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Chemical Reaction Engineering
Lecturer : 郭修伯
Lecture 3
This course focuses on “isothermal ideal reactor design”.
Design equations
• Batch:– The conversion is a function of the time the
reactants spend in the reactor.– We are interested in determining how long to leave
the reactants in the reactor to achieve a certain conversion X.
Vrdt
dXN AA 0
??
Design equations
• CSTR:– We are interested in determining the size of the
reactor to achieve a certain conversion X.
AA rV
XF 0
-1/rA
X
??
Design equations
• PFR:– We are interested in determining the size of the
reactor to achieve a certain conversion X.
AA rdV
dXF 0
PBR
AA rdW
dXF 0Generally, the isothermal tubular reactor volume
is smaller than the CSTR for the same conversion
-1/rA
X
??
Isothermal reactor design
• Design procedure– mole balance– rate laws– stoichiometry– combination of the above three procedures and
solve ODE– obtain the volume/reaction time for the reactor
Do not forget to add some other time required!
Reactor design
• Batch:– constant volume, well-mixed
• CSTR:– constant volumetric flow rate
Damköhler number
– ratio of the rate of reaction of A to the rate of convective transport of A at the entrance to the reactor
– estimation of the degree of conversion in a continuous reactor
• First order irreversible rxn:
• Second order irreversible rxn:
– Da = 0.1 ~ X = 10% ; Da = 10.0 ~ X = 90%
""
""
0
0
rateconvectionA
ratereactionA
Aofrateflowentering
entranceatreactionofrate
F
VrDa
A
A
kCv
VkC
F
VrDa
A
A
A
A
00
0
0
0
000
20
0
0A
A
A
A
A kCCv
VkC
F
VrDa
Example, const.-V, batch, 2nd order rxn, isothermal
• mole balance
• rate laws
• Stoichiometry
• combination
Vrdt
dXN AA 0
2AA kCr
)1(0 XCC AA
20 1 XkCdt
dXA
X
A
t
X
dX
kCdt
0 20
0 1
1)
1(
1
0 X
X
kCt
A
+ some additional time for filling, heating, …etc.
Example 4-1
It is desired to 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, k. Because the reaction will be carried out isothermally, the specific reaction rate 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 40C the reaction does not proceed at a significant rate; consequently, a temperature of 55C has been chosen. Because the water is usually present in excess, its concentration may be considered constant during the course of the reaction. In the laboratory experiment, 500 ml of a 2 M solution of ethylene oxide in water was mixed with 500 ml of water containing 0.9 wt% sulfuric acid, which is a catalyst. The temperature was maintained at 55C. The concentration of ethylene glycol was recorded as a function of time, determine the specific reaction rate at 55C.
The reaction is first-order in ethylene oxide:
CBA catalyst
Because water is present in such excess, the concentration of water at any time t is virtually the same as the initial concentration and the rate law is independent of the concentration of H2O. (CB≈CB0)
Rate law:
no volume change, V=V0
Batch design equation:
Stoichiometry
Combination
?
CBA catalyst
slope = -k = -0.311 min-1
Example, liquid phase CSTR, 1st order rxn, isothermal
• mole balance
• rate laws
• Stoichiometry
• combination
A
A
A
A
r
XCv
r
XFV
000
AA kCr
)1(0 XCC AA
X
X
k 1
1
orA
A
r
XC
v
V
0
0
ork
CC A
A
10
orDa
DaX
1
Example, liquid phase CSTR, 2nd order rxn, isothermal
• mole balance
• rate laws
• Stoichiometry
• combination
A
A
A
A
r
XCv
r
XFV
000
2AA kCr
)1(0 XCC AA
220
00
1 XkC
XCvV
A
A
or
200 1 XkC
X
v
V
A or
Da
DaDaX
2
4121
0
00
2
4121
A
AA
kC
kCkCX
or
CSTRs in series, 1st order rxn, isothermal
20
1122
0
22
12
1111 k
C
kk
C
k
CC AAA
A
• mole balance
• rate laws
• Stoichiometry
• combination
2
210
2
21
2
1
A
AA
A
AA
A
A
r
CCv
r
FF
r
XFV
222 AA Ckr
)1(12 XCC AA
CA0CA1 CA2
... n
An
AAn
Da
C
k
CC
1100
)1(0 XCC AAn nkX
1
11
CSTRs in parallel, isothermal
• mole balance
Ai
iiAi r
XFV 0
FA0
FA01
FA02
....
same T, V, v
A
A
r
X
n
F
n
V 0
A
A
r
XFV
0
XXXX n ...21
AAnAA rrrr ...21
total volumetotal molar flow rate
CSTRs in series
• constant flow rate
• conversion as a function of the number of tanks in series Two equal-sized CSTRs in series will give a higher conversion than two CSTRs in parallel of the same size when the reaction order is greater than zero.
