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This is to certify that the
thesis entitled

MODELING THE EFFECTS OF INITIAL NITROGEN
AND TEMPERATURE ON THE FERMENTATION
KINETICS OF HARD CIDER

presented by

SHANTANU KELKAR

has been accepted towards fulfillment
of the requirements for the

MS. degree in BIOSYSTEMS ENGINEERING

 

 

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MODELING THE EFFECTS OF INITIAL NITROGEN AND TEMPERATURE
ON FERMENTATION KINETICS OF HARD CIDER

By

Shantanu Kelkar

A THESIS
Submitted to
Michigan State University

In partial fulfillment of the requirements
For the degree of

MASTERS OF SCIENCE
Department of Biosystems and Agricultural Engineering

2006

ABSTRACT

MODELING THE EFFECTS OF INITIAL NITROGEN AND TEMPERATURE
ON FERMENTATION KINETICS OF HARD CIDER

By
Shantanu Kelkar

The combined effect of nitrogen and temperature on fermentation of apple juice to
produce hard cider was studied. Flasks containing apple juice (400 ml) were inoculated
with yeast and supplemented with three different levels (100, 300, 600 ppm) of nitrogen
in the form of Diammonium phosphate (DAP). The apple juice was then allowed to
ferment under isothermal conditions at three temperatures between 11 and 22 °C.

Yeast cell, nitrogen, ethanol and sugar concentrations at various times were
evaluted. A simple mechanistic primary model based on Monod kinetics was proposed to
describe the process. Kinetic parameters of the primary model were estimated non-
linearly via Runge-Kutta method for best fit to one set of experimental data. These
kinetic parameters were fit to a secondary model that proposed an Arrhenius relationship
with the two independent variables, temperature and initial nitrogen content. The model
predictions were validated using a second set of experimental data.

Raw data and secondary model fitting showed that nitrogen did not have a
significant Arrhenius effect (p=O.12) on growth rate. Temperature had a significant
Arrhenius effect (p<0.05) on four of the model parameters. The model gave satisfactory
predictions for three of the dependent variables, nitrogen, ethanol and sugar. The study
showed that dessert apples could be used for hard cider manufacture with ethanol
concentrations of over 6.5% and that more complete fermentations could be achieved at

higher temperatures and by supplementing nitrogen at the onset of fermentation.

DEDICATION

To my parents, Mohan and Meenal Kelkar and my sister Shivangi for their unconditional

love, support and faith in me. To all my friends for their encouragement and best wishes.

iii

ACKNOWLEDGEMENT

A big thank you to my major professor, Dr. Kirk Dolan, for his guidance, patience,
encouragement and positive attitude. And for helping me out weekend afier weekend!
Many thanks to Dr. Pat Oriel for being kind enough to allow the use of his laboratory
facilities and for his very valuable inputs on my research. A very special thank you to Dr
Janice Harte for her unstinting support and encouragement. Thanks also to my committee
members, Dr Gale Strasburg and especially, Dr Bradley Marks, for their support and

advice.

Mavis Tan and Darclee Popa, my partners in crime on the hard cider project, thank you
for everything! Norm Matella, Ritu Saini and Maria Suparno: thank you for being my
peer mentors, for you advice and encouragement. I would also like to express my deepest
gratitude to Mitzi Ma, Dharmendra Mishra and Pankaj Kumar for tolerating me,
encouraging me and for being there for me, always. Thanks also to Patnarin Benyathiar,

Harlem Suniaga, George Nyombaire and Kathy Lai.

I would like to thank Michigan Apple Committee, USDA Rural Development and Uncle

John’s Cider Mill for supporting this project.

And of course, a big thank you to my family and all my friends who have made my life

exciting and worth living; for all their love, support, prayers and best wishes.

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii
LIST OF FIGURES ................................................................................. ix
INTRODUCTION ..................................................................................... 1
CHAPTER 1. Literature Review ...................................................................... 3
1.1.Michigan Apple & Cider Industry .................................................... 3

1.1.1. Hard Cider: Introduction and History ................................... 3

1.1.2. Michigan Apple Industry .................................................. 4

1.1.3. Beneficial Effects of Cider Consumption ............................... 5

1.1.4. Dessert Apples .............................................................. 6
1.2. Mainstream Cidermaking ............................................................... 7

1.2.1. Juice Preparation ............................................................ 7

1.2.2. Yeast Fermentation ......................................................... 8

1.2.3. Racking and Clarification ............................................... 10

1.2.4. Blending, Final Filtration and Storage ................................. 11

1.3. Modeling of Alcoholic Beverage Fermentation ................................... 12

1.3.1 Justification for Research ................................................ 12

1.3.2 Nitrogen Limitation ...................................................... 13

1.3.3 Temperature Effect ....................................................... 15

1.3.4 Modeling of Fermentation Kinetics .................................... 16

1.3.5 A Generic Mechanistic Model for F errnentation ..................... 18

1.3.6 Objectives ................................................................. 21

CHAPTER 2. Materials and Methods ............................................................ 22
2.1. Fermentation Setup .................................................................... 22

2.2. Methods of Analysis ................................................................... 27

2.3. Model Development ................................................................... 33

2.3.1. Primary Model ............................................................. 33

2.3.2. Procedure for Non-Linear Parameter Estimation .................... 38

2.3.3. Secondary Model & Linear Parameter Estimation ................... 43

2.3.4. Procedure for Model Validation ........................................ 44

CHAPTER 3. Results and Discussion ............................................................ 46
3.1. Initial Estimates for Parameters ..................................................... 46

3.2. Parameter Estimation ................................................................. 46

3.3. Secondary Model Fitting .............................................................. 51

3.4. Model Validation ...................................................................... 54

3.5. Conclusions ............................................................................. 72

3.6. Novelty of work ....................................................................... 74

3.7. Future work recommendations ...................................................... 75

APPENDIX A ......................................................................................... 77

APPENDIX B ......................................................................................... 83
APPENDIX C ......................................................................................... 89
APPENDIX D ......................................................................................... 95
APPENDIX E ........................................................................................ 101
APPENDIX F ......................................................................................... 103
APPENDIX G ....................................................................................... 1 15
NOMENCLATURE ................................................................................ 1 3 8
REFERENCES ...................................................................................... 139

vi

LIST OF TABLES

Chapter 2
Table 2.1. Experimental Plan ...................................................................... 26
Chapter 3
Table 3.1. Initial Estimates for Model Parameters ............................................. 46
Table 3.2. Non-Linear Parameter Estimates .................................................... 50

Table 3.3. Linearly Estimated Coefficients from Arrhenius Fits

to Secondary Model ................................................................................ 52
Table 3.4. Predicted Parameters from Secondary Model ....................................... 54
APPENDIX F

Parameter Estimation Data Set

Table F.1. Data for T=11 °C, Viable Yeast Cell Concentration, X y ........................ 103
Table F.2. Data for T=17 °C, Viable Yeast Cell Concentration, X y ........................ 104
Table F.3. Data for T=22 °C, Viable Yeast Cell Concentration, X y ........................ 105

Table F.4. Data for T=11°C, Nitrogen Concentration, N... 106

Table F.5. Data for T=17 °C, Nitrogen Concentration, N .................................... 107
Table F.6. Data for T=22 °C, Nitrogen Concentration, N .................................... 108
Table F.7. Data for T=11 °C, Ethanol Concentration, E .................................... 109
Table F.8. Data for T=17 °C, Ethanol Concentration, E .................................... 110

Table F.9. Data for T=22 °C, Ethanol Concentration, E. ....111
Table F.10. Data for T=11°C, Sugar Concentration, S... 1 12
Table F .1 1. Data for T=17 °C, Sugar Concentration, S ...................................... 113

Table F.12. Data for T=22 °C, Sugar Concentration, S... .....1 14

vii

APPENDIX G

Model Validation Data Set

Table G.1. Data for T=11 °C, Viable Yeast Cell Concentration, X y ........................ 115
Table G.2. Data for T=17 °C, Viable Yeast Cell Concentration, X y ........................ 116
Table G.3. Data for T=22 °C, Viable Yeast Cell Concentration, X y ........................ 118
Table (3.4. Data for T=11 °C, Nitrogen Concentration, N .................................... 120
Table G.5. Data for T=17 °C, Nitrogen Concentration, N .................................... 122
Table G.6. Data for T=22 °C, Nitrogen Concentration, N .................................... 124
Table G.7. Data for T=ll °C, Ethanol Concentration, E ..................................... 126
Table 6.8. Data for T=17 °C, Ethanol Concentration, E ..................................... 128
Table G.9. Data for T=22 °C, Ethanol Concentration, E ..................................... 130
Table G.10. Data for T=11 °C, Sugar Concentration, S ...................................... 132
Table 6.11. Data for T=17 °C, Sugar Concentration, S ...................................... 134
Table G.12. Data for T=22 °C, Sugar Concentration, S ...................................... 136

viii

LIST OF FIGURES

Chapter 1

Figure 1.1 Conversion of fermentable sugars to ethanol ......................................... 9
Chapter 2

Figure 2.1. Fermentation Setup ..................................................................... 27
Figure 2.2. Yeast Life Cycle ........................................................................ 33
Figure 2.3. Generic Plot of Dependent Variables vs. time ..................................... 35
Chapter 3

Figure 3.1. Non-Linear Parameter Estimation for T=22° C, DAP=100 ppm

(Yeast Cell Concentration) ......................................................................... 48

Figure 3.2. Non-Linear Parameter Estimation for T=22° C, DAP=100 ppm (N itrogen)..48
Figure 3.3. Non-Linear Parameter Estimation for T=22° C, DAP=100 ppm (Ethanol). . .49

Figure 3.4. Non-Linear Parameter Estimation for T=22° C, DAP=100 ppm (Sugar). . ....49

Figure 3.5. Model Validation for T=22° C, DAP=100 ppm ................................... 55
Figure 3.6. Model Validation: Comparison of All Predicted and Observed Yeast

Cell Concentrations .................................................................................. 62
Figure 3.7. Yeast Cell Concentration Residuals Plot ............................................ 63
Figure 3.8. Nitrogen Residuals Frequency ....................................................... 64
Figure 3.9. Model Validation: Comparison of All Predicted and Observed

Nitrogen Concentration .............................................................................. 64
Figure 3.10. Nitrogen Residuals Plot .............................................................. 65
Figure 3.11. Nitrogen Residuals Frequency ...................................................... 66

Figure 3.12. Model Validation: Comparison of All Predicted and Observed
Ethanol Production ................................................................................... 66

ix

Figure 3.13. Ethanol Residuals Plot ............................................................... 67

Figure 3.14. Ethanol Residuals Frequency ....................................................... 68
Figure 3.15. Model Validation: Comparison of All Predicted and Observed Sugar
Consumption .......................................................................................... 68
Figure 3.16. Sugar Residuals Plot .................................................................. 69
Figure 3.17. Sugar Residuals Frequency ......................................................... 70
Figure 3.18. Secondary Model Fitting of In pm vs (1/N -— I/Nref) ............................. 51
APPENDIX A

Figure A. 1. Semi-log plot of raw Xv versus time for T=11° C, DAP=0 ppm ............... 77
Figure A.2. Semi-log plot of raw Xv versus time for T=11° C, DAP=100 ppm. . . . . . . . ....77
Figure A.3. Semi-log plot of raw Xv versus time for T=11° C, DAP=3OO ppm. . .. . .......78
Figure A.4. Semi-log plot of raw Xv versus time for T=l 1° C, DAP=6OO ppm ............ 78
Figure A.5. Semi-log plot of raw Xv versus time for T=17° C, DAP=O ppm ............... 79
Figure A.6. Semi-log plot of raw Xv versus time for T=17° C, DAP=100 ppm. . .. . . . . ....79
Figure A.7. Semi-log plot of raw Xv versus time for T=17° C, DAP=3OO ppm. . .. . . . . ....80
Figure A.8. Semi-log plot of raw Xv versus time for T=17° C, DAP=6OO ppm. . .. . . . . ....80
Figure A.9. Semi-log plot of raw Xv versus time for T=22° C, DAP=O ppm ............... 81
Figure A.10. Semi-log plot of raw Xv versus time for T=22° C, DAP=100 ppm .......... 81
Figure A.1l. Semi-log plot of raw Xv versus time for T=22° C, DAP=3OO ppm .......... 82
Figure A.12. Semi—log plot of raw Xv versus time for T=22° C, DAP=6OO ppm .......... 82

APPENDIX B

Figure B. 1. Non-Linear Parameter Estimation for T=17° C, DAP=0 ppm .................. 83
Figure 8.2. Non-Linear Parameter Estimation for T=17° C, DAP=100 ppm .............. 84
Figure B.3. Non-Linear Parameter Estimation for T=17° C, DAP=3OO ppm .............. 84
Figure B.4. Non-Linear Parameter Estimation for T=17° C, DAP=600 ppm .............. 85
Figure B.5. Non-Linear Parameter Estimation for T=22° C, DAP=O ppm ................. 85
Figure B.6. Non-Linear Parameter Estimation for T=22° C, DAP=300 ppm .............. 86
Figure B.7. Non-Linear Parameter Estimation for T=22° C, DAP=600 ppm .............. 86
Figure B.8. Non-Linear Parameter Estimation for T=11° C, DAP=O ppm ................. 87
Figure B.9. Non-Linear Parameter Estimation for T=11° C, DAP=100 ppm .............. 87
Figure B.10. Non-Linear Parameter Estimation for T=11° C, DAP=300 ppm ............. 88
Figure 8.11. Non-Linear Parameter Estimation for T=11° C, DAP=600 ppm ............. 88
APPENDIX C

Figure C.1. Model Validation for T=17° C, DAP=0 ppm ..................................... 89
Figure C.2. Model Validation for T=17° C, DAP=100 ppm .................................. 90
Figure C.3. Model Validation for T=17° C, DAP=3OO ppm .................................. 90
Figure C.4. Model Validation for T=17° C, DAP=600 ppm .................................. 91
Figure C.5. Model Validation for T=22° C, DAP=0 ppm .................................... 91
Figure C.6. Model Validation for T=22° C, DAP=300 ppm ................................. 92
Figure C.7. Model Validation for T=22° C, DAP=6OO ppm ................................. 92
Figure C.8. Model Validation for T=11° C, DAP=0 ppm .................................... 93
Figure C .9. Model Validation for T=11° C, DAP=100 ppm ................................. 93

xi

Figure C.10. Model Validation for T=11° C, DAP=300 ppm ................................. 94

Figure C.11. Model Validation for T=11° C, DAP=6OO ppm ................................. 94
APPENDIX E
Figure B. 1. HPLC Chromatogram for hard cider ............................................. 101

Figure E.2. HPLC Chromatogram for hard cider spiked with 99.9% pure ethanol ...... 101

Figure E.3. HPLC Chromatogram showing various sugars .................................. 102

xii

INTRODUCTION

Hard Cider is an alcoholic apple beverage made from fermentation of apple juice.
Hard cider is popular in Europe and was consumed widely in the United States in the 18th
and 19th centuries. Prohibition laws and easy availability of beer after the American Civil
War dealt a blow to consumption of hard cider. After its reintroduction in the 19905 in
North America, hard cider has been growing exponentially in popularity. At the same
time, a combination of factors has led to excess production of apples, Michigan’s most
valuable crop (Michigan Apple Committee, 2006). Hence, Michigan apple growers are
looking to manufacture value-added products from their excess apple produce.

Hard cider is made from cider apples, which are bitter, sharp and sour. However,
North America grows only dessert apples and currently states like Michigan are
experiencing an excess apple production. Dessert apples lack the sugar, acidity and tannin
levels found in cider apples and are not suitable for making hard cider. However,
economics dictate the manufacture of hard cider from dessert apples in the US. Every
hard cider brewed has its own history because many of the fermentation variables like
type of yeast, composition of apple juice, temperature, nitrogen and other nutrients,
fermentation vessel and presence of other microorganisms can change and affect
fermentation and the eventual sensory characteristics of hard cider. As hard cider
continues to grow in popularity, the scale of production will rise, and there will a need to
study and predict fermentation performance. As the industry continues to grow, cider
production will move from microbreweries to larger-scale productions. A mechanistic
model that could predict the fermentation kinetics of hard cider production would be a

useful tool for understanding and designing processes.

Few researchers have studied hard cider fermentation; fewer still have attempted
to model the fermentation kinetics. Hard cider fermentation is a process very similar to
wine fermentation. Slow and incomplete fermentations are a chronic problem for the
wine and beer industries and the factors leading to sluggish and stuck fermentations have
been extensively studied (Bisson 1999; Cramer et a1. 2002; Del Nobile et al. 2003).
Nitrogen compounds are often present in a small amount in grape juice which can be the
limiting factor for yeast grth and activity (Bisson and Butzke 2000; Cramer et a1.
2002; Del Nobile et a1. 2003; Malherbe et a1. 2004).

Temperatures affect the rate of fermentation by giving higher rates and shorter
fermentations at higher temperatures. It has been shown that temperature can affect the
assimilation and uptake of nitrogen and sugar and consequently alter the fermentation
rate (Malherbe et al. 2004; Sablayrolles et a1. 1996). The Arrhenius relationship between
temperature and rate of alcoholic fermentation has also been established (Phisalaphong;
et a1. 2006).

Hence, the objective of this study was to apply a simple mechanistic model to
predict the fermentation kinetics of hard cider made from Michigan apples. The novelty
of this work lies in modeling hard cider fermentation, which has not been attempted
before. This study is helpful in investigating the fermentation characteristics of dessert
apple juice. This study is also amongst the very few to attempt modeling the effect of
initial nitrogen levels and temperature on fruit fermentations concurrently. The basic
mechanistic model proposed in this study can help explain the process of fermentation as

. well predict the rate of ethanol production and nitrogen consumption.

Chapter 1. Literature Review

1.1 American Apple and Cider Industry
1.1.1 Hard Cider: Introduction and History

Hard cider, also known as cider, refers to an alcoholic apple beverage. It is
manufactured by fermenting apple juice, a process similar to wine making. In some cases,
the product is called apple wine. The distinction between hard cider and apple wine is
usually made based on alcohol content, but there is much overlap between the two
products. Apple wine is usually above 7% alcohol content, and hard cider is usually
below 7% (Rowles 2003).

Although hard cider is popular in Europe, it was reintroduced to the American
market only in 1990. The product was consumed widely in the 18th and 19th centuries in
the US, particularly along the East Coast. Hard cider came to the US. with the first
English settlers, who brought apple seeds with them to plant in their new home. Most of
the apple crop was used for the production of hard cider. In fact, in 1767, the per capita
consumption of hard cider in Massachusetts is estimated to have been about 40 gallons
per person annually (Fabricant 1997)!

Hard cider was a family drink in colonial America (Miller 2004). Many people,
even children, drank hard cider with meals. President John Adams was known to drink a
pint of hard cider each morning to settle his stomach. Fermented cider sometimes offered
a safe alternative to water because the alcohol prevented bacterial contamination. Cider
mills were common thrOughout New York and New England. Families even kept barrels

of cider in their basements.

Cider remained a popular beverage until the Civil War when beer began to take its
place in the American market. The influx of German immigrants to the US. boosted the
popularity of beer. Beer was cheaper and easier to produce than hard cider and therefore,
it was more attractive to produce commercially. Early in the 20th century, Prohibition

dealt the final blow to hard cider’s popularity in the US. until its recent resurgence.

1.1.2 Michigan Apple Industry

Apples are Michigan’s largest and most valuable fruit crop, worth $150 million to
the growers and generating a total of nearly $500 million of economic activity in
Michigan annually(Committee 2005). Michigan is the nation’s largest producer of apple
slices for pie filling and frozen pies, and also produces applesauce, dried apples and
fresh-cut apple slices. Today, the demand in the US. for apple juice and cider exceeds,
by far, that for fresh apples. Over the past decade, U.S. apple exports have increased
because of liberalization of export markets, substantial industry export promotion efforts
and increased disposable income in developing countries. However, in the last few years,
US. market share of total world apple exports has dropped. China, the European Union
and New Zealand have gained market share, while the United States market share of
exports has declined (Miller 2004). China has become a major world apple juice producer
and a significant supplier to the US. market. China has affected the demand for Michigan
apples, leading to excess apple production in Michigan. Therefore, Michigan apple
growers are looking at ways to utilize their excess apples through manufacture of value-

added products, such as hard cider.

Since 1990, the US. market for cider has grown rapidly every year with over 4.6
million cases of hard cider sold nationally today, and is expected to exceed 75 million
cases in the next ten years (Rowles 2003). Historically, there has been little alcohol
production in Michigan because of regulation in Michigan and Canada. Legislation
changed in 1996 and the production, as well as the demand in microbreweries and

wineries continues to grow ever since.

Michigan being one of the nation's leading producers of apples, most of the
infrastructure needed to create a hard cider industry already exists. Trends in the wine
and microbrewery industries suggest that locally produced high-quality products are
being accepted and sought after by consumers (Proulx 1997). With this in mind,
numerous cider mills and microbreweries across the state are entering the hard cider
business. The local hard cider market is a small but growing one. Hard cider thus
provides an important potential value-added product for Michigan apple producers,

brewers and Vintners.

1.1.3 Beneficial Effects of Cider Consumption

Many people who do not regularly drink alcohol enjoy hard cider, due to its fruity
flavor and low alcohol content. Within this population, studies have shown that females
prefer the pleasant flavor of hard cider to beer (Anonymous 1998). Research also
suggests that drinking cider may be good for health, as cider is rich in antioxidants known
as polyphenols. Antioxidants may help stop cell damage, prevent cancer and degenerative
diseases like dementia. These factors will go a long way in making cider the alcoholic

beverage of choice in America in future.

Research also suggests that drinking cider may be good for health, as cider is rich
in antioxidants known as polyphenols (Guyot 2003). Antioxidants may help stop cell
damage, prevent cancer, and decrease the risk of heart disease as well as degenerative
diseases like dementia.

Polyphenols in the diet are becoming increasingly recognized as important in
long-term health and reduction in the risk of chronic disease. Various experimental
studies have investigated the effects of the consumption of food products rich in
polymeric polyphenol content such as tea, onions, apples and wine on diseases such as
cardiovascular diseases and cancer. These polymeric compounds are also thought to have
anti-oxidant properties and are still under investigation.

Additionally, polymeric flavan-3-ols also known as procyanidins are major
phenolic constituents in juices and fermented beverages as they are involved in many

quality criteria such as bitterness, astringency and shelf life (Alonso-Salces 2001).

1.1.4 Dessert Apples

Apples are the primary raw material for cider making. Traditionally, European
hard cider is made from bittersweet or bittersharp ‘cider’ apples. Polyphenols present in
cider apples are responsible for mouthfeel characteristics such as the astringency, and

bitter flavor generally associated with fermented beverages (Lea 1990).

Cider apples like Taylor’s or Brown’s Apple have higher sugar levels, a more
fibrous structure and high tannin content as compared to dessert apples like Jonathan or
Macintosh. Although traditionally cider was made from true cider cultivars, not all ciders

are made from true cider apples; many may contain dessert and culinary varieties. It is

however, rare for cider to be made from single cultivar only because the balance of sugar,
acid and tannin required for a successful product is difficult to achieve from any single
cultivar. A mix of fresh juice and apple juice concentrates along with other fermentable
sugars from cane, beet or high fructose corn syrup are now widely used in English

Cidermaking and are permissible to a limited extent in France.

Michigan does not grow cider apples. Michigan apples are sweet and classified as
‘dessert’ apples. Michigan grows more than 20 varieties of apples on a regular basis.
Some of the popular and common varieties are Jonathan, Gala, McIntosh, Northern Spy,
Red Delicious etc. Michigan grown apples may not have the balance of sugar, acids and
tannins required for manufacturing a successful alcoholic product. Michigan apples also
have lower tannin content, and consequently, lower procyanidin content. Thus, cider
made from Michigan apples may not have the same sensory attributes as that made from

cider apples.

1.2 Mainstream Cidermaking (Lea 2004; Proulx 1997)

1.2.1 Juice Preparation

The fruit used in Cidermaking is generally ripe and stored for a few weeks after
harvest so that all the starch can be converted to sugar. Ripe apples are pulped & pressed;
the form of pressing is a specific to region. Most major cider-makers use a high-speed
grater mill that feeds a horizontal piston press in a semi—continuous system.

The juice is clarified and collected in tanks. Before fermentation, the juice is blended
with fermentable sugar sources such as fresh juice, apple juice concentrate and glucose

syrups to the required levels. This mixture may have a specific gravity as high as 1.080-

1.100 to give a final alcohol of 10-12 %, which is then diluted before retail. Nutrients are
also added to ensure a complete and speedy fermentation to dryness. Diammonium
phosphate maybe added to bring up the levels of free amino nitrogen in the must, which
has lower levels than those in grape musts or beer worts. Vitamins like thiamin (0.2
ppm), panthothenate (2.5 ppm) and biotin (7.5 ppb) may also be added.

If clarified concentrates and adjuncts are to be fermented, a source of insoluble solids
is often helpful. This source allows the yeast cells a solid surface to rest on and from
which ethanol and carbon dioxide can be liberated. Otherwise the yeast tends to compact
at the bottom of the vat and a thin layer of these toxic end products builds up around each
cell, so that the metabolic activity ceases. Many cider makers also add pectolytic
enzymes like pectinase prior to fermentation of fresh.

The most significant adjunct is sulfur dioxide in the form of potassium metabisulfite
that controls the growth of acetic and lactic acid bacteria and suppresses the activity of

yeasts. The activity of sulfur dioxide decreases after 24 hours and yeast can then be

added.

1.3.2 Yeast Fermentation

In traditional ciderrnaking, no external source of yeast is added. However, since
the apples themselves contain mixed yeast microflora, spontaneous fermentation
commences within a few hours if the temperature of the juice is above 10 °C.

When no yeast is added and no sulfite is used, the first few days are dominated by
non-Saccharomyces species, which multiply quickly to produce a rapid evolution of gas

and alcohol. They hence generate a distinctive range of flavors. If sulfite is added to the

initial juice, non-Saccharomyces yeast and most bacteria are suppressed or killed. This
situation gives the Saccharomyces time to multiply after a lag phase of several days and
the fermentation proceeds to dryness with a more homogenous and benign microflora
than in the case of unsulfited juice.

