basic kinetics and reactors · 2017-12-22 · 9/9/2015 1 basic kinetics and reactors 1. rate laws...

9/9/2015

1

Basic Kinetics and Reactors

1. Rate Laws2. Basic Ideal Reactors3. Performance and Combinations4. Lab Reactors5. Laboratory Experiments

Basic Equations in CRE

n+1 Equations:

n Mass BalancesEnergy BalanceMomentum Balance

LHS = RHS

rate intrinsic

factoration ess/utilizeffectivencatalyst

indexn eactivatioactivity/dcatalyst

RHS

Mixing Reflects Type,Reactor LHS

r

r

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Rate Laws at the Core of Reaction Engineering

Chemistry Process...) cat, , P, T, ,C ,f(Crtion Interpreta Mechanism BAA

Examples

2

2/3

2

)1(

1

BBAA

BAA

AA

A

AA

CKCK

CkCr

kC

kCr

kCr

kCr

A

A

836 835

A Biochemical Example

(P) Products (S) Substrate (E) Enzyme

Rate

CS

Pkk

SK

KPSEkrate

ESEE

EPESES

m

o

o

1

4

3

4,32,1

)/(

:Analysis

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Amorphous Silicon Fabrication

Rate

H2

221

421 :Law RatekHk

SiHkkr

22

2

221

4

:Mechanism

HSiSiH

HSiHSiH

212

42122

212

412

2221412 )(0)(

:Analysis

Hkk

SiHkkSiHkr

Hkk

SiHkSiH

SiHkHkSiHkdt

SiHd

Hydrolysis in Supercritical Water

k

CH2O

HLOHRLROH k 2 :Mechanism

RLOHRLOH

o CCfkr 2),,(12

2

1.1rT

Increases in CH2O increases density which increases

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Epoxy‐Amine Kinetics

Rate

Conversion

EORCOOHCHNHRNHEOREONHRNH '' 2222

groups OHproduct by sisAutocataly

)"1()'1( OHkkAExkkAEr

1.1rT

Catalytic HDN

lnRN/RNo

time

)(1

)/( :Law Rate

3

3

NHRNK

KNHRHRNkKr

3k

2

1st

2 :Mechanism NHRHH RN

Increasing RNo

Strong competitive adsorption

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Thermal Cracking

logk1st

2/12

2/32/3

)21(1 :Law Rate

KAKA

kA

KA

kAr

CBAstk

1

TP

TP

TP

C

BA

A

2

2

2

Mechanism Underlying

logAo

2/1n 2/1n0n

Zero‐Order Kinetics

ktAA

kdtdA

o /

A/Ao

t

1.0

0

)1/(/ KAkAdtdA

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First‐Order Kinetics

ktAA

kAdtdA

o )/ln(

/

ln(A/Ao)

t

1.0

0

B/AAkkBAr

or

AKAkAr

A

A

high at '

lowat )1/(

Second‐Order Kinetics

ktAA

kAr

o

A

11

2

t

0

okAt

12/1

A

1

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Reversible Reactions

AABB

KBAkdtdA

BA

oo

)/(/

ln[(A-Ae)/(Ao-Ae)]

t

1.0

0))((/)(

)()(/

)1()(/

)()(/

)(/1

/)(/

21

2121

221

221

2121

ee

e

e

oo

oo

ooe

eeooee

AAkkdtAAd

AkkAkkdtdA

AKkAkkdtdA

ABkAkkdtdA

AABkAkBkAkdtdAK

BAA

AAABABK

Simultaneous Reactions

)(

)/(

22

11

21212

2

11

2

1

nnA

nnn

n

AkAkr

AkkAk

AkS

CA

BA

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Series Reactions

)exp()]exp()[exp(/

)exp(/

22112

1

1

21

tkA

Btktk

kk

kAB

tkAA

CBA

o

oo

o

12

2

2

1max

12

12max,

)0(

)/ln()0(

kk

k

oo

oB

k

kABB

kk

kkBt

Figure 2-4 JJC

Van de Vusse Network

DAA

CBA

3

21

•B is the desired product•High A favors D•Backmixing favors C•CSTR-PFR predicament

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Laboratory and Plant Reactors

