~. COMPUTER SIMULATION OF CONTINUOUS …...f — 12. data set from source #14 162 f - 13. data set...

~. COMPUTER SIMULATION OF CONTINUOUS FERMENTATION OF

Computer Simulation of Continuous Fermentation ofGlucose to Ethanol with the Use of an Expert System

for Parameter Calculations and Applications forBioreactor Control

E b Y

Q Richard Allen Miller

Committee Chairman: william VelanderChemical Engineering

(ABSTRACT)

A derivation of the Michaelis—Menton growth

kinetics model is developed to simulate batch

fermentation of glucose to ethanol using yeast,

§.a;..c.h.ac<.m.y.5«@2. ¢;..e1:.e.>1i.ä„„1„a.e. - T h E S 1 mu 1 a 1 1 ¤ ¤ d E f 1 ¤ e 5the growth rate as. a function of substrate

concentration, cell mass concentration, and product

concentration. The computer simulation also

incorporates a specific growth rate function (as a

function of pH level and temperature) and a

specific death rate function (as a function of the

product concentration). The program uses batch

data to calculate the model parameters and

simulates a continuous fermentation in two

continuous stirred tank reactors in series with a

product separator. A constant value was found to

be sufficient to model the specific death rate and

the product separator did not effect the final cell

mass concentration in the reactors. Two continuous

stirred tank reactors, followed by a smaller

reactor, increases the final cell mass

concentration. The study also proposes a control

scheme for the reactor system.

ACKNOHLEDGEMENTS

This thesis is dedicated to the memory of Dr.

David A. Nallis, whose faith in me made this

possible.

iv ~

TABLE OF CONTENTSABSTRACT 11ACKNOWLEDGEMENTS iv

@h„§TQ.-lE.§..!l p.aq„ee.I. INTRODUCTION 1

Il. LITERATURE REVIEW 3

Historical — 3Biological 3

pH Effect 4Temperature Effect 6Substrate Concentration Effect 9Cell Mass Concentration Effect 10Product Concentration Effect 11

Modeling 12Kinetic Models 12Batch Models 17

Dimensionless Variables 24Physical Significance OfDimensionless Groups 25

Continuous Models (CSTR) 28Dimensionless Variables 31Physical Significance OfDimensionless Groups 31

Typical Parameter Values 34Specific Death Rate Function 35

Fermentation Simulation 37Euler or Tangent Line Method 37Runge - Kutta Method 39

Control Scheme 40

III. METHODS AND MATERIALS 44

Batch Simulation and Data Gathering 44Parameter Calculations 44Data Types 45

Cell Mass Concentration & TimeData 46Cell Mass Concentration,{ Substrate Concentration & TimeData 47

‘ v

Lag Phase 49Active Phase 49Stationary Phase 50Death Phase 51Model Of The Lag Phase 51Maximum Specific Growth Rate 58Growth Yield Coefficient 54Maintenance Coefficient &Specific Death Rate 55Saturation Constant and ~Substrate Inhibition Constant 57

Cell Mass Concentration,Substrate Concentration, Time, &Product Concentration Data 59

Maintenance Coefficient &Specific Death Rate 59pH Level and Temperature Data 61Specific Growth Rate Data 68

IV. REACTIDNS AND REACTDRS 63

Continuous Simulation and Control 63Reactors 64

Continuous Stirred Tank Reactors 64Product Seperator 66Variable Change Simulation 69pH Level Change 69

Reaction Induced pH LevelChanges 74Caustic Flow Induced pH LevelChanges 76pH Change Model 77

Temperature 78Heat Produced 78Heat Removed 79Temperature Change 88

Flow Rates 83Start — Up 86Steady — State 88Control Algorithm 88

· ‘ pH 90Temperature 93Flow Rates 94

Reactor #8 94

V. RESULTS AND DISCUSSION 98

Results 99Data Set #1 99Data Set #8 105Data Set #3 105

vi

Data Set #4 111Data Set #5 111Data Set #6 113Data Set #7 _ 121Data Set #8 121

Discussion 126Parameter Calculations 126Steady - State Flow Streams 128Separator Efficiency 129Control Parameters 130

VI. CONCLUSION 131

VI. RECOMMENDATIONS 132

VII. SUMMARY 134

LITERATURE CITED 135

Fäpps11¤.i.z;- 9.9.92.

A. DERIVATION FROM LEE; POLLARD¤ ANDCOULMAN 139

B. DATA FOR SPECIFIC DEATH RATE FUNCTION 142

C. HYDROXIDE ION CONCENTRATION 143

D. DATA SOURCES 144

E. DATA TYPES 148

F — 1. DATA SET FROM SOURCE #1 151

F - 2. DATA SET FROM SOURCE #2 152





_ F — 7. DATA SET FROM SOURCE #7 157


v i i






F — 14. DATA SET FROM SOURCE #17 BATCH 164I

I DATA SET FROM SOURCE #17 CONTINUOUS 165F — 15. DATA SET FROM SOURCE #18 166


G. TYPICAL VALUES FOR PH AND TEMPERATURE 168

H - 1. LISTING OF PROGRAM "PLUSED" 169

H - 2 LISTING OF PROGRAM “FITTR" 193

VITA 206

viii

LIST OF TABLES

TTTa„¤„l.„@. .na1.

Specific Death Rate Values 35For Varying Ethanol Concentration

2. Model Parameters For F — 1 103 .

3. Flow Streams For F — 1 104

4. Effect Of Varying Product Seperator 106For F - 1

5. Model Parameters For F - 3 110

6. Model Parameters For F — 13 116

7. Flow Streams For F — 13 117

3. Effect Of Varying Product Seperator 113For F - 13

1X

LIST OF FIGURES

$5..;..9.91:.I1.

Embden—Meyerhof Pathway 5

2. Effect of pH level on 7 .cell growth rate

3. Effect of Temperature on 8cell growth rate

4. Batch reactor 19

5. Two Continuous CSTR’s with 29 .Product Separator

6. Curve Plot Of Specific Death 36Rate Data

7. Flow Chart Of Computer — Human 43Interaction

8. Different Phases of Growth 48

9. Exponential character of the 53lag phase

10. 1 / RS versus S plot 67

11. Reactor system 68

12. Product seperator 70

13. Reactor system 72

14. Heat exchange in reactor 81

15. Graph of cell mass concentration 85versus dilution rate

16. Reactor system with operatingE

89parameters

17. Control diagram 91

18 Reactor #2 showing all 95flow streams

x

19 Concentation vs time for F — 1 100

20 Log (x) vs time for F — 1 101

21 Inverse raction rate (1/Rs) 102vs Substrate for F—1


23 Log (x) vs time for F — 3 108N

24 Inverse raction rate (1/Rs) 109vs Substrate for F — 3



27 Inverse raction rate (1/Rs) 115vs Substrate for F - 13

28 Concentation vs time for F - 14 119

29 Log (x) vs time for F - 14 12030 Concentation vs time for F - 17 122



33 Log (x) vs time for F - 18 125

xi

Chapter I

INTRDDUCTION

The aim of this research is to create a computer

simulation of the fermentation of glucose ( sugar

solution ) to fuel ethanol in aqueous solution.

The model will be adaptive for varying feed stocks

(Carbon - 6 or sugar sources) and organisms and

will be applied within the process control schemes.

Fermentation of sugar to ethanol is commonly ’

practiced and considered basic biotechnology.

However the proposed simulation is geared toward

direct application by small industries that must

vary their feed stocks and organisms with respect

to current economic conditions. For example, as

grain prices increase these industries may use

waste candy and / or surplus corn syrup as a

supplement to, or a replacement for, conventional

grain feed stocks. With the changes in the feed

stock and organism type, rate kinetics and product

(ethanol) yield changes will occur.

The model will adjust the operating conditions

with respect to the variability of these

lparameters. The feed stock is fermented in a batch

mode initially for the purpose of estimating

1

E

kinetic parameters. These kinetic parameters are

then employed in a steady state model. Since

continuous culture fermentations are desirable for

industrial production scale, this model will be

useful in predicting the performance and operating

conditions for industrial scale operations.

The adaptive system will also use artificial

intelligence to inform the operator as to how the

changes in feed stock will effect the process

operation (such as residence time, feed rate, etc).

This is the dynamic portion of the adaptive

simulation.

Due to the complex nature of living systems and

the inherent errors associated with modeling such

systems, the application of artificial intelligence

will improve the utility of the process simulation.

This occurs by feeding the batch data into the

simulation package. The model adjusts the kinetic

parameters to fit the batch data and adjust the

reactor variables with respect to the parameter

changes.

The simulation, although designed for modeling

and control of ethanol production, is applicable to

any bioreactor process control. This area is one

of the most active in the biochemical field.1*2*3*“

Chapter II

LITERATURE REVIEH

E - 1 H.1-§;K.Q.13.„.1.Q„6l„.

1 5 ¤ Er h a p S b 11 E m c· 6 1:studied yeast in the literature. Over 103 strains

have been studied. It was first named by Meyen in

1838 to distinguish beer yeast from the yeast used

to ferment grape and apple juice. In 1870 it was

given a morphological description by Reess5. These

studies and descriptions were not based on pure

culture samples. Hansen in the years 1883, 1886,

and 1888 used pure cultures and expanded on the

descriptions of Reess by including the physical

characteristics of the yeast. Because of this work

on pure cultures Hansen is considered the "author

of äggghggpmyces cerevisygg". This authorship

¤ 1 a ¤ E d ä·.a.c.s_!.=.a.¤:.¤;m..¤6.¤...¤5.. s; e..„..r¤...v.1.ä.=L..·;s 1 ¤ 1:hclassof yeast.

E-E B10L..Q§..1„Q.9J-.

Of the four classes of yeast, Qsggmyggggs are

the group characterized by production of sexual

3

4

spores in sacklike ascus.Ö In addition to the

C b C· V C C *1 C V C C 1 Cr 1 C t 1Cdisplaysgrowth characteristics that can be

mathematically modeled. Q. cgggglglgg metabolizes I

food via the Embden-Meyerhof Pathway or EMP (see

figure 1). For each step in the pathway specific

enzymes act upon the substrate to create the

product. This characteristic allows the overall

growth kinetics of Q. cerevisigg to be modeled as

an enzymatic growth kinetics. And as in the case

of enzymes,l Q, gg;g¥;gigg_is very sensitive to its

physical environment. Aspects of the environment

that effect the enzyme activity of Q. ggggglglgg

are the following:

1. pH level

2. Temperature

3. Substrate concentration

4. Cell (enzyme) concentration

5. Product concentration

2.2.1 gg Effect

One physical parameter that effects enzyme

kinetics and hence the kinetics of Q. gerevisiae is

the pH level. Enzymes are proteins, and like all

proteins the concentration of hydrogen ion in their

5

CH;ON

ouHO

OHGlenn!-gnnpnn@|

„w®°® • H,0|·|ATPg®l·l, H,O—®1... Q. -*7, Q.

H . ,G‘i"¢****"‘**‘·¢¤l¤¤ Fruit}-qngnn

ATP/ADP„,...® .2..„.§”.Z„ ·‘

M rn- >«wn

NG,.-, ~A¤· TY. Nm

Mon Coon AT, A0, 0\¢/os®

°""'.'Z.""""" ‘°”'§"" ”"'Z""'T "°"i:.§"'_@”'2$•'Z{•_ ÄOOII NAD° NADII cql NADII NAD°

°° cf0”

E? 0 E? ° 0 EIN

EIZEEE

Figure 1: Embden-Meyerhof Pathway (From StuartJ. Baum, "Introduction to Organic &Biological Chemistry", Third Edition,Macmillan Publishing Co., New York,1982).

6

environment effects their conformation and thereby

their reactivity. The extent of the hydrogen

concentration "alters the degree of ionization of

acidic and basic groups both on the enzyme and on Vthe substrate".7 Extremes in the ion concentration

may even denature (cause a loss in all activity or

destroy) the enzyme. Therefore enzymes are active

within a narrow pH level range. The pH level in

which there is maximum enzymatic activity is the V"optimum pH level" for the enzyme (see figure 2).

Another physical parameter that severely effects

the enzymatic activity of Q. ggggvlglgg is the

temperature. U

2.2.2 [emperature Effect

The temperature of the environment of the enzyme

effects its activity in a manner similar to the

exhibited in most chemical reactions. Increases in

temperature increase the activity of the enzyme

until an "optimum temperature" is reached. Above

this optimum temperature, further increases

inversely effect the reaction (see figure 3). Even

further increases in temperature may denature the

enzymes and cause the cell to die.6 Therefore the

temperature of the environment that favors QL

7

_ Maximum rate

p Reaction2 —

rate

Optimum pH (

s 7 °pi-l

Figure 2: The Effect of pH Level onEnzymatic Reaction Rate (From StuartJ. Baum, "Introduction to Organic &

' Biological Chemistry", Third Edition,Macmillan Publishing Co., New York,1 982 . )

6

Mummmnu

IIIII

RwünIVIIIII I

Ommm IIIß§IIIIII {I

20 4¤ °°‘h¤pnmnCO

Figure 3: The Effect of Temperature onEnzymatic Reaction Rate (From StuartJ. Baum, "Introduction to Organic &Biological Chemistry", Third Edition,Macmillan Publishing Co., New York,1962.)

9

cggevisiag is also within a narrow range. Another

physical parameter that effects the enzyme activity

is the substrate concentration.

3 - 3 - 3 Qu b._.S*= ¤·...¤*= 6. Q9..c;6s11t;.·.é1.t.}.9.:~. Ei.f._6.<;.$.As in several enzymatic reactions, excess

substrate inhibits the reaction. In the Michaelis-

Menton model for enzymatic reactions, the reaction

proceeds as follows:

k 1 ‘E + 6 <======> ES <a.1>

*< — 1

kaES -------> P + E + E (2.2)

The enzyme, E, joins with the substrate, S, and

forms the reactive intermediate ES Through the

reversible reaction 'shown above; where kl and k-l

are the reaction rate constants of the respective

forward and reverse reactions. The reactive

intermediate, ES, proceeds to form the product, P,

and releases the enzyme, E. Again the constant,

kg, is the reaction rate constant for the second

reaction. A fraction of the substrate consumed is

used for cell regeneration and hence forms more

10

enzyme, E. In the presence of excess substrate a

third intermediate is formed as follows:

kaI

ES + S <=======> ESE (2.3)*<—a „

where ESE is the third intermediate and the

constants kg and k-3 are the forward and reverse

reaction rate constants respectively. The third

intermediate, ES2, is not reactive, and therefore_

blocks the production of product and the release of

the enzyme. Since this reaction is reversible the

effect of excessive substrate is reversed as the

substrate concentration decreases. The cell or

enzyme concentration also effects the reaction

rate.

