Introduction to Advanced Catalytic Reaction EngineeringDr R K Mewada - ACYRE Notes 2 Objective to study ACYRE Applications Subject overview: • Catalysis - Synthesis and characterization

Dr R K Mewada - ACYRE Notes 1

Introduction to

Advanced Catalytic Reaction Engineering

Dr R K Mewada

Associate Professor, Chemical Engineering Dept.,

Institute of Technology


Objective to study ACYRE

Applications

Subject overview:

• Catalysis - Synthesis and characterization of catalyst

• Kinetics – to study effect of catalyst and performance

evaluation and rate expression development

• Reactor design – using kinetic data and other unit

operations concepts..

• Types of reactors – from fixed bed to multiphase

reactors


Let us revise:

Define catalyst and catalysis

Significance of catalyst and catalytic processes

Purpose of kinetic study

What is outcome of kinetic study

Challenges in study of catalysis

How to use data generated from kinetic study in reactor

design

Types of rectors studied

Steps involved in reactor design

Introduction to Catalysis

What is a “Catalyst” • A catalyst (Greek: καταλύτης, catalytēs) is a substance that

accelerates the rate of a chemical reaction without itself being

transformed or consumed by the reaction. (thank you Wikipedia)

A + B

C

ΔG

Ea

uncatalyzed

A + B +

catalyst

C + catalyst

ΔG

Ea′

catalyzed

k(T) = k0e-Ea/RT

Ea′ < Ea k0′ > k0 k′ > k

ΔG = ΔG

5

http://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Ratehttp://en.wikipedia.org/wiki/Chemical_reaction

Catalysts Open Up New

Reaction Pathways

CH3

C

CH3

O

CH2

C

CH3

OH

propanone propenol

H2C

H O

C CH3

‡

‡

propanone

propenol

6


Reaction Pathways

CH3

C

CH3

O

CH2

C

CH3

OH

propanone propenol

OH− CH2

C

CH3

O−

+ H2O

−OH−

Base catalyzed

propanone

propenol

intermediate

‡ ‡

rate = k[OH−][acetone]

7


Reaction Pathways

CH3

C

CH3

O

CH2

C

CH3

OH propanone

propenol

+ H2O

Acid catalyzed

H3O+

CH3

C

CH3

OH

+

−H3O+

propenol

different

intermediate

‡ ‡

propanone

rate = k[H3O+][acetone]

8

Types of Catalysts - Enzymes • The “Gold Standard” of

catalysts

• Highly specific

• Highly selective

• Highly efficient

• Catalyze very difficult

reactions

– N2 NH3

– CO2 + H2O C6H12O6

• Works better in a cell

than in a 100000 l

reactor

Triosephosphateisomerase

“TIM” Cytochrome C Oxidase

Highly tailored “active sites”

Often contain metal atoms

9

Types of Catalysts –

Organometallic Complexes Perhaps closest man has come to mimicking

nature’s success

2005 Noble Prize in

Chemistry

Well-defined, metal-based

active sites

Selective, efficient

manipulation of organic

functional groups

Various forms, especially

for polymerization

catalysis

Difficult to generalize

beyond organic

transformations

Polymerization:

Termination:

10

Types of Catalysts –

Homogeneous vs.

Heterogeneous

Homogeneous catalysis

Single phase

(Typically liquid)

Low temperature

Separations are tricky

Heterogeneous catalysis

Multiphase

(Mostly solid-liquid and solid-gas)

High temperature

Design and optimization tricky

Zeolite catalyst Catalyst powders

11

Types of Catalysts: Crystalline

Microporous Catalysts • Regular crystalline structure

• Porous on the scale of molecular dimensions – 10 – 100 Å

– Up to 1000’s m2/g surface area

• Catalysis through – shape selection

– acidity/basicity

– incorporation of metal particles

10 Å 100 Å

Zeolite (silica-aluminate) Silico-titanate

MCM-41 (mesoporous silica)

12

Types of Catalysts: Amorphous

Heterogeneous Catalysts • Amorphous, high surface area supports – Alumina, silica, activated carbon, …

– Up to 100’s of m2/g of surface area

• Impregnated with catalytic transition metals – Pt, Pd, Ni, Fe, Ru, Cu, Ru, …

• Typically pelletized or on monoliths

• Cheap, high stability, catalyze many types of reactions

• Most used, least well understood of all classes

SEM micrographs of alumina and Pt/alumina

13

Important Heterogeneous

Catalytic Processes • Haber-Bosch process

– N2 + 3 H2 → 2 NH3 – Fe/Ru catalysts, high pressure and temperature

– Critical for fertilizer and nitric acid production

• Fischer-Tropsch chemistry – n CO + 2n H2 → (CH2)n + n H2O , syn gas to liquid fuels

– Fe/Co catalysts

– Source of fuel for Axis in WWII

• Fluidized catalytic cracking – High MW petroleum → low MW fuels, like gasoline

– Zeolite catalysts, high temperature combustor

– In your fuel tank!

• Automotive three-way catalysis – NOx/CO/HC → H2O/CO2/H2O

– Pt/Rh/Pd supported on ceria/alumina

– Makes exhaust 99% cleaner 14


Reactor Design:

Isothermal Fixed Bed reactor design

0 0

AX

A

A A

dXW

F r

Examples based on it

16

These relationships are shown in Fig. 18.6. If you know D, k"', and L you

can find the reaction rate from MT and Fig. 18.6. However, what if you want

to evaluate k from an experiment in which you measure a rate which

could have been slowed by diffusional resistance, but which you are unsure

of?


Reactor Design:

Non-Isothermal Fixed Bed reactor design

Design according to adiabatic reactors

Design according to isothermal reactors but with heat

removal

18

Solid Catalysed

Isothermal Reactions

19

With many reactions, the rates are affected by materials which are neither

reactants nor products. Such materials called catalysts can speed a reaction

by a factor of a million or much more, or they may slow a reaction (negative

catalyst). There are two broad classes of catalysts: those that operate at

close to ambient temperature with biochemical systems, and the man-made

catalysts that operate at high temperature.

20

The biochemical catalysts, called enzymes, are found everywhere in the

biochemical world and in living creatures, and without their action I doubt that

life could exist at all. In addition, in our bodies hundreds of different enzymes

and other catalysts are busily at work all the time, keeping us alive.

21

The man-made catalysts, mostly solids, usually aim to cause the high-

temperature rupture or synthesis of materials. These reactions play an

important role in many industrial processes, such as the production of

methanol, sulphuric acid, ammonia, and various petrochemicals, polymers,

paints, and plastics. It is estimated that well over 50% of all the chemical

products produced today are made with the use of catalysts.

22

The most important characteristic of a catalyst is its selectivity…..Can we

consider Catalyst with 100% conversion with 10% selectivity is good????

Desired material formation from given feed is very essential aspect….So my

dream reaction…A+B gives C with 100% conversion with 100% selectivity…

How to achieve it? Or what is best bargain??

23

The following are some general observations.

1. The selection of a catalyst to promote a reaction is not well understood;

therefore, in practice extensive trial and error may be needed to produce

a satisfactory catalyst.

2. Duplication of the chemical constitution of a good catalyst is no guarantee

that the solid produced will have any catalytic activity. This observation

suggests that it is the physical or crystalline structure which somehow imparts

catalytic activity to a material.

This view is strengthened by the fact that heating a catalyst above a certain

critical temperature may cause it to lose its activity, often permanently. Thus

present research on catalysts is strongly centred on the surface structure of

solids.

24

3.To explain the action of catalysts, it is thought that reactant molecules are

somehow changed, energized, or affected to form intermediates in the

regions close to the catalyst surface. Various theories have been proposed

to explain the details of this action.