CSTRs in parallel
• constant conversion and rate of reaction in each tank• The sum of the volume of the tanks equals the total volume of a
single large CSTR.
• 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.
• Considering the degree of mixing and the room required, a large tank might not be appropriate.
Example 4-2 Close to 12.2 billion metric tons of ethylene glycol (EG) were produced in 2000, which ranked it the twenty-sixth most produced chemical in the nation that year on a total pound basis. About one-half of the ethylene glycol is used for antifreeze while the other half is used in the manufacture of polyesters. In the polyester category, 88% was used for fibers and 12% for the manufacture of bottles and films. The 2004 selling price for ethylene glycol was $0.28 per pound. It is desired to produce 200 million pounds per year of EG. The reactor is to be operated isothermally. A 1 lb mol/ft3 solution of ethylene oxide (EO) in water is fed to the reactor (shown in Figure E4-2.1) 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, as determined in Example 4-1.
CBA catalyst
The specified ethylene glycol (EG) production rate:
(a) If 80% conversion is to be achieved, determine the necessary CSTR volume.
CSTR Design equation：
Rate law：Stoichiometry：
Combination:
CBA catalyst
The conversion exiting each of the CSTRs in parallel is 81%.
(b) If two 800-gal reactors were arranged in parallel, what is the corresponding conversion?
CSTR Design equation：
Rate law：Stoichiometry：
Combination:
The two equal-sized CSTRs in series will give a higher conversion than two CSTRs in parallel of the same size when the reaction order is greater than zero.
(c) If two 800-gal reactor were arranged in series, what is the corresponding conversion?
PFR
• Gas-phase reactions are carried out primarily in tubular reactors where the flow is generally turbulent.
• Assuming no dispersion and there are no radial gradients in either temperature, velocity, or concentration.
• Should be aware of the change of the volume.
N.B. The majority of gas-phase reactions are catalyzed by passing the reactant through a packed bed of catalyst particles.
PFR, 2nd order rxn, liquid phase, isothermal
X
X
kC
Cv
X
dX
kC
FV
A
AX
A
A
11 20
00
0 220
0
• mole balance
• rate laws
• Stoichiometry
• combination
AA rdV
dXF 0
2AA kCr
)1(0 XCC AA
or2
2
0
0
11 Da
Da
kC
kCX
A
A
No pressure drop
No heat exchange
X
AA r
dXFV
00
Damköhler number for 2nd-order reaction
PFR, 2nd order rxn, gas phase, isothermal
X
A
A dXXkC
XFV
0 220
2
01
1
• mole balance
• rate laws
• Stoichiometry
• combination
AA rdV
dXF 0
2AA kCr
)1(
)1(
)1(
)1(
)1( 00
0
0 X
XC
Xv
XF
Xv
F
v
FC A
AAAA
No pressure drop
No heat exchange
X
AA r
dXFV
00
X
XXX
kC
vV
A 1
1)1ln()1(2
22
0
0
Example 4-3 Ethylene ranks fourth in the Unite States in total pounds of chemicals produced each year, and it is the number one organic chemical produced each year. Over 50 billion pounds were produced in 2000, and it sold for $0.27 per pound. Sixty-five percent of the ethylene produced is used in the manufacture of fabricated plastics, 20% for ethylene oxide, 16% for ethylene dichloride and ethylene glycol, 5% for fibers, and 5% for solvents.Determine the plug-flow reactor volume necessary to produce 300 million pounds of ethylene a year from 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 1100 K at a pressure of 6 atm.
The molar flow rate of ethylene (B):
CBA 24262 HHCHC The activation energy is 82 kcal/g mol.
K����s�k [email protected] 1
PFR design equation：
Rate law (elementary)：
Stoichiometry：
Combination:
(b) It was decided to use a bank of 2-in. schedule 80 pipes in parallel that are 40 ft in length. For pipe schedule 80, the cross-section are, Ac, is 0.0205 ft2. The number of pipes necessary is
Pressure drop in reactors
• In gas-phase reactions, the concentration of the reacting species is proportional to the total pressure and proper accounting for the effects of pressure drop on the reaction system can be a key factor in the success or failure of the reactor operation (e.g. PBR).