A. LaboratoryA. Goal is information, not profitB. Run experiments at well-defined, intrinsic conditions

A. Direct measure of rate? = 1C. IsothermalD. No deactivation

B. PlantA. Use information for profitB. Run reactor at optimal conditions

A. May be integral (likely)B. May be diffusion limitedC. May be adiabaticD. Catalyst may/will deactivate

Basic Ideal ReactorsDifferential Integral

CA0

CA

CA

CSTR

Spatially Uniform

CA 0

CA

PFR

Low Per-Pass Conversion

CA 0

CA

PFR

Reaction Varies Concentration

A

Ao

C

C

AA

AA

AA

AA

AzzAzA

rdC

with

rddC

Q

rdVdF

rdzQCd

zrQCQC

/

/

constant at

/

/)(

0||

kC

C

kCr

CCr

QV

VrQCQC

Ao

A

AA

AAoA

AAoA

1

1

for or,

/

0

AAoA

AA

A

AA

CCr

or

rC

C

rddC

constant ely approximatat

/

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Comparison of PFR and CSTR Flow Patterns

Comparison of PFR and CSTR Performance

Inlet Outlet

A/Ao

PFR approaches outlet conditions

CSTR uniformly at outlet conditions

Driving Force

T/To

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Normal Kinetics Autocatalytic Kinetics

A

Ao

C

C

AA rdC /


PC /

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oAQ /

n CSTR’s Approach PFR

Inlet Outlet

A/Ao

PFR approaches outlet conditions

CSTR uniformly at outlet conditions

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nT

non

oo

o

nkkAA

n

kAA

kAA

kAA

kAA

)/1(

1

)1(

1/

reactors For

)1(

1/ ;

1

1/ ;

1

1/

Q V, equal of reactors For two1

1/

kineticsorder -firstfor Equation CSTR Basic

22121

n An/Ao

1 0.250

2 0.160

3 0.125

4 0.107

5 0.095

10 0.073

15 0.065

20 0.061

25 0.059

50 0.054

PFR 0.050

k = 3

0.0000.0500.1000.1500.2000.2500.300

0 10 20 30 40 50 60

A/A

o

Number of CSTR's n

Subdivision of CSTR V


02468101214161820

0 20 40 60

Total Tau

(blue), Total Tau divided by n

(red) and Cost (green)

Number of CSTR's n

Subdivision at Constant Conversion

ktT

ktT/n

n(ktT/n)^0.6

n kT A/Ao kT/n n(kT/n)^0.61 95 0.010 95 15.3685949

2 17.76612 0.010 8.883061 7.415963569

3 10.82932 0.010 3.609772 6.480508818

4 8.524191 0.010 2.131048 6.298192158

5 7.520166 0.010 1.504033 6.387405228

10 5.813795 0.010 0.581379 7.222304882

15 5.4 0.010 0.36 8.125924063

20 5.2 0.010 0.26 8.912796783

25 5 0.010 0.2 9.518269694

50 4.8 0.010 0.096 12.25554825

PFR 4.605

A/Ao = 0.01

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n CSTR’s Approach a PFR

nx

x

n

comparingk

x

and

nk

xn

nC

P

P

nCC

T

1)1(

)1ln(

)1ln(

1)1(

/1

/1

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60

TauP/TTauC

Number of CSTR's n

n CSTR's Approach PFR

tP/tCT @ xA = 0.5

tP/tCT @ xA = 0.9

tP/tCT @ xA = 0.95

tP/tCT @ xA = 0.99

n CSTR's tP/tCT @ xA = 0.5 tP/tCT @ xA = 0.9 tP/tCT @ xA = 0.95 tP/tCT @ xA = 0.99

1 0.693147181 0.255842788 0.15767012 0.046516871

2 0.836702662 0.532444361 0.431396165 0.255842788

3 0.888920156 0.664852131 0.582458682 0.421534885

4 0.91585771 0.739639602 0.671843991 0.532444361

5 0.932286279 0.787352331 0.730164017 0.609195253

10 0.965742986 0.889285095 0.857680901 0.787352331

15 0.977073033 0.925210059 0.903463906 0.854336679

20 0.982771413 0.943539691 0.926975664 0.889285095

50 0.993084543 0.977150873 0.970341806 0.954655118

The Recycle Reactor

PFR

Pump

Q

C0

F ,C11 F = Q + q

q,c

Q

CRecycle reactor model:

