Continuous –Stirred Tank Reactor Design

CHEMICAL REACTION RATE

The rate of a chemical reaction is the rate of formation or transformation of a

participant in a chemical reaction. It is expressed as the number of mass or mole of material

converted per unit volume of reactor per unit time. Thus, the rate of appearance or

disappearance of a chemical species i in a homogeneous reaction is (Levenspiel, 2003):

( / )

= ii

d n Vr

dt eq 5-1

If i is a reactant, the negative sign is used to signify depletion with time. Whereas, the

positive sign is used if it’s a product. Where in is the number of moles of component i, V

is the reactor volume and t is the reaction time.

For a constant volume reaction,

1= i i

i

dn dCr

V dt dt eq 5-2

As expressed in the Law of Mass Action, the rate of a chemical reaction is proportional

to the active masses of participating reactants. Therefore, the rate is dependent on the

concentration of the participating reactants. In elementary reaction, the stoichiometric

coefficient of the reactants is equal to the order of the reactions. This order becomes the

power to which the reactant is raised.

If the given chemical reaction is

aA bB cC dD eE eq 5-3

then, the rate of reaction for the disappearance of reactant A is

A

A A B C

dCr kC C C

dt eq 5-4

Again, except in elementary reactions, the order of the reaction is not equal to the

stoichiometric coefficients as in a , b , and c . k is the rate constant of the

reaction.

CSTR DESIGN 2

Elementary and Non-Elementary Reactions

Elementary Reaction

Elementary reaction occurs only in a single step.

Example: 1. A Product eq 5-5

2. A+B Product eq 5-6

Non-elementary Reaction

Non-elementary reaction occurs in two or more steps of reactions and there is no

direct correspondence between the stoichiometric coefficient and the rate expression of the

reaction.

Mechanism of Non-Elementary Reaction (Levenspiel, 2003)

Non-chain reaction mechanism

Reactants (intermediates)* eq 5-7

(intermediates)* Products eq 5-8

Chain Reaction Mechanism

Reactants (intermediates)* eq 5-9

(intermediates)* + Reactant (intermediates)*

+ Product eq 5-10

( intermediates)* Product eq 5-11

REACTION RATES OF DIFFERENT MECHNISMS

Reversible Reactions

First Order Reversible Reactions

1

2

k

kA R eq 5-12

The rate expression for substance A and R are written as

AA 1 A 2 Rnet

net

-dCr =k C -k C

dt eq 5-13

CSTR DESIGN 3

R1 A 2 Rnet

net

dC=k C -k C

dtRr eq 5-14

At equilibrium rnet = 0. Therefore,

1 Ae 2 Rek C =k C eq 5-15

Re1C

2 Ae

Ckk = =

k C eq 5-15

After establishing the material balance and upon integration, the final working

equation in terms of fractional conversion is:

A

2 C

Ae

Xln 1- =- k k +1 t

X eq 5-16

Irreversible Reactions in Parallel

1kA R assumed desired product eq 5-17

2kA T unwanted product eq 5-18

3kA S unwanted product eq 5-19

The rate equation is for reactant A

AA 1 2 3 A

-dCr = = (k k k )C

dt eq 5-20

Integration gives

1 2 3-(k +k +k )t

A AoC = C e eq 5-21

Irreversible Reactions in Series (Consecutive Reactions)

Consider the unimolecular first order reaction

1 2k kA B R eq 5-22

The rate equation for component A

A1 A

-dC=k C

dt eq 5-23

CSTR DESIGN 4

Rearranging and integrating :

1-k t

A AoC = C e eq 5-24

B

1 A 2 B

dC=k C -k C

dt eq 5-25

Homogeneous Catalyzed Reactions

In the homogeneous catalyzed type of reactions, the overall rate is the sum of rates of

both the uncatalyzed and catalyzed reactions.

The uncatalyzed reaction is

1kA R eq 5-26

and the catalyzed reaction is 2k

A + C R C eq 5-27

The rate expression of component A is

A

1 A 2 A C

-dC= k C + k C C

dt eq 5-28

The concentration of the catalyst (CC) is assumed to be constant.

A

1 2 C A

-dC= (k +k C )C

dt eq 5-29

Integration gives

A

1 2 C

Ao

Cln = (k +k C ) t

C eq 5-30

Autocatalytic Reactions

An autocatalytic reaction is a reaction in which one of the products of reaction acts as

a catalyst.

