Idea Transcript
ISOTHERMAL REACTOR DESIGN (4)
Marcel Lacroix Université de Sherbrooke
ISOTHERMAL REACTOR DESIGN: OBJECTIVE •
1. 2. 3. 4.
TO DESIGN VARIOUS TYPES OF IDEAL ISOTHERMAL REACTORS USING THE FOLLOWING TOOLS: MOLE BALANCE OR DESIGN EQUATION: ( − rA ,V , X ) RATE LAW:− rA = f (C A ) STOICHIOMETRY: C A = g (C A 0 , X , ε ) COMBINATION OF THE ABOVE TO DETERMINE VOLUME V OF REACTOR FOR ACHIEVING CONVERSION X.
M. Lacroix
Isothermal Reactor Design
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DESIGN STRUCTURE FOR ISOTHERMAL REACTORS 1.
APPLY THE GENERAL MOLE BALANCE EQUATION…
2.
…TO ARRIVE AT THE DESIGN EQUATION; IF THE FEED CONDITIONS ARE SPECIFIED (NA0 OR FA0), ALL THAT IS REQUIRED TO EVALUATE THE DESIGN EQUATION IS THE RATE OF REACTION AS A FUNCTION OF CONVERSION AT THE SAME CONDITIONS AS THOSE AT WHICH THE REACTOR IS TO BE OPERATED (TEMPERATURE AND PRESSURE). WHEN –rA =f(X) IS GIVEN, ONE CAN DETRMINE READILY THE TIME OR REACTOR VOLUME NECESSARY TO ACHIEVE THE SPECIFIED CONVERSION X.
3.
IF THE RATE OF REACTION IS NOT GIVEN EXPLICITELY AS A FUNCTION OF CONVERSION, THE RATE LAW MUST BE DETERMINED (FROM REFERENCES OR EXPERIMENTS). M. Lacroix
Isothermal Reactor Design
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DESIGN STRUCTURE FOR ISOTHERMAL REACTORS 4.
USE STOICHIOMETRY TOGETHER WITH THE CONDITIONS OF THE SYSTEM (i.e., CONSTANT VOLUME, CONSTANT TEMPERATURE, ETC.) TO EXPRESS CONCENTRATION AS A FUNCTION OF CONVERSION.
5.
BY COMBINING THE INFORMATION GATHERED IN THE PREVIOUS STEPS, ONE CAN EXPRESS THE RATE OF REACTION AS A FUNCTION OF CONVERSION.
6.
IT IS NOW POSSIBLE TO DETERMINE EITHER THE TIME OR REACTOR VOLUME NECESSARY TO ACHIEVE THE DESIRED CONVERSION BY SUBSTITUTING THE RELATIONSHIPS RELATING CONVERSION AND RATE OF REACTION INTO THE APPROPRIATE DESIGN EQUATION. THE DESIGN EQUATION IS THEN EVALUATED IN THE APPROPRIATE MANNER (i.e., ANALYTICALLY OR NUMERICALLY). M. Lacroix
Isothermal Reactor Design
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ISOTHERMAL REACTOR DESIGN ALGORITHM
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BATCH OPERATION: SCALE-UP OF DATA TO THE DESIGN OF A CSTR
1.
WE SEEK TO DETERMINE THE SPECIFIC REACTION RATE k OF A LABORATORY-SCALE BATCH REACTOR IN WHICH A CONSTANTVOLUME REACTION OF KNOWN ORDER IS BEING CARRIED OUT.
2.
AND NEXT TO USE THE REACTION RATE k IN THE DESIGN OF A FULL-SCALE CSTR.
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ALGORITHM TO ESTIMATE REACTION TIMES IN BATCH REACTORS
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EXAMPLE No. 1: DETERMINING k FROM BATCH DATA •
IT IS DESIRED TO DESIGN A CSTR TO PRODUCE 200 MILLION KG OF ETHYLENE GLYCOL PER YEAR BY HYDROLYSING 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. SINCE 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 TEMPERATURES THERE IS A SIGNIFICANT BY-PRODUCT FORMATION, WHILE AT TEMPERATURES BELOW 313 K THE REACTION DOES NOT PROCEED AT A SIGNIFICANT RATE. CONSEQUENTLY, A TEMPERATURE OF 328 K HAS BEEN CHOSEN. SINCE 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. M. Lacroix
Isothermal Reactor Design
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EXAMPLE No. 2: DETERMINING k FROM BATCH DATA •
THE REACTION IS H 2 SO4 (CH 2 ) 2 O + H 2O ⎯⎯ ⎯→(CH 2 ) 2 (OH ) 2
A + B ⎯⎯ ⎯→ C catalyst
•
IN THE LABORATORY EXPERIMENT, 500 ml (2 kmole/m3) OF ETHYLENE OXIDE IN WATER IS MIXED WITH 500 ml OF WATER CONTAINING 0.9 wt % SULFURIC ACID, WHICH IS A CATALYST. THE TEMPERATURE WAS MAINTAINED AT 328 K. THE CONCENTRATION OF ETHYLENE GLYCOL WAS RECORDED AS A FUNCTION OF TIME. FROM THESE DATA DETERMINE THE SPECIFIC REACTION RATE AT 328 K.