2.2.ä QQLL ggg; LEnsyme) Concentration Qifggg

As illustrated by equations 2.1 & 2.2 the

enzymatic reactions are autocatalytic. Under ideal

situations (no inhibitions and ample substrate) the

cell growth is exponential. However in nature most

cells are inhibited by each other. That is, they

slow or stop their growth when they come in contact~

with another cell. This phenomenon is discussed

11

further in the following sections. The final

growth inhibitor of Q. ggggg;gigg_treated in this

study is the end product concentration.

2.2.5 Product Concentration Qjjggt

The desired end product from an anaerobic

fermentation of glucose by Q. gerevislgg is ethyl

alcohol. However, ethyl alcohol is toxic to the

cells. This creates the dilemma of creating a _

product that inhibits the growth of the cells and

production of more product. At product

concentrations above the critical product

concentration the product kills the cells. The

effects of this and the previously mentioned

physical parameters on the growth kinetics of Q.

ggggglälag can be predicted and mathematically

modeled. -

Although common in nature, Saccharomyggg

gggevisiae is principally associated with the

production of beers and wines. It has been used

since biblical times and continues to be researched

and utilized.

12

E ·3Several models have been proposed for biological

growth. They range from those that incorporate the

chemical potential of the mixturea to those that”

assume Langmuir—Hirshelwood or Hougen—watson

kineticsq. The emphasis of this study is to

develop a model that can be related to measurable

physical properties. The modeling process begins

with the reaction rate or kinetic models. '

2.3.1 Kinetic Qggels

To model a fermentation reaction one starts with

the basic kinetic equations as proposed by Nihtla

and Virkkunen.1o These equations define the

change in the cell mass and substrate

concentrations as followss

gg = Hx — kDx (2.4)- dt

gg = —_1_gx — mx (2.5)dt Vx/s

13

where x is the dry cell mass concentration, s is

the substrate concentrationQ H is the specific cell

growth rate, Yx/S is the growth yield coefficient,

kD is the specific cell death rate coefficient and

m is the maintenance coefficient. The specific 1

growth rate, H, is expressed ideally by the Monod

kinetic model.11

H = __„)3;„s___ (2.6)KS + 5

where Hm is the maximum specific cell growth rate

and KS is the Michaelis - Menton constant or the

half saturation constant. For very small values of

s and very large cell mass concentrations the model

predicts growth rates much higher than

experimental.12 Part of the higher rate prediction

is the inability of the mathematical analysis to

calculate the instantaneous changes predicted by

equation E.#. The analysis requires assuming a

finite time step for the calculations while the

actual growth is continuous. A second problem

arises in the initial assumptions made by the

Michaelis—Menton model. The model assumes that

regardless of the substrate concentration

additional biomass will yield additional

14

production. This assumption fails in living

systems because part of the substrate consumed is

used for maintenance of the cell. Also the

substrate is consumed in units (molecules). A

specific quantity of of substrate may be equivalent F

to one molecule of substrate and only sufficient

for one _cell to consume. Therefore addition cells

will see no units of substrate available for

consumption. However in this example the

maintenance coefficient will compensate and it is

unlikely that the above conditions will arise

because of the inhibitor effects of the product,

ethanol. The latter characteristic of the

Michaelis—Menton model, the assumption of

additional biomass yielding additional production

regardless of substrate concentration, is examined

in the specific growth rate function development.

The effects of ethanol concentration on the cell

growth rate are modeled by Levenspiel’s product

inhibition correction.13 He proposed that product

inhibition can be modeled as:

H = Hm (1 -Q_)“

(2.7)Pm

15

where P is the ethanol product concentration and Pm

is the concentration of ethanol at which cell

growth terminates, and the superscript n indicates

the magnitude of the product inhibition.

Some authors note a non-linear growth

relationship at high cell mass concentrations, 60 -

100 g/1 of yeast1“ and propose a cell inhibition

term15, such as:

H = Hm(1 — _x_) (2.8)*m

where xm is the maximum cell concentration under _

ideal conditions. This nonlinear growth relation

was found in a continuous reaction with cell V

recycle. It is caused by the build up of

nonvolatiles in the growth medium that inhibit the

cell growth.1“ This author excludes the cell mass

inhibition term because current literature on batch

fermentation by Saccharomyces cerevisiae on glucose

shows a maximum biomass concentration of

approximately 10 g/1.16 High substrate

concentration can also be inhibiting.

16

Gutpa, Kushu and Bhatnagar determined that the

optimum substrate (glucose) concentration for Q.

ggggvisigg is two (2) percent.17 To account for

substrate inhibition, the Monod model is augmented

with the terms sa/KSI in the denominator where KSI

is the substrate inhibition constant.1B Hence the

revised model for specific cell growth rate is:

R = (______Rgä_ ____)*(1 — _ß_)“ (2.9)(K5 + s + sg/KS;) Pm

The maximum specific cell growth rate, Rm, is

affected by the temperature and the pH level of the

system.17 Their effect is predicted by the

function:19

Hm )*KPH)

(2.10)

whene RMAXÜpT is the maximum specific cell growth

rate in an ideal temperature and ideal pH level

environment, T is the operating temperature, TÜpT

is the optimum operating temperature, pH is the

operating pH level, pHÜpT is the optimum operating

17

pH level, KT is the temperature constant, and KPH

is the pH constant. I

The rate of product formation, ethanol

production, is stated as:15 _

gg = _;_ gg (2.11)dt Yx/p dt ‘

where Yx/p is the product yield coefficient. The

product yield coefficient is assumed constant

throughout the fermentation. This assumption is

valid over several pH levels for Qgggharomyggä

gg;gvisiae.2O Along with modeling the effects of

the physical environment on the growth, the effect

of the reactor configuration must be modeled. The

configurations used in this study are batch and

continuous.

2.3.2 ßatgg godels T

A material balance for the system is the same as

the material balance for any reactor system . That

is:

18

accumulation = flow in - flow out + generation.

For a batch reactor, the material balance around

the reactor for the cell mass (biocatalyst), Rproduct and substrate (reactant) reduces to:

d(Vx) = Vrx (2.12)dt _

QLVQL = Vrp (2.13)dt

gLVs) = Vrs (2.14)dt

where V is the reactor volume and rs, rp and rx are=

the substrate, product and cell mass reaction rates

(see figure 4). By substitution of equations

(2.4), (2.5) and (2.11) into equations (2.12),

(2.13) and (2.14) one arrives at:

d(Vx) = V(Hx · kgx) (2.15)dt

19

Figure 4: Batch Reactor

20

g(gQL = v(_1__(ux — kDx)) (2.16)dt Vx/P

q(y;g„ = V(_;1_yx — mx) (2.17)dt Vx/s

In a liquid phase batch reactor the volume is

assumed constant, however, because of the

autocatalytic nature of the reaction, this is not

rigorously accurate. Nevertheless with this

assumption the resulting equations are: ‘

dx = Hx — kDx (2.4) °dt °

gg = 1 (Hx — kDx) (2.19)dt Vx/P

gg = —&; - mx (2.5)dt · Vx/6

By Usubstituting ‘equation (2.9) into equations

(2.4), (2.19) and (2.5), one derives :

dx = ( g¤ä_ ____)*(1 — _ß_ )x - kDx (2.19)dt (KS + 5 + sg/K5;) PM

21

QB. = -.1.... (........).*;;:1;.. -;-..>*<1 ·· .E...>>< — mmdt YX/p (KS + S + 52/KSI) PM _ YX/p

(2.20)

Qg_ = -_1___ (______g¤§_ ____)*(1 — _§_)x — mx Vdt Yx/S (KS + 5 + SE/KSI) PM

(2.21)

Note that the exponential, n, applied to the

product inhibition tern is assumed unity from the

above equations onward. This assumption is

balanced by the specific death rate function’sV

strong dependence on the product concentration.

This is discussed in more detail in the Specific

Death Rate Function section of this paper. At this

point is system is indeterminate with two unique

equations ( equations (2.4) and (2.6)) and three

variables (x, s, and P). However the

characteristics of the equations enable value

determination directly from the data ( see Method

And Materials section). The system of equations

also shed light on the physical significance of the

batch fermentation model.

From the equations one may predict the extreme

physical conditions and evaluate whether or not the

predictions correspond to actual experiences. By

22

reviewing equation (2.19) at its limits this

determination is made. A

The rate of cell mass concentration change is

zero (0) in two instances. The first is when the

cell mass concentration is zero and the other when _the specific death rate and the specific growth

rate are equal. The first condition corresponds to

the law of conservation of mass which states that

mass cannot be created or destroyed.E1 The second

condition corresponds to the stationary growth ephase which is characteristic of yeast (see Method

and Materials section). This growth phase occurs

when the substrate becomes the limiting growth

factor. When the limits applied to equation (2.20)

similar results are predicted.

The rate of ethanol production is zero at the

same conditions as the rate of cell mass change.

The first is also because of the law of

conservation of mass. The second corresponds to

the stationary cell growth phase. At the point

when substrate becomes limiting, cell activity is

decreased to conserve energy. Since ethanol is the

end product of substrate consumption, the rate of

ethanol production will reflect this reduction.

The rate of substrate change also reflects these

trends.

23

The rate of substrate consumption, equation

(2.21) also becomes zero at zero cell mass

concentration. The second point where the

substrate rate of substrate change is zero is

where the sum of the specific growth rate divided ·by the growth yield coefficient and the maintenance

coefficient is zero. Since during the stationary

growth phase the cell is still consuming substrate

there should not be a direct correlation. The

maintenance coefficient and the specific growth Qrate are positive numbers and hence there sum can

never be zero. This relates to actual experience

since as long as the cell is alive it must have

nourishment. Another extreme to evaluate is with

respect to the substrate concentration.

The model predicts that as the substrate

concentration approaches zero the specific growth

rate function approaches zero. This is reasonable

since the cell must have substrate in order to

survive. Also as the substrate concentration

approaches infinity the specific growth rate

function approaches zero. This is also a

reasonable prediction due to the inhibitory effect

of the substrate at large substrate concentrations.

To further predict growth characteristics from the

2ß

equations, they are expressed in their

dimensionless form. _

2.3.2.1 Qigggsionless yariables _

To reduce the above equations to dimensionless

variables, the following variables are defined.

Let:

x* = --5-- P* = -E- 5* = -s-VX/S50 • Fn • so

¢+ = tßnnxopr Ks+ = äs KSI+ = üsi— SO 50

wmf = Kg kp* = Lp, m+ = eiixisHMAXOPT • HMAXOPT • HMAXOPT

_ YX/P+ = Euixla5oVx/S

E5

E - 3 - E - EQi..Q.r;9.Q.as

The physical significance of the dimensionless

groups chosen for the batch equations, in some

instances, will also be applicable to the ‘

continuous models’ dimensionless groups. A brief

description of the batch dimensionless group’s

significance follows.

The dimensionless dry celln mass concentration,

xT, indicates the extent of reaction. ·

Specifically, the fraction of dry cell mass

produced if all the substrate present initially was

used for cell growth. For this term a value of one

(1) indicates complete reaction of initial

substrate to cell mass. Since part of the

substrate is used for cell maintenance, xT can only

approach a value of one (1).

The dimensionless product concentration, PT,

indicates the fraction of product in solution. At

PT equal to one (1) the product concentration is

equivalent to the maximum product concentration

allowable for cell growth.

The dimensionless term ,sT, is the fraction of

the substrate remaining in solution or the extent

Eb

of the substrate reaction. A value of zero (O) for

this term signifies complete substrate reaction.

The term t+ is the dimensionless time.,KST, is the dimensionless half saturation

constant. If KST has a value that is greater than Vone - half (1/E) then the initial concentration of

the substrate is less than the concentration need

to achieve the maximum specific growth rate under

batch reactor conditions.

The term KQIT, is the dimensionless substrate.

inhibition constant.

The dimensionless term HMT, is the dimensionless

maximum specific growth rate. This term indicates

the variance of the maximum specific growth rate at

the operating conditions from the maximum specific

growth rate at the optimum temperature and pH

level. RMT equal to one (1) indicates that the

maximum specific growth rate at the current

operating conditions is equivalent to the maximum

specific growth rate at the optimum conditions. A

list of the optimum conditions is found in the

appendix.

The dimensionless term kD+, is the dimensionless

specific death rate. A value of one (1) for this

term signifies the absence of cell growth for the

27

microorganism. Therefore, in practice, this value

is less than one during the growth phases.

The dimensionless maintenance coefficient m+, is

the ratio of the substrate used for cell growth and

the maximum specific growth rate at optimum _

conditions. This ratio is weighted by the cell

growth yield coefficient.

The final dimensionless term for the batch

system, Yx/p+, is the dimensionless product yield

coefficient. This term represents the ratio of the _cell mass concentration at the maximum product

concentration and the fictitious cell mass

concentration if all of the initial substrate were

used for cell growth.

After substitution of the dimensionless terms

into the batch equations, the resulting

dimensionless equations are: '

ggf = (________g„jgj _____)*(1 — P+>x+ — kD+X+dt* (xgf +

5+(2.22)

ggf gmfsf _____>»(1 - P+>x+ — ggjgfgtf vx/pf (xgf + 5+„(2.23)

28

dt* (KS* + 5* + 5*E/KSI*)(2.24)

E - 3 -3For continuous operations, the rate equations

are similar . Steady state conditions are assumed.

Performing a material balance around the reactor

yields the following:

g(!xl_ = Foxo — Fx + Vrx (2.25) ·dt

Ad(VsL = Foso — Fs + Vrg (2.26)dt ·

d(VP) = FOPO — FP + Vrp (2.27)dt

where Fo and F are the volumetric flow rates and

the subscript 0 signifies the initial or inlet

conditions (see figure 5). Substituting equation

(2.9) into equations (2.25), (2.26) and (2.27) in a

method similar to Lee, Pollard and Coulman with a

slight derivation (see Appendix A)15 yields:

E9

Figure 5: Two Continuous Stirred Tank Reactorswith Product Separator

30

X = ÄQ + so — s — gg (2.22)Y..x-1.S.................bus( __l__ + m„_ )

Vx/s Vx/s

P = Yx/p(>< * MO) + PO (E.E‘?)

D = .....t£¤.€;l.-.-..;E’LE1e1.2.„>.&- .... · .!s„¤.>1(x — xO)(KS + s + sg/KS;) (x - xo)

(2.30)

where D, the dilution rate, is F/V.

Note the use of .two CSTR’s in series yielded

predicted improvements in productivity over a

single CSTR by #0 to 50 percent15. Therefore two

CST2’s in series will be used in this study.

31

E-3-3·1 Qimsmäigmlesä Maxiaglgs

To express the continuous equations in their

dimensionless form the following variables are

defined.

