CATALYSIS AND CATALYTIC
REACTORS
(6)
Marcel Lacroix
Université de Sherbrooke
CATALYSIS AND CATALYTIC REACTORS:
OBJECTIVES
• TO DEVELOP AN UNDERSTANDING OF
CATALYSTS, REACTION MECHANISMS, AND
CATALYTIC REACTOR DESIGN.
M. Lacroix
Catalysis and Catalytic Reactors
2
CATALYSTS: DEFINITIONS
•
A CATALYST IS A SUBSTANCE THAT AFFECTS THE RATE OF A
REACTION BUT EMERGES FROM THE PROCESS UNCHANGED.
•
THE CATALYST (PLATINUM) REDUCES THE POTENTIAL
ENERGY BARRIER OVER WHICH THE REACTANTS ( H2 AND O2)
MUST PASS TO FORM THE PRODUCT (H2O).
M. Lacroix
Catalysis and Catalytic Reactors
3
CATALYSTS: DEFINITIONS
• TWO BROAD CLASSES OF CATALYSTS: ENZYMES
AND MAN-MADE CATALYSTS.
• ENZYMES: BIOCHEMICAL CATALYSTS THAT
OPERATE AT CLOSE TO AMBIENT
TEMPERATURE. ENZYMES ARE CHEMICALS
PRODUCED BY MICROORGANISMS SUCH AS
YEASTS, BACTERIA, ALGAE, MOLDS, PROTOZOA.
• MAN-MADE CATALYSTS: MOSTLY SOLIDS
(HETEROGENEOUS CATALYTIC PROCESS) WHICH
USUALLY AIM TO CAUSE HIGH-TEMPERATURE
RUPTURE OR SYNTHESIS OF MATERIALS.
M. Lacroix
Catalysis and Catalytic Reactors
4
CATALYTIC CONVERTER FOR AUTOMOBILES
• THE CATALYTIC CONVERTER CONTAINS METAL
CATALYSTS SUCH AS Pd, Pt OR Rh THAT CARRY OUT
THE FOLLOWING REACTIONS AND THUS
SIGNIFICANTLY REDUCE POLLUTION :
hydrocarbons + O2 → CO2 + H 2O
2CO + O2 → 2CO2
2 NO + 2CO → N 2 + 2CO2
M. Lacroix
Catalysis and Catalytic Reactors
5
CATALYSTS: PROPERTIES
•
LARGE FLUID-SOLID INTERFACIAL AREA TO
PROMOTE A SIGNIFICANT REACTION RATE.
(FOR EXAMPLE, POROUS SILICA-ALUMINA CRACKING CATALYST:
SURFACE AREA OF Sa= 300 m2/g)
•
1.
2.
3.
CATALYSTS ARE SUBJECT TO DEACTIVATION:
DECLINE IN A CATALYST ACTIVITY AS TIME
PROGRESSES. IT MAY BE CAUSED BY:
AGING: GRADUAL CHANGE IN SURFACE CRYSTAL
STRUCTURE.
COKING: DEPOSITION OF CARBONACEOUS
MATERIAL ON THE CATALYST IN THE CRACKING
OF PETROLEUM NAPHTAS.
POISONING: DEPOSITION OF A FOREIGN MATERIAL
ON ACTIVE PORTIONS OF THE CATALYST SURFACE.
M. Lacroix
Catalysis and Catalytic Reactors
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CATALYSTS: GENERAL OBSERVATIONS
• SELECTION OF A CATALYST TO PROMOTE A
REACTION IS NOT WELL UNDERSTOOD.
• DUPLICATION OF THE CHEMICAL CONSTITUTION
OF A GOOD CATALYST IS NO GUARANTEE THAT
THE SOLID PRODUCED WILL HAVE ANY
CATALYTIC ACTIVITY: THE CRYSTALLINE
STRUCTURE IMPARTS THE CATALYTIC ACTIVITY.
• A CATALYST CHANGES ONLY THE RATE OF A
REACTION. IT DOES NOT AFFECT THE
EQUILIBRIUM.