• When accounting for the effects of pressure drop, the differential form of the mole balance must be used.
PBR, 2nd order rxn, gas phase, isothermal
T
T
P
P
X
XCC A
A0
0
0
1
)1(
2
0
2
0
0
1
1
P
P
X
X
v
kC
dW
dX A
• mole balance
• rate laws
• Stoichiometry
• combination
'0 AA rdW
dXF
2' AA kCr
or
2
0
2
00 1
)1(
P
P
X
XCk
dW
dXF A
A
T
T
P
P
X
XvCC jjA
j0
0
0
1
)(
),( PXfdW
dX
What is the relationship between X and P? If PBR: Ergun equation
Ergun equation
• Pressure drop in a porous bed:
G
DDg
G
dz
dP
ppc
75.1)1(1501
3
Dominant for laminar flow
Dominant for turbulent flow
constant mass flow rate
00vv
00
00
T
T
F
F
T
T
P
Pvv
00
0
03
175.1
)1(1501
T
T
ppc F
F
T
T
P
PG
DDg
G
dz
dP
Ergun equation (cont.)
00
0
03
175.1
)1(1501
T
T
ppc F
F
T
T
P
PG
DDg
G
dz
dP
cC zAW 1
)1(/2 0
0
0
XPP
P
T
T
dW
dP
G
DDg
G
ppc
75.1)1(1501
30
0
0
0
)1(
2
PA CC
00
0
0 /2 T
T
F
F
PP
P
T
T
dW
dP
Pressure drop in terms of Catalyst weight:
XFFF ATT 00
Gas phase, PBR with pressure change
)1(/2 0
0
0
XPP
P
T
T
dW
dP
2
0
2
0
0
1
1
P
P
X
X
v
kC
dW
dX A
Solve simultaneously!
Some special cases in the textbook!...
Pressure drop in pipes without packing
D
fG
dL
duG
dL
dP
22
XFFF ATT 00
constant mass flow rate
00vv
00
00
T
T
F
F
T
T
P
Pvv
uG
D
fG
dL
GdG
dL
dP
22
isothermal
02 2
2
00
D
fG
PdL
dPG
dL
dP
P
Pintegrate
f~const.
P
P
D
Lf
PG
PP 0
0
0222
0 ln22
PBR, 2nd order rxn, gas phase, isothermal
T
T
P
P
X
XCC A
A0
0
0
1
)1(
WXF
kC
dW
dX
A
A 11 2
0
20
• mole balance
• rate laws
• Stoichiometry
• combination
'0 AA rdW
dXF
2' AA kCr
)1/(/)2(11 0 XXkCvW A
BA
)1(/2 0
0
0
XPP
P
T
T
dW
dP
WXCC AA 1)1(0
Spherical packed-bed reactors
• When small catalyst pellets are required, the pressure drop can be significant, and thus the conversion decreases.
• One type of reactor that minimises pressure drop and is also inexpensive to build is the spherical reactor, called an ultraformer.
• Spherical reactor: the cross-sectional area and the weight of catalyst are functions of the position.
• In addition to the higher conversion, the spherical reactor has the economic benefit of reducing the pumping and compression cost because of higher pressure at the exit.
Mole balance and rate laws
• Concentration = f (conversion) We have done!• There are a number of instances when it is much
more convenient to work in terms of the number of moles (Ni) or molar flow rates (Fi) rather than conversion.– Membrane reactors and multiple reactions taking place in
the gas phase are two such cases where molar low rates rather than conversion are preferred.
– Concentration = f (molar flow rate)
Algorithm - liquid phase
• Liquid phase– For liquid-phase reactions in which there is no
volume change, concentration is the preferred variable.
– We have only to specify the parameter values for the system (CA0, vo, etc.) and for the rate law to solve the coupled ODEs for either PFR, PBR, or batch reactors, or to solve the coupled algebraic equations for a CSTR.
Liquid phase – mole balance
Rector Mole Balance (A) Mole Balance (B)
Batch A
A rdt
dC A
B ra
b
dt
dC
CSTR A
AA
r
CCvV
00
A
BB
rab
CCvV
)/(00
PFR A
A rdV
dCv 0 A
B ra
b
dV
dCv 0
PBR '0 AA r
dW
dCv '0 A
B ra
b
dW
dCv
dDcCbBaA
Algorithm - gas phase
• Gas phase– For gas-phase reactions in which there is volume
change, molar flow rate is the preferred variable.– The total molar flow rate is given as the sum of the
flow rate of the individual species.– A mole balance on each species has to be specified.
