Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of

chemical reactions and the design of the reactors in which they take place.

Lecture 16

Web Lecture 16Class Lecture 25 – Thursday 4/14/2011

BioreactorsMonod EquationYield CoefficientsWashout

2

Last LectureA given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.

NH2CONH2 UREASE H2O 2NH3 CO2 UREASE

S E H2O P E

SESE 1k

SESE 2k

EPWSE 3k

Michaelis Menten Equation

SKSVrr

MSP max

The corresponding mechanism is:

3

Bioreactors

Nutrient (S) +

+ Products

cells more cells

4

SS

SCg CK

CCr

max

SKSV

rrM

SP max

5

Bioreactors

6

7

inoculum

t=0 time

8Cells + Substrate More Cells + Product

Bioreactors

Bioreactors

9

Exponential Growth Phase

Death Phase

Stationary Phase

Lag Phase

0 time

lnCc

a) Phases of Bacteria growth:I. Lag II. Exponential III. Stationary IV. Death

b) Monod growth rate law: SS

SCg CK

CCr

max

VvDLet /0

10

Mass Balances:

Accumulation = [In] - [Out] + [Growth] - [Death]

dgCCC VrVrCvCv

dtdCV 000

Bioreactors

dgCCC rrCCD

dtdC

)( 1 0

Rate Laws:

3 rg kOBSmaxCS

KS CS

CC

4 kOBS 1 CP

CP*

n

Cp*= Product Concentration at which all metabolism ceases

11

dgCCC rrCCD

dtdC

)( 1 0

2 dCS

dtD(CS0 CS ) rS

Bioreactors

Stoichiometry:

SCCS Y

Y'1'

A.) Yield Coefficients

cellsnewproducetosubstrateofmassformedcellsnewofmassY SC '

productformtoconsumedsubstrateofmassformedproductofmassY SP '

B.) Maintenance

CPSPCSgS mCYrYrr

5 m mass of substrate consumed for maintainence

mass of cellstime

12

Bioreactors

produced) cells of grams(consumed) substrate of grams(' CSY

CPSPCSgS mCYrYrr ''

13

Stoichiometry: Rate of Substrate Consumption

Can’t separate substrate consumption used for cell growth from that used for product formations during exponenial growth.

CCSgS mCYrr '

Bioreactorsv0CS0

V=V0vCCCS

Volume=V

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1) Mass balance:

(cells) 0 0 VrrCvdtdCV dgC

C

(product) 3

2

1

rate)(dilution 1

)(substrate

(cells) 0

0

0

000

0

PPP

SSSS

dgCC

SSSS

dgCC

rDCdtdC

rCCDdtdC

rrDCdtdC

VvD

VrCvCvdtdCV

VrrCvdtdCV

Bioreactors

15

2) Rates:

4 rg maxCS

kS CS

CCKOBS

5 KOBS 1 CP

CP*

n

6 rP YP /Crg

7 rS YS /Crg mCC

8 rD kDCC 3) Parameters:

VDVvCvmCvmCDmyykknC

PpC

SCPCSDSP

, , , , , , , , , , , ,

000

0//*

max

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Bioreactors

Polymath Setup1.) d(CC)/d(t)=-D*CC+(rg-rd)2.) d(CS)/d(t)=-D*(CS0-CS)-Ysg*rg-m*CC

3.) d(CP)/d(t)=-D*CP+YPC*rg

4.) rg=(((1-(CP/Cpstar))**0.52)*mumax*(CS/(KS+CS))*CC5.) D=0.26.) kd=0.017.) rd=kd*CC

8.) CS0=2509.) YPC=5.610.) m=0.3

11.) mumax=0.3312.) YSC=12.513.) KS=1.7

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Bioreactors – Chemostats - CSTRs

CCSS

SgC CC

CKCrDC

max

SS

S

CKCD

max

1. Steady State - Neglect Death Rate and Cell Maintenance

VrDVC gC 02. Cell

DDKC S

S

max18

D

DKCYCCYC SSSCSSSCC

max00

VrVCCD SSS 00

CCSgCSSSS DCYrYrCCD //0

3. Substrate

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Bioreactors – Chemostats - CSTRs

CSTR Washout

0

0max

SS

SW CK

CD

0CC

CCc DC

VCv

Vm

0

D

DKCDYDC SSSCC

max0

CC

DWD

CC

20Washout dilution rate

Bioreactors

How does this figure relate to drinking a lot of fluids when you have an infection or cold?

0SS

0SmaxW CK

CD

0SS

Smaxprodmax CK

K1D

DCC

DWD

Dmaxpro

d21

Maximum Product Flow Rate

End of Web Lecture 16End of Class Lecture 25

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