Let:

*0+ = ..i0-- P0+ = Bo Vt = V1 T V2Vx/S50 pn

V1+ = V; D+ = ..E.- D = E DT = ..9--V: VVMAXOPT V Pnnxopr

2.3.3.2 Physical Significance Qj QimgnsioolggäGrougs

The physical significance of the dimensionless

terms for the continuous system are discussed

below. As stated previously, some of the terms

from the batch dimensionless terms such as, KST,

KSIT, YX/p+, Rm+, s+, m+, PT, and kD+ are used inthe continuous dimensionless equations. These

terms are not defined again in the following

section.

32

The dimensionless term x0+, is the dimensionless

initial cell mass concentration. It represents the

ratio of the initial cell mass concentration and

the fictitious cell mass concentration if all the

substrate were used for cell growth.

The dimensionless initial product concentration,

PDT, varies from zero (O) to one (1) where zero (O)

is the condition where no product is in the feed

stream and one (1) is the situation where the

initial product concentration is that of the

maximum product concentration obtainable through

fermentation.

The dimensionless volume for reactor #1 VIT,

represents the fraction of the total volume of the

reacting system present in reactor #1. A similar

term for the reactor volume fraction for reactor #2

is not listed but is defined and calculated

similarly. -

The term DT, is the dimensionless dilution rate.

This term, under stable steady — state conditions,

is less than one (1). It represents the ratio of

the dilution of the system and the maximum dilution

rate at optimum pH level and temperature. Y

e° Therefore, after making the proper

substitutions, the resulting equations are:

33

¤+ = .aaI.....:---ll„;all.... (2.31)<-l- · -m:.lVx/s Vx/s

P+ = ll.;laIl · .aIaI. — llagiai + P„*YX/P+ Yx1P+D+ Vx/P+D+

(2.32)

¤+(x+- x°+)(KS+ + 5+ + s+E/KSI+)

(X(2.33)

E-3-# lxglgallßaaamglga Malaga ·

The simulation will initially plot growth,

product and consumption rate curves for a batch

fermentation using äagcharomgcgg ggrevisiae on a

defined medium with glucose as the principle carbon

50 LI T C E •

{he optimum pH and temperature for äagghaggmvggä

gerevisiag growing on glucose are 6.0 and 30°C

respectively17*19. Hence the typical values for

equation (2.10) are 6.0 and 30°C for the

corresponding values of pHÜpT and TÜPT.

34

A typical value for the theoretical ethanol

yield ( with respect to substrate) Yp/S is 0.51 g-

P/g—sEE. A typical maximum specific growth rate is

the average of the values reported by Mehaie and

Lee. This is .23 hr'1. 'Similarly for the substrate saturation constant,

KS, and the maximum product concentration, PM,

values reported by Lee15 are used. These values are

1.6 g/l and 90 g/1 respectively.

2.3.4.1 Qgecific Qggtu Rugg function ‘

The specific death rate function, kD, is derived

using a modified Arrhenius equationaa.

kD = T{gB + exp(Q§ - 6H)} (2.34)h R RT

where T is the temperature in absolute Kelvin, 65

is the change in entropy, 6H is the change in

enthalpy, kB is the Bo1tzmann’s constant, R is the

gas constant, and h is Plank’s constant. Using the

data presented by 5a—CorreiaE“ a curve fit for kD

at 30°C (303K) is generated for the variance of

ethanol concentration (see Table 1). Curve fitting

yields the equation (see figure 6):

35

TABLE 1

SPECIFIC DEATH RATE VALUESFOR VARYING ETHANDL CONCENTRATIDN _

„..„.!5p...!‘.„...l.9.Z.L§L°.!<.!S.ÜÄ.}-.?..„.ÜÜ.3 ..S..25 n..Y.!.Y)...€.§_|1é.¥1Ql·.,.ii-.-hp-..S„h.!;:}..2„. .P...Q.!.lÄ-...i.

ÄÖÄf].'.“..._...«;·.<29._....;.-„-_..;z„£<.i§iÄZ»i§ÄÄ1Ä§§Ä___._._.„..l9.9_„-..__i......„.l.é»......._......i.._...l..L..-...l„...9.L.L3...--....i A.................„.‘§._.......l.......l.£+.......S2s..Ll.„-L.L.._.„.....„.lQ....„i.....l.9..„_..._..„L.......L...L..Q:.$@„--§-„.__-__.„_.._.__..Q_.......L.„.....„.B.Z..i_€?e.‘€[email protected]§.

* Data form Sa-Correiaag* Assumes constant density of media in reaction

tank is 1 g/1

36

GRAPH OF kD VERSUS PRDDUCT CONCENTRATION

2220181614

kp <m-*1) 12SPECIFIC 10 '

DEATH 2RATE64 · ‘

2'

0.06 0.08 0.1 «3_1;= 0.14

P (Q / 1) ETHANÜL CÜNCENTRATIÜN

Figure 6: Plot of Specific Death Rate versusProduct Concentration

37

RD = P4·“9exp(11.59) <2.as>

The constant in the specific death rate function,

exp(11.59) is used as a starting point value forV

the parameter calculation.

2.4 EERMENTATION QLMULATIQQ

The final form of the kinetic rate equations

prohibit solution by analytical means. Therefore

two methods are used to numerically integrate the

equations. The first method, Runge—Kutta with the

Kline predictor corrector algorithm is the

preferred method of the author and will be compared

with the Euler method. ‘

2.4.1 Euler gg Tangent Line Method

The Euler Method is one of the simplest

numerical integration methods for solving initial

value problems. This method solves the initial

value problem in the form:

38

y = f(x,y), y(xO) = Yo (2.36)

Because the initial values are known the slope of

the tangent line at the initialconditions,=

f(x°,yO), is known25. By assuming a uniform step

size, h, between points the following values for x

and y can be predicted by:

and

yn+1 = yn + hf(xn,yn)(xn+1 - xn) (2.39)

= ojlla •••

The Euler method of numerical integration is

accurate only for very small values of h E9. And at

these small values the computer time required for

compilation is relatively long. However as a test

of the accuracy of the initial computer simulations

this method should be sufficient.

39

E - 4 · E R.m.0_Qs. !r;.g..§.$„a P!e5.b.¤.1.<;!.

A more accurate and quick method for numerical

integration is the Runge—Kutta method. This method

is based of the use of a Taylor expansion of the ·derivative and evaluation of the function on

intervals of the independent variable27.

Specifically, the forth—order Runge—Kutta method of

numerical integration is used. In this method as

in the Euler method the initial value of the

function; f(xO,yO), is known. A rigorous

definition of the theoretical basis of the Runge-

Kutta method is presented by Jenson and Jeffreys

and is so referenced for the reader E8. In summary

the function will be evaluated as:

xn+l = xn + h (2.37)

and

_ yn+l = yn + _l_(kl + 2kg + 2k3 + kq) (2.40)6

where

kl = hf(xn;Yn) (2.äl)

40

ka = hf(xn + _I_h,yn + _l_k1) (2.42)2 2

kg = hf(xn + _l_h,yn + _I_ka) (2.43)2 2

kg = hf(xn + h,yn + kg) y (2.44)

and as in the Euler method, h, is the step size.

Certain problems arise in using either the Euler

method or Runge—Kutta method when the step size, h,

is too large. To alleviate these problem the step

size will be reduced by 50 percent each time the

change in the slope is greater than, say five

percent for a given iteration. Previous experience

with fermentation simulation proves that this will

be an effective method for this type of

simulationaa.

2.5 QQQIROL SCHEME

The IBM PC (or industrial compatible) is used to

record manually inputted data from a batch reactor

and use this data with typical and calculated model

values to control a simulation of a series of

continuous stirred tank reactors. The system uses

an updating software program that incorporates

42

the flow chart shows the divisions of the problem

statement (see figure 7).

43

f___———%Ä BEGIN Ä

DATA ADATA

ANALYSIS “FITTR“

HARD ÜUTPUT GRTIURESULTSEND

·INTERACTIUE SYSTEM

Figure 7: Flow Chart of Computer — HumanInteraction

Chapter III

!E.I.!;LQ!‘ä (MQ !f!.9l§.B.L€•..!„.‘-ä

3 · 1 BMP. QBTIB. G.B.I!:LEB.l.N§. V

In this portion of the process the computer

generates a growth curve based on manually inputted

batch data. From this data a prediction of the

optimum operating conditions for a continuous

fermentation in two continuous stirred tank

reactors is computed. This represents an ideal

bioreactor fermentation. The program performs an

analysis of the data to predict continuous

fermentation operating parameters. To perform the

data analysis the system will manipulate the data

to "back out" the actual fermentation parameters.

3.1.1 Parameter Qglculations

The data analysis is not a strict data

regression. The program creates a growth curve

based on the actual data. Since portions of this

44

#5

curve represent particular growth phenomena, those

values are "picked" directly from the plot.

The flexibility of the software is demonstrated

by the choices of data types the user must provide. U

Increasing the data types and points increases the

accuracy of the model parameter calculations.

3 · 1 - 3 Q„9.Lä..LuE.s

As stated previously the environmental factors.

the effect the growth kinetics of the fermentation

reaction are:

1. pH Level

E. Temperature

3. Substrate Concentration

#. Cell Mass (enzyme) Concentration

5. Product Concentration.

These are the data types requested by the program

to be chosen by the user. The equations employed

that relate to each combination of data types

chosen are discussed in the following sections.

The "Specific Growth Rate" and "Time" are also

listed as data choices. The simulation allows the

#6

user to input any combination of the data types

however, it is required that "Time" and "Cell Mass

Concentration" are chosen. Unless the "Product

Concentration" and "Substrate Concentration" are

among the data types chosen, the model will only Wcalculate the parameters for a batch reactor and no

continuous simulation with control data will be

calculated. Beginning with the minimum data types

required and hence the simplest of the simulations, .

the steps for the data analysis follows.

3 - 1 - 3 - 1 .§.sl.L Use.; §.m<;„ é lies 1Z?s.1=.;

with the minimum number of the data types, the

"Cell Mass Concentration" and "Time", the software

analyzes the data and returns the parameters for

the basic Monod model,"

_ Q; = Hx — kgx (2.#)dt

where H - kg is treated as a constant, HOVERALL.

This is not an accurate model but will give the1

user with limited data the ability to plot his /

her data and receive a crude model. For the data

Q7

types of "Time", "Substrate Concentration" and

"Cell Mass Concentration" the simulation uses a

more rigorous model.

3 - 1 - E - 3 ’i§.q.m..;.e1*•4=.c.a.t.i.9..¤ ä Tim; Data.

when given "Cell Mass Concentration", "Substrate

Concentration" and "Time" data the simulation

calculates the parameters for the specific growth

rate, specific death rate and maintenance

coefficient. These calculations are performed by

reviewing the data and locating the periods of the

data that represent the lag growth phase, active

(or logarithmic) growth phase, stationary phase and

death phase (see figure B). The system uses a

portion of the model to find when significant

changes in the growth rate occur and records the

location. At this point a review of the growth

curve and its significant portions is required

beginning with the lag growth phase.

#8

Maximum stationary phaaa

3 u' Pu. Daanh phasPlum of axponaiuial mum

I

3Tlma ——•

Figure 8: Microbial Growth Phases (From James E.Bailey and David F. Ollisa"Biochemical EngineeringFundamentals", Second Edition, McGraw-Hill Book Company, New York, 1986).

49

3 - 1 - E - E -

1Thelag growth phase is found by locating where

the initial growth rate changes to a higher rate.

Specifically, it is found by using the left side of

the equation (2.19):

dx = ( gus _;__)*(1 — _ß_ )x — kDx (2.19)dt (K5 + 5 + sa/K5!) PM

in the form of:

........1 91.2; = ci!.-;>g..<...>s.)- <3 - 1 >x dt dt

and analyzing where the initial change in value is

greater than sixty (60) percent. At this point the

lag phase has terminated and the active growth

phase begins.

3.1.2.2.2 Active Phase

As in the analysis for the lag phase, the system

uses the left side of equation number (2.19) to

review the data. In this instance, however, the

50

program checks for a change of sixty percent in the

negative direction (a sixty percent decrease in the

slope). This point signifies the end of the active

growth phase and the beginning of the stationary

growth phase. _

3- 1 -E-E-3 f5„.ta.1=1.¤..¤a.¤f.x E!!:•.a.s.s

After locating the active growth phase the

system reviews each point of the remaining cell Qmass concentration data to assess when the

stationary growth phase is completed. Unlike the

previous phases, the program is searching for the

point where the cell mass concentration drops

considerably. If this does not occur it is assumed

that the data received covers only the first three

phases ofi growth and the parameters are calculated

accordingly. Data past this phase are not required

for operation and are not weighted heavily in the

parameter calculations. If the cell mass

concentration drops significantly, this point is

recorded as the end of the stationary phase and the

beginning of the death phase.

51

3 - 1 - E - E -

‘+Thedeath phase, the final phase, is assumed to

last from the end of the stationary phase

throughout the remaining cell mass concentration _

data points. However, during the death phase there

can be considerable cell lysis which may provided

nutrients for the remaining cells and create

misleading data. The left side of equation number

(2.19) is used to review the data. In this ~instance when a positive change in the death

greater than sixty percent is encountered it is

assumed that the death phase has ended. The_

remaining data are not used for any parameter

calculations.

Although other authors have suggested fifth and

sixth growth phases, a second active growth phase

during which the substrate is limiting and a lag

phase preceding itao, this author feels the model

will perform within the accuracy of the data.

3.1.2.2.5 Model Qi [gg ggg Rgggg

Since this phase is not modeled by the Monod

equation a simple curve fit of these data is

52

performed. Although this is not the active phase,

this growth phase is exponential (see figure 9).

Therefore it will be modeled based on the

following assumptions:

1. The length of the lag phase in not dependent

on the size of the inoculum.

2. During the lag phase there an abundance of

substrate.

3. The lag phase is not substrate inhibited. _

4. During the lag phase there is not sufficient

product to cause any inhibiting effects.

5. The lag phase can be modeled as a function of

time only._

AHence the lag phase is modeled in a manner similar

to the method for a system with only two data types

(see Cell Mass & Time Data).

