ISOTHERMAL REACTOR DESIGNmarcellacroix.espaceweb.usherbrooke.ca/CRE/lecturesM/...EXAMPLE No. 2:...

ISOTHERMAL REACTOR DESIGNISOTHERMAL REACTOR DESIGN(4)(4)

Marcel LacroixMarcel LacroixUniversitUniversitéé de Sherbrookede Sherbrooke

ISOTHERMAL REACTOR DESIGN:ISOTHERMAL REACTOR DESIGN:OBJECTIVEOBJECTIVE

• TO DESIGN VARIOUS TYPES OF IDEAL ISOTHERMAL REACTORS USING THE FOLLOWING TOOLS:

1. MOLE BALANCE OR DESIGN EQUATION: 2. RATE LAW: 3. STOICHIOMETRY:4. COMBINATION OF THE ABOVE TO DETERMINE

VOLUME V OF REACTOR FOR ACHIEVING CONVERSION X.

)( AA Cfr =−),,( 0 εXCgC AA =

),,( XVrA−

M. Lacroix Isothermal Reactor Design 2

DESIGN STRUCTURE FOR ISOTHERMAL REACTORS 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).


DESIGN STRUCTURE FOR ISOTHERMAL REACTORS 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).


ISOTHERMAL REACTOR DESIGN ALGORITHMISOTHERMAL REACTOR DESIGN ALGORITHM

5

BATCH OPERATION:BATCH OPERATION:SCALESCALE--UP OF DATA TO THE DESIGN OF A UP OF DATA TO THE DESIGN OF A CSTRCSTR

1. WE SEEK TO DETERMINE THE SPECIFIC REACTION RATE k OF A LABORATORY-SCALE BATCH REACTOR IN WHICH A CONSTANT-VOLUME 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.


ALGORITHM TO ESTIMATE REACTION TIMES IN ALGORITHM TO ESTIMATE REACTION TIMES IN BATCH REACTORSBATCH REACTORS


EXAMPLE No. 1:EXAMPLE No. 1:DETERMINING DETERMINING kk FROM BATCH DATA 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 REACTOREXPERIMENT 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.


EXAMPLE No. 2:EXAMPLE No. 2:DETERMINING DETERMINING kk FROM BATCH DATA FROM BATCH DATA

• THE REACTION IS

• 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.

22242

222 )()()( OHCHOHOCH SOH ⎯⎯ →⎯+CBA catalyst⎯⎯ →⎯+

Time (min) 0 0.5 1 1.5 2 3 4 6 10 C (kmole/m3) 0 0.145 0.270 0.376 0.467 0.610 0.715 0.848 0.957


DETERMINING DETERMINING kk WITH POLYMATHWITH POLYMATH

• Nonlinear regression (mrqmin)

• Model: C01 = -ln(C02)/A

• Variable Ini guess Value Conf-inter

• A 1, 0,3141636 3,412E-05

1min31.0 −≈k

;01 tC = ;020

0

A

CA

CCCC −

=


DESIGN OF DESIGN OF CSTRCSTRs: DAMKs: DAMKÖÖHLER NUMBERHLER NUMBER

DESIGN EQUATION FOR A CSTR:

IF THE VOLUMETRIC FLOW RATE CONSTANT, ,

OR

FOR A FIRST-ORDER IRREVERSIBLE REACTION,AND NO VOLUME CHANGE DURING THE COURSE OF THE REACTION ,

exitA

A

rXFV)(

0

−=

0vv =

A

AA

rCCvV

−−

=)( 00

A

AA

rCC

vV

−−

== 0

0

τ

AA kCr =−

)1(0 XCC AA −=

DaDa

kkX

+=

+=

11 ττ Da: DAMKÖHLER NUMBER.