The use of active dry wine yeasts has become almost universal since the 19805 in
the mainstream cider industry. Typically used are S. bayanus strains and S. uvarum or
their mixed inoculum on grounds that the uvarum will provide a speedy start but bayanus
copes better with higher alcohol levels and the fermentation to dryness conditions. The
strain of yeast used significantly affects the flavors in cider.

The juice is fermented in wood or stainless steel vats or barrels at 15—25°C
without mixing. Hard cider is a product of apple juice that has undergone two different
kinds of fermentation. The first fermentation is carried out by yeasts in anaerobic
conditions, which converts fermentable sugars to alcohol (Figure 1.1).

Figure 1.1 Conversion of fermentable sugars to ethanol

C6H1206 —) 2C2H50I‘I + ZCOZ
Sugar Alcohol Carbon Dioxide
(Glucose, Fructose) (Ethyl Alcohol) (Fermentation Gas)

Most UK cidermakers take the view that a complete ‘dry’ fermentation of cider
apple juice yields 10-12% alcohol in as little as two weeks is a desirable objective.
Incomplete fermentation can be obtained by removing the yeast halfway throughout the
process, thus retaining less alcohol and more fermentable sugars than ‘dry’ hard ciders. In
the US, commercial hard ciders usually contain about 5.5% alcohol and most are

carbonated (Lea 2004; Proulx 1997).

:A-‘I

Cider made from traditional methods is frequently subjected to malolactic
fermentation following the yeast fermentation. Malolactic fermentation is the
decarboxylation of malic to lactic acid and the consequent evolution of gas. Malolactic
fermentation is favored by lack of sulfiting, storage and nutrients released from yeast
autolysis. The main organisms effecting this change are Leuconostoc oenos and
Lactobacilli species. In modern factory Cidermaking, malolactic fermentation is
considered a nuisance and is not encouraged; the possibility is minimized by the use of

sulfite.

1.3.3 Racking and Clarification

Once fermentation is complete, the yeast is separated from the cider by a process
known as racking. Racking consists of drawing off the cider into clean casks, which
causes the suspended yeast to become dormant and sink to the bottom of the liquid.
Racking is best done by means of a pump and it may be necessary to repeat the operation

one or two more times for best results.

In commercial processes, racking is immediately followed by a clarification
process for blending and packing of the final product. In smaller units, the cider may be
racked into inert or oak tanks for a maturation period of several weeks. If this process is
carried out in traditional wooden vats, it is known as maturation. Maturation is an active
microbial process where bacterial inocula present in the pores of wooden tanks are
responsible for the flavor character of the cider. If the same process is carried out in
vessels made of oak, there is flavor transfer from the oak barrels to cider and the process

in known as aging.

10

Initial clarification may be performed by natural settling of well flocculating
yeast, by centrifugation, by fining or a combination of all three. Typical fining agents are

gelation or bentonite.

1.3.4 Blending, Final Filtration and Storage

Nearly all ciders are blended before sale. In a large factory, several fermentations
may be running concurrently from different must sources and intended for different
products. These products form the base ciders from which blending is performed
according to the cidermaker’s requirement.

Blending involves more than the cider itself. Water may be added to high-alcohol
bases for correcting the alcoholic strength for retail sale. Sugar and other sweeteners,
malic and other acids, permitted food colors and preservatives may all be added to obtain
the final product. The cider is also carbonated. Nearly all cidermakers add 50 ppm of 802
at filling to give an equilibrium of 25 ppm free SO; in the beverage to inhibit any residual
yeast.

Final filtration may take place just before and after blending. Generally, powder
filters or coarse disposable sheets are used to produce a bright product, followed by
membrane filtration to remove all yeasts and most bacteria. Cross-flow ultra filtration
systems are now becoming widespread in the cider industry despite occasional problems
of membrane blockage and poor throughput. Most ciders are then pasteurized and
carbonated into the final pack. Most large factories have a HTST treatment in a flow-

through pasteurizer followed by a chiller and aseptic filling conditions.

11

Small filters suitable for cider making on the farm are also available. Small filters
may use a method of filtration in which the cider under pressure through a vessel
containing a quantity of wood or paper pulp. For the production of a clean sparkling
natural cider with even a slight degree of sweetness, a filter is almost indispensable. The
only substances removed from the liquid by filtering consist of yeast, particles of pomace
and dirt. The body, flavor and aroma of the cider remain relatively unchanged.

The storage of cider after the fermentation is over naturally or has been artificially
arrested requires extreme care to avoid transformation of the alcohol into vinegar. With
the end of the fermentation, protection afforded by the gas released during fermentation is
no longer available. Hence, precautions must be taken to exclude the air as much as
possible and maintain a low, even temperature in the storehouse. No air lock is now
required but the casks should be completely filled and all wastage caused by evaporation

through the wood made good from time to time.

1.3 Modeling of Alcoholic Beverage Fermentation

1. 3.1 Justification for research

Production of alcoholic beverages always undergoes changes due to modernization.
Improvements to the fermentation step, which, despite being a major part of the
fermentation process, is still carried out empirically, are particularly important.
Mathematical modeling of fermentation kinetics will enable better process control and
thus improve the efficiency of the fermentation process. Mathematical modeling
techniques can be used to scale-up from lab scale to commercial beverage production.

For example, such models would help cidermakers to predict the effect of sugar and

12

nitrogen addition on the progress of fermentation and quality of final product.
Mathematical models also reduce the number of trial-and-error experiments needed and
allow prediction of trends.

Slow and incomplete alcoholic fermentation is a chronic problem for the alcoholic
beverage and especially the wine industry. Under certain circumstances, fermentations
may take significantly longer than usual to finish or leave residual sugar greater than
0.4%, which is classified as sluggish and stuck fermentation (Cramer et al. 2002; Salmon
and Barre 1998). These abnormal fermentation kinetics are considered a serious problem
in an industrial setting and can lead to loss of tank capacity due to longer processing time
and the potential for further fermentation of the final product due to the residual sugar
(Sainz et a1. 2003). Hence, early diagnosis of the cause of such fermentation arrest is
critical. Currently, an incomplete fermentation is not recognizable until the rate of sugar
consumption has been observed to decrease. Thus the ability of a model to predict the
fermentation kinetics prior to yeast inoculation and based solely on the apple juice
characteristics will be a useful tool. Such a model can then be used to prevent and combat

fermentations that may tend be sluggish or stuck.

I. 3.2 Nitrogen Limitation

The most studied cause of sluggish and stuck fermentations is low nitrogen levels.
Nitrogen in the apple juice is made up of an arrunonia component and a more complex
amino-acid based nitrogen component. Nitrogen compounds are often present in a small
amount in the must and it can be the limiting factor for yeast growth and activity (Bisson

and Butzke 2000). Addition of ammonium ions during the stationary phase can partially

l3

reactivate the hexose transport system and hence increase the fermentation rate (Salmon
1989). Several groups have reported a transition point which may correspond to the point
at which biomass no longer increases with increasing initial nitrogen in some juices (Bely
1990, Ingeldew 1985).

Other have shown that nitrogen addition throughout the course of fermentation is
also effective to varying degrees in assuring rapid completion of sugar utilization,
especially when the nitrogen level is low (Bely et a1. 2003). Researchers (Jiranek et al.
1995) found specific amino acids that might limit fermentation in cases and also that
amino acids could be grouped into three categories based on the utilization pattern with
one group (including arginine) preferentially depleted from the medium. While a detailed
mechanism of regulation based on nitrogen components of juice has not been established,
it is clear that nitrogen can play a key role in determining both the rate and extent of
normal and problem fermentations (Cramer et a1. 2002).

It has been observed that exhaustion or near exhaustion of nitrogen corresponds
with the time of cessation of the exponential phase of cell growth. In the later stages of
fermentation that follow exhaustion of nitrogen, the rate-limiting macronutrient is only
sugar.

Slow and incomplete fermentations are a chronic problem for the wine and beer
industries. The factors leading to sluggish and stuck fermentations have been extensively
studied (Bisson 1999; Cramer et a1. 2002; Del Nobile et a1. 2003). Nitrogen has also been
linked with low cellular activity and resultant biomass concentration in yeast (Monteiro

and Bisson 1991; Spayd et al. 1994). Supplementation of nitrogen in the form of

14

diarnmonium phosphate or sulfate can alleviate problems that arise from low initial
nitrogen level.

Cider apples need 100 ppm of supplemented nitrogen in the form of free alpha-
amino nitrogen for complete fermentation. Nitrogen is generally supplemented in the
form of Diammonium phosphate (DAP); 100 mg/L of DAP provides 21.1 mg/L of atomic
nitrogen that is entirely assimilable (Malherbe et a1. 2004). The permissible limit for use

of nitrogen for alcoholic beverage production in US is 203 mg/L.

1. 3.3 Temperature Effect

Temperatures affect the rate of fermentation by giving higher rates and shorter
fermentations at higher temperatures. The yeast cell membrane permeases have been
shown to be highly temperature-dependent due to conformational changes in these
molecules (Entian and Barnett 1992). Leao and van Uden (1985, 1982a, 1982b) and Sa-
Correia and Van Uden (1983) have shown that for temperatures from 15 to 25°C, glucose
transport and glycolytic flux increase steadily with temperature.

Lower temperatures also result in lower rate of amino acid assimilation, which is
consistent with the observation of lower rates of fermentation and yeast grth (Lopez et
al., 1996). For anisothermal fermentations, when temperatures were raised to the value of
an isothermal curve, reactivation was more marked for must with the highest level of
assimilable nitrogen curves (Malherbe et a1. 2004; Sablayrolles et a1. 1996). The rate of
fermentation has also been shown to increase almost linearly with temperature and give

curves with very similar and normalized superimposed curves (Malherbe et a1. 2004).

15

Although several kinetic models have described single-temperature isothermal
conditions(Marin 1999), most fermentations are carried out under anisothermal
conditions. A study published recently investigated the effect of temperature on the
kinetic parameters of ethanol fermentation (Phisalaphong; et a1. 2006). They concluded
that the kinetic parameters of the proposed model have an Arrhenius relationship with
temperature. The study also observed that temperatures higher than 35 °C led to a
decrease in ethanol and cell yields.

Thus, temperature can affect the assimilation and uptake of nitrogen and sugar
and consequently alter the fermentation rate. Hence, we have extended our study to

include the effect of different fermentation temperatures on fermentation kinetics.

1.3.4 Modeling of Fermentation Kinetics

Currently, there is no available literature on modeling of cider fermentation.
However, significant research has been conducted in enology and viticulture. An analogy
can be drawn between cider and wine making, as they are both yeast fermentations of
fruit or fruit juice.

Fermentation kinetics of products like cider are complex and challenging to
model since it may involve numerous yeast strains that adapt to highly variable
environmental conditions. The yeast utilizes chemical signals to determine the
concentrations of some nutrients, such as fermentable sugars, assimilable nitrogen,
oxygen, vitamins, ergosterol and the presence of inhibitory substances such as ethanol,
agrochemical residues, killer toxins, and so on to adapt to changes in the extra cellular

environment during wine fermentation. While the causes of problem fermentations have

16

been well documented, we have not yet understood the basic mechanism that results in
the cessation of the conversion of sugar to ethanol. Such complexity accounts for the
difficulty in predicting the kinetic behavior of the fermentation process. Hence, the
construction of an 'exact' model for fermentation is unrealistic. A model may be
considered satisfactory if it can be used to predict the state of the bioreactor or
fermentation at any point in time in terms of measurable quantities that can be changed or
modified for fermentation management (Malherbe et a1. 2004).

Several models for microbial growth have been developed over the last 40 years
(Marin 1999). Many of these models may be classified as empirical (McKellar and
Knight 2000, Peleg 1996, Schaffner 1995) and they describe sigrnoidal frmctions that
approximate bacterial growth curves (cell concentration compared with time). Whereas
empirical models are usefirl for correlating a wide range of batch grth data and have
predictive value, they fail to provide any real insight into the underlying mechanisms
controlling cell growth. On the contrary, mechanistic models, which are more complex
from a mathematical point of view, give a description of phenomena involved in cell
growth providing valuable quantitative information that can be advantageously used to
control microbial growth.

Mechanistic models developed have typically used growth expressions previously
established by Monod (1956) or Baranyi (1994). Thus, these models have indirectly
linked cell growth and ethanol production using classic kinetic structures. Kinetic
parameters in these models are simultaneously dependent on yeast strain, must
composition and the development of fermentation, which vary significantly with different

fermentation practices.

17

One of the first comprehensive kinetic models for wine fermentation was reported
by Boulton (1980). This mechanistic model included the influence of glucose and
fructose levels, ethanol levels, and temperature on sugar utilization and captured the
general trend found in practice. Caro et a1 (1991) used a similar mechanistic model to
describe sugar utilization but also included sugar utilization pathways other than ethanol
production through respiration in order to address the mismatch in ethanol concentration
found in previous models.

Two of the most recent mechanistic models in enology have been proposed by
Cramer et a1 (2002) and Del Nobile et a1 (2003). Both are unstructured mechanistic
models for wine fermentation kinetics and assume nitrogen as the only growth-limiting
nutrient. However, Cramer et a1. uses Monod relationship to describe the specific growth
rate while Del Nobile et a1 uses the 'inhibition function' derived by Baranyi and Roberts
(1994) to describe the specific growth rate. This specific grth rate accounts for the
dependence of yeast cell growth rate on nitrogen concentration in the must.

During our experiments, it was observed that once assimilable nitrogen had been
exhausted, the growth rate stopped its exponential rise. This phenomenon has been

confirmed by other researchers (Cramer et a1. 2002).

1.3.5 A Generic Mechanistic Model

When yeast cells are inoculated into a new extracellular environment like apple
111106, the cells try to adapt to the new media. Their grth as well as death rate is
negligible during this time and this phase is thus known as the lag phase (Baranyi et al

1993a, 1993b). The environmental conditions are favorable for cell growth with high

18

nutrient concentration in form of fermentable sugars and low levels of toxic metabolites
like alcohol. Hence, once the lag phase is over and the cells adapt to the media, the cell
proliferation rate rises exponentially while the death rate remains negligible (exponential
phase). As the cells grow, they reduce the nutrient concentration and release metabolites
that are toxic for them and their growth rate starts dropping until it drops to zero
(stationary phase). As this continues, the grth finally becomes less than the death rate
leading to a decrease in the cell concentration (death phase). To predict this grth curve,
it is necessary to describe the proliferation and death rate of cells as well as the rate of
change in the extracellular environment.
Most mechanistic models proposed to describe the fermentation kinetics of alcoholic
beverage have the following common features:
1. Nitrogen is the primary growth-limiting nutrient for yeast cell grth (Bailey and
Ollis 1986b; Cramer et al. 2002)
2. Sugar consumption and ethanol production is proportional to the viable yeast cell
concentration;
3. The death rate of cells is proportional only to the alcohol content (Ansaney-
Galeote et a1. 2001; D'Amore et al. 1990)
Simple mechanistic models can be described in terms of four differential equations
that describe the kinetics of yeast cell, total nitrogen, sugar and ethanol concentrations.

The growth rate of microorganisms is given by the following equation:

dX V
dt

 

=1.l.XV—kd.XV (1.1)

19

where X V = viable yeast cell concentration, p. = specific growth rate h", kd = ethanol
dependent death rate h".

The rate of nitrogen consumption or depletion is given by:

dN_,u.XV
7;;— YX/N (1.2)

where Yx/N = Yield co-efficient of biomass on nitrogen.

The rate of sugar depletion in cider is given by:

dS _ ,3.XV
ET:— YE/s (1'3)

where Y E/S = Yield co-efficient of ethanol on sugar,
3 = specific ethanol production rate.

The rate of ethanol production is given by:

dE
—d't—=fl.XV (1.4)

The above set of differential equations needs to be solved simultaneously and the
model predictions need to be compared with the experimental data for validation.

To date, very few researchers have studied hard cider production fiom‘ dessert
apples (Wilson et a1. 2003). None of these studies has attempted to study the fermentation
kinetics of the process. Although several kinetic models have been proposed in enology
literature, very few (Malherbe et a1. 2004) have studied the effect of temperature on

fermentation kinetics, even though a majority of fermentations are performed under

20

anisothermal conditions. Further, none of these models have been applied to hard cider

manufacturing.

1.3.6 Objectives

Based on information presented in the preceding sections, it is hypothesized that initial
nitrogen and external temperature during fermentation will have a significant Arrhenius
type effect on fermentation kinetics (Cramer et a1. 2002; Del Nobile et a1. 2003; Malherbe
et a1. 2004). Hence, the objectives of the present study were:

1) To show that a mechanistic model based on Monod kinetics can adequately
describe hard cider fermentation from dessert apples,

2) To validate the hypothesis that nitrogen is the rate-limiting nutrient for cell
grth and that the concentration of initial nitrogen has a significant (p<0.05)
effect of the Arrhenius type on hard cider fermentation (Cramer et a1. 2002; Del
Nobile et a1. 2003; Malherbe et al. 2004),

3) To validate the hypothesis that external temperature has a significant (p<0.05)
effect of the Arrhenius type on fermentation kinetics of hard cider (Phisalaphong;
et a1. 2006).

Hard cider’s popularity continues to grow in the US and large-scale production will
increase the demand for methods that will help understand and forecast fermentation
results. A simple, mechanistic model that could predict the fermentation kinetics of hard
cider production, especially from dessert apples, will prove useful in understanding and

designing processes.

21

CHAPTER 2: Materials and Methods
2.1 Fermentation Setup
Apple Juice

Hard cider is generally made from fermentation of a blend of as many as dozen
different varieties of mostly cider and some dessert apples. However, using such a blend
for fermentation experiments would increase the variability in the composition of apple
juice and add additional factors to the model. Cider apples are not cultivated on a large
scale in North America. Efforts to grow them in parts of United States have not been very
successful. Since dessert apples are facing the problem of excess production, it makes
economic sense to produce hard cider from dessert apples. Consequently, only one
variety of American dessert apples, i.e., Jonathan apples, was selected for
experimentation.

Jonathan apples are generally small to medium in size and dark to bright red in
color. They are used for cooking and baking as well as fresh eating. The peak time of the
year for the availability of Jonathans is early fall to late winter, and they are the third
highest-volume apple produced in Michigan. However, Red Delicious, Golden Delicious,
Gala and J onagold have a higher consumer demand, resulting in an excess production of
Jonathan apples (Michigan Apple Committee 2005). Jonathan apples are juicy, aromatic
and moderately tart. All these factors make Jonathan apples ideal candidates for
manufacturing value-added products such as cider.

Michigan Jonathan apple juice was obtained at Uncle John‘s Cider Mill (St. Johns,

MI, USA) and stored at —18°C in plastic one-gallon containers for a period of 3-8 months.

22

The approximate sugar concentration of the apple juice was 120 g/L and the nitrogen

concentration was 45 mg/L. The pH was measured to be 3.26 i 0.03.

Yeast

Lalvin's DVlO Saccharomyces cerevisiae (bayanus) yeast (Lallemand Inc,
Rexdale, ON) was selected. The juice was inoculated with 0.3 g dry weight/L of DVlO.
As per the manufacturers’ recommendations, the yeast was not rehydrated before
inoculation. DVlO is one of the most widely used strains for champagne production and
is the most recommended strain for cider and mead (an alcoholic beverage made from
fermented honey and water) production. DVlO has strong fermentation kinetics over a
wide temperature range (IO-35° C) with relatively lower oxygen and nitrogen demands.
DVlO is known for clean fermentations that avoid bitter sensory attributes associated
with many other strains. It has an 18% alcohol tolerance and can ferment under stressful
conditions of low pH or high 802. It is also low foaming and low volatile acid
production, a factor that may affect the sensory attributes of the final cider (Lallemand

Inc, Rexdale, ON).

Nitrogen Supplementation

Apple juice contains considerably less free amino nitrogen than grape must or
beer worts and this lack of nitrogen can place a severe limit on yeast growth,. Therefore,
common practice is to bring the level up to ca 100 mg nitrogen per liter (Lea 2004),
which can be achieved by adding 250 ppm ammonium sulfate or phosphate. 100 ppm of

diarnmonium phosphate (Sigma Chemical Co., St. Louis, MO), henceforth referred to as

23

DAP, provides 21.1 mg/L of atomic nitrogen, entirely assimilable (Malherbe et a1. 2004).
The permissible limit for nitrogen supplementation in the form of DAP in the US is 960

mg/L of DAP, corresponding to 203 mg of nitrogen/L (203 ppm).

Experimentation

Frozen Jonathan apple juice stored in l-gallon containers was thawed. The juice
was sterilized by addition of 50 ppm of potassium metabisulfite (Sigma Chemical Co., St.
Louis, MO) and left to stand for 24 hours. Potassium metabisulfite inhibits the grth of
spoilage yeasts and bacteria thus permitting the desirable fermenting yeasts (such as
Saccharomyces cerevisiae or uvarum) used for inoculation to multiply and dominate the
conversion of sugar to alcohol. For apple juice with pH of 3.0 to 3.3, addition of 50-75
ppm potassium metabisulfite is recommended (Lea 2004). After 24 hours, the sulfited
juice was transferred into 500-ml flasks filled up to the 400-ml level and inoculated with
the DVlO yeast. For each condition of temperature and initial nitrogen level, triplicates
were fermented (Table 2.1). All flasks were fitted with fermentation locks (Michigan
Brewing Company, Webberville, MI). The control was flasks containing sulfited apple
juice that did not contain any added yeast inoculum or DAP. This control sample allowed
us to track any unforeseen changes in experimental conditions or any contamination of
samples after the start of experiments. The fermentation flasks were stored in incubators
with temperature control during experimentation. The flasks were also minimally agitated
at 60 rpm using flask shaker tables for uniformity of the samples and their temperature.

Four levels of initial nitrogen and three levels of temperature were selected. The

four levels of nitrogen were selected to represent the range of total initial nitrogen

24

between the residual concentration (in apple juice) of 45 ppm to the legally permissible
limit of 200 ppm (Lea 2004; Malherbe et a1. 2004). Hard cider fermentations are usually
performed at cooler temperatures. Traditional fermentations are carried out at
temperatures of >10 °C and a range of 15-25 °C is considered preferable (Lea 2004). It
has been found from sensory analysis (unpublished data) that pure, unblended hard cider
produced at higher temperature (>20 °C) has sensory attributes that many consumers do
not like. Hence the three temperatures, 11 °C, 17 °C and room temperature of 22 °C were
selected. Temperature measurements of air inside the incubator at periodic intervals
showed that the variation in these temperatures was 21:2 °C. The cider samples were not
measured for temperature. It was assumed that for the small volumes of fermenting cider,
use of shakers and the natural agitation resulting from the formation of carbon dioxide
inside the cider would help maintain uniformity of temperature of the sample. However,
since fermentation is an exothermic process, it is possible that the internal sample
temperature may be higher than the external environment. However, this is akin to an
actual fermentation in microbreweries where only the external environment is controlled
and the fermenting samples may be at a much higher temperature.

The experimental plan, tabulated below, was repeated three more times giving a
total of four sets of data. One of these sets of data was rejected due many errors in
analyzing the samples. Of the three remaining sets of data, one data set was used for
estimating the parameters of the proposed mathematical model. This data set is
henceforth referred to as the ‘parameter estimation data set’. The two remaining data sets
were combined and used to validate the model. This combined data is henceforth referred

to as the ‘model validation data set’.

25

Table 2.1: Experimental Plan

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Yeast (0.3g/L) DAP
Flask (°C) Y = Yes, N = No (Wu
1 11 N 0
2 11 N O
3 11 N O
4 11 Y 0
5 11 Y 0
6 11 Y O
7 l 1 Y 100
8 11 Y 100
9 11 Y 100
10 11 Y 300
1 1 11 Y 300
12 11 Y 300
13 11 Y 600
14 11 Y 600
15 11 Y 600
16 17 N O
17 17 N 0
18 17 N 0
19 17 Y 0
20 17 Y O
21 17 Y O
22 17 Y 100
23 17 Y 100
24 17 Y 100
25 17 Y 300
26 17 Y 300
27 17 Y 300
28 17 Y 600
29 17 Y 600
30 17 Y 600
31 22 N O
32 22 N O
33 22 N O
34 22 Y 0
35 22 Y O
36 22 Y 0
37 22 Y 100
38 22 Y 100
39 22 Y 100
40 22 Y 300
41 22 Y 300
42 22 Y 300
43 22 Y 600
44 22 Y 600
45 22 Y 600

 

 

 

Figure 2.1 Fermentation Setup

2.2 Methods of Analysis
Sample Preparation

Prior to sampling, each flask was mixed by swirling in order to suspend all solids
and achieve uniformity. Samples were drawn at various time intervals using lO-mL
disposable pipettes to prevent cross contamination, and stored in disposable plastic test-
tubes (Corning Inc., Corning, NY). Each test-tube was agitated to mix the sample. 50 uL
of the sample was withdrawn in triplicate into wells of a 96—well plate for enumeration of
yeast cell counts. Another 3ml was withdrawn and centrifirged (Beckman Coulter Inc.,
Fullerton, CA) at 3000 rpm for 5 minutes to settle suspended solids. The centrifuged
samples were then further clarified by filtration through 25 mm Nylon 0.2 pm disposable
syringe filters (Waters Corp., Milford, MA). The purified samples were stored in 1.5 ml
microcentrifuge vials (BioDot Inc., Irvine, CA) and frozen for analysis later. The original

unfiltered samples were also stored frozen in test tubes.

27

Due to lack of sufficient resources and the large number of samples that needed
sampling and analysis, it was not possible to take samples at periodic intervals.
Additionally, some of samples did not generate any data points due to errors during
analysis. Hence, the number of observed data points differs for different conditions and

variables.

Viable Yeast Cell Concentration

Viable cell numbers were estimated microscopically using a Neubauer-type
Bright Line Counting Chamber (Hausser Scientific, Horsham, PA). Triplicates of each
sample (50 uL) were withdrawn into wells of a 96-well plate. To each well, 50 ul of 0.4%
(w/v) Trypan blue was added to dye the non-viable cells and ensure that only viable cells
were enumerated (Nielsen et a1. 1991). The well was mixed thoroughly using a pipette.
This mixture of sample and trypan blue formed a 1:2 dilution of the cells. The
haemocytometer and the cover slip were cleaned and dried. The cover slip was then
placed over the counting surface prior to loading the cell suspension. From each well, 10
ul of cell mixture was transferred to each of the two V-shaped wells with a Pasteur
pipette. The chamber fills by capillary action. The charged counting chamber was then
placed on the microscope (Reichert Microscope Services, Depew, NY) stage and brought
into focus at 40X power.