In one theory, the intermediate is viewed as an association of a reactant

molecule with a region of the surface; in other words, the molecules are

somehow attached to the surface.

In another theory, molecules are thought to move down into the atmosphere

close to the surface and be under the influence of surface forces. In this

view the molecules are still mobile but are nevertheless modified.

In still a third theory, it is thought that an active complex, a free radical, is

formed at the surface of the catalyst. This free radical then moves back into

the main gas stream, triggering a chain of reactions with fresh molecules

before being finally destroyed. In contrast with the first two theories, which

consider the reaction to occur in the vicinity of the surface, this theory views

the catalyst surface simply as a generator of free radicals, with the reaction

occurring in the main body of the gas.

25

4. In terms of the transition-state theory, the catalyst reduces the potential

energy barrier over which the reactants must pass to form products.

5. Though a catalyst may speed up a reaction, it never determines the

equilibrium or endpoint of a reaction. This is governed by thermodynamics

alone. Thus with or without a catalyst the equilibrium constant for the reaction

is always the same

26

6. Since the solid surface is responsible for catalytic activity, a large readily

accessible surface in easily handled materials is desirable. By a variety of

methods, active surface areas the size of football fields can be obtained per

cubic centimetre of catalyst.

27

Reaction steps in catalytic systems:

Ref.: Elements of Chemical Reaction Engineering, H. S. Fogler, 4th

Ed., Pg 656

28


Ref.: Elements of Chemical Reaction Engineering, H. S. Fogler, 4th Ed., Pg

656

1. Mass transfer (diffusion of the reactants) (e.g.. species A) from

the bulk fluid to the external surface of the catalyst pellet

2. Diffusion of reactant from the pore mouth through the catalyst

pores to the immediate vicinity of the internal catalytic surface

3. Adsorption of reactant A onto the catalyst surface

4. Reaction on the surface of the catalyst (e.g., conv. of A to B)

5. Desorption of the products (e.g., B) from the surface

6. Diffusion of the products from the interior of the pellet to the

pore mouth at the external surface

7. Mass transfer of the products from the external pellet surface to

the bulk fluid

29


Ref.: Elements of Chemical Reaction Engineering, H. S. Fogler, 4th Ed., Pg

656

30

The Spectrum of Kinetic Regimes

Consider a porous catalyst particle bathed by reactant A. The rate of reaction of A

for the particle as a whole may depend on:

1. Surface kinetics, or what happens at the surfaces, interior or exterior of the

particle. This may involve the adsorption of reactant A onto the surface, reaction on

the surface, or desorption of product back into the gas stream.

2. Pore diffusion resistance which may cause the interior of the particle to be

starved for reactant.

3. Particle ∆T or temperature gradients within the particle. This is caused by large

heat release or absorption during reaction.

4. Film ∆T between the outer surface of the particle and the main gas stream. For

example, the particle may be uniform in temperature throughout but hotter than

the surrounding gas.

5. Film diffusion resistance or concentration gradients across the gas film

surrounding the particle.

31

For gas/ porous catalyst systems slow reactions are influenced by (1) alone,

in faster reactions (2) intrudes to slow the rate, then (3)and/or (4) enter the

picture, (5)unlikely limits the overall rate. In liquid systems the order in which

these effects intrude is (1),(2),(5), and rarely (3) and (4).

32

THE RATE EQUATION FOR SURFACE KINETICS USING LHHW

(Langmuir Hinshelwood Houghan Watson) MODEL:

Because of the great industrial importance of catalytic reactions,

considerable effort has been spent in developing theories from which

kinetic equations can rationally be developed. The most useful for our

purposes supposes that the reaction takes place on an active site on the

surface of the catalyst. Thus three steps are viewed to occur successively

at the surface.

Step 1. A molecule is adsorbed onto the surface and is attached to an

active site.

Step 2. It then reacts either with another molecule on an adjacent site (dual

site mechanism), with one coming from the main gas stream (single-site

mechanism), or it simply decomposes while on the site (single-site

mechanism).

Step 3. Products are desorbed from the surface, which then frees the site.

Simple example: reversible

reaction

A B

A* B*

‘Elementary processes’

‘Langmuir adsorption’

1

2

3 A + * A *

k 1

k - 1

A * B * k - 2

k 2

B * B + *

k 3

k - 3

1.

2.

3.

A B

33

34

In addition, all species of molecules, free reactants, and free products as

well as site-attached reactants, intermediates, and products taking part in

these three processes are assumed to be in equilibrium.

Rate expressions derived from various postulated mechanisms are all of the

form

For example, for the reaction

occurring in the presence of inert carrier material U, the rate expression

when adsorption of A controls is

35

When reaction between adjacent site-attached molecules of A and B

controls, the rate expression is

whereas for desorption of R, controlling it becomes

Each detailed mechanism of reaction with its controlling factor has its

corresponding rate equation, involving anywhere from three to seven

arbitrary constants, the K values.

Now, in terms of the contact time or space time, most catalytic conversion

data can be fitted adequately by relatively simple first- or nth-order rate

expressions

Simple example: reversible

reaction

A B

A* B*

‘Elementary processes’

‘Langmuir adsorption’

1

2

3 A + * A *

k 1

k - 1

A * B * k - 2

k 2

B * B + *

k 3

k - 3

1.

2.

3.

A B

36

Elementary processes

• Rate expression follows from rate

equation:

• At steady state:

1 1 1 1 A T * 1 T Ar r r k p N k N

2 2 2 2 T A 2 T Br r r k N k N

3 3 3 3 T B 3 B T *r r r k N k p N

Eliminate unknown surface occupancies

1 2 3r r r r

37

• Site balance:

(7.5)

• Steady-state assumption:

(7.6-7)

• Rate expression:

(7.9)

* A B1

A

B

d0

d

d0

d

t

t

T 1 2 3 A B eq

eq 1 2 3

A B

( / )with:

(.....) (......) (......)

N k k k p p Kr K K K K

p p

Elementary processes contd.

38

Quasi-equilibrium / rate-

determining step

r+1

r +2

r+3

r-1

r-2

r-3

r

rate determining

‘quasi-equilibrium’

r = r+2 - r-2 39

Rate expression r.d.s.

2 2 2 T A 2 T Br r r k N k N

Rate determining step:

Eliminate unknown occupancies

Quasi-equilibrium:

1 1 1 A T * 1 T A r r k p N k N

So:

1A 1 A * 1

1

BB *

3

with: k

K p Kk

p

K

40

Rate expression, contd.

Substitution:

2 2 2 T 1 A * 2 T B * 3

2 T 1 * A B eq

/

/

r r r k N K p k N p K

r k N K p p K

Beq 1 2 3

A eq

pK K K K

p

where:

Unknown still *

41

Rate expression, contd.

Site balance:

* A B * 1 A B 31 1 /K p p K

*

1 A B 3

1

1 /K p p K

Finally:

T 2 1 A B eq

1 A B 3

/

1 /

N k K p p Kr

K p p K

42

Adsorption r.d.s

Surface reaction r.d.s.

Desorption r.d.s.

T 2 1 A B eq

1 A B 3

/

1 /

N k K p p Kr

K p p K

T 3 1 2 A B eq

2 1 A

/

1 1

N k K K p p Kr

K K p

T 1 A B eq

2 B 3

/

1 1 1/ /

N k p p Kr

K p K

Other rate-determining steps

43

44

LHHW with Single site adsorption:

45

Eiley Riedel Model

stoichiometric coefficient i

catalyst effectiveness

rate expression

conversion i

‘space time’

46

Power Law Model

dx

d W Fri

ii

47

Fig 1: Representation of a cylindrical catalyst pore.