FOR Da<0.1, X<10%; FOR Da>10.0, X>90%


DESIGN OF DESIGN OF CSTRCSTRs: 2 CSTRs IN SERIESs: 2 CSTRs IN SERIES

• FIRST-ORDER REACTION WITH NO VOLUME CHANGE ,

0vv =

11

01 1 k

CC AA τ+=

22

210

2

212

)(A

AA

A

AA

CkCCv

rFFV −

=−−

=

)1)(1(1 1122

0

22

12 kk

Ck

CC AAA τττ ++

=+

=


DESIGN OF DESIGN OF CSTRCSTRs: n CSTRs IN SERIESs: n CSTRs IN SERIES

• FOR n CSTRs IN SERIES, nA

nA

An DaC

kCC

)1()1(00

+=

+=

τ

nkX

)1(11τ+

−=

CONVERSION FOR n REACTORS IN SERIES:


DESIGN OF DESIGN OF CSTRCSTRs: CSTRs IN PARALLELs: CSTRs IN PARALLEL

⎟⎟⎠

⎞⎜⎜⎝

⎛−

==−

=Ai

iA

Ai

iiAi r

Xn

FnV

rXFV 0

0 )(

A

A

Ai

iA

rXF

rXFV

−=

−= 00

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


EXAMPLE No. 3:EXAMPLE No. 3:DESIGN OF A DESIGN OF A CSTRCSTR

• 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.


DESIGN OF DESIGN OF PFRPFRss

• 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

• IN THE ABSENCE OF PRESSURE DROP OR HEAT EXCHANGE, THE INTEGRAL FORM OF THE PLUG FLOW DESIGN EQUATION IS

AA rdVdXF −=0

∫ −=X

AA r

dXFV0

0

)( AA Cfr =−

),,( 0 εXCgC AA =M. Lacroix Isothermal Reactor Design 16

EXAMPLE No.4:EXAMPLE No.4:DESIGN OF A DESIGN OF A PFRPFR

• 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 WITHAT 1000 K. THE ACTIVATION ENERGY IS

24262 HHCHC +→CBA +→

AA kCr =−1072.0 −= sk

molekcal /82M. Lacroix Isothermal Reactor Design 17

PRESSURE DROP IN REACTORSPRESSURE 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 LIQUID-PHASE 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.

PRESSURE DROP AND THE RATE LAW: EXAMPLEPRESSURE DROP AND THE RATE LAW: EXAMPLE


• LET US CONSIDER THE SECOND-ORDER ISOMERIZATION REACTION CARRIED OUT IN A PACKED-BED REACTOR.

• MOLE BALANCE:

• RATE LAW:

• STOICHIOMETRY:(FOR GAS-PHASE REACTIONS)

• COMBINATION:

• FOR ISOTHERMAL OPERATION (T=T0), RIGHT-HAND SIDE FUNCTION OF X AND P ONLY:

BA→

'0 AA r

dWdXF −=

2'AA kCr =−

TT

PP

XXCC A

A0

0

0

1)1(

ε+−

=

2

0

2

0

0

11

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+−

=PP

XX

vkC

dWdX A

ε

),(1 PXFdWdX

=

WE NEED ANOTHER EQUATION TO DETERMINE X

FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: ERGUN EQUATION: 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 :

)1(/2 0

0

0

XPP

PTT

dWdP εα

+−=

0

0

)1(2

PA cc φρβα−

= ⎟⎟⎠

⎞⎜⎜⎝

⎛+

−⎟⎠

⎞⎜⎝

⎛ −= G

DDG

pp

75.1)1(15013

00

µφφφ

ρβ


FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: DEFINITIONS: DEFINITIONS

• PRESSURE (N/m2); INLET PRESSURE (N/m2); • POROSITY( ) OR• DIAMETER OF PARTICLE IN BED (m)• VISCOSITY OF GAS PASSING THROUGH BED (N/sm2)• LENGTH DOWN THE PACKED BED OF PIPE (m)• SUPERFICIAL VELOCITY=VOLUMETRIC FLOW OVER

CROSS SECTIONAL AREA OF PIPE (m/s)• GAS DENSITY (kg/m3); INLET GAS DENSITY;