Gas phase – mole balance
Rector Mole Balance (A) Mole Balance (B)
Batch Vrdt
dNA
A AB r
a
b
dt
dN
CSTR A
AA
r
FFV
0
A
BB
rab
FFV
0
PFR A
A rdV
dF A
B ra
b
dV
dF
PBR 'AA r
dW
dF 'A
B ra
b
dW
dF
dDcCbBaA
T
T
P
P
F
FCC
T
ATA
0
00
T
B
T
AToA
A
F
F
F
FCk
dW
dF'
• mole balance
• rate laws
• Stoichiometry
• combination
BAA CkCr
00
0
2 T
T
F
F
T
TP
dW
dP
IDCBAT FFFFFF
PBR, gas phase, isothermal, no ΔP
'AA r
dW
dF
Solve
Microreactors
• High surface area-to-volume ratio
• Reduce or eliminates heat and mass transfer resistances
• Shorter residence times & narrower residence time distributions
• Production of lab-on-a-chip, chemical sensors
• Assume PFR or in laminar flow
Thermodynamically limited rxns
• Catalytic membrane reactors can be used to increase the yield of reactions that are highly reversible over the temperature range of interest.
• The membrane can either provide a barrier to certain components, while being permeable to others, prevent certain components such as particulates from contacting the catalyst, or contain reactive sites and be a catalyst in itself.
Membrane reactors
• The membrane reactor is another technique for driving reversible reactions to the right in order to achieve very high conversion.
• These high conversions can be achieved by having one of the reaction products diffuse out of a semipermeable membrane surrounding the reacting mixtures.
• Two main types– inert membrane reactor with catalyst pellets on the feed side
(IMRCF)
– Catalytic membrane reactor (CMR)
Startup of a CSTR
• Determine the time necessary to reach steady-state operation:– Conversion does not have any meaning in the
startup
– Use concentration rather than conversion as the variable in the balance equations.
t
kk
CC A
A )1(exp11
0
• mole balance
• rate laws
• combination
AA kCr
01 A
AA C
Ck
dt
dC
CSTR, 1st order rxn, liquid phase
dt
dNVrFF A
AAA 0
t = 0
dt
dCrCC A
AAA 0
const. .V
0vV
0AA CC
ASA CC 99.0
t = ts
kts
1
6.4
steady-state concentration
Semi-batch reactors
• When unwanted side reactions occur at high concentration of reactant B, or the reaction is highly exothermic. Examples of reactions:– ammonolysis– chlorination– hydrolysis
• Reactive distillation: Carrying out the two operations, reaction and distallation in a single unit results in lower capital and operating costs.– acetylation reaction
– esterfication reaction (remove water) A
A
B
+B
C
Semi-batch reactor
• Write the reactor equations in terms of concentration / numer of moles of each species
• Write the mass balance of the vessel
• Write the rate laws
A
B
O.D.E solver+B
C
A
B Semi-batch, liquid phase
AA C
vr
dt
dC
V- 0
A
• mole balance (A)
• mole balance (B)
• V is not a constant
• combine
dt
dNVr A
A 00
CBA
dt
Vdv
0000
dt
dNVrF B
BB 00
(overall mole balance)
0
tvVV 00
V00
BBBB CCv
rdt
dC
…..
Example 4-9 The production of methyl bromide is an irreversible liquid-phase reaction that follows an elementary law. The reaction CNBr+CH3NH2CH3Br+NCNH2 is carried out isothermally in a semibatch reactor. An aqueous solution of methyl amine (B) at a concentration of 0.025 mol/dm3 is to fed at rate of 0.05 dm3/s to an aqueous solution of bromine cyanide (A) contained in a glass-lined reactor. The initial volume of fluid in a vat is to be 5 dm3 with a bromine cyanide concentration of 0.05 mol/dm3. The specific reaction rate constant is k = 2.2 dm3/smol. Solve for the concentration of bromine cyanide and methyl bromide and the rate of reaction as a function of time.
Semi-batch reactor design equation:
Rate law:
Combination:
where
Recycle reactors
• They are used when the reaction is autocatalytic, or when it is necessary to maintain nearly isothermal operation of the reactor or to promote a certain selectivity.
• They are used extensively in bio-chemical operations.
• Two conversions: the overall conversion X0 and the conversion per pass Xs
R, recycle parameter
Xs Xo