30 Fig 3: Distribution and average value of reactant concentration within a

catalyst pore as a function of the parameter

Fig 4: The effectiveness factor as a function of the parameter mL called the Thiele modulus

50

52

Power Law model??

53

LHHW or Eiley Riedel or Power Law model??

54

Truth and Predictability:

The strongest argument in favour of searching for the actual mechanism is

that if we find one which we think represents what truly occurs,

extrapolation to new and more favorable operating conditions is much more

safely done. This is a powerful argument. Other arguments, such as

augmenting knowledge of the mechanism of catalysis with the final goal of

producing better catalysts in the future, do not concern a design engineer

who has a specific catalyst at hand.

55

Problems of Finding the Mechanism:

To prove a mechanism, we must show that the family of curves representing the

rate equation type of the favored mechanism fits the data so much better than

the other families that all the others can be rejected.

With the large number of parameters (three to seven) that can be chosen

arbitrarily for each rate-controlling mechanism, a very extensive experimental

program is required, using very precise and reproducible data, which in itself is

quite a problem.

56

Choose the equation of good fit, not one that represents reality. With

this admitted, there is no reason why we should not use the simplest

and easiest-to-handle equation of satisfactory fit.

For example, the statistical analyses and comments by Chou (1958)

on the codimer example in Hougen and Watson (1947) in which 18

mechanisms were examined illustrate the difficulty in finding the

correct mechanism from kinetic data, and show that even in the most

carefully conducted programs of experimentation the magnitude of the

experimental error will very likely mask the differences predicted by the

various mechanisms.

57

Problems of Combining Resistances:

Suppose that we have found the correct mechanism and resultant

rate equation for the surface phenomenon. Combining this step with

any of the other resistance steps, such as pore of film diffusion,

becomes rather impractical. When this has to be done, it is best to

replace the multi-constant rate equation by an equivalent first-

order expression, which can then be combined with other reaction

steps to yield an overall rate expression

58

EXPERIMENTAL METHODS

FOR FINDING RATES

1. Differential (flow) reactor

2. Integral (plug flow) reactor

3. Mixed flow reactor

4. Batch reactor for both gas and solid

59

A differential flow reactor is selected when reaction rate should be constant

at all points within the reactor.

Since rates are concentration-dependent this assumption is usually

reasonable only for small conversions or for shallow small reactors. But this

is not necessarily so, e.g., for slow reactions where the reactor can be large,

or for zero-order kinetics where the composition change can be large.

Differential Reactor.

For each run in a differential reactor the plug flow performance equation

becomes

60

When the variation in reaction rate within a reactor is so large that these

variations are considered in the method of analysis, then it is called as an

integral reactor.

Since rates are concentration-dependent, such large variations in rate may

be expected to occur when the composition of reactant fluid changes

significantly in passing through the reactor.

Integral Reactor

Integral Analysis. Here a specific mechanism with its corresponding rate

equation is put to the test by integrating the basic performance equation to

give,

61

Differential Analysis. Integral analysis provides a straightforward rapid

procedure for testing some of the simpler rate expressions. However, the

integrated forms of these expressions become unwieldy with more

complicated rate expressions. In these situations, the differential method of

analysis becomes more convenient.

62

Mixed Flow Reactor.

64

Recycle Reactor.

65

Batch Reactor

66

Comparison of Experimental Reactors

1. The integral reactor can have significant temperature variations from point to

point, especially with gas-solid systems, even with cooling at the walls. This could

well make kinetic measurements from such a reactor completely worthless when

searching for rate expressions. The basket reactor is best in this respect.

2. The integral reactor is useful for modeling the operations of larger packed bed

units with all their heat and mass transfer effects, particularly for systems where the

feed and product consist of a variety of materials.

3. Since the differential and mixed flow reactors give the rate directly they are more

useful in analyzing complex reacting systems. The test for anything but a simple

kinetic form can become awkward and impractical with the integral reactor.

4. The small conversions needed in differential reactors require more accurate

measurements of composition than the other reactor types.

5. The recycle reactor with large recycle acts as a mixed flow reactor and shares

its advantages. Actually, to minimize heat effects the catalyst need not be all at

one location, but can be distributed throughout the recycle loop.

67

6. In exploring the physical factors of heat and mass transfer, the integral

reactor most closely models the larger fixed bed; however, the basket,

recycle, and batch GIS reactors are more suited for finding the limits for

such heat effects, for avoiding the regime where these effects intrude, and

for studying the kinetics of the reaction unhindered by these phenomena.

7. The batch GIS reactor, like the integral reactor, gives cumulative effects,

thus is useful for following the progress of multiple reactions. In these

reactors it is easier to study reactions free from heat and mass transfer

resistances (simply increase the circulation rate), and it is also simple to

slow down the progress of reactions (use a larger batch of fluid, or less

catalyst); however, direct modeling of the packed bed with all its

complexities is best done with the integral flow reactor.

8. Because of the ease in interpreting its results the mixed flow reactor is

probably the most attractive device for studying the kinetics of solid

catalyzed reactions.

67

68

Examples for isothermal reactor design and rate expression

development:


Fixed Bed Reactor -

Adiabatic


Staged Adiabatic Fixed Bed

Reactors

• Single reaction A R with any kinetics.

• Types:

– Staged Fixed Beds (Plug Flow) with

Intercooling.

– Staged Mixed Flow Reactors.

– Staged Fixed Beds with Recycle.


Heat Effects

Adiabatic Operations

Subscripts 1, 2 refer to temperatures of entering and leaving streams.


Enthalpy of entering feed:

Enthalpy of leaving stream:

Energy absorbed by reaction:


Staged Fixed Beds (Plug Flow) with

Intercooling



Intercooling (Contd...)


Staged Fixed Beds (Plug Flow)

with Intercooling (Contd...) • Two-stage operations with reversible exothermic

reactions.

• Minimize the total area under the versus XA curve in going from XA = 0 to XA2 = some fixed or required conversion.

• In searching for this optimum we have three variables which we can set at will:

– The incoming temperature (point Ta)

– The amount of catalyst used in the first stage (locates point b along the adiabatic) and

– The amount of intercooling (locates point c along the bc line).



Intercooling.

• The procedure to reduce this 3-dimensional search (5-

dimensional for three stages, etc.) to a one-dimensional

search where Ta alone is guessed, is as follows:

1. Guess Ta

2. Move along the adiabatic line until the following

condition is satisfied:

... Eq. (1)


Staged Fixed Beds (Plug Flow)

with Intercooling (Contd...)

3. Cool to point c which has the same rate of reaction

as point b; thus

... Eq.(2)

4. Move along the adiabatic from point c until the

criterion of Eq. 1 is satisfied, giving point d.

5a. If point d is at the desired final conversion then we

have guessed T, correctly.

5b. If point d is not at the desired final conversion try a

different incoming temperature T,. Usually three

trials will very closely approach the optimum.



Intercooling (Contd...) • This procedure was first developed by Konoki

(1956a) and later, independently, by Horn (1961a).

• Overall cost considerations will determine the

number of stages to be used, so in practice we

examine 1, then 2, etc., stages until a minimum cost

is obtained.

• Let us next consider the two other cases of Fig.

19.3: Irreversible exothermic reactions and

endothermic reactions.


Staged Mixed Flow Reactors


Staged Mixed Flow Reactors (Contd...) • For very high recycle the staged recycle reactors

approach mixed flow.

• As shown in Fig. 19.5, in this case the reactors

should operate on the line of optimum temperature

progression, the best distribution of catalyst among

the stages being found by the maximization of

rectangles.