"large" can depend on conversion

ratio recycle/ ;/ ;/

Define

QqRFVQV

C

C C

dC

kF

dV

FdVd

kCddC

1

1

/

/

PFR For the

1

)1(lnln

/ with and1

and

:balance materialBy

1

1

1

Rf

Rf

C

Ck

CCfR

CRCC

qCQCFC

o

o

o

limit CSTR the1

1

then

1/1

/

since

)1(1

1

or

)1(

1

:)derivationfor JJC(seeRlargeFor

kf

RQq

QV

qQ

V

F

V

kRf

Rf

fk

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Models for Intermediate Levels of Mixing

Performance at Intermediate Levels of Mixing

A -> B -> C2A -> C

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Laboratory Reaction Engineering

Overview

Basic Goal: Estimation of intrinsic rate parameters from experimental data. Premise: Rate and adsorption constants, and not conversion or selectivity, per se, can be related to catalyst structure and composition. We can use kinetics as one of many tools for the evaluation of catalysts.

Laboratory Reactors for Evaluation of Catalysts

Mathematically convenient to acquire direct measure of rate. Practical realities often require integral data acquisition; iterative parameter estimation or differentiation of data follows.

1.

2.

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Basic Ideal ReactorsDifferential Integral

CA0

CA

CA

CSTR

Spatially Uniform

CA 0

CA

PFR

Low Per-Pass Conversion

CA 0

CA

PFR

Reaction Varies Concentration

A

Ao

C

C

AA

AA

AA

AA

AzzAzA

rdC

with

rddC

Q

rdVdF

rdzQCd

zrQCQC

/

/

constant at

/

/)(

0||

kC

C

kCr

CCr

QV

VrQCQC

Ao

A

AA

AAoA

AAoA

1

1

for or,

/

0

AAoA

AA

A

AA

CCr

or

rC

C

rddC

constant ely approximatat

/

(Differential analysis)(Integral analysis)

Analysis of Kinetics Data from Ideal ReactorsIntegral PFR Differential PFR CSTR

Integral Method Differential Method

C vs r vs CAAA

r vs C AA

C

A Aln r

Aln C

n

Rate Equation r = r (n, C, k)A A

Integration and Iteration Direct

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Real Reactors

Weekman (AIChE J. 20:833(1974)) summarizes the issues:

1. Sampling and Product Analysis 2. Isothermality 3. RTD and its measurement 4. Selectivity Disguise 5. Construction difficulty and cost 6. Availability, size, phase of reactants

Reactor Ideal Governing Equation Advantages Cautions

Sampling and Analysis of

Product Composition Isothermality

Residence Time

Control

Time Averaging Disquise

ConstructionDifficulty and

Cost

1.0

Fixed Bed Reactor (PFR)

Inexpensive; Common; Strong experience base. Separates contact time from time on stream (tos). High conversion facilitates analytical chemistry

Lab-scale fixed bed reactors can have significant backmixing, complicating data analysis

Good, normal sorts of problems

Poor-Fair, very difficult to achieve uniform temperature

Fair, channeling and vapor-liquid distribution issues

Poor due to transient behavior

Good, fairly straightforward

1.1

Axial Dispersion Reactor (ADR) None

Approximate Pe ~ 2(L/dp) to determine the extent of backmixing

Good, normal sorts of problems

Poor-Fair, very difficult to achieve uniform temperature




1.2

Differential Fixed Bed Reactor (DPFR)

Low per-pass conversion provides rate vs. concentration data

Analytical chemistry can be challenging at low per-pass conversions

Poor-Fair, can be difficult at low conversions

Fair-Good, low heat release



Good, one of the simplest

1.3

Fixed Bed Reactor with Recycle (RPFR)

This is a PFR model with inlet and overall outlet flow rate Q. In the PFR, the flow rate is F = Q + q, where q is the recycle stream. The recycle ratio R = q/Q controls the mixing behavior of the reactor. At R = 0, the RPFR is a PFR. At R -> infinity, CSTR behavior is achieved. Please see Lab Reactor Summary, page 13, for more details

At "high" recycle ratio CSTR behavior is achieved, providing rate vs. concentration data.