M. Lacroix
Catalysis and Catalytic Reactors
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7 STEPS IN A CATALYTIC REACTION
1.
2.
3.
4.
5.
6.
7.
MASS TRANSFER (DIFFUSION) OF THE REACTANTS (e.g.
SPECIES A) FROM THE BULK FLUID TO THE EXTERNAL
SURFACE OF THE CATALYST PELLET.
DIFFUSION OF THE REACTANT FROM THE PORE MOUTH
THROUGH THE CATALYST PORES TO THE IMMEDIATE
VICINITY OF THE INTERNAL CATALYTIC SURFACE.
ADSORPTION OF REACTANT A ONTO THE CATALYST
SURFACE.
REACTION ON THE SURFACE OF THE CATALYST: A → B .
DESORPTION OF THE PRODUCTS (e.g., SPECIES B) FROM THE
SURFACE.
DIFFUSION OF THE PRODUCTS FROM THE INTERIOR OF THE
PELLET TO THE PORE MOUTH AT THE EXTERNAL SURFACE.
MASS TRANSFER OF THE PRODUCTS FROM THE EXTERNAL
PELLET SURFACE TO THE BULK FLUID.
M. Lacroix
Catalysis and Catalytic Reactors
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7 STEPS IN A CATALYTIC REACTION
M. Lacroix
Catalysis and Catalytic Reactors
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RATE LAW FOR A CATALYTIC REACTION
•
•
•
•
•
75% OF ALL HETEROGENEOUS REACTIONS THAT ARE NOT
DIFFUSION-LIMITED ARE SURFACE-REACTION-LIMITED.
THE RATE EQUATION THAT WE RETAIN MUST FIT THE DATA SO
MUCH BETTER THAN THE OTHER FAMILIES THAT ALL THE
OTHERS CAN BE REJECTED.
IT IS NOT GOOD ENOUGH TO SELECT THE MECHANISM THAT
WELL FITS –OR EVEN BEST FITS- THE DATA. DIFFERENCE IN FIT
MAY BE EXPLAINABLE ENTIRELY IN TERMS OF EXPERIMENTAL
DATA.
WHEN A SATISFACTORY RATE EQUATION HAS BEEN FOUND
FOR THE SURFACE MECHANISM, IT MUST BE COMBINED WITH
THE OTHER RESISTANCE PHENOMENA (DIFFUSION). THIS STEP
FURTHER COMPLICATES THE MATTER.
IN LIGHT OF THE ABOVE OBSERVATIONS, WE CONCLUDE THAT
IT IS GOOD ENOUGH TO USE THE SIMPLEST AVAILABLE
CORRELATING RATE EXPRESSION, HENCE FIRST-ORDER OR nth –
ORDER KINETICS, TO RERESENT THE SURFACE REACTION.
M. Lacroix
Catalysis and Catalytic Reactors
10
DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
• TOLUENE AND HYDROGEN ARE REACTED OVER A
SOLID MINERAL CATALYST CONTAINING
CLINOPTILOTITE (A CRYSTALLINE SILICA-ALUMINA)
TO YIELD BENZENE AND METHANE:
C6 H 5CH 3 + H 2 ⎯⎯ ⎯→ C6 H 6 + CH 4
catalyst
• WE WISH TO DESIGN A PACKED-BED REACTOR TO
PROCESS A FEED CONSISTING OF 30% TOLUENE, 45%
HYDROGEN, AND 25% INERTS. TOLUENE IS FED AT A
RATE OF 50 MOLES/MIN AT A TEMPERATURE OF 913
KELVIN AND A PRESSURE OF 40 ATMOSPHERES.
• TO DESIGN THE PBR WE MUST FIRST DETERMINE
THE RATE LAW FROM THE REACTOR DATA.
M. Lacroix
Catalysis and Catalytic Reactors
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DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
M. Lacroix
Catalysis and Catalytic Reactors
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DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
DEPENDENCE ON THE PRODUCT METHANE
•
IF THE METHANE WERE ADSORBED ON THE SURFACE, THE
PARTIAL PRESSURE OF METHANE WOULD APPEAR IN THE
DENOMINATOR OF THE RATE EXPRESSION AND THE RATE
WOULD VARY INVERSELY WITH METAHNE
CONCENTRATION:
−r ≈
'
T
•
[⋅]
1 + K M PM + ...