3.1.2.2.6 Maximum Qggcific Qgggtg ßgjg

The system begins its parameter calculations

with the calculation of the maximum specific growth

rate. Again the program uses the left side of

equation number (2.19) to search for the largest

53

LOS ( CELLHASSCDNCENTRATION)

”L

LAG GROWTH PHASE _

ß Z

LTIME ——>

Figure 9: Exponential Character of the Lag' Growth Phase

5#

growth rate, dLog(x)/dt, within the active growth

phase of the data set. This value is recorded as

the maximum specific growth rate, HM, for the

organism. With this parameter calculated the

program proceeds to calculate the growth yield 'coefficient. _

' 3 - 1 - 3 - 3 - 7 1..;...1•;·.:•_.ä

The growth yield coefficient is calculatedby'

summing (the ratio of the cell mass concentration

over the substrate concentration) from the active

growth phase data through the stationary growth

phase data and averaging the calculated value. In

practice this value is not constant due to the

utilization of substrate for growth and maintenance

of the cell. By including a separate maintenance

coefficient in the kinetic model, the inaccuracies

encountered by averaging the growth yield

coefficient are diminished. Next another constant,

the maintenance coefficient is calculated.

55

3 - 1 - E - E -9For

the data choices of Cell Mass Concentration,

Substrate Concentration, and Time there is no data

on the product concentration given. Therefore itR

is assumed that no product of interest is formed.

In this instance the growth rate equation becomes:

dx = ( En§_ ____)*x — kDx (3.2)dt u<S + 5 + ·§E”1•<SI> ‘

Similarly the equation for substrate consumption

is:

dä = —_1__( Ens ____)*x — mx (3.3)dt YX/5 (KS + S + 5 /KSI)

To solve for the maintenance coefficient and

specific death rate function, a few assumptions are

made.

1. Unlike the function definition for the specific

death rate stated previously, in the absence of

56

product data the specific death rate isassumed constant throughout the fermentation.

E. The maintenance coefficient is a constant.3. During the stationary growth phase the specific

growth rate and the specific death rate areequal.

With the above assumptions the steps for the

calculation of the maintenance coefficient and the

specific death rate constant are as follows.

1. Assume a constant value for the maintenance

coefficient. m.

E. Calculate an average value for the specific

growth rate over the active growth phase using

the relation:

m + _1_gä = ‘HAVG (3.4)x dt

3. Using the average specific growth rate,

calculate the specific death rate constant over

the active growth phase using the relation:

•}·lAVG 'kD (3.5)x dt

57

4. Using equation number (3.4), calculate the

average specific growth rate over the

stationary phase of the growth curve.

5. Compare the value of the specific growth rate Vover the stationary phase of the growth curve

to the calculated value of the specific death

rate constant.

6. If the values correspond within a specified

tolerance then proceed, if not record the

values, increment the current value of the

maintenance coefficient and return to step

number 2.

Once the values for the maintenance coefficient

and the specific death rate are calculated, the

program addresses the constants lumped within the

specific growth rate, the saturation constant and

the substrate inhibition constant.

3.1.2.2.9 Saturatggg_Qggstant ggg QgggjggggInhibitiqg Qpnstant

The saturation and substrate inhibition

— constants are contained within the specific growth

rate function. The saturation constant is

58

calculated first. This is accomplished by assuming

that the specific growth rate can be modeled by the

simplest form of the Monod equation. That is:

H = _gms__ l(2.6) ”

KS+s

The saturation constant is solved by rearranging

equation number (2.6) and using equation (3.4) to

calculate a specific growth rate. The saturation

constant is calculated at each point along thel

active growth phase and averaged. To calculate the

substrate inhibition constant, equation number

(2.6) is again used, however it is augmented with

the substrate inhibition terms, sa/KS}, to form:

H = ______gms_ _____ (3.6)KS + s_+ sg/KS;

Because the substrate inhibition terms contains a

term raised to a power it can exhibit a large

effect over the entire growth curve. Equation

(3.6) is solved for K5} and the data from the

active phase through the death phase are used in

the manner stated above in calculating KS to

calculate KS;. Calculations similar to those above

59

are used when "Cell Mass Concentration", "Substrate

Concentration", "Time", and "Product Concentration"

data are given.

3 · 1 - 3 - 3 @$..1-1. §g.l;.s.t=.:.a.t„a. °‘

when the "Cell Mass Concentration", "Substrate

Concentration", "Time", and "Product Concentration"

data are given a more rigorous model is obtained. °

The values for the maximum specific growth rate,

saturation constant and substrate inhibition

constants are calculated in the same manner as in

the preceding section. The changes occur in the

calculation of the specific death rate, maintenance

coefficient, and the product and growth yields.

3.1.2.3.1 Mainteqgggg Coefficlggg Q Sgggljlg QeatgBa}.;

In this mode, the assumption that the specific

death rate is constant is not taken. It is assumed

that the specific death rate can be modeled by the

equation:

60

kDAlso,the full growth rate equations are used (see

Literature Review). As in the previous section,

the values for these parameters are solved using an '

iterative process. In this instance, the value for

kD is assumed according to equation (2.35).

However by solving equations number (2.19) and

(2.20) for the specific death rate, it is found

that the left side of the equations, the side ‘

opposite the specific death rate, differs in value

by only the pseudostoichiometric constant YX/p.

The value for Yx/p is found in the manner stated

above, so the value of the specific death rate

constant is varied and calculated over the active

growth phase until equations (2.19) and (2.20) are

equal within a specified tolerance.

After solving lfor the specific death rate

function, the maintenance coefficient is

calculated. Once more an initial value of one (1)

is assumed for the maintenance coefficient and the

program iterates until equation (2.21) is equal to

equations (2.19) and (2.20) within the tolerance.

The value for the product inhibition term is

calculated similarly. Equation (2.19) is solved

61

for PM by using the average values of the

variables, calculated over the active and

stationary growth phases.

Several secondary checks are performed on the

parameters to fine tune the model. A different set _

of equations are used when "pH level" or

"Temperature" data are entered.

3.1.2.A gg ggggl ggg_Temgerature Qgta

Nhen pH level and / or temperature data are

given, the system calculates the parameters for the

equations

Hm’(2.10)

Based on the organism type entered by the user, an

optimum temperature and pH are assigned to the data

( see Appendix G for values). The maximum specific

growth rate under operating conditions, optimum

temperature constant, and optimum pH level constant

values are calculated from the active growth phase

of the growth curve. If no pH or temperature data

62

are given the program assumes that the data were

obtained from a batch fermentation that operated at

the optimum temperature and / or pH. Another data

type that invokes equation (2.10) for parameter

calculations is the specific growth rate data. Q

3 - 1 · 3 · 5 §2„¢.=L;.i.f..L$. §J:..@3=.-*.1 B..é$..s Q.a.i=.s.

With these data the system calculates the

parameters in a manner similar to those in the

previous sections. Values for the maximum specific

growth rate and the saturation constant are picked

directly from the data. Depending on the

additional data supplied, the remaining parameters

are calculated in one the fashions mentioned

previously.'

Using basic chemical engineering reactor design

techniques, the program will predict the optimum

operating conditions for the continuous reactor

configuration based on the batch data.

Chapter IV

B„§.£•..Q.I.I„Q„¥!.§ BER R§!iQfLQB.ä

‘*· 1 Q.Q.UlLN.Q.Q!.S. §„.L!i1LJ.1„..€•.I.LQ!! &!§!.Q Q,QHlBQ.L

After completion of the batch analysis of the

data, the user will direct the program to enter the

continuous mode of operation. In this phase the

computer will simulate a start up the fermentation

and bring it to the optimum phases predicted by the“

batch data. The system will then adjust the set

points (pH, flow rate, feed rate, etc) and

calculate the reaction rate. with the goal at

achieving the maximum product yield and growth

rate, with growth rate being the principal goal,

the system will search in a systematic manner for

the corresponding set points. When one optimum

point is found, say for the pH, the computer

program will choose another variable and search for

the optimum. At all times during the search the

program maintains a limited controlled (oscillating

within the critical control region) process. The

program will cease to search when movement from the

set points show no improvement in the growth rate

or yield. At this point the program will control

63

64

the fermentation simulation until the feed is

diminished. Possible interest will be the effect

of a rapid change in the feed concentrations on a

"controlled" fermentation. One begins with the _

simulation of the reactor system.

‘•· E B.§.¢ä.QLQ.F$.‘§. ·

The reactor system consist of two continuous

stirred tank reactors (CSTR’s) in series separated

by a product separator. Based on observations by

Lee, Pollard and Coulman the CSTR’s are of unequal

size with the larger CSTR preceding the smaller

CSTR.15 In this arrangement the maximum

productivity of ethanol can be obtained, where

productivity (DP) is the dilution rate times the

product concentration.

4.2.1 Qpntinuous Btirred Tank Reactors

Based on the batch data the program calculates

the space — time for each of the CSTR’s. This is

65

accomplished by using basic reactor design

principles. Beginning with equation (2.5), one

has:

Q; = —_l_ Mx — mx (2.5) V

dt Vx/6

By setting the right side of the equation equal to

RS one obtains:

_ Q; = R5 (#.1)dt

where R5 is — Mx — mx. By plotting — _; versusVx/s Rs

S and integrating to find the rectangular area

bounded by the curve and the horizontal axis, the

space - times for the CSTR’s are calculated. The

space — time for the first larger reactor is the

rectangular area bounded by the initial substrate

concentration, substrate concentration at the

maximum specific growth rate, the horizontal axis

and the inverse rate curve. The second reactor

space — time is bounded by the first reactor’s

66

space — time on the right and the substrate

concentration at which the death phase begins on

the left. The vertical boundaries for the

rectangle are the horizontal axis and the inverse

rate curve (see figure 10). The other vessel r

simulated is the product separator.

‘•- 1 - E P..v;¤..¤1.u.<;.$. §;·.2.a..¤:.«2.t2.v;

A product separator is located between the

reactors (see figure 11). The user must specify

the efficiency of the separator or a value of

.thirty percent is assumed. Since the kinetic

equations for the continuous reactor systems are

not coupled (see Literature Review), a simple mass

balance models the separator. Also, the initial

batch model used to- calculate the reactor space —

time assumes no product separation, hence no

changes in the space - times are necessary. The

volume of the separator is assumed negligible. The

mass balance for the separator is:

P1 = FE + E (#.2)

where P1 is the outlet stream from reactor #1, FE

67

rs -

0.1 0.5 0.99

l 3

Figure 10: Inverse of the Substrate ReactionRate (1 / RS) versus the SubstrateConcentration (S). _

68

P1 P2F1

E

Figure 11: Fermentation Reaction System

69

is the feed stream to reactor #2 and E is the

separated stream of pure product leaving the

separator (see Figure 12). The separator is

assumed an ideal separator and only product is

separated. The quantities P1, F2, and E have the Uunits of liters per hour. within each reactor,

changes in the physical environment are occurring

during the fermentation. One physical parameter

undergoing such changes is the pH level.

# · 2 YBEÄIAE.-.2 Q.!vß1.~J§.§. $.1 !‘1.U.....!-.6.IAJ.N.

#-2-1 ab gsxal Qhange

During the fermentation the pH level is changed

by the reaction products. The mechanism of this

change is discussed below. It is assumed that

during the fermentation procedures, both batch and

continuous, the pH level is controlled by the

addition of buffers. In the batch fermentation

scheme, the buffers are supplied in the initial

broth at a level that maintains a set pH level

throughout the fermentation. In the continuous

fermentation scheme, buffers are constantly added

to the system via the feed stream. To simulate

70

Figure 12: Product Separator

71

changes in the pH level and test the controlling

aspect of the system, a model of a uncontrolled pH

system is simulated (see figure 13).I

The system is based on the following assumptions:

1. All of the substrate (glucose) consumed is

converted to ethanol and carbon dioxide by the

reaction:

CÖHIEOÖ Egäxnää ECaH5OH + ECOE + Energy

(4.3)

E. Only CO2 in solution effects the pH level of

the solution.

3. Buffer is added in the feed stream until

reactor #1 is eighty (B0) percent full.

4. The buffer in the reactors is sufficient to

maintain a constant pH level for one space -

time. That is fresh media without buffer

completely replaces the buffered media after the

time period required to fill the reactors a

second time.

72

CAUSTI CTANK

REACTOR#2

ISEPARATOR

REACTOR# l '

”Figure 13: Reactor System

73

5. The reactor pressure is atmospheric.

6. The addition of C02 into the reactors can be

modeled as a function of the ethanol produced.

7. Mass transfer effects are negligible based on

the assumption of ideal CSTR’s. _8. The maximum acidic pH level obtainable is that

of carbonated water, pH 3.7

The pH level change is caused by the reversible

reaction:

002 + H20 <=====> HECÜB _<=====> HT + HC02

(4.4)

The latter half of the reaction equation:

HECÜQ <=====> HT + HC02' (4.5)

at 2B° C has an equilibrium constant, KEQ, of 2.5 x10"“

mol / liter.15

In the first half of the reaction:

74

*<1HECÜ3 <=====> CO2 + H20 (#.6)

*<-1

at 25° C, the forward reaction has a reaction V

constant of 20s’1, while the reverse reaction has

a constant of 0.03 s'1·

Therefore the first half of the reaction in

equation number (4.4) is the slow step in the

reaction. Using the above assumptions, the pH °

level change caused by the fermentation is modeled

below.

4 · E - 1 · 1 B„s.é.s.t..L9.!.•. .1„nd.¤1s..s..d. ad l„„sy.s_L Ql;.;1•.9s.·ä

For the model, assume .03 / 20 or .15 percent of

the carbon dioxide in solution becomes carbonic

acid. And of the carbonic acid in solution10'“

moles are in the form of H+ ions. From Bailey and

Dllis, and Atkins the Henry’s constant for CDE at

moderate temperatures in water is in the order of

10°5 mol per liter/mmHg.15*29 Therefore assume that

at 1 atmosphere pressure, 10°3 mol of CO2 produced

75

remains in solution while l mol evolves as overhead

vapor.

The relationship between the ethanol production

rate and the rate of addition of H+ ions into

solution is:

g[H+l = gg *(1O‘3)*(1O‘“)*(.O015) (#.7)dt dt

= KHg‘I_f'_ (#.8)dt

where KH = 1.5 x 1O“1O. By solving the

differential with the initial boundary conditions:

at P = Po, [H+] = [H+o] = 1O“pHo, where PD is the

initial product concentration, [H+OJ is the initial

H+ ion concentration and pH° is the initial pH

level of the solution, the resulting relation is:

EH+] = 1O'pH° + KH(P-PO) (#.9)

Initial, in this instance, corresponds to the

— time and conditions present in the reaction system

at the initiation of the variable change simulation

76

(see Start - Up section). To balance the pH level

changes caused by fermentation, the addition of

caustic into the reactor is modeled.