Time (min) C (kmole/m3)
M. Lacroix
0 0
0.5 0.145
1 0.270
1.5 0.376
2 0.467
Isothermal Reactor Design
3 0.610
4 0.715
6 0.848
10 0.957
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DETERMINING k WITH POLYMATH
C 01 = t ; •
Nonlinear regression (mrqmin)
•
Model: C01 = -ln(C02)/A
• •
Variable A
Ini guess 1,
C A0 − CC C 02 = ; C A0
Value 0,3141636
Conf-inter 3,412E-05
k ≈ 0.31 min −1
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DESIGN OF CSTRs: DAMKÖHLER NUMBER DESIGN EQUATION FOR A CSTR:
FA 0 X V= (− rA ) exit
IF THE VOLUMETRIC FLOW RATE CONSTANT, v = v0 ,
v0 (C A 0 − C A ) V= − rA
OR
V C A0 − C A τ= = v0 − rA
FOR A FIRST-ORDER IRREVERSIBLE REACTION, − rA = kC A AND NO VOLUME CHANGE DURING THE COURSE OF THE REACTION C A = C A 0 (1 − X ),
τk Da X= = 1 + τk 1 + Da M. Lacroix
Da: DAMKÖHLER NUMBER. FOR Da90% Isothermal Reactor Design
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DESIGN OF CSTRs: 2 CSTRs IN SERIES
• FIRST-ORDER REACTION WITH NO VOLUME CHANGE v = v0 ,
C A0 C A1 = 1 + τ 1k1
FA1 − FA 2 v0 (C A1 − C A 2 ) V2 = = k 2C A 2 − rA 2
C A1 C A0 = CA2 = 1 + τ 2 k 2 (1 + τ 2 k 2 )(1 + τ 1k1 ) M. Lacroix
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DESIGN OF CSTRs: n CSTRs IN SERIES
C A0 C A0 = • FOR n CSTRs IN SERIES, C An = n (1 + τk ) (1 + Da) n CONVERSION FOR n REACTORS IN SERIES:
1 X =1− (1 + τk ) n
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DESIGN OF CSTRs: CSTRs IN PARALLEL
Xi V FA 0 ⎛ X i ⎞ ⎟⎟ ⎜⎜ )= = Vi = FA 0 i ( − rAi n n ⎝ − rAi ⎠ FA 0 X i FA 0 X V= = − rAi − rA 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
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EXAMPLE No. 3: DESIGN OF A CSTR •
IT IS DESIRED TO PRODUCE 100 MILLION KG OF ETHYLENE GLYCOL PER YEAR. THE CSTR IS TO BE OPERATED ISOTHERMALLY. 0.016 kmole/liter SOLUTION OF ETHYLENE OXIDE IN WATER IS FED TO THE REACTOR TOGETHER WITH AN EQUAL VOLUMETRIC SOLUTION OF WATER CONTAINING 0.9% wt OF SULFURIC ACID (CATALYST). IF 80% CONVERSION IS TO BE ACHIEVED, DETERMINE THE NECESSARY REACTOR VOLUME. HOW MANY 4000-liters REACTORS WOULD BE REQUIRED IF THEY ARE ARRANGED IN PARALLEL? WHAT IS THE CORRESPONDING CONVERSION? HOW MANY 4000-liters REACTORS WOULD BE REQUIRED IF THEY ARE ARRANGED IN SERIES? WHAT IS THE CORRESPONDING CONVERSION? THE SPECIFIC REACTION RATE CONSTANT IS 0.311 min-1.