HOWEVER, FROM RUNS 1 AND 2 WE OBSSERVE THAT A
FOURFOLD INCREASE IN THE PRESSURE OF METHANE HAS
LITTLE EFFECT ON − rT' . CONSEQUENTLY, WE ASSUME
THAT METHANE IS EITHER VERY WEAKLY ADSORBED
K M PM << 1 OR GOES DIRECTLY INTO THE GAS PHASE.
M. Lacroix
Catalysis and Catalytic Reactors
13
DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
DEPENDENCE ON THE PRODUCT BENZENE
•
IN RUNS 3 AND 4, WE OBSERVE THAT FOR FIXED
CONCENTRATIONS (PARTIAL PRESSURES) OF HYDROGEN
AND TOLUENE THE RATE DECREASES WITH INCREASING
CONCENTRATION OF BENZENE:
−r ≈
'
T
•
[⋅]
1 + K B PB + ...
THE TYPE OF DEPENDENCE OF − rT ON PB SUGGESTS
THAT BENZENE IS ADSORBED ON THE CLINOPTILOLITE
SURFACE.
M. Lacroix
'
Catalysis and Catalytic Reactors
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DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
DEPENDENCE ON TOLUENE
•
AT LOW CONCENTRATIONS OF TOLUENE (RUNS 10 AND 11),
THE RATE INCREASES WITH INCREASING PARTIAL
PRESSURE OF TOLUENE, WHILE AT HIGH TOLUENE
CONCENTRATIONS (RUNS 14 AND 15), THE RATE IS
ESSENTIALLY INDEPENDENT OF THE TOLUENE PARTIAL
PRESSURE:
P
− rT' ≈
•
T
1 + KT PT + ...
COMBINATIONS OF THE RATE EXPRESSION FOR BENZENE
AND TOLUENE SUGGESTS THAT THE RATE LAW MAY BE OF
THE FORM
PT
−r ≈
1 + KT PT + K B PB + ...
'
T
M. Lacroix
Catalysis and Catalytic Reactors
15
DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
DEPENDENCE ON HYDROGEN
•
EXAMINATION OF RUNS 7,8 AND 9 REVEALS THAT THE RATE
INCREASES LINEARLY WITH INCREASING HYDROGEN
CONCENTRATION AND WE CONCLUDE THAT THE REACTION IS
FIRST-ORDER IN H2 :
'
− rT ≈ PH 2
•
•
HYDROGEN IS EITHER NOT ADSORBED ON THE SURFACE OR ITS
COVERAGE OF THE SURFACE IS EXTREMELY LOW ( K P << 1)
H2 H2
FOR THE PRESSURES USED.
IF HYDROGEN WERE ADSORBED, − rT WOULD HAVE A
DEPENDENCE ON PH ANALOGUOUS TO THE DEPENDENCE OF
2
'
− rT ON THE PARTIAL PRESSURE OF TOLUENE PT .
'
M. Lacroix
Catalysis and Catalytic Reactors
16
DEDUCTION OF A RATE LAW
FROM EXPERIMENTAL DATA
OVERALL DEPENDENCE
•
COMBINATION OF ALL THE ABOVE RATE EXPRESSIONS
SUGGESTS:
−r =
'
T
kPH 2 PT
1 + K B PB + KT PT
•
THIS IS THE BEST RATE LAW OUT OF 25 MODELS TESTED BY
Papp, Kallo and Schay, J. Catal., 23, 168, 1971.
•
TO PERFORM THE REGRESSION ANALYSIS WITH POLYMATH,
THE RATES OF REACTIONS (FIRST COLUMN IN TABLE) ARE
MULTIPLIED BY 1010.