For an uncatalyzed reaction:

1k

A R eq 5-31

For which the equation rate is:

A

A A R

-dCr = =k C C

dt eq 5-32

CSTR DESIGN 5

The corresponding catalyzed reaction where product R acts as a catalyts is

1kA + R R + R eq 5-33

the rate equation is

A

A A R

-dCr = =k C C

dt eq 5-34

Establishing the material balance and upon integration, the final rate expression is

o A Ao

o

o Ao A

C -C Cln =C kt

C -C C eq 5-35

CLASSIFICATION OF REACTORS

Although the purpose of this chapter is to present the determination of CSTR

specifications, Batch and Plug flow reactors will be briefly described

Batch Reactor

Batch reactors are usually simple in design with minimum auxiliary and

instrumentation requirements. It is commonly employed for small scale production, testing of

new productions, manufactured of expensive and easily contaminated system. High

conversion could be easily obtained by increasing the reaction time, although production

output is reduced correspondingly. It is usually not applicable for large industrial scale

production where labor cost would be high and production output is low compared to

continuous flow reactors. In batch reactor there is neither inflow nor outflow of both

reactants and products while the reaction is in progress.

Plug Flow Reactors (PFR)

In Plug flow reactor, reactant continually flows through a cylindrical vessel or pipe.

The reactant diminished along the length, and there is no radial variation in concentration.

This type of continuous flow reactors are simple in design and practically has no power

requirement.

reactat product

Figure 5-1. Plug Flow Reactor.

CSTR DESIGN 6

reactan

productow

Continuous-Stirred Tank Reactor (CSTR)

CSTR is commonly used for industrial production. It is assumed of having no spatial

variation in concentration and temperature. As name implies the reactor is well mixed,

allowing the assumption of same concentration at any point within the reactor and the

product. It is also called Backmix Reactor (Fogler, 1999). Even a well designed and

operated CSTR will produce lower conversion per unit reactor volume against Plug Flow

type reactors. In this chapter, design of Continuous Stirred Tank Reactor will be discussed.

Most homogeneous liquid phase reactions employs CSTR.

Figure 5-2. Continuous Stirred Tank Reactor.

CSTR DESIGN EQUATIONS

Space Time and Space Velocity concept

The space time, τ , is the time required to process one reactor volume of feed and is

given by the following equation:

Ao

Ao o

C V V

F v eq 5-36

where

CAo is the initial concentration

V is the volume of the reactor,

FAo is the molal flowrate of component A and,

vo is the volumetric flow rate.

CSTR DESIGN 7

Whereas, space velocity (S) refers to the number of reactor volumes of reactant fed

into the reactor per unit time and is given by the following equation:

1 Ao o

Ao

F vS

C V V eq 5-37

Overall Material Balance

Volume element reactant leaves

Reactant disappears by reaction

Reactant accumulates

Reactant enters Volume element reactant leaves

Reactant disappears by reaction

Reactant accumulates

Reactant enters

Figure 5-3. Over-all Material Balance.

rate of reactant rate of reactant rate of disappearance due rate of accumulation of

flow into element = flow out of element + to chemical rxn within + reactant in element of volume

of volume of volume the element of volume

eq 5-38

Input = output + rate of disappearance + rate of accumulation of A

At steady- state process, rate of accumulation of reactant = 0

FAo = FA + (-rA) V eq 5-39

However,

FA = FAo – FAo XA eq 5-40

Then,

-

A

A Ao

X V

r F eq 5-41

CSTR DESIGN 8

Where XA is the fractional conversion of reactant A

In terms of space time

-

Ao A

A

C X

r eq 5-42

REACTION RATES AND SPACE TIME

Zero Order irreversible chemical reaction

A-----------Product eq 5-43

(-rA) = k eq 5-44

substituting ( –rA) into space time equation,

Ao AC X

k eq 5-45

First Order irreversible chemical reaction

A-----------Product eq 5-46

(- )A Ar k C eq 5-47

substituting ( –rA) into space time equation,

Ao A

A

C X

kC eq 5-48

Second order irreversible chemical reaction

2A------------Product eq 5-49

2(- )A Ar k C eq 5-50

substituting ( –rA) into space time equation,

22 2 1-

Ao A Ao A

A Ao A

C X C X

k C k C X eq 5-51

CSTR DESIGN 9

N’th order irreversible chemical reaction

nA------------Product eq 5-52

(- ) n

A Ar k C eq 5-53

substituting ( –rA) into space time equation,

1-

Ao A Ao A

nn nA Ao A

C X C X

k C k C X eq 5-54

CSTR SIZING

CSTR sizing is dictated by residence time requirement. The longer the residence time,

the bigger the reactor volume at constant volumetric flow rate. This is expressed below:

τ = V / vo eq 5-55

where:

τ = Space time or Residence time, sec [hr]

V = Volume of Reactor, m³ [ft3]

vo = Volumetric flowrate, m³/sec [ft3/s]

Overall chemical kinetics which includes, chemical specie, amount of specie, reaction

temperature, presence of catalyst, agitation etc determines the degree of residence time as

shown in Table 5-1.

