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1

Batch Fermentation: System

Batch Fermentation: System

Important variables of the system are

the biolo ical dr mass or cell X,

substrate concentration S and product

concentration P. The reactor volume V.

The growth is assumed to follow X

.

Substrate consumption is related to cell P

.

Product formation is the result of both

-

rates of production.

The la and decline hases of cell

growth are not included in the model. Stirred batch fermenter

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2

Batch Fermentation: Model Mass Balance

Batch Fermentation: Model Mass Balance

=

Mass Balances:

(1)Vrdt

V X = Xrdt

=orFor Cells

dS dS2

dtS Sr

dt=

(3)VrdP

V P = PrdP

=orFor Production

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3

Batch Fermentation: Model Kinetics

Batch Fermentation: Model Kinetics

4=For Cells

Reaction Rate:

5Xrr =

6

SXY /

=

)( SKS

m

+

=

Monod relation (7)

k1 is the non-growth associated coefficient and

k2 is the coefficient associated with growth.

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4Information Flow DiagramInformation Flow Diagram

X0 XBiomassBalance

rX

X

Growth Monod

S0S

S

rate ne cs

Substrate

rSrX

Substrate

Balance

P0 P

rate

Product

rP

Balance

X

rate

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5Batch Fermentation: ProgramBatch Fermentation: Program

As first step in solving the problem with MATLAB is to write the function file.This file will be saved in the folder bin and the name of the file will later be

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6Batch Fermentation: ProgramBatch Fermentation: Program

In this section the ODEs with initial condition values are solved and plottedin diagram.

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7Batch Fermentation: ProgramBatch Fermentation: Program

In this section the kinetic parameters are calculated.

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8Batch Fermentation: ProgramBatch Fermentation: Program

In this section the range values for KS are varied.

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9Batch Fermentation: NomenclatureBatch Fermentation: Nomenclature

Symbol Description Unit

k1,k2 Product formation constants L/h, kg/kg

KS Saturation constant kg/m3

P Product concentration kg/m3

r eac on ra e g m

S Substrate concentration kg/m3

V Reactor volume m3

X Biomass concentration kg/m3

Y Yield coefficient kg/kg

Index Descri tion S mbol Descri tion

1Refers to non-growth associationrate

P Refers to Product

m Refers to maximum X Refers to Biomass

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10Batch Fermentation: ResultsBatch Fermentation: Results

KineticConstants

UM = 0.3;

Plot of X, S and P during the batch growth

KS = 0.1;

K1 = 0.03;

= . ;

Y = 0.8;

ReactionDuration

Tint = 1;

Tfin = 40;

n t a va ues ovariables

X0 = 0.01;

S0 = 10;

P0 = 0;

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11Batch Fermentation: ResultsBatch Fermentation: Results

Plot of vs. S and rX vs. rS