Because the counting chamber has an exact volume under the cover slip, one can
determine the concentration (cells/mm3) of live and dead cells in the chamber. The cell
concentration of the original cell suspension will be the same as that of the chamber.

Dead cells take up the trypan blue dye and appear blue under the microscope. Living cells

28

exclude trypan blue, and appear white. Thus, the percentage of viable cells can be
calculated.

The viable cell density of the original mixture was determined according to the
following formula:
The number of cells per cubic millimeter = number of non-dyed cells counted per square

millimeter of counting chamber X Dilution X 10

Assimilable Nitrogen

Nitrogen that can be utilized by yeast cells for their growth or maintenance is
known as assimilable nitrogen. Assimilable nitrogen in cider is in the form of ammonium
ions and free (rt-amino nitrogen compounds. It is necessary to estimate the concentration
of both these forms as they represent all the total nitrogenous compounds that are directly
utilized by the yeast for growth. Detailed below are the two procedures for determining
ammonium ion concentration and the (1 —amino nitrogen concentration.

Ammonium ion concentration was determined using an Ammonium Ion Selective
Electrode (Cole-Parmer Instrument Co., Vernon Hills, IL). The electrode was connected
to a pH meter (Corning pH meter 440, Cole-Parmer Instrument Co., Vernon Hills, IL)
and the reading scale was changed to millivolt. The Ion Selective Electrode method was
selected for its ease of use and has been shown to be accurate and consistent with
readings obtained by an enzymatic assay (Turbow, S.B., Wehmeier, G.H., et al., 2002).

The electrode was first calibrated as recommended by the manufacturer. A 1000-
ppm standard ammonium solution was prepared by adding 2.97 grams of reagent grade

ammonium chloride (Sigma Chemical Co., St. Louis, M0) to 1 liter of distilled water in a

29

 

volumetric flask. Standard solutions of 100 and lO-ppm ammonium solutions were
prepared by dilutions from this lOOO-ppm solution. A standard curve of ammonium ions
versus voltage reading was obtained by plotting the readings in triplicates for the above
solutions. The concentration of ammonium ions was determined from the standard curve
and the voltage reading of the cider samples. All readings were taken in triplicate at room
temperature with a 3 m1 sample in a 25 ml test tube. Sodium chloride (5M) was added at
a concentration of 2m] for 100ml sample as a standard base ion concentration.

The (1 -amino nitrogen was determined using the enzymatic method of Dukes and
Butzke (1998). The method uses a spectrophotometric procedure to measure the primary
amino nitrogen fraction and thus quantify the levels of yeast assimilable nitrogenous
compounds in cider. The assay is based on the derivatization of primary amino groups
with an o-phthaldialdehyde/N-acetyl-N-cysteine (OPA/NAC) reagent. The resulting
isoindole derivatives form rapidly and are stable (absorbance) at 335 nm.

The reagent solution consisted of 0.671 g of ortho-phthaldialdehyde or OPA
dissolved and made to 100 ml with 95 % ethyl alcohol. This solution was added to a
lOOO-ml volumetric flask that contained an aqueous solution of 3.84 g sodium hydroxide,
8.47 g ortho-boric acid and 0.816 g N—acetyl-L—cystiene. The flask was then made up to
volume with deionized water. The same buffer was made without OPA. Both the
solutions were stored at 4 °C and are stable for three weeks. All of the above chemicals
were sourced from Sigma-Aldrich Chemical Co., St. Louis, MO.

For analyzing a-amino nitrogen, 50 ul of the centrifuged cider sample was placed
in a 10 ml test tube to which 3 ml of the above reagent containing OPA was added. The

tube was vortexed and decanted into a UV-grade methyl acrylate cuvette. A juice blank

30

was also analyzed using the reagent buffer that did not contain OPA. The absorbance of
the samples was measured at 335 nm using a DU 520 General Purpose UV/V is
spectrophotometer (Beckman, Fullerton, CA, USA). All measures were carried out at
room temperature and the net absorbance was calculated by subtracting the absorbance of
the blank from than of the sample.

Total assimilable nitrogen was determined from the sum of nitrogen in the form
of ammonium ions and (1 -amino nitrogen.
Sugar

Individual sugars were measured using a Waters 6100 HPLC system with
Hamilton PRP-X300 Ion Exclusion column. The HPLC apparatus consisted of 717
Autosampler, a 996 Refractive Index Detector and Breeze 32 Manager System. The
method used a mobile phase containing 1 mM Sulfuric acid and 0.001 N HZSO4. The
sample injection volume was 20 ul while the elution conditions included an isocratic
gradient and a flow rate of 2ml/min. The column and detector were both at room
temperature (~25 °C).

Standard peaks of glucose, fructose and sucrose (Sigma-Aldrich Chemical Co., St.
Louis, M0) were monitored at ambient column temperature. The samples were loaded
into the HPLC in a Waters l-ml glass vial with polyethylene snap cap for a run time of 5
minutes.

Apple juice and hard cider samples were spiked with glucose to validate the

above process. The chromatograms are shown in Appendix E.

31

Ethanol

Ethanol concentration was measured using a Waters 6100 HPLC system with
Hamilton PRP-X300 Ion Exclusion column. The HPLC apparatus consisted of 717
Autosampler, a 996 Refractive Index Detector and Breeze 32 Manager System. The
method used a mobile phase containing 1 mM sulfuric acid. The sample injection volume
was 10 ul while the elution conditions were as follows: isocratic gradient, flow rate of
lml/min. The column and detector were both at room temperature (~25 °C).

Standard peaks of 99.9 % pure ethanol (Sigma-Aldrich Chemical Co., St. Louis,
M0) were measured at ambient column temperature to develop a standard curve. The
samples were loaded into the HPLC in a Waters l-ml glass vial with polyethylene snap
cap for a run time of 15 minutes.

The above process of ethanol detection was validated by spiking hard cider

samples with ethanol. The chromatograms are shown in Appendix E

32

 

2.3 Model Development & Validation

2.3.1 Primary Model

 

   

Stationary
Phase

    

Log of cell numbers

 

 

Age of Culture

 

 

 

Figure 2.2. Yeast Life Cycle

When yeast cells are inoculated into a new extracellular environment like apple
juice, the cells try to adapt to the new media. Their growth, as well as death rate, is
negligible during this time. This phase is thus known as the lag phase (Baranyi and
Roberts 1993a; Baranyi and Roberts 1993b). The environmental conditions are favorable
for cell growth with high nutrient concentration in form of fermentable sugars and low
levels of toxic metabolites like alcohol. Hence, once the lag phase is over and the cells
adapt to the media, the cell proliferation rate rises exponentially while the death rate
remains negligible (exponential phase). As the cells grow, they reduce the nutrient
concentration and release metabolites that are toxic for them and their growth rate starts
dropping until it drops to zero (stationary phase). As this continues, the growth rate

finally becomes less than the death rate leading to a decrease in the cell concentration

33

(death phase). To predict this grth curve, it is necessary to describe the proliferation
and death rate of cells as well as the rate of change in the extracellular environment.
Most mechanistic models proposed for alcoholic beverage fermentation kinetics
have the following common features:
1. Nitrogen is the primary growth-limiting nutrient for yeast cell growth (Cramer et
a1. 2002);
2. Sugar consumption and ethanol production are proportional to the viable yeast
cell concentration;
3. The death rate of cells is proportional only to the alcohol content (Ansaney-
Galeote et a1. 2001)
A simple mechanistic model that describes the kinetics of yeast cell, total nitrogen, sugar
and ethanol concentrations in terms of four ordinary differential equations was used to
describe the fermentation process.

The growth rate of microorganisms is given by equation (1.1):

dX V
dt

 

=Ll.XV—kd .XV

Where X. = viable yeast cell concentration, cells/L, ,u = specific growth rate (h'l),

kd = ethanol dependent death rate (g L ethanol'l h").

34

T p-- W - . w —— e ~~i
; 120 y- —~— —- ~ — — —- —* -— — -—'"— — "‘ "“ +N,Nitrogen(mg/L)
\\ ' +11 Ethanol (g/L) i

——t—— S, Sugar (g/L)

S
o
l
l
l 2‘
m
l
l
l
l
l
i
l
l
l

—x—— Xv, Yeast Conc.
W Jlflcsfli/PB W l

60 “F -W W W -W W. W W. W -W .W- -W--W, W--_W .W- W W

 

Dependent Variable value A

i
i
i
|
l
l
l
i
l
l
l

 

 

 

 

O 50 100 150 200 250
'llme (hours) '

Figure 2.2. Generic Plot of Dependent Variables vs. time

The proposed model is based on Monod kinetics. The figure above shows a
generic plot for the four dependent variables as a function of time and helps explain the
principles behind Monod kinetics. Y represents any dependent variable. It has been
proven that the growth rate of microorganisms is hyperbolic in nature when only one
nutrient is growth limiting and all other nutrients remain the same (Bailey and Ollis
1986a). Monod (1942) proposed a functional relationship between the specific growth
rate u and the limiting nutrient’s concentration (Bailey and Ollis 1986a). It has been
observed in this and other studies that the sugar concentration does not change
appreciably until the end of the exponential phase of growth and the beginning of the
stationary phase (Cramer et a1. 2002; Del Nobile et a1. 2003; Malherbe et a1. 2004). Most

of the sugar is utilized during the stationary phase; thus, sugar is not a growth rate-

35

limiting nutrient. It has also been observed that near exhaustion of nitrogen in the
fermenting juice coincides with the end of the exponential phase of cell growth and the
start of the process of significant ethanol production (Cramer et a1. 2002; Del Nobile et
a1. 2003; Malherbe et a1. 2004). Hence, nitrogen was considered as the rate-limiting
nutrient and cell growth was proportional to the total nitrogen concentration. Of the same
form as the Langmuir adsorption isotherm (1918) and the standard rate equation for
enzyrne-catalyzed reactions with single substrate (Henri, 1902 and Michaelis and
Menten, 1913), the Monod equation states that
[.1 m N

,u = KN + N (2‘1)

Where pm = maximum specific growth rate (hr'l)
N=nitrogen concentration (ppm)
K Ar: Monod constant for Nitrogen (ppm)
The rate of nitrogen consumption or depletion is given by (1.2):
fl _ ,u . XV

dt YXW
where YX/N = Yield co-efficient of biomass on nitrogen. This is different from Y, which

represents any dependent variable.

The rate of sugar depletion in cider is given by (1.3):

iii_fl.XV
dt YE/S

where Yg/S = Yield co-efficient of ethanol on sugar. This is different from Y, which

represents any dependent variable.

36

,8 = specific ethanol production rate, (g ethanol/cell-hour).

It has been shown that most of the conversion from sugar to ethanol occurs during
the stationary phase and is non-growth associated (Cramer et a1. 2002; Del Nobile et a1.
2003; Ludeking and Piret 1959). Although this does not rule out ethanol formation during
the growth phase, it assumes that ethanol produced during the growth phase is an
insignificant part of the total ethanol production, a trend also shown by the experimental
data. Hence the model does not include any term to describe the relationship between
grth rate and ethanol production rate.

The model does not distinguish between the types of sugars in fermenting juice.
Although most of the sugar is in the form of glucose and fructose and can be directly
used by the yeast, a small quantity is sucrose. Yeast breaks down sucrose into assimilable
components, namely, glucose and fructose, using the enzyme invertase synthesized by the
yeast itself.

Thus

,BmS
._. Ks+S <22)

Where Bm= maximum specific ethanol production rate, (g ethanol/cell-hour)
S=sugar concentration (g/L)
KS: Monod constant for sugar (g/L)

This form of specific ethanol production rate is consistent with previous
observations that sugar transport is facilitated by diffusion, which in turn, is governed by
the concentration of sugar and ethanol.

The rate of ethanol production is given by equation (1.4):

37

dE
—= .X
dt fl V

The primary model is defined as the set of equations from (1.1) to (1.4) and equations

(2.1) and (2.2).

2.3.2 Procedure for Parameter Evaluation

The following plan of action was adopted to estimate the model parameters:

Step 1: Initial Estimates for Parameters

The primary model contains seven parameters of which six can be estimated initially
from previous literature and our experimental data. Observations from studies by (Cramer
et a1. 2002) and (Del Nobile et al. 2003) were used to obtain initial estimates.

The estimate for ,Um, maximum specific growth rate (hr'I), was obtained from the slope

of the semi log plot of viable cell concentration and versus time. These values were
plugged into the model and the model was solved using a program in MATLAB© to
compare the predictions with raw data. The parameter was then manually adjusted along
with other parameters until a ‘visual fit’ to the experimental data was obtained.

,Bm , specific ethanol production rate, (g ethanol/cell-hour), was similarly obtained from
equation (1.3) from the slope of a plot of specific ethanol production rate versus time.
The yield co-efficient of biomass on nitrogen, Y m; (no. of cells/ g N), is the stoichiometric
yield coefficient of biomass on nitrogen. The initial estimate for YX/N was obtained from
literature (Shuler and Kargi 2001).

kd (g L ethanol'l h") is the ethanol-independent death rate constant and was obtained

from literature (Cramer et al. 2002). Its value was fixed at 0.005. This value cannot be

38

 

easily calculated from experimental data and little previous literature is available on the
subject. The ethanol independent death rate constant shows a noticeable effect on the
stationary and death phases of cell growth; however it was observed to have a minor
effect on the prediction of other dependent variables.

The yield co-efficient of ethanol on sugar, YE/S (g ethanol/ g sugar), is the
stoichiometric yield coefficient of ethanol on nitrogen and can be obtained from simple

stoichiometric calculations from the equation in figure 1.1 on the experimental data.

C6H1206 —'> 2C2H50H + ZCOZ

Sugar Alcohol Carbon Dioxide
(Glucose, Fructose) (Ethyl Alcohol) (Fermentation Gas)
~116 g ~ 45 g

Based on experimental data it was found that the conversion of sugar into ethanol was
approximately 38%. Hence the value of this parameter, Yg/S (g ethanol/ g sugar), was
fixed at 0.38.

From preliminary data fitting, it was observed that due to complexity of non-
linear parameter estimation, the model would not converge and terminated without results
when more than five parameters were included in the parameter estimation process.
Hence, the five more important parameters that showed an effect of change in
independent variables were selected for the non-linear estimation process. The remaining
two, Y55 and kd were given fixed values and were excluded from the non-linear parameter

estimation process.

39

Step 2: Primary Model & Non-Linear Estimation of Parameters

To obtain a solution to the primary model, the above set of non-linear, coupled,
ordinary differential equations need to be solved simultaneously using numerical
integration techniques. A program was written in MATLAB© (Mathworks Inc, Natick,
MA) to solve the set of four differential equations using 4’h-order Runge Kutta formula.
The model consists of ordinary differential equations (ODE) for which we have only one
value for each of the dependent variables, that is, the value at time i=0. A numerical
solution to this problem can be obtained as given below.

The model is a coupled set of 1St order differential equations of the form

dy

E sz’J) (2.3)

Where f, y = n-dimensional vectors; y (or Y) is any dependent variable, t is time.

Formulae of the Runge-Kutta type are among the most widely used for numerical
solutions to ODE (Hombeck 1975). The Runge-Kutta formulae require the calculation of
several intermediate values of the function between tj and t 0+1), Before each of these
values can be calculated, a corresponding ‘y’ value must be found.

When we have a coupled set of equations as in the proposed model, complete
vectors, that is, all the vectors in this coupled set must be calculated, at each intermediate '
point before moving to the next intermediate point.

The 4th order Runge-Kutta formula is as follows:

1 1 1 1
yj+r=y)+At[-6—f(yj,t_,)+-3-f(y*j+r/2,tj+r/2)+§f(y**)+1/2,t;+r/2)+gf(yj+l,t,+i)]

(2.4)

40

 

Where

At
y*)+1/2=yj+—§-.f(yj,tj‘)

y**_/+I/2:M+éz£.f(y*j+I/2,tj+I/2)

y*j+l=yj+At.f(y**j+1/2,tj+I/2)

Since there is a cross coupling between the equations for these vectors, it becomes
necessary to update all the components of each vector before moving on to the next
vector. The intermediate values must be computed in the order given above because they
are interdependent. This formula requires four evaluations of f which is quite time
consuming. It is essential to verify that the step size is sufficiently small to give accurate
answers.

The advantages of using Runge-Kutta formulae are (Hombeck 1975):

1) Ease of programming,

2) Good stability characteristics,

3) Step-size can be changed without complications,

4) Self starting.
The disadvantages are:
1) Require significantly more computing time than other methods,
2) Local error estimates are difficult to obtain

The initial parameter estimates were substituted into the model, which Was solved
using 4th order Runge-Kutta formula and the software MATLAB©. Graphs comparing
the experimental data with the model predictions were plotted in MATLAB©. The initial

parameter estimates were manually adjusted until a good visual fit with the experimental

41

data was observed. The ‘parameter estimation data set’ (~ 110 data points per each
condition), that is, data from one set of experiments was selected as the experimental data
for this procedure.

Non-linear fitting estimates the coefficients (parameters) of a non-linear regression
function using least squares estimation. The values of the parameters were estimated
using non-linear regression for best fit to experimental data in MATLABQ.

Since the numerical value of XV, yeast cell concentration was many magnitudes
higher than the rest of variables; the error was highly magnified, skewing the non-linear
regression fitting process. This skewing led to termination of the data-fitting process
without any results or incorrect estimations of model parameters and poor fits to
experimental data. Weights were therefore assigned to each of the dependent variables
for the least squares estimation. Even for very small weights for the dependent variable
Xv, there were errors in the execution of the data-fitting process. Hence it was decided to

assign a zero weight to this variable.

WS=1
Where W= weight assigned for non-linear least squares estimation

Although Xv, yeast cell concentration, was assigned a zero weight for least
squares estimation, all the dependent variables were inter-connected. Due to cross
coupling of all the model equations, the parameters affecting Xv were estimated with

reasonable accuracy. Consequently, all the dependent variables including Xv were

42

predicted with reasonable accuracy in most cases. However, as a result of excluding Xv
from the data fitting process, prediction and asymptotic confidence bands for this variable
were not obtained.

The confidence and predictions bands for the predicted dependent variables and
the confidence intervals for the non-linear estimated parameters were calculated in
MATLAB© using the following commands:
ci=n1parci (Pp/NAL,r,.])
where ci=confidence interval for the parameters
PFINAL = vector of all the non-linear estimations of parameters
[ypred, delta] = nlpredci ('function', t, PFINAL, r, J, 0.05, 'on', 'curve')

Where ypred= predicted dependent variables;

t= time;

J=Jacobian matrix of predicted data

r=residuals from model predictions

The function ‘curve’ and the value ‘0.05’ tells MATLAB© to calculate 95% confidence
bands for the mean, the predicted curve for the dependent variable.

Similarly, the use of function ‘observation’ results in calculation of 95% prediction bands

for the observed data.

2.3.3 Secondary Model & Linear Estimation of Parameters
It is hypothesized that the kinetic parameters of the model have an Arrhenius
relationship with the independent variables. This relationship can be described in terms of

a secondary model as follows:

43

k=f(T,M-)

EN 1 1
Ink: lnkr+ %+(—-—r-)+ REM—N?) (2.5)

 

Where k= non-linearly estimated parameter from the previous section

T = temperature at which parameter was evaluated (°K)
N,~=initial nitrogen level at which parameter was evaluated (ppm)
T ,=reference temperature (°K)

E 7=activation energy for temperature effect (J/gmol)

E N=activation energy for nitrogen effect (J/gmol)

k,= value of the same parameter at reference temperature and reference initial nitrogen

R= Universal gas constant, 8.31 J K'] mol'l.

The non-linear parameter estimates from Step 2 were fitted to the above equation using

multiple linear regression in Excel©. The linear estimation yielded parameters k,, E MR

and E N/R for each non-linearly estimated parameter. The linearly estimated parameters

were substituted into the above equation to determine all k for each condition of

temperature and initial nitrogen.

Step 2.3.4 Procedure for Model Validation

The non—linear parameter estimates were fitted by multiple linear regression to

equation (2.5). This secondary model was then used to calculate the predicted parameter

44

values for 12 different conditions of temperature, T and initial nitrogen content, N,- using
the ‘model validation data set’. Note that this data consists of more data points (~250 per
condition of nitrogen and temperature) and is different from the ‘parameter estimation
data set’ used for estimating the parameters. These predicted parameters were substituted
into the primary model to get the model predictions for the four dependant variables (X,,
N, S, E) over time. These predicted values of Xv, N, S, and E were compared to the
validation data set.

A plot of each dependent variable versus time at every temperature-initial
nitrogen condition was obtained. This plot included the experimental and predicted data
as well as the asymptotic confidence bands and prediction bands (using function
’nlpredci’ in MATLAB©.) for the three dependent variables, N, E and S. A plot of the
predicted versus observed values was obtained for each of the 4 variables X, N, E and S
to evaluate the accuracy of predictions along with the root mean square error. The root

mean square error (RMSE) of the prediction was calculated as

SS
"-17

RMSE =

 

(2.6)

Where SS=sum of squared errors between predicted and experimental value of each
dependent variable

n=number of data points

p=number of estimated parameters.

Thus the effect of initial nitrogen content and temperature on fermentation kinetics was

studied.

45

Chapter 3. RESULTS & DISCUSSIONS

3.1 Initial Estimates for Parameters
The initial estimates for the seven parameters were obtained from literature and
experimental data as described in section 2.3.1.

Table 3.1: Initial Estimates for Model Parameters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DAP
Temp added Nitrogen I‘m flm K N K; Y m
(g ethanol (g (g (no. of cells/

(°C) (ppm) (ppm) (hr") cell”l hr") N/L) sugar/L) g N)
11 0 45 0.14 7 .37E-10 172.32 14.589 5.00E+06
11 100 65 0.1 8.00E-10 2000 10 1.50E+06
11 300 110 0.2 8.00E-10 2000 10 1.50E+06
11 600 165 0.45 1.50E-09 4000 90 2.00E+06
17 0 45 1.25 5.00E-10 500 10 2.00E+O6
17 100 65 1.9 9.00E-10 2000 1.00E+06
17 300 110 2 1.00E-09 5000 50 1.00E+06
17 600 165 2.3 9.10E-10 7700 10 1.20E+06
22 0 45 2.17 9.71E-10 243.11 100 1.00E+06
22 100 65 2.45 1.20E-09 200 40 2.00E+O6
22 300 110 2.9 1.50E-09 2500 80 1.8OE+06
22 600 1 65 3 9.00E-10 14200 38 2.50E+06

 

 

 

 

 

 

 

 

 

3.2 Non-Linear Parameter Estimation from Primary Model

Using these initial estimates, the model was solved for each condition by the
odelSs routine in MATLAB© that uses 4th-order Runge-Kutta formula. After solving the
model once using the initial estimates, the program compared the predictions of the
model with the observed values. It then used non-linear regression to iterate and estimate
the parameters for the best fit (minimization of least squares) to experimental data. The

program code and the experimental data are elaborated in Appendix A.

46

Due to the complexity of representing all the information obtained from fitting the
model to data, the Results section will demonstrate the working of the model for one
condition of independent variables, temperature (22 °C) and initial nitrogen content (65
ppm, corresponding to 100 ppm of added DAP). This condition was selected as good fits
of the model predictions to experimental data were observed for this time-temperature
condition. Data and results for all other combinations of temperature and initial nitrogen
concentration are included in the Appendix B. Other conditions may or may not show
better fits to experimental data.

Figure 3.1 shows the four dependent variables with the plots of observed data and
the best-fit predictions obtained from the model by using the above described procedure
for T=22 °C and N; =65 ppm (DAP=100 ppm). The asymptotic confidence bands (95%
GB.) and the 95% prediction bands (95% RB.) are also depicted for three dependent
variables. As Xv was given a weight WXV = 0 for the parameter estimation process,
MATLAB© was unable to calculate the CB. and PB. for yeast cell concentrations. In
figure 3.2, 3.3 and 3.4, the band formed by two thin lines on either side of the model
prediction line represents the 95% confidence band for the model prediction line. The
thick lines form a band outside of this confidence band. This band represents the 95%
prediction band, that is, it represents the region in which the data points predicted by the

model would lie 95% of the time.

47

 

 

 

 

35' i 'T ' T T *7 f i
i l j j l j l i l a '
‘. i . ‘ i i
3 j W ...; W W. - .. J W W . W Wi W l - l W W. W
Cell 1: *— ‘
Conc. 1 ‘i . f p l .
XV, 25 I.-. t .W- Wis . . 2 - W . -.. , W W. .WW . W ..
cells/L ‘ . ‘ ‘ ‘
2"‘rf' ,W, .---
15 : 4~ ‘ r e r* ~ — r r - i
i ‘ Ir
i i. i
i j l i ;
1.W_r. .W1.WW- W. ‘ W- .. W W- WW. . . . .. r,
j . a I i j i l i l .
: .1 i 1 ‘ l i 1 . .
05 115-.....“ - -i W__..W _ -W. .. .W_ - :W WWj «i—. .W_ i .__ ._ n _ - ..
.- l . . l ”I
_. l . l i ‘
* ‘ i ! i | i .
O l.__ _W‘1_W_. _1W__ _ _. i _ l l i i i l I
0 50 100 150 200 250 300 350 400 450 500

Time (in hours)

Figure 3.1. Non-Linear Data Fitting: Predicted and Observed Yeast Cell
Concentration for T=22 °C and N=65 ppm (DAP=110ppm)

 

 

 

 

 

 

 

80. y y _ a ' -__.WWW' .
} i ; . -> Predicted ‘
70 ,- r~i~~wi + » Observed
. ' 3 é . l -— - 95% 0.8. , '
60 #3» ~ , , ,. . i flyyyAw g I, ——95% PB. ., J
Nitrogen 50 . W W- .W W n. -
mg/L 1 '
40 i” ‘ “ j " ‘
i l l l
30 _WW _ {WuW -jfl- 1 W1 WWWW; W
‘ f ‘ i
i l j l l l
20 . i r r ' t‘ i ‘ r ' V t i
I : I i _
10 .- . . -
0 3 —~' ' 1;“. - '— - -+-——~h -__- ”awful—”H“ 3W. ...-Wn —- ----[L—-.= :TTmT-v-fi—rmzn: . T
' l . i l l l
- _ .1. WW WL ‘ ’ i '

 

 

 

- . l . |
150 200 250 300 350 400 450 500
Time (in hours)

Figure 3.2. Non-Linear Data Fitting: Predicted and Observed Nitrogen for T=22 °C
and N=65 ppm (DAP=100ppm)

48

  

 

  
    
 

i , Predicted
50 ‘ Observed
i , ~ 95% GB.
‘ 95% PB.
40 7 . , ~
Ethanol ‘
g/L 30
20 L
10 r
o (I i
l 1 i
_10 : . 1W ..1 WW‘, W ..‘W 1 . . .1 l . l
o 50 100 150 200 250 300 350 400 450 500

Time (in hours)

Figure 3.3. Non-Linear Data Fitting: Predicted and Observed Ethanol for T=22 °C
and N=65 ppm (DAP=100ppm)

       

140 ‘ T ‘ f 1 7 7 I if i i7 1
‘ 1 . i 7 Predicted ‘
120 5' 1 WWW .. . . - . r . l , : Observed ,
" ‘ ‘ ‘ 95% CE.