M. Lacroix
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DESIGN OF PFRs • GAS-PHASE REACTIONS ARE CARRIED OUT PRIMARILY IN TUBULAR REACTORS • ASSUMING NO DISPERSION AND NO RADIAL GRADIENTS, WE CAN MODEL THE FLOW IN THE REACTOR AS PLUG FLOW dX FA 0 = − rA dV • IN THE ABSENCE OF PRESSURE DROP OR HEAT EXCHANGE, THE INTEGRAL FORM OF THE PLUG FLOW DESIGN EQUATION IS X
V = FA 0
∫ 0
M. Lacroix
dX − rA
− rA = f (C A ) C A = g (C A 0 , X , ε ) Isothermal Reactor Design
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EXAMPLE No.4: DESIGN OF A PFR •
IT IS DESIRED TO PRODUCE 150 MILLION KG OF ETHYLENE A YEAR FROM CRACKING A FEED STREAM OF PURE ETHANE USING A PLUG-FLOW REACTOR. 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 REACTION IS
•
THE PROPOSED RATE LAW IS − rA = kC A WITH k = 0.072 s −1 AT 1000 K. THE ACTIVATION ENERGY IS
C2 H 6 → C2 H 4 + H 2 A→ B+C
82kcal / mole M. Lacroix
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PRESSURE DROP IN REACTORS • IN LIQUID-PHASE REACTIONS, THE CONCENTRATION OF REACTANTS IS INSIGNIFICANTLY AFFECTED BY EVEN RELATIVELY LARGE CHANGES IN THE TOTAL PRESSURE. • AS A RESULT, THE EFFECT OF PRESSURE DROP ON THE RATE OF REACTION WHEN SIZING LIQUIDPHASE CHEMICAL REACTORS CAN BE IGNORED. • IN GAS-PHASE REACTIONS, THE CONCENTRATION OF THE REACTING SPECIES IS PROPORTIONAL TO THE TOTAL PRESSURE AND CONSEQUENTLY, PROPER ACCOUNTING FOR THE EFFECTS OF PRESSURE DROP ON THE REACTION SYSTEM CAN, IN MANY INSTANCES, BE A KEY FACTOR IN THE SUCCESS OR FAILURE OF THE REACTOR OPERATION. M. Lacroix
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PRESSURE DROP AND THE RATE LAW: EXAMPLE •
LET US CONSIDER THE SECOND-ORDER ISOMERIZATION REACTION A → B CARRIED OUT IN A PACKED-BED REACTOR.
dX FA0 = − rA' dW
•
MOLE BALANCE:
•
RATE LAW:
•
C A0 (1 − X ) P T0 CA = STOICHIOMETRY: 1 + εX P0 T (FOR GAS-PHASE REACTIONS)
− rA' = kC A2
dX kC A0 ⎛ 1 − X ⎞ = ⎜ ⎟ dW v0 ⎝ 1 + εX ⎠
2
⎛P⎞ ⎜⎜ ⎟⎟ ⎝ P0 ⎠
2
•
COMBINATION:
•
FOR ISOTHERMAL OPERATION (T=T0), dX RIGHT-HAND SIDE FUNCTION OF X AND P ONLY: M. Lacroix
Isothermal Reactor Design
WE NEED ANOTHER EQUATION TO DETERMINE X
dW
= F1 ( X , P ) 19
FLOW THROUGH A PACKED BED: ERGUN EQUATION •
•
MAJORITY OF GAS-PHASE REACTIONS ARE CATALYSED BY PASSING THE REACTANT THROUGH A PACKED BED OF CATALYST PARTICLES. THE EQUATION USED MOST TO CALCULATE THE PRESSURE DROP IN A PACKED POROUS BED IS ERGUN EQUATION :
α T P0 dP =− (1 + εX ) 2 T0 P / P0 dW 2β 0 α= Ac ρ c (1 − φ ) P0 M. Lacroix
⎞ G ⎛ 1 − φ ⎞⎛⎜ 150(1 − φ ) µ + 1.75G ⎟⎟ β0 = ⎜ 3 ⎟⎜ Dp ρ 0 D p ⎝ φ ⎠⎝ ⎠ Isothermal Reactor Design
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FLOW THROUGH A PACKED BED: DEFINITIONS • • • • • • • • • • • •
PRESSURE (N/m2); P0 INLET PRESSURE (N/m2); φ POROSITY( VOLUME _ VOID ) OR (1 − φ ) = VOLUME _ OF _ SOLID TOTAL _ BED _ VOLUME TOTAL _ BED _ VOLUME D p DIAMETER OF PARTICLE IN BED (m) µ VISCOSITY OF GAS PASSING THROUGH BED (N/sm2) z LENGTH DOWN THE PACKED BED OF PIPE (m) u SUPERFICIAL VELOCITY=VOLUMETRIC FLOW OVER CROSS SECTIONAL AREA OF PIPE (m/s) ρ GAS DENSITY (kg/m3); ρ 0 INLET GAS DENSITY; ρ c SOLID DENSITY (kg/m3); G = ρu = (total _ mass _ flow _ rate) / Ac (kg/m2s) T TEMPERATURE (K); T0 INLET TEMPERATURE (K) FT TOTAL MOLAR FLOW RATE (moles/s); FT 0 INLET RATE Ac CROSS SECTIONAL AREA (m2) W MASS OF CATALYST (kg)
P
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FLOW THROUGH A PACKED BED: SPECIAL CASE
• FOR ISOTHERMAL OPERATION, WE HAVE TWO EQUATIONS FOR TWO UNKNOWNS: X AND P
dP = F2 ( X , P ) dW
AND
dX = F1 ( X , P ) dW
• SPECIAL CASE: ε = 0 OR εX