• In effect we need to choose the distribution of

catalyst so as to maximize area KLMN which then

minimizes the shaded area in Fig. 19.5


Staged Fixed Beds with Recycle



(Contd...)

• In recycle operations the heat exchangers can be

located in a number of places without affecting what

goes on in the reactor.

• Figure 19.6 illustrates one of these; other

alternatives are shown in Fig. 19.7.

• The best location will depend on convenience for

startup, and on which location gives a higher heat

transfer coefficient.



(Contd...)



(Contd...) Cold Shot Cooling:

• One way of eliminating the interstage heat exchangers

is by properly adding cold feed directly into the second

and succeeding stages of the reactor (Fig. 19.8).

• Criterion for optimal operations by Konoki (1960). They

found that the extent of interstage cooling is given by

Eq. 2, and this is shown in Fig. 19.8.

• Cold shot cool with inert fluid which will affect both the

versus XA and T versus XA curves.



(Contd...)



(Contd...)

Choice of Contacting System:

• With so many contacting alternatives let us suggest

when one or other is favored:

1. For endothermic reactions the rate always

decreases with conversion; hence we should always

use plug flow with no recycle.

2. For exothermic reactions the slope of the

adiabatic line determines which contacting scheme

is best.



(Contd...) • Advantage of cold shot cooling: Lower cost because

interstage heat exchangers are not needed.

• Limitations of cold shot cooling:

• Feed temperature is very much below the reaction

temperature.

• When the temperature does not change much during

reaction.

• Cold shot cooling is practical when



(Contd...)



(Contd...)

• For exothermic reactions if the slope of the adiabatic

line is low, use high recycle approaching mixed flow.

• If the slope is high (small temperature rise during

reaction) the rate decreases with conversion and

plug flow is to be used.

• Typically, for pure gaseous reactant the slope of the

adiabatic is small; for a dilute gas or for a liquid it is

large.


Staged Fixed Beds with

Recycle (Contd...) • As an example, consider a reactant having Cp = 40

J/mol K and H, = -120 000 J/mol and inerts with CA

= 40 J/mol.K:

• For a dilute 1% reactant gas stream



(Contd...)

• For a 1-molar liquid solution

• The adiabatic lines for these cases are sketched in

Fig. 19.10 and illustrate this point.



(Contd...)



(Contd...)

For exothermic reactions in staged reactors the

above discussion can be summarized as follows:

• Numerical based on each topic


DESIGN OF A SINGLE ADIABATIC PACKED BED SYSTEM

Work out a good design for 80% conversion of a feed consisting

of 1 mol A and 7 mol inert.

Solution:

First determine the slope of the adiabatic line. For this note that 8

moles enter1mole of A.

Thus

Cp = (40 J/mol K) (8) = 320 J/(mo1 of A + inerts) . K

Thus the slope of the adiabatic is


The feed is available at 300 K, but enters the reactor at 600 K

(from Fig. E19.la), so it must be heated. Thus

The product stream leaves the reactor at 800 K and must be cooled to

300 K, thus


Recommended design in Fig. E19.1C


DESIGN OF A TWO ADIABATIC PACKED BED SYSTEM

Work out a good design for 85% conversion of a pure A feed to two

packed beds.

Solution:

First determine the slope of the adiabatic line and draw it lightly on

Fig. 18.11


This gives a very shallow adiabatic, as sketched in Fig.

E19.2~T. he rate continually increases as you move along

this adiabatic, thus use a mixed flow reactor operating at the

optimum. To minimize the amount of catalyst needed,

Chapter 6 says, use the method of maximization of

rectangles,


Then from the performance equation


to go to 66% conversion at 820°C the amount of heat needed

per mole of A is

But for 100 molls of feed

For the second reactor. To go from X = 0.66 at 820 K to X

= 0.85 at 750 K requires, per mole

So for 100 molls


Recommended design is shown in Fig. E19.2C.


Overview of Energy Balances

1. Adiabatic (Q = 0) CSTR, PFR, Batch, or PBR:

The relationship between conversion, XEB, and temperature for Ws =

0, constant Cp and Cp = 0, is

For an exothermic reaction

(- HR,) > 0


ADIABATIC PFR/PBR ALGORITHM


Solution Procedure for Adiabatic PFR/PBR Reactor


Reactor design –

Non-Isothermal reaction-

With Heat Removal


CSTR with heat exchanger, UA (Ta - T), and large coolant flow rate.


[Nomenclaturr: U = overall heat-transfer coefficient, (J/m2s K)

A = CSTR heat-exchange area, m2.

a = PFR heat-exchange area per volume of reactor. (m2/m3);

CS = mean heat capacity of species i, (J/mol K)

Cp = the heat capacity of the coolant, (kJ/kg K),

ni, = coolant flour rate, (kg/s);

HRX = heat of reactLon, (J/mol)

HRXij = Heat of reaction with respect to species j in reaction i, (J/mol);

Q = heat added to the reactor, (J/mol);


Characteristics of Plant-Scale Fixed Bed

Reactors

Advantages

1. Ideal plug (or mixed) flow

2. Simple analysis

3. Low cost, low maintenance

4. Little loss or attrition

5. Greater variation in operating

conditions and contact times is

possible

6. Usually a high ratio of catalyst to

reactants long residence time

complete reaction

7 Little wear on catalyst and equipment

8. Only practical, economical reactor at

very high pressures

Disadvantages

1. Poor heat transfer in a large fixed bed.

a. Temp. control and measurement

difficult

b. Thermal catalyst degradation

c. Non uniform rates.

2. Non uniform flow patterns e.g.

channeling

3. Swelling of the catalyst; deformation

of the reactor

4. Regeneration or replacement of the

catalyst is difficult - shut down is

required.

5. Plugging, high pressure drop for small

beads or pellets - ∆P is very expensive.

6. Pore diffusion problems intrude in

large pellets


Overcoming the Disadvantages

1. Monolithic supports overcome disadvantages 2, 5 & 6

2. Temperature control problems are overcome with:

a. Recycle

b. Internal and external heat exchanges

c. Staged reactors

d. Cold shot cooling

e. Multiple tray reactor - fluid redistributed & cooled between

stages. Catalyst is easily removed - varied from tray to tray.

f. Use of diluents

g. Temperature self regulation with competing reactions, one endo

and one exothermic.

h. Temp control by selectivity and temporarily poisoning the catalyst

Characteristics of Plant-Scale Fixed Bed

Reactors (Cont.)


Common Types of Catalytic Plant Reactors

1. Fixed-bed Reactors

a. Packed beds of pellet or monoliths

b. Multi-tubular reactors with cooling

c. Slow-moving pellet beds

d. Three-phase trickle bed reactors

2. Fluid-bed and Slurry Reactors

a. “Stationary” gas-phase

b. Gas-phase

c. Liquid-phase

i. Slurry

ii. Bubble Column

iii. Ebulating bed


Reactor Definitions

•Catalytic Packed Bed: Gas or Liquid Reactants flow over a fixed bed of

catalysts.

•Catalytic Fluidized Bed: The up-flow gas or liquid phase suspends the fine

catalyst particles.

•CSTR Gas-Liquid: Liquid and gas phases are mechanically agitated

•Bubble Gas-Liquid Bed: Liquid phase is agitated by the bubble rise of the

gas phase. Liquid phase is continuous.


Reactor Definitions (Contd..)

•Trickle-Bed: Concurrent down-flow of gas and liquid over a fixed-bed of

catalyst. Liquid trickles down, while gas phase is continuous

•Bubble-Fixed Bed: Concurrent up-flow of gas and liquid. Catalyst bed is

completely immersed in a continuous liquid flow while gas rises as

bubbles.