95% PB.

Sugar 80 ‘
g/L

l .. W W. l WW 1 W W l W W WWWW. l.
0 50 100 150 200 250 300 350 400 450 500
Time (in hours)

Figure 3.4. Non-Linear Data Fitting: Predicted and Observed Sugar for T=22 °C
and N=65 ppm (DAP=100ppm)

49

Similarly, the non-linear regression routine was applied to all the conditions and the non-
linear parameters estimates were obtained (Table 3.2).

Table 3.2: Non-linear Estimated Parameters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temp Nitrogen [IL [3,! K N Ks Yx/N
(g ethanol cell'I (g (no. of cells/

(°CL £99m) (hf!) hr") N/ L) (g sugar/L) g N)
11 45 0.1442 7.37E—10 172.32 14.589 5.00E+06
11 65 0.16443 4.17E-10 206.96 3.9181 5.00E+O6
11 110 0.39818 1.43E-09 1991 9.8417 8.50E+05
11 165 0.50891 1.56E-09 2546.5 35.945 2.00E+06
17 45 1.9244 3.39E-10 769.26 8.5546 1.10E+O7
17 65 2.5465 5.09E-10 2492.2 5.0503 5.00E+06
17 110 2.6444 8.52E-10 5104 128.06 8.00E+06
17 165 2.8017 1.89E-09 7705.5 279.97 1.00E+07
22 45 2.9714 1.25E-09 1199.4 35.631 5.00E+06
22 65 3.0157 1.82E-09 2252.6 72.028 5.00E+O6
22 110 3.2545 3.48E-09 4984.7 208.03 5.00E+06
22 165 4.0419 5.99E-09 7073 297.44 4.50E+06

 

 

 

 

 

 

 

 

The non-linearly estimated parameters above (Table 3.2) may be used directly in the
primary model to predict fermentation kinetics. However this would mean that the model
is applicable only for the three temperatures and four levels of nitrogen used for in
current experiments. The use of a secondary model (2.5) not only increases the
applicability of the model, it also gives the level of significance of the effect of nitrogen
or temperature on the model parameters and dependent variables. In this particular case,
the fitting of the above (Table 3.2) to secondary model (2.5) will show if an Arrhenius
relationship exists between the model parameters and the two independent variables,

fermentation temperature and initial nitrogen content.

50

3.3 Linear Parameter Estimation from Secondary Model
The figure 3.18 below shows a plot of In pm vs (l/N — l/Nref). It can be seen that the log
of specific grth rate increases with increasing nitrogen and also with increasing
temperature. Although figure 3.18 shows that nitrogen and temperature have an
Arrhenius type effect on the growth rate, whether this effect is significant or not cannot

be determined at this time.

-0.004 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014
WWW, . _ .. . . __.WWWWW_ _ 1,. 2000

_WW- WWW . - . . W ~ , ~ W— -—+ 1.500

lyl—Wl - - AM: 111000

c. _ _ _W. . .W_. _ — , «~#e~~ , irO.500

.. . We. W - -- $0.000

l

.W WWW WW - W WWW -~ [- 0500

 

In pm

    
  

___ -WWW .. -WW . -1.000

{ .3. 1281.??—
‘ +r=295k

_ __ ___-.- + -1.500

 

___- W. 5 -2500
1/N-1IN(ref)

 

Figure 3.18 Secondary Model Fitting of In p,” vs (1/N - 1/N ref)

The non-linear parameter estimates were different for each condition of temperature and

initial nitrogen levels (Table 3.2). The multiple linear regression estimated parameters

fitted to the Arrhenius equation (2.5) are shown in Table 3.3.

51

Table 3.3: Linearly Estimated Coefficients from Arrhenius Fits

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i Coefficients Std Error Lower 95% Upper 95% P-value
In k, 0.51303 0.17927 0.10749 0.91856 0.018
137/11 -19707 2777.4 259% -13424 5.7 x10'05
EN/R -40.609 24.0389 -94.988 13.7712 0.12

_Emf

Coefficients Std Error Lower 95% Upper 95% P-value
In k, 20157 0.19019 -20.588 .19.727 3 x10'5
Ep/R —7609.7 2946.61 -14275 -944.01 0.03
EN/R -84.373 25.5035 -l42.07 -26.681 0.009
KN

Coefficients Std Error Lower 95% Upper 95% P-value
In k, 8.16322 0.17806 7.76042 8.56601 5.6 X10"l2
Ep/R -12287 2758.64 -18528 -6046.7 0.0016
EN/R -146.15 23.8765 -200.17 -92.141 0.00018
Ks

Coefficients Std Error Lower 95% Upper 95% P-value
In k, 4.25128 0.32425 3.51778 4.98479 3.6 x10 4’7
Ep/R -16989 5023.56 -28353 -5624.6 0.008
EN/R -142.03 43.4798 -240.39 -43.674 0.01
Y X/N

Coefficients Std Error Lower 95% Upper 95% P-value
In k, 15.2493 0.22498 14.7403 15.7582 1.7 X10'13
Ez/R -5362.9 3485.52 -l3248 2521.9 0.16
EN/R 32.0288 30.1678 -36.215 100.273 0.32

 

From Table 3.3, the following observations can be made:

 

1) The P-value for p," with respect to initial nitrogen is 0.12. This shows that

nitrogen does not have a significant effect of the Arrhenius-type on the specific

52

grth rate at the 95% confidence level (p=O.12). Temperature however does
have a significant effect on the growth rate (p<0.05).

2) Fermentation temperature and initial nitrogen content have a significant
Arrhenius-type effect on ,6", and KS. This means that sugar consumption and
ethanol production are significantly affected. In many cases, the confidence level
is much higher than 95%.

3) YX/N, that is, the parameter that represents the yield of biomass per gram of
nitrogen, does not show an Arrhenius relationship with fermentation temperature
(p=O.16) or initial nitrogen level (p=0.32) in the fermenting juice. Thus, it may be
possible to fix the value of this parameter and exclude it from the data fitting
process.

Thus, hypothesis (4), which proposes that the kinetic parameters of the primary model
have an Arrhenius-type relationship with the two independent variables, temperature and
initial nitrogen, proves to be true only for three parameters ,6", , KS and KN at a 95%
confidence level. Temperature is shown to have a very significant (<0.05) effect on ,u,,.,
flm, KS and KN proving hypothesis (3). Nitrogen does not have a very significant (<0.05)
Arrhenius-type effect on the specific growth rate; however it should be noted that the
effect is still significant at an 88% confidence level. Thus, even though hypothesis (2)
may have be true at a 95% confidence level, its still holds true at an 88% confidence
level.

Plugging the secondary model coefficients from Table 3.3 in equation (2.9), the

parameters for various temperature-initial nitrogen conditions were predicted (Table 3.4).

53

Table 3.4: Predicted Parameters from Secondary Model Eq. 2.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temp Nitrgen J‘m L, KN Ks YXflV
(g ethanol (g (no. of cells/
(°C) (ppm) (hr'l) cell'l hr") (g N/L) sugar/LL g N hr)
11 45 0.233 3.33X10"° 209.710 3.150 4.32x10+06
11 65 0.980 5.80x10‘10 513.299 10.859 6.39x10*°6
11 110 3.100 9.05x10‘l0 1052.567 29.308 8.75x10“06
11 165 0.308 5.93x10'10 569.662 8.318 3.47x10+06
17 45 1.294 1.03x10'09 1394.338 28.677 5.13x10+06
17 65 4.093 1.61x10'09 2859.218 77.402 7.03x10+06
17 110 0.397 1.01x10'09 1429.197 20.335 2.84x10+06
17 165 1.670 1.76X10'09 3498.187 70.105 4.20x10“°"
22 45 5.284 2.74x10'O9 7173.354 189.220 5.74x10+06
22 65 0.450 1.30x10‘09 2225.522 31.273 2.58x10+06
22 110 1.889 2.27x1009 5447.319 107.813 3.81x10+06
22 165 5.977 3.54x10'09 11170.229 290.995 5.21x10+06

 

 

 

 

 

 

The predicted parameters in Table 3.4 show that the specific growth rate increases with
temperature for a particular level of initial nitrogen. The specific growth rate also
increases with increasing initial nitrogen at constant temperature. KN and Ks also show
this trend. No such continuous trend is observed for specific sugar consumption rate, Bm,
or the parameter for the yield of biomass on nitrogen, YX/N . The parameters predicted
above (Table 3.4) from the secondary model were plugged into the primary model. The
results from solving the primary model with the predicted parameters for the 12

conditions of temperature and initial nitrogen represent the model predictions.

3.4 Model Validation
The model predictions as compared with the experimental values are shown below. The
figure below shows predicted and observed values of yeast cell concentration, nitrogen

concentration, ethanol concentration, and sugar concentration versus time for cider

54

fermentation at T=22 °C and N1 =65 ppm (DAP=100 ppm). The predictions were based

on parameters estimated from the ‘parameter estimation data set’ while the experimental

values that these predictions were compared with are from the ‘model validation data

set’.

‘parameter estimation data set’.

 

 

 

 

 

 

 

 

x18 YeastCellCmoentratim
1 I 1 '1 ' Predicted
CelConCXv.41’ 1 *1 1 1 -
mils/L 1 ; 1
311$ 22 1 W 7914
1 1; 1 '- 1' 1 1 1
21'1“ ‘2' 1 . 12' 2-...
.11? 1 1 9 1 1 1
1 a 1 .
111' 2212 471 1 1 7 ii
'1 1 I 1 1 1
1 1
1' 1' 1 1
0.22 .
0 100 230 31') 400
Tlnnanhours)
Naomi
50:;W '1 .2 ”7”“ '7'
1 2 Predict 11 1 1
1 (beamed 1 *7’
402 . _. 2 22.2
01 1
Ethanolg’L so») 4‘ 1’ 1 7 fig 21
:1 z 1 1 1 1
m2. W1. .W2.. 1 ,i2222
1' 1
1 1 1
1 ‘ 1
10 4 . 2 1 .2 2 2 2222
1 1 1
J 100 21X) 300 400 3D
Timeanhouts)

As mentioned before, the ‘model validation data

set’ is much bigger than the

 

 

 

AssinilableNitmgen
70L L 7 W
1 Predicted
80111 2 Gaserved'
5031 7 77777 1° *1 1
W 11 1 1 1 1
"UL 40242 2 ‘ 7.. 1 22 1. 2
1 1 1
301W£W W. 2 1 -.
1 1 1 1 1 1
20» 1 1 22., 1 L 1 2 L
L 1L 1 L 1 LL1
,1 F 1 1 1 2
0 100 200 300 400 500
Tlmaantws)
5098"
120 ...- LWL 2.2.2 TL .
1OOLLW‘TW1WL 1 .
1‘ ‘ 1 ‘ 1
.. .111 ..- 1 1. 1 .1
Sugarg/L '1 1 1
502.22 2.122222. 1 1W22 1 W .1
1 1 1
40—1W72L222 1W1-
1 '1 1
2° LLL1 . 1
. 1 1 .
0 ‘2 22_22.L22 2 22 2:2 :2’21“_"_'i
0 100 21) 400 50)
Timeanhours)

Figure 3.5. Model Validation for T=22 °C and Ni =65 ppm (DAP=100 ppm)

55

As can been seen from the above figure, the model is able to predict the production
of ethanol, E, consumption of nitrogen, N, and sugar, S, with reasonable accuracy for
T=22 °C and Ni =65 ppm (DAP=100 ppm). Comparisons between the model predictions
and experimental data for other conditions are shown in Appendix C.

Nitrogen depletion curves were predicted with reasonable accuracy by the model
for all most conditions of temperature (T=22 and 17°C) and initial nitrogen. For some
conditions, particularly, figure C.3. (T=17°C and DAP=6OO ppm) and at T=1] oC
(figures C8 to CU), nitrogen curve predictions were not very good. However, for all
conditions, the model predicted the nitrogen exhaustion point (N~O ppm) quite
accurately.

The model was able to predict the trend for ethanol production curves very well for
all cases except T=11° C, DAP=O ppm (figure CS.) The model under predicted the final
ethanol levels in cider slightly for all conditions except T=22° C, DAP=O ppm (figure
C.3.) T=17° C, DAP=3OO ppm (figure C5.) and T=22 °C and DAP=100 ppm (figure
3.5.).

Although the model captured the trend for sugar consumption very well for all
conditions, the predictions were not very accurate for most cases except T=22 °C and
DAP=100 ppm (figure 3.5.), T=17 °C and DAP=6OO ppm (figure C.4.), T=22 °C and
DAP=3OO ppm (figure C.6.), T=1] °C and DAP=100 ppm (figure C9.) and T=11 °C and
DAP=6OO ppm (figure C.11.).

Further study of figure 3.5 not only helps understanding of the operation of the
model but also explains the errors on model predictions for except T=22 °C and

DAP=100 ppm. The exponential phase of growth coincides with the exhaustion of

56

nitrogen. At this point in time (t~90 hours), there is considerable sugar (> 70 g/L) still left
in the sample, and only 15 g/L approx. of a total of 45 g/L approx. of ethanol has been
produced at this time. However, this does not mean that no ethanol production occurred
during the grth phase, but that this value is not significant. From the observed and
predicted value of viable yeast cell concentration, X y, it is seen that the cell concentration
reaches its peak around 50 hours. At this time, there is insignificant production of ethanol
and less than 15% of the total sugar available has been consumed. This concurs with the
model’s assumption that cell growth is not dependent on sugar or ethanol concentration.
This does not mean that no ethanol is produced during the grth phase, only that the
growth rate is ethanol independent. At the same time, however, ethanol production is
determined by the cell concentration, especially during the stationary phase.

The model predicts the depletion of nitrogen, N, and its exhaustion point accurately,
as seen in figure 3.5. The ethanol production, E, is over predicted but the final value of E
produced is slightly less than the observed value. This coincides with the model
predictions for viable cell concentration, X y. The model overestimates the X y during the
exponential phase and the peak value of X y. The model predictions also show an absence
of a stationary phase. This may have resulted in the final predicted E at the end of
fermentation being lower than the observed E, even though E was being over predicted
during fermentation.

According to the model assumptions, the consumption of sugar, S, is strongly related
to both E and X y. The model over predicts the consumption of S but is able to predict the
final residual S value accurately. This concurs with the discussion above on the model

predictions for E and X y. Higher sugar consumption during the period after the

57

exponential phase results in higher production of ethanol. Ethanol being toxic to cell
viability, the model prediction for viable cells is less than the observed value. The model
reacts to the over-prediction of sugar consumzption by under predicting the viable cell
concentration. Thus, although the model does not predict sugar consumption accurately,
it shows the effect of change in sugar consumption on ethanol production and cell
viability.

The model is not able to predict the yeast cell concentration X y_ very well for T=22 °C
and N, =65 ppm (DAP=100 ppm), as seen in figure 3.5. The observed X y is very scattered
and shows the presence of a stationary phase up to 300 hours. However, the model
overestimates the growth rate and the maximum X y_ The model predictions also show an
absence of a stationary phase.

The model predicts the change in cell concentration very well for the following
conditions: T=17 ° (figures C.2, CB. and C.4.), T=1] °C and DAP=3OO ppm (figure
C.10.) and T=11 °C and DAP=6OO ppm (figure C.11.). In some of the cases like T=22
°C and DAP=3OO ppm (figure C6.) and =11 °C and DAP=O ppm (figure C.8.), the
experimental data itself is extremely scattered making the model predictions inaccurate
by default. For most conditions, the model is able to predict the transition out of the
exponential phase into the stationary phase, which is crucial to ethanol and sugar
predictions.

For the current set of experiments, certain common traits were observed as below.
The model predictions for T=11 °C seemed to be less accurate than for the other two

temperatures. The predictions of X V were inaccurate for a majority of temperature-initial

58

nitrogen conditions. These observations may change when the model is applied to a new
case; the reasons for which are identified in the following paragraphs.

The current study has shown that it is possible to obtain ethanol levels of as high
as 6.5% (>50 g/L for a YE/s=0.38 g ethanng sugar) in hard cider with more complete
fermentations. Nitrogen was the key limiting nutrient and supplementation of apple juice
with appropriate amount of nitrogen in the form of diarnmonium phosphate helps achieve
better fermentation yields. It has been recommended that hard cider fermentations should
start with a nitrogen level of 100 ppm for good results (Lea 2004). This was shown to be
true in the current study. Initial nitrogen levels of less than 110 ppm gave incomplete or
sluggish fermentations as can be seen in figure 3.5, model validation for T=22 C and
N=65 ppm (DAP added=100 ppm), where even at the high temperature, there is some
residual sugar left in the product. Thus the model can be used to predict sluggish or stuck
fermentations.

The effect of temperature on hard cider fermentation too was distinct. At T=ll °C,
sluggish fermentations were a norm. Fermentations at this temperature seemed to reach
completion only at very high nitrogen levels. Although fermentations at this temperature
may give us lower ethanol levels in the final hard cider, other by-products and residual
sugar may prove help improve the sensory attributes (such as aroma, flavor profile and
sprarking effect due to release of C02) of the final product. Similarly, although
fermentations at a higher temperatures like T=22°C may yield faster and more complete
fermentation at lower nitrogen levels, the effect on the sensory characteristics of such

fermenting conditions may not be positive (unpublished observations).

59

At this point, it is necessary to note that the comparison of model predictions with

experimental data above only applies to the experiments conducted during this research.

Some of the comparisons and the accuracy of model predictions will change when

applied to other cases or a different set of experiments. The model depends on good data

for grth and growth rates. Lack of data during the exponential phase and inaccuracy in

measurements will affect the model predictions.

Reasons for inaccuracies in model predictions, especially, the high errors in

estimation of yeast cell concentration may have resulted from the following:

a)

b)

WY: 0 to X y during the non-linear data fitting process: A weight of zero was
assigned to dependent variable X y (viable yeast cell concentration) to allow
the program in MATLAB© to execute without errors. This meant that the
effect of cell concentration, X y , was ignored during the non-linear parameter
estimation process and best fits to experimental data were obtained only for
the other three dependent variables E, S and N. However, X y affects all the
other three dependent variables. This may have been an important reason for
inaccuracy in model predictions. At the same time, it should be noted that
despite the exclusion of X y from the non-linear parameter estimation process,
the predicted data, even for X y, compared well with its experimental
counterpart.

Model too simplistic: Biological processes are extremely complex. However
to study them using mathematical models, it is necessary to keep the model
simple by making assumptions or ignoring certain unimportant variables. This

helps solve the model without excessive effort and helps us understand the

60

d)

6)

process without making it too complex. However, these assumptions may
cause the model to predict with less accuracy.

Inaccurate assumptions made by the model: The model assumes that all of the
viable cells will take part in the process of converting sugar into alcohol.
However, this may not always be true. As alcohol concentrations increase,
they have a increased toxicity effect on the transport of products to and from
the cell (Ansaney-Galeote et al. 2001; Bisson and Butzke 2000). Thus, as the
fermentation progresses, some cells may be alive but may not contribute to the
alcohol formation process making the model predictions inaccurate.

Errors in Observed Cell Concentration Values: Total viable cell
concentrations (X,) were established using haemocytometry (Hausser
Scientific, Horsham, PA). Haemocytometry is a labor intensive process and
the possibility of humar error in cell enumeration cannot be eliminated
(Cramer et al. 2002). The method was preferred nevertheless, due to its ease
of use and comparable accuracy with other methods like plate counts.
Parameter Estimation Method: The non-linear parameter estimation process
employs 4th order Runge Kutta formulae. Runge Kutta methods have their
disadvantages as explained in section 2.3.2. Combined with all of the other
factors listed above, the use of this method may have led to errors in

estimation of Xv.

61

The accuracy of model predictions can be determined by a plot of predicted versus
experimental data directly as shown below. The line on the plot was a 45-degree line
intersected at (0, 0).
Figure 3.6 below shows a plot of all predicted versus observed yeast cell
concentrations at all conditions. These data points were obtained as a result of non-linear
parameter estimation process. Since the ‘parameter estimation data set’ was used for non-
linear parameter estimation, the observed data consists of all the yeast cell concentrations .~

in the ‘parameter estimation data set’. The total number of such data points for X V ~ 600.

l.000E+09 .. 7 7
9.000E+08 ~ 7

8.000E+08

7.000E+08 3 , . ,,

6.000E+08

  

5.000308. . 1L

Xv predicted

4.000E+08 »

 
   

RMSE¥1.52E¥083
3.000E+08 7. ,2, .. . . . J
R = 0.3821 ‘

2.000E+08 g
1.000E+08

0.000E+00 77* 7
0.000E+00

i

2.000E+08 4.000E+08 6.000E+08 8.000E+08 1.000E+09;

A .A .,,.,,7_ ,‘fl

Xv observed

Figure 3.6. Model Validation for Viable Cell Concentration (Xv), cells/ml. Total

number of data points = 600

62

0.000300 ” * 04:000E+O8V

i.000i~:+08i "6.00013108 3 ‘8.000E+08
600000000 .W W W W W W a. -- or- 3 -- i 3 i _, a a _- _ . ,
f o
0
400000000 ,m WWWW WWW W W W W W a “fitm, mm‘ha

 

l ’0 g 0 l
00‘: ° 0 ‘1 1

200000000 -.h WW W W , v

t
,3.
W"

 

 

i -200000000WWW. W * WWWW W W W W W l
0 l
0
4000000001 « —»—-—‘ -—- — — — —~ — — — W — W W W W ‘
l Viable Cell Concentration Xv
-6000OOOOO -, — ~ ~ , ~ Wu —~~ 7-— W—WW W- W

l
l

l

Figure 3.7. X V predicted vs. Residuals: Total number of data points = 600

From the above data analysis, it is seen that plot 3.6 of X. predicted versus observed
values has a R2 = 0.3059. Although this may seem like a poor fit, most of the data points
lie close to the 45 degree line while those that do not have a great variation leading to a
lower R2 value. This can also be observed from figures 3.7 and 3.8. It is also observed
from figure 3.7 that the residuals for lower X y values are smaller than those for higher X y
values. The highest X y values correspond with the end of the exponential phase and the
peak cell concentration value. This means that the errors in predicting the end of the
exponential phase and the stationary phase are higher which corresponds well with what
is observed in figure 3.1. The possible reasons for incorrect predictions of X V have

already been enumerated in section 3.4 on model validation.

63

Frequency

 

Residual of Viable Cell Conc. , Xv

Figure 3.8. Frequency of X y Residuals
The figure below shows a comparison of all predicted and observed nitrogen
concentration. The predictions were based on parameters estimated from the parameter

estimation data set. The total number of data points in this plot ~575. The total number

of data points changes as the number of observations made for a particular dependent

variable at various conditions is different.

N predicted

   
 

RMSE=10.98
R2 = 0.9547

Figure 3.9. Model Validation for Nitrogen, N: Total number of data points = 575

64

f

From the above plot, it can be seen that there is good agreement (R2=0.9547)
between the predicted and observed values for ethanol production. This is also proven by
a relatively low overall RMSE value of 10.98. The line on the plot was a 45-degree line
intersected at (0, 0). The plot of residuals between the observed and predicted values and
the model predictions for nitrogen is shown below.

The residual plot in figure 3.10 and the frequency plot in figure 3.11 show that
there is a trend for the model to predict lower nitrogen consumption than actual. The
residuals seem to show a tendency towards the negative side in the frequency plot for low
values. However, the mean of the residuals was only 8.6 x 10 "'4. From figure 3.11, it is
seen that positive residuals large in value compensate for a large number of small

negative residuals giving a mean very close to zero.

0 20 40 60 80 100 120 140 160 180
‘ 50 T W W 1 WWW . WW 1W W .
0
40 - W W W WW
0 . .
30 § , W W W
l 201 W W‘WW . W . W
l o . O O
, 10- , ~7~~~ 1.. . W.
0
a ’i "‘

.1.
o

ReSIduals
O
F’ Vt
“ O
. 9.
. 9 2:»
1 d
0*
0
l
.1

Figure 3.10. N predicted vs. Residuals

Frequency
.—. ... N N U) DJ
O U! 0 Ln 0 U.
o o o o o o
‘ A
l
l
l l
1 l
l
l
l
l
l
l

U:
0
l

  

0 f . .. ___-F ,, , h
-45 -40 W35 -30 -25 -20 W15 -10 -5 0 5 10 15 20 25 30 35 40 45 '
Nitrogen Residual

Figure 3.11. Frequency of Residual for Nitrogen
The figure below shows a Comparison of All Predicted and Observed Ethanol
Production. The predictions were based on parameters estimated from the parameter

estimation data set. Total number of observed points for this plot = 510.

    
 

RMSE=5.40

E predicted
b)
o

20 WW W W
RZ=O.8855
10 . W
0 .
0 10 20 30 40 50 60 ‘

E observed

Figure 3.12. Model Validation: Predicted and Observed Ethanol Comparison, Total

number of data points = 510

66

From the above plot, it can be seen that there is good agreement (R2=0.8855)

between the predicted and observed values for ethanol production. This is also proven by

the RMSE value of 5.40, which is less than 10% of the total range of 0-55 g/L for

ethanol. The line on the plot was a 45-degree line intersected at (O, O).

The plot of residuals between the observed and predicted values and the model

predictions for sugar is shown below. The residual plot above shows that there is more

deviation in the model predictions from the observed ethanol values as fermentation

progresses and ethanol concentration rises. The residuals seem to show a tendency

towards the positive side in the frequency plot but have a very low mean of 2.76 x 10 "4.

