lecture 16

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

BioreactorsMonod EquationYield CoefficientsWashout

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Web Lecture 16Class Lecture 25 – Thursday 4/18/2013

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Enzymes - Urease A given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.

UREASECONH2UREASECONHNH 23OH

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EPES OH2

SESE 1k SESE 2k

EPWSE 3k

The corresponding mechanism is:

Review Last Lecture

Michaelis Menten Equation

SKSVrr

MSP max

Bioreactors

4

Nutrient (S) + + Productscells more cells

SS

SCg CK

CCr

max

SKSV

rrM

SP max

Bioreactors

5

Batch Bioreactor

6

Phases of Cell Growth and Division

7

inoculum

t=0 time

8Cells + Substrate More Cells + Product

Bioreactors

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Exponential Growth Phase

Death Phase

Stationary Phase

Lag Phase

0 time

lnCc

a) Phases of bacteria growth:I. Lag II. Exponential III. StationaryIV. Death

b) Monod growth rate law: SS

SCg CK

CCr

max

Bioreactors

VvDLet /0

Bioreactors

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1) Mass Balances

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

dgCCC VrVrCvCv

dtdCV 000

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 ceases11

dgCCC rrCCD

dtdC

)( 1 0

2 dCS

dtD(CS0 CS ) rS

Bioreactors

3) 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

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Bioreactors

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

CPSPCSgS mCYrYrr ''

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3) StoichiometryRate of Substrate Consumption

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

CCSgS mCYrr '

Bioreactors

v0

CS0

V=V0vCC

CS

Volume=V

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1) Mass Balance:

(cells) 0 0 VrrCvdtdCV dgC

C

Bioreactors

(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

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Bioreactors

2) Rate Laws:

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

1.) 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

Polymath Setup

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Bioreactors – Chemostats - CSTRs

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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

max

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

DW

D

CC

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Washout dilution rate

Bioreactors – Chemostats - CSTRs

Maximum Product Flow Rate

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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

DW

DDmaxprod

End of Web Lecture 16End of Class Lecture 25

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