4.Ideal Reactors

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CONTINUOUS IDEAL REACTORS

A. SARATH BABU

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Continuous Stirred Tank Reactor

CSTR Contd. . . 3

CSTR Animation 4

CSTR Contd. . . 5

• Also called as Mixed, Backmix, Ideal stirred tank reactor

• Open system, operates under steady state conditions

• Reactants are continuously introduced and products are

continuously withdrawn

• Perfect mixing – contents have uniform properties

– No spatial variations

• Conditions at the exit are same as inside the reactor

• Used for homogenous liquid phase reactions where

constant agitation is required

• Eg. Sulfonation, Polymerization, plastics, explosives,

synthetic rubber etc.

CSTR Contd. . . 6

Advantages:

• Cheap to construct

• Good temperature control

• Reactor has large heat capacity

• Easy access to interiors

Disadvantages:

• Conversion per unit volume of the reactor is

smallest compared to other flow reactors

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Fractional Conversion (xA):

0

0

A

AAA F

FFx

0

0

A

AAA C

CCx

Space time ():

Space time is the time required to process one reactor volume of inlet material (feed) measured at inlet conditions. is the time required for a volume of feed equal to the volume of the vessel (V) to flow through the vessel.

= V/v0 = sec N.B. : Volume of vessel here means volume of Reaction Mixture.

(for constant density)

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Space Velocity (S): Space velocity (S) is the reciprocal of space time, the number of reactor volumes of feed, measured at inlet conditions, processed per unit time.Mean Residence time tm:

The residence time is the length of time species spend in the reactor. All molecules that enter may not spend the same time in the reactor.

The distribution of residence times – RTD

The average length of time that molecules spend in the reactor – mean residence time (tm)

tm = V/vE

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)1(0 AAA xFF

000 / AA CFv lit

molmollit

secsec

For constant density:

)1()1(

00

0AA

AAAA xC

v

xF

v

FC

For variable density:

)1(

)1(

)1(

)1(0

0

0

AA

AA

AA

AAAA x

xC

xv

xF

v

FC

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Stoichiometric Table – Flow Systems

B FB0 -(b/a)FA0xA FB= FA0(MB-(b/a)xA)

R FR0 +(r/a)FA0xA FR= FA0(MR+(r/a)xA)

S FS0 +(s/a)FA0xA FS= FA0(MS+(s/a)xA)

I FI0 0 FI = FI0

Total FT0 FT = FT0 + NA0δxA

Where: MI = FI0/FA0

δ = (r/a + s/a – b/a – 1)

aA + bB rR + sS

For Constant density: CA = CA0(1-xA)

Species Initial Change Final moles A FA0 -FA0xA FA= FA0(1-xA)

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Design Equation

General Mass Balance Equation:

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

FA0 = FA + 0 + (-rA) V

FA0 - FA = (-rA) V

FA0 xA = (-rA) V

V / FAo = xA / -rA

FA0

CA0

v0

FA

CA

VxA

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V / FAo = xA / -rA

General Design eqn. for a CSTR:

V / (v0 CA0) = xA / -rA

/ CA0 = xA / -rA

Design eqn. for a CSTR under constant density:

= (CA0 – CA) / -rAtm = V/vE

Note that the space time and the mean residence time are equal only in the case of constant density.

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DA =kCA0n-1

Comparison of Different orderReactions in a CSTR

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Plug Flow Reactor

PFR Animation 16

The necessary and sufficient condition for plug flow is the residence time in the reactor to be the same for all elements of the fluid.

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• PFR is also called as tubular reactor

• Residence time is same for all fluid elements

• Operated under steady state conditions

• Reactants are consumed as they flow down along the

length of the reactor

• Axial concentration gradients exist

• One long tube or a number of short tubes (see fig.)

• Choice of diameter depends on fabrication cost,

pumping cost and heat transfer needs

• Wide variety of applications in gas/liquid phase

• Eg.: Production of gasoline, cracking, synthesis of

ammonia, SO2 oxidation

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(1) The flow in the vessel is Plug flow.

(2)There is no axial mixing of fluid inside the vessel (i.e., in the direction of flow).

(3)There is complete radial mixing of fluid inside the vessel (i.e., in the plane perpendicular to the direction of flow).

(4)Properties may change continuously in the direction of flow

(5)In the axial direction, each portion of fluid, acts as a closed system in motion, not exchanging material with the portion ahead of it or behind it.

PFR Contd. . . 20

Advantages:

• Easily maintained as there are no moving parts

• High conversion per unit volume

• Unvarying product quality

• Good for studying rapid reactions

Disadvantages:

• Poor temperature control

• Hot spots may occur when used for exothermic

reactions

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Design Equation General Mass Balance Equation:

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

FA = FA + dFA + 0 + (-rA) dV

-dFA = (-rA) dV

FA0 dxA = (-rA) dV

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Ax

AAA rdxFV0

0 //

General Design eqn. for a PFR:

Ax

AAA rdxC0

0 //

Design eqn. for a PFR (under constant density):

Ax

AA rdC0

/ V

m vdVt0

/

Note that the space time and the mean residence time are equal only in the case of constant density.