Qsgsiis Elsa Lodges; ab gsxsl.Qngn9es

To counter the change in pH level caused by the

reaction, a 0.1 M ammonium hydroxide solution is

added to the broth. In the model for this addition

the only variable is the volumetric flow rate of

the ammonium hydroxide to the reactor. For each

liter of ammonium hydroxide solution added to the

reactor, 1.3 x 10'3 mol of hydroxide ions are added _

(see Appendix C for calculations). The resulting

relation is:

[OH'] (4.10)Vs0L~

where VSÜLN is the volume of the reacting solution

in liters, VBASE is the volumetric flow rate of the

ammonium hydroxide solution in liter / hr, and EOHT

J is the concentration of the hydroxide ions in the

77

reaction solution. The pH level change model uses

both of the above change aspects.

#-2-1-3 ad Qbsmgs Mage;

The change in pH level is modeled by combining

the effects of the reaction and addition of caustic

into the system. The assumption made here is that

for the addition of each mole of hydroxide ion, one

hydrogen ion is reduced to produce water. The

result of the combination of equations number (4.9)

and number (4.10) yieldsz

cH+1 = 1o·¤HO + xH(P — PO) — [OH'] (4.11)

Hence, by applying the definition of pH as the

negative of the log of the hydrogen ions

concentration yields for pH:

pH = 1og[(10“PHO + KH(P — Po) — VBAgE*1.§*10'3)'1]Vsopu

(4.12)

78

By applying the above techniques to the

temperature, a similar model is developed.

4.2.2 Tgmggrature

A heat balance around the reactor is performed

to model the temperature changes during a

fermentation reaction . The reactor is assumed

adiabatic and the remaining components, the heat

produced and heat removed are separated and

modeled. Beginning with the heat produced the

model is developed as follows.

4.2.2.1 ßeat ßggduced

To simulate the heat generated during the

fermentation, the assumption of the reaction of the

substrate proceeding as in equation number (4.3) is

made; The energy released during this reaction,

with the substrate in an aqueous state, is 56000

Btu / (lbmole sugar) or 30000 cal / (mol sugar).3O

This equates to approximately 340 cal / (g ethanol

produced). It is the aim of this treatment to

79

* relate the heat produced to the product.

Therefore:

QPRÜDUCED = 34O6P*VS0LN (4.13)

where 6P is the positive change in product

concentration, VSOLN is the active volume of the

reactor (volume of the reaction medium), and

QPRÜDUCED is expressed in the units cal / hr. The

positive nature of the energy terms indicate that

this heat is being added to the system. The

removal of heat from the system is model below.

4.2.2.2 Heat Bgmgved

To model the heat removed from the reactor the

following assumptions are made:

1. 'The heat can be removed directly from the

reactor. Heat transfer is assumed to occur

instantaneously.

2. All of the fluid in the tank is at the same

temperature at all times. This is based on the

ideal CSTR assumption.

B0

For simplicity, the only model variable is the

cooling fluid’s flow rate (see figure 14). The

cooling fluid is water entering at 500 F and

exiting at 700 F. This leaves an approach W

temperature of 200 F to the typical optimum reactor

temperature of 900 F (see Appendix G). The heat

capacity of water is assumed constant at 1 Btu /

(lbm*0F). The heat removed is the product of the

mass flow rate of the cooling, heat capacity of the -cooling fluid and the temperature change of the

cooling fluid. Which in equation form is:

QREMOVED = · M*CpST (#.10)

Ol" QREMDVED = • M*5000 (‘+.l‘I·)P•

where M is the mass flow rate of the cooling fluid

(water) in lbm / hr, Cp is the heat capacity of the

cooling fluid in cal / (lbm*0F) , and 6T is the

temperature change of the cooling fluid in 0F. The

constant 5000 is the product of the heat capacity

of water and the temperature difference of 200 F.

The quantity QREMÜVED -in equation (4.14)A is

expressed in the units cal / hr. The negative sign

81

O

Figure 14: Heat Exchange in the Reactor System

BE

indicates that the energy is being removed from the

system. As in the model for pH level change, the

model for the temperature change also is a

combination of fermentation and mechanical effects.

#-2-2-3 Ismgsgaigge Qnangs

The heat capacity of the reacting fluid is ~

assumed to be that of water, 1 Btu /(lbm *OF).

The temperature change of the solution is modeled

by the equation:

OTSOLN = QBRODUCED.i..QREMDMED <#·15)*h¤*Vs0LN*CPs¤Lu

where STSOLN is the temperature change of the

reaction fluid, rho is the density of the reaction

fluid (assumed the density of water), VSQLN is the

reacting volume, and CpSgLN is the heat capacity of

the reacting fluid (also assumed the heat capacity

of water).

GTSDLN = QQOSP — ß(EOOEl (#.16)Vh¤*CPsoL~ OOOVSOLN

_ 83

The flow rate will also appear as a variable

quantity.

‘+- 2 - 3 !i„l.<.:.·.•:e. Batzsä

The initial flow rates are based of the ideal

reactor operating condition obtained from the batch Y

data. The system will operate in that mode through

the first two space - time periods. However,

following these period the flow rates will vary

throughout the simulation in order to achieve the

desired final product concentration and the

intermediated conditions. The intermediate

condition is the cell mass concentration exitingthe first reactor. The system examines the exiting

stream from the first reactor, to determine if the

cell mass concentration is that of the cell mass

concentration corresponding to the maximum specific

growth rate from the batch data. If below this

concentration, the system slows the flow rate

exiting reactor #1. If this concentration is above

this concentration, the system varies the flow rate

to find a new maximum. In a similar fashion the

Bä

stream exiting reactor #2 is examined for productconcentration and cell mass concentration. Sincethe product concentration is the principalvariable, the system will vary the exiting flowrate to find the maximum product concentration.Note that the maximum dilution ratio, D (F/V), is

V

assumed equal to the maximum specific growth rateor in equation form:

DMAXwhereDMAX is the maximum dilution rate. This is4the upper limit of flow in both reactors (see

figure 15). Beyond this point wash - out occurs.

Hash — out is the condition at which the only

steady — state solution to the kinetic equations isat the cell mass concentration, x, equal to zero.15

The system will avoid values near this point

because of the high sensitivity (instability) ofthe system at these conditions. The simulation

models the entire fermentation. The first aspect

of the continuous fermentation is the start—up.

85

6 _ _- , _ _ 0.6J , AS E; Zs - Egl 04; _1 E

äQ 2 g. O.:

ä

°0 0.2 0.4 0.6 0.0 .0 °u

Dilutkm nu. D.h°‘

Figure 15: Cell Mass Concentration versusDilution Rate (From James E. Baileyand David F. Dllis, "BiochemicalEngineering Fundamentals", SecondEdition, McGraw—Hill Book Company,New York, 1986).

B6

‘»- 3 QR

Based on the batch data recorded for the

species, the system will simulate start — up of the

fermentation. The user is requested to input the V

initial operating conditions. These parameters are

initial flow rate (the reactor volume is sized

based on this value) in liter / hr, the inoculum

size in grams, the initial operating temperature in

degrees Centigrade, the substrate concentration

inthefeed in gram / liter, the initial product

concentration in the feed in grams / liter, and the

_ pH level of the feed. If any of these values are

not given, the system assumes typical values (see

appendix).

Although the operating pH level and temperature

are requested, unless batch data for these values

were included initially, the simulation calculates

the maximum specific growth rate based on the

typical values for the organism and the function

presented in equation number (2.10). lf the user

has not entered batch pH and / or temperature data

but wishes to insert specific values for the

optimum pH and / or temperature, this change can be

made when prompted for such information by the

program. Ütherwise the tabulated values are used.

97

The program uses eighty (BO) percent of the reactor

volume as the active reaction volume for the

simulation. This restriction is based on the

foaming characteristics of most fermentation broths

and the vortex caused by agitation of the CSTR’s. VThe program therefore oversizes the reactors by

twenty (20) percent during its reactor volume

calculations.

The start — up simulation begins by filling

reactor #1 to eighty (BO) percent full. The

reactions begin immediately. when the reaction

rate reaches its maximum value reactor #2 is filled

to eighty (BO) percent full. Reactors #1 and #2

are filled at the rate specified by the user,

however there may be a delay in the filling of

reactor #2 based on the above conditions. Once

both reactors are full, the simulation proceeds at

the specified flow rates. This continues for one

space — time (the time required to fill reactor #1

for a second time at the rate specified by the

user}. The system then reports the cell mass,

substrate and product concentrations of the flow

streams. The pH level and temperature of the

reactors are also reported. This point is titled

the initial steady - state conditions. Following

start-up, the steady state simulation begins.

BB

4 · 4 )$.I.€B..Q.Y. §.I&I.§

The simulation following the start — up, will

begin to simulate changes in the operationl

environment. The system will simulate sampling at

thirty (30) minute intervals. These values are ’

recorded and used by the control algorithm to

assess the control direction. This simulation

continues for three days or until six hours pass_

the first twenty-four hours pass with no

significant change in the sample composition.

4.5 Qgßlßgg QLGORITHQ

The controlling algorithm for the simulation

will strive to control the pH levels in the

reactors, flow rates into and between the reactors

and ·temperatures within the reactors. By

controlling these variables it indirectly controls

the product concentration, cell mass concentration,

substrate concentration and reaction rate (see

figure 16).

B9

VG1 (G2) ·

° C1 (C2)

(Q2)P1 (P2)

Figure 16: Reactor System with Parameters

90

4.5.1 gg

A control algorithm taken from Shinskey is used

to control the pH level in each reactor (see figure A17)31. Based on the dynamics of the simulated

system the control parameters are calculated

accordingly.

The process gain is calculated based on the pH

change model discussed previously. From this model

and equation number (4.12), Kp, the process gain

is:

1-äälgläälgglslKn =-gg =-Qaä- = L--- --------Zsgcu--------.----- >

dm dVBASE (10-pROVSOLN

- (4.17)

Hhene c is the control output and m is the

manipulated variable. Figure 16 shows an

interaction PID ( proportional, integral and

derivative action) controller. For this type of

control the parameters are calculated accordinglyz

91

· .+ •

P + * '•n^ '

¤7;

Figure 17: Control Diagram (From F. G. Shinskey,"Process-Control Systems: Application/ Design / Adjustment", SecondEdition, McBraw—Hill Book Company,New York, 1979).

92

PGAIN = 1OÜXKp (#.18)

mn = 100x(en - KDER(cn — yn)) + bn (#.19)

Yn = Yn—1 + €$...1E..1..§.n,-.-T,.Xn—1„). (#-20) bSt + DEFF/KD

bn = bn-1 + (#.21)61; + IEFF

where St is the sampling time, 1 s ( one second),

IEFF is the effective integrating time and is equal

to the sum of the integrating time ( I ) and the

derivative time ( D ), DEF; is the effective

derivative time and calculated by:

DEF}: = ____}_____; (#.22)1/I + 1/D

KD is the derivative gain limit (assumed 10), f is

the feedback, b is the lagged value of the

feedback, the subscripts nl and n-1 are the nth

values.

93

Equations (4.19) through (4.22), taken from

Shinskey , represent a position control algorithm.

The system calculates values for the reactors

assuming Kp equal to 1 (one), The integrating time

equal to Kpxöt, the dead time is 1 s (CSTR

assumption) D = I = 2x(dead time)/n.

4.5.2 Temperature

For control of the temperature , the same

approach as used in the pH control is taken. In

this instance the process gain, Kp, from equationl

number (4.16) is:

Kn = QL; = 5.2 = -...;.5.9..... <‘+-E3)l dm dM rhO*vSOLN

Because of the predictable nature of the

temperature a simple proportional controller is

used. The parameters are predicted as above only

for the single mode controller.

Note that for the pH level and temperature control

systems each tank is controlled independently and

no overall algorithm is proposed.

94

4 - 5 - 3 ELQ! 8.€1lE.‘-ä

One of the major problems of biological systems

is the effect of contamination on the reaction.

Since the disturbance of contamination on the

system flows downstream and can shut down an entire

operation, the flow rates are controlled such that

the reactors can be isolated. This is accomplished

by controlling from the exit stream to the raw feed

stream ( opposite the direction of flow). In this

fashion the down stream deviations are limited and‘ those upstream are increasedaa.

Because of the upstream controlling scheme, one

begins with reactor # 2.(see figure 18)

4.5.8.1 Reactor #2 .

The material balance around reactor #2, using

the assumption of constant volume is:

FE + C2 = PE + G2 (4.24)

where F2 is the reaction media feed to reactor #2

in liters per hour, Ca is the caustic feed into

95

G2F2 C2

P2

Figure 18: Reactor # 2

96

reactor in l/hr, PE is the is product stream from

reactor #2 in l/hr and GE is the CO2 vented from

reactor #2. It is assumed that the caustic flow

rate into the reactor is negligible. This

assumption reduces equation (4.24) to:

FE = PE + Ga (4.25)

A further assumption is that that gaseous CO2

vented from the tank can be modeled by the method

proposed in the pH Changes section of this writing.

From that model, approximately all CO2 produced by

equation (4.3) evolves as gas and is vented from

the reaction vessel.

Also assume that the CDE produced leaves the

reaction mass instantaneously and has no effect on

the reaction volume. Hence equation (4.25)

becomes:

FE = P2 (4.26)

Utilizing this equation the control of the flow

rate keeps the dilution ratio below the specific

growth rate and near the optimum rate predicted

97

from the reaction rate data (see Flow Rate section

under Continuous Simulation and Control).

An analogous approach is used for reactor #1.

Chapter V

B..E.§„L!.Ll§„.„&!!l2..-„M.$.§.LL$.$..L9„b!.

I 5 - 1 B.E..I.5iJ.LI§„ __

The results of the simulation are divided into

sections according to their respective data sets.

Data sets with sufficient data types, cell mass

concentration, product concentration, and substrate —concentration are fully analyzed with continuous

production predictions. Each data analysis

includes graphs of the data. A results sheet for

each data set is included in the appendix. The

headings on the data sheet of "Three Data Types"

etc, indicate that the data used contain cell mass,

product and substrate data. "Two Data Types"

indicates that cell mass and substrate data were

used. And "One Data Type" indicates that cell mass

data were used. When the data used are sufficient

to perform an analysis, the analysis is undertaken.

Therefore a data set containing cell mass,

substrate and product data is analyzed in three

methods.

The Euler —Method was used exclusively in the

development of the model equations. The model was

99 I

99

deemed operable when the data from data set #1 were

matched through the stationary phase by the model.

5 - 1 - 1 Q.; $a..„’=äs.12..--.=i1

Data set #1 is the data from source #1 from

appendix E and a listing of the data is supplied in gappendix F — 1.