Table 5-1. Residence Time and/or Space Velocities in Industrial Chemical Reactors.

Product

(raw materials)

Reactor

Phase

(CSTR)

Catalyst T, °C P, atm

Residence

Time or

Space

Velocity

Alkylate (i-C4, butanes) L H2SO4 5-10 2-3 5-40 min

Alkylate (i-C4, butanes) L HF 25-38 8-11 5-25 min

Butadiene sulfone (butadiene, SO2) L t-Butyl catechol 34 12 0.2 LHSV

Caprolactam (cyclohexane oxime) L Polyphosphoric acid 80-110 1 0.25-2 h

Chloral (Cl2, acetaldehyde) LG None 20-90 1 140 h

Cumene hydroperoxide (cumene, air) L Metal porphyrins 95-120 2-15 1-3 h

Cyclohexanone (cyclohexanol) L N. A. 107 1 0.75 h

Dextrose (starch) L H2SO4 165 1 20 min

Dextrose (starch) L Enzyme 60 1 100 min

Dodecylbenzene (benzene, propylene tetramer)

L AlCl3 15-20 1 1-30 min

Ethyl acetate (ethanol, acetic acid) L H2SO4 100 1 0.5-0.8 LHSV

Ethylene, propylene chlorohydrins (Cl2, H2O) LG None 30-40 3-10 0.5-5 min

CSTR DESIGN 10

Table 5-1 continued...

Product

(raw materials)

Reactor

Phase

(CSTR)

Catalyst T, °C P, atm

Residence

Time or

Space

Velocity

Glycerol (allyl alcohol, H2O2) L H2WO4 40-60 1 3 h

o-Methyl benzoic acid (xylene, air) L None 160 14 0.32 h 3.1 LHSV

Nitrobenzene (benzene, HNO3) L H2SO4 45-95 1 3-40 min

Phenol (cumene hydroperoxide) L SO2 45-65 2-3 15 min

t-Butyl methacrylate (methacrylic acid, i-butene)

L H2SO4 25 3 0.3 LHSV

Aldehydes (diisobutene, CO) LG Co Carbonyl 150 200 1.7 h

LHSV – Space velocity (hourly) – liquid N. A. – Not Available Adapted from Table 23 - 1 Section 23 - 7 Perry’s Chemical Engineer’s Handbook 7th ed.

Standard Stirred Tank Configuration

Stirred tank configuration for a six flat blade turbine Trambouze et. al., (1988),

provide for the standard type agitation system. As shown below, the following are standard

configuration:

Figure 5-4. Dimensions for CSTR Design.

Dd

DI

m

I

b

ZI

ZL

W

H

T

D

T

CSTR DESIGN 11

1L

T

Z

D eq 5-56

1

3

I

T

D

D eq 5-57

1

10T

W

D eq 5-58 1I

I

Z

D eq 5-59

3

4

d

I

D

D eq 5-60

1

4I

I

D eq 5-61

1

5I

b

D eq 5-62

1

5T

m

D eq 5-63

where:

LZ = Static liquid depth

TD = Tank diameter

ID = Impeller diameter

IZ = Impeller distance from tank bottom

W = Baffle width

dD = Impeller disc diameter

I = Impeller blade length

b = Impeller blade width

TH = Tank height

m = Baffle tip distance from tank bottom

Mixing Time

To estimate the mixing time, Norwood and Metzner correlation provides for the

equation applicable for six flat blade turbine:

2 0.5

1

65I Lm Fr

T T

D ZN t N

D D eq 5-64

where:

mt = Mixing time

N = Impeller revolutions per unit time

ID = Impeller diameter

TD = Tank diameter

LZ = Static liquid depth

FrN = Froude Number

CSTR DESIGN 12

2

IFr

N DN

g eq 5-65

where g = acceleration due to gravity

Impeller Selection

Agitation is designed to increase fluid turbulence, and is often employed in the

following (Mc Cabe, 2001):

1. homogenization of a fluid phase

2. increased heat transfer between a solid surface and a fluid phase

3. creation of interfacial area between two immiscible fluid phases.

4. maintenance of a divided solid in suspension in a fluid phase

Agitation as used in the process industries is the production of irregular disturbances

or turbulent motion within a fluid by means of mechanical devices acting on that fluid

(Brown, 1950). Most of the fluids handled in the process industry are low viscosity

Newtonian fluids.