This is observed in the figure for frequency of residuals given below. Thus the model

seems to be under-predicting ethanol concentrations very slightly.

15W- 1
101
5 .

‘rn
‘5 8
5
g- :0:
- :
,L, W

0 i 57 10» 15 if 20" i 7 i

E predicted

I -20W2W . fi-iw.. WW7

Figure 3.13. E predicted vs. Residuals

67

iifi35 7 40 45

r ..., =*“--:

 

-20 -15 -10 -5 0 5 10 15 20
i Residual for E i

Figure 3.14. Frequency of Residual for Ethanol
The figure below shows a Comparison of All Predicted and Observed Sugar
Consumption. The predictions were based on parameters estimated from parameter

estimation data set. Total number of observed points = 672.

  
  

fl
8
.2
g 60 . ,3 ,w
‘ ‘5. RMSE=ll.93
1 m 40 7 i in
R2=0.9087
l 20 ‘ ,,, fl .7,
l
0 WW .. W W. ‘
l 0 20 40 6O 80 100 1201

Figure 3.15. Model Validation: Predicted and Observed Sugar Comparison, Total

number of observed points = 672

68

From the above plot, it can be seen that there is a high correlation (R2=0.9077)
between the predicted and observed values for sugar consumption. This is also proven by
the RMSE value of 11.93, which is less than 10% of the total sugar concentration range
of 0-120 g/L. The line on the plot was a 45-degree line intersected at (0, 0).

The plot of residuals between the observed and predicted values and the model

predictions for sugar is shown below.

60TWWWWWWW+WWWWTWWWWWWWWWWWW
O
n_g_ “_O_#_____i , a ,

 

Residuals

 

S predicted

 

1*.

Figure 3.16. S predicted vs. Residuals

 

 

The residual plot above shows that the model is able to predict sugar
concentrations at the start and end of fermentations more accurately than at the time
points between them. The residuals seems have a tendency to be on the positive side (in
quantity) showing that the model tends to over predict the consumption of sugar slightly.
This is observed in the figure for frequency of residuals given below. However, the mean

of the residuals was found to 2.69x10'l3.

69

Frequency
Nwwwrs‘
o u- echo
0 o 000

l

1
ll
1

l

l
l

l
l

l

p—A
KI]
O

l

l

l

   

0 % ~ . , , . , ,
—60 —50 -40 -30 -20 -10 0 10 20 30 40 50 60
‘ Residual

Figure 3.17. Frequency of Residuals for Sugar, S, from model predictions

The model is mechanistic in nature, thus it is able to explain the cider
fermentation process in terms of well established and accepted principles in biochemistry
(Bailey and Ollis 1986a). Many other models that been non-mechanistic give good
predictions but do not help understanding of the process. The model has only seven
parameters, two of which are fixed. This makes the model relatively simple to use and
solve. However its simplicity does not prevent the model predicting with reasonable
accuracy, especially when. compared with many other complex and non—mechanistic
models in wine (Mann 1999).

Although the model in its current state may not be an accurate predictor of yeast
concentrations, it utility lies in its ability to accurately predict ethanol and nitrogen rates
while giving us a scientific understanding of the process. Although the effects nitrogen

and sugar addition midway through the process of fermentation was not studied, other

70

researchers have shown that similar models (mechanistic, based on Monod kinetics) are
able to predict satisfactorily even in such cases (Cramer et al. 2002; Malherbe et al.
2004)

The model proves that a significant Arrhenius relationship exists between four of the
model kinetic parameters and fermentation temperature (p<0.05). The level of initial
nitrogen also affected the sugar consumption and ethanol production rates significantly
(p<0.05). On the other hand, specific growth rate was significantly affected by nitrogen at
p=0.12 only. Thus the model may be used 88% confidence to predict the specific growth
rate and fermentation kinetics.

To further evaluate whether growth was nitrogen-limited, log of raw experimental
data, log Xv was plotted versus time for all conditions. These plots are shown in
Appendix A. These plots showed that the level of nitrogen did not seem to have a strong
effect on the growth rate; however, it did affect the final concentration attained by the
yeast cells at the end of the exponential phase.

This research showed that an increase in temperature within the range of 11-22 °C
and initial nitrogen level within the range of 45 to 165 ppm would yield more complete
fermentation with higher ethanol concentration. It was observed that higher temperature
and initial nitrogen level resulted in higher cell concentration at the end of exponential
phase. This in turn gave more complete fermentation and higher level of ethanol in the

final product.

71

3.5 Conclusions

A simple, mechanistic model based on Monod kinetics for predicting
fermentation kinetics was successfully applied to hard cider made from dessert apples.
The non-linear data fitting process used 4th order Runge Kutta and functions available in
MATLAB© to estimate model parameters.

The model gave satisfactory predictions for three of the dependent variables,
Nitrogen consumption (RMSE=10.98, R2=0.95), sugar consumption (RMSE=5.4,
R2=0.90), and Ethanol production (RMSE=11.93, R2=O.88) for fermentation experiments
conducted in the temperature range 11 to 22 °C and initial nitrogen levels of 45 to 165
ppm (corresponding to supplementation of DAP in the range 0 ppm to 600 ppm). While
yeast cell concentrations were not predicted accurately (RMSE=1.52 x 10mg, R2=O.3 821),
this does not prevent the usability of the model since the predictions for other three
dependent variables, which may be more crucial to hard cider manufacture, were
reasonably accurate.

The model shows that a significant Arrhenius relationship exists with temperature
for four of the model kinetic parameters, flm , Ks and KN , ,u,,. (p<0.05). An Arrhenius
relationship between initial nitrogen level and parameters ,8," and Ks was also established
(p<0.05) proving that sugar consmnption and ethanol production rates were significantly
affected by nitrogen. The parameter for maximum specific grth rate, p... , showed an
Arrhenius relationship with the level of initial nitrogen at p=0.12, however the effect was
not significant at p=0.05.

A significant effect of initial nitrogen on growth rate was not seen in plots of raw

growth data (log Xv versus time). From the above observation and information obtained

72

from secondary model data fitting, it may be concluded that the hypothesis that cell
grth rate was significantly nitrogen-limited was false at a 95% confidence level and
was only true at a weaker 88% confidence level.

The current study showed that dessert apples could be used to obtain hard
cider with ethanol concentrations of over 6.5% and that more complete fermentations
could be achieved at higher temperatures and by supplementing nitrogen at the onset of
fermentation. Using data generated from simple experimentation, the proposed model
can be used with reasonable success to predict the effect of change in initial nitrogen
content and temperature on fermentation kinetics of hard cider production. The
mechanistic nature of the model helps explain and study the fermentation process. The
model provides a framework, using which; models with better predictive capabilities may

be established.

73

3.6. Novelty of work

The current study is the first known application of a mathematical model to hard
cider fermentation process. Additionally, unlike regular hard cider manufacturing which
uses mostly cider apples, this study specifically involved the fermentation of hard cider
from locally grown dessert Jonathan apples. This model is amongst the few mechanistic
models applied to fermentation of alcoholic beverages. Most models proposed are non-
mechanistic and do not help understanding of the process. Even with mechanistic models
proposed in wine, none have attempted non-linear least squares fitting of the data.

Although many researchers have attempted to study the effect of nitrogen on
wine fermentations, none using mechanistic models have studied the combined effect of
temperature and nitrogen on the fermentation process. Further, no known study has
established an Arrhenius relationship between its model parameters and the independent

variables of temperature and initial nitrogen content.

74

3.7. Future Work

1)

2)

3)

Larger Fermentation Volumes: In the current experimental setup, the volume of
fermenting apple juice was small (400 m1) due to limited resources. Larger
samples (> 2 liters) may be used in future experiments. This will be a better
replication of cider manufacturing in microbreweries. Large fermentations may
exhibit characteristics that are slightly different from the current setup and will be
a better test of the model’s predictive capabilities.

Sensory Analysis: The ultimate test for a hard cider manufacturer is the likeability
of the sensory characteristics of hard cider by consumers of wine, beer or other
alcoholic beverages. Although making hard cider at a particular temperature may
give higher alcohol levels it may not be the best tasting hard cider. Hence, a
sensory analysis of the hard ciders made at different temperatures with apple juice
containing various amounts of initial nitrogen levels will help determine the best
tasting cider.

GC Analysis of Volatile Products: For fi'uit-based alcoholic beverages, the ‘taste’
or likeability of the product depends not only on the flavor and texture of the
beverage but also on the aroma from the volatile compounds being released. It has
been shown by other researchers that the concentration and variety of aromatic
compounds released by an alcoholic beverage changes with chemical composition
and fermenting conditions of the raw material. A gas chromatograph of the
volatile products from hard cider will determine the type and concentration of
these compounds. Together with sensory analysis, it will be possible to determine

which compounds are produced under specific conditions and their effect on the

75

4)

5)

6)

sensory attributes. GC analysis is also the preferred method of evaluating ethanol
levels in hard cider samples and may be used instead of HPLC.

Sluggish and stuck fermentations: Sluggish and stuck fermentations are major
problems faced by the industry. The effect of nitrogen or sugar addition midway
through the process of such fermentations and the ability of the model to predict
the effect of this addition can be studied.

Initial sugar concentration: The current study dealt with temperature and initial
nitrogen levels in apple juice. However, the amount of sugar in apple juice also
affects the rate of fermentation and the amount of alcohol produced. Hence, a
study of effect of sugar on fermentation will help better prediction of the process.
Algorithms in MATLAB© : The 4th order Runge-Kutta formula is very labor
intensive and may not be the most accurate. It is, however, widely used due to its
simplicity and good results. For modeling hard cider fermentation based on
Monod kinetics, this numerical technique is unable to converge in MATLAB© for
more than 5 parameters and is very time consuming for smaller time steps.
However our model contains a maximum of 7 parameters that may be non-
linearly estimated from the primary model and 21 parameters that may be linearly
estimated from the secondary model. This is not possible using the current
numerical techniques. Hence, a more efficient method for solving the model and

non-linear data fitting may improve results.

76

Appendix A

Semi-Log Plot of Raw Growth Data

 

 

 

 

 

 

 

 

 

 

0 100 200 300 400 500‘.
l Time (hours)

 

Figure A.1. Semi-log plot of raw X yversus time for T=11 C, DAP=0 ppm: Slope=

 

ll—I—Iog (Xv) DAP=100 ppm:
S--; g l
l

 

 

 

 

 

 

 

 

 

i

l ' ‘ ' I
I 0 100 200 300 400 500

1 Time (hours) !

 

Figure A.2. Semi-log plot of raw X y versus time for T=11° C, DAP=100 ppm

77

 

‘ ‘ ‘ +Iog (Xv)DAP=3OO ppm 1 I
1 8.3004 ,, W W -L .__L__-_-_-_._ I ,

     
 
 
 

 

 

 

l 0 100 200 300 400 5001
Time (hours)

 

Figure A.3 Semi-log plot of raw X y versus time for T=11°C, DAP=300 ppm

 

 

 

 

 

 

 

 

8.600
( a +Iog (Xv) DAP=60
. 8.400 ' - __. l
l .
i 8.200 , W 1
l ,2 l

a, 8.000 , W ~ .
l 9 l
f 7.800 4 l
i l
1 7.600 - — _‘ ______________ , i
i 7.400 . T 1
l 0 100 200 300 400 500;

Time (hours)

 

Figure A.4. Semi-log plot of raw X y versus time for T=11° C, DAP=600 ppm

78

 

8.600
8.400
8.200

8.000 ,
>

X
l a, 7.800
O

7.200
7.000

Figure A.5.

8.600
8.400
8.200

8.000

log Xv

7.600

7.400 1

7.200

7.000

Figure A.6.

" 7.600 -
7.400 4

 

 

 

 

0 100 200 300 400 500

Time (hours)

Semi-log plot of raw X y versus time for T=17° C, DAP=0 ppm

 

7.800 1

 

 

 

 

0 100 200 300 400 500

Time (hours)

Semi-log plot of raw X yversus time for T=17° C, DAP=100 ppm

79

 

 

 

Time (hours)

Figure A.7. Semi-log plot of raw Xv versus time for T=17° C, DAP=300 ppm

1

87.0007 7

 

8.800
8.600 ~
8.400 4

8.200 ~
>

X
a, 8.000
O

_ 7.800 W
7.600 -
7.400 W
7.200
7.000

 

 

 

 

Time (hours)

Figure A.8. Semi-log plot of raw Xv versus time for T=17° C, DAP=600 ppm

80

 

0 100 200 300 400 5001

 

 

 

 

 

 

 

 

1 Time (hours)

 

Figure A.9. Semi-log plot of raw Xv versus time for T=22° C, DAP=0 ppm

 

:k—I—‘lr chells/mL DAP-€100 ppm_l ‘2

 

 

 

 

log Xv

 

 

 

 

 

0 100 200 300 400 500 ’
Time (hours)

Figure A.10. Semi-log plot of raw Xv versus time for T=22° C, DAP=100 ppm

81

log Xv

6.000

8.800 ,

8.600

8.400 ~

8.200
8.000
7.800

7.600 -.
7.400 -.
7.200 W

7.000

 

 

 

_+ 7 ‘xv pens/mt oAP=300 ppip ,1

 

 

 

 

100

200 300 400 500

Time (hours)

Figure A.11. Semi-log plot of raw Xv versus time for T=22° C, DAP=300 ppm

log Xv

9.000

8.800 4
8.600 ~

:(—)fi(vrcells/mL DAP=600 ppm

 

8.400 - ,

8.200 ~
8.000 .
7.800 -
7.600 -
7.400 .
7.200 >

7.000

 

 

 

 

 

100

200 300 400 500 .

Time (hours)

Figure A.12. Semi-log plot of raw Xv versus time for T=22° C, DAP=600 ppm

82

EthmolgIL

 

B.l.

Appendix B

Plots of Predicted & Observed Dependent Variables

from Parameter Evaluation

Yeast Cell Concentration

Time (in hours)

Alcohol

Predicted

200
Time (in hours)

Mm ML
N
O

 

? 1OA

" oi

l

-7“ _1oi
500 0

WW 140,
7“ 120$r
10°?

1 3 ”i
"""""" . r .0,
l 40‘

mi

9 0

500 O

Assimilable Nitrogen

Time (In hours)

Sugar

200 300
Time (in hours)

Predicted 1
Observed .
95% CS.
95% PB. _ ,

Predicted
Observed "
95% GB. ‘
95% P.B. '

Non-Linear Parameter Estimation for T=17° C, DAP=0 ppm

83

x 10'

4r.........r

3.5»

“MIG!“
N

501

 

B.2.

(z (211:. Y. GEM.
‘4

a

 

mdL
N
o L

3.3.

YoutCoiIGoncontr-tlon
..... ....fi. .., ...“..w,

1 00 206 300 460
Time (In hours)

Alcohol
Bredicted'i ' i 7'
Obserwdqm --' ..
95%c.B.‘i‘

 

200 460
Time (in hours)

106"

_L. L ..i.

Em

WM

 

 

Non-Linear Parameter Estimation for T=17° C, DAP=100 ppm

Yeast Cell Concentration

.i ,7_ ,,,,, W 1 L71,"

200 300
Time (In hours)

Alcohol
fire’dicied 7

 

"26077 >366
Tlme (In hours)

N'mwmvl-

SIM-

 

 

 

r . ..

E ‘ W Predicted
60‘ i Chase

3 - 95% c a ’

. 95% P 8
40E 3

l .,

20} 4
i ‘ -= ; * '
0f 3' -l- e o

i .

-201 m . . . i

0 50 100 150

Time (in hours)
Sugar
140 W . 7.

,, Predicted ‘
120‘“ » i - Ob! r
1008.}. 4:7 . . - esssce...

. z i 7 95% PB. ‘
go. ..... ..,. .,. .W :_. ..J.
- l

i ‘ i
so) , i
405 . - ; ‘

. '7 A, i
20- ~ ~ ;

l t

o. .e
_2oi LL. 7. . .
0 100 200 300 400 500
Time (in hours)
Assimllable Nitrogen
1407 W WWW . _ réuW .

i A Predicted N.
120i ~ . ‘ ‘ T
10°...;.. J ' 95%C.B.1i

‘ l W 95% Pie. N
50v . V-u Wl'i’..---*"TTW"J

3 x ‘

so,» .- W. . ..... 4
4oi ........ i: I Hi)
. . .i
20W .j W...__ _, i. 7 .

01.. . 7;: W}, ...W.

.20L ,,,, .4 _VLIS ”‘ "l; ' L
50 1 150
11mg (in hours)
Sugar

140 .,,. .:. ' '
120‘ I W Predicted .

e 7 Ohm“ M

100 . _. . - 95% 0.3. :1
e" 95% P.B.
°°i .: ‘ 7r .
eo- -‘ ,‘
40, . I.‘ . . i . .' . . 4
20,1 - i, --W __WL; '1
o, . . I . ... ‘ : {rW-WWWWWWW_ .
.20-...” n,..,, rut. , ..
O 100 400 500

£66" 300 "
Time (In hours)

Non-Linear Parameter Estimation for T=17° C, DAP=300 ppm

84

 

1.5i .
i i ‘
>- 1
5. 1 W .
B osi J.
I a l
I l ‘Ir .
l ‘ , i
o r 7.. . A 7 7
0 100 400 500
Time (inhoura)
Alcohol
60W . W W
50» . -... WWWWWW 7 1
4o . ‘ii '7” _.
i =‘ W WWW W ,.
3 :30V a X 7, . i
[ g . Predicted i
g 20 . 1.. , . - Obeerwd i f
. . ' - 95% 0.8.
10: ,,. . ....95%p.8_,
: .
0V ~W 1
.10' 7 . .7777 l
0 100 400 500

 

200 300
Time (In hours)

 

    

 

x 10 Yeast CellConcentrution
5, . - ...-. ..7- .-. _ .
‘ l
4W - ,3 i
s ‘ ' .
8 31 .i‘ ii ..........
>' i g _.
,. l
52- W
8 ' 1
12‘ .
1f:
i.’ 0
‘.
0L . 7 7 7,7 l
0 1“) 200 300 400 500
Time (in hour!)
Alcohol
eo‘W WW W 7 777, W W.
50:
40L.
1,; . W 7 Predicted l
g 20. .1 ' . Observed:1
‘ j ‘ .. - 95% ca!
10y , WWWWWWWWWW ‘ 7'7—95%P.B.«i
of. ............ ' ......i
_10. 7,7 ' _ ,7 7
O 100 400 5CD

3.5.

Time (In hours)

Nlmaannw-

 

 

Aselmllabie Nitrogen
am
.. i . Predicted
f' Obserwd ‘ .
. ‘ , z .
‘50) W, - 95% c B. , 3
1‘ 85% P B 1
100} . .. ' l

l a:

50' W - 1 W .
’s '1
ol ..’.-L!, W 77..)
I 2
50W W W W . .
1(1) 150 200
Time (in hours)
Sugar
140W W . ' ’
2°, Predicted
’ V 4 4 Obeened ‘
100, . .3. . - 95% 0.8. .

. 95% P.B.
30‘ . - .. - . :W
40;» v- i
2°i *= :

oW _ . .‘:I -' ‘ Cl
.201. 7 i 7 ., ,
0 1(1) 400 500

200 300
Time (in hours)

Aeeimilebie Nitrogen

Sugar

-20 ‘77 .7- . .. r

260 300
Time (in hours)

Non-Linear Parameter Estimation for T=17° C, DAP=600 ppm

Predicted
Observed ‘1

95% ca 1 ‘

95% P3. 1'

téo

Non-Linear Parameter Estimation for T=22° C, DAP=0 ppm

85

A

i

 

 

x 10' Yeast Cell Concentration Aaalmilabie Nitrogen
2.53 7 7 W 7 W. W eoW W - WW - W ; W
' ‘ 3 . Predicted .
2. .t.‘ 1 . 50"" °°'°"“°“ ‘
3 o ' ‘ - 95% 0.3.
a 3 . ‘ “Di 95% P.a.
1.5L ‘1‘ V e E 5 r
,. 33 i 3
g 1 r. g 203: 5 *1
8 i 103% .‘ - 3 i
°-5‘r ~~ r ; W . 7 7’ 7 3
‘ 0W: ~' :7 ~e~—W~>-~-+-»v—-i~~-~—W---v4
i I - .
0.. W W W W W W -10iW W W < W W W
o 100 200 300 400 500 o 100 150
Time (In hours) Time (In houra)
Alcohol Sugar
50, W 7- W VW WWW WW 7.3 W W W3 1403W 7 3 .7 7. 73 W 3
3 ‘ z 3 .. 4 i ; 1‘ WW Predicted .
. ' i ..
403 . ....v " .7.3333...4 ”or!" ' " ‘ Observed 3
3. 3 - 3 10° . X 3 - 95% 6.3. 3
303 ' ‘ 3....: ’ - X. 1 7 1’9i'éP-B-
'8 ‘ . . _ 7, i i; eoWW ..L WWWWWWW 4
303' ‘ 3 — Predicted‘ :: 3
3 Observed 603 W - WWWWWWW i
101 . ' ..... - 95% c a :3 ‘
- . 95%?31 ‘0" 3 ‘- """
°3" """ 1 """" zoiWW ----- '1 j ’ .3
: : ' i I W i
.10 7 a A . . A.7. Oi l7
0 100 400 500 o 100 50
Time (in hours)

 

 

B.6. Non-Linear Parameter Estimation for T=22° C, DAP=300 ppm

 

 

 

 

 

 

x 10" Yeast Cell Concentration Assimilable Nitrogen
7 20cr r
3 3 W Predicted 3
a3 ...... 4 - Observed l
‘ , i 1503 ' ’ - 95%c.e.3‘i
i 5?’ ‘ . ‘ """"""" ‘ g- F W - 95% PB.
'8 l 3 ‘ § 1003 A1,. . i V V 4
>- 43 3b - WWWWWWWWWWWWWWWWWWWWWWWWWW 3 ; ,
g 3 i ' —3 E 503 3333333333 3 ’3
8 2i .4 ..... .. . .3' ., 4‘ 3
'i 1 i . 0L \:4\ '9‘7“’ 7 A ‘5" " "
1 ,‘V ‘ .. l V :
i i 3 ,3
. 3 .
o 7 777777777 7 _ .77. 50 r . i _ -77. 7 -..
TN 200 300 400 500 100 50 200
Time (in hours) Time (in houra)
Alcohol Sugar
603 :7 c - .777 r . 140: ~ — **** . . - ~ 7: ' .
‘ WW Predicted i : W W . Predicted .
soi i“ - Obeemd ft ”’01., 3 ‘ .1 Observed ‘ ‘
o. - W 'i - 95% ca. ii 100‘. . 3 . . - 95% ea. .‘
‘° '. . 7" L'.‘ 795%5'3. 3‘ ' ‘ 95% PB.
I z W 30. W W ..
i 30‘— , W- .......... i 3 3
E . i 3 60 i
20 , ,. ‘
m y . 403‘. E
i. '1... 4 I ’ ‘
10' . i 203 1r 7
. .. .
at i o. . J..- .4- .’ ::-- -:
l 3 3 a VA .3
.10.. .... i. .. 7 r 7 L 777 .20. 777 7 , r ‘
0 100 300 400 500 0 100 400 500

B.7.

200 ‘200 7 3’
Time (in houra) Time (In hours)

Non-Linear Parameter Estimation for T=22° C, DAP=600 ppm

86

GChndeL
N

{838

N

arm: on.
I. N
"‘ 797“.

B.8.

0 Di
0 I v
a

Yeeet Cell Concentration

7 i 7
P redlcted

I § ' ‘; - Oblennd j
i
i
a r g
WWWWW W i
‘ ' . i
’ . I
. .. .3
760 260 300 460 500
Time (In hour.)
Alcohol
. 7 . .
Predicted
Obaenedi ‘ -- ~' . H;
‘i
E t
I . ,1 . l
. ;
too too 500

260 300
Time (In hour!)

 

0 too

Alelmilebie Nitrogen
3 .7 7 7

200 300
Time (In hours)

 

. . I
Predicted ‘
Obeennd , .

Non-Linear Parameter Estimation for T=11° C, DAP=0 ppm

 

a, 10' Yeast Cell Concentration
2.5 WWWWWWWWWWW
i 2 ...............
ii , i E
> 1.5» WWWWWW 3
g = . i
3 1' """ 4
0.5L. Wi
" I
0.. 777777 .. 7.
0 100 400 500
Time (in hours)
Alcohol
40; ...-.3-..7 . 7773
'1 Predicted 3 ‘
1 Observed }
3°} . 95%03 :. , ‘3' .. " 3
‘3 95% 9.3. 33 i a 3 ‘3
‘4 2°: ' ' " i ' ~ 3 s
i 8 ’5 I I;
10- g 'r
. g - . 3
oi-W' I . .
.1017. 77 i777-.. . 7 . 7_ 7
0 100 400 500

83.

2(1) 300
Time (in hours)

8

..§7..-.§75‘
? 3

30'r

B .

 

10r-

.10t

140 7-77.,
120r-WW .
‘1':

100» WWWWW

0 50

100
Time (in hours)

200 300
Time (in hours)

 

Non-Linear Parameter Estimation for T=11° C, DAP=100 ppm

87

mmYJflh/L

tar-ugL

Cd Can Y. eels/L

StratigL

‘ 10‘ Yeest Cell Concentration

 

 

2, s
1.53 V
1‘.
0.5,
' . .
o. ..t
0 100 200 00 400
Time (In hours)
Alcohol
50 ,7 . .. r7 . ’77 .. r” r"’
3 7 Predicted 333 3 3
403 Observed 3.‘ . 3 ..-.J,""
3 95% C B 3 '3 '
3
am 95%? B J WWa- 3}"
203 WWWWWW . 3 if 7' p: WWWWWWWWWW
1 3 .
1o . ...... . r .............
: {3
03* WW WWWWWWWWWWWW
3 3
to?" . ‘ i
0 1“) 400

500
Time (in noun)

B.10.

x 10' Yeast Cell Concentration
3,........-.. ........._. ...-.. < - WW-Wi-W-WW-W—
2,5- .. ~.~ WWWWWWWWWWWWW i
3 ‘33 3
23 WWWWWWW <
1.5> [
3 3
13 -
0.5- 4 ............ 3
1' - 3
of 160 7206 300 100 7500
Time (in hours)
Alcohol
: W W W W t
40- e '
O 7 7 4
303 .z 7 7 J
3 ,3 . Predictede i
‘ 1 ‘ Observed 3 ‘
Oi .
2 3 - 95% 0.5. 3 3
3 3 95% no.3 3
103 r . . .. 7 .
, I
03+ -
_10.7..7 t .77 . 7._7L.7 7.. ,
0 100 400 500

200 300
Time (in hours)

B.ll.