•CSTR Slurry: Mechanically agitated gas-liquid-catalyst reactor. The Fine

catalyst particles are suspended in the liquid phase by means of agitation.

(Batch liquid phase may also be used)

•Bubble Slurry Column: Liquid is agitated by means of the dispersed gas

bubbles. Gas bubble provides the momentum to suspend the catalyst

particles.

•Three-Phase Fluidized Bed: Catalyst particles are fluidized by an

upward liquid flow while gas phase rises in a dispersed bubble regime.


Figure 12.7 Liquid-phase slurry reactors: (a) forced-circulation, slurry-bed reactor, (b) bubble-column, slurry-bed reactor.

128

Figure 12.8 Batch-slurry reactor for hydrogenation of specialty chemicals.


Fig. 12.9 Design of typical FCC transfer-line (riser) reactor with fluidized-bed regenerator.


Products

Riserreactor

Catalyststripper

Steam

Reactorfeed

Steam

Air

Overflowwell

Regenerator

Fluegas

Cyclone

a. Products

Cyclone

Reactor

Catalyst stripper

Steam

Air

Reactor

Regenerator

Flue gas

feed

b.

Figure 12.10 Commercial FCC riser reaction designs (a) Exxon, (b) UOP.

131 Fluid Cat Cracker (Chevron) Stacked Fluid Cat Cracker (UOP)


Shell Cat-Cracker All-riser Cracking FCC Unit


Reactor Types Included in the Reactor Simulation Tool,

ReaCat (Contd..)

Gas /Liquid

Catalytic Reactors

Fixed Bed

Fluidized

Bed

Gas-Liquid Reactors

Gas

Liquid

Gas-Liquid

CSTR

Liquid

Gas

Gas-

Liquid

Bubble

Column

Two-Phase Reactors:


Reactor Types Included in the Reactor Simulation Tool, ReaCat

(Contd..)


Industrial Examples of Multi-phase and Catalytic

Reactors

Three-phase Reactor:

Trickle-Bed Catalytic hydro-desulfurization

Catalytic hydrogenation

Catalytic hydrocracking

Fixed-bed upward bubble-flow Fischer-Tropsch

Coal liquefaction

CSTR Slurry Hydrogenation of fatty oils and unsaturated fats.

Hydrogenation of acetone

Bubble-Slurry Column Catalytic oxidation of olefin

Liquid-phase xylene isomerization

Three-phase fluidized Bed Production of calcium acid sulfite

Coal liquefaction, SRC process


Industrial Examples of Multi-phase and Catalytic

Reactors

Gas-Liquid Continuous Stirred Tank Reactor:

Oxidation of cyclohexane to adipic acid, cumene to cumene

hydroperoxide, and toluene to benzoic acid.

Absorption of SO3 in H2SO4 for manufacture of Oleum

Absorption of NO2 in water for the production of HNO3

Addition of HBr to alpha olefins for the manufacture of alkyl

bromide.

Addition of HCl to vinyl acetylene for the manufacture of

chlroprene.

Absorption of butenes in sulfuric acid for conversion to

secondary butanol.


Multi-phase Reactors- Advantages and

Disadvantages

Advantages Disadvantages

Catalytic FixedBed Reactor

The fluid flow regimesapproach plug flow, sohigh conversion can beachieved.

Pressure drop is low.

Owing to the high hold-up there is better radialmixing and channelingis not encountered.

High catalyst load perunit of reactor volume

The intra-particlediffusionresistance is veryhigh.

Comparatively lowHeat and masstransfer rates

Catalystreplacement isrelatively hard andrequires shutdown.



Disadvantages


Catalytic

Fluidized-bedReactor

The smooth, liquid-like flow of particles

allows continuous controlled operations

with ease of handling.

Near isothermal conditions due to the rapid

mixing of solids.

Small Intra-Particle resistance leads to a

better heat and mass transfer rate.

This violent particle motion of

particles tends to homogenize all

intensive properties of the bed.

Thus it is not generally possible to

provide an axial temperature

gradient which might be highly

desirable in some instances.

Erosion by abrasion of

particles can be serious.

Particle attrition


Three-phase Reactors- Advantages and

Disadvantages


Trickle-BedReactor

Gas and liquid flow regimesapproach plug flow; highconversion may be achieved.

Large catalyst particle, therefore,catalyst separation is easy.

Low liquid holdup, therefore liquidhomogenous reactions areminimized.

Low pressure drop

Flooding problems are notencountered.

High catalyst load per unit reactorvolume.

Poor distribution of theliquid-phase

Partial wetting of the catalyst

High intra-particle resistance

Poor radial mixing

Temperature control isdifficult for highly exothermicreactions

Low gas-liquid interactiondecreases mass transfercoefficients.


Three -phase Reactors- Advantages and

Disadvantages


BubbleFixed- BedReactor

High liquid holdup,therefore, catalyst arecompletely wetted, bettertemperature control, and nochanneling problems.

Gas-liquid mass transfer ishigher than in Trickle beddue to higher gas-liquidinteraction.

Axial back mixing ishigher than trickle-beds, conversion islower.

Feasibility of liquid sidehomogeneousreactions

Pressure drop is high

Flooding problems mayoccur.


Three -phase Reactors- Advantages and

Disadvantages


Slurry and3-phase FluidizedReactor

Ease of heatrecovery andtemperaturecontrol.

Ease of catalystsupply andregenerationprocess.

Low intra-particleresistance.

High external

Mass transfer rate (Gas-liquid and Liquid Solid)

Axial mixing isvery high

Catalystseparation mayrequire filtration.

High liquid to solidratio may promoteliquid sidereactions.

Low catalyst load.



Disadvantages


Gas LiquidContinuousStirredTankReactor

Very effective for viscousliquids and at very low gasrates and large liquid volumes.

Best for system with largeheat effects because ofsuperior heat transfercharacteristics.

Useful for slow reactionsrequiring high liquid holdup.

Residence time of liquid and

extent of agitation can be easily varied.

Both liquid and gas phase are almost completely backmixed.

High power consumption per unit volume of the fluid.

Sealing and stability of Shaft in tall reactors.


Comparison of Three Phase Trickle- Bed and

Bubble Fixed Bed Reactors

Characteristics Trickle- Beds Bubble Fixed-Beds

Pressure Drop Channeling at low liquidflow rates

No Liquid flowmaldistribution

Heat Control Relatively Difficult Easy

Radial mixing Poor radial mixing Good mixing

Liquid/Solid ratio Low High

Catalyst Wetting Partial wetting is possible Completewetting

Conversion High Poor due toback mixing


Comparison of Three Phase Suspended Bed

Reactors

Characteristic CSTR Slurry Bubble Slurry Three- phaseFluidized

Catalyst Attrition Significant Insignificant Insignificant

Mass and HeatTransferEfficiencies

Highest High High

MechanicalDesign

Difficult Simple Simple

CatalystSeparation

Easy Easy Easiest

PowerConsumption

Highest Intermediate Lowest

CatalystDistribution

Uniform Nonuniformitymay exist

Nonuniformitymay exist


Gas-Liquid-Solid Contact in Three-phase Reactors

External

Diffusion

Internal

Diffusion

Catalytic Surface

Bubble Particle


Theory of Catalytic Gas- Liquid Reactions

A(G) + B(L) C

Gaseous reactant A reacts with non-volatile liquid reactant B on

solid catalyst sites.

Mechanism Of Three- Phase Reactions:-

Mass Transfer of component A from bulk gas to gas-liquid

interface

Mass transfer of component A from gas-liquid interface to bulk

liquid

Mass transfer of A& B from bulk liquid to catalyst surface

Intraparticle diffusion of species A& B through the catalyst pores

to active sites.

