Last time 3/6/08

D=vo / V

Bioreaction Engineering

Wash Out:

1.) Neglect Death Rate and Cell Maintenance

2.) Steady State

Wash Out:

Maximum Production Rate =

Dividing by V

Ý m

VDCC

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

Lecture Thursday 3/11/08

Energy Balance Fundamentals Adiabatic Reactors

User Friendly Equations Relate T and X or Fi

User Friendly Equations Relate T and X or Fi

Last Time 3/6/08

Intro to heat effects

Da

dC

a

cB

a

bA

Q W

s

molFi 0

mol

JEi 0

iF

iE

Rate of energy in by flow

Rate of energy out by flow

Heat added to the system

Work done by the system

Rate of energy accumulation

- -+ =

state)steady (at 0

00

sJsJsJsJ

dt

dEWQEFEF sys

iiii

Assumptions:

mol

mVVPFVPF

W

KEPEUE

iiii

iiii

3

000

~

~~ work flow

shaft work work flow

internal tocompared small energiesother

=0 =0

0

0~~

0~~

00

0000

00000

Siiii

Siiiiii

Siiiiiiii

WQHFHF

WQVPUFVPUF

WVPFVPFQUFUF

0

0

0

000

0000

000

0

0000

Si

iAiiiA

SiAiiAiiA

SiiAiiA

iAi

AiiiAi

WQHa

iXFHHF

WQXHa

iFHFHF

WQHXa

iFHF

XaiFF

FFFF

- Assuming no phase change during reaction

- Assuming constant heat capacity

K mol

J PiC

RPiRii

T

T PiRii TTCTHTHdTCTHTHR

00

Enthalpy of formation at temperature TR

RPiRPiii TTCHTTCHHH 00

0

RPiii

Piii

TTCHaiHai

TTCHH

0

00

Heat of reaction at temperature T

0000

00000

0

SRPiAPiiA

PAPBPCPDP

ABCDX

RPXRXi

WQTTCHXFTTCF

CCa

bC

a

cC

a

dC

HHa

bH

a

cH

a

dH

TTCHTHHai

Example – Adiabatic and no work

0

0

0

P

0

0

00

C neglecting

0 ,0

Pi

X

RPX

Pii

RPXPii

S

C

XHTT

TTCH

TTCX

TTCHXTTC

WQ

FA0 cancels from remaining terms

Usually ΔCP is small compared to other terms

X X

TT

exothermic

endothermic

Example – PFR A ↔ B

1) Mole balance

2) Rate Laws

3) Stoichiometry

4) Energy Balance

0A

A

F

r

dV

dX

TTk

HkkC

TTR

Ekk

k

CCkr

XCCP

C

BAA

11exp 0

11exp

2

0

2

11

XCCXCC ABAA 00 1

Pii

X

C

XHTT

0

0

Pii

X

C

XHTT

0

0

T

XC Adiabatic equilibrium conversion

C

Ceq k

kX

1