The value of R needed for CSTR behavior depends on the conversion level

Fair-Good, rapid catalyst-reactant separation esential Good, well mixed

Good, well mixed at high circulation velocities

Poor, steady state operation

Fair-Poor, requiresrecirculating pumpor jets

2.1

CSTR/Internal Recycle Reactor (IRR)

Provides spatial uniformity in concentration and temperature at the outlet values. Provides rate vs concentration/temperature data. Separates contact time = V/Q from tos. Common realizations include Berty and Robinson-Mahoney reactors

The value of R needed for CSTR behavior depends on the conversion level

Good, normal sorts of problems Good, well mixed

Fair-Good, Solid acccurately known and gas-vapor known if good mixing

Poor, transient behavior

Fair-Good, more complex than batcor fixed bed

3.0

Batch Reactor (BR) Simple; Easy to use

Contact time and time on stream (tos) not separated

Fair, difficult on-line analysis problems Good, well mixed

Good, accurate residence time if rapid quenching

Poor, transient behavior


Table 1. Laboratory Reactors for Kinetics Studies: Pros and Cons

)/()/(

)/(

)/(

)/(12

2

uCoLrLzd

CoCd

Lzd

CoCd

Pe i

jji

i rV

F

j

jii r

dV

dF

j

iji r

d

dC

jji

i rV

F

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Real Reactors: The Fixed Bed Reactor

Gas-Liquid, Powdered Catalyst, Decaying Catalyst System

Problem Comments Rating

Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficulty and Cost

Normal Problems Very Difficult to Achieve Uniform Temperatures Channeling or Liquid Distribution may be a Problem Transient Behavior Fairly Straight- Forward

Good Poor-Fair Fair Poor Good

Axial Dispersion ModelPFR: -u dC/dz = r

Superimpose a diffusive flux:

D d C/dz - u dC/dz = ra

2 2

Letting: Z = z/L f = C/C Pe = Lu/D = L/u

a

0

The balance equation reduces to:

d f/dZ - df/dZ = r/C2 2

01

Pe

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RTD for Various Values of Pe

= t/

Peclet Number for Axial Diffusion (Pellet)

5

1.0

.2

Re = dpG/

Pe = u d /Di p z

thumbof rule useful a is /Then

/2~)/)(/()/)(/(/

2~/

Suppose

P

PPPPPR

PP

dL

dLdLDudddDuLDuLPe

DudPe

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Influence of Axial Dispersion on First-Order Conversion

Conversion in PFR

PFR

n

x

x

1

1

PFRn

n

PPPP

P

xx

PedLdLPen

dLn

before, As

.2 when /2/

/ mixers CSTR ofnumber Define

seriesin sCSTR'n th analogy wi JJC

Real Reactors: The Differential Reactor




Can be Difficult at Low Conversions Low Heat Release Channeling Fatal V-L Distribution Problem Transient Behavior One of Simplest

Poor-Fair Fair-Good Fair Poor Good

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Real Reactors: A Collection of Other Type Reactors




Rapid Catalyst-Reactant Separation Essential Well Mixed Well Mixed at Highly Circulating Velocities Steady State Operation Requires Recirculating Pump or Jets

Fair-Good Good Good Poor Fair-Poor

The Recycle Reactor

PFR

Pump

Q

C0

F ,C11 F = Q + q

q,c

Q

CRecycle reactor model:

"large" can depend on conversion

ratio recycle/ ;/ ;/

Define

QqRFVQV

C

C C

dC

kF

dV

FdVd

kCddC

1

1

/

/

PFR For the

1

)1(lnln

/ with and1

and

:balance materialBy

1

1

1

Rf

Rf

C

Ck

CCfR

CRCC

qCQCFC

o

o

o

limit CSTR the1

1

then

1/1

/

since

)1(1

1

or

)1(

1

:)derivationfor JJC(seeRlargeFor

kf

RQq

QV

qQ

V

F

V

kRf

Rf

fk

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Real Reactors: The Carberry, Robinson-Mahoney, Berty Type Reactors




Normal Problems Well Mixed Solid Accurately Known; Gas-Vapor Known if Good Mixing Transient Behavior More Complex Than Batch or Fixed Bed

Good Good Fair-Good Poor Fair-Good

Real Reactors: The Stirred Batch Reactor



Sampling and Analysis of Product Composition Isothermality Residence-Contact Time Measurement Selectivity Time Averaging Disguise Construction Difficult and Cost

Difficult On-Line Analysis Problems Well Mixed Accurate Residence Time if Rapid Quenching Transient Behavior Fairly Straight Forward

Fair Good Good Poor Good

basic kinetics and reactors · 2017-12-22 · 9/9/2015 1 basic kinetics and reactors 1. rate laws...

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