M. Lacroix
Catalysis and Catalytic Reactors
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REGRESSION OF DATA:
POLYMATH PROGRAM AND RESULTS
Nonlinear regression (mrqmin)
Model: C01 = k*C02*C03/(1+KB*C05+KT*C02)
Variable
k
KB
KT
•
THUS,
Ini guess
100,
1,
1,
Value
144,76731
1,3905262
1,0384106
Conf-inter
0,124044
0,0045798
0,0013161
k = 144.7 ⋅ 10 −10 mole _ of _ T / g _ catalyst ⋅ s =
8.7 ⋅ 10 − 4 mole _ of _ T / kg _ catalyst ⋅ min
•
CONSEQUENTLY,
8.7 ⋅ 10 − 4 PH 2 PT
mole _ of _ T
−r =
1 + 1.39 PB + 1.038 PT kg _ catalyst ⋅ min
'
T
M. Lacroix
Catalysis and Catalytic Reactors
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EXAMPLE No. 1:
DESIGNING A PACKED BED REACTOR
•
THE HYDRODEMETHYLATION OF TOLUENE IS TO BE
CARRIED OUT IN A PBR. WE WANT TO FIND THE
CONVERSION X, THE PRESSURE RATIO AND THE PARTIAL
PRESSURES AS A FUNCTION OF THE CATALYST MASS. THE
MOLAR FEED RATE OF TOLUENE TO THE REACTOR IS 50
moles/min AND THE REACTOR IS OPERATED AT 40
ATMOSPHERES AND 913 K. THE FEED CONSITS OF 30%
TOLUENE, 45% HYDROGEN, AND 25% INERTS. HYDROGEN IS
USED IN EXCESS TO PREVENT COKING. THE PRESSURE DROP
PARAMETER IS α = 9.8 ⋅ 10 −5 kg −1 .
•
THE CHEMICAL REACTION IS:
C6 H 5CH 3 + H 2 ⎯⎯ ⎯→ C6 H 6 + CH 4
catalyst
OR
M. Lacroix
aA + bB → cC + dD
Catalysis and Catalytic Reactors
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EXAMPLE No. 1: PACKED BED REACTOR
1.
DESIGN EQUATION:
2.
RATE LAW:
−r =
3.
STOICHIOMETRY:
'
T
dX
FA0
= − rT'
dW
(1)
kPH 2 PT
(2)
1 + K B PB + KT PT
PT = PT 0 (1 − X ) y (3); PH 2 = PT 0 (1.5 − X ) y (4); PB = PT 0 Xy (5)
1
P
y = = (1 − αW ) 2
P0
(6)
4.
PRESSURE DROP:
5.
SUSBSTITUTION OF EQUATIONS (2)-(6) IN (1) AND SOLUTION
YIELDS THE CONVERSION OF THE PBR X AS A FUCTION OF
THE CATALYST MASS W.
M. Lacroix
Catalysis and Catalytic Reactors
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EXAMPLE No. 1:
PACKED BED REACTOR
•
•
•
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(X)/d(w) = -rt/FTo
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•
•
•
•
•
•
•
•
•
•
•
•
•
•
Explicit equations as entered by the user
[1] FTo = 50
[2] k = 87e-05
[3] KT = 1038e-03
[4] KB = 139e-02
[5] alpha = 98e-06
[6] Po = 40
[7] PTo = 3e-01*Po
[8] y = (1-alpha*w)^(1/2)
[9] P = y*Po
[10] PH2 = PTo*(15e-01-X)*y
[11] PB = PTo*X*y
[12] PT = PTo*(1-X)*y
[13] rt = -k*PT*PH2/(1+KB*PB+KT*PT)
[14] RATE = -rt
•
•
•
•
Independent variable
variable name : w
initial value : 0
final value : 10000
M. Lacroix
POLYMATH PROGRAM
Catalysis and Catalytic Reactors
21
CONVERSION X AND PRESSURE RATIO y
VERSUS CATALYST MASS (KG) FOR THE PBR
M. Lacroix
Catalysis and Catalytic Reactors
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PARTIAL PRESSURES (ATM)
VERSUS CATALYST MASS (KG) FOR THE PBR
M. Lacroix
Catalysis and Catalytic Reactors
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CATALYST DEACTIVATION
•
•
THUS FAR, WE HAVE ASSUMED THAT THE ACTIVITY OF THE
CATALYST REMAINS CONSTANT THROUGHOUT THE
CATALYST’S LIFE. THAT IS, THE TOTAL CONCENTRATION OF
ACTIVE SITES ACCESSIBLE TO THE REACTION DOES NOT
CHANGE WITH TIME.