88

mm

Mummi-

Steers/L

Assimilable Nitrogen

140. W . .7. .
120E 3 7. Predicted
3 V H I” 3 ' Observed
100.3. . . I 3 . - 95%C.B. 3
.' 3 95% P.8. . i
303 W 7 ... . .
307 4!
3 a
4035 ~s
zoi t ........
I . i
o’. WWWWW x 7 I
i
.zo’L- . . ..7
O 50 100 150
Time (in hours)
Suger
”Or 7 7- 7 .. .773
i 33 .7 Predicted
1203 ‘ Observed 3"
3 g 33 3 33 - 05% ca. 3 ‘
‘°° ‘ 3: '3 ' " Waste P3."
803 s ‘ ;
I
so ......... .‘. .. ....... 3
. : 5 - :
403,... WWWWWW g ‘ _
. .-
2o3WWWW WWWWWWW .. W1
01. t.77 .7 l 7 i
0 100 400 500

200 5:
Time (in hours)

Non-Linear Parameter Estimation for T=11° C, DAP=300 ppm

Assimilable Nitrogen

 

 

zoo-WW-W-W-WW-W-1 - 7;: 3
W 3 .77 redicted
' E 3 3 - Obsenied
1503”" 1 ”'3’" F - 959603.33
s ‘3 ‘ W 95% P.8.
100‘ ~W‘ l
50‘, J. . ..... .‘
3 I W . 3
"\‘7- 3 . -
03 WWWWWWWWWWWWWWWWWWWW 7 W'W‘3WL
60‘ I
50 100 150 200
Time (in hours)
Sugar
1403 . 7 i _ WWWW ... .. . 3
1 0‘ Predicted
2 k Observed "
100, 3.. 3 - 95% ca. 3.
3 1': W 45% PB. 3 .
303.. .3 ..... W WWWWWWWW . 3
I 3 .
60‘ .. 3 3 ~~~~~~ ‘3
40- --. ~
It
203 ‘. :~ i
0‘ '. :‘ :i‘ ' 4
.203 . . 1....7 7 .‘7 7 .
0 100 400 500

200 300
Time an hours)

Non-Linear Parameter Estimation for T=11° C, DAP=600 ppm

 

x10

mmxdfl

C.l.

i160

Appendix C

Plots of Predicted & Observed Dependent Variables
from Model Validation

r

7 00 260 7360
Time (In hours)
Alcohol
Predicted
l"‘3:
; .
" a
' zoo 33¢? 7

Time (In hours)

Model Validation for T=17° C, DAP=0 ppm

Yeast Cell Concentrntlon

*rPredlctecIi: 3
Observed ‘

V #730

7 Roof

89

mm

8|va

1403 7 7
120’
100W '.

BO-

 

 

3

'F

Time (In hours)

Sugar

.3
I

260 306 I

Time (In houre)

Aneimllnble Nltrogen

Predicted 3
Observed ‘

150

Predicted
Observed , .

400

Chmxcdls/L

OdC‘nnXoels/L

eanandgyL

 

x 10' Yeast Cell Concentration
4 .’"""_ ' __T "H’— '—._“' "— ’_'-T L ___. 7'”.— 77'7 _ 7_'_’ fl“
3 53 ‘ '3 _3___ Predicted 3 3
‘ ‘ 3 Observed 3H3
3. 3, I 3 .4
3 7 ‘1 3
:25. . ° .73
. 3 3 .
2:. . ~ .I
1.53 3 t 3
(>53 3
037. _ . __4. _ l __, __, .'.__ 7. . 7 3
O 100 200 300 400 500
Time (in hours)
Alcohol
50. _W77__ W , 777 7777 777 7777
33 , 7 Predicted ' 3 3
Obeerwd “___” _—_;
40- ~— 7 . ~- .,3
3
i 3
aorWW r .79- WWWWWWWWWW 3,., 74
r ‘ a 3
20,, 3
3 ; l
3 , .
I 3 I
O . 7 7 - _. - 3 . r , 77,.
O 100 200 300 400 500

C.2.

x 10' Yeast Cell Concentration
4r ,7 ~ 77777737777777 7377, 33 3
;3 - -< —- Predicted 3
3.5» -. r4
3 3 .3 - Obsened 3 .
W 7777777 3
3 I . .1 i
2.53 33,, . 3 . W:r~7 3
I 3' 7
1.53 3 WWWWWWW r W WNW—WW3
3 33:3 '
1 33“ - ----------- 3
3
0.53 ..,,7t
0 3.77 V Z . I ., 77 1,7,-77
0 100 200 300 400 500
Time (in hours)
Alcohol
503, 7 . __777 - 7 j— »W- *3
3 _ .
3 3 3
30;. e» ' r‘--«‘----—----Y-“-O-"‘-':
3 3 ’-' 7 Predicted
3 : Obsened 3
20. i * 7 - 3
103 ......... 3
i. 3 3 3
o '. 7 __ _7 77- .7_____.; ._ ___,7 __ J 77_ _ __, .77. .
0 100 200 300 400 500

C3.

Time (in hours)

70377—7—

WM
you
00

 

 

 

103 7,!
0r"
3
-10 .....
0
120I -7
3 33!
100»
3
803W 3
g 60» -------
403‘“
20»
3
0‘ 4
0

Assimilable Nitrogen

100 ""'m260 ' “"360
Time (in hours)

Sugar
7 T — :3
3? i
3,. 3 3.
_ 5, ......... '3, .
'r
100 77 260 ’4 306

Time (in hours)

Model Validation for T=17° C, DAP=100 ppm

Time (in hours)

 

120377777777 — WW 37,,
3 i 3

1oo,___.;t33_,

3
803WWWW-~~~-~;3

60’

$039“-

403. .

20:77.7.

Ntrom'mo’L
Q
o

 

- _,7_ émdict2d3 3

Observed ’ '
3
3
3
__ 466 "I 500

.. i " fl 3
W-mwmwfl
Obsemd
7, fl 3

3
3
3

Assimilable Nitrogen

7B7777W ' 77 7 , 7

‘“§ba*“"‘ zoo ’ _ 360

Time (in hours)

160 fl—FC2OOi—fifimsoo
Time (in hours)

Model Validation for T=17° C, DAP=300 ppm

90

i
l
400 560
"~— ineduned
Observed 3
4' 3
3

C460 500

__—rfleduned33

Obsem 3 3

<77 .g. .7

400 500

in.

CdmxodlflL

amugrL

warnxwlle

 

x 10‘ Yeast Cell Concentration Asslmlleble Nitrogen
,777,,,,7 ,,,,,

 

 

103 3 7 3 773 7 ,
73 7 Predicted 3 3 7 Predlcted 3
83 ,, - _ ‘ Oblened 33 3 - Obsened ‘
: +3 15037 ‘i «
3 :3 , - 7 i 3 7 3: 7 7 7 3; a 3
B . .__3 3, § 3 3 3
3 3 3 3 3 3 3
3 , 3 3 100,: - 3,3 7
3 . 3 3- 3 3
433 7 4‘ :77 3 3‘:
3 3‘ ‘2 3 2 * .
3 7' 3 5037 '37
23 '1' ‘ 3 3'
3 3 3: l
03' , 7, ,' 7, ,7 ,3 7, ,3 03.7 7, 7, 7 7 . '7, 7 7777777777.;
100 00 3 O 400 500 100 150
Time (In hours) Time (In hours)
Alcohol Sugar
603 7 7 7 7 77,7377 ,7 120377 3 33 7, :7 ,
3 77 Predicted 3 3 I 1 : '3 7 7 Predicted3
503 77 77 7 E 3 9‘13”“:933 1003 . I ‘ 9"“ '3
3 I 7 7,7 7 7, 3 3 I 3
407 ’1 3 303 “~37 3
3 3 I Z 3 s 3 3 I
3037 7 ,- 77 , 7 3 603 7 -3
3 _‘7 : . I 3
3 , . 3
7 ,7): 3 _. , ' .....
203 , 3 33 3 3 403 33
3 3 3 3 3333
3 3 3
103 u 7 ,,,,,, 3 203 3: i' 3
. 3 ‘ I 3
0L , 7,, , 777,, , ,7 7 03777-, 77 537—4
0 1 00 200 300 400 500 0 1 00 200 300 400 500
T'lrne (in hours) Time (in hours)
. .
C.4. Model Validation for T=17° C, DAP=600 ppm
x 10 Yeast Cell Concentrntlon Asslmlleble Nltrooen
4 ' 7 7 ,rfiq 50." 77,, ' ‘ "i7‘7'7'7," 33
3 777 redicted 3‘ 3 3‘ - ' Predicted ‘ E‘
3'53 erved 3 403 .7 ' 7 7. - Obsenad 3
3’ r
3 3o , , 3 4
2.5 77 7 ,. 3 E ‘
uf .. ‘ 3 b
277 ‘ i I A 77777 203 t 3
3 : ’ ' g 3 :'
1_53 3 3: , .............. 3 1033 3 3
i 3 " 3 3 3 33
1 1"3 ‘ 7 3 3 r 33 33
0533337, 777777777 3 0 fl ’7 ’4 7A 7'33
o 7, 3 A7 ,7 3 r, ,, ,77, , ,_ ,,,3 -10 77,7 777,, 7 7 r
0 100 200 300 400 500 50 100 150 200
Time (in hours) Time an hours)
Sugar
12037 7 7 77 77 77 33 33 77 77 3, 77
7‘3 3 : "7- 7Predlcted3‘
10037107., . - 3Observe3d3.
3 ‘3' z 3 ‘ ‘ 7f 3
303, ,,,,, \l ,,,,,,,,,, L ,,,,,,,,,, 3,, ,, 3
S 3 ' I _ 3' 3
g 303 ‘
3 I
4037
.3
20 3 A I
3 ‘ ‘ 3 ‘ '
o ,777777,77, ., A, ,,,7,, . , , I 07 ,7 , 7‘ 7,7,, . f ' <
0 100 200 300 400 500 0 100 200 300 400 500
Time (In hours) Time (In hours)

C.5. Model Validation for T=22° C, DAP=0 ppm

91

Cel
Co
nc.

cell

OdCanxwls/L

 

 

 

x 10 3 Yeast Cell Concentration
5 L T T T . _ . _ _ fl
L sl 7 Pmdlcted L
5 f 7 7 ~~7 — 7 1 Observed _L
L l . L |
‘ "r: ° -: 7 ~ * 1
3 L _ ‘ L
3,77,,7 7e _- ..77.7L #71
l ‘ L
L L L ‘ r
L
21 *9 _fi-iT 7— 7 AL 77 7 T777 7757; _____ 7“
l L ‘. L ~.
1 L“ # x, . .7 7 _L .7 .7 7 L 777 7 7L 7 .7 777 l
i . L L l i L
o _ i 7 l 7 ,7 V, -7, _* _, 1 , "A V__ _ ,_ ,l
0 100 200 300 400 500
Time (In hours)
Alcohol
50 C A 7 f '7 i 1 I"— i —‘ i _ — _
$ 7 Predicled i I I L }
L Observed 2 L __77477 — "I ~—— --
‘0 f ‘7 "z _* - A717. ‘ .2. 47___7_
i L m L L
”7747777'77777L
20 L J L L L L
L L i L T
‘ L
10 L7 7 7.7 7f 7 7L1 7 77 — f7 77 7L -_ 7771
L i | L
L . l I
0 ‘- 7— _‘ law _A __ Ma l+_ + ._7 _h .'
0 100 200 300 400 500

Time (in hours)

C.6.

x 10' Yeast Cell Concentration
71 73 3L i; rrlsredigted L i
i 7 7". . .. .< . ‘r 7 - 7 J Obse .‘
6L +++++ .7 L:
| 1 : L
5‘7 7 r . ‘7 7 ..........
;‘ . i; . L
4L ‘f I 'TL‘ ’L' L """ LL
3 r .......... g A L
1' .
2; \ L ' 1L
1;-'-- ————————————
L ' '
0L' ,7; #7. I ,i 7; l * L
O 100 200 300 400
Time (in hours)
Alcohol
60r - 77 v ,7 777 77
~ Predicted
§ - Observed. § l
50g--4---~-----m-—~ g- 77
L ; 7.; _7 _L
40 L 77f * ,,,,,, L 7 1
30L 'L‘ L
L L
20 L ,L
L : L
10‘, VVVVVVVVVV LL
0L 7 27 . _k; L 7, L
O 100 200 300 400

Time (in hours)

C7.

92

 

 

 

Assimilable Nllrogen
120 177777 — 7,7 7- 7 77 7 .77 77
u L - Predicted L ;
N", 100 7‘ 7. 7 77 L777 7 ’L 7 1 _‘ommw L7]
no Li ‘ L '
on 80 f ‘r ' TV ' 4L 7 7 ¥’ 7 '1
mg L ‘.
IL L 7. L ‘
60 ~ ‘ , - , L d 7 r 7 L 7 ~
. _ L
L ‘x‘ L L
40r 7 7 7. 77 7 7 L 7 7. 7
IL ‘ L p L
20 L7 __ _ __. i‘ _ _ .1. _ .‘ _
L i L '
o L, # A . k ,, ,7, 7 .1 .__L __.“
O 50 100 150
Tlme(inhours)
Sugar
120 77 7 77 7 . 777 7 7
l‘. L L ——~ — Predicted L i
100 771,- t,__7_ _ 2 __ _71L Observed ]
v. I ~ 7* ‘ ~ ‘
3:, .0 7 77477777177 7 177777177 77 -L
”L : L

SUIHO’L

 

‘ L

60 7 7 17777 7777 77 7777. 7- 7
L Li L L L .
. * L

40.7 7.7 7 7x77 7: 7 \7 7
| L' " i L L
: |

20‘77777 r _7 1 77 7 i 7 .

I
. L _Y", i L
0L7 ._ 7-7 _l . L 1L "_x: ‘7 7 i .L

0 100 200 300 400 500

 

Time (in hours)

Model Validation for T=22° C, DAP=300 ppm

Assimilable Nitrogen

 

:7 i 77 7 " :— ‘ 7 7 "L
:j 1 v- _,7 Predictedl ‘
L L - Observed ;
150E ~ L
{f l
100 L ------- 7‘
I;
so ;
O _Lfi 7 i .L “7 : 2" _ 1. ——-v -—.-‘
50 100 150
Time (In hours)
120 Sugar
Li'. L ' _fi L H Predicted L ‘
100:7 L Observed L}
L . Ly
60 3 ‘l‘ I 1
4o; 77777 ‘~
i ' L
20% . L
0L W, A _ L, ,_ fig; ;- ,_,_ - L
O 100 200 300 400 500

Time (in hours)

Model Validation for T =22° C, DAP=600 ppm

C.8.

 

Model Validation for T=11° C, DAP=0 ppm

 

 

 

 

 

 

 

 

 

 

 

 

 

x 10‘ Veal Cell Ooricomrsflm Aulrnllnbln Nitrogen
2 7,7 70 r l . l ,#71‘_l‘1
3 —— Pmdlctad ,_ E g ; i Prsdlctod L
Dbl-nod L 0° '*§""E ************ ‘ ----- 01:..de
"Ii -7 ---- 50 ,5 ,,,,,,,,,,,,,,, . ,,,,,,,,,,,,, ; ......
,‘ I ‘x‘
L E ‘5‘. 1L
. , 4° _ '. ' .......
7" . I ‘ . L
. g 30 ..... . . ,
‘7 2° """"""" L L'L; L
3 ,0 ,,,,,,,,,,,, '.. f? ,,,,,,,,,,,, .1
: , o z s a 7 ‘L
100 300 400 530 ) 50 100 150 200 250 300
11m (in hours) Time (In hours)
Sugar
1207—7r——-777——»7C A 77 7:, .
‘ ‘3 i 77— Pndlc I.
, 1M ‘ VVVVVVVVVVVVVVV omen-«1L
L ‘3,
s 9,5 ....... b. ............................
1 g 5
60 ........... 77.‘
4° .............................. I :7 .L
0L;_L, IL L L' 29 J i ‘ 1 AJ
0 100 300 400 500 ) 100 200 300 400 500

C9.

 

 

Tlmo (in hours) Time (In hours)

Model Validation for T=ll° C, DAP=100 ppm

93

 

Time On hours)

 

x 10 Yeast Cell Concentration Assimilable Nllrogen
2.57 7 7 77 . 7; fl 7 3 120, 7 7 7 . _ 7L , L .
' 7 Predlcledr L ‘ Predicted ;
2L » Observed 1°07 Observed
, . . 7. 77 .7 ., L 7
g i ; I so: 7; .3
1.5 ; - t E ;
" L L so; 7 « L
5 17 g L ‘ L
a ' ‘ ‘°' -‘ ‘
L ' L‘ L L L.
0.5; ; 20L ,
L ; .. 2
or L 7 0‘7 7, .7L i‘ 7.77 7L7 .
O 100 2 400 500 O 50 100 150 200 250 300
Time (In hours) Time (in hours)
Alcohol Sugar
50"; ,’ 7T 7:7fr ‘— r ’ ' 77 o 120(' 7 ’ 7 7 "' ’ 7, ‘7 ’7 if}
L 7 7 Predicted L _ L L ; L 7 Predicted
4.3L 77°me 77; 100777» \; 7 L. ' °,"”T‘7"“"
. L \ . I L
L 8 50 o - —
g SOL A ‘ A L s L L IL L
L 9 my
20 ‘7 7 ‘ . I
; i L “L X .
10, y i L 7 ‘ — L
L *1 L 20L l
L
s L L .
o . 77 7 7A 7 7 7 7 L o .7 7 7 i
100 0 300 400 500 0 100 300 400 500
um (In hours) Time (In hour!)
C.10. Model Validation for T=11° C, DAP=300 ppm
x 10' Yeast Cell Concentratlon Asslmllnble Nitrogen
15"“ , , . 7‘7" T"l 20077 7 o 7 t ’ , ; .
L 7 Predicted ‘L L Predicted
3; ' "L Obeonad L‘ L Obsened ;
3275» ,7 777777 777777 1°: 7 7*
,_ .U L _
e ' u L
3 2L , ' 77777 e E L L
L L 100; 7
g 1.51- 7 ----- 7 7;? L L
‘ ........................ ' L
8 1 L r g ' ' ' ; 50L , 1 \ 7,
0.5L 77777777 L T
' L
0L 7 7 777,77777, 7 7 7. o, 7 77777. 7", Z' * L <
0 100 200 300 400 500 O 50 1 DO 1 50 200 250
Tlme (In hours) Tlrne (In hours)
Alcohol Sugar
50 —————7——— 7 7 77 77 7 7 7 1207 7 7 1
Predlcted v r ' Predicted
L - Observed 7 -_7 " ‘ L 100,, Observed . L
4or 77 777 - 7 7 7 L
i 3 97.; L
L ‘ so, .L
so 7 777777 L
i L L % L 7
9 L g 60 i Li; I L
20L 5 _ L . ;
;L 40 7 ‘,_ .
L L L _
10; r ‘ 20L ,,,,, ‘,
L y
L
o. L 7 , 7' 7 177 77777‘ 0. 7 7 7,—771 7‘ 7-77‘.—.
100 200 300 400 500 0 100 200 300 400 500

Trrne (In hours)

C.ll. Model Validation for T=11° C, DAP=600 ppm

94

 

Appendix D

Program A: Non-Linear Parameter Estimation in MATLAB©
at T=22 C and DAP=100 ppm

‘nlf.m’
% 22 C DAP=100 added
%Read all observed data. Raw observed data is read from an Excel© file.

clear all
global t4 y4 pf4 p1 p2 p3 p4 p5 p6 p7 tn ts te tx n s e x;
global nhat shat ehat xhat that tmptO sumsq count2 counter;

t4=xlsread('C:\. ..\expt-1-data.xls', 'SSQ7', 'A35:A1 09');
y4=xlsread('C:\. . .\expt- 1 -data.xls', 'SSQ7', 'B35:B109');

tx=xlsread('C:\. ..\expt-1-data.xls', 'SSQ7', 'A22A34');
tn=xlsread('C:\. . .\expt- 1 -data.xls', 'SSQ7', 'A35 :A58');
te=xlsread('C:\. . .\expt- 1 -data.xls', 'SSQ7', 'A592A76');
ts=xlsread('C :\. . .\expt- 1 -data.xls', 'SSQ7', 'A77:A109');

x=xlsread('C:\. ..\expt-1-data.xls', 'SSQ7', 'B2:B34');
n=xlsread('C:\. ..\expt-1-data.xls', 'SSQ7', 'B35:B58');
e=xlsread('C:\. . .\expt-l -data.xls', 'SSQ7', 'B59:B76');
s=xlsread('C:\. . .\Thesis\expt-1-data.xls', 'SSQ7', 'B77:B 1 09');

po4=textread('C :\MATLAB 7\work\New F iles\par4.txt')
% this is a text file containing the initial parameter estimates

count2=1;

counteFO;

%Call another function for non-linear data fitting
[pf4,r,J] = nlinfit(t4,y4,'nested4',po4);

pf4=pf4

subplot (2,2,1)
plot(that,xhat, '7-
rs',‘LineWidth',1,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',2)
hold all % hold plot and cycle line colors
plot(tx,x)
hold off
grid on

95

xlabel('Time (in hours)')
ylabe1(' Cel Conc. X, cells/uL')
title('Yeast Cell Concentration')

subplot (2,2,2)
plot(that,nhat, '--rs', 'LineWidth',1,'MarkerEdgeColor','k','MarkerFaceColor','g','
MarkerSize',2)
hold all % hold plot and cycle line colors
plot(tn,n)
hold off
grid on
xlabel('Time (in hours)')
ylabe1('Nitrogen g/L')
title('Assimilable Nitrogen')

subplot (2,2,3)
plot(that,ehat, '--rs','LineWidth',1 ,‘MarkerEdgeColor','k','MarkerFaceColor','g',
'MarkerSize',2)
hold all % hold plot and cycle line colors
plot(te,e)
hold off
grid on
xlabel('Time (in hours)')
ylabel('Ethanol g/L')
title('Alcohol')

subplot (2,2,4)
plot(that,shat, '--rs','LineWidth', 1 ,'MarkerEdgeColor','k','MarkerFaceColor','g',
'MarkerSize',2)
hold all % hold plot and cycle line colors
plot(ts,s)
hold off
grid on
xlabel('Time (in hours)')
ylabe1('Sugar g/L’)
title('Sugar')

Program B: Solve model in MATLAB© using 4th-order Runge—Kutta formula
for T=22 C and DAP=100 ppm

‘nested4.m’

% This program solves the model using 4th-order Runge-Kutta formula

96

 

function out=nested4(po4,t4)
global p1 p2 p3 p4 p5 p6 p7 counter nhat shat ehat xhat that;
global tx tn te ts x n e s;
opts=optimset('disp','iter','T01X',1e-0012);
%options=['Vectorized' 'On']

% Input initial parameter estimates%

P1=p04(1);
p2=po4(2);
p3=3.5E-OO3;
P4=p04(3);
p5=p04(4);
p6=po4(5);
p7=0.38;

 

%ICs =txtread('C:\MATLAB7\work\New Files\ic1.txt') ;. .
ICs =[23E6 65 0 116];
tmpt0=[0:0.01:500];

count=0;

% Call function odelSs to solve coupled differential equations in ode1.m
[t,Y]=ode1Ss(@ode1,tmptO,ICs,opts);

countchounter+1

% for i=1:[length(tx)]

% temp=tx(i);

% Ytemp=find(t==temp);
% %pause

% out(i)=(Y(Ytemp, 1 ));
% end

% count=count+i;

% Select the output of [t,Y] those predicted values that correspond to the observed data

for i=1:[1ength(tn)]
temp=tn(i);
Ytemp=find(t==temp);
out(count+i)=Y(Ytemp,2);

end

count=count+i;

for i=1:[1ength(te)]

temp=te(i);
Ytemp=find(t==temp);

97

% out(count+i)=Y(Ytemp,3)/7.89;
out(count+i)=Y(Ytemp,3);
end
count=count+i;

for i=1 :[1ength(ts)]
temp=ts(i);
Ytemp=find(t==temp);
out(count+i)=Y(Ytemp,4);
end

out=out';
nhat=Y(:,2); shat=Y(:,4); ehat=Y(:,3); xhat=Y(:,1); that=t;

return
end

Program C: Compare raw observed data with model predictions and
check accuracy of initial estimates

‘odesolver.m’
clear all
po4=textread(’C:\MATLAB7\work\New F i1es\par4.txt')

global p1 p2 p3 p4 p5 p6 p7 counter nhat shat ehat xhat that;
global tx tn te ts x n e s;
opts=optimset('disp','iter','TolX',1 e-012);
%options=['Vectorized' 'On']

p1=po4(1);

p2=p04(2);

p3=3.5E-OO3;

p4=p04(3);

p5=po4(4);

p6=p04(5);

p7=0.38;

%ICs =txtread('C :\MATLAB 7\work\New F iles\icl .txt’)
ICs = [23E6 65 O 116];

tmpt0=[0:0.01:500];

count=0;

[t,Y]=ode1 Ss(@odel ,tmptO,ICs,opts);

98

 

nhat=Y(:,2); shat=Y(:,4); ehat=Y(:,3); xhat=(Y(:,1)); that=t;
% ehat=(Y(:,3)/7.89);

tx=xlsread('C:\. . .\expt- 1 -data.xls', 'SSQ7', 'A22A34');
tn=xlsread('C:\. . .\expt- 1 -data.xls', 'SSQ7', 'A35 :A5 8');
te=xlsread('C:\. ..\expt-1-data.xls', ’SSQ7', 'A59:A76');
ts=xlsread('C:\. . .\expt— 1 -data.xls', 'SSQ7', 'A771A109');

x=xlsread('C:\. . .\expt-l-data.xls', 'SSQ7', 'B2:B34');
n=xlsread('C:\. . .\expt-l-data.xls‘, 'SSQ7', 'B35:BSS');
e=xlsread('C:\. . .\expt-l-data.xls', 'SSQ7', 'B59:B76');
s=xlsread('C:\. . .\expt-l—data.xls', 'SSQ7', 'B77:B109');

subplot (2,2,1)
plot(that,xhat)
hold all % hold plot and cycle line colors
plot(tx,x, '--
rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor’,'g','MarkerSize',2)
hold off
grid on
xlabel('Time (in hours)')
ylabel(' Cel Conc. X, cells/uL')
title('Yeast Cell Concentration')

subplot (2,2,2)
plot(that,nhat)
hold all % hold plot and cycle line colors

plot(tn,n, '7-
rs','LineWidth’,2,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',2)

hold off

grid on

xlabel('Time (in hours)')

ylabel('Nitrogen mg/L')

title('Assimilable Nitrogen')

subplot (2,2,3)
plot(that,ehat)
hold all % hold plot and cycle line colors

plot(te,e, '--
rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',2)
hold off
grid on
xlabel('Time (in hours)')
ylabel('Ethanol g/L')
title('Alcohol')

99

subplot (2,2,4)
plot(that,shat)
hold all % hold plot and cycle line colors
plot(ts,s, '7-
rs','LineWidth',2,‘MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',2)
hold off
grid on
xlabel('Time (in hours)')

ylabel('Sugar g/L')
title('Sugar')

Program D: Program describing the ordinary differential equations that constitute
the proposed model

function dy = odel(t,y)

dy = zeros(4,1);
global p1 p2 p3 p4 p5 p6 p7;
%PARAMS=[MEUmax BETAmax kd Kn Ks yx/n yE/S]

% dy = [ Xv N E S ]
%Equations (1 .1) to (1.4) and equations (2.1) and (2.2)

%dXv/dt
%dy(1)= (((params1(1) * y(1)/(params1(4) + ya») * y(1»- (params1(3)*y(1»)

%dN/dt
dY(2)= ((-1)*Y(1)*(P1*Y(2)/((P4+Y(2))))/P6);

%dE/dt
dy(3)= (p2*y(4)/(p5+y(4)))*y(1) ;

%dS/dt
d)’(4)= ((-1)*Y(1)*(P2*Y(4)/(P5+Y(4))))/P7;

return
end

100

Appendix E

HPLC Analysis of Ethanol, E

The figures below show a typical HPLC Chromatogram for hard cider followed by a

Chromatogram for hard cider spiked with ethanol.

