Reactors Lec 4 Stu

8/6/2019 Reactors Lec 4 Stu

1/20

Reactor Design

Lecture 4

Fall 2007ChEE ABE 481a/581a


2/20

Mass Balance on Reactive System

In - out + gen - cons = accumulation

A mass balance for the system is

NA is the mass of A inside the system.

GARate of

generation/

consumption

FA0Rate of flow in

FARate of flow out

System

GARate of

generation/

consumption

FA0Rate of flow in

FARate of flow out

System

dt

dNGFF AAAA !0


3/20

The reaction term can be written in more familiar

terms,

GA = rA V

Vis volume of the system.

Note that the units for this relation are consistent:

IfGA (and hence rA) varies with position in thesystem volume, we can take this into account by

evaluating this term at several locations. Then

(GA1 = rA1(V1,

volumetimevolume

mass

time

massy

!


4/20

Summing the reactions over the entire

volume yields:

As (that is, as we decrease the size of these

cubes and increase their number)

which gives

!!

(!(!k

i

iAi

k

i

AiA VrGG

11

gpk

!V

AA dVrG

0p(V


5/20

Generalized Design Equation for

Reactors

In - out + gen - cons = accumulation

dt

dNdVrFF A

V

AAA !

0


6/20

Types of Reactors

BatchNo flow of material in or out of reactor

Changes with time

Fed- Batch

Either an inflow or an outflow of material but not both

Changes with time

Continuous

Flow in and out of reactor

Continuous Stirred Tank Reactor (CSTR)

Plug Flow Reactor (PFR)

Steady State Operation


7/20

Batch Reactor

GeneralizedDesign Equation for

Reactors

No flow into or out of the reactor,then,FA = FA0 = 0

Good mixing, constant volume

dt

dNdVrFF A

V

AA0A !

!V

AA dVr

dt

dN

Vr

dt

dNA

A !

AAA r

dt

dC

dt

VNd!!or


8/20

Enzyme Batch Reactor

(constant volume, well mixed)

integrate from t= 0 to t= t, we obtain

Kmln (S0/S) + (S0 -S) = vmax t

Batch reactors are often used in the early stage of

development due to their ease of operation and

analysis

SK

Sv

dt

dSr

M

!! max


9/20

Fed Batch Reactor Reactor Design Equation

No outflow FA = 0

GoodMixing rA dV

term out of the integral

dt

dN

dVrFFA

V

AAA!

0

dt

VCd

dt

dNVrF AAAA

!!0


10/20

Fed Batch Continued

Convert the mass (NA) to concentration. Applyingintegration by parts yields

Since

Then

Rearranging

dt

dVC

dt

dCVVrF A

AAA !0

0AFdt

dV!

00 AAA

AA FCdt

dCVVrF !

V

FCr

V

F

dt

dC AAA

AA 00 !


11/20

Fed Batch Continued Or

Used when there is substrate inhibition and

for bioreactors with cells.

AAAA rCV

F

dt

dC! 10


12/20

Assumptions for a fed batch reactor

include

Onlyafe

edin

Eith

erafeed

inora

...

Stead

ystat

e

2and

3

All

oftheab

ove

0%

64%

7%

29%

0%

1. Only a feed in

2. Either a feed in or a

removal stream3. Steady state

4. 2 and 3

5. All of the above


13/20

Continuous Stirred Tank Reactor

Assume rate of flow in = rate of flow out

FA = v CA and FA0 = v CA0

v = volumetric flow rate (volume/time)


14/20

CSTR - continued General Reactor Design Equation

Assume Steady State

WellMixed

So or

dt

dNdVrFF A

V

AAA !

0

0!dt

dNA

A

V

A VrdVr !

00 ! AAA VrFFA

AA

r

FFV

! 0


15/20

CSTR for Enzymes

(Enzyme remains inside) Input - output + generation - consump = accumulation

F- flow rate l/hr

S- substrate conc.

V- reactor volume r- reaction rate

at Steady State dS/dt= 0

dt

dS

vrVFSFS !0


16/20

CSTR - enzymes

rV = F(S0 - S)

or r = F/V(S0

- S) =D(S0

- S)

D= dilution Rate (hr-1)

X= residence time (hr)

If

Then

SK

Svr

! max

SS

SvKS

!

0

max X


17/20

Plug Flow Reactor (PFR)

Tubular Reactor

Pipe through which fluid flows and reacts.

Poor mixing

Difficult to control temperature variations.

An advantage is the simplicity of construction.


18/20

PFR Design Equation

Design Equation

Examine a small volume element ((V) with length

(y and the same radius as the entire pipe.

If the element is small, then spatial variations in rAare negligible, and

dtdNdVrFF A

V

AAA ! 0

VrdVr AV

A (!

Flow of

A into

Element

Flow of

A out of

Element

Assumption of good

mixing applies only to

the small volume

element


19/20

If volume element is very small, then assume steady

state with no changes in the concentration of A.

Simplify design equation to:

rA is a function of position y, down the length of thepipe and reactant concentration

The volume of an element is the product of the length

and cross-sectional area,

(V = A (y

Design Equation becomes:

0!dt

dNA

0!(( VryyFyF AAA

A

AA Ary

yFyyF!

(

(


20/20

take the limit where the size of a volume

element becomes infinitesimally small

or because (y A = V,

This is the Design Equation for a PFR Bioapplications - Sometimes hollow fiber

reactor analysis is simplified to a PFR

AA

y

Ardy

dF!

p(lim

0

AA r

dV

dF!

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Reactors Lec 4 Stu