IN REALITY, THE ACTIVITY OF THE CATALYST AT TIME t, a(t),
HAS DECREASED AND IT MAY BE DEFINED AS THE RATE OF
REACTION ON A CATALYST THAT HAS BEEN USED AT TIME t TO
THE RATE OF REACTION ON A FRESH CATALYST:
− rA' (t )
a (t ) = '
− rA (t = 0)
M. Lacroix
Catalysis and Catalytic Reactors
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CATALYST DEACTIVATION:
RATE OF DISAPPEARANCE OF REACTANT A
•
THEREFORE, THE RATE OF DISAPPEARANCE OF REACTANT A
ON A CATALYST THAT HAS BEEN UTILIZED FOR A TIME t IS:
− rA' = a (t )k (T ) f (C A , C B ,..., C P )
a(t): CATALYTIC ACTIVITY, TIME-DEPENDENT.
k(T): SPECIFIC REACTION RATE, TEMPERATURE-DEPENDENT.
Ci: GAS-PHASE CONCENTRATION OF REACTANTS, PRODUCTS,
OR CONTAMINANTS.
M. Lacroix
Catalysis and Catalytic Reactors
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CATALYST DEACTIVATION:
RATE OF CATALYST DECAY
•
THE RATE OF CATALYST DECAY, rd ,CAN BE EXPRESSED IN A
SIMILAR RATE LAW:
da
rd = − = p(a (t ) )k d (T )h(C A , C B ,..., C P )
dt
•
•
•
kd:
SPECIFIC DECAY CONSTANT.
h(Ci): FUNCTIONALITY OF rd ON THE REACTING SPECIES
CONCENTRATIONS. IN MANY CASES, THIS
FUNCTIONALITY IS EITHER INDEPENDENT OF
CONCENTRATION (i.e., h=1), OR IS A LINEAR FUNCTION OF
SPECIES CONCENTRATION (i.e., h=Ci).
p(a(t)): FUNCTIONALITY OF THE ACTIVITY TERM. FOR A FIRSTORDER DECAY, p(a)=a. FOR A SECOND-ORDER DECAY,
p(a)=a2.
M. Lacroix
Catalysis and Catalytic Reactors
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DEACTIVATION BY SINTERING (AGING)
•
IT IS THE LOSS OF SURFACE ACTIVE AREA RESULTING FROM
THE PROLONGED EXPOSURE TO HIGH GAS-PHASE
TEMPERATURES.
THE CATALYST SUPPORT BECOMES SOFT AND FLOWS, RESULTING IN PORE CLOSURE.
THE ATOMS MOVE ALONG THE
SURFACE AND AGGLOMERATE.
RULE OF THUMB: SINTERING IS USUALLY NEGLIGIBLE AT TEMPERATURES BELOW 40%
OF THE MELTING TEMPERATURE OF THE SOLID.
M. Lacroix
Catalysis and Catalytic Reactors
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DEACTIVATION BY SINTERING: DECAY LAW
•
ONE OF THE MOST COMMONLY USED DECAY LAWS FOR
SINTERING IS SECOND-ORDER WITH RESPECT TO THE PRESENT
ACTIVITY:
da
rd = k d a = −
dt
2
•
INTEGRATING, WITH a=1 AT TIME t=0 YIELDS
1
a (t ) =
1 + kd t
•
THE ALGORITHM FOR THE REACTOR DESIGN OF A FLUIDSOLID SYSTEM WITH DECAYING CATALYST IS: (1) MOLE
BALANCE; (2) REACTION RATE LAW; (3) DECAY RATE LAW; (4)
STOICHIOMETRY; (5) COMBINE AND SOLVE; (6) NUMERICAL
TECHNIQUES.