 

400.00 L
L
200.00 L
L
W 0.00 T
720000

«400.00

'57_L_4._A._A7l L—A—J $7.; 5
L

-600.00

Minutes

 

 

 

Figure E.l. HPLC Chromatogram for hard cider: Ethanol is detected by a positive
peak at 7.5 minutes

 

7772.00 14.00' 6.00 3.00 I 10.00 1 i200 ‘ 14.00!

 

 

 

Figure E.2. HPLC Chromatogram for hard cider spiked with 99.9% pure ethanol:
The positive peak at 7.5 minutes is greater in height and area

101

 

Hlucose, Fructose

 

7/Lr—W

 

Figure E.3. HPLC Chromatogram showing various sugars: Glucose, Fructose is
detected at 6.3 minutes and sucrose at 6.9 minutes following the procedure
described in section 3.2 on Methods of Analysis

102

Appendix F

Parameter Estimation Data Set

F.1. Data for T=1] °C, Viable Yeast Cell Concentration, X y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 27000000 23000000 3 8000000 29000000

0 283 3 3 3 3 3 .3 24000000 40000000 30000000

0 286666667 236666667 41000000 30000000

76 52000000 61000000 71000000 83000000
76 57333333 .3 656666667 72000000 826666667
76 626666667 753333333 73000000 893333333
103 123000000 128600000 170000000 208000000
103 1 1 8000000 1 32200000 1 75000000 228000000
103 1 1 3000000 13 5300000 1 80000000 23 1000000
210 128000000 177000000 196000000 245000000
210 13 1000000 168000000 201000000 252000000
210 l 3 5000000 174000000 199000000 254000000
330 90000000 125000000 165000000 232000000
330 90000000 121670000 15 8666667 213000000
330 91000000 123300000 152333333 228000000
500 91000000 105000000 105000000 171000000
500 92413793.] 103448276 106551724 171000000
500 87400000 982 1 4285 .7 108214286 172000000

 

 

 

 

 

 

103

F.2.

Data for T=17 °C, Viable Yeast Cell Concentration, X y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 3143000000 5536000000 5536000000 2857000000

0 4179000000 6393000000 6393000000 3143000000

0 5214000000 7036000000 7036000000 3607000000
24 6200000000 20700000000 20700000000 29000000000
24 6533000000 22033000000 22033000000 30600000000
24 7067000000 23367000000 23367000000 32167000000
55 1 3300000000 28000000000 28000000000 39000000000
55 13467000000 29733000000 29733000000 38500000000
55 1 3 800000000 28433000000 28433000000 3 8000000000
76 24100000000 3 1700000000 3 1700000000 33000000000
76 23767000000 32633000000 32633000000 32300000000
76 23 767000000 32300000000 32300000000 31667000000
101 3 1000000000 3 5300000000 35300000000 3 7500000000
101 30700000000 34000000000 34000000000 3 7133000000
101 30533000000 34000000000 34000000000 3 8000000000
212 29900000000 32533000000 32533000000 32233000000
212 28900000000 31967000000 31967000000 33333000000
212 28433000000 31867000000 31867000000 33833000000
351 1 6700000000 28800000000 28800000000 32500000000
351 17867000000 27133000000 27133000000 32333000000
351 17967000000 28933000000 28933000000 27264000000
500 1 5 533000000 24766000000 24766000000 30700000000
500 16000000000 25733000000 25733000000 31069000000
500 1 5100000000 24233000000 24233000000 29276000000

 

 

 

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F.3. Data for T=22 °C, Viable Yeast Cell Concentration, X y
Time Xv cells/mL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 1 800000000 2320000000 37600000 14000000
0 1541666667 2560000000 36800000 13600000
0 1565217391 2520000000 35600000 15600000
15 12600000000 6440000000 124800000 58400000
15 11875000000 6160000000 134000000 63200000
15 1 1478260870 6240000000 136800000 67200000
24 14900000000 23080000000 403200000 203600000
24 14700000000 24800000000 405200000 191 600000
24 15650000000 1 8600000000 377200000 171600000
48 20360000000 28300000000 388000000 403600000
48 20166666670 30800000000 382000000 391600000
48 20173913040 29920000000 376000000 371600000
63 21000000000 29400000000 424000000 488000000
63 21166666670 29400000000 412000000 462000000
63 19000000000 29200000000 408000000 412000000
84 23480000000 26500000000 340000000 51 8000000
84 23400000000 25400000000 348000000 494000000
84 23330000000 25200000000 356000000 466000000
110 20160000000 23400000000 352000000 464000000
110 20583333330 25320000000 352800000 468400000
110 20826086960 22500000000 354000000 370400000
193 1 8520000000 21200000000 3 16000000 423600000
193 17800000000 20400000000 308000000 404000000
193 1 8200000000 19200000000 321 500000 402000000
295 16200000000 15600000000 242000000 254000000
295 15540000000 14800000000 226400000 283300000
295 15800000000 14400000000 219100000 278000000
351 1 5000000000 13000000000 164000000 193200000
351 14791666670 14120000000 170000000 182400000
351 145 652 1 73 .90 14920000000 172000000 176400000
500 4760000000 4320000000 78400000 89000000
500 495 833 33 .3 3 4560000000 74400000 136400000
500 4913043478 5040000000 70800000 147600000

 

 

 

 

 

105

 

 

 

F.4. Data for T=1] °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration mg/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 45 64 112 164

0 45 64 112 164

0 45 64 112 164

24 39.7830354 57.60316804 87.24022043 149.6533641
24 39.7830354 57.60316804 87.24022043 149.6533641
24 39.7830354 57.60316804 87.24022043 149.6533641
52 303383215 43.04205617 57.72935041 122.2379552
52 30.3383215 43.04205617 57.72935041 122.2379552
52 30.3383215 43.04205617 57.72935041 122.2379552
76 206564055 260384072 37 .1 1 125123 91 .30099612
76 20.6564055 26.0384072 37.11125123 91 .30099612
76 20.6564055 26.0384072 37.11125123 91 .30099612
103 11.3068194 1080806622 21 .34729962 5680542436
103 1 1.3068194 10.80806622 21 .34729962 56.80542436
103 1 1.3068194 10.80806622 21 .34729962 56.80542436
125 633884107 4603436231 1343309598 35.27500181
125 6.33884107 4.603436231 13.43309598 35.27500181
125 6.33884107 4.603436231 13.43309598 35.27500181
193 1.01410429 0339103514 3.486024468 7.093196487
193 1.01410429 0.339103514 3.486024468 7.093196487
193 1.01410429 0.339103514 3.486024468 7.093196487
210 066432363 0189522586 2.571621406 4.835573916
210 066432363 0.189522586 2.571621406 4835573916
210 0.66432363 0.189522586 2.571621406 4.835573916

 

 

 

 

 

 

106

 

F.5.

Data for T=17 °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration mg/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 45 65 127 165

0 45 65 127 165

0 45 65 127 165

24 223431924 38.15045585 104.3271583 156359136
24 22.3431924 38.15045585 104.3271583 156.359136
24 22.3431924 38.15045585 104.3271583 156.359136
42 4.33806745 1601722754 68.61728958 137.9959603
42 4.33806745 16.01722754 68.61728958 137.9959603
42 4.33806745 16.01722754 68.61728958 137.9959603
55 101394586 7.065134792 41.01991383 114.096778
55 1.01394586 7.065134792 41.01991383 114.096778
55 1.01394586 7065134792 41 .01991383 114.096778
76 009881884 1.658353357 13.64341851 62.89816682
76 0.09881884 1.658353357 13.64341851 62.89816682
76 0.09881884 1.658353357 13.64341851 62.89816682
101 000750595 0286216576 3.224695001 19.40497316
101 0.00750595 0.286216576 3.224695001 19.40497316
101 0.00750595 0.286216576 3.224695001 19.40497316
125 000077222 0054099652 0842491706 4.959377215
125 000077222 0.054099652 0.842491706 4.959377215
125 000077222 0.054099652 0842491706 4.959377215
193 2.9649E-06 0.000591548 0030947666 0.081403109
193 2.9649E-06 0.000591548 0.030947666 0.081403109
193 2.9649E-06 0000591548 0.030947666 0081403109

 

 

 

 

 

107

 

 

F .6.

Data for T=22 °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration ng/L
hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600me

0 45 65 110 165

0 45 65 110 165

0 45 65 110 165

24 21 .4270081 54.90532244 97.36440943 156.34515
24 21 .4270081 54.90532244 97.36440943 156.34515
24 21 .4270081 54.90532244 97.36440943 156.34515
42 4.46851567 43.85542894 84.16440719 143.6076667
42 4.46851567 43.85542894 84. 16440719 143.6076667
42 4.46851567 43.85542894 84.16440719 143.6076667
55 1.15086761 3045588295 6697349415 121 .3479307
55 1.15086761 3045588295 6697349415 121.3479307
55 1.15086761 30.45588295 66.97349415 121.3479307
76 0 18.29589934 48.31115162 89.92936739
76 0 18.29589934 48.31115162 89.92936739
76 0 18.29589934 48.31115162 89.92936739
101 0 1.461745516 7.32207622 9.10062081
101 0 1.461745516 7.32207622 9.10062081
101 0 1.461745516 7.32207622 9.10062081
125 0 0207625667 1.473091544 1 . 143798166
125 0 0.207625667 1.473091544 1.143798166
125 0 0.207625667 1.473091544 1.143798166
193 0 000072462 0012510934 0002510864
193 0 000072462 0.012510934 0.002510864
193 0 000072462 0.012510934 0.002510864

 

 

 

 

 

108

 

 

 

F.7. Data for T=11 °C, Ethanol Concentration, E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Ethanol Concentration gi
(Hours) DAP=0 ppm DAP=100 ppm DAP=300 ppmlDAP=600 ppm

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

52 0.56 0 1.8936 4.4184
52 0.78 0 2.8404 5.6019
52 0.81 0 2.5248 5.2863
92 3.1835 2.7615 7.2588 10.0203
92 2.6569 4.5762 6.4698 10.4937
92 2.789 3.4716 7.6533 9.7836
143 8.523 6.2331 16.8846 21.6975
143 9.5762 7.2588 15.4644 22.3287
143 9.6551 8.2845 17.6736 23.2755
193 16.4955 9.9414 21.8553 25.5636
193 16.2056 10.257 22.2498 26.3526
193 16.679 9.0735 21.9342 24.459
245 19.8625 15.3855 28.7985 34.4793
245 22.4148 15.1488 29.1141 35.8206
245 21.5726 14.5176 30.0609 34.716
330 28.4076 23.3544 34.1637 41.2647
330 27.1452 23.9067 33.138 41.8959
330 26.9085 23.1966 33.2958 41.2647
330 28.4076 23.3544 34.1637 41.2647
330 27.1452 23.9067 33.138 41.8959
330 26.9085 23.1966 33.2958 41.2647
500 30.0609 33.6114 43.395 45.2886
500 28.8774 34.2426 42.4482 45.8409
500 29.193 32.8224 43.6317 45.2097

 

 

 

 

 

109

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F.8. Data for T=17 °C, Ethanol Concentration, E
Time Ethanol Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 0 0 O 0

0 O 0 0 0

0 0 0 0 O

48 1.1835 2.7615 7.2588 8.4423
48 1.6569 4.5762 6.4698 8.9157
48 0.789 3.4716 7.6533 9.7836
92 5.523 15.3066 20.1984 21.0663
92 6.6276 14.5965 18.6993 21.6186
92 5.4441 15.1488 20.8296 21.8553
143 16.6479 22.0131 29.5086 31.7178
143 15.5433 23.0388 31.2444 30.2187
143 16.1745 24.0645 28.7196 31.1655
193 23.2755 30.2976 37.6353 39.6867
193 23.9856 30.1398 36.4518 42.9216
193 24.459 29.5875 36.1362 41 .2647
500 37.2408 39.6867 45.2886 48.918
500 37.3986 40.3179 44.3418 49.7859
500 36.0573 38.8188 44.6574 47.8134

 

 

 

 

110

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F.9. Data for T=22 °C, Ethanol Concentration, E
Time Ethanol Concentration g/L
flours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

48 5.9964 12.1506 11.9928 12.1745
48 6.6276 13.2552 12.7818 15.8057
48 7.2588 13.6497 11.5983 13.6736
92 16.9635 20.0406 24.7746 32.0609
92 16.2534 20.9085 23.8278 33.982
92 15.3855 20.6718 26.5104 31.2444
143 24.5379 24.3801 29.5086 43.2958
143 23.4333 25.4058 31.2444 42.7435
143 23.9856 24.0645 28.7196 42.5857
193 31.9545 36.294 37.6353 47.7142
193 34.716 38.0298 36.4518 48.0298
193 33.2169 34.3215 36.1362 45.8206
500 37.6353 44.3418 46.7088 50.7327
500 37.3197 43.9473 45.8409 49.9437
500 36.294 45.762 45.6042 50.3382

 

 

 

 

 

 

111

F.10. Data for T=1] °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sigar Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=30(me DAP=600 ppm

0 116 116 116 116

0 116 116 116 116

0 116 116 116 116

52 111.201266 112.4847114 1060967261 1063316382
52 111.201266 112.4847114 106.0967261 106.3316382
52 111.201266 112.4847114 106.0967261 106.3316382
92 102.959187 104.6837317 95.03607745 88.98096031
92 102.959187 104.6837317 95.03607745 88.98096031
92 102.959187 104.6837317 95.03607745 88.98096031
143 88.5952773 9077985775 79.98023197 57.65329257
143 88.5952773 90.77985775 79.98023197 57.65329257
143 88.5952773 90.77985775 79.98023197 57.65329257
193 74.7125694 78.19086024 6652078682 3006040873
193 74.7125694 78.19086024 66.52078682 30.06040873
193 74.7125694 78.19086024 66.52078682 30.06040873
245 62.3076042 67.36716282 54.65013978 12.34262544
245 62.3076042 67.36716282 54.65013978 12.34262544
245 62.3076042 67.36716282 54.65013978 12.34262544
330 465924344 53.9500996 39.68056648 2.408089893
330 46.5924344 53.9500996 39.68056648 2.408089893
330 46.5924344 53.9500996 39.68056648 2.408089893
405 365499563 45.46426771 301996127 0679179924
405 36.5499563 45.46426771 30.1996127 0.679179924
405 365499563 45.46426771 30.1996127 0.679179924
500 27.5931765 37.88714237 21 .87583241 0197031307
500 27.5931765 37.88714237 21 .87583241 0.197031307
500 27.5931765 37.88714237 21.87583241 0.197031307

 

 

 

 

 

112

 

 

 

 

F.11. Data for T =17 °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sugar Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 116.00 116.00 116 116
0 116.00 116.00 116 116
0 116.00 116.00 116 116
48 105.47 106.26 102.7333856 1064694394
48 105.47 106.26 102.7333856 106.4694394
48 105.47 106.26 102.7333856 106.4694394
92 89.19 90.34 68.71753135 62.42043055
92 89.19 90.34 68.71753135 6242043055
92 89.19 90.34 68.71753135 62.42043055
143 73.32 73.05 35.16326314 15.75405745
143 73.32 73.05 35.16326314 15.75405745
143 73.32 73.05 35.16326314 15.75405745
193 60.58 58.28 1606795658 2.964851871
193 60.58 58.28 16.06795658 2.964851871
193 60.58 58.28 16.06795658 2.964851871
212.00 56.37 53.24 11.71686095 1.534290748
212.00 56.37 53.24 11.71686095 1.534290748
212.00 56.37 53.24 11.71686095 1.534290748
351.00 33.86 25.43 1.404251642 0.011796163
351.00 33.86 25.43 1.404251642 0.011796163
351.00 33.86 25.43 1.404251642 0.011796163
500 20.82 10.34 0308015517 6.46724E-05
500 20.82 10.34 0.308015517 6.46724E-05
500 20.82 10.34 0.308015517 6.46724E-05

 

113

 

F.12. Data for T =11 °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sugar Concentration g/L
hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0.00 116 116 116 116
0.00 116 116 116 116
0.00 116 116 116 116
15.00 114.54387 114.084991 113.0371973 114.1000532
15.00 114.54387 114.084991 113.0371973 114.1000532
15.00 114.54387 114.084991 113.0371973 114.1000532
24.00 112.38142 111.5625198 109.5500385 111.1527944
24.00 112.38142 111.5625198 109.5500385 111.1527944
24.00 112.38142 111.5625198 109.5500385 111.1527944
48.00 102.049076 97.85182154 909807048 87 .52709999
48.00 102.049076 97.85182154 90.9807048 87 .52709999
48.00 102049076 97.85182154 90.9807048 87.52709999
63.00 94.7545835 8649300368 74.49529182 62.95072964
63.00 94.7545835 86.49300368 74.49529182 62.95072964
63.00 94.7545 835 8649300368 7449529182 62.95072964
84.00 85.1170423 71.210665 84 52.32328035 34.64154636
84.00 85.1170423 71.21066584 52.32328035 34.64154636
84.00 85.1170423 71 .210665 84 52.32328035 34.64154636
110.00 74.375303 55.17397849 31.74062889 15.78144938
110.00 74.375303 55.17397849 31.74062889 15.78144938
110.00 74.375303 55.17397849 31.74062889 15.78144938
193.00 47 .9677234 23.79321627 6079927888 1 .69273 8265
193.00 47.9677234 23.79321627 6.079927 888 1 .69273 8265
193.00 47.9677234 23.79321627 6.079927888 1.692738265
295.00 28.0740084 9.279564716 1.161020665 0222923986
295.00 28.0740084 9.279564716 1.161020665 0222923986
295.00 28.0740084 9.279564716 1.161020665 0.222923986
351.00 21 .2436649 6037606593 0575723601 0095897917
351.00 21 .2436649 6.03 7606593 0.575723601 0.095897917
351.00 21.2436649 6.037606593 0.575723601 0.095897917
500.00 11.2510679 2.596126198 0153309599 0019685051
500.00 11.2510679 2.596126198 0.153309599 0.019685051
500.00 11.2510679 2.596126198 0.153309599 0.019685051

 

 

 

 

 

114

 

APPENDIX G
Model Validation Data Set

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G.1. Data for T=11 °C, Viable Yeast Cell Concentration, X y, cells/mL
Time
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0.00 29555658 24989500 3721841332 30305000
0.00 2618787918 2571383337 4015670911 31350000
0.00 3235321925 25189416 3645290237 31668725
0.00 3395090905 26284608 3837147618 32760750
0.00 2392343077 2591954404 3933076308 32760750
76.00 47503 594.74 66276500 6953966699 86735000
76.00 6276016263 7134683337 7051909892 863866667
76.00 6859831737 8184966663 7149853085 933533333
76.00 4339599064 66806712 6810937022 90638075
76.00 6870066306 7191760804 7249363369 902740667
76.00 750914225 8250446396 7350048972 975542333
103.00 134642442 139723900 166503428 217360000
103.00 1077966188 143635300 171400587.7 238260000
103.00 123695902 147003450 1762977473 2210526316
103.00 147386887.7 1408416912 171165524 227141200
103.00 9847551723 1447843824 1761998041 248981700
103.00 1354042139 1481794776 1812340842 2115336187
210.00 140115712 ' 192310500 1919686582 2344497608
210.00 143399674 182532000 1968658 1 7 .8 2411483264
210.00 147778290 189051000 194906954 243062201
210.00 1533782246 193848984 1973437806 2243538381
210.00 1569730267 183992256 1928166678 2307639477
210.00 1617660963 190563408 190898094 2325954076
330.00 98518860 135812500 1616062684 2220095694
330.00 98518860 132194455 1554031998 2038277512
330.00 99613514 133965450 1492001303 2181818182
330.00 1078440642 136899000 1582823392 2124493487
330.00 1078440642 1332520106 1522068558 1950504796
330.00 1090423316 1350371736 1461313716 2087864289
500.00 99613514 114082500 1028403526 1636363636
500.00 1011611283 1123965519 1043601606 1636363636
500.00 956727596 1067098214 1059885269 164593301.4
500.00 1090423316 114995160 100725125 156589821.7
500.00 1107364337 1132957243 1022136735 156589821.7
500.00 104728569 107563500 1038085474 1575055516

 

 

 

 

 

115

 

G.2.

Data for T=17 °C, Viable Yeast Cell Concentration, X y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(Hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0.00 41 790000.00 4600000000 5 145000000 2857000000
0.00 3 143000000 5 100000000 6393000000 3045000000
0.00 41 790000.00 3900000000 7036000000 3245000000
0.00 5214000000 1 7200000000 31065400000
0.00 3040000000 20100000000 6393000000 32576700000
0.00 3120000000 1 8800000000 7036000000 34054500000
24.00 6200000000 27500000000 20700000000 66734300000
24.00 6533000000 27600000000 22033000000 68045000000
24.00 7067000000 28900000000 23367000000 61575750000
24.00 4170000000 31400000000 20700000000 7053 50000.00
24.00 7210000000 28700000000 22033000000 71635400000
24.00 6540000000 26200000000 23367000000 66943000000
55.00 13300000000 28000000000 28000000000 65000000000
55.00 13467000000 29400000000 29733000000 68500000000
55.00 1 3 800000000 27700000000 28433000000 70100000000
55.00 6200000000 25500000000 28000000000 62200000000
55.00 12100000000 26500000000 29733000000 65000000000
55.00 14820000000 26200000000 28433000000 61200000000
76.00 24100000000 22300000000 31700000000 61500000000
76.00 23767000000 24500000000 32633000000 53400000000
76.00 23767000000 24800000000 32300000000 59800000000
76.00 23 800000000 21200000000 31700000000 44700000000
76.00 24850000000 23000000000 32633000000 56100000000
76.00 21 1 330000.00 23400000000 32300000000 52100000000
101.00 3 1 000000000 144000000 3 53000000 405 30000
1 01.00 3 0700000000 1 5 1000000 340000000 30450000
101.00 305 330000.00 155000000 340000000 34330000
101.00 23 767000000 172000000 353000000 333000000
101.00 3 1000000000 201000000 340000000 347000000
1 01.00 3 1050000000 222000000 340000000 31 7000000
212.00 29900000000 275000000 325330000 456000000
212.00 28900000000 298000000 3 19670000 432000000
212.00 28433000000 297000000 318670000 475000000
212.00 305 3 30000.00 323000000 325330000 662000000
212.00 30933000000 287000000 3 19670000 680000000

 

 

 

 

 

116

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(Hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
351.00 1 7867000000 294000000 27 1330000 881000000
351.00 17967000000 284000000 289330000 795000000
351.00 20433000000 288000000 288000000 670000000
351.00 18267000000 265000000 271330000 691000000
351.00 17867000000 262000000 289330000 703000000
500.00 1 5 5 3 30000.00 247000000 247660000 663000000
500.00 1 6000000000 245000000 257330000 634000000
500.00 1 5 100000000 23 1000000 242330000 647000000
500.00 1 7967000000 212000000 247660000 590000000
500.00 15 533000000 242000000 257330000 624000000
500.00 16000000000 235000000 242330000 612000000
212.00 30130000000 294000000 318670000 691 000000
351.00 16700000000 340000000 288000000 782000000

 

 

 

 

 

117

 

G.3. Data for T=22 °C, Viable Yeast Cell Concentration, X y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0.00 1800000000 2400000000 35460000 14910000
0.00 2100000000 2360000000 36000000 14484000
0.00 2000000000 2530000000 32000000 16614000
0.00 12200000000 6770000000 127000000 15879150
0.00 1 1900000000 6475000000 133000000 15425460
0.00 12700000000 6867400000 136000000 17693910
15.00 15600000000 21564000000 395000000 62196000
15.00 16100000000 22154600000 391000000 67308000
1 5.00 1 7000000000 21845400000 402000000 630985915 5
15.00 22400000000 29039000000 388000000 66238740
15.00 23100000000 28847900000 378000000 71683020
15.00 22800000000 29428000000 384000000 592475038
24.00 22500000000 30400000000 395000000 191 1737089
24.00 23400000000 30100000000 390000000 1 799061033
24.00 25 100000000 29900000000 3 82000000 161 1267606
24.00 21000000000 30100000000 364000000 179505830
24.00 23500000000 29300000000 380000000 1689259186
24.00 21 100000000 28700000000 327000000 1512927329
48.00 21900000000 22800000000 354360000 3789671362
48.00 2 1400000000 25 100000000 354000000 422928000
48.00 21 100000000 23400000000 326000000 401 328000
48.00 20100000000 22600000000 341000000 3558376865
48.00 19500000000 21500000000 335000000 456762240
48.00 20400000000 16400000000 304000000 433434240
63.00 1 8300000000 1 7100000000 290000000 527040000
63.00 1 7700000000 1 6800000000 297000000 498960000
63.00 1 8100000000 16400000000 285000000 438780000
63.00 1 6800000000 1 3200000000 204000000 569203200
63.00 16400000000 12800000000 201 000000 53 8876800
63.00 16100000000 13300000000 210000000 467300700
84.00 1 2500000000 6400000000 104000000 55 1 670000
84.00 14100000000 5800000000 108000000 526110000
84.00 13300000000 5300000000 1 12000000 496290000
84.00 1600000000 24240000 35920980 587528550
84.00 1540000000 23 836000 36468000 560307150

 

 

 

 

 

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Xv cells/mL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm

84.00 1710000000 25553000 32416000 528548850
110.00 13400000000 68377000 128651000 4356807512
110.00 13100000000 65397500 134729000 4398122066
110.00 12200000000 69360740 137768000 3477934272
110.00 14500000000 217796400 400135000 4090899072
110.00 15400000000 223761460 396083000 412969208
110.00 15300000000 220638540 407226000 3265665983
193.00 20100000000 293293900 393044000 3977464789
193.00 19000000000 291363790 382914000 430260000
193.00 18500000000 297222800 3 88992000 428130000
193.00 21 100000000 307040000 400135000 3734708722
193.00 22500000000 304010000 395070000 458226900
193.00 21500000000 301990000 386966000 455958450
295.00 24500000000 304010000 368732000 270510000
295.00 24100000000 295930000 37 5 1233959 301714500
295.00 23800000000 289870000 3228035538 296070000
295.00 205 000000.00 230280000 3498124383 288093150
295.00 20200000000 2480237164 3494570582 3213259425
295.00 19500000000 2312252964 321816387 315314550
351.00 17800000000 2233201581 3366238894 205758000
351.00 18100000000 2124505929 3307008885 194256000
351.00 18300000000 162055336 3000987167 187866000
351.00 15500000000 168972332 286278381 219132270
351.00 14600000000 1660079051 2931885489 206882640
351.00 14500000000 162055336 2813425469 200077290
500.00 10300000000 1304347826 2013820336 94785000
500.00 1 1300000000 1264822134 1984205331 145266000
500.00 1 1800000000 1314229249 2073050346 157194000
500.00 6500000000 63241 106.72 1026653504 100946025
500.00 7100000000 5731225296 1066140178 154708290
500.00 5600000000 523715415 1105626851 167411610

 

 

 

 

 

119

 

G.4.