The program initially plots the concentration

versus time data for the data found in appendix F —

1 (see figure 19). A plot of the

dlog( cell mass concentration) (dlog(x)) or

1(cell mass concentration) d(time)

(1/x)dx/dt is then produced (see figure 20). In

this mode, three data types, a plot of the negative

inverse substrate reaction rate versus the

substrate concentration (1/RS versus S) is also

produced ( see figure 21). A table of the model

parameters calculated for each mode used is

produced (Table #2), a model of the process streams

concentration at steady — state (Table #3) and a

table of the effects of varying the separator

100

52 so mmmu us mz m mmm mmsSubstrate,QEteääulgiss,8.Concentration I( g / 1)

eu0.9 20.7 41.8. 62.7 83.6 104.58 — TIE (151185)

Figure 19: Concentration versus Time Plot forData Set F — 1

101

0.51 '

Ä. I

.2Äß . „0.0 20.9 41.8 62.7 83.6 104.5

. TIE —

Figure EO: Log (cell $assDc:nc;n:r;tio?) versusTime Plot or a a e —

102

2571/RsUERSlI5C0!4UERS10N· (11.1.-0.15¤

(hr•1 /g-S)-2.86*

I-.-

-11.00 · .0.0 0.2 0.4 0.6 0.8 1.0

CUMERSIOIQ ·

Figure 21: Inverse of the Substrate ConsumptionRate (1 / RS) versus SubstrateConversion (S) for Data Set F - 1.

103

TABLE B

Model Parameters for Data Set F — 1

Results of Paraneter Calculation FollowszUsing three uf datanaxinm spec; 10 growth rate (1/hr) : 0.107half satu‘atu;n_constant (g-S/1) : 0.002 _suhstrate mhibition constant 1g-S/1) : 1238.665naaginm product concentration (g-P/1) : 18.000 Tnaintenance coefficient tg-S/9-ce11¥1·r) : 1.482growth yield coefficient g-cell/3-S) = 0.061 3product vield coeffic;ent_ g-cell g-P) =_ 0.152— specific death rate fmct 1on constant (liter/hrltg-P^4.49) : 24.503E·15space ve1oc;tv for reactor no. 1 (hr) : 28.929space velocity for reactor no. 2 (hr) = 19.167Using two tvpes of data .naxinuw specific growth rate (1/hr) = 0.107half satu·at1on_constant tg-S/1) : 0.0üsihstrate 1rh1bit;on constant (9-5/1) : 1238.665naintenance coeffxcxent (TS/g-cell¥1·r) : 1.250growth_v1e1d coefficxent g-ce1l%5) = 0.061specific death rate constant (1 ) = 0.016Using one data_tvpeaverage specific growth rate 11/hr) : 0.028 _

I

104

TABLE B

Flow Streams for Data Set F — 1

PREDICTED CDHCENTRIITIUNS IN STREMS (Q/l)FEED TO PRIDUCT 4 PRIDUCT FEB) TO PRIDUCTL REQCUR FRI]! FRUI REQCTOR FRI}!M. l RERCTIR SEPARRTUI M.2 REQCTIR EM. 1 M. 2

CELL MSS 0.0% L555 0.000 l.5S5 2.044PRMUCT 0.000 9.% 2.366 6.687 9.90lE SMSTRNE *3.000 22.0W 0.000 22.000 ll.000

105

efficiency (Table #4) are produced. The

significance of these graphs and tables is

discussed in the discussion section of the chapter.

5.1.2 Qéta Set #2

Data set #2 is the data from source #3 of

Appendix E. A listing of the data is found in

Appendix F — 3.

The next source of batch data is source F — 3.l

This calculation proceeded as in the previous

section but encountered difficulties because of the

lack of a stationary growth phase (see figures 22 &

23), and large fluctuations in the substrate

consumption rate (see figure 24). The parameter

values calculated (Table 5) are analyzed in the

discussion section. -

5.1.3 Data Set #3

Data set # 3 in the data from source #8 in

Appendix E.

106.

TABLE A

Effect of Varying Product SeparatorEfficiency for Data Set F - 1

EFFECT IF WNIN3 PRIDUCT SFPNIFIIIR EFFICIENCY U1 FIM CII1CENTR11I101(SEFFICIENCY CELL M35 PRIDUCT SIBSIRRTE( Z) 9/111eI* 9 /I_11er 9/ hier10.000 2.044 11.812 11.00020.000 2.044 10.856 11.000 ‘30.000 2.044 9.901 11.00040.000 2.044 . 8.946 11.00050.000 2.044 - 7.990 11.00060.000 2.044 7.035 11.00070.000 2.014 6.079 11.00080.000 2.044 5.124 11.00090.000 2.044 4.169 11.000 _

107

HNO CÜHCEPITRQTIÜNUSTIPE FÜR FERIENTQTIÜN PRÜCESS ··

Substrate;Cell Mass,&ProductConcen ra iongt! E) 63.64 ‘ _

6.76 Ä

„ „ L1° I4!0.0 1.7 3.3 5.0 6.6 3.3

_ T11! (HMS)

° Figure E2: Concentration versus Time Plot forData Set F - 3

108

'mv VLOG (CELL ‘

V

°•TI!

Figure 23: Log (cell mass concentration) versusTime Plot for Data Set F - 3

109

I‘ I

1 1 RS 0.33 ° '“(hr·1 / g-S) ·

I II· _

_·

0.0 0.2 0.4 0.6 0.8 1.0CUNERSIO1!


110

111

The batch data set F — 3 was not in a form that

allowed it to be used in the analysis. However a

growth yield, Yxgy of .57 g cells produced per g

glucose consumed was extracted from the source for

use in later comparisons of parameter values for Ä. Igamgggstgig fermentation on glucose medium.

5 · 1 ·

4Data set ## is the data from source # 10 in

Appendix E.

The batch data form source F - 10 was not used ‘

because CDE is not a parameter in the derived

model.

5 - 1 - 5 9;;; .5;; #..5. -

Data set #5 is the data from source # 13 in


Appendix F - 13.

The batch data from F - 13 was analyzed as in

the prior sections. The concentration versus time

plot shows an extended stationary phase (see figure

E5). From the dlogtx) versus time plot several

112

228.80Substrate, 1 1 1 1 1 iCell Mass,z.Product Q ' Q Q Q EConcentration f‘ f ; Q s E1 9 ’ 1*

‘11"·‘*°§0.0— 4.8 9.7 14.5 19.4 24.2TIIE (MRS) ··

Figure 25: Concentration versus Time Plot forData Set F - 13

113

growth phases are clearly evident (see figure E6).

The 1/RS versus conversion of S plot illustrates

the erratic aspect of the data (see figure E7).

The Parameter Calculation Table, Concentration Of

Process Streams Table, and Effect Of Varying VSeparator Efficiency Tables are discussed in the

following section (Tables 6, 7, and B).

5-1-6 .Q.·ä-1=.a iäst. *16 V

Data set #6 is the data from source # 16 in


Appendix F — 16.

The batch data from source F — 16 was analyzed

as in the previous examples. The concentration

versus time plot is unique in that cell mass

concentration continues to increase while substrate

is exhausted and product concentration decreases

(see figure EB ). The plot of dlog(x) versus time

shows a two dlog growth curves separated by a

V stationary growth phase (see figure E9).

114

(LOG (CELLlJ4(MASS) ä é ä ä ä 4

·°°“81•418 917 14.5 1914 24.2E TIE

·Figure 26: Log (cell mass concentration) versus

Time Plot for Data Set F — 13

115

1 1 RS

rr V 1

•.••;20.00.2 0.4 0.6 0.8 1.0

_ CMERSI1]4


116

TABLE 6

Model Parameters for Data Set F — 13

Results ot Paraneter Calou1ationFollous: °Usia;9 three tgpes ot‘ datanaxiiun spec; ic grouth rate 11/tr) = 0.661half SITlI‘Q1l¢]'t_01]‘1S1'I|‘\‘Ü (9-S/I) : 0.000sabstrate inhibitaon constant (9-5/1) : 0.000naiguui product concentration (9-P/1) : -0.000naintenapce coetficient ts-S/9-ce1l¥|·r) : 33.332wcuth yield coefficient s-cell/$5) : 0.031product yield coet‘t‘1cient_ 9-cell 9-P) :_ 0.64 ·specific degth rate Fmction cmstant (liter/hrlo-P^4.49) : 25.82611-16space veloc;ty For reactor no. 1 (hr) = 2.50space velocity for reactor no. 2 (hr) : 25.667Usir;9 tvo types otdatanaxinuaspec;t‘1c youth rate tl/hr) = 0.6611tIlÜSI1'1.I‘§11(]'I_1}1]‘E1'I|1‘1 (9-S/1) = 251.000s1t;st1·ate 1rh1h1t;oa; cmstant (9-S/D =0.0001

‘= .mi"‘“2im$aiéa2„*r‘t“"°ii$"§t" ‘ . äa1°‘Mariä mai. rate ooiastgaäeti/1,1:) = -0.ara 1

Us' dat tIVg‘2;!SP€01$i0§N11\Pl1!(l/Öl') = am y _

1 1 7

TABLE 7

Flow Streams for Data Set F — 13

PREDICTED CIIICEIITRATMS IN STMHS (9/I1FEED 10 PRIIJUCT PREDUCT FEED 10 PRGJUCTMCM FRII1 FRU1 MCM FRG1ID. 1 MCM SEBARAM N1. 2 MCM

ml l „ ml 2l

CELL 1'A55 0.000 1.379 0.000 1.379 2.2%PRIDUCT 0.000 8.1% 2.66 5.731 21.169SWSMTE 260.000 200.000 0.000 200.000 100.000

1 1B

TABLE 6

Effect of Varying Product SeparatorEfficiency for Data Set F — 13

EFFECI U WIYIII1 PRIDUCI SEPANCR EFFICIEIICY {I1 FIM CIIICENINIIIISEFFICIENCY CEL1. MSS PRIDUCI SEINE„ (Z) 9/hier 9/hier ?/hier _10.% 2.2% 22.% %.%20.000 2.2% 21.987 1%.%E 30.% 2.2% T 21.169 1%.% E40.% 2.2% 20.350 1%.0%50.% 2.2% 19.51 1%.%60.% 2.2% 18.712 100.%70.% 2.2% 17.893 1%.%80.% 2.2% 17.75 1%.%1 90.% 2.2% 16.256 1%.0%

119

Substrate, éA

_ ÜS1 ( - ‘ .

Cell Mass, & g W § § § § ·Prod ct E-——JPé-·————%-**—*-********’*** ‘Concäntration '

( g 1 1)

,;ßjsf".S é'“'”-Ü::?*‘*"-"l

‘ ATIIE (MRS)

Figure EB: Concentration versus Time Plot forData Set F - 14

120

1.2s1.06

(CELL 0.87Ä gmass 1 T Q Y ·

.•glI.! 2.2 4.4 6.6 8.8 11.0TIE

Figure 29: Log (cell mass concentration) versusTime Plot for Data Set F — lk

121

5 - 1 -

'7Data set #7 is the data from source # 17 in


Appendix F — 17. V

The data from source F — 17 was analyzed as

before. The concentration versus time curve shows

the cell mass concentration and the product

concentration increasing after the substrate

concentration is zero (O) (see figure 30). The log

(x) versus time curve shows several log growth

regions (see figure 31).

5-1-5 !?.a.t.@. ää. §!.§.

Data set #8 is data from source # 18 in Appendix

E. A listing of the data in found in Appendix F —

18.

The data from source F · 18 was submitted to the

analvsis. The concentration versus time curve was

irregular although it followed the expected trends

(see figure 32). The log (x) versus time curve

likewise is irregular but follows established

trends (see figure 33).

122

MSubstrate, ‘

Cell Mass, Z-QProductQ ·\ QConcentration Q S

( g / 1) 2 12‘“·°°&°

622.0020.00

Q .2

0.0 _ 5.3 10.6 15.8 21.1 26.4THE (PIIRS)

' Figure 30: Concentration versus Time Plot forData Set F - 17

123

*

MASS ) E ä T é L é T

***1 1*126.4

_ TI!

Figure 31: Log (cell mass concentration) versusTime Plot for Data Set F — 17

124

21.66;LI5 Ta E;

Q

IProduct Q ? \ g 6 IConcentration § 1 \ Q é ä I‘

°’" 10781

‘°'°°•.•26.1 62.0 79.2 106.6 162.06 111: 111011161

Figure 32: Concentration versus Time Plot forData Set F — 18

125

IIIII1.06 <cE1.L 1,12 I"“SS ’ Ä-.-

1-.----u-I

26.4 52.8 16.6 132.0

Figure 33: Log (cell mass concentration) versusTime Plot for Data Set F - 18

126

5 - E Q...l,.§„Q!§.§„L¤„N

The simulation package contains a batch

simulation using the Runge — Kutta method.

However, the system only models batch growth when ·the operation pH and / or temperature are different

from that of the batch data given. This requires

that pH and / temperature data are given in the

initial data sets.

5 - E — 1 E.a.¤:.·=1.m.¢=;„.i¤.•;.c Qslc ¤..1..a..1=.-i9_usa

The system performed well when data containing

all growth phases was given. In data set #1, the

system calculated all the parameters for the

proposed model. In this example the parameters

calculated are close to those used by the data’s

author. For example, the data source’s specific

growth rate is .15 hr—1 and the system calculated

.11 hr—1 (see Appendix D for reference).

The two mode parameter calculations, under

similar conditions, gave parameter values that

corresponded well with the three mode calculations.

However, when insufficient data are given the model

attempts to force fit the data to the model. This

attempt is not very successful.

127

with source F — 3, there is no stationary growth

phase. This resulted in values of zero for the

parameters contained in the specific growth rate

function (KS, KS} and PM). To compensate the

maximum specific growth rate and the maintenance

coefficient were artificially high. Although the

yield coefficients were correct the parameter

calculations were inaccurate for both the three

data and two data modes. In this case the only

accurate parameter calculation is that for the one

data type mode.

Hith data source F -13 the fluctuations in the

substrate data caused problems. Once more the

model program attempted to force fit the data. The

same approach as above was used and the same

results achieved. The only accurate parameter

calculation again is that for the one data type

mode. -

with data source F - 14, an attempt was made to

check the limitations of the model. As stated in

the literature review the model encounters problems

at low substrate concentration. This attempt shows

that limitation to be valid. This data also show a

change of substrate when the initial substrate is

depleted. The proposed model does not contain any

parameters for switching of substrate. This

188

demonstrates one of the limitations of the!Wonod

model.

With source F — 17, the data show growth beyond

the depletion of the substrate. This however does

not illustrate switching of substrate since the

product also continues to rise. This represented

an attempt to model a microbial growth system that

defied the basic conservation of mass laws. The

system failed to produce any parameter

calculations.‘ with source F — 18, the data show rapid

fluctuations in the cell mass concentration and

substrate. Also a two data type input. The system

was not (able to force fit the data to the model.

The data show four (4) distinct logarithmic growth

phases. The system is designed to pick three

growth curves. This represents another outer limit

of the model and no parameter values were

calculated.