M. Lacroix
Catalysis and Catalytic Reactors
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CONVERSION WITH CATALYST DECAY BY
AGING IN BATCH REACTORS: EXAMPLE
•
THE FIRST-ORDER ISOMERIZATION A → B IS CARRIED
OUT ISOTHERMALLY IN A BATCH REACTOR ON A CATALYST
THAT IS DECAYING AS A RESULT OF AGING. DERIVE AN
EQUATION FOR CONVERSION AS A FUNCTION OF TIME.
dX
= − rA' W
dt
1.
DESIGN EQUATION: N A0
2.
REACTION RATE LAW: − rA
3.
DECAY LAW FOR SECOND-ORDER SINTERING: a (t ) =
4.
STOICHIOMETRY: C A = C A0 (1 − X ) =
5.
6.
'
= k 'a (t )C A
N A0
(1 − X )
V
dX W '
= k a (t )(1 − X )
dt V
W YIELDS:
SOLVING WITH k = k '
V
COMBINING:
M. Lacroix
X =1−
Catalysis and Catalytic Reactors
1
1 + kd t
1
(1 + k d t )
k
kd
29
DEACTIVATION BY COKING OR FOULING
•
THIS MECHANISM OF DECAY IS COMMON TO REACTIONS
INVOLVING HYDROCARBONS. IT RESULTS FROM A
CARBONACEOUS (COKE) MATERIAL DEPOSITED ON THE
SURFACE OF A CATALYST.
M. Lacroix
Catalysis and Catalytic Reactors
30
DEACTIVATION BY POISONING
•
•
•
•
DEACTIVATION BY THIS MECHANISM OCCURS WHEN THE
POISONING MOLECULES BECOME IRREVERSIBLY
CHEMIABSORBED TO ACTIVE SITES, THEREBY REDUCING THE
NUMBER OF SITES AVAILABLE FOR THE MAIN REACTION.
THE POISONING MOLECULE MAY BE A REACTANT AND/OR A
PRODUCT IN THE MAIN REACTION, OR IT MAY BE AN IMPURITY
IN THE FEEDSTREAM.
LEAD, USED AS AN ANTIKNOCK COMPONENT IN GASOLINE,
POISONES THE CATALYTIC AFTERBURNER THEREBY
AFFECTING ITS EFFECTIVENESS IN REDUCING THE
CONCENTRATION OF NOx, CO AND HYDROCARBONS IN THE
EXHAUST.
A NUMBER OF EMPIRICAL DECAY LAWS ARE AVAILABLE FOR
DESCRIBING DEACTIVATION BY COKING AND POISONING
a (t , C )
M. Lacroix
Catalysis and Catalytic Reactors
31
EXAMPLE No. 2:
CATALYST DECAY IN A FLUIDIZED BED
MODELED AS A CSTR
•
THE GAS-PHASE CRACKING REACTION
crude _ oil ( g ) → products ( g )
A→ B+C
IS CARRIED OUT IN A FLUIDIZED CSTR REACTOR. THE FEEDSTREAM CONTAINS
80% CRUDE (A) AND 20% INERT. THE CRUDE OIL CONTAINS SULFUR
COMPOUNDS WHICH POISON THE CATALYST. AS A FIRST APPROXIMATION WE
WILL ASSUME THAT HE CRACKING REACTION IS FIRST-ORDER IN THE CRUDE
OIL CONCENTRATION. THE RATE OF CATLYST DECAY IS FIRST-ORDER IN THE
PRESENT ACTIVITY, AND FIRST-ORDER IN THE REACTANT CONCENTRATION.