Adsorption of both or one of the reactant species on catalyst

active sites

Surface reaction involving at least one or both of the adsorbed

species

Desorption of products, reverse of forward steps .


Common Flow Regimes in Industrial Catalytic

Gas- Liquid Reactors

Catalytic Gas-Liquid Reactor Common Flow Regime

Cocurrent Down-Flow Fixed-Bed

Trickle-Flow

Cocurrent Up- Flow Fixed-Bed Bubble- Flow

Bubble Column Slurry Reactor Homogeneous Bubble- Flow

Three- phase Fluidized- Bed Bubble- Flow


Design Models For Catalytic Gas- Liquid Reactors

Flow Regime Gas-phase Design Model

Liquid- Phase Design- Model

Trickle Flow Cocurrent Down-Flow Fixed-Bed

Dispersion Dispersion

CSTR Slurry, Continuous or Semi- Batch

CSTR CSTR/ Batch

Homogeneous Bubble- Flow Continuous Bubble Column Slurry Reactor


Homogeneous Bubble- Flow Semi-Batch Bubble Column Slurry

Dispersion Batch

Bubble Flow Three- phase Fluidized Bed



Correlations Used for the Three-Phase Catalytic Reactors

Correlation Trickle-Bed Fixed Up-Flow CSTR Slurry Bubble Slurry 3-PhaseFluidized

Pressure drop Larkins et al.1961Ellman et al.1988

Turpin &Hintington 1967 - - -

L & G Holdup Sato et al. 1973Ellman et al.1989

Fukushima &Kuasaka 1979Achwal &Stepanek 1976

Galderbank1958Yung et al.1979

Yamashita &Inoue 1975Maselkar 1970

Kim et al.1975

L-S MassTrans. Coeff.

Van Krevelen1948Dharwadker &Sylvester 1977

Specchia et al.1978

Sano et al.1947

Kobayashi &Saito 1965

Lee et. Al1974

L DispersionCoeff.

Michell &Furzer 1972

Stiegel & Shah1977 -

Deckwer etal.1974

El-Temtamy1979

G DispersionCoeff.

Hochman &Effron 1969 - -

Mangartz &Pilhofer 1981 -

Wall HeatTransf. Coeff.

Baldi 1979- -

Fair 1967 -

PowerConsumption - -

Luong &Volesky 1979Michel andMiller 1962

- -

Fluidized Bed Reactor Design

and Applications

Contents 1. Introduction

2. Industrial Application.

3. Types of Fluidized Beds.

4. Advantages and Disadvantages of FBR.

5. An overview

6. Flow Regimes in Fluidized Bed.

7. Minimum and maximum Fluidization velocity

8. Bubble velocity and cloud size

9. Fraction of bed in bubble phase

10. Mole Balance on the Bubble, Cloud, and Emulsion

Phases.

A Fluidized Bed Reactor is a type of

reactor device that can be used to

carry out a variety of multiphase

chemical reactions. In this type of

reactor, a fluid (gas or liquid) is

passed through a granular solid

material (usually a catalyst possibly

shaped as tiny spheres) at high enough

velocities to suspend the solid and

cause it to behave as though it were a

fluid. .

Gas distributor

Inlet to cyclone

Introduction

Basic Principle When a fluid flows upwards through a packed bed of solids, at low velocity

the particles remain stationary. An increase in velocity results in a balance of

pressure drop times the cross-sectional area equals the gravitational forces on

the particle's mass. The particles begin to move and this is known as the

minimum fluidization velocity.

In Liquid-Solid systems, an increase in flow rate above minimum

fluidization usually results in smooth, progressive expansion of the bed

known as particulately or Homogeneously fluidized bed.

In Gas-Solid systems an increase in flow rate above minimum fluidization

usually results in large instabilities with bubbling and channeling of gas. In

addition the bed does not expand much beyond its volume at minimum

fluidization. Such a bed is referred to as Heterogeneous or bubbling

fluidized bed.

History of FBR

The first fluidized bed gas generator

was developed by Fritz Winkler in

Germany in the 1920s. One of the

first United States fluidized bed

reactors used in the petroleum

industry was the Catalytic Cracking

Unit, created in Baton Rouge, LA in

1942 by the Standard Oil Company of

New Jersey (now ExxonMobil).This

FBR and the many to follow were

developed for the oil and

petrochemical industries.

Industrial Applications of FBR

1) Acrylonitrile by the Sohio Process.

2) Fischer-Tropsch Synthesis.

3) Phthalic anhydride synthesis.

4) Methanol to gasoline and olefin processes.

5) Cracking of Hydrocarbons (Fluid Catalytic Cracking, etc).

6) Coal combustion.

7) Coal gasification

8) Cement clinker production.

9) Titanium dioxide production.

10) Calcination of AL(OH)3.

11) Granulation drying of yeast.

12) Heat exchange

13) Absorption

14) Nuclear energy (Uranium processing, nuclear fuel fabrication, reprocessing of fuel and waste disposal).

Types of Fluidized beds

Bed types can be coarsely classified by their flow behaviour, including :

1) Stationary or bubbling beds, where the fluidization of the solids is relatively stationary, with some fine particles being entrained.

2) Circulating beds, where the fluidization suspends the particle bed, due to a larger kinetic energy of the fluid. As such the surface of the bed is less smooth and larger particles can be entrained from the bed than for stationary beds. These particles can be classified by a cyclone separator and separated from or returned to the bed, based upon particle cut size.

3) Vibratory Fluidized beds are similar to stationary beds, but add a mechanical vibration to further excite the particles for increased entrainment.


1) It is suitable for large –scale operations.

2) Excellent gas-solid contacting.

3) Heat and mass transfer rates between gas and particles are high when compared with other modes of contacting.

4) No hot spot even with highly exothermal reaction.

5) Ease of solids handling.

1) Broad residence time

distribution of the gas due

to dispersion and bypass in

the form of bubbles.

2) Broad residence time

distribution of solids due

to intense solids mixing.

3) Erosion of internals.

4) Attrition of catalyst

particles.

5) Difficult Scale-up due to

complex hydrodynamics.

Flow Regimes in Fluidized Beds

Fast

fluidized

bed

Source: O. Levenspiel, Chemical Reaction

Engineering, Third ed., Chap. 3, pg 43,

Wiley, New York

This figure presents the pressure drop across a bed of solid particles as a

function of gas velocity. The region covered by the Ergun equation is the

rising portion of the plot (Section I: 1 < U0 < 4 cm/s). The section of the

figure where the pressure drop remains essentially constant over a wide

range of velocities is the region of bubbling fluidization (Section II: 4 < U0 <

50 cm/s). Beyond this are the regions of fast fluidization and of purely

entrained flow.

Section II: 4 < U0 < 50 cm/s Section I: 1 < U0 < 4

cm/s

purely entrained

flow

The drag exerted on the particles equals the net

gravitational force exerted on the particles.

• The fluid velocity is sufficient to suspend the particles, but it is not large enough to carry them out of the vessel.

• The solid particles swirl around the bed rapidly, creating excellent mixing among them.

• The material “fluidized” is almost always a solid and the “fluidizing medium” is either a liquid or gas.

• The characteristics and behavior of a fluidized bed are strongly dependent on both the solid and liquid or gas properties.

Mass Transfer In Fluidized Beds

• There are two types of mass transport important

in fluidized-bed operations.

The transport between gas and solid

The transfer of material between the bubbles

and the clouds, and between the clouds and the

emulsion

• It is important to deduce how a bed will operate if

one were to change operating conditions such as

gas flow rate or catalyst particle size.