5 - E -E; [email protected]!.z z €—§1=„a„§..e F.l..s:1.v; 5..t.1;e9„¤As

Steady — state conditions were predicted for two

of the data sources. These conditions were based

on the steady — state equations at the optimum

reactor conditions based on the batch data.

129

with data source F -1, the steady — state cell

mass concentration is less than the batch

concentrations at the maximum growth rate. This

results because the maximum substrate consumption

rate does not correspond to the maximum cell growth

rate. There is substantial growth of cells and

increase in product in the second reactor, which

was the desired results.

With source F -13, although the substrate

consumption rate fluctuated greatly in the batch

data, a continuous simulation was obtained. In

this case the cell mass concentration was well

· below the maximum as quoted from the batch data.

The results here is also desired. The second

reactor increased cell mass concentration and

product.

5 - 3 - 3 $§„E.ä.‘T..é.§.QI. Eitl ;..;-„La.v1s.x

In all setting for the separator efficiency, the

efflciency showed no effect on the final cell

concentration of the second reactor. This is the

result of the operating the second reactor in the

stationary growth phase. The simulation is

~ designed to hold the fermentation reaction at its

maximum in the first reactor and to take the

130

fermentation reaction through its stationary growth

phase in the second reactor. During the stationary

growth phase cell mass concentration is constant

and shows very little change with respect to

substrate and product concentration. The effect of

substrate and product_concentration on the cell

mass concentration is great during the death phase,

hut the system is designed to keep the reaction out

of the death phase.

5 - E -‘> 9.9..0;.:9..1- P„a..r.am.ä„s.¤.;s.

The control parameters were not tested in the

simulation. These should be tested in further

studies (see Recommendations).

T 4

Chapter 6

Q.Q.h!„Q„l„.L!§..I..„Q.h!.

The proposed model performs well on smooth data

that display all stages of growth. The limitations

of the model are organisms that switch substrates

and organisms that display more than three growth

phases (the stationary growth phase is included in

the three).

The continuous model produces the expected

results. A large reactor followed by a smaller

reactor increases the cell mass concentration and

product concentration in the final product stream.

The product separator did not effect the final

cell mass concentration because the second reactor

contains cells in the stationary growth phase (see

Discussion).

The specific death rate function varies little

with changing product concentration. A constantl

value for the specific death rate is sufficient.

1 3 1

Chapter VII

RE.Q„.QP'!T.U.§.NT.Q£%IT_l-„QThe

study suggest additional subject areas which”

need to be addressed. These shortcomings are

mentioned in the Discussion and Conclusion sections

of this paper. The areas in need of a path forward

direction are the control, and batch simulation.

The control algorithm was not tested in this

study. Further study should test the algorithm.

·In both algorithms the constant, KP, will vary with

respect to the reaction volume and thereaction.Actual

test should be performed to verify this

relation. Other types of data should also be

tested.

This study held the pH level and temperature

constant. The original thrust of the study was to

allow the batch fermentation to proceed initially

to completion holding no variables constant. This

would allow the program to "learn" the batch

fermentation system and control the continuous

system. This concept should be investigated

further.

132

T V

133

Since there are several small industries that

could benefit from this and other similar studies,

a joint study, wherein the industry supplied the

hardware and laboratory and the investigator

supplied the programming, should be pursued.

Chapter VIII

5 |„|„§MH.B)i.

A model of the fermentation of glucose to

E t h a¤¤ 1 ¤ S 1 ¤ 9 S §.EE..D.ä.LQ.!91.§§.‘ä qe.r.¤;x3..ä19.¢. 1 S ¤ r E S E ¤ t Edin this study. The model incorporates a separate

function to simulate the specific death rate. A

computer program uses batch data to calculate the

model’s parameter values. These values are used in tthe model to simulate a continuous fermentation in

two continuous stirred tank reactors in series with

a product separator between them. The simulation

also provides for varying feed stock and organisms.

A control algorithm is presented to be used with

continuous fermentation. The simulation test the

effect of varying the efficiency of the product

separator on the final cell mass concentration.

134

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Q.11 B..1...Q„1..e.C.b.n.Q-.1.9.91 F QJQn n W 1 1 ev 8- SQ ne , New vo 1- k ,19869 P, 649.

2. D. Williams, P. Yousefpour, and E. M. H.Wellington, "Dn-Line Adaptive Control of Fed-B Q 1 C n F Q 1 me n 1 Q 1 1 Q n Q 1 5.Q.1;.C.?1..§.c-Q.m.x..C..e.§.

»·andVol.XXVIII, Pp. 631-645, John Wiley & Sons,Inc., 1986.

3. Liang-Heng Chen and Hsueh-Chia Chang, "GlobalStabilization of a Biological Reactor byLinear Feedback Control", Qngnigal_Enginee;lngQgnnnniggtigns, Vol. 27, pp 231-254, Gordon ‘

and Breach, Science Publishers, Inc., 1984.

4. D. Martin Comberbach and John D. Bu’Lock,"Automatic On-line Fermentation Headspace GasAnalysis Using a Computer - Controlled GasC h r Q m a 1 Q Q ¤‘ a Q h '° ,13..1.gggggnginggnlngVol. XXV, Pp. 2503-2518, JohnWiley & Sons, Inc., 1983.

5 - J · LQ d d er » lbs. §f..e.a„.e1=.= 6. I..é..äQl'!9.Q.i..§c $.1..11.91. » Sec Q ndRevised And Enlarged Edition, North—HollandPublishing Company, London, England, Pp 596-979 1971.

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·MaC n 1 1 1 an

Publishing Co.,Inc., New York, 1982,p. 152.

8. Rodney P. Jones and Paul F. Greenfield, "RoleOf Water Activity In Fermentations",

Vo 1 . x x v 1 1 1 ,Pp 29-40, 1986.

9. James E. Bailey and David F. Ollis, Qiocheniggl.E.nQ.1..¤1ee.1‘.111Q E.Q..n.d.e.m.e.n;e.1._e , sec 1, nd Ed 1 1; 1 O n , Q105, McGraw-Hill Book Company, New York, 1986.

135

136

10. Markku Nihtila & Jouka Virkkunen, "PracticalIdentifiability Of Growth And SubstrateC¤“5UmPti°“ Mddala"- Bigkaanngldgx. andälgénganganing, Vdl- XIX, pp 1831-1850, 1977.

11- J- M¤n¤d· ann- Ran- Maanaa1a1,, v¤1. 2, P 371,1949.

12. Brian W Mar, " Challenge Of Michaelis—MentonC¤na1anta"· laghnagaa Napaa- pp. 1119*1117,Oct. 1976.·

13. Octave Levenspiels, Bioteghnglggg andgiganginaaning, Val- 88, pp 1671, 1980-

14. G. R. Cysewski and C. R. Wilke, BigteghnglggyBigengiggerigg, Vol. 19, p 1125, 1977.

15. J. M. Lee, J. F. Pollard and G. A. Coulman,"Ethanol Fermentation With Cell Recycling:Ü°mP¤t€V 81m¤1at1¤n"• gignagnnnlggx angBiggngiggering, Vol. XXV, Pp 497-511, 1983.

16. Mohamed A Mehaia and Munir Cheryan, "EthanolProduction In A Hollow Fiber Bioreactor UsingSaggnangnxgaa Qanaxiaaaa", épgixadmigngniglggx ang Bignagnnglggx, Val- 80, Pp100-109, 1984.

17. K. G. Gutpa, Kamini Kushu and LakshmiBhatnagar, "Effect Of Some Physical AndChemical Factors On The Biomass And Sterols OfQangaga v1annana;nia» Q- paagggnnggigalxa....andäaganangnxgaa.ganaxiaiaa", Lngaan Jag;naL Exa-Bigl, Vol,. 11, Pp 584 — 86, November 1973.

18. Gary C Gray, "Mathematical Modeling Of The_ Acetone—Butano1 Fermentation For The Proposes

Of Bioreactor Design", Master’s Thesis,Virginia Polytechnic Institute And StateUniversity, Blacksburg, Va., May, 1983.

19. Conversations With Dr. David A. Wallis,Virginia Polytechnic Institute Institute AndState University, Blacksburg, Va., 1985.

20. A. S Aiyar and Robert Luedeking, "A Kinetic

137

Study Of The Alcoholic Fermentation Of GlucoseBy Sagshacdmxeee Derexieiae", BiaehgineenipdAnd Feed Pnnseesipg, Val- 62, Pp 55-59, 1966-

21. R. Bryon Bird, Warren E. Steward, and Edwin N.Li¤htf¤¤t» Tgahäpgxj- Ehenamenai Jahh Wiley 6Sons, New York, p. 555, 1960.

22. David A. Wallis and Richard A. Miller,"Bioprocess Simulations For The PersonalComputer: Convenient Tools For Education AndExperimental Design", Poster Session at theSeventh Symposium On Biotechnology For FuelsAnd Chemicals, Gatlinburg, Tenn., May 1985.

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24. Isabel sa - Correia and N Van Uden "Ethanol- ‘Ihdueed Death Df Sasshacsnyses secexisiae AtLow And Intermediate Growth Temperatures",Qidtesnnglgsx and.Biasnginee5ing, Val- xxviii,Pp 301-303, .

25. William E. Boyce and Richard C. DiPrima,Elementagx Diiiezsntial Egdatigns And BQHHQQLXVslgs Pjgglsgs, Third Edition, John Wiley &Sons, New York, Pp 338 - 339, 1977.

26. S. D Conte and Carl de Boor, ElsmsggsgyMgmsnisal Analxsis; An Algnxithmis Anocgasn,Second Edition, McGraw-Hill Kogakusha, Ltd.,MEXiCO9 P 329) 1972.

av. Jon M. Smith, mathsmaiisal usdslins AndDigital äimdlatign En; Engineexs AndSsssggssgs, John Wiley & Sons, New York, P268, 1977.

28. V. G. Jenson and G. V. Jeffreys, Qsggsgsgissinstngds In Qhemisal änginegging, SecahdEdition, Academic Press, New York, Pp 379-381,1977.

29. P. W. Atkins, Physical Chemistry, SecondEdition, Oxford University Press, SanFrancisco, 1982, p. 949,

l30. Richard M. Felder and Ronald W. Rousseau,

139

5. Of. B1? 5.55 »John Hiley & Sons, New York, p. 428.

3 1 - F - 6 - Sh 1 ¤51<5v » EäL..¢.=s..<;.5.5.5. ··@5..5-1-9p. Seccmd

Edition, McGraw—Hill Book Company, New York,1979, pp 95 - 111.

32. James E. Doss, Thomas N. Doub, James J. Downs,and Ernest F. Vogel, " New Directions For 'Process Control In The Eighties", A.I.Ch.E.Diamond Jubilee ·Meeting, washington, D.C.,November 2, 1983, p 27.

Appendix A

DERIVATION FROM LEE: POLLARD, AND COULMAN15

Fox — Fx + Vrx

— Vrx = Foxo — Fx

- V dä_ = Fogo — Fxdt

¤1.>< = Ex — E.¤>< 0.dt V V

Also:

dt V V ·

From equations (2.4) and (2.5) the relations are:

dx = Hx — kDx (2.4)dt

ds = —gx — mx (2.5). d E Yx [ S

Note that the terms for flow rate and volume are

omitted here. Rearranging (2.4) yields:

Hx = dx + kgx (2.4)Adt

139

140

Substitution of equation (2.4)A into (2.5) yields:

dä. = --1- < dx + kpx > — mx A1dt YX/S( dt )

Following the derivations of the aforementioned,

assume the derivative can be substituted by the

change, which yields:

SS = —gQÄ_ - möx A2

Vx/sNowby substituting the definition of delta, 8 the

resulting equation is:

S0 — S = _1_ ( xn - x + kDx ) + mx A3Vx/s

Solving the above equation for x yields equation

(2.28). Similarly for P starting with (2.27) and

(2.18).

QR = __1__( Hx — kDx ) (2.18)dt Vx/P

141

—VrP = FOPO — FP (2.27)

and substituting (2.4)A into (2.18) and solving for

P in the fashion shown above yields equation

(2.29). repeating the procedure with equation

(2.5) and solving for D yields equation (2.30).

APPENDIX B

DATA FOR SPECIFIC DEATH RATE FUNCTION

RD/TT % EtOH RD Et0H —1n(EtOH) ln(RD);eg"1 %V/V hr“1 g/1

K

200 17.5 21.82 0.14 1.98 3.08100 16 10.91 0.13 2.07 2.3940 14 4.36 0.11 2.20 1.4710 10 1.09 0.08 2.54 0.096 8 0.65 0.06 2.76 -0.42

T Indicates value multiplied by 107. ·

142

APPENDIX C

HYDROXIDE ION CONCENTRATIDN

Assume .1 M Ammonium Hydroxide Solution

In solution ammonium hydroxide disassociation

reaction is illustrated by the‘equation:

NHQOH <=====> NH“+ + OH'

CNHg+] = [0H’] = x

ENHQOHI = 0.1 - x

The disassociation constant; Kb, is 1.8 x 10'5.

Therefore the concentration of the hydroxide ion is

calculated by the equation:

Kb = cqgbjzcogga = ___;§__ = 1.BxlO_5ENHQOHJ 0.1 — K

Solving for x yields:

x = [OH"] = 1.3E37x1O'3 moles / liter

143

APPENDIX D

1191.91.

David F. Ollis, "A Simple Batch Fermentation

Model: Theme and Variations," Bioghemigal

Eggiggegigg lll, The New York Academy of Sciences,

New York, 1983, pp- 149 — 156.

2. Alician V. Quinlan, "The Influence of Dilution

Rate, Temperature, and Influent Substrate

Concentration on the Efficiency of Steady — State

Biomass Production in Continuous Microbial

Cu 1 1 ¤ r E • " El1.s>„¢;.hs.m.1.;.é.1. E.n.Q1mgs.s:-1.0.9. 1. .1-1- » T h E Ne wYork Academy of Sciences, New York, 1983, pp. 197

- 210.

3. Isao Endo and Teruyuk Nagamune, "Application of

Kalman Filter to Automatic Monitoring System of

Microbial Physiological Activities," Bigggggigal

Epgigggring lll, The New York Academy of Sciences,

New_York, 1983, pp. 228 — 230

4. P. Linko, M. Sorvari, and Y. Y. Linko, "Ethanol

Production with Immobilized Cell Reactors,"

Bioggemiggl_EngiggeriQg 111, The New York Academy

of Sciences, New York, 1983, pp. 424 — 434.

1 4 4

145

5. E. C. Clausen and J. L. Gaddy, "Production of

Ethanel frgm B1¤meS5·" BigenemieelEnggneeringLL},The New York Academy of Sciences, New York,

1983, pp. 435 - 447.

