)
t=0, CA=0.05 gmol/, CB=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
Re
act
ion
rat
e [
mo
le/s
•L)
![Page 93: Chemical Reaction Engineering 1 Chapter 4 Isothermal Reactor Design 반응공학 1](https://reader033.vdocuments.mx/reader033/viewer/2022061413/56649eaa5503460f94baef1d/html5/thumbnails/93.jpg)
Reactor Equations in terms of Conversionin semibatch reactor
DCBA The number of moles of A remaining at any time , t
XNNN AAA 00
B
A
B
A
0 0
t timeto
up reactedA of
moles ofnumber
initially
vatin theA of
moles ofnumber
tat time
vatin theA of
moles ofnumber
where X is the mole of A reacted per mole of A initially in the vat.
The number of moles of B remaining at any time , t
XNdtFNN A
t
BBiB 00
0
t timeto
up reacted B of
moles ofnumber
vat the
toadded B of
moles ofnumber
initially
vatin the B of
moles ofnumber
tat time
vatin the B of
moles ofnumber
For a constant molar feed rate
XNtFNN ABBiB 00 (4-61)
(4-60)
(4-59)
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Reactor Equations in terms of Conversionin semibatch reactor
DCBA
A mole balance on specials A:
dt
dNVr A
A
B
A
B
A
0 0
The number of moles of C and D cab be taken directly from the stoichiometric table
The rate law (reversible 2nd-order reaction)
XNNN
XNNN
ADiD
ACiC
0
0
(4-62)
C
DCBAA K
CCCCkr (4-65)
The concentration of A and B
tvV
XN
V
NC
tvV
XN
V
NC
tvV
XNtFN
V
NC
tvV
XN
V
NC
ADA
ACC
ABBiBB
AAA
00
0
00
0
00
00
00
0 )1(
tvV
KXNXNtFNXk
dt
dX CAABBi
00
2000 /1
Combine (4-66)
(4-66) can be solved numerically
(4-63)
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Equilibrium conversionin semibatch reactor
B
A
B
A
0 0
For reversible reactions carried out in a semibatch reactor, the maximum attainable conversion (i.e., the equilibrium conversion) will change as the reaction proceeds because more reactant is continually to the right.
The rate law (reversible 2nd-order reaction)
C
DCBAA K
CCCCkr
DCBA
)/)(/(
)/)(/(
VNVN
VNVN
CC
CCK
BeAe
DeCe
BeAe
DeCeC
))(1(
))(1(
))((
00
20
000
00
eABe
eA
eABeA
eAeA
BeAe
DeCeC
XNtFX
XN
XNtFXN
XNXN
NN
NNK
(4-68)
e
eeC
BC
A
X
XXK
FK
Nt
1
2
0
0 (4-69)
)1(2
)1(4110
0
2
0
0
0
0
C
A
BCC
A
BC
A
BC
e K
N
tFKK
N
tFK
N
tFK
X(4-70)
Equilibrium conversion in a semiba
tch reactor
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Reactive Distillation
The distillation of chemically reacting mixtures has become increasingly common in chemical industries.
Carrying out these two operations, reaction and distillation, simultaneously in a single unit results in significantly lower capital cost and operating costs.
Reactive distillation is particularly attractive when one of the reaction products has a lower boiling point, resulting in its volatilization from the reacting liquid mixture.
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Reactive Distillation
By continually removing the volatile reaction product, methyl acetate, from the reacting liquid-phase reaction, the reverse reaction is negligible and the reaction continues to proceed towards completion in the forward direction.
An example of reactive distillation is the production of methyl acetate:
Reactive distillation is used with reversible, liquid phase reactions. Suppose a reversible reaction had the following chemical equation :
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Reactive Distillation
However, if one or more of the products are removed more of the product will be formed because of Le Chatlier's Principle :
For many reversible reactions the equilibrium point lies far to the left and little product is formed :
Removing one or more of the products is one of the principles behind reactive distillation. The reaction mixture is heated and the product(s) are boiled off. However, caution must be taken that the reactants won't boil off before the products.
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Homework
P4-11B
P4-12B
P4-13B
P4-14C
Due Date: Next Week