ASSUMING THAT THE BED CAN BE MODELED AS A WELL-MIXED CSTR,
DETERMINE THE REACTANT CONCENTRATION, ACTIVITY, AND CONVERSION
AS A FUNCTION OF TIME. THE VOLUMETRIC FEED RATE TO THE REACTOR IS
5000 m3/h. THERE ARE 50000 kg OF CATALYST IN THE REACTOR AND THE BULK
DENSITY IS 500 kg/m3. ADDITIONAL INFORMATION:
C A0 = 0.9mole / dm3 ; CT 0 = 1.0mole / dm3 ;
k = ρ B k ' = 45h −1 ; k d = 9dm3 / mole ⋅ h;
M. Lacroix
Catalysis and Catalytic Reactors
32
EXAMPLE No. 2:
CATALYST DECAY IN A FLUIDIZED BED
•
ODE Report (RKF45)
•
•
•
Differential equations as entered by the user
[1] d(a)/d(t) = -kd*a*Ca
[2] d(Ca)/d(t) = Ca0/tau-((1+yao)/(1+Ca/Ct0)+tau*a*k)*Ca/tau
•
•
•
•
•
•
•
•
Explicit equations as entered by the user
[1] kd = 9
[2] Ca0 = 8e-01
[3] tau = 2e-02
[4] Ct0 = 1
[5] k = 45
[6] yao = Ca0/Ct0
[7] X = 1-(1+yao)/(1+Ca/Ct0)*Ca/Ca0
•
•
•
•
Independent variable
variable name : t
initial value : 0
final value : 0,5
M. Lacroix
POLYMATH PROGRAM
Catalysis and Catalytic Reactors
33
CATALYST DECAY IN A FLUIDIZED BED:
RESULTS
M. Lacroix
Catalysis and Catalytic Reactors
34
EXAMPLE No. 3: Catalytic reactor
With the increasing demand for xylene in the petrochemical industry, the production of xylene
from toluene has gained attention in recent years. This reaction is
2Toluene → Benzene + Xylene
2T → B + X
or
was studied over a hydrogen mordenite catalyst that decays with time. As a first approximation,
assume that the catalyst follows second-order decay, i.e., rd = k d a 2 and the rate law for low
conversion is − rT' = k T PT a with k T = 20mol / h ⋅ kg _ cat ⋅ atm and k d = 1.6h −1 at 735K.
1. Compare the conversion time curves in a batch reactor containing 5 kg of catalyst at
different initial partial pressures (1 atm, 10 atm, etc.). The reaction volume containing
pure toluene initially is 1 dm3 and the temperature is 735K.
2. What conversion can be achieved in a moving-bed reactor containing 50 kg of catalyst
with a catalyst feed rate of 2 kg/h? Toluene is fed at a pressure of 2 atm and a rate of 10
mol/min.
3. Examine the effect of the catalyst feed rate on conversion.
M. Lacroix
Catalysis and Catalytic Reactors
35
Example No. 3: Batch reactor
•
•
•
Differential equations as entered by the user
[1] d(x)/d(t) = -rt*w/nto
[2] d(a)/d(t) = -kd*a^2
•
•
•
•
•
•
•
•
•
•
•
Explicit equations as entered by the user
[1] w = 5
[2] kd = 16e-01
[3] kt = 20
[4] pto = 1
[5] v = 1
[6] R = 82e-03
[7] T = 735
[8] pt = pto*(1-x)
[9] rt = -kt*pt*a
[10] nto = pto*v/(R*T)
•
•
•
•
Independent variable
variable name : t
initial value : 0
final value : 0,001
Polymath Program
M. Lacroix
Catalysis and Catalytic Reactors
36
Example No. 3: Batch reactor
M. Lacroix
Catalysis and Catalytic Reactors
37
Example No. 3: Moving bed reactor
• Differential equations as entered by the user
• [1] d(a)/d(w) = -kd*a^2/Us
• [2] d(x)/d(w) = -rt/fao
•
•
•
•
•
•
•
•
Explicit equations as entered by the user
[1] fao = 600
[2] kd = 16E-01
[3] Us = 2
[4] kt = 20
[5] pto = 2
[6] pt = pto*(1-x)
[7] rt = -kt*pt*a
•
•
•
•
Independent variable
variable name : w
initial value : 0
final value : 50
Polymath Program
M. Lacroix
Catalysis and Catalytic Reactors
38
Example No. 3: Moving bed reactor
M. Lacroix
Catalysis and Catalytic Reactors
39