6. Charles D. Scott, "Fluidized — Bed Bioreactors

Using a Flocculating Strain ·of gymomgnas mgbilis

fer Ethangl Pr¤d¤¤ti¤¤»" §igenemiee}_ Engineering.„..lll, The New York Academy of Sciences, New York,

1983, pp. 448 — 456—

7. Ninoru Nagashima, Masaki Azuma, and Sadao

Noguchi, "Technology Developments in Biomass

Alcohol Production with Immobilized MicrobialG Celle-" Brgenenieel Engeneering All,

The New York Academy of Sciences, New York, 1983,

pp. 457 - 468

8. Alician V. Quinlan, "Kinetics of Secondary

Metabolite Synthesis in Batch Culture when Two

Different Substrates Limit Cell Growth and

Metabolite Production: Xanthan Synthesis by

Xenengnenee.gengere$rie»" Bigenenieel. EngineeringLV, The New York Academy of Sciences, New York,

1986, pp. 259 — 269

9. Gregory Stephanopoulos, "Application of

Macroscopic Balances and Bioenergetics of Growth to

146

the On - Line Identification of Biological

R E a C 1 ¤· v' S » " E£.,1„c•.<;.,h. 1 • T h E N E wYork Academy of Sciences, New York, 1986, pp. 338

— 349

10. Charles L. Meyer, Joseph K. McLaughlin, and

Eleftherios T. Papoutsakis,‘ "On — Line

Chromatographic Analysis and Fermenter State

Characterization of Butanol / Acetone

F Er m E vv 1: a 1 1 ¤ ¤ 5 • " B-1s;s;„h.e;¤„1Ä¢:ä.l.„ E11gi„x1e2r:.„1..n.Q 1.5/. » T h ENew York Academy of Sciences, New York, 1986, pp.

350 - 363

11. Tsuneo Yamané and Shoichi Shimizu, "Fed - Batch

Culture with Automatic Feedback Control: An

Advanced Operational Mode of Microbial Reaction,"

T h E N E w Y ¤ r k A c a d E- m vof Sciences, New York, 1986, PP- 364 — 381

18. Lee, Pollard, and Coulman. Cited earlier.

13. Jones and Greenfield. Cited earlier.

14. B. Sonnleitnert and 0. Kappeli, "Growth of

I 5 C ¤ ¤ 1 ¤· ¤ 1 1 ed b v 1 1 5Limited Respiratory Capacity: Formulation and

Verification of a Hypothesis,” Qigtgghgglogy ang

147

Eieengineening, Vel- XXVlll• Jehn Wiley & eene,Inc., 1986, DD- 927 * 937

15. C. G. Sinclair and D. N. Ryder, "Models for the

Continuous Culture of Microorganism under both

Oxygen and Carbon Limiting . Conditions,"

Eieäeennglegy eye Bigeggigeegipg, vol. xv11, JohnWiley & sons, Inc., 1975, pp. 375 — 398

lb. Y. R. Chen and A. G. Hashimoto, "Substrate

Utilization Kinetic Model for Biological Treatment

Pr¤¤eee•" Qigseennelegy. eng Qlääßälßäällßäv Vel-XXll, John Wiley & sons, Inc., 1980, pp. 2081 —

2095

17. Mehaia and Cheryan. Cited earlier.

18. Nihtila and Virkkunen. Cited earlier.

19. Stephen Simkins and Martin Alexander,

"Nonlinear Estimation of the Parameters of Monod

Kinetics That Best Describe Mineralization of

Several Substrate Concentrations by Dissimilar

Bacterial De¤eitiee," Qeeliee eng. äpxiggnmenäelMiggggiglggy, American Society for Microbiology,

Oct. 1985, pp. 816 — 824.

APPENDIX E

DATA TYPES

SOURCE SOURCE REACTOR ORGANISM . DATAA

NUMBER AUTHOR MODE TYPE CONTENTS

1 OLLIS BATCH K. SAMSSS]R1S_ BIOMASSETHANOLSUBSTRATE

E OUINLAN CONT MIXED TEMPERATURE<MUNICIPAL SENAGE INLET

TREATMENT PLANT> SUBSTRATEDILUTION

RATESTEADY —

STATESUBSTRATE

BIOMASS

3 ENDO & BATCH BREwER’S YEAST SUBSTRATENAGAMUNE BIOMASS

ETHANOL

4 LINKO, CONT S. QSR§!lS1AS ETHANOLSORVARI & K. ERASLSLSL I NKO Z - 11951 1.-1-5.

5 CLAUSEN & CONT S. SEREQLSLAS BIOMASSGADDY ETHANOL

148

149

SUBSTRATEDILUTION

RATE

6T

SCOTT CONT Z. MOBILIS SUBSTRATE(FLUID ETHANOL

BED) PRODUCTION. RATE

BIOMASS

7 NAGASHIMA, CONT YEAST ETHANOLAZUMA & (TYPE NOT CONVERSION

PUBLISHED) YIELDSPACE —VELOCITY

B OUINLAN BATCH Ä. QAMESRSIRIS BIOMASSpH

9 STEPHANOPOULOS CONT S. CEREVÄSIAES BIOMASSFED- SUBSTRATEBATCH ETHANOL

10 MEYER, BATCH Q. ACSTOBUTÄLIQUM SUBSTRATEMELAUGHLIN & CARBONPAPOUTSAKIS DIOXIDE

ACETONE

11 YAMANE & BATCH Q. BRASSLQAE VOLUMESHIMIZU FED- BIOMASS

BATCH ETHANOLPRODUCTIVITY

_ GRONTH RATE

1E LEE, CONT 5- §„E_FiF&'5T^..E.-9„ SUBSTRATEPOLLARD, & ETHANOLCOULMAN BIOMASS

DILUTIONRATE

T13 JONES 2. BATCH _S_- QEBE;/.l.älB.€§ BIOMASS

GREENFIELD ETHANOL

150

SUBSTRQTE

IQ SONNLEITNERT BQTCH Q. QEBEQIQIQQQ BIUMASS& KQPPELI ETHQNOL

SUBSTRQTE

15 SINCLQIR & CONT Q. QTIQIQ BIOMQSSRYDER ‘ SUBSTRQTE

DILUTIONRQTE

16 CHEN & CONT Q. QEQQQENEQ SUBSTRQTEHQSHIMOTÜ MIXED CULTURE EXIT

RETENTIONTIME

17 MEHQIQ & BQTCH Q. SUBSTRQTECHERYQN CONT BIÜMQSS

ETHQNOLPRODUCTIVITYYIELD_ DILUTIÜN

RQTE

18 NIHTILQ & BQTCH T. YIRIQE BIÜMQSSVIRKKUNEN SUBSTRQTE

19 SIMKINS & BQTCH QQQQQQQQQQQ QB. TYPICQLQLEXQNEDER §. TXEQIMQQIQM MONOD

CONSTQNTS

APPENDIX F DATA TYPE

APPE}U)IX F — 1

DATA SET FROM SOURCE #1

CELL MASS SUBSTRATE PRODUCT TIMECONCENTRATION CONCENTRATION CONCENTRATION

Q / liter Q / liter Q / liter hr

0.1 48 0 00.4 48.7 3 71.1 43 4 151.7 38 7 25 _2.1 35 10 302.45 29 14 392.3 22 16 482.3 17 18 552.4 11 23 652.1 ° 5 26 752.25 3 28 782.15 0 27 851.7 0 29 95

151

APPENDIX F — 2


Temperature d S0 S’ So—S’ 3’(OC) (Khr“1) (ppm) (ppm) (ppm) (ppm)

10 42 943 72 ‘371 330*56 954 55 399 390*33 973 92 331 402*167 1109 313 291 106*333

20 42 970 19 951 34656 933 23 910 32733 992 53 939 361*167 979 54 925 434333 921 375 546 301

30 *42 909 16 393 30056 931 14 917 34633 939 23 916 395*167 996 97 399 330333 943 77 371 423

* Indicates data not used in the s0urce’s analysis.SO — Initial substrate concentrationS’

- Final substrate concentrationB’ — Biomass concentrationK — Half saturation constant

152

1

APPENDIX F — 3


CELL MAS8 SUBSTRATE PRODUCT TIMECONCENTRATION CONCENTRATION CONCENTRATIONg / liter g / liter g / liter hr

1.2 104 0 01.5 102 - 1 12 92 3 23 89 7 35 73 12 48 55 20 512 30 29 b17 1.2 37 718 0 38 7.5

153

APPENDIX F — 4


Biocatalyst Initial Yeast Residence ProductivityDry Matter Quantity Time (based on vol

catalyst bed)

(percent) (g/100 — g) (hr) ‘(g / I —hr)

9.0 (wet) 25 4.3 1912.4 25 2.7 1927.2 25 1.2 3977.5 25 1.2 3350.6 15 1.1 4520.3 5 0.96 52

For continuous production of ethanol from grape

juice (14.2 Z wt/ vol sugar) with immobolized S.

ceggvlslgg and a residence time of 5 hr the ethanol

concentration in product is approximately 7 g/l.

For continuous production of ethanol from barley

malt wort with immobolized S. ggggg};}ae_ and a

residence time of 2 hr the ethanol concentration in

product is approximately 5 g/1.

For continuous production of ethanol from

commercial whey (5 Z wt/vol lactose) with

1 nmdbn 1 1 rad Q- and 6.- n.1.„<a.a„r„ 6%..-ggiggtgsidase and immobolized 5. fggglliä with a

residence time of 4 to 5 hrs the ethanol

concentration in product is approximately E2 g/l

and 20 g/1 respectively.

154

APPENDIX F — 5


CELL MASS SUBSTRATE PRODUCT DILUTIONCONCENTRATION CONCENTRATION CONCENTRATION RATE

No / ml x 10-B g / liter g / liter hr-1

220 0 13.5 0.04210 0.5 13 0.07200 1 12 0.12160 3 10 0.17145 6 S 0.21110 13 6.5 0.2440 24 3 0.27

155

APPENDIX F — 6


TRIAL RUN FEED FEED ETHANOL OVERALLNO. TIME FLOW GLUCOSE PRODUCTION GLUCOSE

RATE CONC. _ CONV.<hr> (1/hr) (g/1) (X of (X)

the0retica1>

1 283 0.72 121 99 732 391 0.78 126 99 853 331 0.48 104 97 944 185 1.44 97 98 915 283 1.43 93 96 96

THEORETICAL YIELD IS FOR EVERY MOLE OF GLUCOSECONSUMED TWO MOLES OF ETHANOL ARE PRODUCED.

FLOW RATE IS EQUIVALENT TO THE DILUTION RATE(RATIO).

„ 156

APPENDIX F — 7


INLET OUTLET SUGAR SPACESUGAR ETHANOL CONVERSION VELOCITVCONCENTRATION CONCENTRATION YIELD

(Z) · <% \//V) (Z) (1//K/——ga1—hr>

15 8.5 92 0.4515 10 95 0.2514 8.5 95 0.45

SUGAR CONVERSION YIELD BASED ON COMPLETE CONVERSIONOF SUGAR TO ETHANOL.

157

APPENDIX F — 8


Values for yield from Ä. camgggsygis fermentation.

Yield is 0.57 g cells produced per g glucoseconsumed. T

158

APPENDIX F — 9


Data shows final cell mass concentration of 170

g / 1. This supports the assumption \of no cell

mass concentration inhibition. The data was not

uniform so systematic analysis by the program is

prohibited.

159

APPENDIX F — 10


CELL MASS SUBSTRATE PRODUCT DILUTIONCONCENTRATION CONCENTRATION CONCENTRATION RATE

g / liter g / liter g / liter hr—l

8.2 50 38 0.069.2 20 35 0.153 0 20 0.19

160

APPENDIX F — 11


LOG CELL MASS SUBSTRATE PRODUCT TIMECONCENTRATION CONCENTRATION CONCENTRATION

q / liter g / liter hr

-0.067 260 3.3 0.530.333 255 6.7 3.30.67 247 10 4.30.9 237 12 6.21.07 230 14 7.71.33 223 25 10.11.433 200 27 11.31.53 135 33 12.11.6 167 40.3 141.67 143 51.7 16.31.7 137 52.7 17.31.72 117 60.7 13.71.76 103 70 21.31.73 100 70.3 22

161

APPENDIX F — 12

DATA SET FROM SOURCE #1#


Q / liter Q / liter Q / liter hr

0.7 S.3 0.5 0.S1 6.2 1.3 1.31.9 1.6 2.6 2.S2.1 0.2 3.3 3.32.2 0.1 3.2 3.62.3 0.1 3 #.S2.5 0.1 2.6 63.2 0.1 2.2 73.5 0.1 1.6 7.S#.3 0.1 1 9 ’

#.5 0 0 10

162

APPENDIX F — 13


Maximum specific growth rate = 0.54 hr“1

Other data not in one to one correspondence.

163l

APPENDIX F — 14

DATA SET FROM SOURCE #17 BATCH


g / liter g / liter g / liter hr

2.6 1OO O O2.9 91 4.4 23.7 76 11.2 47.1 42 28.2 78.6 O 47.9 ll9.5 O 49 199.4 O · 49.5 24

164

DATA SET FROM SOURCE #14 CONTINUOUS

SUBSTRATE PRODUCT DILUTION PRODUCTIVITYCONCENTRATION CONCENTRATION RATE (ETHANOL>

g / liter q / liter hr—l g / liter /hr

18 40 0.25 10-28 32 0.55 15

”

45 25 1 2560 20 2 3670 18 3 4078 12 4 36

165

APPENDIX F — 15


CELL MASS SUBSTRATE TIMECONCENTRATION CONCENTRATION

g / liter g / liter days / hr

0.4 24.5 0' 0.7 27.5 0.09

0.9 25 0.121.1 23 0.151.5 22 0.171.2 19 0.202.5 22.5 13.9 19 1.027.7 16 1.142.2 7.5 22.7 3 2.092.5 2 2.142.5 2 2.177.9 2.5 3.176.4 1.6 4.126.0 1.2 5

166

APPENDIX F — 16


Typical Values

Orqanism Specific Growth Half SaturationRate

(1/hr) (g—S/1)

Räeogggohgä SE 0.56I.r-xp„h...i..m;4.r..i.64.m 0 - 59 1 · 9 >< 10*+

Sewage _ 0.256 7.2x10—5

167

Appendix G

TYPICAL VALUE8 FOR PH AND TEMPERATURE

Organism Type Optimum pH Optimum Temperature

Funqi3O 5 E6 OC

Bacteria3O 7 E9 OC

vea5:l“ Q 37 ¤c

168

Appandix H — 1

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Appendix H — E

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