Several references classify impellers according to their form, functions and uses in the

mixing operations (Brown, 1950; Foust et. al, 1980 and McCabe, 2001) as shown in Figure 5-

5. Figure 5–6 may be used I n the selection of appropriate impeller type.

Figure 5-5. Types of Impeller. Adapted from Doran, Pauline M. 1995

Bioprocess Engineering Principles.

Anchor Propeller 6 flat blade disc-turbine

Paddle Gate anchor Helical screw

CSTR DESIGN 13

Impeller Type

Vis

co

sit

y (

cen

tip

ois

e)

103

104

105

106

107

102

10

1

An

ch

ors

Prop

ell

ers

Fla

t-b

lad

e tu

rb

ines

Pad

dle

s

Gate

an

ch

ors

Hel

ical

Scre

ws

Hel

ical

Rib

bon

s

A graphical method of impeller selection is presented on Figure 5-6.

Figure 5-6. Viscosity Ranges for Different Impellers. Adapted from F.A Holland and

F.S. Chapman, 1966, Liquid Mixing and Processing in Stirred Tanks

as cited by Doran, Pauline M. (1995) Bioprocess Engineering

Principles.

Baffles

Baffles are flat vertical strips set radially along the tank inner wall. They are mounted

inside the tank to produce higher mixing and horizontal liquid surface (Perry and Green,

1997). In the absence of baffles in a stirred tank, vortex are formed because of the centrifugal

force acting on the liquid and could reach deep to the impeller which is undesirable (Mc Cabe,

2001). Due to the motion of the impeller in the fluid and the resultant movement of the liquid

past the baffles and wall, the skin friction and the drop form have to be considered in relation

to the speed of rotation and design of blade and tank.

Figure 5-7 provides for baffle inclination and attachment selection guide.

CSTR DESIGN 14

Figure 5-7. Baffle Arrangements (a) Baffles are attached to the wall for low-viscosity

liquids. (b) Baffles set away from the wall for moderate-viscosity

liquids. (c) Baffles set away from the wall and at an angle for high-

viscosity liquids. Adapted from F.A Holland and F.S. Chapman, 1966,

Liquid Mixing and Processing in Stirred Tanks as cited by Doran, Pauline

M. 1995. Bioprocess Engineering Principles)

Power Dissipation

Power dissipated by the agitator maybe computed by:

53

IPa DNNP eq 5-66

where

Pa = Power dissipated by an agitator

N = RPM of the impeller

ρ = Density of the mixture

DI = Impeller diameter

NP = Power number

CSTR DESIGN 15

An estimation of typical horsepower for agitators is given below (Parker, 1964; Schlegel,

1972): This maybe used to approximate power requirement due to mixing of CSTR.

Fluid Approximate Horsepower

Blending vegetable oil 1.0 hp per 100,000 lb

Blending gasoline 0.019 hp per m3

Clay dispersion 10 – 12 hp per 1,000 gal

Fermentation (pharmaceutical) 3 – 10 hp per 1,000 gal

Suspension polymerization 6 – 7 hp per 1,000 gal

Emulsion polymerization 3 – 10 hp per 1,000 gal

Solution polymerization 15 – 40 hp per 1,000 gal

Radius of Action of an Agitator

Radius of action of an agitator should be checked after reactor, blade and baffle sizes

have been calculated to ensure there is enough intensity of mixing inside the reactor, as this

will affect reaction conversion. Radius of Action AR may be calculated as:

2

1

2109P

RA eq 5-67

Horizontal radius of action HRa and vertical radius of action VRa are 50% and 20%

respectively of the computed radius of action.

where

P = Power, watts

= Viscosity, Pa . s

aR = Radius of action, m

HRa = Half major axis ellipsoidal

VRa = Half minor axis ellipsoidal

To ensure high degree of agitation a linear speed at blade tip should be greater than 4. Where

tip speed is given by:

Vp = πNDI (m/s) eq 5-68

Another indicator of high degree of agitation is Power dissipated per unit volume of fluid

which should have at least 1,500 3m

Wvalue.

Below is the summary of degree of agitation against tip blade speed and Power per unit

volume (Trambouze et. al, 1988):

CSTR DESIGN 16

Degree of Agitation Tip Speed s

m 3m

watt

VolumePower

Low 3.25 750

Medium 3.25 to 4 750 to 1500

High 4 up 1500 up

For an initial condition, a 50% on blade tip speed of 4 s

m and Power per unit volume of

1500 3m

watt could be a good choice. On the other hand, a good compromise should be

reached, so that just enough mixing is provided for certain required residence time for power

requirement to be justifiable. An acceptable criteria used is:

tm

τ eq 5-69

< 0.1