SOLID DENSITY (kg/m3); • (kg/m2s)• TEMPERATURE (K); INLET TEMPERATURE (K)• TOTAL MOLAR FLOW RATE (moles/s); INLET RATE • CROSS SECTIONAL AREA (m2)• MASS OF CATALYST (kg)

PVOLUMEBEDTOTALVOIDVOLUME

___φ

VOLUMEBEDTOTALSOLIDOFVOLUME

____)1( =−φ

pDµzu

ρ

cArateflowmasstotaluG /)___(== ρ

0P

T 0TTF 0TFcA

cρ

W

0ρ


FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: SPECIAL CASE: SPECIAL CASE

• FOR ISOTHERMAL OPERATION, WE HAVE TWO EQUATIONS FOR TWO UNKNOWNS: X AND P

AND

• SPECIAL CASE: OR , WE OBTAIN AN ANALYTICAL SOLUTION FOR THE PRESSURE FOR ISOTHERMAL OPERATION:

),(2 PXFdWdP

= ),(1 PXFdWdX

=

0=ε 1<<Xε

21

0

)1( WPP α−=


EXAMPLE No. 5:EXAMPLE No. 5:FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED

• CALCULATE THE CATALYST MASS W NECESSARY TO ACHIEVE CONVERSION X WHEN ETHYLENE OXIDE IS TO BE MADE BY THE VAPOR-PHASE CATALYTIC OXIDATION OF ETHYLENE WITH AIR:

• ETHYLENE AND OXYGEN ARE FED IN STOICHIOMETRIC PROPORTIONS TO A PACKED-BED REACTOR OPERATED ISOTHERMALLY AT 533K. ETHYLENE IS FED AT A RATE OF 0.136 kmole/s AT A PRESSURE OF 10 atm. IT IS PROPOSED TO USE 10 BANKS OF 100 TUBES PER BANK PACKED WITH CATALYST. CONSEQUENTLY, THE MOLAR FLOW RATE TO EACH TUBE IS 0.136/1000 kmoles/s. THE CROSS SECTIONAL AREA OF EACH TUBE IS 0.001313 m2. THE PROPERTIES OF THE REACTING FLUID ARE TO BE CONSIDERED IDENTICAL TO THOSE OF AIR AT THIS TEMPERATURE AND PRESSURE. THE DENSITY OF THE 0.635 cm CATALYST PARTICLES IS 1922 kg/m3 AND THE BED VOID IS 0.45.

OCHCHOHC 22242 2/1 →+CBA →+ 2/1


FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: MODEL: MODEL

1. MOLE BALANCE:

2. PROPOSED RATE LAW :

3. IDEAL GAS LAW:

4. STOICHIOMETRY:

5. COMBINING:

6. PRESSURE LOSS:

7. SOLUTION OF (5) AND (6) FOR X AND P VERSUS W; INITIAL CONDITIONS: AT W=0, X=0 AND P=P0

'0 AA r

dWdXF −=

32

31'

BAA PkPr =−

RTCP jj =

;1

)1(0

0

PP

XXC

vFC AA

A ε+−

==0

0

1)2/(

PP

XXC

vFC BAB

B εθ+−

==

000 )1(

)1(63.0PP

XXkP

dWdXF AA ε+

−=

)1(/2 0

0 XPP

PdWdP εα

+−=


FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: : POLYMATH COMPUTER PROGRAMPOLYMATH COMPUTER PROGRAM

ODE Report (RKF45)Differential equations as entered by the user[1] d(x)/d(w) = rate/fa0[2] d(y)/d(w) = -alpha*(1+eps*x)/2/y

Explicit equations as entered by the user[1] fa0 = 49e-02[2] alpha = 366e-04[3] eps = -15e-02[4] kprime = 266e-04[5] f = (1+eps*x)/y[6] rate = kprime*((1-x)/(1+eps*x))*y

Independent variable variable name : winitial value : 0

final value : 2525

FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: SOLUTION: SOLUTION

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FLOW THROUGH A FLOW THROUGH A PACKED BEDPACKED BED: SOLUTION: SOLUTION

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