• To have some general guides as to how changes

will affect bed behavior, two limiting

circumstances of reaction control and transport

control can be considered.

• Use the Kunii-Levenspiel bubbling bed model to describe

reactions in fluidized beds.

• In the Kunni-Levenspile (K-L) bubbling bed model,

reaction occurs within the three phases of the bed, and

material is continuously transferred between the phases.

• Two limiting situations thus arise.

The interphase transport is relatively fast, and transport

equilibrium is maintained.

the reaction rate is relatively fast, and the performance is

controlled by interphase transport between the bubbles,

clouds, and emulsions.

Rate of Reaction in Fluidized Bed Reactor:

• Kunii-Levenspiel bubbling bed model is used to describe reactions

in fluidized beds.

• In this model, the reactant gas enters the bottom of the bed and

flows up the reactor in the form of bubbles. As the bubbles rise,

mass transfer of the reactant gases takes place as they flow

(diffuse) in and out of the bubble to contact the solid particles where

the reaction product is formed.

165

• The product then flows back into a bubble and finally exits the bed

when the bubble reaches the top of the bed. The rate at which the

reactants and products transfer in and out of the bubble affects the

conversion, as does the time it takes for the bubble to pass through

the bed.

166

• The velocity at which the bubbles move through the

column and the rate of transport of gases in and out of

the bubbles is to be found out.

• To determine the velocity of the bubble through the bed:

Porosity at minimum fluidization, εmf

Minimum fluidization velocity, umf

Bubble size, db

• To calculate the mass transport coefficient:



Velocity of bubble rise, ub

• To determine the reaction rate parameters in the bed:

Fraction of the total bed occupied by bubbles, δ

Fraction of the bed consisting of wakes, αδ

Volume of catalyst in the bubbles, clouds, and emulsion, γb,

γc, and γe 167

30/12/2013

168

ASSUMPTIONS

30/12/2013

169

• The bubbles are all of one size.

• The solids in the emulsion phase flow smoothly downward,

essentially in plug flow.

• The emulsion phase exists at minimum fluidizing conditions.

The gas occupies the same void fraction in this phase as it had

in the entire bed at the minimum fluidization point. In addition,

because the solids are flowing downward, the minimum

fluidizing velocity refers to the gas velocity relative to the

moving solids.

• In the wakes, the concentration of solids is equal to the

concentration of solids in the emulsion phase, and therefore

the gaseous void fraction in the wake is also the same as in the

emulsion phase. The wake is quite turbulent, and the average

velocities of both solid and gas in the wake are assumed to be

the same and equal to the upward velocity of the bubbles.

If ρc is the density of the solid catalyst particles, A c the cross-sectional area, h s

the height of the bed settled before the particles start to lift, h the height of the

bed at any time, and εs & ε the corresponding porosities of the settled and

expanded bed, respectively, then the mass of solids in the bed, W s, is

Once the drag exerted on the particles equals the net gravitational force

exerted on the particles, that is,

The Ergun equation, can be written in the form

The Minimum Fluidization Velocity

At the point of minimum fluidization the weight of the bed just equals the

pressure drop across the bed:

For the minimum fluidization velocity, to give

This first is ψ, the “sphericity,” which is a measure of a particle’s nonideality in both

shape and roughness. It is calculated by visualizing a sphere whose volume is equal to

the particle’s, and dividing the surface area of this sphere by the actually measured

surface area of the particle. Since the volume of a spherical particle is

and its surface area is

Measured values of this parameter range from 0.5 to 1, with 0.6 being a normal

value for a typical granular solid.

• The second parameter of special interest is the void fraction at the point of

minimum fluidization, εmf. It appears in many of the equations describing

fluidizedbed characteristics. There is a correlation that apparently gives

quite accurate predictions of measured values of εmf (within 10%) when the

particles in the fluidized bed are fairly small

• If the gas velocity is increased to a sufficiently high value,

however, the drag on an individual particle will surpass the

gravitational force on the particle, and the particle will be

entrained in a gas and carried out of the bed. The point at

which the drag on an individual particle is about to exceed the

gravitational force exerted on it is called the maximum

fluidization velocity

• When the upward velocity of the gas exceeds the free-fall

terminal velocity of the particle, ut, the particle will be carried

upward with the gas stream. For fine particles, the Reynolds

numbers will be small, and two relationships presented by

Kunii and Levenspiel are

Maximum Fluidization

The entering superficial velocity, u0, must be above the minimum

fluidization velocity but below the slugging ums and terminal, ut,

velocities.

Bubbles in Dense bed A dense bubbling fluidized bed

has regions of low solid density, sometimes called gas pockets or voids. The region of high density is called as emulsion or dense phase.

Based on experimental bubble observation in fluidized beds, the following correlation was presented by Clift and Grace (1985) for the bubble rise velocity and is often used for bubbles in any kind of fluidized bed:

Grace and Harrison (1969) showed that bubbles in a swarm rise more rapidly than a single bubble, due to interaction with neighbouring bubbles.

Bubble Velocity and Cloud Size When many bubbles are present, this velocity would be affected by other

factors. The more bubbles that are present, the less drag there would be

on an individual bubble; the bubbles would carry each other up through

the bed. The greater number of bubbles would result from larger amounts

of gas passing through the bed (i.e., a larger value of u0). Therefore, the

larger the value of u0, the faster should be the velocity of a gas

bubble as it rises through the bed.

Bubble Velocity and Cloud Size

Other factors that should affect this term are the viscosity of the gas

and the size and density of the solid particles that make up the bed.

Both of these terms also affect the minimum fluidization velocity, and so

this term might well appear in any relationship for the velocity of bubble

rise; the higher the minimum fluidization velocity, the lower the velocity of

the rising bubble.

Bubble Velocity and Cloud Size

• Adopting an expression used in gas-liquid systems, Davidson and

Harrison proposed that the rate of bubble rise in a fluidized bed

could be represented by simply adding and subtracting these terms:

Bubble size

• The equations for the velocity of bubble rise are functions of the bubble diameter.

As might be expected, it has been found to depend on

such factors as bed diameter, height above the distributor

plate, gas velocity, and the components that affect the

fluidization characteristics of the particles. Unfortunately,

for predictability, the bubble diameter also depends

significantly upon the type and number of baffles, heat

exchangers tubes, and so forth, within the fluidized bed

(sometimes called “internals”). The design of the distributor

plate, which disperses the inlet gas over the bottom of the

bed, can also has a pronounced effect upon the bubble

diameter.

Bubble size

Mori and Wen, who correlated the data of studies covering bed

diameters of 7 to 130 cm, minimum fluidization velocities of 0.5 to 20

cm/s, and solid particle sizes of 0.006 to 0.045 cm.

db is the bubble diameter in a bed of diameter Dt, observed at a height

h above the distributor plate; dbo is the diameter of the bubble formed

initially just above the distributor plate, and dbm is the maximum

bubble diameter attained if all the bubbles in any horizontal plane

coalesce to form a single bubble.

Bubble size

The maximum bubble diameter, dbm has

been observed to follow the relationship

for all beds, while the initial bubble diameter

depends upon the type of distributor plate.