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CA/CA0

DA = kCA0n-1

Comparison of Different orderReactions in a PFR

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Item BR CSTR PFR

XA (NA0-NA)/NA0 (FA0-FA)/FA0

CA NA/V FA/v

-rA (NA0/V)dxA/dt FA0xA/V FA0dxA/dV

t NA0dxA/V(-rA) = V/v0

Constant density

XA (CA0-CA)/CA0 (CA0-CA)/CA0

-rA -dCA/dt (CA0 -CA)/ -dCA/d

t -dCA/(-rA) = V/v0

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Algorithm for Isothermal Reactor Design

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CSTR PFR

/ CA0 = xA / -rA Ax

AAA rdxC0

0 //

1 /-rA

xA

/ CA0

/ CA0

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CSTR PFR

V / FA0 = xA / -rA Ax

AAA rdxFV0

0 //

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CSTR PFR

1 /-rA

= (CA0 – CA) / -rA Ax

AA rdC0

/

CA CA0

1 /-rA

CA CA0

(Constant Density)

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CSTR PFR

1 /-rA

CA CA0

1 /-rA

CA CA0

(Constant Density)

CVBR

1 /-rA

t

CA CA0

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CSTR PFR

VVBR1 /-rA

xA

/ CA0

1 /-rA

xA

/ CA0

xA

t / CA0

)1(

1

AAA xr

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CSTR PFR

= (CA0 – CA) / -rA A

A

C

C

AA rdC0

/(Constant Density)

Zero Order

= (CA0 – CA) / k A

A

C

C

A kdC0

/

k = CA0 – CA k = CA0 – CA

Constant Density BR

kt = CA0 – CA

k = CA0 xA k = CA0 xA

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CSTR PFR

= (CA0 – CA) / -rA A

A

C

C

AA rdC0

/(Constant Density)

First Order

= (CA0 – CA) / kCA A

C

C

A CkdCA

A

0

/

k = (CA0 – CA)/CA

Constant Density BR

kxC

CA

A

A )1ln(ln0

ktC

C

A

A 0

ln

k = xA /(1-xA)

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CSTR PFR

= (CA0 – CA) / -rA A

A

C

C

AA rdC0

/(Constant Density)

Second Order

= (CA0 – CA) / kCA2

2

0

/ A

C

C

A CkdCA

A

k = (CA0 – CA)/CA2

Constant Density BR

kCC AA

0

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ktCC AA

0

11

k CA0 = xA /(1-xA)2

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Constant Density

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For constant density:• The performance of the Batch reactor is

similar to that of PFR for all orders•The performance of all the three reactors is the same in case of zero order reaction•The performance of PFR is superior to that of a CSTR for all orders > 0

For all reaction orders > 0• The volume of a CSTR required for obtaining a given conversion is larger than that of PFR• For the same volumes of PFR & CSTR, the conversion obtained is larger in the case of PFR

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CSTR PFR

= CA0xA / -rA Ax

AAA rdxC0

0 /(Variable Density)

Zero Order

= CA0 xA / k Ax

AA kdxC0

0 /

k = CA0 xA k = CA0xA

Variable Density BR:

tkxC AAAA )1ln(0

AA

A

A

A

x

x

C

C

1

1

0

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CSTR PFR

= CA0xA / -rA Ax

AAA rdxC0

0 /

(Variable Density)

First Order

= CA0 xA / kCA A

x

AA CkdxCA

0

0 /

k = CA0 xA/CA

Variable Density BR:

AAAA xxk )1ln()1(

ktxA )1ln(

AA

A

A

A

x

x

C

C

1

1

0

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CSTR PFR

= CA0xA / -rA Ax

AAA rdxC0

0 /(Variable Density)

Second Order

= CA0 xA / kCA2

2

0

0 / A

x

AA CkdxCA

Variable Density BR:

)1ln()1(20 AAAA xkC

)1/()1( 22AAAAA xxx

tkCxxx AAAAAA 0)1ln()1/()1(

AA

A

A

A

x

x

C

C

1

1

0

k = CA0 xA / CA2

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Variable Density

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Relative performance of plug flow and continuous-flow stirred tank

reactors

Fraction unreacted is larger in CSTR for a given Da

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Comparison of reactor volume required for a given conversion for a first-order reaction in a PFR and a CSTR

• For small conversions VCSTR/VPFR = 1 (selection of reactor not very critical).

• For large conversions, VCSTR/VPFR is very large (selection of reactor very critical).

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For Variable density:

•The performance of CSTR & PFR is similar in case of zero order (irrespective of constant / variable density)

•The performance of BR is different from the performance of PFR (the performance was similar in the case of constant density)

•The performance of PFR is superior to that of a CSTR for all orders > 0 (same as constant density)

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Criteria Batch CSTR PFR

Reactor size for given conversion + - +

Simplicity and Cost + + -

Continuous operation - + +

Large throughput - + +

Cleanout + + -

On-line analysis - + +

Product quality - + +

Comparison of possible advantages (+) and Disadvantages (-)for Batch, CSTR and PFR Reactors

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ANY CLARIFICATIONS ?

Abbey, EdwardThat which today calls itself science gives us more and more information,

an indigestible glut of information, and less and less understanding.