Data for T=1] °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration mg/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 45.20 64.00 112.00 163.67
0 44.90 63.26 11.45 163.45
0 45.00 64.22 112.30 163.45
0 44.89 63.90 112.03 163.78
0 44.96 64.30 111.89 163.25
0 45.02 64.86 112.00 163.67
24 38.45 58.24 88.46 149.26
24 38.89 57.99 88.56 149.35
24 38.37 58.65 88.66 149.47
24 38.44 58.45 89.01 148.98
24 38.67 58.44 87.99 149.35
24 38.93 57.04 88.03 149.80
52 29.32 43.52 58.54 122.05
52 29.27 42.88 58.70 121.89
52 29.35 43.87 57.13 12.48
52 29.46 43.49 59.35 122.00
52 29.79 43.50 58.75 121.98
52 29.69 42.62 59.36 121.99
76 19.97 26.32 37.63 91.12
76 20.35 26.78 37.55 91.76
76 20.46 26.32 37.63 90.45
76 20.21 25.48 36.38 90.98
76 20.79 25.07 37.47 91.47
76 20.15 25.78 36.38 91.12
103 10.93 10.93 21.65 56.98
103 11.03 11.26 22.02 55.90
103 11.07 10.36 21.98 55.42
103 1078 10.90 21.14 55.63
103 10.69 11.07 20.90 56.46
103 11.06 10.70 20.92 56.69
125 6.13 4.65 13.62 35.20
125 6.24 4.36 13.44 34.89
125 6.07 4.66 12.57 35.47
125 6.38 4.66 13.46 35.13
125 6.20 4.56 13.99 35.47

 

 

 

 

 

120

 

 

Time

Nitrogen Concentration ngL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
125 6.20 4.56 13.81 35.20
193 0.98 0.34 3.53 7.08
193 0.90 0.34 3.44 6.98
193 0.98 0.65 3.27 7.13
193 0.98 0.39 3.89 7.25
193 0.94 0.41 3.47 7.05
193 0.99 0.34 3.58 7.08
210 0.64 0.19 2.61 4.83
210 0.63 0.20 2.47 4.57
210 0.65 0.19 2.79 4.68
210 0.63 0.21 2.01 5.03
210 0.68 0.19 2.64 5.10
210 0.65 0.19 2.64 4.88

 

 

 

 

 

 

121

:f

 

G.5.

Data for T=17 °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration mg/L
hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 45.00 65.00 127.00 165.00
0 45.00 65.00 127.00 165.00
0 45.00 65.00 127.00 165.00
0 45.00 65.00 127.00 165.00
0 45.00 65.00 127.00 165.00
0 45.00 65.00 127.00 165.00
24 32.34 28.60 101.34 153.45
24 32.54 39.77 98.54 152.86
24 32.17 39.77 100.40 153.45
24 32.76 40.56 97.45 156.36
24 32.34 40.56 97.33 155.67
24 32.17 42.40 98.74 153.45
42 14.34 16.01 56.43 134.46
42 14.34 16.64 55.34 134.66
42 14.34 16.64 58.43 134.33
42 14.34 20.45 65.82 138.00
42 14.34 20.45 67.49 135.57
42 14.34 22.10 66.53 134.61
55 4.01 7.06 38.82 109.56
55 4.01 8.56 37.45 108.84
55 4.46 8.82 37.91 108.28
55 4.46 8.82 40.31 114.10
55 4.87 9.65 38.45 110.67
55 4.87 10.45 40.10 110.27
76 0.99 1.74 10.56 55.67
76 0.99 1.85 9.44 55.35
76 0.99 1.85 10.34 56.71
76 0.99 1.92 12.56 57.45
76 0.99 1.92 11.49 62.90
76 0.99 2.12 12.48 55.34
101 0.08 0.29 4.55 17.57
101 0.08 0.36 3.19 17.79
101 0.08 0.39 2.60 18.24
101 0.08 0.39 2.33 19.65
101 0.08 0.42 2.84 20.54

 

 

 

 

 

122

 

 

Time

Nitrogen Concentration mg/L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
101 0.08 0.45 2.42 20.05
125 0.00 0.06 0.69 3.77
125 0.00 0.08 0.73 4.12
125 0.00 0.09 0.71 3.95
125 0.00 0.09 0.54 4.55
125 0.00 0.10 0.41 4.62
125 0.00 0.10 0.38 4.49
193 0.00 0.00 0.03 0.06
193 0.00 0.00 0.02 0.07
193 0.00 0.00 0.02 0.04
193 0.00 0.01 0.01 0.04
193 0.00 0.01 0.01 0.04
193 0.00 0.01 0.00 0.04

 

 

 

 

 

123

 

 

G6.

Data for T=22 °C, Nitrogen Concentration, N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Nitrogen Concentration mg/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 45.00 65.00 110.00 165.00
0 45.00 65.00 110.00 165.00
0 45.00 65.00 110.00 165.00
0 45.00 65.00 110.00 164.67
0 45.00 65.00 110.00 164.67
0 45.00 65.00 110.00 164.67
24 24.20 52.36 95.32 156.35
24 24.10 53.15 96.35 156.35
24 23.67 53.86 95.53 156.35
24.00 21.43 54.12 94.47 156.03
24.00 20.54 54.93 95.49 156.03
24.00 23.53 55.67 94.68 156.03
42.00 6.23 41.37 82.33 143.61
42.00 4.47 42.67 81.95 143.61
42.00 4.47 42.74 82.48 143.61
42.00 4.76 42.75 81.60 143.32
42.00 4.56 44.11 81.22 143.32
42.00 4.63 44.17 81.74 143.32
55.00 2.13 28.78 68.00 121.35
55.00 1.89 27.56 68.00 121.35
55.00 2.04 28.35 68.00 121.35
55.00 1.34 29.75 69.05 121.11
55.00 1.36 28.49 69.05 121.11
55.00 1.42 29.30 69.05 121.11
76.00 0.35 17.46 49.06 89.93
76.00 0.26 17.27 49.06 89.93
76.00 0.21 17.37 49.06 89.93
76.00 0.22 18.05 49.81 89.75
76.00 0.23 17.84 49.81 89.75
76.00 0.24 17.95 49.81 89.75
101.00 0.02 2.19 7.43 9.10
101.00 0.04 1.84 7.43 9.10
101.00 0.03 1.98 7.43 9.10
101.00 0.01 2.26 7.55 9.08
101.00 0.01 1.90 7.55 9.08
101.00 0.01 2.05 7.55 9.08

 

 

 

 

 

124

 

 

Time

Nitrogen Concentration mg/L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(hours) DAP=0 ppm DAP=100 ppm DAP=300me DAP=600 ppm
125.00 0.00 0.50 1.50 1.14
125.00 0.00 0.47 1.50 1.14
125.00 0.01 0.35 1.50 1.14
125.00 0.00 0.52 1.52 1.14
125.00 0.01 0.49 1.52 1.14
125.00 0.01 0.36 1.52 1.14
193 0.00 0.00 0.01 0.00
193 0.00 0.00 0.01 0.00
193 0.00 0.00 0.01 0.00
193 0.00 0.00 0.01 0.00
193 0.00 0.00 0.01 0.00
193 0.00 0.00 0.01 0.00

 

 

 

 

 

 

125

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G.7. Data for T=11 °C, Ethanol Concentration, E
Time Ethanol Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=60043pm
0 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00
52 0.58 2.73 1.94 4.48
52 0.80 4.53 2.90 5.68
52 0.83 3.43 2.58 5.36
52 0.58 6.17 1.96 4.54
52 0.81 7.18 2.94 5.76
52 0.85 8.19 2.61 5.44
92.00 3.27 9.83 7.42 9.81
92.00 2.73 10.37 6.61 10.28
92.00 2.86 9.17 7.82 9.58
92.00 3.33 15.55 7.51 9.61
92.00 2.78 15.32 6.69 10.07
92.00 2.91 14.68 7.92 9.39
143.00 8.75 23.61 17.26 21.25
143.00 9.83 24.17 15.80 21.87
143.00 9.92 23.45 18.06 22.80
143.00 8.90 23.61 17.46 20.81
143.00 10.00 24.17 15.99 21.42
143.00 10.08 23.45 17.50 22.33
193 16.94 33.98 22.34 25.92
193 16.64 34.62 22.74 26.72
193 17.13 33.18 22.42 24.80
193 17.23 0.00 21.64 26.28
193 16.93 0.00 22.03 27.10
193 17.42 0.00 21.72 25.15
245 20.40 0.00 29.43 34.96
245 23.02 0.00 29.75 36.32
245 22.16 0.00 30.72 35.20
245 20.75 2.70 28.52 35.45
245 23.41 4.48 28.83 36.83

 

 

 

 

 

126

 

 

 

Time

Ethanol Concentration g/L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(hours) DAP=0 ppm DAP=100ppm DAP=300 ppm DAP=600 ppm
245 22.53 3.40 29.77 35.69
330 29.17 6.10 34.92 41.84
330 27.88 7.10 33.87 42.48
330 27.64 8.11 34.03 41 .84
330 29.17 9.73 34.92 41.84
330 27.88 10.48 33.87 42.48
330 27.64 9.27 34.03 41 .84
330 29.67 15.73 33.83 42.43
330 28.35 15.48 32.82 43.08
330 28.10 14.84 32.97 42.43
330 29.67 23.87 33.83 42.43
330 28.35 24.44 32.82 43.08
330 28.10 23.71 32.97 42.43
500 30.87 23.87 44.35 45.92
500 29.66 24.44 43.38 46.48
500 29.98 23.71 44.59 45.84
500 31.40 34.35 42.97 46.57
500 30.16 35.00 42.04 47.13
500 30.49 33.55 43.21 46.48

 

 

 

 

 

127

 

G.8. Data for T=17 °C, Ethanol Concentration, E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Ethanol Concentration g/L
(hour Time DAP=100
s) DAP=0 ppm DAP=300 ppm DAP=600 ppm (hours) ppm
0 0.00 0.00 0.00 0 0.00
0 0.00 0.00 0.00 0 0.00
0 0.00 0.00 0.00 0 0.00
0 0.00 0.00 0.00 0 0.00
0 0.00 0.00 0.00 0 0.00
0 0.00 0.00 0.00 0 0.00
48 1.18 7.15 10.04 48 2.70
48 1.34 6.85 9.52 48 2.76
48 1.58 7.05 9.56 48 3.11
48 1.18 7.26 10.06 48 3.15
48 1.66 7.14 10.24 48 3.47
48 0.79 7.04 10.38 48 3.71
92 5 .52 21.45 20.47 92 13.24
92 5.13 22.46 21.62 92 14.60
92 4.81 20.20 21.13 92 15.15
92 5.52 22.34 22.87 92 15.86
92 6.63 21.56 23.61 92 16.64
92 5.44 20.20 23.25 92 16.65
143 12.07 31.33 32.45 143 19.33
143 15.54 31.28 33.04 143 19.44
143 14.99 30.88 32.46 143 21.09
143 16.65 31.48 33.45 143 21.44
143 15.54 31.24 32.89 143 22.01
143 16.17 32.94 33.25 143 23.04
193 25.41 39.66 41.46 193 27.23
193 24.62 39.19 42.38 193 28.44
193 24.14 40.60 42.05 193 28.66
193 23.28 38.48 43.67 193 29.59
193 23.99 37.65 44.02 193 30.14
193 24.46 39.56 44.21 193 30.30
500 35.51 47.43 50.06 212 27.22
500 36.53 46.49 49.54 212 27.99
500 34.72 46.23 50.15 212 27.99
500 37.24 47.33 50.56 212 28.10

 

128

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ethanol Concentration g/L
Time Time
(Hou DAP=100
rs) DAP=0 ppm DAP=300 ppm DAP=600 ppm (Hours) me
500 37.40 46.45 51.71 212 28.11
500 36.06 45.61 51.97 212 28.43
212 29.43
212 29.43
212 29.88
212 30.06
212 30.61
212 30.61
500 35.65
500 35.65
500 36.32
500 38.82
500 38.82
500 40.32

 

 

 

 

 

 

129

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G.9. Data for T=22 °C, Ethanol Concentration, E
Time Ethanol Concentrationg/L
(hour DAP=100 Time DAP=300
s) DAP=0 ppm ppm (hours) ppm DAP=600 ppm
0 0.00 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00 0.00
0 0.00 0.00 0.00 0.00 0.00
48 5.44 10.64 48.00 12.17 12.45
48 5.64 11.46 48.00 12.97 16.17
48 5.63 10.37 48.00 11.77 13.99
48 5.15 10.82 48.00 12.48 12.74
48 5.24 11.66 48.00 13.30 16.54
48 5.75 10.54 48.00 12.07 14.31
92 15.36 18.45 92.00 25.15 32.80
92 15.94 18.46 92.00 23.48 33.22
92 17.01 19.21 92.00 26.12 30.54
92 14.64 18.77 92.00 25.77 33.55
92 16.73 18.78 92.00 24.06 32.47
92 15.17 19.54 92.00 26.77 29.86
143 22.35 22.36 143.00 29.07 42.32
143 23.47 22.75 143.00 31.71 43.73
143 23.92 23.74 143.00 29.15 43.57
143 22.64 22.74 143.00 29.80 41.37
143 23.43 23.14 143.00 32.19 44.73
143 24.19 24.14 143.00 29.59 44.57
193 32.56 35.67 193.00 38.20 48.81
193 34.72 35.83 193.00 37.00 49.13
193 31.05 34.32 193.00 36.68 46.87
193 32.40 36.28 193.00 37.08 49.93
193 32.95 36.44 193.00 35.91 50.26
193 33.22 34.90 193.00 35.60 47.95
500 35.46 45.75 295.00 38.77 50.19
500 36.22 43.95 295.00 37.55 51.44
500 34.57 44.32 295.00 37.23 50.82
500 35.62 46.53 295.00 36.53 51.70
500 35.19 44.69 295.00 35.38 52.99

 

 

 

 

 

 

130

 

 

 

Ethanol Concentration g/L

 

 

 

 

 

 

 

 

 

Time
(hour DAP=100 Time DAP=300
s) DAP=0 ppm ppm (hours) ppm DAP=600 ppm
500 36.29 45.07 295.00 35.08 52.34
500.00 47.41 52.25
500.00 46.53 51.44
500.00 46.29 51.85
500.00 48.12 53.82
500.00 47.23 52.99
500.00 46.98 53.40

 

 

 

 

 

 

131

 

 

G.10. Data for T=11 °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Spgar Concentration g/L
hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 116.03 115.40 116.05 115.46
0 115.69 116.10 116.05 114.57
0 116.10 116.10 116.02 116.23
0 116.12 115.99 113.26 116.25
0 116.24 115.92 116.25 116.03
0 115.99 115.95 116.08 116.11
52 108.81 115.18 100.79 104.45
52 108.98 115.10 100.46 104.37
52 108.57 114.99 100.24 104.31
52 108.13 115.02 101.22 102.37
52 109.65 116.24 100.37 100.36
52 106.47 117.25 100.68 103.47
92 100.74 107.20 90.28 87.41
92 100.59 107.24 90.36 87.27
92 100.34 107.65 90.67 87.15
92 101.24 109.35 92.63 85.86
92 100.47 109.77 92.34 85.12
92 98.57 109.49 92.88 85.97
143 86.69 92.96 75.98 58.11
143 86.14 93.20 76.17 58.49
143 85.99 92.76 75.24 58.60
143 86.13 95.19 74.40 58.58
143 86.98 95.19 75.16 58.21
143 84.82 95.36 75.16 58.35
193 73.10 80.24 66.12 58.13
193 73.13 80.12 64.84 30.30
193 73.57 80.07 64.52 30.47
193 73.55 81.99 63.79 30.54
193 71.53 82.15 64.27 30.34
193 71.94 81.80 64.79 30.98
245 63.68 68.98 51.95 12.12
245 63.81 68.46 51.46 12.22
245 63.49 68.80 51.35 12.46
245 65.08 70.64 51.40 11.95
245 65.54 69.27 51.44 11.91

 

 

 

 

 

132

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sugar Concentration gL
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
245 65.13 69.27 51.95 11.65
330 47.62 54.71 38.68 2.37
330 47.30 54.71 36.57 2.23
330 47.38 54.71 38.59 2.69
330 48.67 55.47 38.46 2.35
330 48.17 55.18 38.65 2.76
330 48.95 55.24 38.12 2.32
405 37.35 45.65 28.69 0.88
405 37.22 45.88 29.46 0.75
405 37.94 45.24 28.65 0.71
405 38.18 45.27 29.43 0.73
405 38.16 46.20 29.48 0.70
405 38.35 45.36 29.35 0.72
500 28.20 38.04 21.32 0.19
500 28.69 38.02 20.35 0.19
500 28.44 38.13 20.95 0.18
500 28.82 37.90 20.78 0.20
500 28.72 38.13 19.90 0.19
500 28.82 38.19 20.49 0.19

 

 

133

 

G.11. Data for T=17 °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sugar Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 112.00 116.00 116.00 116.00
0 112.00 116.00 116.00 116.00
0 112.00 116.00 116.00 116.00
0 112.00 116.00 116.00 116.00
0 112.00 116.00 116.00 116.00
0 112.00 116.00 116.00 116.00
48 108.40 108.22 103.45 108.35
48 106.20 106.26 99.56 108.45
48 108.10 110.45 101.45 107.78
48 105.47 108.40 100.98 106.34
48 105.47 110.13 100.30 108.46
48 105.47 109.45 101.46 107.26
92 90.50 91.45 62.33 65.33
92 92.80 94.54 65.35 64.21
92 94.38 95.30 64.75 66.29
92 89.19 90.34 63.57 64.13
92 89.19 92.65 64.22 63.69
92 89.19 94.32 63.46 64.83
143 75.60 76.35 30.44 17.39
143 78.33 75.00 36.34 18.35
143 73.32 75.33 30.79 17.92
143 73.32 76.80 31.07 16.38
143 73.32 74.22 34.25 16.83
143 73.32 73.05 35.76 17.16
193 64.22 60.43 12.68 3.58
193 61.30 61.34 14.66 3.14
193 60.58 59.87 13.98 3.24
193 60.58 61.10 12.36 2.87
193 60.58 61.34 13.64 2.80
193 60.58 59.87 14.15 2.72
212.00 58.40 56.67 9.45 1.84
212.00 60.20 54.12 10.54 1.73
212.00 59.80 55.34 8.67 1.63
212.00 56.37 53.24 8.27 1.84
212.00 56.37 53.24 9.45 1.95

 

 

 

 

 

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Time Sugar Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300ppm DAP=600 ppm
212.00 56.37 28.54 9.33 1.93
351.00 31.30 26.34 0.88 0.06
351.00 31.33 25.43 0.56 0.03
351.00 33.86 28.63 0.89 0.08
351.00 33.86 23.45 0.94 0.20
351.00 33.86 25.43 0.65 0.09
351.00 33.86 25.43 0.63 0.11
500 22.40 14.14 0.19 0.00
500 24.60 13.26 0.07 0.00
500 24.20 15.44 0.24 0.00
500 20.82 10.34 0.16 0.03
500 20.82 15.44 0.10 0.03
500 20.82 13.26 0.11 0.02

 

 

 

 

 

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G.12. Data for T=1] °C, Sugar Concentration, S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Sugar Concentration g/L
(hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
0 116.00 116.00 116.00 116.00
0 116.00 116.00 116.00 116.00
0 116.00 116.00 116.00 116.00
0 116.00 116.00 116.00 116.00
0 116.00 116.00 116.00 116.00
0 116.00 116.00 116.00 116.00
15 115.35 113.34 114.56 112.70
15 113.98 112.95 114.56 111.44
15 114.26 112.48 114.56 112.70
15 115.35 113.34 116.10 111.32
15 115.12 112.95 116.10 111.44
15 115.40 112.48 116.10 111.32
24 111.57 110.87 111.02 109.79
24 112.85 110.65 111.02 108.45
24 111.62 110.48 111.02 109.79
24 112.69 110.87 112.52 108.45
24 113.98 110.65 112.52 108.45
24 112.74 110.48 112.52 108.45
48 100.63 98.38 92.20 86.46
48 100.98 96.94 92.20 87.45
48 101.63 99.92 92.20 86.46
48 101.64 98.38 93.44 85.40
48 101.99 96.94 93.44 87.45
48 102.65 99.92 93.44 85.40
63 92.65 85.32 73.51 62.18
63 93.70 86.90 73.51 67.35
63 92.98 87.34 73.51 62.18
63 93.57 62.38 72.53 61 .42
63 94.64 62.38 72.53 67.35
63 93.91 62.38 72.53 61.42
84 81.49 70.32 51.63 34.22
84 82.49 69.12 51.63 33.56
84 82.14 69.34 51.63 34.22
84 82.30 83.17 50.94 33.80
84 83.31 83.17 50.94 33.56
84 83.84 83.17 50.94 33.80

 

 

 

 

 

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Time Sugar Concentration g/L
(Hours) DAP=0 ppm DAP=100 ppm DAP=300 ppm DAP=600 ppm
110 72.50 52.74 32.17 15.59
110 73.09 53.82 32.17 16.20
110 72.58 52.83 32.17 15.59
110 73.23 52.74 32.60 15.40
110 73.82 53.82 32.60 16.20
110 73.31 52.83 32.60 15.40
193 46.87 24.66 6.16 1.67
193 45.26 23.15 6.16 1.54
193 46.14 22.76 6.16 1.67
193 47.34 23.15 6.24 1.65
193 45.71 23.15 6.24 1.54
193 46.60 22.76 6.24 1.65
295 25.64 10.42 1.18 0.22
295 25.82 11.29 1.18 0.31
295 26.26 10.92 1.18 0.22
295 25.90 10.42 1.19 0.22
295 26.08 11.29 1.19 0.31
295 26.52 10.92 1.19 0.22
351 20.46 5.04 0.57 0.09
351 21.05 5.64 0.57 0.09
351 19.74 5.02 0.57 0.09
351 20.66 5.04 0.56 0.09
351 21.26 5.64 0.56 0.09
351 19.94 5.02 0.56 0.09
500 10.57 2.42 0.15 0.02
500 11.83 2.55 0.15 0.00
500 10.82 2.24 0.15 0.02
500 10.68 2.42 0.15 0.02
500 11.95 2.55 0.15 0.00
500 10.93 2.24 0.15 0.02

 

137

 

 

 

 

NOMENCLATURE

E Ethanol concentration, g/L

E r activation energy for temperature effect, J/gmol

E N activation energy for nitrogen effect, J/gmol

KN Monod constant for Nitrogen, mg/L

KS Monod constant for Sugar, g/L

kd ethanol independent death rate constant, L g ethanol’1 h'1

k any non-linearly estimated parameter

k, value of the same parameter at reference temperature and initial nitrogen
N,- nitrogen concentration at t=0, ppm

N nitrogen concentration, ppm

NO nitrogen concentration, ppm

R Universal gas constant, J/gmol K

S sugar concentration, g/L

So sugar concentration, g/L

t time, hour

T temperature, °C

T k temperature, K

T , reference temperature, K

X y viable yeast cell concentration, cells/L

y generic dependent variable

Y generic dependent variable

Y m; stoichiometric yield coefficient of biomass on nitrogen, no. of cells/ g N
Y g/s stoichiometric yield coefficient of ethanol on sugar, g ethanol/g sugar
Greek symbols

,8 specific ethanol production per gram of sugar consumed, g ethanol g sugar’l hr'1
,6", maximum specific ethanol production rate, g ethanol g sugar'l hr'l

,u specific growth rate hr'1

,um maximum specific growth rate, hr"1

138

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