For porous plates, the relationship

for perforated plates, the

relationship

following correlation based on

a statistical coalescence model

Fraction of Bed in the Bubble

Phase • Using the Kunii-Levenspiel model, the fraction of the bed occupied

by the bubbles and wakes can be estimated by material balances on

the solid particles and the gas flows. The parameter δ is the

fraction of the total bed occupied by the part of the bubbles that

does not include the wake, and α is the volume of wake per

volume of bubble. The bed fraction in the wakes is therefore αδ

bed fraction in the emulsion

phase (which includes the

clouds)

Ac and ρc represent the cross-

sectional area of the bed and the

density of the solid particles,

respectively so Us

Fraction of Bed in the Bubble

Phase A material balance on the gas flows gives

The velocity of rise of gas in the emulsion phase is

The emulsion phase exists at minimum

fluidizing conditions. The gas occupies the

same void fraction in this phase as it had in the

entire bed at the minimum fluidization point. In

addition, because the solids are flowing

downward, the minimum fluidizing velocity

refers to the gas velocity relative to the moving

solids, that is, From above two equation we

obtain volume fraction of the bed

occupied by bubble

Mole Balance on the Bubble, Cloud, and Emulsion

Phases

Balance on the Bubble Phase

The amount of A entering at Z is the bubble phase by flow

Balance on the Cloud Phase

30/12/2013

186

Using the Kunii-Levenspiel model,

the fraction of the bed occupied

by the bubbles and wakes can be

estimated by material balances on

the solid particles and the gas

flows.

Balance on the Emulsion Phase:

1-δ-αδ

30/12/2013

188

• The overall reaction rate in the bed is

proportional to KR

• so the reciprocal of KR can be viewed as

an overall resistance to the reaction.

30/12/2013

191

Specific reaction rate of solid catalyst , kcat

• Example- Maximum Solids Hold-Up

A pilot fluidized bed is to be used to test a chemical reaction. The bed diameter is 91.4 cm. You wish to process 28.3 × 103 cm3 of gaseous material. The average particle diameter is 100 μ. The reactor height is 10 feet. Allowing for a disengaging height of 7 feet, this means we have a maximum bed height of 91.4 cm. The distributor plate is a porous disc. What is the maximum weight of solids (i.e., holdup) in the bed? Other data.

Colour of Pellet: Brown ,ψ: 0.7 ρg: 1.07 × 10–3 g/cm3

ρc: 1.3 g/cc ,μ: 1.5 × 10–4 poise

192

For Problem solution Purpose We can Know

About

• A. Calculation of εmf.

• B. Calculation of Volume Fraction of Bubbles.

• C. The Amount of Solids Hold-Up, Ws

193

A. Calculation of εmf (Porosity at minimum fluidization)

εmf= 0.586ψ^0.72(µ^2/ρgηdp^3)^0.029(ρg/ρc)^0.021….(A) 1. Calculate gravity term

η = g( ρc − ρg )=(980 cm^2 /s)(1.3 − 0.00107) g /cm^3………..(a) =1270 g /(cm)^2(s^2)

2. Cross-sectional area

Ac =πD^2/4=(π )(91.4 cm)^2 /4………………………………(b)

=6.56 ×10^3 cm^2

3.Superficial velocity

u0 = (v 0/ Ac )=(2.83×10^4 /6.56 ×10^3)= 4.32 cm/ s……(c)

Putting ,a,b in Equation (A)…..getting value of .εmf= 0.58 194

• The amount of solids in the reactor is given by

Equation.

Ws = ρcAchs (1− εs )=ρcAch (1−ε)

The two parameters which need to be found are

εmf and δ

195

B. Calculation of Volume Fraction of Bubbles

δ= u0 − umf/ub − umf (1+α)…………………………………(B) Here we see we must calculate umf and ub. Step 1. First the minimum fluidization velocity is obtained from Equation

umf= (ψdp )^2/ 150μ [g(ρ c −ρ g)] εmf^3/(1−εm)…..Re

• Maximum bubble diameter

dbm = 0.652[Ac(u0 − umf )]^0.4 ……………(E1)

dbm = (0.652)[(6.56 × 10^3 cm^2)(4.32 − 1.28) cm/s]^0.4

dbm = 34.2 cm

• Minimum bubble diameter

db0 = 0.00376(u0 − umf )^2, cm………………….(E2)

db0 = (0.00376)(4.32 −1.28)^2

db0 = 0.0347 cm

For solving db……putting E1&E2 in Equation E

db = 34.2(1− e^ −0.3h /91.4 )

At h = 45.7 cm (h /2) db = 4.76 cm

197

Step 4. We now can return to calculate the velocity of bubble rise and the

fraction of bed occupied by bubbles from Equation (D) ,ub = 52.8 cm/s.

From figure below 100 μ size particle corresponds to a value of α of 0.5.

198

Example

• Massimilla and Johnstone studied the catalytic oxidation of

ammonia in a fluidized-bed reactor. Under their experimental

conditions, the reaction was first order, dependent only upon

the ammonia concentration, and without a significant change

in volumetric flow rate. In one of their runs, 4 kg of catalyst

were used with a gas flow rate of 818 cm3/s at reaction

conditions. A conversion of 22% of the entering ammonia was

obtained. Predict this conversion using the Kunii- Levenspiel

model.

30/12/2013

199

Notations Density of catalyst, ρc

Density of fluid, ρg

Sphericity, ψ

Cross-section area, Ac

Volumetric flow rate of feed, v0

Reactor diameter, Dt



Bubble size, db

Velocity of bubble rise, ub

Fraction of the total bed occupied by bubbles, δ

Fraction of the bed consisting of wakes, αδ

Volume of catalyst in the bubbles, clouds, and emulsion, γb, γc, and γe

30/12/2013

200

Data given

Operating conditions

P = 840 torr =1.11 atm

T = 523 K (250° C)

Reactor

Dt =11.4 cm

Distributor plate is porous stainless steel.

Feed

v0 = 818 cm3/s @ reaction conditions

Composition : 10% NH3, 90% O2

30/12/2013

201

Catalyst

dp = 105 μm (0.0105 cm)

ψ = 0.6 (assumed)

ρc = 2.06 (g cm3)

hs = 38.9 (cm)

Reaction rate

−rA = kCNH3 (gmoles NH3 (s)(cm3 of catalyst ))

kcat = 0.0858 s−1 @ reaction conditions

Fluid properties

ρg = 7.85 ×10−4 g cm3

μg = 2.98 × 10−4 g cm⋅ s

DAB = 0.618 cm2 s

30/12/2013

202

Mechanical Characteristics of

Bed

30/12/2013

203

30/12/2013

204

30/12/2013

205

u0, must be above the minimum fluidization velocity, umf but below the

terminal velocity, ut.

30/12/2013

206

30/12/2013

207

30/12/2013

208

Figure 1

30/12/2013

209

30/12/2013

210

30/12/2013

211

Mass Transfer and Reaction

Parameters

30/12/2013

212

30/12/2013

213

30/12/2013

214

The overall

transport

coefficient KR for

1st order reaction

Design

Equation

Specific reaction rate of solid catalyst , kcat

30/12/2013

215

This obtained value is close to the given 22% conversion

30/12/2013

216

h = t*ub

30/12/2013

217

ALGORITHM FOR

FLUIDIZED-BED

REACTOR DESIGN

Example

• Calculate each of the resistances to

reaction and transfer, and the relationship

between CAb, CAc and CAe for the ammonia

oxidation reaction described in Example

R12-2. Assume γb = 0.01.

Solution

• The analog of this system can be shown in

terms of electrical resistance system.

• If the major resistance in this side, the

resistance to reaction in the emulsion Rre ,

could be reduced, a greater conversion

could be achieved for a specific catalyst

weight.

• To reduce Rre, one needs to look for ways

of increasing γe.


Thank You

Documents

Introduction to Advanced Catalytic Reaction EngineeringDr R K Mewada - ACYRE Notes 2 Objective to study ACYRE Applications Subject overview: • Catalysis - Synthesis and characterization